The value of angle x = 114°.
How to find angle x?From the figure, it is clear that The interior angle of a triangle is 39°, by the law of opposite angle.
The sum of the interior angle of a triangle is 180°
37° + 39° + ∠unknown1 = 180°
∠unkonown1 = 180° - 37° - 39°
∠unknown1 = 104°
The sum of the exterior angle and the interior angle is 180°.
∠unknown2+ ∠unknown 1= 180°
∠unknown2 = 180° - 104°
∠unknown2 = 76°
The sum of the interior angle of a triangle is 180°
∠unknown3 + ∠unknown2 + 38 = 180
∠unknown3 + 76° + 38 = 180
∠unknown3= 66°
The sum of the exterior angle and the interior angle is 180°.
∠X + <unknown3 = 180°
∠X = 180° - 66°
∠X = 114°
The value of the angle x is 114°.
Learn more about Angle here:
https://brainly.com/question/28451077
#SPJ1
Jamie jogged x km. Anabel jogged 1/4 less than Jamie. Choose the equation that best represents the situation. A
y = 3/4x
b
x = 4/3y
c
y = 1/4x
d
x = 1/4y
The equation that best represents the situation is y = 3/4x. The correct answer is A.
The given problem involves two people, Jamie and Anabel, who jogged a certain distance. Let's say Jamie jogged x km. Anabel jogged 1/4 less than Jamie, which means she jogged 3/4 of x km (since 1 - 1/4 = 3/4).
To represent this situation in an equation, we need to find the relationship between the distance jogged by Jamie and the distance jogged by Anabel. Since Anabel jogged 3/4 of the distance jogged by Jamie, we can write:
distance jogged by Anabel = 3/4(distance jogged by Jamie)
Using the given variable x for the distance jogged by Jamie, we can rewrite the equation as:
distance jogged by Anabel = 3/4x
And since the question is asking for an equation that best represents the situation, the correct answer is:
Cy = 3/4x
Therefore, Cy = 3/4x is the equation that best represents the situation where Jamie jogged x km and Anabel jogged 1/4 less than Jamie. The correct answer is A.
Learn more abou equation at https://brainly.com/question/27358888
#SPJ11
Help with problem in photo
Answer:
(x-6)²+(y+3)²=17²
Step-by-step explanation:
The equation of a circle with center (a,b) and radius r is given by the formula:
(x - a)² + (y - b)² = r²
In this case, the center of the circle is (6,-3), and it passes through the point (-9,5). To find the radius of the circle, we need to calculate the distance between the center and the point on the circle. Using the distance formula, we get:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-9 - 6)² + (5 - (-3))²]
= √[225 + 64]
= √289
= 17
So, the radius of the circle is 17. Now we can plug in the values for the center and radius into the equation of a circle:
(x - 6)² + (y + 3)² = 17²
Amy borrows $1,000 on a simple interest loan. She pays an annual rate of 3. 5%. She will take 3 years to pay back the loan. How much interest will Amy pay?
The amount of interest Amy will pay over the 3 years is $105.
Simple interest is a method of calculating the interest amount on a loan or investment by multiplying the principal amount, the annual interest rate, and the time in years. In Amy's case, she borrowed $1,000 with an annual interest rate of 3.5% and will take 3 years to pay back the loan.
To calculate the interest Amy will pay, use the formula: Interest = Principal x Rate x Time
Interest = $1,000 x 0.035 (3.5% as a decimal) x 3 years
Interest = $1,000 x 0.035 x 3 = $105
Amy will pay $105 in interest over the 3 years.
Learn more about Simple interest here: https://brainly.com/question/25845758
#SPJ11
What is the difference in credit score between those over the age of 55 and those between 18-24 years old?
According to recent studies, there is a notable difference in credit scores between those over the age of 55 and those between the ages of 18-24.
On average, individuals over the age of 55 tend to have higher credit scores than those in the 18-24 age range. This is primarily due to the fact that older individuals have had more time to establish and build their credit history, whereas younger individuals are just starting out and may not have had the opportunity to establish credit yet.
Additionally, older individuals tend to have more stable financial situations and may have less debt compared to younger individuals who may be dealing with student loans or other types of debt.
However, it's important to note that credit scores can vary greatly between individuals, regardless of age, and there are many factors that contribute to credit score, such as payment history, credit utilization, and length of credit history.
To know more about credit score:
https://brainly.com/question/29548283
#SPJ11
Misty needs 216 square inches of metal
to make a yield sign. If the height of the sign is 18 inches,
how long is the top edge of the sign?
24 inches
12 inches
198 inches
22 inches
pls give explanation not just the awnser
The answer is 96 inches, which is equivalent to 8 feet.
Find out the length of the top edge of the yeild sign ?To find the length of the top edge of the yield sign, we need to use the formula for the area of a trapezoid:
A = (b1 + b2)h/2
where A is the area of the trapezoid, h is the height, b1, and b2 are the lengths of the two parallel bases of the trapezoid.
In this case, we are given the area of the sign (216 square inches) and the height (18 inches), but we don't know the length of either base. However, we do know that the shape of a yield sign is that of a regular octagon, which means it has eight equal sides and eight equal angles.
If we draw a line from the top of the sign to the midpoint of one of the sides, we will form a right triangle with the height of the sign as one leg, half the length of the top edge as the other leg, and the length of one of the sides as the hypotenuse. We can use the Pythagorean theorem to find the length of the side:
a^2 + b^2 = c^2
where a is the height of the sign (18 inches), b is half the length of the top edge (what we are trying to find), and c is the length of one of the sides.
Since the sign has eight sides, we can divide the total area by 8 to get the area of one of the eight triangles that make up the sign. We can then use this area to find the length of one of the sides:
A = (bh)/2
216 sq. in. = (bh)/2
432 sq. in. = bh
Since the sign is a regular octagon, each of the eight triangles has the same base (the side of the octagon) and height (half the length of the top edge), so we can use this equation to solve for b:
432 sq. in. = b(18 in.)/2
b = 48 in.
Now we know that half the length of the top edge is 48 inches, so the full length of the top edge is:
2(48 in.) = 96 in.
Learn more about Signs
brainly.com/question/14304253
#SPJ11
Express tan H as a fraction in simplest terms.
F
H
28
7
G
Answer:
4 or [tex]\frac{4}{1}[/tex]
Step-by-step explanation:
To solve this we need to remember SOH-CAH-TOA. With SOH being Sine, CAH being Cosine, and TOA being Tangent. In the last term (TOA), the O means opposite and the A is adjacent. This means the segment opposite of angle H you have to divide that by the segment adjacent to H.
In this case, the opposite is 28 and the adjacent is 7. So we have to do [tex]\frac{28}{7}[/tex]. This is tan(H). Now we have to simplify this. Now we get our tangent of H to be [tex]\frac{4}{1}[/tex] or 4. So 4/1 or 4 is our answer
Jocelyn is considering taking out one of the two following loans. loan h is a three-year loan with a principal of $5,650 and an interest rate of 12.24%, compounded monthly. loan i is a four-year loan with a principal of $6,830 and an interest rate of 10.97%, compounded monthly. which loan will have the smaller monthly payment, and how much smaller will it be? round all dollar values to the nearest cent. a. loan h's monthly payment will be $42.46 smaller than loan i's. b. loan h's monthly payment will be $140.79 smaller than loan i's. c. loan i's monthly payment will be $11.88 smaller than loan h's. d. loan i's monthly payment will be $26.98 smaller than loan h's.
Loan H's monthly payment will be $42.46 smaller than loan I's (rounded to the nearest cent). The correct option is a.
To determine which loan will have the smaller monthly payment, we need to calculate the monthly payments for both loans using the given information.
For loan H, the monthly interest rate is 12.24%/12 = 1.02%, and the number of payments is 3 years x 12 months/year = 36. Using the formula for the monthly payment on a loan with monthly compounding, we have:
P = (r(PV))/(1 - (1+r[tex])^{(-n)})[/tex]
where P is the monthly payment, r is the monthly interest rate, PV is the principal value of the loan, and n is the total number of payments.
Plugging in the values given for loan H, we get:
P = (0.0102 x $5,650) / (1 - (1+0.0102)⁻³⁶) = $186.25
For loan I, the monthly interest rate is 10.97%/12 = 0.9142%, and the number of payments is 4 years x 12 months/year = 48. Using the same formula as above, we have:
P = (0.009142 x $6,830) / (1 - (1+0.009142)⁻⁴⁸) = $227.04
Therefore, the monthly payment for loan H is $186.25 and the monthly payment for loan I is $227.04.
To find the difference between the monthly payments, we subtract the monthly payment for loan H from the monthly payment for loan I:
$227.04 - $186.25 = $40.79
Therefore, the answer is (a) loan H's monthly payment will be $42.46 smaller than loan I's (rounded to the nearest cent).
To know more about monthly payment, refer to the link below:
https://brainly.com/question/2053367#
#SPJ11
Describe and correct the error in finding the circumference of ⊙C
Step-by-step explanation:
C= 2πr
Given,
Diameter= 9
so, radius = 9÷2 = 4.5
C= 2 x π x 4.5
= 28.3 (3.s.f)
The cost to produce x kilograms of whatchamacallits is given by the function C(x) = 50x + 1000 where Cix) is in hundreds of dollars. The revenue for the sale of x whatchamacallits is given by R(x) = 450x where R(x) is in hundreds of dollars. How many kilograms should be produced and sold to realize a maximum profit? What is that maximum profit?
The maximum profit will be realized by producing and selling 2.5 kilograms of whatchamacallits.
The maximum profit, in hundreds of dollars, will be $500.
To find the maximum profit, we need to first calculate the profit function P(x), which is the difference between the revenue and the cost functions:
P(x) = R(x) - C(x)
P(x) = 450x - (50x + 1000)
P(x) = 400x - 1000
To find the amount of kilograms that should be produced and sold to realize a maximum profit, we need to find the value of x that maximizes the profit function.
We can do this by taking the derivative of the profit function and setting it equal to zero:
P'(x) = 400
400 = 0
Since the derivative is a constant value, there is no critical point or inflection point. Therefore, the profit function is increasing at a constant rate, and the maximum profit will be achieved at the highest possible value of x.
To find that value, we can set the profit function equal to zero and solve for x:
P(x) = 400x - 1000 = 0
400x = 1000
x = 2.5
Therefore, the maximum profit will be realized by producing and selling 2.5 kilograms of whatchamacallits.
To find the maximum profit itself, we can substitute this value of x into the profit function:
P(2.5) = 400(2.5) - 1000 = 500
So the maximum profit, in hundreds of dollars, will be $500.
To learn more about profit function, refer below:
https://brainly.com/question/16866047
#SPJ11
QUESTION IN PHOTO I MARK BRAINLIEST
The value of measure of arc QI is,
⇒ m QI = 94°
We have to given that;
⇒ m YS = 180°
⇒ m ∠QBI = 137°
Hence, We can formulate;
⇒ m ∠QBI = 1/2 (m YS + m QI)
⇒ 137 = 1/2 (180 + m QI)
⇒ 274 = 180 + m QI
⇒ m QI = 274 - 180
⇒ m QI = 94°
Thus, The value of measure of arc QI is,
⇒ m QI = 94°
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ1
Suppose a homing pigeon is released on an island at point C, which is 9 mi directly out in the water from a point B on shore, Point B is 20 mi downshore from the pigeon's home loft at point A. Assume that a pigeon flying over water uses energy at a rate 1.29 times the rate over land. Toward what points downshore from A should the pigeon fly in order to minimize the total energy required to get to the home loft at A? Point S ismiles away from point A. (Type an integer or decimal rounded to three decimal places as needed.)
The pigeon should fly directly from point C to point B, then fly along the shoreline to a point 10.387 miles away from point A (rounded to three decimal places). This can be found using the principle of minimizing the total distance traveled, taking into account the different energy rates over water and land.
To minimize the total energy required for the homing pigeon to get to its home loft at Point A, we need to find the optimal point downshore, Point S, to fly to. Using the given information, we can set up a function for the total energy.
Let x be the distance from Point A to Point S. Then, the pigeon will fly x miles over land and the remaining distance, 20-x miles, downshore from Point B to Point S. The distance from Point C to Point S can be found using the Pythagorean theorem:
CS = sqrt((20-x)^2 + 9^2)
Since the pigeon uses energy at a rate 1.29 times over water compared to land, we can write the total energy function as:
E(x) = x + 1.29 * CS
Now we need to minimize this function. To do so, we can take the derivative of E(x) with respect to x and set it equal to zero:
dE(x)/dx = 0
By solving this equation for x, we will find the optimal distance downshore from Point A to Point S. Once you have the value of x, you can say that Point S is x miles away from Point A (rounded to three decimal places, as needed).
Visit here to learn more about Pythagorean theorem brainly.com/question/14930619
#SPJ11
Mara putting together pieces of string for an art project. She has a piece of string that is 30 inches, a piece that is 22 inches, and a piece that is 20 inches. Once she puts together the pieces, what will be the total length in feet?
Step 1 - What will be the total length of the string in inches?
Step 2 - How many feet is this equal to? (Inches -> Feet)
2. A water jug holds 300 ounces of water. The football team has 2 water jugs. How many cups of water will both water jugs hold altogether?
Step 1 - How many ounces do both water jugs hold?
Step 2 - How many cups is this equal to? (Ounces -> Cups
Please help me if you help me and explain all the answer I will give you brainiest!!!
The total length of the string in feet is 6 feet, and the combined capacity of both water jugs in cups is 75 cups.
What is the total length of the string, and how many cups of water can the two water jugs hold altogether?Step 1: To find the total length of the string in inches, Mara needs to add the lengths of the three pieces of string:
30 inches + 22 inches + 20 inches = 72 inches
So the total length of the string in inches is 72 inches.
Step 2: To convert inches to feet, we need to divide the number of inches by 12 (since there are 12 inches in a foot):
72 inches ÷ 12 = 6 feet
Therefore, once Mara puts together the three pieces of string, the total length will be 6 feet.
Step 1: To find out how many ounces of water both water jugs hold altogether, we need to add the capacity of the two jugs:
300 ounces + 300 ounces = 600 ounces
So both water jugs together can hold 600 ounces of water.
Step 2: To convert ounces to cups, we need to divide the number of ounces by 8 (since there are 8 ounces in a cup):
600 ounces ÷ 8 = 75 cups
Therefore, both water jugs together can hold 75 cups of water.
Learn more about ounces
brainly.com/question/29374025
#SPJ11
There are 39 students in a class 22 offer maths,14 offer physics,and 16 offer biology if 5 offer both biology and math 7 offer at least one of the subject where every student offer at least one of the subjects. Find
Where every student offer at least one of the subjects, there are 4 students who offer all three subjects.
To find the number of students who offer only one subject, we can use the formula:
number of students offering only one subject = total number of students offering the subject - number of students offering both subjects
For math, there are 22 students offering math and 5 offering both math and biology, so the number of students offering math only is:
22 - 5 = 17
Similarly, for physics and biology, the numbers of students offering the subjects only are:
14 - 7 = 7 (physics)
16 - 5 = 11 (biology)
To find the number of students offering all three subjects, we can use the formula:
number of students offering all three subjects = total number of students offering at least one subject - number of students offering only one subject in each subject + number of students offering no subject
We know that there are 7 students offering at least one subject. To find the number of students offering no subject, we can subtract this from the total number of students:
39 - 7 = 32
Now we can plug in the numbers:
number of students offering all three subjects = 7 - 17 - 7 - 11 + 32
= 4
Therefore, there are 4 students who offer all three subjects.
More on subjects: https://brainly.com/question/16295210
#SPJ11
Subtract.3 1/3−5enter your answer as a simplified mixed number by filling in the boxes.
The result of subtracting 5 from 3 1/3 is -2 2/3.
To subtract 5 from 3 1/3, we need to first convert the mixed number to an improper fraction. This can be done by multiplying the whole number (3) by the denominator of the fraction (3), and adding the numerator (1) to get 10/3. Therefore, 3 1/3 is equivalent to 10/3.
Next, we can subtract 5 from 10/3 by finding a common denominator of 3, which gives 15/3 - 10/3 = 5/3. This is the result in improper fraction form.
To convert back to a mixed number, we can divide the numerator (5) by the denominator (3), which gives a quotient of 1 and a remainder of 2. Therefore, the answer is -2 2/3.
For more questions like Subtract click the link below:
https://brainly.com/question/2346316
#SPJ11
The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $350.00. What was it worth a year ago? A. $260.00 B. $250.00 C. $270.00 D. $230.00
Answer: B
Step-by-step explanation: 250 x 140% = 350
A binomial experiment has the given number of trials n and the given success probability p.
n=10, p=0. 2
(a) Determine the probability P (2 or fewer). Round the answer to at least three decimal places.
P(2 or fewer)
The probability P(2 or fewer) is 0.678.
To find the probability of 2 or fewer successes in a binomial experiment with 10 trials and a success probability of 0.2, we can use the binomial probability formula:
P(2 or fewer) = P(0) + P(1) + P(2)
where P(0), P(1), and P(2) represent the probabilities of getting 0, 1, or 2 successes, respectively.
P(0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3020
Therefore,
P(2 or fewer) = 0.1074 + 0.2684 + 0.3020 = 0.6778
Rounded to at least three decimal places, the probability P(2 or fewer) is 0.678.
To learn more about Probability
https://brainly.com/question/24870672
#SPJ11
Amanda wants to add 6732 and 4975 how can Amanda use mental math to add the numbers is Amanda answer correct explain
she can add each number one by one , and whenever she needs to carry numbers over. She can add them to the already existing numbers. she cna check with a calculator
Curtis loves Pokémon! He went to school on Thursday and traded a bunch of cards to get new ones. He saw Dino and traded 3 of his cards for one of Dino's. Then a girl he liked, Tippi, wanted to trade cards. He was really nice to her because he liked her, so he traded 5 of his cards for 2 of hers. He then put his cards away. When he got home he noticed that 10 of his cards were missing. He was so upset that his mom bought him another pack of 12 cards. He hid half of his cards at home and took the rest to school the next day. He traded ¼ of the cards he brought to school to Dino again and got back 3 of Dino's cards. Curtis now has 9 cards at school. How many cards did he start with? How many cards total does he have now?
Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
How to find cards?To find how many card ,We see Curtis has 9 cards at school after trading with Dino again, which means he had 12 cards before the trade.
Before his mom bought him another pack of 12 cards, he had 10 missing, so he must have had 24 cards in total (12 + 12).
He hid half of his cards at home, so he has 12 cards at home.
He traded ¼ of the cards he brought to school to Dino and got back 3 of Dino's cards. Let's call the number of cards he brought to school "x".
So, he traded x/4 cards to Dino, and got back 3 cards, which means he now has (x/4) - 3 cards.
We know that he now has 9 cards at school, so we can set up an equation:
(x/4) - 3 = 9
Solving for x, we get:
x/4 = 12
x = 48
So, Curtis brought 48 cards to school, which means he started with 24 + 12 + 48 = 84 cards in total.
Therefore, Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
Learn more about Cards
brainly.com/question/31598744
#SPJ11
The following data points represent the number of holes
that moths ate in each of grandma marion's dresses.
7,8,8, 5, 7,8
using this data, create a frequency table.
number of holes
number of dresses
5
6
7
8
A frequency table was created using data points representing the number of holes in each of Grandma Marion's dresses. The table shows the number of dresses with 5, 7, and 8 holes, respectively.
To create a frequency table for the given data, first, the unique values in the data set are identified, which are 5, 7, and 8. Then, the number of occurrences of each unique value is counted, resulting in the frequencies 1 for 5, 2 for 7, and 3 for 8.
Count the frequency of each data point
5: 1 dress
7: 2 dresses
8: 3 dresses
Finally, these values are organized into a table with two columns, one for the unique values and another for their corresponding frequencies. The resulting frequency table shows the number of dresses with each number of holes eaten by moths.
To know more about frequency table:
https://brainly.com/question/31189964
#SPJ4
Choose the function table that matches the given rule. Output = Input – 3 (1 point) Input Output –2 –5 1 –2 6 3 Input Output 2 –1 –2 3 0 –6 Input Output 5 2 2 –5 0 9 Input Output 6 3 –6 –3 5 0
The function table that matches the given rule output = input - 3 is
Input = -2, 1, 6 and output = -5, -2, 3
A) first function table
Output = Input - 3
Value of input:- -2
Putting the value of the input
Output = -2 -3
The value of output we get
Output = -5
Value of input:- 1
Putting the value of the input
Output = 1 -3
The value of output we get
Output = -2
Value of input:- 6
Putting the value of the input
Output = 6 -3
The value of output we get
Output = 3
Hence function table A is correct match
To know more about function click here :
https://brainly.com/question/12431044
#SJP1
PLSSS HELP.
Apples are on sale at a grocery store for per pound. Casey bought apples and used a coupon for off her purchase. Her total was. How many pounds of apples did Casey buy?
Part A: Write an equation that represents the problem. Define any variables.
Part B: Solve the equation from Part A. Show all work.
Part C: Explain what the solution to the equation represents
A: An equation that represents the problem is 1.75x - 0.45 = 4.45. B: Solving the equation from Part A gives x = 2.8. C: The solution to the equation represents the number of pounds of apple bought by Casey.
Part A: Write an equation that represents the problem. Define any variables.
Let x represent the number of pounds of apples Casey bought. The cost of apples is $1.75 per pound, so the total cost before using the coupon would be 1.75x. After using the $0.45 coupon, her total was $4.45. The equation representing this situation is:
1.75x - 0.45 = 4.45
Part B: Solve the equation from Part A.
Now, let's solve the equation:
1.75x - 0.45 = 4.45
Add 0.45 to both sides:
1.75x = 4.90
Now, divide both sides by 1.75:
x = 4.90 / 1.75
x = 2.8
Part C: Explain what the solution to the equation represents
The solution, x = 2.8, represents that Casey bought 2.8 pounds of apples at the grocery store.
Note: The question is incomplete. The complete question probably is: Apples are on sale at a grocery store for $1.75 per pound. Casey bought apples and used a coupon for $0.45 off her purchase. Her total was $4.45. How many pounds of apples did Casey buy? Part A: Write an equation that represents the problem. Define any variables. Part B: Solve the equation from Part A. Show all work. Part C: Explain what the solution to the equation represents.
Learn more about Equation:
https://brainly.com/question/27887972
#SPJ11
Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
The evaluated missing length in right triangle by using the Pythagorean theorem is 9 yards under the condition given the triangle is a right triangle.
The Pythagoras theorem projects that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides,
It is given to us that in a right triangle,
Hypotenuse = 15 yd
Perpendicular = 12 yd
Therefore, applying Pythagoras theorem;
Base² = 15² - 12²
Base² = 225 - 144
Base² = 81
Base = √81
Base = 9 yards
Hence, The missing length present in the right triangle by applying the Pythagorean theorem is,
9 yards
To learn more about Pythagoras theorem
https://brainly.com/question/27997683
#SPJ4
The complete question is
Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
a strawberry field, you will find 4 plants per square foot. How many strawberry plants will you find in a square field that has a length of 208 ft (approx 1 acre )?
Answer: 832 plants
Step-by-step explanation:
If there are 4 plants for every 1 square ft the ratio is 4:1.
This tells us to multiply 208x4 giving us 832.
A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals then how many of them can be dogs
The pet boarder can accommodate 70 dogs.
To determine the number of dogsLet's calculate how many dogs and cats the pet boarding facility can hold using the ratio of dogs to cats, which is 5:2.
First, we can figure out how many parts there are in the ratio: 5 + 2 = 7.
This indicates that there are 7 equal components in the ratio, 5 of which are dogs and 2 of which are cats.
We need to multiply the result by the number of dog components (5) after dividing the total number of parts (7) into the 98 available locations to get the number of dogs:
Number of dogs = (5 / 7) * 98
Number of dogs = 70
Therefore, the pet boarder can accommodate 70 dogs.
Learn more about ratio here : brainly.com/question/26460724
#SPJ1
Ao
Del
5. An archway has vertical sides 10 feet high. The top of an archway can
be modeled by the quadratic function f(x) = -0. 5x2 + 10 where x is the
horizontal distance, in feet, along the archway. How far apart are the
walls of the archway? Round your answer to the nearest tenth of a foot.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
293
The walls of the archway are approximately 8.9 apart.
Find out the distance between the walls of the archway?To find the distance between the walls of the archway, we need to find the horizontal distance where the function f(x) intersects the x-axis. This is because the archway's walls are vertical, and their distance apart is the same as the horizontal distance between the points where the archway meets them.
To find the x-intercepts of the function f(x) = -0.5x^2 + 10, we need to set f(x) = 0 and solve for x:
0 = -0.5x^2 + 10
0.5x^2 = 10
x^2 = 20
x = ±√20
Since the archway is a physical object, we can discard the negative value for x, which means the archway meets the walls at x = √20 feet.
To find the distance between the walls of the archway, we can double this value:
2√20 ≈ 8.94
Then it's concluded that the walls of the archway are approximately 8.9 feet apart.
Learn more about Function
brainly.com/question/5975436
#SPJ11
Write and simplify the integral that gives the arc length of the following curve on the given integral. b. If necessary, use technology to evaluate or approximate the integral. y = -x² -5 on [-1,2]
To find the arc length of the curve y = -x² -5 on the interval [-1,2], we use the formula to evaluate:
L = ∫√(1 + (dy/dx)²) dx
where dy/dx is the derivative of y with respect to x.
First, we find dy/dx:
dy/dx = -2x
Next, we substitute dy/dx into the formula and simplify:
L = ∫√(1 + (-2x)²) dx
L = ∫√(1 + 4x²) dx
To evaluate this integral, we can use a trigonometric substitution. Let x = (1/2)tanθ, then dx = (1/2)sec²θ dθ. Substituting, we get:
L = ∫√(1 + 4(1/2)²tan²θ)(1/2)sec²θ dθ
L = (1/2)∫sec³θ dθ
To integrate sec³θ, we use integration by parts:
u = secθ, du/dθ = secθ tanθ
dv/dθ = sec²θ, v = tanθ
∫sec³θ dθ = secθ tanθ - ∫tan²θ secθ dθ
= secθ tanθ - ∫secθ dθ + ∫sec³θ dθ
Rearranging, we get:
2∫sec³θ dθ = secθ tanθ + ln|secθ + tanθ|
Therefore:
L = (1/2)(secθ tanθ + ln|secθ + tanθ|) + C
To evaluate L on the interval [-1,2], we need to find θ when x = -1 and x = 2. Using the substitution x = (1/2)tanθ:
When x = -1, θ = -π/4
When x = 2, θ = π/3
Substituting these values into the equation for L and simplifying, we get:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Therefore, the integral that gives the arc length of the curve y = -x² -5 on the interval [-1,2] is:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Note: If technology is used to evaluate or approximate the integral, the answer may differ slightly due to rounding errors.
MORE RELATED QUESTIONS on integrals: https://brainly.com/question/27419605
#SPJ11
Benjamin went shopping for a new phone
because of a sale. The price on the tag was
$28, but Benjamin paid $15. 40 before tax.
Find the percent discount
The percent discount on the phone because of a sale is 45%.
To find the percent discount, we need to calculate the difference between the original price and the discounted price, and then express that difference as a percentage of the original price.
First, let's find the difference between the two prices: $28 - $15.40 = $12.60. This means that Benjamin saved $12.60 on the phone.
Now, let's find the percent discount. We can do this by dividing the savings by the original price, and then multiplying the result by 100: ($12.60 / $28) * 100 = 45%.
So, Benjamin received a 45% discount on the phone before tax. This calculation shows that the sale allowed him to save a significant amount on his purchase. It's important to compare original and discounted prices to determine if a sale provides good value.
Learn more about discount here: https://brainly.com/question/27519306
#SPJ11
Height of 10th grade boys is normally distributed with a mean of 63. 5 in. And a standard deviation of 2. 9 in. The area greater than the z-score is the probability that a randomly selected 14-year old boy exceeds 70 in. What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?Use your standard normal table.
Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard deviation of 2. 9 in. Find the z-score associated with the 96th percentile. Find the height of a 16-year-old boy in the 96th percentile. State your answer to the nearest inch
The probability that a randomly selected 10th grade boy exceeds 70 in is approximately 0.0127 or 1.27%.
The height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
For the first question, we need to find the z-score for a height of 70 inches using the formula:
z = (x - μ) / σ
where x is the height of 70 inches, μ is the mean of 63.5 inches, and σ is the standard deviation of 2.9 inches.
z = (70 - 63.5) / 2.9 = 2.241
Using a standard normal table, we can find the area to the right of this z-score, which represents the probability that a randomly selected 10th grade boy exceeds 70 inches. The area to the right of 2.24 is 0.0127. Therefore, the probability is approximately 0.0127 or 1.27%.
For the second question, we need to find the z-score associated with the 96th percentile using a standard normal table. The 96th percentile is the point below which 96% of the data falls and above which 4% of the data falls. This corresponds to a z-score of approximately 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:
x = μ + z * σ
where x is the height we want to find, μ is the mean of 68.3 inches, σ is the standard deviation of 2.9 inches, and z is the z-score we just found.
x = 68.3 + 1.75 * 2.9 = 73.28
Therefore, the height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
To know more about probability, refer to the link below:
https://brainly.com/question/27372639#
#SPJ11
By comparison a car with one of the worst car depreciations is a BMW 7 series. In 5 years it losses 72.6% of its value. If brand new the car costs $86,000, how much will the car be worth in 8 years?
The value of the car after 8 years is given as follows:
$10,836.76.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The parameter values for this problem are given as follows:
a = 86000, n = 5, b = 1 - 0.726 = 0.274.
Hence the function for the value of the car after x years is given as follows:
[tex]y = ab^\frac{x}{n}[/tex]
[tex]y = 86000(0.274)^\frac{x}{5}[/tex]
The value of the car after 8 years is then given as follows:
[tex]y = 86000(0.274)^\frac{8}{5}[/tex]
y = $10,836.76.
More can be learned about exponential functions at brainly.com/question/2456547
#SPJ1
The surface area of the square pyramid is 84 square inches. The side length of the base is 6 what is the value of x
With the surface area of the square pyramid 84 square inches and side length of the base is 6, the value of x is 4 inches, by assuming x as the slant height of the square pyramid.
Assuming that x refers to the slant height of the square pyramid, we can use the formula for the surface area of a square pyramid to solve for x:
Surface area of a square pyramid = base area + (0.5 x perimeter of base x slant height)
Since the base of the square pyramid is a square with side length 6,
the base area is 6² = 36 square inches.
The perimeter of the base is 4 times the side length, so it is 4 x 6 = 24 inches.
Substituting these values into the formula and simplifying, we get:
84 = 36 + (0.5 x 24 x x)
84 - 36 = 12x
48 = 12x
x = 4
Therefore, the value of x, the slant height of the square pyramid, is 4 inches.
To learn more about surface area : https://brainly.com/question/16519513
#SPJ11