If st - sv, m∠sut - w + °10, and m∠suv =3w, the measure of angle SUT is 52.5°.
Given the information provided, we can set up the following equations:
1) m∠SUT + m∠SUV = 180° (since they are supplementary angles)
2) m∠SUT = w + 10°
3) m∠SUV = 3w
Now we can substitute equations (2) and (3) into equation (1):
(w + 10°) + (3w) = 180°
Combining like terms, we get:
4w + 10° = 180°
Now, subtract 10° from both sides:
4w = 170°
Finally, divide both sides by 4:
w = 42.5°
Now we can find m∠SUT by substituting the value of w back into equation (2):
m∠SUT = 42.5° + 10°
m∠SUT = 52.5°
So, the measure of angle SUT is 52.5°.
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Astha had $5,700 in her savings account when Henry opened a savings account with zero dollars.
Astha deposited $100 into her account each week for x weeks.
Henry deposited $75 into his account each week for x weeks.
The accounts did not earn interest.
Which inequality represents this situation when the amount of money in Astha's account was greater than the amount of money in Henry's account?
Answer choices:
100x < 5,700 + 75x
75x > 5,700 + 100x
100x > 5,700 + 75x
75x < 5,700 + 100x
Astha's account was greater than the amount of money in Henry's account is:
5700 + 100x > 75x
Why Astha's account was greater?Let's start by finding the total amount of money deposited by Astha and Henry after x weeks.
Astha deposited $100 into her account each week for x weeks, so the total amount she deposited is 100x.
Similarly, Henry deposited $75 into his account each week for x weeks, so the total amount he deposited is 75x.
To find the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account, we need to compare the total amount of money each of them deposited.
Astha started with $5,700 and deposited $100 each week for x weeks, so the total amount of money in her account after x weeks is:
5700 + 100x
Henry started with zero dollars and deposited $75 each week for x weeks, so the total amount of money in his account after x weeks is
75x
Therefore, the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account is:
5700 + 100x > 75x
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Based on the box-and-whisker plot shown below, match each term with the correct value. PLEASE ANSWER QUICKLY!!!
The value of the median is 18. The range of this plot is 6. The 25th percentile is 17 and the 75th percentile is 20. The interquartile range is 3.
We are given a box-and-whisker plot and we have to find the correct value of the median, range, 25th percentile, 75th percentile, and inter-quartile range with the help of this box-and-whisker plot.
We find the median with the help of the box. The line which splits the box into two halves is the median for the given data. Therefore, the median will be 18. To find the range, we subtract the minimum value from the maximum value. The minimum value is 15 and the maximum value is 21. Therefore, the range will be (21 - 15) = 6.
From the plot, we can see that the 25th percentile is 17, Q1, and the 75th percentile is 20, Q3. Now, we have to find the interquartile range. To find the interquartile range, we subtract Q1 from Q3. Therefore, our interquartile range will be (20 -17) = 3.
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Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
A motorboat is headed due east, directly across a river at 5 m/s. the current of the river is 2 m/s downstream (due south). find the following: a) the resulting true speed of the boat; b) the compass direction of the boat; and c) the distance downstream the boat will land on the shore if the river is 800 meters wide.
a) The resulting true speed of the boat is approximately 5.39 m/s.
b) The compass direction of the boat is 21.8° south of east.
c) The distance downstream the boat will land on the shore if the river is 800 meters wide is 320 meters.
a) To find the true speed of the boat, we can use the Pythagorean theorem. Since the boat's speed is 5 m/s due east and the current's speed is 2 m/s due south, we can treat these as perpendicular vectors. The true speed can be found using the formula:
True Speed = √((5 m/s)² + (2 m/s)²) = √(25 + 4) = √29 ≈ 5.39 m/s
b) To find the compass direction of the boat, we can use the inverse tangent function. The angle θ can be calculated using:
θ = arctan(opposite/adjacent) = arctan(2 m/s / 5 m/s) ≈ 21.8°
Since the boat is headed east and the current is pushing it south, the true direction is 21.8° south of east.
c) To find the distance downstream where the boat will land, we first need to calculate the time it takes to cross the river. The boat's speed across the river (due east) is 5 m/s and the width of the river is 800 meters. The time taken to cross the river is:
Time = Distance / Speed = 800 m / 5 m/s = 160 seconds
Now, we can use the time to find the distance downstream by multiplying the current's speed (2 m/s) by the time:
Distance downstream = 2 m/s × 160 s = 320 meters
So, the boat will land 320 meters downstream from its starting point on the opposite shore.
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We feed the okapi about 5,024 cubic centimeters of pellets and hay
each day. How many times a day would we have to fill the container
shown below?
80 times
40 times
16 times
4 times
HELPPPPP PLEASEEEEEE!!!!!!!
To determine how many times a day we would need to fill the container shown below, we need to calculate its capacity in cubic centimeters. Let's assume that the container is a rectangular prism with dimensions of 30 centimeters (length) x 20 centimeters (width) x 25 centimeters (height). The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
Plugging in the values we have, we get:
Volume = 30 cm x 20 cm x 25 cm
Volume = 15,000 cubic centimeters
Therefore, the container has a capacity of 15,000 cubic centimeters. To determine how many times we would need to fill it each day, we need to divide the amount of pellets and hay we feed the okapi daily (5,024 cubic centimeters) by the capacity of the container (15,000 cubic centimeters):
5,024 / 15,000 = 0.3356
This means that we would need to fill the container approximately 0.3356 times a day, which is not a practical answer. We need to round this up to the nearest whole number.
The options given to us are 80 times, 40 times, 16 times, and 4 times. Out of these options, the closest whole number to 0.3356 is 1, which means we would need to fill the container once a day.
Therefore, the answer is that we would need to fill the container shown below 1 time a day to feed the okapi their daily amount of pellets and hay.
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The volume of a gas varies inversely as the pressure and directly as the temperature (in Kelvin). If a certain gas occupies a volume of 2.4 liters at a temperature of 340 K and a
pressure of 24 newtons per square centimeter, find the volume when the temperature is 408 K and the pressure is 12 newtons per square centimeter. Round your answer to the
nearest tenth.
O 58L
1.0 L
48.0 L
O 340L
Using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
The area that any three-dimensional solid occupies is known as its volume.
These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
So, the volume can be obtained using the equation:
V = k*T/P
The value of the constant k is:
K = PV/T = 16N/cm²*2.2L/340K = 0.104N*L*K⁻¹*cm⁻²
We can now determine the volume when:
T = 408 K
P = 24 N/cm²
V = k*T/P = 0.104N*L*K⁻¹*cm⁻²*408K/21Ncm = 1.77L
Therefore, using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.
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Correct question:
The volume of a gas varies inversely to the pressure and direction of the temperature (in degrees Kelvin). If a certain gas occupies a volume of 2.2 liters at a temperature of 340 K and a pressure of 16 newtons per square centimeter, find the volume when the temperature is 408 K and the pressure is 24 newtons per square centimeter.
Solve for x Trigonometry
The size of the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
For the given triangle;
sin X = 3/5 {opposite/hypotenuse}
X = sin⁻¹(3/5) {cross multiplication}
X = 36.8699°
Therefore, the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
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Find parametric equations for a line in the direction of the vector 57 - 7 and through the point
(0, 0, - 3).
Write the equations so that one term is just the parameter - t.
х (t) = y(t) =
z(t) =
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:
r = r0 + tv
where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).
Substituting the given values, we have:
r = (0, 0, -3) + t(57, -7, 0)
Expanding, we get:
x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t
Simplifying, we have:
x(t) = 57t
y(t) = -7t
z(t) = -3
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
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If Franco's Pizza Parlor knows that the marginal cost of the 500th pizza is $3.50 and that the average total cost of making 499 pizzas is $3.30, then
a. average total costs are falling at Q = 500.
b. average variable costs must be falling.
c. average total costs are rising at Q = 500.
d. total costs are falling at Q = 500.
If Franco's Pizza Parlor knows that the marginal cost of the 500th pizza is $3.50 and that the average total cost of making 499 pizzas is $3.30, then Average total costs are rising at Q = 500. The correct answer is (c)
The marginal cost is the additional cost of producing one more unit. In this case, the marginal cost of the 500th pizza is $3.50.
The average total cost is the total cost of producing all units up to a certain level, divided by the number of units produced. In this case, the average total cost of making 499 pizzas is $3.30.
If the marginal cost of producing the 500th pizza is greater than the average total cost of making the first 499 pizzas, then the average total cost will increase when the 500th pizza is produced.
Therefore, the correct answer is (c) average total costs are rising at Q = 500.
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Joe and Mike ran the same race. Joe finished the race 4 minutes before Mike. If Mike finished the race at 4:02 p.m., what time did Joe finish the race?
Answer:3:58 p.m.
Step-by-step explanation:
consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. you first regress y on x1 only and find no relationship. however when regressing y on x1 and x2, the slope coefficient changes by a large amount. this suggests that your first regression suffers from:
When a multiple regression model created incorrectly then leaves out one and more than one important factors are omitted.
Multiple regression is a statistical way that can be used to analyze the relationship between a single dependent variable and several independent variables. Equation is written as y =
We have regressors x₁ and x₂ where both variables are determinants of the dependent variable. you first regressor y on x₁ only and find no relationship. however when regressing y on x₁ and x₂.
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Complete question:
consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. you first regress y on x1 only and find no relationship. however when regressing y on x1 and x2, the slope coefficient changes by a large amount. this suggests that your first regression suffers from:
Translate each problem into a mathematical equation.
1. The price of 32'' LED television is P15,500 less than twice the price of the
old model. If it cost P29,078. 00 to buy a new 32'' LED television, what is
the price of the old model?
2. The perimeter of the rectangle is 96 when the length of a rectangle is
twice the width. What are the dimensions of therectangle?
a) The price of the old model is P22,289.
b) The dimensions of the rectangle are 16 by 32.
a) Let x be the price of the old model. According to the problem, the price of the new 32'' LED television is P15,500 less than twice the price of the old model.
This can be expressed as 2x - P15,500 = P29,078. Solving for x, we can add P15,500 to both sides to get 2x = P44,578, and then divide both sides by 2 to get x = P22,289.
b) Let w be the width of the rectangle. According to the problem, the length of the rectangle is twice the width, so the length is 2w. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is 2w + 2(2w) = 6w.
We are given that the perimeter is 96, so we can set up an equation: 6w = 96. Solving for w, we can divide both sides by 6 to get w = 16. Since the length is twice the width, the length is 2(16) = 32.
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The population P of an organism
is growing exponentially. Select all
the functions that could represent
the population.
A. P = 400(0.85)t
B. P = 2(1.35)t
C. P = 10(1.15)t
D. P = 215(0.95)t
E. P = 75(2.85)t
F. P = 900(0.05)t
Answer: B, C and E
Step-by-step explanation: the term growing means the value is increasing, and a number multiplied by 1 gives the same number; therefore in order for that number to increase, it need to be multiplied by a bigger number which is greater than 1, in this case it can not be a number less than 0 like 0.85, so all the number which are greater than 1 in the bracket are correct.
the number before the bracket is the population before increasing, so you can substitute any value for t and try out different outcomes, you will get only B, C and E as number greater than the original number
An initial amount of $600 is invested in a compound savings account with an annual interest rate of 3. 5%.
1. Define variables
2. Substitute into formula
3. Evaluate
Formula=A = P(1+r)t
What is the total amount after 2 years?
What is the total amount after 4 years?
After 2 years, the total amount is approximately $642.45. After 4 years, the total amount is approximately $690.27.
1. Define variables:
A = total amount after a certain number of years
P = initial amount ($600)
r = annual interest rate (3.5% or 0.035)
t = number of years
2. Substitute into formula:
A = 600(1+0.035)^t
3. Evaluate:
For 2 years (t=2):
A = 600(1+0.035)^2
A = 600(1.035)^2
A ≈ 642.45
The total amount after 2 years is approximately $642.45.
For 4 years (t=4):
A = 600(1+0.035)^4
A = 600(1.035)^4
A ≈ 690.27
The total amount after 4 years is approximately $690.27.
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There are approximately 2,720 people per square mile in Charlotte. If
Charlotte is 297. 7 square miles, approximately how many people live in
Charlotte?
Round to the nearest person.
809,304 people live in Charlotte, rounded to the nearest person.
To calculate the approximate population of Charlotte, you can use the given information:
Population density = 2,720 people per square mile
Area of Charlotte = 297.7 square miles
To find the total population, multiply the population density by the area:
Total population = Population density × Area
Total population = 2,720 people/sq mile × 297.7 sq miles
Total population ≈ 809,304 people
So, approximately 809,304 people live in Charlotte, rounded to the nearest person.
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What is the sum of 2 / 10 + 6/100 not simplified
Answer: 26/100 OR 0.26 (I would put the answer as a fraction)
Step-by-step explanation:
We need both fractions to have the same denominator before we add them. The denominator of 6/100 is 100. The denominator of 2/10 is 10. We need to turn 10 into 100. To do that, we can do 10*10. This gives us 100. However what we do to the bottom must be done to the top therefore we have 20/100 + 6/100
Now the two fractions can be added together. 20/100 + 6/100 = 26/100.
Normally we would simplify this down to 13/50 but if you want it unsimplified 26/100 would be your answer.
Chelsea Menken, of Providence, Rhode Island, recently graduated with a degree in food science and now works for a major consumer foods company earning $70,000 per year with about $58,000 in take-home pay. She rents an apartment for $1,100 per month. While in school, she accumulated about $38,000 in student loan debt on which she pays $385 per month. During her last fall semester in school, she had an internship in a city about 100 miles from her campus. She used her credit card for her extra expenses and has a current debt on the account of $8,000. She has been making the minimum payment on the account of about $240 a month. She has assets of $14,000. Calculate Chelsea’s debt-to-income ratio. Comment on Chelsea’s debt situation and her use of student loans and credit cards while in college
1. Chelsea Menken's debt-to-income ratio is 35.7%.
2. Her debt situation is concerning because she accumulated significant student loan debt and credit card debt.
What is Chelsea debt-to-income ratio?The debt-to-income ratio means percentage of gross monthly income that goes to paying your monthly debt payments
Her total monthly debt payments is:
= $385 (Student loans) + $240 (Credit card) + $1,100 (Rent)
= $1,725.
Her total monthly income after taxes is:
= $58,000 / 12 months
= $4,833.33 per month.
The debt-to-income ratio will be:
= Total monthly debt payments / Monthly income after taxes
= $1,725 / $4,833.33
= 0.357
= 35.7%.
Her debt situation is concerning, so, it important for to develop a plan to pay off the debts in order to avoid accruing more interest and damaging her credit score.
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devide 240g in to the ratio 5:3:4
which amount is greater than four hundred forty-five and fifty-seven hundredths? a. four hundred forty-five and five tenths b. four hundred forty-five and seven tenths c. four hundred forty-five and five thousandths d. four hundred forty-five and fifty-seven thousandths
The amount which is greater than the given amount four hundred forty-five and fifty-seven hundredths is given by option b. 445.7.
Amount representing the number is 445.57.
Amount greater than this number,
Compare the decimal parts of the numbers given in the options.
445.5 has a decimal part of 0.5, which is not greater than 0.57.
Option a is not greater than 445.57.
445.7 has a decimal part of 0.7, which is greater than 0.57.
Option b is greater than 445.57.
445.005 has a decimal part of 0.005, which is less than 0.57.
Option c is not greater than 445.57.
445.057 has a decimal part of 0.057, which is not greater than 0.57.
Option d is not greater than 445.57.
Therefore, the only option that is greater than 445.57 is option b. 445.7.
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A fractal is a geometric figure that has similar characteristics at all levels of
magnification. One example of a fractal is Koch's (sounds like "Cokes")
snowflake. To build this fractal, start with an equilateral triangle whose sides
each have length 1. Then on the middle of each side, create a triangular
"bump" to make a new figure having 12 sides. On the middle of each of
these 12 sides, create a smaller bump, and so on. The upper part of the
illustration shows the first four stages in the construction of a Koch's
snowflake. The "real" snowflake is the result of carrying on this process
forever!
The lower part of the illustration shows how, when a bump is added to any
side, the ležgth you have is multiplied by If a bump is added to every side
of a snowflake figure, then the entire perimeter is multiplied by
The perimeter of Koch's snowflake fractal will be infinite.
Find out how Koch's snowflake fractal is created by adding triangular bumps to the side of an equilateral triangle?Koch's snowflake fractal is created by adding triangular bumps to the sides of an equilateral triangle at progressively smaller scales. At each stage, the number of sides of the resulting figure increases by a factor of 4, and the perimeter of the figure increases as well.
To see how the perimeter changes as bumps are added to all sides of the figure, we can use the fact that each bump adds a segment of length 1/3 to the original side. So if we start with a triangle of side length 1 and add a bump to each side, the new perimeter is:
P = 3(1 + 1/3) = 4
Now we have a figure with 12 sides. If we add a bump to each of these sides, the new perimeter is:
P = 12(1 + 1/3 + 1/9) = 16/3
In the next stage, we have 48 sides, and each side has a length of 1/3^2, so the new perimeter is:
P = 48(1 + 1/3 + 1/9 + 1/27) = 64/3
At each stage, we can see that the perimeter is multiplied by a factor of 4/3. So if we carry on this process forever, the perimeter of Koch's snowflake fractal will be infinite.
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Plsss help
The following two-way frequency table displays the number of adults and children attending a sporting event.
Sporting Event Attendance
Males Females Total
Adults 804 641 1,445
Children 431 268 699
Total 1,235 909. 2,144
What percentage of males attending the sporting event are adults?
A.
55. 64%
B.
65. 1%
C.
37. 5%
D.
34. 9%
The percentage of males attending the sporting events that are adults is:
65.10%.
How to obtain the percentage?A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.
The number of males attending sporting events is given as follows:
1235.
Of those 1235 males, 804 are adults, hence the percentage of males attending the sporting events that are adults is given as follows:
p = 804/1235 x 100%
p = 65.10%.
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Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at least once?
2.
Number of Tails
Probability
0
0. 06
1
0. 25
3
0. 25
4
0. 06
?
O 0. 06
O 0. 25
0. 69
O 0. 94
Mark this and return
Save and Exit
Next
Sunmit
The probability that the coin will show tails at least once is 0.56.
To find the probability that the coin will show tails at least once, you can sum the probabilities of getting 1, 3, or 4 tails, as shown in the table:
Probability of 1 tail: 0.25
Probability of 3 tails: 0.25
Probability of 4 tails: 0.06
Now, add these probabilities together:
0.25 + 0.25 + 0.06 = 0.56
So, the probability that the coin will show tails at least once is 0.56.
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I need help what is the approximate area, in square feet, of the shaded region in this figure use 3. 14
To find the approximate area of the shaded region in this figure, we need to subtract the area of the smaller circle from the area of the larger circle. The radius of the larger circle is 6 feet and the radius of the smaller circle is 3 feet.
The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius.
So, the area of the larger circle is A = 3.14 x 6^2 = 113.04 square feet.
The area of the smaller circle is A = 3.14 x 3^2 = 28.26 square feet.
To find the area of the shaded region, we subtract the area of the smaller circle from the area of the larger circle:
Area of shaded region = 113.04 - 28.26 = 84.78 square feet (rounded to two decimal places).
Therefore, the approximate area of the shaded region in this figure is 84.78 square feet.
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Given that abcd is a rhombus, determine the length of each diagonal, ac, and bd if m∠ade=20° and ad = 8cm. please help and show me how you did it
The length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
Rhombus is a special type of parallelogram in which all four sides are congruent. The opposite angles of a rhombus are also congruent, and the diagonals bisect each other at right angles.
Now, let's consider the given rhombus abcd, where ad = 8cm and m∠ade=20°. We need to determine the length of diagonals ac and bd.
First, let's use the law of cosines to find the length of side ae. We know that ad = 8cm, and m∠ade=20°, so we can use the formula:
ae² = ad² + de² - 2ad(de)cos(m∠ade)
Substituting the values, we get:
ae² = 8² + de² - 2(8)(de)cos(20°)
Next, we can use the fact that a rhombus has all sides congruent to find the length of side de. Since abcd is a rhombus, we know that ac and bd are also congruent diagonals that bisect each other at right angles. Therefore, we can draw diagonal ac and use the Pythagorean theorem to find the length of ac:
ac² = (ae/2)² + (de/2)²
Substituting ae² from the previous equation, we get:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Simplifying the equation and using the fact that ac and bd are congruent, we get:
bd² = ac² = (8² + de² - 2(8)(de)cos(20°))/2
Finally, we can use the Pythagorean theorem to find the length of diagonal bd:
bd² = ab² + ad²
Substituting ab = ac/2 and ad = 8cm, we get:
bd² = (ac/2)² + 8²
Substituting ac² from the previous equation, we get:
bd² = ((8² + de² - 2(8)(de)cos(20°))/8)² + 8²
Simplifying the equation, we get:
bd ≈ 12.22 cm
Similarly, we can solve for ac using the equation we derived earlier:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Substituting de ≈ 9.84cm (which we can solve for from the equation ae² = 8² + de² - 2ad(de)cos(m∠ade)), we get:
ac ≈ 15.58 cm
Therefore, the length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
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Identify the volume of the composite figure. The figure shows a rectangular prism with a cube removed. The prism is 9 meters long, 8 meters wide, and 3 meters high. The cube has a side of 4 meters
The volume of the composite figure is 152 m³.
How to solve for the volume of the shapeThe volume of a rectangular prism can be found using the formula V = lwh, where l is the length, w is the width, and h is the height.
For the rectangular prism:
V_prism = lwh = 9m * 8m * 3m = 216 m³
For the cube:
V_cube = s^3 = 4m * 4m * 4m = 64 m³
Now, subtract the volume of the cube from the volume of the prism:
V_composite = V_prism - V_cube = 216 m³ - 64 m³ = 152 m³
The volume of the composite figure is 152 m³.
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Suppose that f(x) = (x + 6)/(2-6) (A) Find all critical values of f. If there are no critical values, enter- None. If there are more than one, enter them separated by commas. Critical value(s) =?
The function f(x) = (x + 6)/(2-6) does not have any critical values. A critical value of a function is a value of x where the derivative of the function is either zero or undefined.
However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator.
The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function.Explanation: To find the critical values of a function, we need to find the values of x where the derivative of the function is either zero or undefined. However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator. The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function. Therefore, the answer is None.
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Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
The expression to represent the situation is 2.85g + 3.15c.
How to represent sentence with an expression?Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can.
An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.
Therefore, the expression that can be used to determine the total amount Joe spent on gasoline and oil can be calculated as follows:
Therefore,
total cost = 2.85g + 3.15c
where
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The ratio of an objects weight on earth to its weight on the moon is 6:1 the first person to walk on the moon was neil armstrong. he weighed 165 pounds on earth. what would be the proportion of this word problem?
The proportion of this word problem is 6 : 1 where Neil Armstrong weighed approximately 27.5 pounds on the moon.
The proportion of a word problem represents the relationship between two or more quantities. In this case, the proportion can be set up as:
Weight on Earth : Weight on Moon = 6 : 1
Using the information provided in the problem, we know that Neil Armstrong weighed 165 pounds on Earth. We can use this information to find his weight on the moon by setting up a proportion:
165 : x = 6 : 1
where x represents his weight on the moon. To solve for x, we can cross-multiply and simplify:
165 * 1 = 6 * x
x = 165/6
x ≈ 27.5
Therefore, Neil Armstrong weighed approximately 27.5 pounds on the moon.
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Ive been stuck on this one question for a long time can someone help me learn how to solve this?
The calculated value of x is 8 and the perimeter is 80 units
Calculating the value of x and the perimeterFrom the question, we have the following parameters that can be used in our computation:
The figure
If the lines that appear to be tangent are tangent, then we have the following equation
x = 26 - 18
Evaluate the like terms
x = 8
The perimeter is the sum of the side lengths
So, we have
Perimeter = 26 + 18 + 14 + 14 + x
This gives
Perimeter = 26 + 18 + 14 + 14 + 8
Evaluate
Perimeter = 80
Hence, the perimeter is 80 units
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Step 2: Construct regular polygons inscribed in a circle.
B) The completed construction of a regular hexagon is shown below. Explain why △ACF is 30°-60°-90° triangle. (10 points)
The explanation on why △ACF is 30°-60°-90° triangle is given below.
How to explain the informationWith a regular hexagon, each of its sides and angles are equal in measure. Consider the centre of the encompassing circle, connected to two neighbouring vertices - labeled A and B here. This then creates a radius wherein the length of AB is basically equal to any other side, denoted as 's'. Furthermore, △ABF will be an isosceles triangle (with AB = BF).
From these facts, we can produce △ACF which is a right angled triangle – with AC being its hypotenuse, A F and FB both equating to s/2, finally concluding that ∠AFB is equivalent to 120°/2 = 60° while establishing that ∠ACF is also a right angle constituent making △ACF essentially a 30°-60°-90° triangle.
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