The zero #1 is (-3, 0) and the zero #2 is (1, 0).
To find the zeros of the quadratic equation y = 2x² + 4x - 6, we need to solve for the values of x when y = 0.
We can start by setting y to zero:
0 = 2x² + 4x - 6
Next, we can divide both sides by 2 to simplify the equation:
0 = x² + 2x - 3
We can then factor the left-hand side of the equation:
0 = (x + 3)(x - 1)
Using the zero product property, we can set each factor equal to zero and solve for x:
x + 3 = 0 or x - 1 = 0
x = -3 or x = 1
So the zeros of the quadratic function are (-3,0) and (1,0).
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!!PLEASEE HELPPP!! I’m having a hard time!!
a. A customer would save $492 during the first year by switching from ElectroniSource to Intellivision. b. A customer who would save $207 in the second year. c. Intellivision's total cost of $1654.56.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of variables, symbols, and equations. In algebra, variables represent unknown quantities, and equations represent relationships between those unknown quantities.
The fundamental operations in algebra are addition, subtraction, multiplication, and division. Algebraic equations involve variables and constants, which are combined using these operations to form algebraic expressions. These expressions can be simplified by applying algebraic rules and properties, such as the distributive property, associative property, and commutative property.
a. To calculate the savings during the first year, we need to find the total cost for each company for all three services during a year and compare them.
For ElectroniSource, the total cost for a year would be:
$42/month x 12 months = $504 for phone service
$35/month x 12 months = $420 for Internet service
$59/month x 12 months = $708 for cable TV service
Total cost for a year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the flat monthly fee is $95, so the total cost for a year would be:
$95/month x 12 months = $1140
Savings during the first year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1140
= $492
Therefore, a customer would save $492 during the first year by switching from ElectroniSource to Intellivision.
b. After the first year, Intellivision raises the rates by 25%. The new monthly fee would be:
$95 + 25% of $95 = $118.75
To calculate the savings for the second year, we need to find the total cost for each company for all three services during the second year and compare them.
For ElectroniSource, the total cost for the second year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the second year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the second year would be:
$118.75/month x 12 months = $1425
Savings during the second year = Cost with ElectroniSource - Cost with Intellivision
= $1632 - $1425
= $207
Therefore, a customer who switched from ElectroniSource to Intellivision would save $207 in the second year.
c. If Intellivision raises the rates by 16% for the third year compared to the second year, the new monthly fee would be:
$118.75 + 16% of $118.75 = $137.88
To compare the total cost for each company for the third year, we need to find the total cost for each company for all three services during the third year and compare them.
For ElectroniSource, the total cost for the third year would still be:
$504 for phone service
$420 for Internet service
$708 for cable TV service
Total cost for the third year with ElectroniSource = $504 + $420 + $708 = $1632
For Intellivision, the total cost for the third year would be:
$137.88/month x 12 months = $1654.56
Therefore, ElectroniSource is cheaper for the third year, with a total cost of $1632 compared to Intellivision's total cost of $1654.56.
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Calculate the perimeter and area of the shaded region in the drawing of two circles at right. Round to the nearest tenth. Show all work. 10 5cm 21 cm
The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).
To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.
The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.
To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.
To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:
c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72
So the length of the shared segment is approximately 11.72 cm.
Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).
To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).
The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².
To find the area of the shared segment, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:
A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²
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To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted _______ because a treatment _____ applied to the sales representatives. This is the best statistical study for this situation because the sales director is trying to establish _______.
1. ) An experiment
An observational
A survey
2. ) was
was not
3. ) causality
correlation
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find the missing side length
Answer:
Step-by-step explanation:
[tex]x^{2}[/tex]=a²+b²
x²=6²+2.5²
x²=36+6.25
x²=42.25
√x=√42.25
x=6.5
Answer:
6.5
Step-by-step explanation:
6^2 + 2.5^2 = c^2
•36 + 6.25 = c^2
•42.25 = c^2
• find square root of 42.25 = 6.5
• 6.5 = C
solve for x:
6x+26=16x
Step-by-step explanation:
[tex]6x + 26 = 16x\\ 16x - 6x = 26 \\ 10x = 26 \\ x = 2.6[/tex]
If a and b are positive numbers, prove that the equation
a/x^3+2x^2-1 + b/x^3+x-2 = 0
has at least one solution in the interval (- 1, 1).
The equation has at least one solution in the interval (-1, 1).
To prove that the equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem.
First, let's simplify the equation by finding a common denominator:
a(x^3+x-2) + b(x^3+2x^2-1) = 0
Now, let's define a new function f(x) = a(x^3+x-2) + b(x^3+2x^2-1). This function is continuous on the interval (-1, 1) because it is a sum of continuous functions.
Next, we will evaluate f(-1) and f(1) to see if the Intermediate Value Theorem can be applied.
f(-1) = a(-1^3-1-2) + b(-1^3+2(-1)^2-1) = -a-b < 0
f(1) = a(1^3+1-2) + b(1^3+2(1)^2-1) = a+3b > 0
Since f(-1) is negative and f(1) is positive, there must be at least one value of x in the interval (-1, 1) such that f(x) = 0, by the Intermediate Value Theorem.
To prove that the given equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem (IVT). Let's define the function f(x) as follows:
f(x) = a/(x^3 + 2x^2 - 1) + b/(x^3 + x - 2)
Since a and b are positive numbers, we can examine the behavior of f(x) at the endpoints of the interval (-1, 1).
f(-1) = a/((-1)^3 + 2(-1)^2 - 1) + b/((-1)^3 + (-1) - 2)
f(-1) = a/(-1) + b/(-4) < 0
f(1) = a/(1^3 + 2(1)^2 - 1) + b/(1^3 + 1 - 2)
f(1) = a/(2) + b/(0) = a/2 > 0
Since f(-1) < 0 and f(1) > 0, by the Intermediate Value Theorem, there must be at least one point c within the interval (-1, 1) where f(c) = 0. This means that the given equation has at least one solution in the interval (-1, 1).
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A bee flies for 4.0 min at 32.5 in/min find the bees distance in ft
The distance that the bees cover in feet is 10.84 feet.
The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.
We know that
1 inch=1/12feet.
so 32 inches/min=32.5 *(1/12) feet/min.
which is roughly equal to 2.71 feet/min (rounded to two decimal places).
Now by using the speed, distance, and time formula which is:
distance=speed*time
we can calculate the distance covered by bees at the given speed and time.
Substituting the values in the equation.
distance=2.71 feet/minute * 4.0 minutes.
=10.84 feet
Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).
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What is the scale factor for the similar figures below?
The scale factor of the similar figure is 2.
What is scale factor?
Scale factor is the ratio of the length of a new object to the original object.
To calculate the scale factor of the similar figures, we use the formula below
Formula:
S.F = New length/Original length.................. Equation 1Where:
S.F = Scale factorFrom the diagram,
Given:
New length = 14Original length = 7Substitute these values into equation 1
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Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
A peregrine falcon can dive at the speed of 320km/h. Create a problem that you can solve by finding an equivalent rate for this speed. Then solve the problem.
I'm fairly new to this concept and I'm a bit confused on these 3 questions. Please help :)
1) All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
2) Solutions are,
⇒ x = 3, 3, - √3 / 2, - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
Given that;
1) Expression is,
⇒ x² = y, and y² = 4
2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Now, We can simplify as;
⇒ x² = y,
⇒ x⁴ = y²
x⁴ = 4
x⁴ - 2² = 0
(x²)² - 2² = 0
(x² - 2) (x² + 2) = 0
This gives,
x² = 2
x = ± √2
x² = - 2
x = ±√2 i
Hence, We get;
y² = 4
y = ± 2
Thus, All the solution are,
(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),
Since, 2) Expression is,
⇒ (x - 3)² (2x + √3) (x + 5) = 0
Simplify as;
⇒ (x - 3)² = 0
⇒ x = 3, 3
⇒ (2x + √3) = 0
⇒ x = - √3 / 2
⇒ (x + 5) = 0
⇒ x = - 5
3) All the even integers which are divisible by 5 is,
⇒ 10, 20, 30, 40, 50, ....
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The circumference of a circle is 12.56 millimeters. What is the circle's radius?
C=12.56 mm
Use 3.14 for .
The radius of the circle is 2mm
How to determine the circumferenceIt is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.
The equation is written as;
C = 2πr
Such that the parameters are;
C is the cicumference of the circle.r is the radius of the circle.πtakes the constant value of 22/7From the information given, we have thatt;
The radius of the circle = r
The circumference = 12.56mm
Substitute the values, we have;
12. 56 = 2×3.14r
Multiply the values
r = 12. 56/6. 28
divide the values
r = 2mm
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The value of a car that depreciates over time can be modeled by the function
G(t) = 24000(0.95)2t. Write an equivalent function of the form G(t) = abt
An equivalent function of the given function in the form G(t) = [tex]ab^t[/tex] is G(t) = 24000[tex](0.9025)^t[/tex].
The given function for the value of a car that depreciates over time is G(t) = 24000[tex](0.95)^{2t[/tex]. To write an equivalent function of the form G(t) = [tex]ab^t[/tex], we need to rewrite the function using exponent rules.
First, we can rewrite [tex](0.95)^{2t[/tex] as [tex][(0.95)^{2}]^{t[/tex], which simplifies to [tex](0.9025)^t[/tex]. Therefore, we have:
G(t) = 24000[tex](0.9025)^t[/tex]
Next, we need to express 24000 as a product of two factors, a and b. We can choose a = 24000 and b = 0.9025, so we have:
G(t) = 24000[tex](0.9025)^t[/tex] = 24000[tex](0.9025)^t[/tex]
This function gives the value of the car at time t, where t is the number of years after the initial purchase, with a starting value of 24000 and a depreciation rate of 9.75% per year.
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7 Plot (6,2) on the grid.
My teacher never thought us this and this was on my homework I give you 59 points if you give me a answer
Answer:Go to the 6 number on the bottom line.Then go up until you reach 2
Step-by-step explanation:
|
|
|
|
| .
|______
Should look like that-ish
Answer:
Step-by-step explanation:
Put the point to the right 6 times and up two times
PLS HELP ME WITH THIS 50 POINTS!
Answer: The transformation is up one and to the left 5
(-5, 1)
Step-by-step explanation:
Please Give brainliest, have a great night!
Answer: h(x) = g(x+5)+1
Step-by-step explanation:
h(x) = g(x+5)+1
You went 5 in the negative direction x direction; take the opposite sign
Also went up 1 in the y direction so add 1 to equation
During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
A company estimates that 0. 5% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $500. 0. If they offer a 2 year extended warranty for $33. 00, what is the company's expected value of each warranty sold? Please format your answer using a dollar sign and two decimal points for the cents. For example, if the expected value was 50, please enter it as $50. 0
The expected value of each warranty sold is $2.47.
The expected value of each warranty sold can be calculated by subtracting the cost of the warranty from the expected value of the potential savings on replacement costs.
Let's assume that the company sells 1000 warranties. Then, the expected number of products that will fail within 2 years is:
0.5% of 1000 = 0.005 x 1000 = 5
The expected cost of replacing these products is:
5 x $500 = $2500
Therefore, the expected value of the warranty is:
($2500 - $33 x 1000) / 1000 = $2.47
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Rosita is writing an explicit function for the geometric sequence:
80, 40, 20, 10, \dots80,40,20,10,…80, comma, 40, comma, 20, comma, 10, comma, dots
she comes up with t(n)=160\left( \dfrac12 \right)^nt(n)=160(
2
1
)
n
t, left parenthesis, n, right parenthesis, equals, 160, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript.
what domain should rosita use for ttt so it generates the sequence?
The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.
An explicit function is a mathematical expression that directly relates an independent variable to a dependent variable. In the case of Rosita's function, t(n) represents the nth term in the geometric sequence and is dependent on the value of n, the term number.
The explicit function that Rosita came up with is t(n)=160(1/2)^n, which can be simplified to t(n)=80(1/2)^(n-1). This function represents the relationship between the term number and the corresponding value in the sequence.
To determine the domain of the function, we need to consider the values of n that generate the given sequence. Looking at the sequence, we can see that the first term is 80 and each subsequent term is half of the previous term. This means that the sequence is generated by multiplying 80 by (1/2) raised to a power. We can write this as:
80(1/2)^(n-1)
where n is the term number. The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.
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A piece of wire of length 50 is out, and the resulting two pieces are formed to make a corde and a square. Where should the wre be cut to day minance and provimine the continet water who? (e) To minimize the combined area, the wire should be cut so that a length of 25.964 used for the circle and a longen er 3.04 es lo quem (Round to the nearest thousandth as needed) (1) To maximize the combined uros, there should be cut so that a length of used for the circle and we canned tere dere (Round to the nearest thousandth as needed) Evaluate the following limit. Use Thôpitals Rule when it is convenient and applicable Iim cox How should the given timt be evaluated? Select the correct choice below and, if necessary, in the answer box to complete your choice A. U topitals Rule more than once to rewrite the imtin ta final fomas tim 9. Multiply the expension by a una traction to obtain im (1) OG UTHopitals Rule exactly once to rewrite the imit im OD. Vse direction Evaluate the limit imetype an exact answer
To minimize the combined area of a circle and a square made from a wire of length 50, you should cut the wire so that 25.964 units are used for the circle (as the circumference) and 24.036 units are used for the square (as the perimeter).
To maximize the combined areas, the optimal cutting point cannot be determined due to the lack of information provided in the question. For the limit evaluation, it's not clear which limit should be evaluated, as the question has some typos and irrelevant parts. If you can provide the correct limit expression, I will be happy to help you evaluate it using the appropriate method, such as Hsopital's Rule or other techniques.
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You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test your suspicion, you rolled the die in question 200 times and obtained the following frequencies for each of the six possible outcomes of the die:
Number Frequency 1 2 3 4 5 6 45 39 35 25 27 29
Can you conclude that the die is loaded? Use a 0. 05 as the significance level and perform a hypothesis test. Remember to state the null and alternative hypothesis
Based on the hypothesis test, with a significance level of 0.05, there is no evidence to suggest that the die is loaded, as the p-value is greater than the significance level. The null hypothesis that the die is fair is failed to rejected.
To determine if the die is loaded, we need to perform a hypothesis test.
Null Hypothesis (H0) The die is fair; all outcomes are equally likely.
Alternative Hypothesis (Ha) The die is loaded, and not all outcomes are equally likely.
We will use a significance level of 0.05.
To test the hypothesis, we can use a chi-square goodness-of-fit test.
First, we need to calculate the expected frequencies for each outcome, assuming that the die is fair. Since there are six possible outcomes, each with an expected frequency of 200/6 = 33.33.
Number Observed Frequency (O) Expected Frequency (E) (O - E)² / E
1 45 33.33 3.48
2 39 33.33 0.87
3 35 33.33 0.07
4 25 33.33 1.83
5 27 33.33 0.99
6 29 33.33 0.44
The test statistic is the sum of (O-E)² / E, which is 7.68.
The degrees of freedom for this test are (number of categories - 1) = 5.
Using a chi-square distribution table or calculator, we find that the p-value associated with a test statistic of 7.68 and 5 degrees of freedom is approximately 0.177.
Since the p-value is greater than our significance level of 0.05, we fail to reject the null hypothesis. We cannot conclude that the die is loaded based on this data alone.
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In a right triangle, angle λ has a measure of 19º. If the hypotenuse of this right triangle has a measure of 24 feet, what is the measure of the side adjacent to angle λ?
Answer:
22.69 ~ = 23 feet
Step-by-step explanation:
cos 19 = adj/24
24cos 18 = adj
adj = 22.69~= 23
AC B Round your answer to the nearest hundredth.
Answer:
4.28
Step-by-step explanation:
To find what the length of AC is, we can use the tangent of angle A, which is 35°. Here's the equation:
tan(35)=3/x
multiply both sides by x
x·tan(35)=3
divide both sides by the tangent of 35
x=4.28 (rounded to the nearest hundredth)
This means that AC=4.28
Hope this helps! :)
What is the maximum height of Anna’s golf ball? The equation is y=x-0. 04x^2.
The maximum height is____ feet
The maximum height of Anna's golf ball is 6.25 feet.
To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
In this case, the coefficients a and b are:
a = -0.04
b = 1
Substituting the values into the formula:
x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5
Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:
y = 12.5 - 0.04(12.5)^2
y = 12.5 - 0.04(156.25)
y = 12.5 - 6.25
y = 6.25
So, the maximum height of Anna's golf ball is 6.25 feet.
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Help me with these questions pls
The volume of the cones are;
1. 84. 78 in³
2. 564. 15 ft³
3. 4710 yd³
How to determine the value
The formula for calculating the volume of a cone is expressed as;
V = 1/3 πr²h
Given that;
r is the radius of the cone.h is the height of the coneFrom the information given, we have;
1. Volume = 1/3 × 3.14 × 3² × 9
Multiply the values and find the square
Volume = 254. 34/3
divide the values
Volume = 84. 78 in³
2. Volume = 1/3 × 3.14 × 7² × 11
Multiply the values
Volume = 1692. 46/3
Volume = 564. 15 ft³
3. Volume = 1/3 × 3.14 × 15² × 20
Multiply the values
Volume = 4710 yd³
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Given that MNPQ is a rectangle with vertices M(3, 4), N(1, -6), and P(6, -7), find the coordinates Q that makes this a rectangle
Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.
First, let's find the vector MN and MP:
MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)
Now, let's add the vector MN to point P:
Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)
Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).
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Find each arc length. Round to the nearest hundredth.
If EB = 15 cm, find the length of CD.
mCD = ____ cm.
(30 points) will give brainiest for effort
The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm
How do i determine the length of arc CD?First, we shall determine ∠CED. Details below:
∠BEC = 68°∠CED =?2∠CED + 2∠BEC = 360
2∠CED + (2 × 68) = 360
2∠CED + 136 = 360
Collect like terms
2∠CED = 360 - 136
2∠CED = 224
Divide both sides by 2
∠CED = 224 / 2
∠CED = 112°
Finally, we shall determine the length of the of arc CD. Details below:
Radius (r) = EB = 15 cmAngle (θ) = ∠CED = 112°Length of arc CD = ?Length of arc = 2πr × (θ / 360)
Length of arc CD = (2 × 3.14 × 15) × (112 / 360)
Length of arc CD = 29.31 cm
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The area of a rectangle park is 53 square mile. The length of the park is 87 mile. What is the width of the park? URGENTTT PLS ANSWER STEP BY STEP
A 3 ox serving of roasted skinless chicken breast contain 140 cal, 24 g of protein, 2 g of fat, 11 mg of calcium, and 61 mg of sodium. One half cup of potato salad contains 160 cal, 4 g of protein, 13 g of fat, 21 mg of calcium, and 656 mg of sodium. One brooccoli spear contains 40 cal, 5 g of protein, 1 g of fat, 81 mg of calcium, and 23 mg of sodim. Use this information to complete following parts.
a) Write a 1×5 matrices, C, P, and B that represent the nutritional values of the chicken, potato salad, and broccoli, respectively. Give the nutritional values in the following order: Cal, g of protein, g of fat, mg of calcium, and mg of sodium.
C=
P=
B=
The matrices are: C = [140, 24, 2, 11, 61] P = [160, 4, 13, 21, 656] B = [40, 5, 1, 81, 23]
To represent the nutritional values of the chicken, potato salad, and broccoli in matrices, we can use a 1x5 matrix for each food, where each column represents a different nutritional value in the following order: calories, protein, fat, calcium, and sodium.
Therefore, we have:
C = [140 24 2 11 61]
P = [160 4 13 21 656]
B = [40 5 1 81 23]
In matrix C, the values are 140 calories, 24 grams of protein, 2 grams of fat, 11 milligrams of calcium, and 61 milligrams of sodium for a 3 ounce serving of roasted skinless chicken breast. In matrix P, the values are 160 calories, 4 grams of protein, 13 grams of fat, 21 milligrams of calcium, and 656 milligrams of sodium for one half cup of potato salad. In matrix B, the values are 40 calories, 5 grams of protein, 1 gram of fat, 81 milligrams of calcium, and 23 milligrams of sodium for one broccoli spear.
These matrices can be used to perform calculations and comparisons between the nutritional values of the different foods.
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Find all solutions of the equation in radians.
sin(2x)sin(x)+cos(x)=0
Answer:
[tex]x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n[/tex]
Step-by-step explanation:
Given equation:
[tex]\sin(2x)\sin(x)+\cos(x)=0[/tex]
Rewrite sin(2x) using the trigonometric identity sin(2x) = 2sin(x)cos(x):
[tex]\implies 2\sin(x)\cos(x)\sin(x)+\cos(x)=0[/tex]
[tex]\implies 2\sin^2(x)\cos(x)+\cos(x)=0[/tex]
Factor out cos(x):
[tex]\implies \cos(x)\left[2\sin^2(x)+1\right]=0[/tex]
Applying the zero-product property:
[tex]\textsf{Equation 1:}\quad\cos(x)=0[/tex]
[tex]\textsf{Equation 2:}\quad2\sin^2(x)+1=0[/tex]
Solve each part separately.
[tex]\underline{\sf Equation \; 1}[/tex]
[tex]\begin{aligned}\cos(x)&=0\\x&=\arccos(0)\\x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\end{aligned}[/tex]
[tex]\underline{\sf Equation \; 2}[/tex]
[tex]\begin{aligned}2\sin^2(x)+1&=0\\\sin^2(x)&=-\dfrac{1}{2}\;\;\;\;\;\;\leftarrow\;\textsf{No solution}\end{aligned}[/tex]
Therefore, the solutions of the equation in radians are:
[tex]\boxed{x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n}[/tex]
solve by completing the square x^2-14x+49=16
ANSWER:
(x+7)^2=16
Step-by-step explanation:
x^2-14x+49=16
x^2-14x+49-16=0
x^2-14x+33=0
subtract -33 on both sides
x^2-14x+33-33=-33
x^2-14x=-33
Add 49 on both sides
x^2-14x+49=-33+49
x^2-14x+49=16
x^2-7x-7x+49=16
x(x-7)-7(x-7)=16
(x-7)(x-7)=16
(x-7)^2=16
