The graph of F(x), shown below, resembles the graph of G(x) = x², but it has been stretched and shifted. Which of the following could be the equation of F(x)?
A. F(x) = 2/5 x² +6
B. F(x) = (1/3x)^2 +2
C. F(x) = 3x² -2
D. F(x) = (9x)² +2 ​

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

After answering the provided question, we can conclude that As a result, trigonometry angle XYZ is the smallest angle in triangle XYZ.

The study of the relationship between triangle side lengths and angles is known as trigonometry. The topic first emerged in the Hellenistic era, around the third century BC, due to the application of topography in astronomical studies. The branch of math and science known as precise methods deals with certain trigonometric functions and about there potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, non sequitur, cotangent, secant, and cosecant are their independent names and acronyms (csc). The investigation of triangle properties, notably those of right triangles, is known as trigonometry. As a result, geometry is the survey of the properties of all geometric shapes.

angle XYZ is opposite side XY

angle XZY is opposite side YZ

angle YXZ is opposite side XZ

\(cos(XYZ) = (XY^2 + XZ^2 - YZ^2) / (2 * XY * XZ)\\cos(XZY) = (YZ^2 + XZ^2 - XY^2) / (2 * YZ * XZ)\\cos(YXZ) = (XY^2 + YZ^2 - XZ^2) / (2 * XY * YZ)\)

\(cos(XYZ) = (5^2 + 13^2 - 12^2) / (2 * 5 * 13) = 0.4\\cos(XZY) = (12^2 + 13^2 - 5^2) / (2 * 12 * 13) = 0.96\\cos(YXZ) = (5^2 + 12^2 - 13^2) / (2 * 5 * 12) = 0.48\\\)

We can compare the three values above to see which angle has the smallest cosine. We can see that cos(XYZ) = 0.4 is the smallest, indicating that angle XYZ is the triangle's smallest angle.

As a result, angle XYZ is the smallest angle in triangle XYZ.

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The approximate price of the new car in 2014 is:

B. $32,200

The general form of a linear equation is given by:

y = mx + c

where y is the future price of the car, x is the number of years, m is the rate of change of price and c is the initial price of the car

c = $27,700

m = ($29,200 - $27,700)/(2010 - 2008)

m = 1500/2

m = $750 per year

In 2014, x = 2014 - 2008 = 6 years

Substituting into y = mx + c:

y = 750(6) + 27,700

y = 4500 + 27700

y = $32,200

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SOLUTION:

Case: Sample space

Method:

Let

Blue shirt be B

White shirt be W

Green shirt be G

Khaki pants be K

Denim pants be D

The sample space:

There are a total of 6 sample spaces

Final answer: Option (D)

6

The measure of the angle ADC is: 20°

The parameters are given as:

∠ABC = 40°

∠ADC = ?

We know from circle geometry that:

Angle subtended at the center is twice the angle subtended at the circumference.

Therefore:

∠ABC = 2 x ∠ADC

On substituting the value we get:

40° = 2 * ∠ADC

∠ADC = 20°

Therefore, the measure of the angle ADC is 20°

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Complete question is:

A circle is centered on point B. Points A, C and D lie on it's circumference.

If ABC measures 40 degrees, what does ADC measure?

Answer:

Your answer is: 1/80 or -1/729

Simplify the expression.

↓

Step-by-step explanation:

Hope this helped : )

Answer:

rectangle above = 3 x 5 = 15 cm²

rectangle below = 8 x 5 = 40 cm²

2 by 7 + – is equals to 1 so we can say that x.

x=1-2/7

x=7/7-2/7

x=5/7

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

3.5

Step-by-step explanation:

because 7÷4 is 3.5 because seven division of 4 is three point five

Solution

For this case we can do the following:

Statement Reason

AB = DC , AD= BC Given

AC = AC Common side

△ABC≅△ACD SSS criteria

∠DAC = ∠BCA By CPCT

CD∥AB Alternate angles are equal

∠DCA=∠CAB By CPCT

AD∥BC Alternate angles are equal

ABCD is parallelogram Opposite sides of quadrilateral are parallel.

a) The smallest number of tiles needed to make a square is 3.

b) The smallest number of tiles needed to make a square is 11.

a) To make a square using rectangular tiles that are 12 cm long and 4 cm wide, we need to find the side length of the square that is divisible by both 12 and 4. The smallest common multiple of 12 and 4 is 12, so a square with a side length of 12 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 12 cm ÷ 4 cm = 3.

Therefore, the smallest number of tiles needed to make a square is 3.

b) To make a square using rectangular tiles that are 11 cm long and 3 cm wide, we need to find the side length of the square that is divisible by both 11 and 3. The smallest common multiple of 11 and 3 is 33, so a square with a side length of 33 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 33 cm ÷ 3 cm = 11.

Therefore, the smallest number of tiles needed to make a square is 11.

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Meghan got 10 number of t - shirts.

What is mean by purchase?

Everything that has been purchased for resale in the firm is best referred to as a purchase.

Given that:

Meghan received $350 to spend for her birthday.

She spend $80 on an urban outfitters sweatshirt and the rest on t-shirts.

Each t-shirt having cost $27.

After spending $80 on an urban outfitters sweatshirt the remaining value is,  

$350 - $80 = $270.

She spend $270 on t - shirts, each of $27.

So,

\(\frac{270}{27} = 10\)

Therefore, Meghan got 10 number of t - shirts in $270.

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A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

The proposition can be proven by showing that the left and right cosets of H in G form a partition of G.

As H is a G subgroup, it comprises the identity element e within G. For any g element in G, the left coset gH comprises ge = g and the right coset Hg contains eg = g. Thus, there are non-empty left as well as right cosets.

G's each element belongs to both the left and the right cosets of H. Hence, all left (or right) cosets' union in G covers every G element. The left and right cosets of H in G build non-empty subsets that do not intersect with one another. Their union equals G; thus, they certainly construct a partition for G.

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Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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Answer:

When he first starts with two cans he id doubling the number by multiplying the number by the power of 2. so every day it would be 2,4,8,16,32,64,128,256,512,1024. So they would have 1024 cans on the tenth day.

Step-by-step explanation:

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

16 sqft.

Step-by-step explanation:

A=L(W)

A=4(4)

A=16

Hope that helps

Answer:

a) The standard deviation of the annual income σₓ = 2045

b)

The calculated value Z = 0.608 < 1.645 at 10 % level of significance

Null hypothesis is accepted

The average annual income is greater than $32,000

c)

The calculated value Z = 1.0977 < 1.96 at 5 % level of significance

Null hypothesis is accepted

The average annual income is  equal to  $33,000

d)

95% of confidence intervals of the Average annual income

(26 ,746.8 ,34, 763.2)

Step-by-step explanation:

Given size of the sample 'n' =100

mean of the sample x⁻ =  $30,755

The Standard deviation = $20,450

a)

The standard deviation of the annual income σₓ = \(\frac{S.D}{\sqrt{n} }\)

                                               = \(\frac{20,450}{\sqrt{100} }= 2045\)

b)

Given mean of the Population μ =  $32,000

Given size of the sample 'n' =100

mean of the sample x⁻ =  $30,755

The Standard deviation ( σ)= $20,450

Null Hypothesis:- H₀: μ > $32,000

Alternative Hypothesis:H₁: μ <  $32,000

Level of significance α = 0.10

\(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

\(Z = \frac{30755-32000 }{\frac{20450}{\sqrt{100} } }\)

Z= |-0.608| = 0.608

The calculated value Z = 0.608 < 1.645 at 10 % level of significance

Null hypothesis is accepted

The average annual income is  greater than $32,000

c)

Given mean of the Population μ =  $33,000

Given size of the sample 'n' =100

mean of the sample x⁻ =  $30,755

The Standard deviation ( σ)= $20,450

Null Hypothesis:- H₀: μ =  $33,000

Alternative Hypothesis:H₁: μ ≠ $33,000

Level of significance α = 0.05

\(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

\(Z = \frac{30755-33000 }{\frac{20450}{\sqrt{100} } }\)

Z = -1.0977

|Z|= |-1.0977| = 1.0977

The 95% of z -value = 1.96

The calculated value Z = 1.0977 < 1.96 at 5 % level of significance

Null hypothesis is accepted

The average annual income is equal to  $33,000

d)

95% of confidence intervals is determined by

\((x^{-} - 1.96 \frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} })\)

\((30755 - 1.96 \frac{20450}{\sqrt{100} } , 30755 +1.96 \frac{20450}{\sqrt{100} })\)

( 30 755 - 4008.2 , 30 755 +4008.2)

95% of confidence intervals of the Average annual income

(26 ,746.8 ,34, 763.2)

I believe its either c

So just look at each expression carefully 2 books per student their are 6,7 tables full of students so those will be mutiplied by 2 sooner or later and the rest you can figure it out very easily

Answer: Area 6 Perimeter 12

Step-by-step explanation:

First, you have to find the perimeter. 4+5+3=12. Then, you need to find the area, which is base*height/2. The base is 3 and the height is 4. 4*3=12. Then you need to do 12/2=6. The area is 6

Answer:

The answer for P=12cm,A=6cm²

Step-by-step explanation:

Perimeter of triangle=a+b+c

P=5+3+4

P=12cm

Area of triangle =1/2bh

A=1/2×3×4

A=2×3

A=6cm²

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

C. No -12 is to the left of -2 on the number line

Answer: 9 bottles in each box and they bought 2, 4 & 5 boxes respectively.

Step-by-step explanation:

As it is clearly mentioned at the start of question that store only sells 'boxes' of juice bottles so all three of them bought perfect boxes.

So we'll find out how many boxes they'd have bought.

The largest possible divisor of 18, 36 and 45 is 9 so each box contains 9 juice bottles and guys purchased 2, 4 and 5 boxes respectively.

If you've still not understood, you can ask me for more detailed answer :)

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                         P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean weight = \(\frac{\sum X}{n}\) = 21.88 ounces

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\)  = 0.201 ounces

            n = sample of boxes = 12

            \(\mu\) = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, \(\mu\) is ;

P(-1.796 < \(t_1_1\) < 1.796) = 0.90  {As the critical value of t at 11 degrees of

                                                  freedom are -1.796 & 1.796 with P = 5%}  

P(-1.796 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 1.796) = 0.90

P( \(-1.796 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

P( \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ) = 0.90

90% confidence interval for \(\mu\) = [ \(\bar X-1.796 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+1.796 \times {\frac{s}{\sqrt{n} } }\) ]

                                        = [ \(21.88-1.796 \times {\frac{0.201}{\sqrt{12} } }\) , \(21.88+1.796 \times {\frac{0.201}{\sqrt{12} } }\) ]

                                        = [21.78, 21.98]

Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

From the question, we have the following parameters that can be used in our computation:

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

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Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.