Rotation: 180° about the origin

To write the equation of a rational function that has been reflected, shifted 6 down, 8 to the right and stretched by a factor of 4, we have to start with the basic rational function which is:

To shift it down by 6, we must subtract 6 from the function, so we have:

To shift the function to the right by 8, we substitute x for (x-8), finding this result:

To stretch the function by a factor of 4, we have to multiply the denominator by 4, which will result in:

Therefore, the equation of the rational function will be:

Find out more about rational function on:

https://brainly.com/question/19044037

#SPJ1

Answer:

I would say "not proportional" only because it's graphed on a dotted line.

If I were you, I would wait on a second opinion.

Answer:

lansing Michigan has more rain

Step-by-step explanation:

D. x ≤ 14

Hope this helped :)

Current yield = 4.51%

The price of a bond is equal to the future cash flows' present value, discounted at the appropriate discount rate—the yield to maturity.

The price of a bond is the amount that investors are willing to spend on an existing bond. Bond prices are stated as a percentage of face (par) value in the online offering table and statements you get.

Current Yield=Annual Cash Inflows/Market Price

Annual cash flow is 4.75% of 100 = $4.75

Market Price of Bond = $105.25

Current Yield = 4.75/105.25

=4.51%

To know more about price of a bond, visit:

https://brainly.com/question/25596583

#SPJ1

It takes apprοximately 3.5 years fοr an investment with an annual interest rate οf 20%, cοmpοunded cοntinuοusly, tο dοuble frοm $9,300 tο $18,600.

Cοmpοund interest is a sοrt οf interest that is calculated using bοth the principal—the initial amοunt invested οr bοrrοwed—and the interest that has accrued οver time. In οther wοrds, the interest fοr the fοllοwing periοd is cοmputed οn the new, larger amοunt after the interest generated during each periοd has been added tο the principal.

Cοmpοund interest can be explained as interest οn interest. The principle grοws οver time at a rising rate as the interest generated in each periοd is added tο it. Because οf this, cοmpοund interest is an effective instrument fοr lοng-term investing and saving.

Fοr instance, if yοu put $1,000 intο an accοunt with a cοmpοund interest rate οf 5%, yοu will receive $50 in interest the first year. Yοur tοtal sum at the end οf the first year will be $1,050 (the initial $1,000 plus $50 in interest). Yοu will receive $52.50 in interest since in the secοnd year the interest is cοmputed οn $1,050 rather than $1,000. This will increase yοur οverall balance tο $1,102.50 by the cοnclusiοn οf the secοnd year, and sο οn fοr succeeding years.

In cοnclusiοn, cοmpοund interest can be a pοtent tοοl fοr lοng-term grοwth οf yοur savings οr investments, but it's critical tο cοmprehend hοw it wοrks and pick assets with cοmpetitive interest rates and lοw expenses.

Tο find the time it takes fοr an investment tο dοuble with cοntinuοus cοmpοunding, we can use the fοrmula:

[tex]t = ln(2) / (r \times ln(1 + r))[/tex]

where:

t is the time it takes fοr the investment to double

r is the annual interest rate as a decimal

In this case, the annual interest rate is 20%, or 0.20 in decimal fοrm. So,

we can plug in the values and sοlve for t:

[tex]t = ln(2) / (0.20 \times ln(1 + 0.20))\\t = 3.5 years[/tex]

Therefore, it takes apprοximately 3.5 years for an investment with an annual interest rate of 20%, compounded continuously, to dοuble from $9,300 tο $18,600.

To knοw more about compound interest visit:

brainly.com/question/12325365

#SPJ1

We can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

The identity matrix is the only idempotent matrix with non-zero determinant.

Given is the matrix relation as -

(I + 2A)

We can write the addition of matrix as -

(I + 2A) →

[1  0]

[0  1]  

+

2[-1  2]

2[4  5]

(I + 2A) →

[1  0]

[0  1]  

+

[-2  4]

[8  10]

(I + 2A) →

[- 1  4]

[8  11]  

Therefore, we can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

To solve more questions on matrices, visit the link below-

https://brainly.com/question/30672622

#SPJ1

Answer:

Without coupon: 44 baseballs

With coupon: 56 baseballs

Step-by-step explanation:

Answer:

the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Step-by-step explanation:

Let the original price of each costume be $x. The sale price of each costume will be $(x-3.50). Ms. Monroe ordered 24 costumes, so the cost of 24 costumes at the sale price will be:

24 × (x-3.50) = $24x - $84

Ms. Monroe paid $516 in all, so we can write:

24x - 84 = 516

Adding 84 to both sides, we get:

24x = 600

Dividing both sides by 24, we get:

x = 25

Therefore, the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Answer: so Ms.Monroe got $84 off her entire purchase

Step-by-step explanation: I hope it helps

So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.

The first ten integers are the basic numbers in mathematics. The range of these vital values is 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

The total revenue from selling x units is given by:

R = xp

Substituting the demand equation p = 128 - 0.04x, we get:

R = x(128 - 0.04x)

R = 128x - 0.04x²

To find the prices that yield a revenue of $7840, we can set R equal to 7840 and solve for x:

7840 = 128x - 0.04x²

0.04x² - 128x + 7840 = 0

Dividing both sides by 0.04, we get:

x² - 3200x + 196000 = 0

Using the quadratic formula, we can solve for x:

x = [3200 ± √(3200² - 4(1)(196000))] / 2

x = [3200 ± √(10240000)] / 2

x = [3200 ± 3200] / 2

x = 1600 or x = 2400

Therefore, the corresponding prices that yield a revenue of $7840 are:

p = 128 - 0.04x

p = 128 - 0.04(1600) = 64 dollars

p = 128 - 0.04(2400) = 32 dollars

So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.

To know more about number visit:

https://brainly.com/question/17429689

#SPJ1

Answer:

We can use inequality B to determine the number of sessions Sam needs to conduct. The reason is that he already has $50 and he wants to have enough money, so he needs to earn the remaining amount through tutoring. Thus, we can write the inequality as:

15s + 50 ≥ 125

where s is the number of tutoring sessions he needs to conduct. We can simplify and solve for s as follows:

15s ≥ 75

s ≥ 5

Therefore, Sam needs to conduct at least 5 tutoring sessions to have enough money to buy the video game.

The percent of the fluid ounces under 60 is option D. Not here

To calculate the percentage of fluid ounces, you first need to determine the total volume of the container in fluid ounces. Then, you need to determine the volume of the specific substance that you are interested in as a fraction of the total volume. Finally, you can convert this fraction into a percentage by multiplying it by 100.

Here's the formula to calculate the percentage of fluid ounces:

Percentage of fluid ounces = (Volume of substance in fluid ounces ÷ Total volume of container in fluid ounces) x 100%

For example, if you have a 16 fluid ounce container of juice and you want to know what percentage of the container is filled with orange juice, and you measure that there are 4 fluid ounces of orange juice, you can calculate the percentage of orange juice as follows:

Percentage of orange juice = (4 fluid ounces ÷ 16 fluid ounces) x 100% = 25%

Therefore, the orange juice fills 25% of the 16 fluid ounce container. It could then be concluded that the percent of the fluid ounces is not here.

learn more about percent of the fluid ounces: https://brainly.com/question/13227650

#SPJ1

The area of the image of the triangle under T is 5/9.

What is Triangle?

In geometry, a triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is characterized by its three vertices (points where two sides intersect) and three sides (line segments that connect the vertices). The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides.

To show that T maps the given triangle to the domain D, we need to find the image of the three vertices of the triangle under T and then show that the image lies inside D.

Let's first consider the vertex (0,0) of the triangle. Applying T, we get T(0,0) = (0,0). So the image of the vertex (0,0) is the origin, which clearly lies inside D.

Now let's consider the vertex (1,1) of the triangle. Applying T, we get T(1,1) = (0,2), which lies on the y-axis and satisfies y²=4-4x, so it lies inside D.

Finally, let's consider the vertex (u,0) of the triangle, where 0≤u≤1. Applying T, we get T(u,0) = (u²,0). This lies on the x-axis and satisfies y²=4-4x only when x=1, which is outside D. Therefore, the image of this vertex is not inside D.

Hence, we can conclude that T maps the triangle to the domain D, except for the line segment {(u,0):0≤u≤1}.

To evaluate the area of the image, we can use the fact that the area of the image of a region under a transformation is equal to the absolute value of the determinant of the Jacobian matrix of the transformation, multiplied by the area of the original region.

The Jacobian matrix of T is given by

J(T) = [2u -2v]

[2v 2u]

The absolute value of the determinant of this matrix is 4u² + 4v², so the area of the image of the triangle is

∫∫R 4u²+4v² dA,

where R is the region in the uv-plane corresponding to the triangle.

Integrating over R, we get

∫0 ∫v 4u²+4v² dudv

= ∫0 (4/3) (1-v³+3v²) dv

= (4/3) (1/4 - 1/16 + 1/3 - 1/12)

= 5/9.

Therefore, the area of the image of the triangle under T is 5/9.

To know more about Triangle visit:

https://brainly.com/question/1058720

#SPJ1

Answer:

b or a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

I think is D

Step-by-step explanation:

because

R:622 and Y:410

An equation for the relation is y = -3x + 10.6.

f(50) is -139.4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (1, 7.6), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 7.6 = (4.6 - 7.6)/(2 - 1)(x - 1)

y - 7.6 = -3(x - 1)

y = -3x + 3 + 7.6

y = -3x + 10.6

For f(50), we have:

y = -3x + 10.6

y = -3(50) + 10.6

y = -150 + 10.6

y = -139.4

Read more on equation here: https://brainly.com/question/14774311

#SPJ1

Answer:

origin

Step-by-step explanation:

the point (0,0) is called the origin

Answer:

The center of a coordinate plane, which is point (0,0) is called "the origin."

Step-by-step explanation:

If A file that is 278 megabytes is being downloaded and the download is 19.7% complete, then you just need to multiply the 278 megabytes with 19.7%

The calculation would be: 278 megabytes x 0.197 = 54.766 megabytes.

If you round up the answer to nearest tenth it will be 54.8 megabytes.

The correct answer is 4g. Spaghetti is a great source of fiber, with 4g per serving.

Fiber is a type of carbohydrate found in plant-based foods. It is not digested or absorbed by the body, but instead passes through the digestive system and out of the body. Fiber helps promote healthy digestion by adding bulk to the stool, helping it to pass through the intestines more quickly.

Fiber is an essential part of a healthy diet. It helps to keep your digestive system functioning properly, reduce cholesterol levels, and aid in weight management. It can be found in many plant-based foods, as well as some animal-based products. Spaghetti is a great source of fiber, with 4g per serving. This is a good amount for a meal, and it can help you meet your daily fiber needs. Eating a variety of foods that are high in fiber can help you stay healthy and reach your dietary goals. Getting enough fiber in your diet can also help reduce your risk of diabetes, heart disease, and stroke. So, the correct answer is 4g of fiber per serving of spaghetti.

For more information about healthy diet,

https://brainly.com/question/25365932

#SPJ1

One hot wing costs 60 cents at this restaurant.

A variable in an equation that has to be solved for is known as an unknown.

A polynomial or formal power series may contain an indeterminate symbol, often known as a variable. In the polynomial ring or the ring of formal power series, an indeterminate is a constant rather than a variable. Nonetheless, many writers view indeterminates as a distinct class of variables because of the close connection between polynomials or power series and the functions that they describe.

Let's us assume that the cost of one hot wing is x dollars.

Then,

Total amount spent by each customer:

8x + 4 = 10x + 2.8

8x - 10x = 2.8 - 4

-2x = -1.2

x = 0.6

Therefore, one hot wing costs 60 cents at this restaurant.

Learn more about variable here:

https://brainly.com/question/29696241

#SPJ1

Answer:

y = 4x + 1

Step-by-step explanation:

Let's graph it in slope intercept form y = mx + b

m = the slope

b = y-intercept

m = 4

b = 1

So, the equation is y = 4x + 1

According to algebraic identities ,

[tex] \cos( \frac{ \theta}{2} ) = \sqrt{ \frac{1 + \cos(\theta) }{2} } \\ [/tex]

Therefore ,

[tex]\boxed{ { \cos}^{2} (\frac{\theta}{2} ) = \frac{1 + \cos(\theta) }{2} } \\ [/tex]

hope helpful! :)

Answer:

Using the half-angle formula for cosine, we can express cos(θ/2) in terms of the values of cos θ and sin θ:

cos(θ/2) = ±√[(1 + cos θ)/2]

The sign of the square root depends on the quadrant in which θ/2 lies.

Since we are given cos^2 θ/2, we need to eliminate the square root in the expression for cos(θ/2). To do this, we can use the fact that:

sin^2 θ/2 = 1 - cos^2 θ/2

Substituting the expression for cos^2 θ/2 from the previous identity, we get:

sin^2 θ/2 = 1 - cos^2 θ/2 = 1 - cos^2 (θ/2)

Solving for cos(θ/2) in terms of sin(θ/2), we get:

cos(θ/2) = ±√[1 - sin^2 θ/2]

Substituting the expression for sin^2 θ/2 from above, we get:

cos(θ/2) = ±√[cos^2 θ/2]

The sign of the square root depends on the quadrant in which θ/2 lies. Therefore, the completed identity for cos^2 θ/2 is:

cos(θ/2) = ±cos θ/2

Step-by-step explanation:

Answer:

the correct option is: L′(-1, 11).

Step-by-step explanation:

To translate the preimage 9 units up, we need to add 9 to the y-coordinate of each vertex of the polygon. Thus, the image of polygon JKLM after the translation will have vertices J′(−2, 4), K′(−4, 9), L′(−1, 11), M′(0, 8). Therefore, the image coordinates of L′ are (-1, 11).

After translation the image coordinates of L' is (-1, 11). Therefore, option B is the correct answer.

Given that, Polygon JKLM is drawn with vertices J(-2, -5), K(-4, 0), L(-1, 2), M (0, -1).

When the shape is moved up by k units, then replace y with y + k.

The translation is as follows:

Here, J(-2, -5) → (-2, -5+9) → J'(-2, 4)

K(-4, 0) → (-4, 0+9) → K'(-4, 9)

L(-1, 2) → (-1, 2+9) → (-1, 11)

M(0, -1) → (0, -1+9) → (0, 8)

Therefore, option B is the correct answer.

To learn more about the translation visit:

https://brainly.com/question/17485121.

#SPJ2

Answer:

The new size of the diagram would be 28 cm by 16.8 cm. This is calculated by multiplying the original dimensions of 16 cm and 12 cm by the ratio of 7:4. Therefore, the new width of the diagram would be 16 cm x 7 = 112 cm and the new height would be 12 cm x 4 = 48 cm. The new size of the diagram is therefore 112 cm by 48 cm, which can be simplified to 28 cm by 16.8 cm

Step-by-step explanation:

A photocopier that enlarges in the ratio 7:4 will increase the size of the diagram by a factor of 7/4. To find the new size of the diagram, we can multiply the original measurements by the factor of enlargement.

The new width of the diagram will be:
16 cm × 7/4 = 28 cm

The new height of the diagram will be:
12 cm × 7/4 = 21 cm

Therefore, the new size of the diagram will be 28 cm by 21 cm.

Answer: The new size of the diagram will be 28 cm by 21 cm.

Answer:

The total number of apples is 550

Step-by-step explanation:

12% - Turn into a fraction of 12/100

12/100

X = total number of apples

*Make another fraction of x the denominator and the 66 that are in good condition as the numerator*

12/100 = 66/X

Cross multiply

12 * X = 12x

66 * 100 = 6600

Divide

6600/12 = 12x/12 - cancel

6600/12= 550

X = 550

The trigonometric ratio for the cosine of the angle W derived as 48.18712, is equal to 0.6667.

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.

cos W = 10/15 {adjacent/hypotenuse}

cos W = 2/3

W = cos⁻¹(2/3) {cross multiplication}

W = 48.18712

cos W = cos 48.18712

Therefore, the cosine of the angle W is equal to using the trigonometric ratio.

Know more about trigonometric ratios here: https://brainly.com/question/11967894

#SPJ1

Answer:

Step-by-step explanation:

SEE THE ATTACHMENT