Which symbol correctly compares these fractions?
9 36
10 40

[tex]y=2^{\left(x-2\right)}+3[/tex]

To solve this problem, we need to start with the parent function of the exponential function, which is [tex]f(x)=a^x[/tex], where [tex]a[/tex] is the base. In our problem, [tex]a=2[/tex], so our parent function here is [tex]y=2^x[/tex]. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

[tex]g(x)=cf(x)[/tex]

where [tex]c[/tex] in this problem equals 0.25 because:

[tex]y=0.25(2^x) \\ \\ y=\frac{1}{4}(2^x) \\ \\ y=\frac{2^x}{2^2} \\ \\ y=2^{(x-2)}[/tex]

2. Vertical shift:

The graph of the function [tex]y=2^{(x-2)}[/tex] get a vertical shift given by:

[tex]y=2^{(x-2)}+3[/tex]

So the graph is shifted 3 units up. So the result is the graph shown above.

Answer:

The answer is C

Step-by-step explanation:

Answer:

C = 58.88 degrees

Step-by-step explanation:

We can use the law of cosines to find the missing angle measurement

c^2 = a^2 +b^2 -2ab cosC

Rearranging and solving for cos C

2ab Cos C = a^2 +b^2 - c^2

Divide by 2ab

cos(C) =  a^2 + b^2 − c^2

             ------------------------

                         2ab

Substituting what we know  a = 31 b = 21   c = 27

                            31^2 + 21^2 - 27^2

     cos C        =  -----------------------------

                             2(31)(21)

      cos C = .516897081

Take the inverse cos on each side

cos^-1 cos C = cos ^-1 (.516897081)

C = 58.88 degrees

Answer:

r = 3

Step-by-step explanation:

The common ratio r of a geometric sequence is the ratio between consecutive terms, that is

r = [tex]\frac{4}{\frac{4}{3} }[/tex] = 3

r = 12 ÷ 4 = 3

r = 36 ÷ 12 = 3

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The geometric mean of 2 numbers a and b is

[tex]\sqrt{ab}[/tex]

Hence

The geometric mean of 5 and 10 is

[tex]\sqrt{5(10)}[/tex]

= [tex]\sqrt{50}[/tex]

= [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

7.071

Step-by-step explanation:

To find geometric mean of two numbers given , you multiply numbers then find the square root of the result.

For this question we have  the numbers given as 5 and 10. So multiply 5 by 10 then get the square root of the answer.

[tex]=5*10=50\\\\\\\\\sqrt{50} =7.071[/tex]

Answer:

x = 3

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠QRT is an exterior angle of the triangle

∠RTS and ∠RST are the 2 opposite interior angles, thus

45x = 25x + 57 + x

45x = 26x + 57 ( subtract 26x from both sides )

19x = 57 ( divide both sides by 19 )

x = 3

All real numbers.

[tex]\boxed{TRUE}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

Expand: 4(a+2)=4a+8

Expand again: 14-2(3-2a)=4a+8

4a+8=4a+8

You subtract by 8 from both sides of an equation.

4a+8-8=4a+8-8

Simplify.

4a=4a

Then, subtract by 4a from both sides of an equation.

4a-4a=4a-4a

Finally, simplify.

4a-4a=0

0=0

True

All real numbers is the final answer.

Hope this helps you!

Have a nice day! :)

The expressions (x-5)/(x+3) and 4/(x-3) can be rewritten with a common denominator of (x+3)(x-3) to become ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

The expressions stated are: (x-5)/(x+3) and 4/(x-3). In order to rewrite these expressions with a common denominator, you need to multiply the denominators together to create a common denominator. Therefore, the common denominator would be (x+3)(x-3).

Next, each expression must be rewritten so that they have this common denominator. For the first expression, we multiply the numerator and denominator by (x-3) so we get: ((x-5)(x-3))/((x+3)(x-3)).

For the second expression, we multiply the numerator and denominator by (x+3) so we get: 4(x+3)/((x+3)(x-3)). So, the expressions rewritten with a common denominator are ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

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To find a common denominator for the given expressions, multiply the denominators together. The expressions, rewritten with the common denominator, are [tex](x-3)*(x-5)/(x+3)(x-3)[/tex] and [tex]4*(x+3)/(x+3)(x-3).[/tex]

The goal here is to find a common denominator for the expressions x-5/x+3 and 4/x-3. A common denominator can be found by multiplying the denominators of both expressions together. So for these expressions, the common denominator would be [tex](x+3)*(x-3).[/tex]

Then you multiply the top and bottom of each fraction by the missing factor from the other denominator. The expressions rewritten with a common denominator would then be:

So the expressions with a common denominator are: [tex](x-3)*(x-5)/(x+3)*(x-3)[/tex]and [tex]4*(x+3)/(x+3)*(x-3).[/tex]

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Answer:

The oven mitts cost

$13.80

But, Cook-n-Serve buys from a wholesaler, so they receive a discount of 40%

This means that they pay

(1-0.4)*($13.80) = 0.6*($13.80) = $8.28 for each pair

The markup rate on cost is 60%

And they sell for

$13.80/$8.28 = 1.67 times the price

1.67*100% = 167%

The markup rate on selling price is  167%

Answer:

Brown's experimental probability is closest to it's theoretical probability.

Step-by-step explanation:

Theoretical:

There are 5 colors so the probability of getting orange is 1/5

The probability of getting purple is 1/5

and so on... each color has the probability of 1/5 of being used

We just need to see what experimental probability is closest to .2

Experimental probability:

So Orange 118/625=.1888

Purple 137/625=.2192

Brown 122/625=.1952

Yellow 106/625=.1696

Green 142/625=.2272

So the closest from below .2 is .1952 (which is brown)

The closest from above .2 is .2192 (which is purple.

If you aren't sure which one is closer.. you can see which difference is closer to 0.

.2-.1952=.0048

.2192-.2=.0192

.1952 is the winner since .0048 is closer to 0 than .0192 is

So Brown !

Answer:

Exponential growth is called growth because its curve increases really fast, so that's the main characteristic of exponential growth. I'm attaching an example of a function with exponential growth, which is the change of population size over time.

Answer:

2 whole 1/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1.  The leading coefficient must be 1.  

2.  Divide b by 2.

3.  Square (b/2)

4.  Add (b/2)^2 to both sides to keep the polynomial balanced.

5.  You can now write the perfect square trinomial and solve.

x^2 - 3x  

-3/2

(-3/2)^2 = 9/4 = 2 1/4

Answer:

The answer is 2 1/4

Step-by-step explanation:

You are welcome.

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

73

Step-by-step explanation:

F(c)= 9/5 c + 32

Let C = 23

F(23) = 9/5 (23) +32

          = 41.4 +32

        =73.4

To the nearest degree

73

Answer:

2

Step-by-step explanation:

1/2 is the same as saying 0.5

0.5 x 4     is the same as saying      0.5 + 0.5 + 0.5 + 0.5

0.5 + 0.5 + 0.5 + 0.5 = 2

Answer:

1152

Step-by-step explanation:

First we need to find the area of the wall in square inches

8 ft = 8*12 = 96 inch tall

36 ft = 36 * 12 = 432 inches wide

The area = 96 * 432 =41472 in^2

Each ounce of paint cover 72 in^2 so divide by 72

41472/72 =576

We need 576 ounces to cover the wall

At 2 dollars per ounces

576*2 =1152 dollars to paint the wall

Answer:

Yhe equation that jas the steepest gradient is D

Step-by-step explanation:

look at the numbers infront of the 'x' without looking at the negative sign. The

larger the number the steeper the gradient. Negative gradient only means that it is a downward slope

Answer:

Step-by-step explanation:

D

Answer:

d.no change

Step-by-step explanation:

There will be no change in the quantity of products sold.

Option D will be the correct answer.

Given that the turnover is increased by 10 % when the price increases by 10 %.

Let us consider that the price of the product is x and the quantity sold is n numbers. Then the turnover t will be given as,

[tex]t = x\times n[/tex]

An increase in the price of the product is 10 % results in an increase in turnover by 10%. Hence the increased price is,

[tex]x' = x+\dfrac{10}{100}\times x[/tex]

[tex]x' = 1.1 x[/tex]

Hence new turnover will be,

[tex]t'= x\times n + \dfrac {10}{100} \times x\times n[/tex]

[tex]t'= 1.1\times x\times n[/tex]

The quantity sold can be calculated by dividing the new turnover by the increased price of the product. Thus, the new quantity of the product will be,

[tex]n' = \dfrac {t'}{x'}[/tex]

[tex]n' = \dfrac {1.1\times x\times n}{1.1\times x}[/tex]

[tex]n' =n[/tex]

We can see that the quantity of the product sold remains unchanged.

Hence option D will be the correct answer, there will be no change in the quantity of product sold.

To know more about the price and quantity, follow the link given below.

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Recall that

[tex]1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})[/tex]

So we have

[tex]x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1[/tex]

Then for any [tex]n[/tex], we have

[tex]x^{3n}=(x^3)^n=1^n=1[/tex]

Answer:

25 m

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

Or just know you are finding the hypotenuse and use c=sqrt(a^2+b^2)

If you were finding a leg use a=sqrt(c^2-b^2).

So sqrt(15^2+20^2)

=sqrt(225+400)

=sqrt(625)

=25

Answer: I make 15 dollars every week at my job

Step-by-step explanation: your x is likely representing a time like weeks and your y is most likely going to be the amount of something like money. so if x increases by one every time and y increases by 15 every time your scenario could be i make 15 dollars every week at my job.

To find the midpoint, add the 2 x values together and divide by 2, then add the 2 Y values together and divide by 2.

(5-13)/2, (-4+12)/2

-8/2 , 8/2

-4,4

The answer is (-4,4)

Answer:

x = 6

Step-by-step explanation:

Given the 2 equations

x - y = 4 → (1)

x + y = 8 → (2)

Adding the 2 equations term by term eliminates the y- term

(x + x) + (- y + y) = (4 + 8), that is

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

That is < 3.

Step-by-step explanation:

It is the angle between the (dotted)  horizontal  from B and the line going B and C.

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x-1}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{We have the slope}\ m=\dfrac{1}{4}\ \text{and the y-intercept}\ (0,\ -1)\to b=-1.\\\\\text{Substitute:}\\\\y=\dfrac{1}{4}x-1[/tex]

Answer:

The reflected point is (3,6)

Step-by-step explanation:

we know that

The reflection Ry = 5, means a reflection is across the line y= 5

we have

the point P(3,4)

Since the point P has y-coordinate  4, its distance to the line y= 5 is equal to 1 units (P is located 1 units down the line y=5).

therefore

The reflection of the y-coordinate will be 1 units above the line y=5, which is  equal to

5+1=6

Hence

the y-coordinate of the image is 6.

The reflected point is (3,6)

To reflect a point about the y-axis, negate the x-coordinate while keeping the y-coordinate the same.

In this question, you are given the point P(3,4) and asked to find Ry=5(P). The notation Ry=5(P) represents the reflection of point P about the y-axis. To reflect a point about the y-axis, you need to replace the x-coordinate with its opposite (negate it) while keeping the y-coordinate the same.

So, P(3,4) reflected about the y-axis becomes (-3,4). The x-coordinate changes from 3 to -3, but the y-coordinate remains the same at 4.

Therefore, Ry=5(P) is (-3,4).

The next step is to add (b/2a)^2 to both sides to complete the square, then balance the equation by adding the inverse of that value outside the parentheses.

The student has asked for the next step in solving the quadratic equation 0 = −2x2 + 2x + 3 by completing the square.

After rewriting the equation and factoring out the coefficient of the x2 term, the next step is to add a specific value to both sides to form a perfect square trinomial.

This value is found by taking (b/2a)2, where a is the coefficient of x2 and b is the coefficient of x. For this equation, we therefore add −(2/2*(-2))2 = 1 to both sides inside the parentheses.

The completed equation becomes −3 + 1 = −2*(x2 − x + 1/4). Finally, we must balance the equation by adding the inverse of −<strong>2*1/4</strong> outside the parentheses.

Then, we can continue solving for x.

Answer:

0.009 units in the positive y direction.

Step-by-step explanation:

Vertical shift is simply the value of the constant.

In this case, if you expand the formula by multiplying 0.9 into the parentheses,

y = 0.9 sin [(π/3) - x] + (0.9)(0.01)

y = 0.9 sin [(π/3) - x] + 0.009

Here the value of the constant is 0.009 and it is positive, hence the vertical shift is 0.009 units in the positive y direction.

ANSWER

[tex]y = 2x - 8[/tex]

EXPLANATION

To find the equation of a straight line, we need the slope and a point on that line.

We were given the equation of another line that will help us determine the slope . The given line has equation:

[tex]y = 2x + 4[/tex]

This equation is of the form

[tex]y = mx + b[/tex]

where

[tex]m = 2 \: \: is \: the \: \: slope.[/tex]

Since our line of interest is parallel to this line, their slopes are the same.

The line also contains the point (3,-2).

So we substitute the slope and point into the slope-intercept formula:

[tex] - 2= 2(3)+ b[/tex]

[tex] - 2 =6 + b[/tex]

[tex] \implies \: b = - 2 - 6 = - 8[/tex]

The required equation is

[tex]y = 2x - 8[/tex]

Final answer:

The equation of a line parallel to y = 2x + 4 and passing through the point (3, −2) is y = 2x − 8.

Explanation:

To find the equation of a line parallel to line AB with the equation y = 2x + 4 that passes through the point (3, −2), we need to use the fact that parallel lines have the same slope. Line AB has a slope of 2, so our new line will also have a slope of 2. Now, we use the point-slope form of a line: y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting our point and slope in, we get y − (−2) = 2(x − 3). Simplifying, we get y + 2 = 2x − 6, and after moving the 2 to the other side, the final equation in slope-intercept form is y = 2x − 8.

Answer:

[tex]\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Step-by-step explanation:

We can simplify the expression under the root first.

Remember to use  [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]

Thus, we have:

[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}[/tex]

We know 4th root can be written as "to the power 1/4th". Then we can use the property  [tex](ab)^{x}=a^x b^x[/tex]

So we have:

[tex]\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Option D is right.

The coordinates of the point A before dilation is (-12,-12)