The model represents an equation. What value of x makes the equation true?
A)
3
4
B)
9
2
C) −
3
4
D) −
9
2

[tex]c. \: add \: 15n \: from \: each \: side.[/tex]

I think the answer is b. y= -1

Answer:

  9 cm

Step-by-step explanation:

Side lengths of similar triangles are proportional. BC is 1.5 times the length of AC, so EF will be 1.5 times the length of DF:

  1.5·6 cm = 9 cm

Answer:

[tex] \frac{ {8}^{2} }{ {5}^{2} } = \frac{64}{25} [/tex]

B) 64:25

Step-by-step explanation:

Ratio of Lengths = a/b

Ratio of Areas = a^2/b^2

Ratio of Volumes = a^3/b^3

Answer:

12. Option A is correct

13. Option A is correct

14. Option C is correct

15. Option D is correct

16. Option A is correct

Step-by-step explanation:

12) Lowest Common Denominator of

[tex]\frac{p+3}{p^2+7p+10} \,\, and \,\, \frac{p+5}{p^2+5p+6}[/tex]

We should find the factors of denominators and then find the LCM of the denominators.Finding LCD is same as finding LCM.

Factors of p^2+7p+10 = p^2 +2p +5p+10 = p(p+2)+5(p+2) = (p+5)(p+2)

Factors of p^2+5p+6 = p^2+2p+3p+6 = p(p+2)+3(p+2) = (p+3) (p+2)

Now, rewriting the above equation with factors and finding the LCM

[tex]\frac{p+3}{(p+5)(p+2)} \,\, and \,\, \frac{p+5}{(p+3)(p+2)}\\[/tex]

LCM of (p+5)(p+2) and (p+3)(p+2) = (p+5)(p+3)(p+2)

The LCD is (p+5)(p+3)(p+2).

So, Option A is correct.

13. Divide

[tex]\frac{40x}{64y} \,\,by\,\, \frac{5x}{8y}[/tex]

by stands for division. The equation can be written as:

[tex]\frac{40x}{64y}\div\frac{5x}{8y}[/tex]

Division sign changed into multiplication, we take reciprocal of second term i.e,

[tex]\frac{40x}{64y}*\frac{8y}{5x}\\\\Solving\\\frac{40x*8y}{64y*5x}\\\\\frac{320xy}{320xy} \\\\1[/tex]

So, Option A is correct.

14. Simplify:

[tex]\frac{x+2}{x^2-6x-16} \div \frac{1}{9x} \\[/tex]

Factors of x^2-6x-16= x^2 -8x +2x -16 = x(x-8)+2(x-8) = (x-8)(x+2)

Putting factors in the above equation and changing division sign with multiplication we get,

[tex]\frac{x+2}{(x-8)(x+2)} * \frac{9x}{1}\\\frac{9x}{x-8}[/tex]

So, Option C is correct.

15. Simplify

[tex]\frac{4}{\frac{1}{4}-\frac{5}{2}}[/tex]

Solving denominator,

Taking LCM of 4 and 2 and subtracting we get

[tex]\frac{4}{\frac{1-(5*2)}{4}}\\\frac{4}{\frac{1-10}{4}}\\\frac{4}{\frac{-9}{4}}\\\frac{4*4}{-9}\\\frac{16}{-9} \,\,or\,\,\\\frac{-16}{9}[/tex]

Option D is correct.

16. Simplify:

[tex]\frac{7x+42}{x^2+13x+42}[/tex]

Making factors of x^2+13x+42= x^2 +6x+7x+42 = x(x+6)+7(x+6) = (x+7)(x+6)

Taking 7 common from numerator and putting factors in denominator we get,

[tex]\frac{7(x+6)}{(x+7)(x+6)}\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\\frac{7}{(x+7)}[/tex]

Option A is correct.

Answer: 6 outfits

Step-by-step explanation:

She can make 6 outfits out of the clothes given.

(p)=pink dress

(b)=blue dress

(y)=yellow dress

(bl)=black shoes

(w)=white shoes

p can combo with bl and w which makes 2 outfits

b can combo with bl and w which makes 2 outfits

y can combo with bl and w which makes 2 outfits

2+2+2=6 outfits

the answer is D) x^2 = 20y

Answer

a) 2π

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.

The function is

f(x) =  3*sin(2*x) + 4*cos(3*x)

Which can be seen in the picture below

We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283   ≈ 2π

The maximum and minimum values are

Max = 6.695

Min = -6.695

Answer:

you are correct

Step-by-step explanation:

p.s the way you worded this was confusing

Answer: 15 cm

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=l*w[/tex]

Where "l" is the lenght and "w" is the width.

You know that the area of this rectangle is 75 square centimeters and the width is 5 centimeters. Then, you can substitute these values into the formula [tex]A=l*w[/tex] and solve for the lenght. Then you get:

[tex]75cm^2=l(5cm)\\\\\frac{75cm^2}{5cm}=l\\\\l=15cm[/tex]

Therefore, the lenght of the rectangle is 15 centimeters.

Answer:

15 centimeters.

Step-by-step explanation:

To find the area of a rectangle, you have to multiply the length by the width.

In this case, the width is 5 centimeters.

So, so find the area, you would have to multiply 5 by the length. Let's call the length "x".

The equation to solve this problem would be:

5x - 75

Now we can solve the equation...

Divide both sides by 5...

5x / 5 = 75 / 5

x = 15

Since x is equal to 15, that means that the length is 15, because we said that the length is equal to x.

Length = x = 15

------------------

Hope this helped!

Amber plus 2 family members = 3 total people on the plan.

They share the minutes equally so divide the minutes by 3 to find how many she can use:

720 / 3 = 240 minutes per month.

Now divide the monthly minutes by 30 days:

240 / 30 = 8 minutes per day.

Answer:

$36.00

Step-by-step explanation:

40% of 60 is 24. Subtract from the origanl amount, you get the price after sale, $36.00. Hope this helps :)

Answer:

Step-by-step explanation:

Both lines have y-intersects y=3. So, it can be A,B or D

Both lines are solid, so it could be A, or B.

The colored areas are under the line, that means that signs will be ≤.

So, answer is A.

Answer:

A

Step-by-step explanation:

Add up all of the numbers:

110+142+120+180+ 151+110+159+173+173+144+110 = 1572

Next you divide by how many number there are (there are 11 numbers)

1572 ÷ 11 = 142.9090909

142.9090909 rounded to the nearest tenth is 142.9

Answer:

A.  142.9

Step-by-step explanation:

There are 11 members in the data set, therefore:

The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11

= 1572/11

= 142.9.

Answer:

The correct answer option is C. 0.

Step-by-step explanation:

We are given the following data set and we are to find its median value:

[tex] - 1 0 0 0 , - 9 9 9 , 1 9 9 8 , ... , -1 , 0 , 1 , ... , 9 9 8 , 9 9 9 , 1 0 0 0 [/tex]

Median is the middle value of a data set which divides it into to halves.

The data set we have starts from -1000 and goes till 1000 which means there are total 2001 elements in it.

Therefore, 0 will the middle value which is the median for this data set.

Answer:

C) 0

Step-by-step explanation:

Median is the middle value of a data set which divides it into to halves.

So then 0 will the middle value which is the median for this data set.

0 is the in the middle.

Answer:

[tex]A(t)=(100-8t)^{2}[/tex]

Step-by-step explanation:

Let

t-----> the number of years

A-----> the area of the cement parking lot

we know that      

The function that represent this situation is

[tex]A(t)=(100-8t)^{2}[/tex]

Final answer:

The function A(t) = [tex](100-8t)^2[/tex] can be used to calculate the area of the cement parking lot after t years by substituting the side length (100-8t) into the formula for the area of a square.

Explanation:

The function that can be used to calculate the area of the cement parking lot after t years is: A(t) = [tex](100-8t)^2[/tex].

To calculate the area of the square parking lot at any given time t, you substitute the side length (100-8t) into the formula for the area of a square, A = side [tex]length^2[/tex].

For example, after 2 years, the area A(2) would be[tex](100-8(2))^2[/tex] = [tex]84^2[/tex]= 7056 square meters.

Answer:

D. would be your answer

Step-by-step explanation:

Yes, the triangles ΔAYM ∼ ΔEDC by SSS criterion of similarity.

If the respective angles are congruent and the corresponding sides are proportional, two triangles are said to be similar.

The two triangles are similar if the three sides of one triangle are proportional to the three sides of the other.

According to SSS criterion of similarity:

CE / AM = ED / AY = CD / MY

3 / 6 = 4 / 8 = 5 / 10

1/2 = 1/2 = 1/2

Hence  ΔAYM and ΔEDC are similar by SSS criterion of similarity.

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Answer:

3225

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]

where a is the first term and d the common difference

here a = 6 and

d = 13 - 6 = 20 - 13 = 7, hence

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex][ (2 × 6) + (29 × 7) ]

                          = 15(12 + 203) = 15 × 215 = 3225

Answer:

hello : h =5 and K= 1

Step-by-step explanation:

look this solution :

As per the given quadratic function, the value of the vertex of the graph is written as (5, 1)

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0. However, the given quadratic function is already expressed in the desired form, f(x) = a(x - h)² + k, which is known as vertex form. In this form, (h, k) represents the coordinates of the vertex of the parabola.

Now, let's rewrite the given quadratic function f(x) = 2x² - 20x + 51 in the vertex form. To achieve this, we'll complete the square:

Step 1: Factor out the leading coefficient 'a' from the x² and x terms. f(x) = 2(x² - 10x) + 51

Step 2: Complete the square inside the parentheses by adding and subtracting the square of half of the coefficient of the x-term (in this case, -10/2 = -5, and (-5)² = 25). f(x) = 2(x² - 10x + 25 - 25) + 51

Step 3: Group the perfect square trinomial and the constant term inside the parentheses. f(x) = 2((x - 5)² - 25) + 51

Step 4: Distribute the leading coefficient 'a' back into the parentheses. f(x) = 2(x - 5)² - 50 + 51

Step 5: Combine the constants. f(x) = 2(x - 5)² + 1

Now, the quadratic function is in the form f(x) = a(x - h)² + k, where a = 2, h = 5, and k = 1.

Therefore, the vertex of the parabola is (h, k) = (5, 1).

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Answer:

Option D. A sector

Step-by-step explanation:

we know that

A circular sector is the portion of the circle enclosed by two radii and an arc

so

In this problem we have a slice of the pizza enclosed by two radii and an arc

therefore

The shape of the slice is a sector

Answer:

Option C is correct: A Sector

Step-by-step explanation:

A-p-e-x :)

Answer:

Y=3x(x-4)

Step-by-step explanation:

Answer: Option C  

[tex]r ^ 2 = 0.684[/tex]

Step-by-step explanation:

The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.

 If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.

If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.

Then for a  relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.

The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.

In this problem we have that the correlation coefficient r is

[tex]r = 0.827[/tex]

then the coefficient of determination is:

[tex]r ^ 2 = 0.827 ^ 2[/tex]

[tex]r ^ 2 = 0.684[/tex]

The answer is option C

Answer:

its A

Step-by-step explanation:

Answer:

Choice A is correct

Step-by-step explanation:

We have been given the expression;

[tex]x^{\frac{9}{7} }[/tex]

In order to re-write this expression, we shall use some laws of exponents;

[tex]a^{\frac{b}{c} }=(a^{b})^{\frac{1}{c} }[/tex]

Using this law, the expression can be written as;

[tex](x^{9})^{\frac{1}{7}}[/tex]

The next thing we need to remember is that;

[tex]a^{\frac{1}{n} }=\sqrt[n]{a}[/tex]

Therefore, the expression becomes;

[tex]\sqrt[7]{x^{9} }[/tex]

Next,

[tex]x^{9}=x^{7}*x^{2}[/tex]

This implies that;

[tex]\sqrt[7]{x^{9} }=\sqrt[7]{x^{7}*x^{2}}\\=\sqrt[7]{x^{7} }*\sqrt[7]{x^{2} } \\=x\sqrt[7]{x^{2} }[/tex]

ANSWER

A.

[tex]x \sqrt[7]{{x}^{2} } .[/tex]

EXPLANATION

The given expression is

[tex] {x}^{ \frac{9}{7} } [/tex]

We want to rewrite the given expression in radical form:

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

This implies that:

[tex] {x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{9} } [/tex]

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} \times {x}^{2} } [/tex]

Split the radicals.

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} } \times \sqrt[7]{{x}^{2} } [/tex]

This finally simplifies to:

[tex]{x}^{ \frac{9}{7} }=x \sqrt[7]{{x}^{2} } [/tex]

The correct answer is A.

Answer:

Hence correct choice is B. 58,381

Step-by-step explanation:

Given equation is [tex]y=18000(1.04)^x[/tex].

There x represents number of years. We need to find about which is the best prediction for the population in year 30.

To find that we will plug x=30 into above formula and simplify

[tex]y=18000(1.04)^x[/tex]

[tex]y=18000(1.04)^{30}[/tex]

[tex]y=18000(3.24339751003)[/tex]

[tex]y=58381.1551805[/tex]

Which is approx 58381

Hence correct choice is B. 58,381.

A) the graph is a linear and the slope is negative and positive .

B) (-1,-1) is not a solution because that point does not appear in the shaded region, therefore there is no solution.

:D

Answer:

60

Step-by-step explanation:

If you do 25% + 6 * 10 , it gives you 62.5 and you round that and it's 60.

Answer:

60

Step-by-step explanation:

25% + 6 * 10

=62.5

round 62.5

=60.

Give brainliest plz :'D

Answer:

a

Step-by-step explanation:

plato answer

Answer:

B The measurement found using Ruler 2 is more accurate and more precise.

Step-by-step explanation:

We have to understand the concept here for accuracy and precision.

Accuracy is against some standard. So it is the measured value which is closely against a standard. Accuracy is less if the measured value is deviated from the standard.

Precision is about how closely individually measured values agree with each other. Precision doesn't concern with the standard value.

Now, third concept is significant numbers. It is up to how much decimal numbers an instrument can produce a result.

In ruler 2, you can see that there are more divisions for a whole inch. This means that the ruler 2 can measure more nearly to the standard value, as well as, for repeated measurements, it can give more precised figures due to the ability to read up to more decimal numbers after the decimal point.

Answer:

The capacity of the remaining bottles = 4 pints.

Step-by-step explanation:

6*3 + 6*b = 42

6b = 42 - 18

6b = 24

b = 4.

The required quantity of the remaining 6 bottles is 4 pints.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.

Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4

Thus, the required quantity of the remaining 6 bottles is 4 pints.

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Answer:

It's D.

Step-by-step explanation:

The figure is rotated 90 degrees clockwise then translated down 3 units and left 2 units.

The blue triangle becomes the purple triangle by rotating 90° clockwise then translated down 3 units and left 2 units, so, option D is correct.

A shape is translated when it is moved to the left, right, up, or down without turning. Congruence is demonstrated by the fact that the translated shapes (or the image) seem to be the same size as the original ones. Simply said, they have changed their path or directions.

Given:

The blue triangle becomes the purple triangle in the graph,

All rotations are about the origin,

The Clockwise motion, also known as CW, moves from top to bottom, then down and left, and then back to top in the same manner as a clock's hands.

As you can see, The blue triangle is firstly rotated at 90° clockwise and then translated 3 units in the down y-axis and 2 units in the left x-axis.

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