In one grade of 150 students, the ratio of boys to girls is 2 : 3.

How many boys are in that grade?

Answer:

Step-by-step explanation:

Rule for the dilation of a point by a scale factor 'k',

(x, y) → (kx, ky)

If we impose this rule in this problem,

k = [tex]\frac{\text{Distance of A' from P}}{\text{Distance of A from P}}[/tex]

1). If k = 3

   Therefore, Distance of A' from P = 3(Distance of A from P)

   And point A' will be on the third circle.

2). If k = 2

   Distance of B' from P = 2(Distance of B from P)

   Since, B is on circle 2, B' will be on circle 4.

Now we can plot these points A' and B' on the graph.

After the dilation point A becomes A' and it is at a distance of 3 units from point P and after the dilation point B becomes B' and it is at a distance of 2 units from point P.

1)

Given :

Dilate A using P as the center of dilation and a scale factor of 3.

Let the coordinates of point A be (x,y) then after dilation point A becomes A'(3x , 3y). So, the distance of the point A' from the point P is 3 units

2)

Given :

Dilate Busing P as the center of dilation and a scale factor of 2.

Let the coordinates of point B be (x',y') then after dilation point B becomes B'(2x' , 2y'). So, the distance of the point B' from the point P is 2 units

For more information, refer to the link given below:

https://brainly.com/question/2856466

Answer:

The y intercept is (0, 8). The equation of the function is f(x) = 10x + 8

Step-by-step explanation:

Given that after 1 hour of work, Jack will make 18 dollars and the slope is 10, subtract 10 dollars from 18 dollars to find his set amount, or y-intercept.

18 - 10 = 8 dollars.

Now that we have the m and b values, we can create our equation.

The equation in standard form is f(x) = mx +b, where m = the slope and b = the y-intercept. Plug our values in and the equation will be f(x) = 10x + 8. You can test if this is correct by plugging in x values from the table and seeing if your calculated value correctly corresponds to the given y value in the table.

Answer:

x=30⁰

Step-by-step explanation:

4x-55+3x+25=180

7x-30=180

7x=210

x=30⁰

Proof

3(30)+25=115

4(30)-55=65

115+65=180⁰

Answer:

88°

Step-by-step explanation:

m∠AOB = m∠DOE = 88°

Answer:

7

Step-by-step explanation:

Answer:

O Yes, (0, 2) is a solution

Step-by-step explanation:

The Solution of an Equation

Given the equation

-2x + y = -1

An ordered pair (a,b) is a solution of the equation if

-2a + b = -1

Let's test the point (0,2) to check if it's a solution of the equation:

Replacing x=0, y=-1

-2(0) + (-1) = -1

0 - 1 = -1

-1 = -1

Since the equation is satisfied, the pair (0,2) is a solution.

Answer: O Yes, (0, 2) is a solution

Answer:

No, (0, 2) is not a solution.

Step-by-step explanation:

I did the test

Answer:

The two expressions are;

4(3x + 5)

and

(6x + 10) + (6x + 10)

Step-by-step explanation:

Here, we want to write two different expressions to represent the perimeter of the square

The perimeter is given as 12x + 20

Using factoring, we can have this as;

4(3x + 5)

Otherwise, we can have

(6x + 10) + (6x + 10)

Answer:

Answer: 3) [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Radical Form and Exponent Form

A radical can be expressed as a rational exponent following the identity:

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

We should also recall that:

[tex](x^n)^m=x^{nm}[/tex]

We are given the expression:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}[/tex]

Applying the power of power:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\left(5^{\frac{3}{4}\cdot \frac{2}{3}}\right)[/tex]

Simplifying:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=5^{\frac{1}{2}}[/tex]

Converting to radical form:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\sqrt{5}[/tex]

Answer: 3) [tex]\sqrt{5}[/tex]

Answer:

Matching the population trend to a contributing factor:

Contributing Factors                                                 Population Trends

government-sponsored family control programs    Low birth rate

agricultural economies                                              increase in food supply

medical advancements                                             low death rate

Industrial Revolution                                                 high birth rate

Step-by-step explanation:

a) Contributing factors are some negative or positive factors that influence or cause a single event or chain of events that result to the incident.

b) Defining population trends:

1) High birth rate: the industrial revolution triggered high birth rate, following increased food supply and medical advancements.

2) Low death rate: medical advancements brought about low death rate as better healthcare is provided to the sick.

3) Increase in food supply: large-scale agricultural economies ensured increasing food production and supply.

4) Low birth rate: when governments started sponsoring family control programs, the resulting effect was low birth rate.

Answer:

The first one is children and adolescents

the second one is adults

the third one is pregnancy

the last one is indivisuals with brittle bones

Step-by-step explanation:

hope this helps :D

Answer:

$65

Step-by-step explanation:

Let

x = original price of the item

Mai buys one item and saves $13,

This means 20% of the original price of the item = $13

20% of x = 13

20/100 * x = 13

0.2 * x = 13

0.2x = 13

Divide both sides by 0.2

x = 13 / 0.2

= 65

x = $65

Therefore, the original price of the item is $65

Answer: 35 minutes

Step-by-step explanation:

For us to solve the question, we have to calculate the amount of gallons of water that is drained every minute. This will be:

= (1320 - 1040) / (9 - 2)

= 280/7

= 40 gallons per minute

Since we are told that 1,320 gallons of water remain in the pool after 2 minutes. This means that the total water in the pool at the beginning was:

= 1320 gallons + (40 × 2)

= 1320 gallons + 80 gallons

= 1400 gallons

The time taken for the pool to be completely drained will be:

= Total water in pool / Gallons drained per minute

= 1400 / 40

= 35 minutes

Answer:

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Step-by-step explanation:

Answer:

It's 576 if you mean 64 times 9!

Step-by-step explanation:

Answer:

The answer is 14

Step-by-step explanation:

The taxi driver charges $4 per mile so you multiply that by 3 miles because that is what your trying to find. So you get 12 and from their you have to add the $2 fee thus leading to an answer of 14.