In Psychology 101, the ratio of the number of girls to the number of boys is $3:1$. After one girl drops the class and three more boys sign up, the ratio of the number of girls to the number of boys becomes $5:2$. How many students are in the class after these changes?

Answer:

X=-10

Step-by-step explanation:

Collinear points are points on the same line.

Use the equation of gradient to find the gradient. Then use the gradient to find X

[tex]\frac{Y2-Y1}{X2-X1}=Gradient of a slope[/tex]

[tex]\frac{2-(-4)}{3-0}=\frac{2+4}{3}=\frac{6}{3}=2[/tex]

[tex]\frac{x+4}{-3-0}=2[/tex]

Multiply both sides of the equation to get rid of the fraction.

[tex]\frac{x+4}{-3}*-3 =2*-3[/tex]

x+4=-6

x=-6-4

x=-10

Answer:

F

Step-by-step explanation:

x - x1/ x2-x1= y - y1/ y2 -y1

x - 3 / -2 -3= y -3/6-3

x-3/-5=y-3/3

3(x-3)= -5(y-3)

3x-9= -5y +15

5y = -3x +24

y= -3x/5 +24/5

Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b  form

        5y = -6x + 30

          y = [tex]\frac{-6}{5}x+\frac{30}{5}[/tex]

          [tex]y=\frac{-6}{5}x + 6[/tex]

Slope of this line m₁ = -6/5

m₁ * m₂ = -1

      m₂ = -1÷m₁ = -1 * [tex]\frac{5}{-6}[/tex]  

[tex]m_{2}=\frac{5}{6}[/tex]     & (-6 , -7)

Equation of the required line: y - y₁ = m (x - x₁)

[tex]y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2[/tex]

Answer: AAS

Step-by-step explanation:

Lets call the intersection point between AC and DE F.

I think he meant the two triangles AFE and DFC.

We know angle A is congruent to angle D.

We also know AE is congruent to DC.

There is also a hidden piece of evidence which is AFE is congruent to DFC due to vertical angles.

We know two angles and 1 side, so we can use AAS to figure out that the two smaller triangles are congruent.

Given:

Points D, E, and F are non-collinear.

To find:

Number of lines that pass through F and are perpendicular  to DE.

Solution:

Points D, E, and F are non-collinear. It means points D, E and F are not lie on a  single straight line.

We know that, the number of perpendicular lines on a line from a particular point is 1.

So, number of lines that pass through F and are perpendicular  to DE is 1 as shown in the below figure.

Answer:

b is the lowest and d is the highest y axis

Step-by-step explanation:

Answer:

Step-by-step explanation:

i believe it would be A...

Given:

x gets  larger and larger in the negative direction.

To find:

The polynomial function which gets larger and larger in the negative direction.

Solution:

In options a, c and d, degree of polynomials are even and leading coefficient is positive. So,

[tex]f(x)\to \infty\text{ as }x\to -\infty[/tex]

In option b, degree of polynomial is odd and leading coefficient is positive. So,

[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]

Therefore, the function in option b, [tex]f(x)=6x^3+4x^2-15x+32[/tex] gets larger and larger in the negative direction as x gets  larger and larger in the negative direction.

Hence, the correct option is b.

We want to see which polynomial function gets larger and larger as the variable increases in the negative direction. We will see that the correct option is d: f(x) = 8x^6 + 1

Here you need to remember two things.

As the larger the exponent is, the faster the polynomial grows.

When we evaluate a negative number in an even exponent, the outcome is always positive.

Then the polynomials that get larger and larger as x increases in the negative direction are all the polynomials with a even leading exponent, particularly, the one that increases faster is the one with the largest leading exponent, which is:

d. f(x) = 8x^6 + 1

If you want to learn more, you can read:

https://brainly.com/question/23792383

Answer:

its actually 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Step-by-step explanation:

Hey there!

Here;

Given is; angle AEB = 88°

angle AEB + angle AED = 180° { being linear pair}

88° + angle AED = 180°

angle AED = 180° - 88°

Therefore, angle AED = 92°

Therefore, answer is Option C.

Hope it helps...

Step-by-step explanation:

1. (1/10 × 1/10 × 1/10 × 1/10)^2

(10^-4)^2

10^-8

2. (1/10 × 1/10 × 1/10)^3

(10^-3)^3

10^-6

3. (10 × 10 × 10)^-2

(10^3)^-2

10^-6

Question

Write as a single exponent.

1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2

2. ( 1/10 x 1/10 x 1/10 )^3

3. ( 10 x 10 x 10 )^-2

Answer:

a

Step-by-step explanation:

proportional relationship start from the origin (0,0)

they also have a line that goes upwards in an even relationship

they also can make points

follows the slope

The midpoint would be (1/2, -3/2). Hope this helps! Please mark brainliest:)

Step-by-step explanation:

a. 8,435 is divisible by 5

b. 981 is divisible by 3 and 9

Answer:

20

Step-by-step explanation:

start by using system of equations

x = cola

y = root beer

x + y = 30

x = 2y

now either use substitution or elimination. for me, substitution is easier.

the second equation already has one variable isolated ( x ) so, plug that into the first equation.

2y + y = 30

y = 10

now plug your answer into the original equation.

x + 10 = 30

x = 20

hope this helps :)

Answer:

What is the starting temp?

Step-by-step explanation:

Answer:

theres no answer

Step-by-step explanation:

is there more?

Answer:

I think the answer would be 16?

Step-by-step explanation:

if you plug in the given numbers that represent each letter it would be 6(4)-16/2 = 24-8= 16

Answer:

should be 65

Step-by-step explanation:

if not then hmu

Answer:

integer and rational

Step-by-step explanation:

Answer/Step-by-step explanation:

An easy way to be sure two lines are perpendicular is if the product of both slopes equals -1.

That is: [tex] (m_1)(m_2) = -1 [/tex]. Where, m1 and m2 are slopes of both lines respectively.

Let's find the slope of the both lines.

Slope of the line that slants upward from left to right using coordinates (0, 0) and (2, 2) of two points on the line:

[tex] m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} [/tex]

[tex] m_1 = 1 [/tex]

Slope of the line that slants downwards from left to right using coordinates (2, 2) and (0, 4) of two points on the line:

[tex] m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{0 - 2} = \frac{2}{-2} [/tex]

[tex] m_2 = -1 [/tex]

Find the product of both slopes

[tex] (m_1)(m_2) = (1)(-1) = -1 [/tex]

Therefore, we know the lines are perpendicular because [tex] (m_1)(m_2) = -1 [/tex].

Answer:

39.25

Step-by-step explanation:

the formula is a = (3.14 × [tex]r^{2}[/tex]) / 2

the equation is a = (3.14 ×[tex]5^{2}[/tex]) / 2

5 is the radius

1. [tex]5^{2}[/tex] = 25

2. 3.14 × 25 = 78.5

3. 78.5 / 2 = 39.25

I hope this helped! :)

Answer:

12.5π or 39.25

Step-by-step explanation:

10 is diameter, we first find the radius which is 10/2 = 5 and so we know the area formula of the circle is πr^2 so 5^2 is 25 and then there's a π at the end so 25π, but it's a semicircle so 25π/2 which is 12.5π, if it's in base 10 (decimal form) then simply do 12.5 x 3.14 = 39.25

Answer:  y = 3/2x + 1

Step-by-step explanation:  For a perpendicular line, take the reciprocal of  "m"  and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b   Substitute for b in y = (3/2)x + 1

Answer:

hujikmnjhu

Step-by-step explanation:

egyiru9epojgtur9iokejrue

Answer:

i cant help i do not know answer

Answer:i-

Step-by-step explanation: good luck

Answer:

1. C) 0.009

2. B) 8/15

3. C) 111

4. D) 1/5

5. B) 6/7

6. A) 6/11

Hope this helps and have a nice day.

1. (1.) -24, (2.) 6, (3.) -3

2. Positive

3. Difference = Subtraction

Product = Multiplication

Quotient = Division

Answer:

-4

Step-by-step explanation: