Sebastian mixed 2 cups of red paint with 7 cups of blue paint to make his favorite shade of purple. Which ratio of red to blue paint will make the same shade of purple?​

Answer:

The possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Step-by-step explanation:

From statement we know that [tex]AB = 2\cdot BC[/tex]. By Analytical Geometry, we use the equation of a line segment, which is an application of the Pythagorean Theorem:

[tex]AB = 2\cdot BC[/tex]

[tex]\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}} = 2\cdot \sqrt{(x_{C}-x_{B})^{2}+(y_{C}-y_{B})^{2}}[/tex] (1)

Where:

[tex]x_{A}[/tex], [tex]x_{B}[/tex], [tex]x_{C}[/tex] - x-Coordinates of points A, B and C.

[tex]y_{A}, y_{B}, y_{C}[/tex] - y-Coordinates of points A, B and C.

[tex](x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2} = 4\cdot (x_{C}-x_{B})^{2}+4\cdot (y_{C}-y_{B})^{2}[/tex]

Then, we expand and simplify the expression above:

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} +x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot (x_{C}^{2}-2\cdot x_{C}\cdot x_{B}+x_{B}^{2})+4\cdot (y_{C}^{2}-2\cdot y_{C}\cdot y_{B}+y_{B}^{2})[/tex]

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} + x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot x_{A}^{2}-8\cdot x_{C}\cdot x_{B}+4\cdot x_{B}^{2}+4\cdot y_{C}^{2}-8\cdot y_{C}\cdot y_{B}+4\cdot y_{B}^{2}[/tex]

If we know that [tex]x_{A} = 5[/tex], [tex]y_{A} = 6[/tex], [tex]x_{B} = 1[/tex], [tex]y_{B} = b[/tex], [tex]x_{C} = 1[/tex] and [tex]y_{C} = -3[/tex], then we have the following expression:

[tex]1 -10 +25 +b^{2} -12\cdot b+36 = 100 -8 +4 +36+24\cdot b +4\cdot b^{2}[/tex]

[tex]b^{2}-12\cdot b +52 = 4\cdot b^{2}+24\cdot b +132[/tex]

[tex]3\cdot b^{2}+36\cdot b +80 = 0[/tex]

This is a second order polynomial, which means the existence of two possible real solutions. By Quadratic Formula, we have the following y-coordinates for point B:

[tex]b_{1} \approx -2.944[/tex], [tex]b_{2} \approx -9.055[/tex]

In consequence, the possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Answer:

x = 28

Step-by-step explanation:

Angles on a straight line = 180°

4x + 3 + 2x + 9 = 180

4x + 2x + 3 + 9 = 180

6x + 12 = 180

6x = 180 - 12

6x = 168

6x/6 = 168/6

x = 28

Answer:

days 7

weeks 4

Step-by-step explanation:

there are 7DAYS Iin a week

there are 4WEEKS in a month

Answer:

The awnser is 14

Step-by-step explanation:

If you multiply length x width then divide u get 14

Answer:

C (y=5x-7)

Step-by-step explanation:

First, you find the slope between the 2 points which is 5, then you use one of the points to form an equation.  

You then find it's y=5x-7.

Answer:

Step-by-step explanation:

B. The data clustered from 0 to 2

Answer:

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 1.60 mg/L.

This means that [tex]\sigma = 1.6[/tex]

Collection of 10 samples:

This means that [tex]n = 10, s = \frac{1.6}{\sqrt{10}} = 0.506[/tex]

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.

82% of the candidates did not have a chance for an interview.

We have,

To find the percentage of candidates who did not have a chance for an interview, we need to subtract the percentage of candidates who scored above 85% from 100%.

Number of candidates who scored above 85%: 45

Total number of candidates: 250

Percentage of candidates who scored above 85%:

= (45/250) x 100%

= 18%

Percentage of candidates who did not have a chance for an interview:

= 100% - 18%

= 82%

Therefore,

82% of the candidates did not have a chance for an interview.

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Answer:

looks like D but im not sure

Step-by-step explanation:

Look at the slope in each equation. For the first one is 15, the second is 25, the third is 40, and the fourth is 45.

Answer:

B

Step-by-step explanation:

The first probability is 10/24, and the second is 9/23. If you multiply these two fractoins you get 15/92. 15/92 is approximately equal to 16%.

Answer:

I thin its b.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

basically the number with x is always the slope and I really just put the equations into a inspire and got the answer by which one matched

The equation of line passing through the point (8, 9) with a slope of 3

will be;

⇒ y = 3x - 15

Option A is true.

What is Equation of line?

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The slope of the line = 3

And, The point on the line = (8, 9)

Now,

Since, The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Hence, The equation of line passing through the points (8, 9) with slope '3' is defined as;

⇒ y - y₁ = m (x - x₁)

⇒ y - 9 = 3 (x - 8)

⇒ y - 9 = 3x - 24

⇒ y = 3x - 24 + 9

⇒ y = 3x - 15

Thus, The equation of line passing through the point (8, 9) with a slope of 3 will be;

⇒ y = 3x - 15

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The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

[tex]\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}[/tex]

[tex]\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}[/tex]

[tex]\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}[/tex]

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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Answer:

A.[tex]x(x+12) -7(x+12)[/tex]

Step-by-step explanation:

Factoring is the process of taking common terms out of an expression such that one can represent the expression as the result of smaller values. When given the following expression:

[tex]x^2 +5x - 84[/tex]

First, represent the linear term as the sum of two terms such that each term shares a common factor with the other terms in the expression.

[tex]x^2 +12x - 7x - 84[/tex]

Now take out the common factors,

[tex]x(x+12) -7(x+12)[/tex]

Thus, the correct option is choice (A).

Answer:

3 textbooks

Step-by-step explanation:

Well 7 notebooks were brought.

She brought 4 more notebooks then textbooks.

7-4=3

Answer:

If Anna bought seven notebooks and the number of notebooks she bought was four more than textbooks, all you have to do it subtract four from seven to get three.

Step-by-step explanation:

7 - 4 = 3

Answer:

d = -6

Step-by-step explanation:

common difference, d = -7-(-1) = -6

Answer:

33 cm

Step-by-step explanation:

volume of the under the pyramid Is 3×3×3=27

volume of pyramid is 3×3×2=18

divide 18 ÷3 =6

27+6=33

the reason why we divide by 3 because ti's is the formula

Answer:

1. B 130 2/3ft^3

2. B 226 in^3

3. B 33 cm^3

4. A 4 m

5. D 15m

Step-by-step explanation:

I got a 100! For connexus students, hope this helps!!

Answer:

I’m coming back to this hold on a sec brotha and be patient

Step-by-step explanation:

Answer:

Yes??

Step-by-step explanation:

7+3x5+3x+1

7+15+3x+1

22+3x+1

3x+23

7+5x+10

5x+17

Yes, much difference

---

hope it helps

sorry if i'm wrong, sum of the x's confused me

Answer:D

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

9514 1404 393

Answer:

  C  83°

Step-by-step explanation:

The measure of inscribed angle BDA is half the measure of the arc it intercepts.

  ∠BDA = (1/2)arcBFA = (1/2)(166°)

  ∠BDA = 83°

Answer:

The mean of the data is 3237888

Step-by-step explanation:

12*16*8*31*28*17(Don't include 0)

22665216/7 (The number of days)

3237888(Answer)

Tell me if you have any questions. :)

Answer:

The mean is 16

Step-by-step explanation:

Add all the values together to get 112.

12 + 16 + 0 + 8 + 31 + 28 + 17

= 112.

To find the mean, divide the sum by how many values we added.

We added 7 values, including 0.

112 ÷ 7 =

16. <--- the mean

Answer:

QUESTION:

Simplify: 90 - 5 (19 + 17-1-26)​

ANSWER:

45

Step-by-step explanation:

I hope that this helps you out! :)    

Have a great rest of your day/night!    

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Garrick's measurement was 2 mm off. (10 - 8 = 2)

Zan's measurement was 12 mm off. (100 - 88 = 12)

Garrick's percent error was 20% (2 / 10 x 100)

Zan's percent error was 12% (12 / 100 x 100)

Answer:

Interquartile range: 5

Outlier: 71

Potential outlier: none

Step-by-step explanation:

See attatched picture

Answer:

Step-by-step explanation:

The crater shape can be modelled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.

 d(h) = 0.25×|h -1600| -400

We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.

__

At a depth of 250 ft, the distance from the west edge can be found from ...

 -250 = 0.25|h -1600| -400

 150 = 0.25|h -1600| . . . . . . . . add 400

 600 = |h -1600| . . . . . . . . . . . multiply by 4

This resolves to two equations:

-600 = h -1600   ⇒   h = 1000

600 = h -1600   ⇒   h = 2200

The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.

Answer:

0.25|x-1,600|-400 / 1,000 / 2,200

Step-by-step explanation:

99% sure