Find the surface area of
the prism.
12 in.
6 in.
5 in.
The surface area is in.2.

Answer:

I. x = 14.115 and y = 9.115

II. x = 0.885 and y = -4.115

Step-by-step explanation:

Translating the word problem, we have;

x - y = 5  ......equation 1

x² + y² = 100  ...... equation 2

x = y + 5  ...... equation 3

Substituting eqn 3 into eqn 2, we have;

(y + 5)² + y² = 100

Simplifying further by opening the bracket, we have;

(y + 5)(y + 5) + y² = 100

y² + 5y + 5y + 25 + y² = 100

y² + 10y + 25 + y² = 100

2y² + 10y + 25 = 100

2y² + 10y + 25 - 100 = 0

2y² + 10y - 75 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 2, b = 10 and c = -75

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] y = \frac {-10 \; \pm \sqrt {10^{2} - 4*2*(-75)}}{2*2} [/tex]

[tex] y = \frac {-10 \pm \sqrt {100 - (-600)}}{4} [/tex]

[tex] y = \frac {10 \pm \sqrt {100 + 600}}{4} [/tex]

[tex] y = \frac {10 \pm \sqrt {700}}{4} [/tex]

[tex] y = \frac {10 \pm 26.46}{4} [/tex]

[tex] y_{1} = \frac {10 + 26.46}{4} [/tex]

[tex] y_{1} = \frac {36.46}{4} [/tex]

[tex] y_{1} = 9.115 [/tex]

Or

[tex] y_{2} = \frac {10 - 26.46}{4} [/tex]

[tex] y_{2} = \frac {-16.46}{4} [/tex]

[tex] y_{2} = -4.115 [/tex]

Next, we would find the value of x;

x = y + 5

When y = 9.115

x = 9.115 + 5

x = 14.115

When y = -4.115

x = -4.115 + 5

x = 0.885

Check:

x - y = 5

14.115 - 9.115 = 5

Answer:

Step-by-step explanation:

J and k are parallel if

angle 1 = angle 4 (vertically opposite angles)

angle 2 + angle 5 = 180 degree (being co interior angles)

angle 4 = angle 5 (being alternate interior angles)

angle 1 = angle 5 (being corresponding angles)

Answer:

2 and 5 are co - interior angles

1 and 3 are corresponding angles

1 and 4 are alternate

6 and 8 are corresponding angles

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

In a right triangle, there are three sides, A, B, and C.

A and B are the short sides, while C is the long side.

So we know that A = 6 cm, and B = 8 cm.

We can then use the Pythagorean theorem which states that

[tex]C=\sqrt{(A^2)+(B^2)[/tex]

Once we plug in the numbers we get

[tex]C=\sqrt{6^2+8^2}[/tex]

[tex]C=\sqrt{36+64}[/tex]

[tex]C=\sqrt{100}[/tex]

C=10 cm

Answer:

Step-by-step explanation:

Distance formula:

[tex]\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}[/tex]

Distance for AB

[tex]\sqrt{(4-2)^2+(1-(-5))^2}=\sqrt{4+36}=\sqrt{40}\\[/tex]

Distance for AC

[tex]\sqrt{(8-2)^2+(-3-(-5))^2}=\sqrt{36+4}=\sqrt{40}[/tex]

2.

same formula solve when positive

[tex]5=\sqrt{(6-3)^2+(y-2)^2}\\25=9+(y-2)^2\\16=(y-2)^2\\4=y-2\\6=y[/tex]

Now when it's negative

[tex]5=\sqrt{(6-3)^2+(y-2)^2}\\25=9+(y-2)^2\\16=(y-2)^2\\-4=y-2\\y=-2[/tex]

so y can equal 6 or -2

Answer:

First Part;

As the temperature in the city increases, the number of cups of hot chocolate sold decreases

Second Part;

The approximate value of the slope in number of cups sold per change in temperature is -0.12222

The approximate value of the y-intercept is 20.944 degrees temperature

Step-by-step explanation:

Question;

First Part

What is the relationship between temperature in the city and the number of cups of hot chocolate sold, using your own words

Second Part

How can the line of best fit be made. Give the approximate values of the slope and the y-intercept of the line of best fit

Explanation

The data points are presented in the following table;

[tex]\begin{array}{lcl}x&&y\\20&&20\\30&&18\\40&&20\\35&&15\\50&&20\\45&&20\\60&&14\\65&&18\\80&&10\\70&&8\\40&&2\end{array}[/tex]

A scatter plot is formed from the given data using MS Excel

First part;

From the values of the number of cups sold, y, and the temperature at which they are sold, x, there is correlation between the x and y values, such that as the temperature increases, the number of cups sold decreases, the becomes more rapid as the temperature increases past 50, such that the reason for taking the hot chocolate decreases with increasing temperature

Second Part;

The line of best fit can be found using the least squares regression formula to draw a straight line from the regression equation as follows;

y = a + b·x

[tex]b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }[/tex]

a = [tex]\bar y[/tex] - b·[tex]\bar x[/tex]

Where;

b = The slope

a = The y-intercept

From MS Excel, we have;

[tex]\bar y[/tex] = 15, [tex]\bar x[/tex] = 48.63636

[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) = -410[/tex]

[tex]\sum \left(x_i - \bar x\right )^2 = 3354.545[/tex]

Therefore;

[tex]b = \dfrac{-410}{3354.545} = -0.12222[/tex]

The approximate value of the slope, b = -0.12222 (number of cups sold per unit change in temperature)

a = 15 - (-0.12222)×48.63636 ≈ 20.944

The approximate value of the y-intercept, a = 20.944 (in degrees of temperature).

Answer:

it's AAAAAAAAAAAAAAAAAAA

Answer:

It's A <3

I took the test. ^^

Answer:

Independent variable - type of cola drink

dependent variable - taste rating of cola drink

extraneous variable - type of cola drink

Step-by-step explanation:

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable.

The extraneous variable is the variable  that is not been researched in the experiment but it has the potential to influence the results of the experiment.

The type of cola drink given to participants can be manipulated to derive different ratings. the ratings that participants would give the cola drink is determined by the type of cola drink served. Here, the type of drink served is the independent variable while the ratings given is the dependent variable.

the extraneous variable is the type of drink cups used. this is not relevant to the experiment but can affect the results of the experiments. for example, imagine a red cup is used for the experiment and a participant hates red cups. it is more likely that the participant would give a low rating for the cola drink even if the drink tastes good

Answer:

Step-by-step explanation:

In this case "solving" involves isolating the variable, x, on the left side of this equation.  

Starting with x - 1/3 = 1/3, we add 1/3 to both sides.  This results in:

x = 1/3 + 1/3, or x = 2/3.

Answer:

5/18

Step-by-step explanation:

conditional probability formula:

A|B (a given b)  = (A∩B)/(B)

so

Moderate|college (moderate given college)= (moderate∩college)/college

moderate∩college= 15

college= 11+15+28= 54

15/54= 5/18

Answer:

She will need to pay $206.50 per month.

Step-by-step explanation:

Divide the total cost ($2,478) by the number of months (12 mos) to obtain Sam's monthly payment:

 $2,478

---------------- = $206.50/month

12 months

She will need to pay $206.50 per month.

Answer:

Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

Step-by-step explanation:

Given that Michelle invested $ 10,000 for one year, part at 8% interest and the rest at 12% annual interest, and her total interest for the year was $ 944, to determine how much money did she invest at 12% interest, the following calculation must be done:

10,000 x 0.08 + 0 x 0.12 = 800

8,000 x 0.08 + 2,000 x 0.12 = 880

4,500 x 0.08 + 5,500 x 0.12 = 1,020

6,000 x 0.08 + 4,000 x 0.12 = 960

6,500 x 0.08 + 3,500 x 0.12 = 940

6,400 x 0.08 + 3,600 x 0.12 = 944

Therefore, Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

do you have a clearer picture please? I can help :))

Answer:

11/1//11/1

Step-by-step explanation:

ans is c it is simple c only meet the need of questions

x^3= 125000 m^3

x=50 m

Answer:

Step-by-step explanation:

x+15 = 2x-40

Move x to the right side and you get 15 = x-40

Move -40 to the left side and you get x = 55

In order for the parallelogram to be a rhombus, x must equal 55.

A rhombus is a quadrilateral that has four equal sides.

Some of the properties we need to know are:

- The opposite sides are parallel to each other.

- The opposite angles are equal.

- The adjacent angles add up to 180 degrees.

We have,

If a parallelogram is a rhombus, it means that all four sides of the parallelogram have equal length.

We can set the expressions for the opposite sides of the parallelogram equal to each other and solve for x.

x + 15 = 2x - 40

First, we can simplify by adding 40 to both sides and getting:

x + 55 = 2x

Next, we can subtract x from both sides and get:

55 = x

Therefore,

In order for the parallelogram to be a rhombus, x must equal 55.

To verify this, we can substitute x = 55 back into the expressions for the sides:

x + 15 = 55 + 15 = 70

2x - 40 = 2(55) - 40 = 70

Both opposite sides have an equal length of 70, so the parallelogram is a rhombus.

Thus,

In order for the parallelogram to be a rhombus, x must equal 55.

Learn more about Rhombus here:

https://brainly.com/question/27870968

#SPJ2

Answer:

6ab + 8a² - 15b - 20a

Step-by-step explanation:

Expand by using FOIL method

4(2a-5) + 3b(2a-5)

4a(2a) + 4a × -5 + 3b × -5

Simplify terms

8a² - 20a + 6ba -15b

6ab + 8a² - 15b - 20a

Answer:

La circunferencia del círculo es igual a Pi π veces el diámetro d. Dado que el diámetro d es igual a 2 veces el radio r, la fórmula para la circunferencia que usa el radio es 2πr 2 π r.

Step-by-step explanation:

Answer:

sorry bro......sis

Step-by-step explanation:

don,t know its answer

Answer:

2 solutions for this equation because the highest power is 2

Answer:

A.{-2,3,1,5 } or D. {-2, -1, 0,5}

Answer:

3 Pounds

Step-by-step explanation:

2.82 rounded to the nearest whole number is 3.

If we wanted to round 2.82 to 2, it would have to be 2.49 or less

Answer:

b is 12.99

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

Since the triangles are similar we can use ratios to solve

4.5     7.5

---- = ------

3            x

Using cross products

4.5x = 3 * 7.5

4.5x = 22.5

Divide each side by 4.5

x = 22.5/4.5

x=5

Answer:

question a is technically 7.5 and question b is 7.5

Step-by-step explanation:

half half

Answer:

Decreased

Strong negative

Step-by-step explanation:

The correlation Coefficient is used to show the strength and type of relationship which exists between the dependent and independent variable. The correlation Coefficient value ranges from - 1, to 1. With values closer to either - 1 or 1 depicting a strong relationship while those closer to 0 represents weak relationship. And correlation Coefficient of 0 indicates that no relationship exiata at all. Depending in the sign, that is positive or negative, positive sign means positive relationship while a negative sign represents a negative association. Positive association is interpreted as, for every increase in A, Variable B also increase and vice versa. For negative association, When A increases, B decreases and vice versa

Answer:

3x+34+23y, You can not add in this equation as there are no like numbers.

Step-by-step explanation:

Answer:

isnt it 60xy

Step-by-step explanation:

Answer:

IRR = -5.19%

MIRR =  3.33%

The company should reject the project

Step-by-step explanation:

Internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested

IRR can be calculated with a financial calculator

Cash flow in year 0 = -$12,000

Cash flow in year 1 = $2,360

Cash flow in year 2 =  $4,390

Cash flow in year 3 = $1,520

Cash flow in year 4 = $980

Cash flow in year 5 = $1,250

IRR = 5.19%

The modified internal rate of return is a capital budgeting method used to determine the profitability of an investment. The MIRR assumes that cash inflows are reinvested at the firm's cost of capital and outflows are financed at the firm's financing cost.

MIRR = (Future value of a firm's cash inflow / present value of the firm's cash outflow)^ (1/n)  - 1

n = number of years

present value of the firm's cash outflow = $12,000

Future value of a firm's cash inflow

Future value of year 1's cash flow = $2,360 x (1.12^4) = $3,713.51

Future value of year 2's cash flow =$4,390 x (1.12^3) = $6167.63

Future value of year 3's cash flow =$1,520  x (1.12^2) = $1906.69

Future value of year 4's cash flow = $980 X 1.12 = 1097.60

Future value of year 5's cash flow = 1250

Add the future values together = $14,135.43

($14,135.43 / $12,000)^0.2 - 1 = 3.33%

The project should be rejected because the IRR is negative.  

To find the IRR using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the IRR button and then press the compute button.