The quantity a varies jointly with b and c. When b= 7 and c = 3, a = -42. What is the value of k, the constant of variation?

Answer:

14x^2y^2 - 21x^2y + 56xy^2 + 63xy

Step-by-step explanation:

Remark

This is a disguised form of the distributive property. Nothing can be simplified inside the brackets. So the plan is to remove them.

7xy*2xy - 3x*7xy + 8y*7xy + 9*7xy      Combine the terms

14x^2y^2 - 21x^2y + 56xy^2 + 63xy

You cannot symplify anything further. If nothing could be combined before, it cannot be simplified now.

it's a mixed fraction

hope it helps..,!!!

Using proportions, that is, finding 25% of 12 km, it is found that she has already biked 3 km on Tuesday.

A proportion is a fraction of a total amount.

In this problem, she has already biked 25% out of her goal of 12 km, hence the distance that she has biked is given by:

d = 0.25 x 12 = 1/4 x 12 = 3 km.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

Step-by-step explanation:

First Container.

Total = 7 + 2 + 6 = 15

Probility blue = 7 / 15 = 0.467

Second Container

Total = 4 + 2 +2 =  8

Probability Blue = 4/8 = 1/2 = 0.5

Answer: You are much better off drawing from the Second Container.

Answer:

there is no picture attached here I really wish I could help

Answer:

2.5

Step-by-step explanation:

3 hours after 7 is 10 so add 1.9 to 0.6

Answer:

3:6

Step-by-step explanation:

27=3*3*3

216=6*6*6

Therefore the answer is 3:6

then to the lowest term = 1:2

Reason:

Subtract any pair of adjacent terms

Each time we get the same value to confirm that we have an arithmetic sequence of common difference 18.

Answer:

There would be 40 dogs in the shelter.

Explanation:

4 rooms times 10 dogs in each room = 40 dogs total

Answer:

40!

Step-by-step explanation:

is this logical question?

Answer:

Step-by-step explanation:

We can calculate probability by looking at the outcomes of an experiment or by reasoning about the possible outcomes.

An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The factors of the expression by grouping can be done as,

[tex]4x^3+x^2-8x-2[/tex]

Take x² as the common factor from the first two terms while -2 from the last two terms,

[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]

Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

Learn more about Expression:

https://brainly.com/question/13947055

Explanation:

We have y = -0.9x^2 + 76x - 250 which is in the form y = ax^2+bx+c

where,

The vertex (h,k) is when the profit is maxed out.

h = -b/(2a)

h = -76/(2(-0.9))

h = 42.222 approximately

Let's plug in x values around x = 42

Try x = 41

y = -0.9x^2 + 76x - 250

y = -0.9(41)^2 + 76(41) - 250

y = 1353.10

Now try x = 42

y = -0.9x^2 + 76x - 250

y = -0.9(42)^2 + 76(42) - 250

y = 1354.4

Now try x = 43

y = -0.9x^2 + 76x - 250

y = -0.9(43)^2 + 76(43) - 250

y = 1353.9

We see that the largest profit happens when x = 42.

Answers:

Final velocity = 29 m/s

Distance traveled = 73.5 meters

========================================================

Work Shown:

The given data is

[tex]v_i = 20 \text{ m}/\text{s} = \text{initial velocity}\\\\a = 3 \text{ m}/\text{s}^2 = \text{acceleration}\\\\t = 3 \text{ s} = \text{time duration}\\\\[/tex]

This leads to

[tex]v_f = v_i + a*t\\\\v_f = 20 + 3*3\\\\v_f = 20 + 9\\\\v_f = 29\\\\[/tex]

The final velocity is 29 m/s.

----------

We can use that final velocity to find the distance traveled.

[tex]x = 0.5*(v_i+v_f)*t\\\\x = 0.5*(20+29)*3\\\\x = 0.5*(49)*3\\\\x = 24.5*3\\\\x = 73.5\\\\[/tex]

The distance traveled is 73.5 meters.

----------

An alternative way to calculate the distance is to do this

[tex]x = \frac{(v_f)^2 - (v_i)^2}{2a}\\\\x = \frac{(29)^2 - (20)^2}{2*3}\\\\x = \frac{841 - 400}{6}\\\\x = \frac{441}{6}\\\\x = 73.5\\\\[/tex]

Or you could do this

[tex]x = v_i*t + 0.5*a*t^2\\\\x = 20*3 + 0.5*3*3^2\\\\x = 20*3 + 0.5*3*9\\\\x = 60 + 13.5\\\\x = 73.5\\\\[/tex]

For more information, check out the Kinematics equations.

Answer:

139 ft³

Step-by-step explanation:

Diameter of the cylinder is 3 ft. Therefore, the radius is 1.5 ft

Volume of the cylinder = πr²h

= 3 × 1.5 × 1.5 × 4

= 27 ft³

Volume of the cuboid (rectangular prism) = lbh

= 7×4×4

= 112 ft³

Volume of the figure = 112 + 27 = 139 ft³

Answer:

240

Step-by-step explanation:

V = L x W x H

L= 3

W= 10

H= 8

V = 3 x 10 x 8

= 240 cubic meters

Answer:

240

Step-by-step explanation:

All you have to do is multiply all of these numbers to get the answer.

Answer:

Hope the picture will help you.......

Answer:

200

Step-by-step explanation:

The amount you need to increase your monthly net savings by is C. $200.

Amount to save next year

= Goal - Current savings

= 4,500 - 900

= $3,600

Monthly savings amount

= 3,600 / 12

= $300 per month

Amount to increase savings by

You care already saving $100 so you need to increase by:

= 300 - 100

= $200

Answer:

200

Step-by-step explanation:

Edge 2022

The rational expression for the ratio between the perimeter and the area is:

R = 4/3x

We want to find the ratio, as a rational expression, between the perimeter and the area.

Remember that for a square of sidelength S, the perimeter is:

P = 4*S

And the area is:

A = S^2

Then the ratio between these two is:

R = P/A = (4*S)/(S^2) = 4/S

In this case, the sidelength is 3x, then S = 3x, replacing that we get:

R = 4/3x

If you want to learn more about rational expressions, you can read:

https://brainly.com/question/1851758

Answer: 6217728

Step-by-step explanation: The formula for a Rectangular Prism is (Base/Length)(Width)(Height). (12)(512)(1012).

Answer:

22°

Step-by-step explanation:

The square in the corner indicates that this is a right angle = 90° and the line separates this into two angles, x and 68°

x + 68 = 90

x = 22°

Hope this helps!

Check the picture below.

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{9}}{\underset{hypotenuse}{15}}~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{15}}~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{9}}{\underset{adjacent}{12}} \\\\\\ cot(\theta )=\cfrac{\stackrel{adjacent}{12}}{\underset{opposite}{9}}~\hfill sec(\theta )=\cfrac{\stackrel{hypotenuse}{15}}{\underset{adjacent}{12}}~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{15}}{\underset{opposite}{9}}[/tex]

Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:

2/3 cups - 1/2 batch

x cups - 1 batch.

Applying cross multiplication:

[tex]\frac{1}{2}x = \frac{2}{3}[/tex]

[tex]x = \frac{4}{3}[/tex]

The unit rate is of 1.33 cups of brown sugar for a batch of cookies.

More can be learned about proportions at https://brainly.com/question/24372153

$4.76 per card

hope it helps...!!!

Answer:

(-2,1)

Step-by-step explanation:

1 unit up will change the y-value as it is moving vertically. Will make it (-2,-1)

Then, reflecting over x-axis means x-value stays the same and the sign of y-value switches.

so,

(-2,1)

a = 12, b = 3*sqrt(17)

========================================================

Work Shown:

3/a = a/48

3*48 = a^2

a^2 = 144

a = sqrt(144)

a = 12

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

a^2 + 3^2 = b^2 ... pythagorean theorem

12^2 + 3^2 = b^2

144 + 9 = b^2

b^2 = 153

b = sqrt(153)

b = sqrt(9*17)

b = sqrt(9)*sqrt(17)

b = 3*sqrt(17)

Answer:

Side = 3 cm

Step-by-step explanation:

Given:

[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]

The formula to calculate the volume is (Side)³.

Thus, we obtained the following equation:

[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]

Cube root both sides to obtain the side length of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

Evaluate the side of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]

[tex]\implies \text{Side = 3 cm}[/tex]

Answer:

3 cm

Step-by-step explanation:

Formula

Volume of a cube = [tex]a^3[/tex]  (where a is the side length)

Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:

[tex]\implies 27\: \sf cm^3=a^3[/tex]

Cube root both sides:

[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies 3\: \sf cm=a[/tex]

[tex]\implies a=3\: \sf cm[/tex]

Therefore, the length of each side of the cube is 3 cm.