Express the quotient in simplest form

Answer:

See below.

Step-by-step explanation:

4x + 3y = -24

We convert to slope/intercept form ( y = mx + b):

3y = - 4x - 24

Divide through by 3:

y = (-4/3)x - 8

Comparing this with y = mx + b:

we see that b ( the y-intercept) is -8.

To find the x -intercept solve (-4/3)x - 8 = 0

(-4/3)x = 8

Multiplying through by -3/4:

x = 8 * -3/4 = -6 = x-intercept.

To draw the graph  draw a line through the points (-6,0) and (0, -8).

Answer:

  -3/4 y-6

Step-by-step explanation:

Answer:

[tex]\boxed{320}[/tex]

Step-by-step explanation:

    Let x = calories in chocolate bar

       ¼x = ¼ of the calories

¼x – 10 = 10 calories less than half the calories

¼x – 10 = 70

       ¼x = 80

          x = 320

There are [tex]\boxed{320}[/tex] calories in the chocolate bar.

Answer:

1st prize

Step-by-step explanation:

Not all people use a car. Some people walk, take a bike, etc. So, if you won free gas for life, you might not be able to use it.

1st prize. To decide between $250,000 in cash or free gas for life, one must analyze projected gas consumption, inflation, and investment opportunities. The cash offers immediate value and investment potential, whereas the value of free gas depends on driving habits and future fuel prices.

Answer:

a = -8

b = -2

Step-by-step explanation:

We have been given the following radical expression;

[tex]\sqrt[3]{x^{10} }[/tex]

The radical can be expressed using the law of exponents;

[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex]

The radical can thus be re-written as;

[tex]\sqrt[3]{x^{10} }=(x^{10})^{\frac{1}{3} }[/tex]

Using the law of exponents;

[tex](a^{b})^{c}=a^{bc}[/tex]

The last expression becomes;

[tex](x^{10})^{\frac{1}{3} }=x^{\frac{10}{3} }=x^{3}*x^{\frac{1}{3} }\\\\=x^{3}\sqrt[3]{x}[/tex]

substituting x with -2 yields;

[tex]-2^{3}\sqrt[3]{-2}=-8\sqrt[3]{-2}[/tex]

The number generator is fair. it picked the approximate percentage of red most of the time.

Answer:

The number generator is fair, It picked the approximate percentage of red s*ckers most of the time.

Step-by-step explanation:

7*3+9*3+8*4 = 80

80 divided by 10 gives you an average of 8 red s*ckers each time which is exactly 80% of the amount of s*ckers picked

(s*ckers is banned for some reason)

Answer:

25%

Step-by-step explanation:

Assuming the catching of a fish is a random process and that the probability of catching any of the listed kinds of fish is proportional to their population, then the probability of catching a sturgeon is 50%. The probability of catching another one is also 50% (assuming the events are independent). So, the joint probability is the product of these:

0.50 × 0.50 = 0.25 = 25% . . . . . probability of catching 2 sturgeon in a row.

The probability of both fish being white sturgeon is 0.25.

To calculate the probability, we need to multiply the probabilities of catching a white sturgeon each time. Since 50% of the fish are white sturgeon, the probability of catching one is 0.5. Therefore, 0.5 multiplied by 0.5 equals 0.25.

Answer:

The answer is confirmed 1.  Just took it.

Step-by-step explanation:

Answer:

Company 1 is greater.

Step-by-step explanation:

Given,

The function that shows the production cost of company 1,

[tex]f(x)=0.15x^2-6x+400[/tex]

Differentiating with respect to x,

We get,

[tex]f'(x)=0.30x-6[/tex]

Again differentiating,

[tex]f''(x)=0.30[/tex]

For minimum or maximum,

f'(x) = 0,

[tex]\implies 0.3x-6=0[/tex]

[tex]\implies x = 20[/tex]

Since, at x = 20, f''(x) = Positive,

So, f(x) is minimum at x = 20,

⇒ Minimum cost in company 1 is,

[tex]f(20)=0.15(20)^2-6(20)+400[/tex]

[tex]=340[/tex]

Also, by the given table,

The minimum cost of company 2 is at x = 70,

g(70) = 55,

Since, 340 > 55,

Hence, Based on the given information, the minimum production cost for company 1 is greater.

Answer:

B

Step-by-step explanation:

If a sinusoidal function is given in the form y = B Sin x or y = B Cos x, then,

B is called the amplitude of the function. It will define minimum and maximum.

The minimum & maximum of this form of a cos function is B and -B.

The function given is y = 7 Cos x, so the Maximum is 7 and Minimum is -7

Correct answer is B.

C seem reasonable to me

Answer:

P = 1/2 = 0.5

Step-by-step explanation:

Total amount of cans = 100

Cans of cola = 34

Cans of orange soda = 50

Cans of ginger ale = 12

Cans of root beer = 4

Probability of selecting

- a can of cola = 34/100 = 0.34

- a can of orange soda = 50/100 = 0.5

- a can of ginger ale = 12/100 = 0.12

- a can of root beer = 4/100 = 0.04

Since we are asked the probability that the can selected is a root beer​, cola, or ginger ale, we need to add together the probabilities of each.

P = 0.04 + 0.34 + 0.12 = 0.5 = 1/2

Answer:

It is easy it is a 2 step equation if you know the 2 four boxes

Step-by-step explanation:

is the variable alone?

No

what is it attached to?

you always do adding or subtracting first so it is attached to 3

How is it attached?

by subtraction

what is the inverse operation?

it is addition

then all you do is the same thing but with multiplication or division

Answer:

Use Substitution.

Plug in 2x-3 in place of y in the second equation.

4x - 3(2x-3) = 31

4x - 6x + 9 =31

            -9     -9

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

-2x=22 so x=-11

Then, y=2(-11)-3, so y=-25

So the solution would be (-11,-25).

Answer:

The required paint for a total of [tex]1.404\ ft^{2}[/tex] is approximate 6 gallons

Step-by-step explanation:

we know that

To find how much paint would I need to buy to paint the walls of all three bedrooms, calculate the area of all three bedrooms

Master Bedroom

The area is equal to

[tex]A1=(16+16+12+2+18)*9=576\ ft^{2}[/tex]

2 Bedroom

The area is equal to

[tex]A2=(12+14+10+10)*9=414\ ft^{2}[/tex]

3 Bedroom

The area is equal to

[tex]A3=(10+10+14+10+2)*9=414\ ft^{2}[/tex]

The total area is equal to

A=A1+A2+A3

[tex]A=576+414+414=1.404\ ft^{2}[/tex]

Approximate one gallon of paint covers 250 square feet

so

[tex]1.404/250=5.6\ gal[/tex]

C. shifted 4 units left and 3 units up

If you compare the graphs (ABCD=Blue; A’B’C’D’=Red), you see that ABCD was moved left 4 and up 3 to become A’B’C’D’.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is A.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

To know the steps that were applied to ABCD to obtain A'B'C'D, we need to observe the coordinates of any one point of the polygon given.

Now, if we look at the coordinates of the points D and D', then it can be observed that point D is shifted 3 units left and 3 units up to form A'B'C'D.

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Answer:

The coordinates of the solution that lies in quadrant IV are (2, -5)

Step-by-step explanation:

We have 2 equations, the first of an ellipse and the second of a circumference.

[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]

To solve the system solve the second equation for x and then substitute in the first equation

[tex]x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y[/tex]

So Substituting in the first equation we have

[tex]x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0[/tex]

Now we must factor the quadratic expression.

We look for two numbers that multiply as a result -5 and add them as result 4.

These numbers are -1 and 5.

Then the factors are

[tex]y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0[/tex]

Therefore the system solutions are:

[tex]y = 1[/tex]; [tex]y = -5[/tex]

In the 4th quadrant the values of x are positive and the values of y are negative.

So we take the negative value of y and substitute it into the system equation to find x

[tex]y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4[/tex]

[tex]x = 2[/tex], and [tex]x= -2[/tex]

In the 4th quadrant the values of x are positive

So we take the positive value of x

the coordinates of the solution that lies in quadrant IV are (2, -5)

Answer:

V=2197

Step-by-step explanation:

Equation for volume of a cube:

V= side length cubed

V=(13)(13)(13)

V=2197

Answer:

V = 2,197 ft3

Step-by-step explanation:

Your welcome ;)

FED is 5/4 times bigger than CBA. So, 44×1.25 is 55. 40×1.25 is 50. The perimeter is 125

Answer:

S =  264π m²

Step-by-step explanation:

Left cone

= π(6)(8)

= 48π m²

Central cylinder

= 2π(6)(14)

= 168π m²

Right cone

π(6)(8)

= 48π m²

Surface area = 48π + 168π + 48π = 264π m²

The surface area of the composite figure is 264π [tex]m^{2}[/tex]

r = 6m

h = 14m

l = 8m

The curved surface area of the cylinder = 2πrh

= 2*[tex]\pi[/tex]*6*14

=168π [tex]m^{2}[/tex]

The curved surface area of the cone = πrl

=π*6*8

=48π [tex]m^{2}[/tex]

The total surface area of the composite figure  

= CSA of cylinder + 2( CSA of cone )

= 168π + 2*48π

=168π + 96π

= 264π [tex]m^{2}[/tex]

Therefore, option S =  264π [tex]m^{2}[/tex]  is the correct answer

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Tan(angle) = opposite leg / adjacent leg.

Tan(64) = x /30

x = 30 * tan(64)

x = 61.51

Answer:

the answer is d 61.51

Step-by-step explanation:

For this case we have to:

[tex]cos (F) = \frac {h} {27}[/tex]

That is, the cosine of the angle F, will be equal to the adjacent leg on the hypotenuse.

So, by clearing h we have:

[tex]h = 27 * cos (54)\\h = 27 * 0.58778525\\h = 15.87020175[/tex]

Rounding out the value of h we have:

[tex]h = 15.9[/tex]

Answer:

Option B

Answer:

The correct answer is option b.   15.9

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Cos θ = adjacent side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of h

It is given that, g=27 and F=54°

Cos F =  adjacent side/Hypotenuse

Cos 54 =  adjacent side/Hypotenuse

     = FG/FH = h/g

h = g * Cos F = 27 * Cos 54 = 27 * 0.5878 = 15.87 ≈ 15.9

Therefore the correct answer is option b.  15.9

Answer:

C2 + a2 +2 = b

Would be the new formula

Answer:

the correct answer is:

a =  √ c^2 − b^2

Step-by-step explanation:

a^2 + b^2 = c^2

Explanation:

a^2 + b^2 = c^2

a^2 = c^2 − b^2

a =  √ c^2 − b^2

The depth of the lake is 1.4 kilometers after converting the result to kilometers.

To find the depth of the lake in kilometers when it is 100 centimeters less than 1401 meters, first convert the depth difference to meters.

Since 100 centimeters is equivalent to 1 meter, the actual depth of the lake in meters is 1400 meters (which is 1401 meters - 1 meter).

To convert this depth into kilometers, we divide by 1000, since there are 1000 meters in one kilometer.

Hence, the depth is 1.4 kilometers.

Answer:

0 Kesha is already home 8+4 is 12 and it's 12 miles from the store to her house .-.

Step-by-step explanation:

Answer:

0 more miles.

Step-by-step explanation:

If 12 miles is the total distance from her house to the store the answer should be 0.  She should be at home because 8 miles on the bike + the 4 walked = 12 miles, which is how many she rode to the store in the first place.

Answer:

13.3 cm

Step-by-step explanation:

Apply the Pythagorean Theorem:

hyp² = (2nd longest side)² + (shortest side)².  Here the numbers are:

(24 cm)² = (20 cm)² + (shortest side)², or

576 - 400 = 176 = hyp²

Taking the square root of both sides, we get (shortest side) = 13.3 cm

Answer: the answer is 13.3

Answer:

The same number was not added to both sides.

Step-by-step explanation:

The same number was not added to both sides.

In line 2,  6 was added to the left side  and 78 was added to the right side.

The best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved as shown below.

t - 6 = 78

t - 6 + 6 = 78 + 6

t = 84

Now, if we compare it with the given equation, we can find that the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

Hence, the best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

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Answer:

by 5

Step-by-step explanation: because tgey wou;d nred help

Answer:

C.) If events A and B are DEPENDENT, then A's occurrence can affect the probability of B's occurrence. For example, when two cards are chosen from a deck without replacement, the possibilities change for the second card.

Check the picture below.

Answer:

Step-by-step explanation:

55

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]

ANSWER

B.) 72

EXPLANATION

Recall the expansion for the factorial notation:

[tex]n! = n \times (n - 1) \times (n - 2) \times ...3 \times 2 \times 1[/tex]

We want to simplify

[tex] \frac{9!}{7!} [/tex]

Let us expand the numerator up to 7! while maintaining the denominator.

[tex] \implies \: \frac{9 \times 8 \times 7!}{7!} [/tex]

When we cancel out the common factors,we obtain:

[tex]\implies \: \frac{9 \times 8 \times 1}{1} [/tex]

This simplifies to

[tex]\implies \: \frac{72}{1} = 72[/tex]

The correct answer is B.

False.

Replace x with -2 and simplify. 5(-2) + 3 = 13

Multiply. -10 + 3 = 13

Add. -7 = 13

This is not true, so -2 is not a solution, therefore the answer to the question is false.

Answer:

Tangent is positive in Quadrant III.

Step-by-step explanation:

All trigonometric functions are positive in QUADRANT I

The Sine function is positive in QUADRANT II

The Tangent function is positive in QUADRANT III

The Cosine function is positive IN QUADRANT IV

*ASTC JUST REMEMBER THAT :)*

There are four quadrants in a plane, and the true statement is (b) Tangent is positive in Quadrant III.

There are four quadrants in a coordinate plane, and they have the following properties

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

The above means that the true statement is (b) Tangent is positive in Quadrant III.

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