A grandsons age in years is equal to his grandfather's age in years. The difference of the grandsons age in years and the grandfather's age in years is 77. Find the grandsons age in years.

3x + 2y=-10 equation 1

y=-x -4 equation 2

use the substitution method of elimination to get the answer to the question.

*using substitution

substitute equation 2 in one and we get

3x +2(-x-4)=-10

3x- 2x-8=-10

x=-2 and y=-2

Answer:

B

Answer:  Choice A

(-2, -2)

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Explanation:

I'll use the substitution method to solve this system.

Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.

So,

3x + 2y = -10

3x + 2( y ) = -10

3x + 2( -x-4 ) = -10 .... substitution

3x - 2x - 8 = -10

x - 8 = -10

x = -10+8

x = -2

Then use this to find y

y = -x-4

y = -(x) - 4

y = -(-2) - 4

y = 2 - 4

y = -2

We have x = -2 and y = -2 pair up together

They form the ordered pair solution (x, y) = (-2, -2)

This shows why Choice A is the answer.

Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.

See below.

The two lines intersect at (-2, -2) which is the solution.

Answer:

Down below

Step-by-step explanation:

150 - (2 + x)^3

150 - (2 + 2)^3

150 - (4)^3

150 - 64

= 86

I would check my math but I believe this is correct.

Answer:

86

150-(2+x)^3

⇒ x = 2

2 + 2 = 4

4^3(4 • 4 • 4) = 64

150 - 64 = 86

Answer: 996 free ride passes were given away

Step-by-step explanation:

If each child was given 3 free ride passes, then you have to do 332 x 3 which is 996

Answer

whats the question

Step-by-step explanation:

The answer is:

(-2/9, 35/9) in rounded decimal form is (-0.22, 3.89)

x = - 2 / 9 which in decimal form as well as rounded is -0.22

y = 35 / 9 which in decimal form as well as rounded is 3.89

Hope this helps...

The number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Rita wants to save her babysitting money to buy a $249.99 camera. she makes $64.33 a month, and her fixed expenses are $34.50 a month.

Let x be the number of months in which Rita has a budget to buy a camera.

The linear equation in one variable can be framed as follows:

(64.33 - 34.50)x = 249.99

29.83x = 249.99

x = 8.38 = 8.5

Thus, the number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.

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Answer:

6000 pounds or lbs.

Step-by-step explanation:

A ton=2000 lbs.

Hope this helps! ;-)

Answer:

(x-6)^2+(y-5)^2=16

Step-by-step explanation:

Focus on the center point ONLY and change the signs of those numbers to negative for your equation. Count how much the outer circle moves back (which is 4) and times that as your radius

Answer:

22 pounds of watermelon

Step-by-step explanation:

First find cost per pound
19.60/8=2.45
$2.45 per pound
Then divide $53.90 by $2.45 to determine how many pounds you can buy
53.90/2.45=22
22 pounds of watermelon

Answer:

4

Step-by-step explanation:

Mean is another way to say the average of a set of numbers. To find the average you need to add all the numbers in the set together, and then divide by the amount of numbers that where given.

In this case:

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

there are 7 numbers given in the set, so you divide 28 by 7 to get your mean.

28 / 7 = 4

Answer:

4

Step-by-step explanation:

To find the mean of a set of numbers, you add up all the numbers and then divide them by the amount of numbers there are.

So, let's add up these numbers.

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

Now, there are a total of 7 numbers, so we divide 28 by 7.

28 / 7 = 4

Therefore, the mean of this data set is 4. I hope this helps! Have a lovely day!!

Answer:

b because it is

Step-by-step explanation:

153.2 is a cool number

ANWER:

rounded o the nearesr tens is 88.6

Answer:

88

Step-by-step explanation:

Because 6 is greater than 5 it will rounded off and 87.6 = 88

Answer: The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

(f ∘ f)(–1) = –1

Step-by-step explanation:

To solve a composite function, rewrite using brackets and solve from inside to outside.

(f ∘ f)(x) is the same as:    f[f(x)]

Given that x = –1 in (f ∘ f)(–1), we are solving for:

f[f(–1)] = ?

Solve for f(–1) inside the square brackets first.

f(x) = x³

f(–1) = (–1)³    Simplify.

f(–1) = –1       Solved the inside.

Substitute f(–1) = –1 into the square brackets.

f[f(–1)] = f[–1]

Now, we can solve the outside.

Solve with the equation of the function, x³.

f[–1] = x³

f[–1] = [–1]³     Substitute x = –1.

f[–1] = (–1)³     Simplify.

f[–1] = –1        Final answer

The two inequalities will be L>W-4 and (L x W) ≤ 32.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

It is given that:-

The length of the garden should be at least 4 ft shorter than the width

The distance around should be no more than 32 ft

The two inequalities will be as follows:-

a)The length of the garden should be at least 4 ft shorter than the width

L>W-4

b)The distance around should be no more than 32 ft

(L x W) ≤ 32.

Hence the two inequalities will be L>W-4 and (L x W) ≤ 32.

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If 10 donuts are sold. Then the expected value of the number of sprinkles will be 5.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be given as

E(X) = np

At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data.

If 10 donuts are sold.

Then the number of the sprinkles will be

The probability will be

p = 3/6

p = 0.5

n = 10

Then the expected value of the number of the sprinkles will be

E(x) = 10 x 0.5

E(x) = 5

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Answer:

12

Step-by-step explanation:

7 times 12 is 84. 4 times 21 is 84. The digits have a sum of 3.

Answer:

/TS/=12cm

/QP/=

/QR/²=16²+12²

/QR/²=256+144

/QR/²=400

/QR/=√400

/QR/=20

/QP/=20/2=10

let /PT/ be x

hyp²=opp²+adj²

16²=20²+x²

x²=400-256

x²=144

x=√144

x=12.

Answer:

here is the required answer hope it help u

Step-by-step explanation:

−2(−5n+6)+5(2−7n)

10n-12+10-35n

-25n-2

Answer:

x=3, Aly is correct.

Step-by-step explanation:

a. angle YWZ

b. ZY = 9

c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3

Answer:

x = 10.9 cm

Step-by-step explanation:

Formula for a cone

Here, we are given :

Solving

Answer:

x ≈ 3.6 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = πr²h ( r is the radius and h the perpendicular height )

here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then

π × 3.5² × x = 140

π × 12.25x = 140 ( divide both sides by 12.25π )

x = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )

Answer:

Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .

1x − 2+1x + 2=4(x − 2)(x + 2)

(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)

(x−2)+(x+2)=4

2x=4

x=2

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed!  .  Therefore, it cannot be a root of the original equation.  So, 2 is an extraneous solution. So, the equation has no solutions.

Step-by-step explanation:

An equal when substitute x = 4, the solution is not extraneous the solution x = 4 is valid for the original equation.

The equation is: √(2x - 7) = 1

Step 1: Square both sides of the equation to remove the square root:

(√(2x - 7))² = 1²

Simplify:

2x - 7 = 1

Step 2: Add 7 to both sides to isolate the term with "x":

2x - 7 + 7 = 1 + 7

Simplify:

2x = 8

Step 3: Divide both sides by 2 to solve for x:

2x / 2 = 8 / 2

Simplify:

x = 4

Now, we have found that the solution for x is 4.

To check if the solution is extraneous, we need to substitute the value of x back into the original equation and see if both sides are still equal:

Original equation: √(2x - 7) = 1

Substitute x = 4:

√(2(4) - 7) = 1

Simplify:

√(8 - 7) = 1

√1 = 1

1 = 1

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Step-by-step explanation:

1 min 4 cals

60 cals how many mins?

1min. 60cals

____. × _______ = 15 mins

4cals. ?mins

we simplify the matter by simplifying 60 with 4 and striking out cals... then we will have 15 on the top right and then we multiply 1 and 15 together at the end we add the mark of the answer which is (min).

Answer:

  200 miles

Step-by-step explanation:

Each inch represents 50 miles, so 4 times 1 inch will represent 4 times 50 miles.

  4(1 in) ⇔ 4(50 mi)

  4 in ⇔ 200 mi

It is about 200 miles from Chelsea to New York City according to the map.

The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

5⁻³ = 1/5³ = 1/125

-5⁻³ = -1/5³ = -1/125

(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125

(-5⁻³)⁰ = 1   [tex]\rm (a^0 = 1)[/tex]

Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

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Answer:

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

Step-by-step explanation:

Exponent Property Rules:

⟹ Zero Exponent Property - ex: x⁰ = 1

An integer (excluding 0) with an exponent of zero equals one.

⟹ Negative Exponent Property - ex: x⁻ⁿ = [tex]{\dfrac{1}{x^n}[/tex]

Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.

⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ

To find the power of a product, multiply the power of each factor.

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

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Answer:

The rule is "add 5, add 10, add 20" and the rule keeps doubling.

Answer:

2.25 square inches

Step-by-step explanation:

SOLUTION,

HERE,

AREA OF SQUARE = L²

=(1.5)²

= 2.25 INCHES²

Answer:

2.25 inches

Step-by-step explanation:

The area of a square is two of its sides multiplied together. Each side is 1.5 inches. If you multiply 1.5x1.5, you get 2.25 inches.