The sum of two integers is 2. Their difference is 10.
What are the two integers?

-14 and -4
4 and 14
-2 and 4
-4 and 6

Answer:

○ A) 21 ft.²

Step-by-step explanation:

[tex] {a}^{2} + 2a \sqrt{ \frac{ {a}^{2}}{4} + {h}^{2} } = S. A. \\ \\ {3}^{2} + 2(3) \sqrt{ \frac{ {3}^{2} }{4} + {2}^{2}} = 24 \\ \\ 24 ≈ 21[/tex]

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Answer:

672,800

Step-by-step explanation:

672,800 672800

Answer:

The simplified form of \((2+1)\cdot 3\div 3^{2}\).

Answer:

The answer would be 'D'.

Step-by-step explanation:

An expression does NOT have an equal sign while a formula does. A variable is some letter symbol that you are solving for, but a constant would be a number such as 2 or 4 that could be added, multiplied, subtracted, or divided in an equation. 

I hope this helps!

Answer:

Step-by-step explanation:

a formula

Answer:

The given equation not represent a proportional relationship

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

[tex]y=\frac{2}{5}x-4[/tex]

This line not passes through the origin

Verify

For x=0

[tex]y=\frac{2}{5}(0)-4=-4[/tex]

therefore

The given equation not represent a proportional relationship

Answer:

The value of x is [tex](+/-)\sqrt{6}[/tex]

Step-by-step explanation:

The question in English is

Find the value of x so that the distance between the given points is 2V5 units.

(2x - 1,2) and (1 + x,x + 4)

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(x+4-2)^{2}+(1+x-2x+1)^{2}}[/tex]

[tex]d=\sqrt{(x+2)^{2}+(-x+2)^{2}}[/tex]

[tex]d=\sqrt{x^2+4x+4+x^2-4x+4}[/tex]

[tex]d=\sqrt{2x^2+8}[/tex]

Remember that

[tex]d=2\sqrt{5}\ units[/tex]

substitute

[tex]2\sqrt{5}=\sqrt{2x^2+8}[/tex]

squared both sides

[tex]20=2x^2+8\\\\2x^{2}=12\\\\x^{2}=6\\\\x=(+/-)\sqrt{6}[/tex]

therefore

The value of x is [tex](+/-)\sqrt{6}[/tex]

Answer:

y = (8/5)x + 15

Step-by-step explanation:

First change the equation to standard form (y=mx+b)

5x + 8y = 16

8y = 16 - 5x

y = - (5/8)x + (16/8)

y = - (5/8)x + 2

Perpendicular Lines have the inverse opposite sign of slope

[For example: inverse opposite sign of 2 is - (1/2)]

Original equation slope (m) : - (5/8)

2nd Equation (m) : 8/5

After finding the slope, plug in the slope and points the standard form equation (y=mx+b)

Point: (-5,7)     x : -5     y : 7

Slope (m) : 8/5

y = m x + b

7 = (8/5) (-5) + b

'b' is the y-intercept and the last thing to solve for the equation

7 = - 8 + b

15 = b

Now, put the slope (m) and y-intercept (b) back into the equation

y = (8/5)x + 15

Step-by-step explanation:

(3 × 10) × 8 = 3 × (10 × 8)

It's an Associative Property of addition:

(a + b) + c = a + (b + c)

Check it:

Left side: (3 × 10) × 8 = 30 × 8 = 240

Right side: 3 × (10 × 8) = 3 × 80 = 240

CORRECT

Answer:

29/1000

Step-by-step explanation:

Answer:

29/1,000

Step-by-step explanation: it says thousands so u put thousand at the bottom then you put 29 on top

The translation rule is T

Answer:3^2

Step-by-step explanation:

Find prime numbers that go into nine.

3 goes into to 9 3 times. 3 is a prime number so the prime factorization for nine is

3*3=3^2

The Prime factorization of 9 is expressed as: 3 * 3 or 3²

A prime factor is defined as a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Now we can also use what's called prime factorization for numbers which actually consist of using factor trees.

Now, some of the factors of 9 are 1, 3, 9. Thus:

Prime factorization of 9 = 3 * 3 = 3²

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The answer is 101/1000

Happy to help

Answer: The GCF of 12 and 360 is 12

Answer:

no

Step-by-step explanation:

a natural number has to be a whole number

Answer:

6

Step-by-step explanation:

i know for sure

if you want to know... well then ok

draw a diagram and put 12 and 30 on the outsides of each box than factor 12 and 30 put the numbers that they both have on each side in the middle circle and the rest on the big circles. Then multiply the numbers in the middle you get dun.. dun... dun...

6

Answer:

B. 54π yd^2

Step-by-step explanation:

On god it is right trust mee!    

Answer: Our required area is 54π sq. yd.

Step-by-step explanation:

Since we have given that

Diameter of an ice skating = 44 feet

Radius of an ice skating = 22 feet

as we know the formula for area :

Area would be

[tex]\pi r^2\\\\=\pi \times 22^2\\\\=484\pi\ ft^2[/tex]

As we know that

9 sq ft = 1 sq yd

So, it becomes,

[tex]\dfrac{484\pi}{9}=53.77\pi\ yd^2\approx 54\pi\ yd^2[/tex]

Hence, our required area is 54π sq. yd.

Answer:

(4, 0 )

Step-by-step explanation:

A translation of 1 unit left, subtract 1 from the original x- coordinate

A translation of 2 units down, subtract 2 from the original y- coordinate

The rule is (x, y ) → (x - 1, y - 2 ), thus

(5, 2 ) → (5 - 1, 2 - 2 ) → (4, 0 )

The image point of (5,2) after a translation left 1 unit and down 2 units is (4, 0).

To find the image point of (5,2) after a translation left 1 unit and down 2 units, we need to subtract 1 from the x-coordinate and subtract 2 from the y-coordinate.

The translated image point would be (5-1, 2-2) = (4, 0).

So, the image point of (5,2) after the translation left 1 unit and down 2 units is (4, 0).

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Answer:

If you solved this, it wouldn't have a remainder. First you would solve the numbers in the parenthesis, (15 - 3), which is 12. Now it should look like, 12 ÷ 12 + 1. Next you divide 12 by 12 and that equals 1. And all you need to do now is add 1 + 1, which is 2. So your answer will be 2.

Answer:

2

Step-by-step explanation:

To be able to solve this equation, you would use PEMDAS. This stands for the order of operations, and which order you would do them in.  P stands for parenthesis, E stands for exponents, M stands for multiplication, D stands for division, A stands for addition, and S stands for subtraction. Using this order, you would solve what is inside the parentheses first. So, 15-3 is 12. Once this piece is solved, you would have 12÷12+1. Then, since you don't have any exponents or multiplication, you would skip to division. 12 ÷ 12 is 1. So then your equation would be: 1+1. 1+1 is equal to 2. So your answer is 2! There is not remainder in the solution of this problem.

Answer:

If x-2 is a factor of p(x) = x^{4} - 3 x^{2} + 2 x - 8 ,then p(x)  = 0

Solution:

According to factor theorem of polynomials,  

x-a is a factor of polynomial p(x), if and only p(a)=0

Step 1:

Since x-2 is factor of p(x),

x - 2 = 0

x = 2

Step 2:

[tex]p(x) = x^{4} - 3 x^{2} + 2 x - 8 ------ (equation 1)[/tex]

By substituting x = 2 in equation 1,

[tex]p(x) = 2^{4} - 3(2)^{2} + 2(2) - 8[/tex]

p(x) = 16 - 3(4 ) + 4 -8

p(x) = 16 - 12 - 4

p(x) = 16 - 16

p(x) = 0

Since x - 2 is a factor of p(x)  , we get p(x)=0

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

2x-3+4x=21

2x+4x=21+3

6x=24

x=4

Answer:

13

Step-by-step explanation:

If Chad had 7 sandwiches and that was 6 fewer than the amount Sarah has then Sarah made 6 sandwiches. The working is as follows :

Chad = 7 sandwiches (6 fewer than Sarah)

Sarah = ?

Sarah = 7 + 6 = 13 sandwiches.

In order for Chad to have eaten that many sandwiches, Sarah would have had to have made 13 sandwiches.

Sarah made x number of sandwiches and Chad ate 7 out of it.

The 7 that Chad ate remained 6 sandwiches out of the total that Sarah made.

The number of sandwiches Sarah made is therefore:

= Number that Chad ate + Number that was left

= 7 + 6

= 13 sandwiches

In conclusion, Sarah made 13 sandwiches

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Answer:

n=68

Step by step explanation:

When a number n is increased by two means n+2 so we can put parenthesis around it

(n+2)/5 = 14  

now we solve for the equation (for the variable n)

First multiply both sides by 5 to isolate the parenthesis on the left side by itself

(n+2) = 14*5

then we can simply isolate n by itself by subtracting both sides by 2

n = 70 -2 = 68

n = 68

To find the value of n when [tex]\frac{(n + 2) }{5}[/tex]  = 14,  resulting in n = 68.

The question asks to define an equation based on a described operation with a given result, and then solve it to find the value of n. The operation described is increasing a number n by two, then dividing the result by five to get a quotient of 14.

To translate this into an equation, you would set up the following equation:

[tex]\frac{(n + 2) }{5}[/tex] = 14

To find the value of n, you would first multiply both sides by 5 to isolate n on one side:

n + 2 = 70

Then, subtract 2 from both sides to solve for n:

n = 68

Therefore, the value of n is 68. This solves the equation and provides the value that n must be for the operation to result in a quotient of 14.

Answer:

[tex]5811 \frac{1}{1} [/tex]

Step-by-step explanation:

You could do this.

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Answer:

Thus, to make 4 pecan pies one need to buy approximately 1.3 pounds of pecan.        

Step-by-step explanation:

We are given the following information in the question:

Number of pecan pies to be made = 4

Pecan required to make 1 pie = [tex]1\frac{1}{2} \text{ cups}[/tex]

Pecan required to make 4 cups =

[tex]4\times 1\frac{1}{2} = 4\times \frac{3}{2} = 6\text{ cups}[/tex]

Now, 1 bag of pecan has a serving size of 1 cup . Hence, we need to buy 6 such bag.

Now, weight of one bag = 99 grams

Weight for 6 cups of pecan = [tex]6\times 99 = 594\text{ grams}[/tex]

We know that:

1 gram = 0.00220462 Pounds

594 grams of pecans = [tex]594\times 0.00220462 =1.30954428 \text{ pounds of Pecan}[/tex]

Thus, to make 4 pecan pies one need to buy approximately 1.3 pounds of pecan.

To solve this problem, first determine the information you need to answer. As we need to make 4 pecans of the pies, take the values for the one piece and multiply it with four.

To make 4 pecans pies one will required to by 1.30 pounds of pecan.

Given information:

Number of pecan pies to be made is 4

The pecan needed to make 1 pie is [tex]1.5[/tex]  cups.

Now, Pecan required to make 4 cups will be:

[tex]4 \times 1.5 = 6[/tex] cups.

As, 1 bag of pecan has a serving size of 1 cup

Hence, we need 6 such bags.

Now, weight of the bag is 99 grams

so,

weight of 6 such bags will be

[tex]=6\times 99\\=594 \;\text{gm}[/tex]

And we have

[tex]1 \; \text{gm}=0.00220462 \; \text{pound}[/tex]

So,

594 grams of pecans = [tex]594\times 0.00220462[/tex]

[tex]=1.3095 \;\text{pounds}[/tex]

Hence, to make 4 pecans pies one will required to by 1.30 pounds of pecan.

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Answer: The smaller number is 30, the larger is 38

Step-by-step explanation:

x + (x - 8) = 68

2x - 8 = 68

2x = 60

x = 30

Answer:

B. +29 + +18

Step-by-step explanation:

+18- -29 what you do is you make the minus signs addition because when you are subtracting a negative it becomes a positive.

+29 + +18 is your answer.

Your answer will be option B "+29 + +18." Equivalent means the same amount and according to the rules of KCC (Keep Change Change) +18 - -29 will convert into +18 + +29 which would equal 47 which is equivalent to option B.

[tex]+18 -29[/tex]

[tex]KCC=18+29[/tex]

[tex]18+29=47[/tex]

Option A -18 + 18 = 0

Option B +29 + +18 = 47

Option C -18 - +29 = -18 + -29 = -47

Option D -29 - -18 = -29 + 18 = -11

Therefore your answer is option B.

Hope this helps.

Answer:

Step-by-step explanation:

[tex]\dfrac{y}{x}=a\to y=ax\\\\\text{We have}\ x=1,\ y=0.5.\\\\\text{Substitute:}\\\\a=\dfrac{0.5}{1}=0.5\\\\\text{Therefore}\ y=0.5x[/tex]

Answer:

y = 0.5x

Step-by-step explanation:

x = 1; y = 0.5; 0,5 is [tex]\frac{1}{2}[/tex] of 1

1 * 0.5 would equal 0.5

So, y = 0.5x

Hope this helps :)

Answer:

1) The question is aimed to determine the number that Laura is trying to come up with.

Such question is solved by stating an algebraic equation from the word statement, which is done step by step.

2) Using the name x for the unknown, the expression "three less than 8 times the number" is translated to: 8x - 3

3) The expression "half of 16 times the number after it was increased by 1" is translated to: (1/2) (16x + 1)

4) Finally, since they are equal, you can set the equation:

8x - 3 =  (1/2) (16x + 1)

5) And solve for x in this way:

i) Distributive property:

8x - 3 = 8x + 1/2

ii) At this stage you can see that the both 8x terms (on the left and on the right) cancel each other, which leads to the impossibility to determine the value of the unknown:

-3 = 1/2 which is alwasy false, meaning that the equation has no solution.

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Step-by-step explanation:

hope it help

Laura can’t find a number that works because the equation is inconsistent and has no solution.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "Three less than eight times the number is equal to half of 16 times the number after it was increased by one," we can logically deduce the following algebraic equation;

8n - 3 = 1/2 × (16n + 1)

16n - 6 = 16n + 1

16n - 16n = 1 + 6

0 = 7 (False).

Therefore, this equation has no solution because the coefficients are the same on both sides.

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Complete Question;

Laura is now trying to come up with a number where three less than eight times the number is equal to half of 16 times the number after it was increased by one. She can’t seem to find a number that works explain why

Answer:

The number 24 is called the dividend ('that which is to be divided'). The number 8 is called the divisor ('that which divides'). The number 3 is called the quotient, (from the Latin quotiens meaning 'how many times'). Division without remainder can be visualized as skip-counting.

Answer:

4(a-2)+a=4a-2 No solution

Step-by-step explanation:

This  would never be true. Try plugging in a as 1.

4(1-2)+1 isn't equal to 4(1)-2.