Write an equation for each sentence and then solve.
The sum of two numbers is seventy-two. One of the numbers
is two times the other. What are the numbers?

Answer:

10 remainder 0

Step-by-step explanation:

60/8 = 7.5

6/6 = 10 remainder 0

8 - (3 + b) = b - 9

Opening the brackets changes the symbol to it's opposite symbol, which gives us

8 - 3 - b = b - 9

By using the transposition method, we get

8 - 3 + 9 = b + b

or, 14 = 2b

or, 14/2 = b

or, 7 = b

The value of b is 7.

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

For what values of x is the equation x² − x = 20 true?

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex] \sf \: x ^ { 2 } - x = 20[/tex]

Subtract 20 from both sides.

[tex] \sf \: x^{2}-x-20=0 [/tex]

To solve the equation, factor [tex]\sf\: x^{2}-x-20[/tex] using formula [tex]\sf\:x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)[/tex]. To find a and b, set up a system to be solved.

[tex] \sf \: a+b=-1 \\ \sf \: ab=-20 [/tex]

As ab is negative, a and b have the opposite signs. As a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -20.

[tex] \sf1,-20 \\ \sf 2,-10 \\ \sf4,-5 [/tex]

Calculate the sum for each pair.

[tex] \sf1-20=-19 \\ \sf2-10=-8 \\ \sf 4-5=-1 [/tex]

The solution is the pair that gives sum -1.

[tex] \sf \: a=-5 \\ \sf \: b=4 [/tex]

Rewrite factored expression [tex]\sf \left(x+a\right)\left(x+b\right) [/tex] using the obtained values.

[tex] \sf\left(x-5\right)\left(x+4\right) [/tex]

To find equation's solutions, solve x-5=0 and x+4=0.

[tex] \bf \: x=5 \\ \bf x=-4[/tex]

⇨ The values of x are 5 & - 4.

Complete the solution of the equation. find the value of y when x = -14.

To find the value of y we need to plug and substitute the equation if x = -14.

Answer:

C=78

D=102

Step-by-step explanation:

co-interior angles are sepplementary

Answer:

1) 6n+9

2) -309

Step-by-step explanation:

Let say 2n+1,2n+3,2n+5 the three consecutive odd numbers (n in Z)

1) sum= (2n+1)+(2n+3)+(2n+5=6n+9

2) 2n+5=-101

2n=-106

n=-53

S=6n+9=6*(-53)+9=-309

Answer: the answer is in the screenshot

Step-by-step explanation:

The hypotenuse of each set of legs of a right triangle are:

1. 5 and 6 => √61

2. 4 and 1 => √17

3. 2 and 5 => √29

4. 9 and 12 => 15

In a right triangle, the hypotenuse is the longest side that is opposite to the right angle. The hypotenuse can be determined by finding the square root of the sum of the other two legs.

1. √(5² + 6²) = √61

2. √(4² + 1²) = √17

3. √(2² + 5²) = √29

4. √(9² + 12²) = 15

Learn more about the hypotenuse on:

https://brainly.com/question/2217700

Answer:

18 / 19

Step-by-step explanation:

Divide it by 2

Answer:

280cm^2

Step-by-step explanation:

[tex]area \: of \: rhombus = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 35cm \times 16m \\ = 280 {cm}^{2} [/tex]

Answer:

280

Step-by-step explanation:

→ State the rhombus formula

( p × q ) ÷ 2

→ Substitute in the values

( 35 × 16 ) ÷ 2

→ Simplify

280

If U = {1, 2, 3, …, 12} is the universal set, and

A = {1, 2, 6, 10}

B = {3, 6, 9, 10, 11}

C = {1, 2, 4, 7, 11}

then

(1) A U B is the set containing all elements from A and B,

A U B = {1, 2, 3, 6, 9, 10, 11}

(2) A ∩ B is the set of elements that are contained in both A and B,

A ∩ B = {6, 10}

(3) Unfortunately, A ∩ B U C is somewhat ambiguous. It could mean (A ∩ B) U C or A ∩ (B U C ). Then either

(A ∩ B) U C = {6, 10} U {1, 2, 4, 7, 11} = {1, 2, 4, 6, 7, 10, 11}

or

A ∩ (B U C ) = {1, 2, 6, 10} ∩ {1, 2, 3, 4, 6, 7, 9, 10, 11} = {1, 2, 6, 10}

The first interpretation is probably the intended one, since that essentially reads the set operations from left to right.

(4) A' U B is the union of A' and B, where A' is the complement of A, or all elements in U that are not in A. We have

A' = U - A = {3, 4, 5, 7, 8, 9, 11, 12}

and so

A' U B = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(5) We have

A U C = {1, 2, 4, 6, 7, 10, 11}

so that

(A U C )' = U - (A U C ) = {3, 5, 8, 9, 12}

(6) We have

B' = U - B = {1, 2, 4, 5, 7, 8, 12}

and so

A ∩ B' = {1, 2}

(7) Using the complements found in (4) and (6), we have

A' U B' = {1, 2, 3, 4, 5, 7, 8, 9, 11, 12}

Alternatively, we can use the fact that

A' U B' = (A ∩ B)'

and since we know from (2) that A ∩ B = {6, 10}, we end up with the same result,

(A ∩ B)' = U - (A ∩ B) = {1, 2, 3, 4, 5, 7, 8, 9, 11, 12}

(8) We have

A U B U C = {1, 2, 3, 4, 6, 7, 9, 10, 11}

so that

(A U B U C )' = {5, 8, 12}

Explanation:

There's a 9 in the thousandths place. The next digit to the right is 1, which is not 5 or more. So we'll just drop that 1 and that's why the answer is 3.569

Answer:

3.569

Step-by-step explanation:

Rounding is the process of shortening a number to a certain number of digits by finding the closest number with the desired number of digits. When rounding, look one digit to the right of the desired decimal place. In this case, you want the thousandths place. The thousandths place is 3 digits after the decimal, so look at the number next to the 9, the 1. If the number is 5 or greater round up, if it is 4 or less round down. Therefore, 3.5691 should be rounded down to 3.569.

Other examples include,

4.8736 being rounded up to 4.874

6.3168 being rounded up to 6.317

9.7340 being rounded down to 9.734

Answer:

4-10.5

5-no because the nearest thousandth is not 5 or more

6- Tu is correct because the tenth is 6 which is more than 5 so it can be rounded up to $79

The text of the Pythagorean Theorem The Pythagorean Theorem states: “The sum of the squares of the lengths of the two sides of the right triangle, which are the shortest sides in a right-angled triangle, is equal to the square of the length of the hypotenuse, which is the longest side of the triangle.”

And in symbols: Pythagorean theorem = ( A² + B² = C²)

where ;

● A, B: the two sides of a right triangle ABC.

● C: The hypotenuse of a right triangle is ABC, which is the longest side.

It should be noted that the inverse of the theory is also true; Since the triangle to which the Pythagorean theorem applies, namely: A² + B² = C², is necessarily a right-angled triangle.

Nội dung của Định lý Pitago Định lý Pitago phát biểu: “Tổng bình phương độ dài hai cạnh của tam giác vuông, là cạnh ngắn nhất của tam giác vuông, bằng bình phương độ dài của cạnh huyền, là cạnh dài nhất của tam giác. "

Và trong các ký hiệu: Định lý Pitago = (A² + B² = C²)

ở đâu ;

● A, B: hai cạnh của tam giác vuông ABC.

● C: Cạnh huyền của tam giác vuông ABC là cạnh dài nhất.

Cần lưu ý rằng điều ngược lại của lý thuyết cũng đúng; Vì tam giác áp dụng định lý Pitago, cụ thể là: A² + B² = C², nhất thiết phải là tam giác vuông.

I hope I helped you^_^

Answer:

875

Step-by-step explanation:

Hey there!

Just do PEMDAS to solve

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

8 + (7 - 1)^2 / 20 - 9 * 2

= 8 + 6^2/ 20 - 9 * 2

= 8 + 36/10 - 9 * 2

= 8 + 9/5 - 18

= 49/5 - 18

= - 41/5

Therefore, your answer is:

-41/5 ≈ 8 1/5 or 8.2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

12.

[tex]x = \frac{PQ-14}{3}[/tex] and [tex]x = \frac{QR + 10}{7}[/tex]

Step-by-step explanation:

Hope this helps!

Have a nice day! :-)

Answer:

x = 6

Step-by-step explanation:

If PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, then PQ = QR.

[tex]PQ = 3x + 14 = QR = 7x - 10\\3x + 14 = 7x - 10\\3x + 24 = 7x\\24 = 4x\\6 = x\\x = 6[/tex]

Answer:

Yes.

Step-by-step explanation:

While there are no labels to be COMPLETLY sure, they both APPEAR to be 90 deg, which checks out as they APPEAR to combine to make a straight angle.

Hope this helps!

8(2)^2 + 8(2) + 9 = 57

your answer is 57

have a nice semester :)

Answer:

57

Step-by-step explanation:

8(2)^2 + 8(2) + 9

8×4+16+9

32+16+9=57

Answer:

39.9 grees

Step-by-step explanation:

Since 4.2 kribs = 18 grees

Then,

1 krib = 18/4.2 grees

9.3 kribs = (18/4.2) x 9 3

9.3 kribs = 39.9 grees.

Answer:

below

Step-by-step explanation:

this is very simple one I don't study mathematics but also know this

-18<-15<-5<0<9<18

Answer:

9 sec

Step-by-step explanation:

because it decends 12 feet evry second so the answer is nine sec

Answer:

Step-by-step explanation:

Answer:

The equation is 12x=180. You worked for 15 hours.

Step-by-step explanation:

Do 12x=180 then divide by 12. You get x=180/12. Then simplify

Answer:

$15/hr

Step-by-step explanation:

y= mx + b

180= 12h+ b

solution = 15 hrs

Answer:

LN = 12

Step-by-step explanation:

L______M_____N

LM = x+3

MN = 2x

LN = 4x

M is the midpoint of LN

LN= ?

LM + MN = LN

x + 3 + 2x = 4x

x + 2x + 3 = 4x

3x + 3 = 4x

-3x         -3x

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

3 = 1x

/1    /1

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

3 = x

LN = 4x

= 4 (3)

= 12

LN = 12

Answer:

LN = 12

Step-by-step explanation:

If LM = X+3, MN = 2x, LN = 4x, and M is between L and N, then LN = 12.

Step-by-step explanation:

0.0003÷0.0000000009=

333,333.33333333

Answer:

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

AN = NC,

4x - 7 = 5x -15,

-7 = x -15,

8 = x