What multiplies to negative 4 and adds to 7

Answers

Answer 1

Answer: 1. multiply to -18 add to -17 = Multiplying -18 and 1 will give -18 as the result and then on adding -18 and + 1 the result comes to -17

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Solve this linear equations: x + y + z = 34 1x + 10y + 5z = 100

Answers

Answer

To solve this system of linear equations, we can use the method of substitution.

First, let's solve the first equation for x:

x = 34 - y - z

Now, we substitute this value of x into the second equation:

1(34 - y - z) + 10y + 5z = 100

34 - y - z + 10y + 5z = 100

34 + 9y + 4z = 100

Next, we simplify the second equation:

9y + 4z = 100 - 34

9y + 4z = 66

We can rewrite this equation as:

9y = 66 - 4z

y = (66 - 4z) / 9

Now, we substitute this value of y back into the first equation:

x + (66 - 4z) / 9 + z = 34

Multiplying through by 9 to eliminate the fraction:

9x + 66 - 4z + 9z = 306

9x + 5z = 240

Now we have a system of two equations in two variables:

9x + 5z = 240

9y + 4z = 66

We can solve this using the method of substitution or elimination. Let's use the method of elimination:

Multiplying the first equation by 4 and the second equation by 5, we get:

36x + 20z = 960

45y + 20z = 330

Subtracting the second equation from the first, we eliminate z:

36x - 45y = 630

We can simplify this equation by dividing through by 9:

4x - 5y = 70

Now, let's solve the new system of equations:

4x - 5y = 70

9y + 4z = 66

We can multiply the first equation by 9 and the second equation by 4 to eliminate x:

36x - 45y = 630

36y + 16z = 264

Now, subtracting the first equation from the second, we eliminate y:

36y + 16z - 36x + 45y = 264 - 630

81y + 16z = -366

Dividing through by 3, we get:

27y + 16z = -122

Now, we have a system of two equations in two variables:

4x - 5y = 70

27y + 16z = -122

We can solve this system using the method of substitution or elimination.

If the number of professors in a college is p and the number of students is s, and there are 18 times as many students as professors, what is an algebraic equation that shows the relationship?

Answers

Answer:

Step-by-step explanation:

let p be number of professors and s be number of students

18 times of students as professors

s = p * 18

s = 18p

What is the simplified form of square root 48n^9?

Answers

Answer:

$4n^4√(3n)$

Step-by-step explanation:

Use the exponent rules:

$\sqrt[n]{x^a} = x^{(a)/(n)}$

$\sqrt[n]{a^n} =a$

To find the simplified form of :

$√(48n^9)$

We can write 48 and $n^9$ as:

$48 = 4 \cdot 4 \cdot 3 = 4^2 \cdot 3$

$n^9 = (n^4)^2 \cdot n$

then;

$√(4^2 \cdot 3 \cdot (n^4)^2 \cdot n)$

Apply the exponent rule:

⇒ $4 \cdot n^4 \cdot √(3n)$

⇒ $4n^4√(3n)$

Therefore, the simplified form of square root 48n^9 is, $4n^4√(3n)$

$√(48n^9)=√(16n^8\cdot3n)=√(16n^8)\cdot√(3n)=4n^4√(3n)$

The quotient of a number and 3 is decreased by 121. The result is -164.

Answers

quotient of number and 3 decreased by 121 is -164
change them to equations

121 - $(n)/(3)$ = - 164
- $(n)/(3)$ = -285
- n = -855
n = 855

check:
121 - $(855)/(3)$ = -164
121 - 285 = -164
-164 = -164

What is the range of the data set 22 30 49 71 85 88 92 97 99

Answers

the range is 77. you calculate range by subtracting the smallest number from the biggest number.

Solve by elimination
8x+9y=-55
-8x+y=65

Answers

8x+9y=-55
-8x+y=65 (+)

10y=10 /:10

y=1

-8x+1=65

-8x=64 /:(-8)

x=-8

1. Add the 2 systems and get 10y = 10.
2. Divide both sides by 10 so you get y = 1.
3. Substitute that in either equation (I'm going to use the 2nd equation).
4. -8x + 1 = 65.
5. Subtract 1 from each side.
6. -8x = 64.
7. Divide by -8 on both sides.
8. x = -8.
9. Check in the other equation.
10. 8(-8) + 9(1) ?= -55
11. -64 + 9 ?= -55
12. -55 = -55

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