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3 years ago

Given: Point C is the midpoint of AB¯¯¯¯¯.

Mathematics

1 answer:

suter [353]3 years ago

3 0

Answer:

See proof below

Step-by-step explanation:

If C is the midpoint of AB, then AC = CB

Given

AC=7x−10;

CB=3x+10

Then 7x - 10= 3x+10

Add 10 to both sides

7x-10+10 = 3x +10+10

7x = 3x + 20

7x - 3x = 10+10

4x = 20

x = 20/4

x = 5

Get AC

AC = 7x - 10

AC= 7(5) - 10

AC = 35-10

AC = 25 (Proved)

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What is the roots of f(x)=-x^2-6x-14

Nutka1998 [239]

Answer:

$x=-3\pm i \sqrt{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

Imaginary roots: √-1 = i

Step-by-step explanation:

Step 1: Define function

f(x) = -x² - 6x - 14

Step 2: Set up

Set equation equal to 0: -x² - 6x - 14 = 0
Factor out -1: -(x² + 6x + 14) = 0
Divide both sides by -1: x² + 6x + 14 = 0

Step 3: Define variables

a = 1

b = 6

c = 14

Step 4: Find roots

Substitute: $x=\frac{-6\pm\sqrt{6^2-4(1)(14)} }{2(1)}$
Exponents: $x=\frac{-6\pm\sqrt{36-4(1)(14)} }{2(1)}$
Multiply: $x=\frac{-6\pm\sqrt{36-56} }{2}$
Subtract: $x=\frac{-6\pm\sqrt{-20} }{2}$
Factor: $x=\frac{-6\pm\sqrt{-1} \sqrt{20} }{2}$
Simplify: $x=\frac{-6\pm2i \sqrt{5} }{2}$
Factor: $x=\frac{2(-3\pm i \sqrt{5} )}{2}$
Divide: $x=-3\pm i \sqrt{5}$

8 0

3 years ago

Ronald is distributing writing supplies to campers. He must give the same number of supplies to each camper and use all the supp

Liula [17]

Answer:

Robert can give writing supplies to at most 7 campers.

Step-by-step explanation:

The problem states that Robert must give the same number of supplies to each camper and use all the supplies. It means that the greatest number of campers that Robert can give writing supplies is the greatest common divisor(gcd) between the number of pencils and the number of note pads.

The gcd between two integers is the largest positive number that divides each of the integers. We can find this value by prime factorization.

The problem states that he has 14 pencils and 21 note pads. So we have to find gcd(14,21).

21 is not divisible by 2, so we try factoring by 3

14 is not divisible by 3, so we try factoring by 5

None of them are divisible by 5, so we move to 7

Both are divisible by 7, so

14 - 21 | 7

2 - 3

2<7, 3<7, so gcd(14,21) = 7.

Robert can give writing supplies to at most 7 campers.

3 0

4 years ago

On which number line are -6 and its opposite shown?

Alekssandra [29.7K]

Answer: #2

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

ALGEBRA by bundling cellular land line high speed internet connection and cable service Joyce abbot was able to save 48.50 per m

andreyandreev [35.5K]

Answer: She should budget $672.89 monthly next year for this service.

Step-by-step explanation:

Since we have given that

Amount he was able to save per month = $48.50

Total amount he spent for the year = $1254.89

Amount he saved for the year would be

$48.50\times 12\\\\=\$582$

Amount left from total would be

$1254.89-582\\\\=\$672.89$

Hence, She should budget $672.89 monthly next year for this service.

6 0

3 years ago

A lamp manufacturer has daily production costs of C = 0.25n2 – 10n + 800, where C is the total cost in dollars for n lamps produ

Oliga [24]

I think the answer is C) all positive integers. It makes the most sense in the context of the problem.

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4 years ago