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3 years ago

The difference of the square of a number and 8 is equal to 7 times that number. Find the positive solution.

Mathematics

1 answer:

postnew [5]3 years ago

7 0

Answer:

Correct answer: x₁ = 8

Step-by-step explanation:

Given equation is:

x² - 8 = 7x ⇒ x² - 7x - 8 = 0 ⇒ x² - 8x + x - 8 = 0 ⇒ x ·(x - 8) + (x - 8) = 0

(x - 8) · (x + 1) = 0 ⇒ x₁ = 8 or x₂ = -1

we accept a positive solution

x₁ = 8

God is with you!!!

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I have to verify each equation here by substituting identities to match the right hand side of the equation to the left.

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1+sec^2×sin^2×= sec^2×

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4 years ago

Problem Set:

Hoochie [10]

Answer:

Part a) $\frac{132}{89}$

Part b) 132:89 vs 132 to 89

Part c) $\frac{66}{7}$

Part d) 66:7 vs 66 to 7

Step-by-step explanation:

Let

x ----> the number of boys

y ----> the number girls

z ----> the number of adults

we have

x=132, y=89, z=14

Part a) Write the ratio of the number of boys to the number of girls.

To find the ratio of the number of boys to the number of girls, divide the number of boys by the number of girls

$\frac{x}{y}$

substitute

$\frac{132}{89}$

Part b) Write the same ratio using another form (A: B vs. A to B)

we have

$\frac{132}{89}$

The other form is

132:89 vs 132 to 89

Part c) Write the ratio of the number of boys to the number of adults

To find the ratio of the number of boys to the number of adults, divide the number of boys by the number of adults

$\frac{x}{z}$

substitute

$\frac{132}{14}$

Simplify

$\frac{66}{7}$

Part d) Write the same ratio using another form

The other form is

66:7 vs 66 to 7

7 0

3 years ago

Hey everyone!!!!!!!!!!!

Ronch [10]

Answer:

P(0, 1)

Step-by-step explanation:

Using the section formula

$x_{P}$ = $\frac{(3(-2))+(2(3))}{2+3}$ = $\frac{-6+6}{5}$ = 0

$y_{P}$ = $\frac{(3(5))+(2(-5))}{2+3}$ = $\frac{15-10}{5}$ = 1

Hence P(0, 1)

8 0

3 years ago

last month , he sold 50 chickens and 30 ducks for $550 . This month , he sold 44 chickens and 36 ducks for $532. How much does a

Kazeer [188]

Hello there, my fellow human being!
So, the chicken costs $8 and the duck costs $5, here's why.

Let's say x is the cost of a chicken while y is the cost of a duck.
We can make two linear equations using the information above.
Last month, he sold 50 chickens and 30 ducks for $550: 50x + 30y= 550
This month, he sold 44 chicken and 36 ducks for $532: 44x + 36y = 532

50x/10 + 30y/10 = 440/10
44x/4 + 36y/4 = 532/4

5x + 3y = 44
11x + 9y = 133

So, now that we have our answer simplified, we have to use elimination to solve this system of equations. But, first we need to make sure that at least one of our variables is able to be canceled out.
Let's multiply this equation by -3.
(5x + 3y = 44) * -3.

-15x-9y=-165.

11x + 9y = 133
-15x - 9y = -165
______________
-4x/4 = -32/4
x = 8
11x + 9y = 133
11(8) + 9y = 133
88 + 9y = 133
-88 -88
________________
9y/9 = 45/9
y = 5.

4 0

3 years ago

Read 2 more answers

A website offers a free trial membership for an online streaming service from a list of 25 channels. Another website is also off

sashaice [31]

There are 750 many outcome pairs you can have

<h3>How to determine the number of outcome pairs?</h3>

The given parameters are:

Website 1 = 25

Website 2 = 30

The number of outcome pairs is calculated as:

Outcome = Website 1 * Website 2

So, we have:

Outcome = 25 * 30

Evaluate the product

Outcome = 750

Hence, there are 750 many outcome pairs you can have