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2 years ago

Find the value of z.

Mathematics

1 answer:

nataly862011 [7]2 years ago

8 0

Answer:

z = $\frac{50}{3}$

Step-by-step explanation:

The ratio of corresponding sides are equal, that is

$\frac{z}{10}$ = $\frac{20}{12}$ ( cross- multiply )

12z = 200 ( divide both sides by 12 )

z = $\frac{200}{12}$ = $\frac{50}{3}$

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Why are tenths, fifths, fourths, and halves easy to express as percent?

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Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function. Typ

Georgia [21]

The y-intercept of a function is the point where the graph crosses the $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

The factors of the Jared's graph are: (x - 10), (x + 3) and (x + 9)
The y-intercept is -13.5
The standard equation of the function is: $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

(a) The factors

First, we write out the points where the function cross the x-axis.

The points are:

$\mathbf{x = 10}$

$\mathbf{x = -3}$

$\mathbf{x = -9}$

Equate the above points to 0

$\mathbf{x -10 = 0}$

$\mathbf{x +3 = 0}$

$\mathbf{x +9 = 0}$

Hence, the factors are: (x - 10), (x + 3) and (x + 9)

(b) The y-intercept

This is the point where the graph crosses the y-axis.

From the attached graph, the graph crosses the y-axis at -13.5.

Hence, the y-intercept is -13.5

(c) The standard form

In (a), we have:

$\mathbf{x -10 = 0}$

$\mathbf{x +3 = 0}$

$\mathbf{x +9 = 0}$

Multiply the above equations

$\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 \times 0 \times 0}$

$\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 }$

Expand

$\mathbf{(x - 10) \times (x^2 + 3x + 9x + 27) = 0 }$

$\mathbf{(x - 10) \times (x^2 + 12x + 27) = 0 }$

Expand

$\mathbf{x^3 + 12x^2 + 27x - 10x^2 - 220x - 270 = 0 }$

Collect like terms

$\mathbf{x^3 + 12x^2 - 10x^2+ 27x - 220x - 270 = 0 }$

$\mathbf{x^3 + 2x^2 - 193x - 270 = 0 }$

Replace 0 with y

$\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

Hence, the standard form is: $\mathbf{y = x^3 + 2x^2 - 193x - 270 }$

Read more about graphs and functions at:

brainly.com/question/18806107

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2 years ago

Classify the system of equations and identify the number of solutions.

mestny [16]

Answer:

x = all real numbers

Step-by-step explanation:

first you need to solve the first equation to figure out what y is.

4x - y = 2

add y to both sides of the equation

4x = 2 + y

subtract 2 from both sides of the equation

4x - 2 = y

now that you know what y is, you can substitute it in the next equation.

3y = 12x - 6

3(4x - 2) = 12x - 6

open the parenthesis

12x - 6 = 12x - 6

subtract 12x from both sides of the equation

-6 = -6

regardless of what x is, -6 will always equal -6.

so, the answer is all real numbers.

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3 years ago

Jerome spent $20 on supplies to make 50 cookies for a bake sale. Write and solve an inequality to find the price that Jerome sho

Semenov [28]

Answer:

Each cookie will have to be sold for at least $0.90 if the profit is to be made is more than $25.

Step-by-step explanation:

The amount spent on supplies is $20.

The number of cookies baked is = 50.

If the profit to be made is more than $25.00 .

Then we can safely say that all the cookies have to be sold for

= $20.00 + $25.00

= $45.00

Therefor the required inequality can be written as

50 x ≥ $45.00 ⇒ x ≥ $\frac{45.00}{50}$ ⇒ x ≥ $0.90.

Therefore we can say that each cookie will have to be sold for at least $0.90 if the profit is to be made is more than $25.

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2 years ago