Given that y varies directly as x when y = 2 and x = -12, find x when y = 5.

Answer:

$17,535

Step-by-step explanation:

 Original (old) salary:  $16,700/year

+ raise:                          0.05($16,700/year) = $835/year

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

 New salary:  Original salary plus amount of raise:

                        $16,700/year + $835/year   =  $17,535

A faster but still valid approach to finding the new salary involves multiplying the original salary by 1.05:

1.05($16,700) = $17,535.  Here the '1.00' represents the original salary and the '0.05) the raise.

Answer:

C

Step-by-step explanation:

173.6 • 9= 1562.4

Answer:

prime factorization of 225 = 32•52.

Step-by-step explanation:

The number 225 is a composite number so, it is possible to factorize it. 225 can be divided by 1, by itself and at least by 3 and 5.

A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.

Answer:

C 80 R36

Step-by-step explanation:

See attached image for explanation.

Answer:

the first one

Step-by-step explanation:

Hope this helps!

Answer: it is a linear line

Step-by-step explanation:

They both together make 0

Answer:

7√2

Step-by-step explanation:

Leg of the right triangle = greater base - smallest base = 10- 3 = 7

Leg 2 = height = 7

x = [tex]\sqrt{7^2 + 7^2} = \sqrt{49 * 2} = 7\sqrt{2}[/tex]

Answer:

3 mi of fencing would be required to enclose this field.

Step-by-step explanation:

Here we are finding the perimeter of a field with given length and width.  We apply the perimeter formula P = 2L + 2W.  Substituting the given dimensions, we get:

P = 2(1 mi) + 2(0.5 mi), or

P = 2 mi + 1 mi = 3 mi

3 mi of fencing would be required to enclose this field.

Answer:

15840 feet of fencing = Perimeter = 15840ft

However, if fencing is 6ft or 10ft we need to divide by the length of each fence for panels.

See bold.

Step-by-step explanation:

6ft fencing = 5280/6 = 880 fences one length

880 x 2 = 1760 6ft fences 2 sides

0.5 x 1760 = 880

1760+ 880 = 2640 fences each 6ft

Total feet of fence = 2640 x 6 =15840 feet of fencing

Answer:

Given function:

This is the third degree polynomial, so it has total 3 roots.

Lets factor it and find the roots:

The roots are:

It has highest degree 3 so 3 roots

Lets find

Roots are

Answer:

120 yards is the answer to the equation

Answer:

7>h

Step-by-step explanation:

Answer:

- 0.125

Step-by-step explanation:

Given the equation :

(0.020(5/4) + 3 ((1/5) – (1/4)))

0.020(5/4) = 0.025

3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15

0.025 + - 0.15 = 0.025 - 0.15 = - 0.125

Answer:

[tex]area \: = \frac{165}{360} \times \pi {8}^{2} \\ = 92.1533845053 \\ = 92 \: in^{2} [/tex]

Answer:

Complex roots

Step-by-step explanation:

Given

[tex]8v^2 + 8 = -11v[/tex]

Required

The type of solution

Rewrite as:

[tex]8v^2 +11v+ 8 = 0[/tex]

To determine the type of solution, we simply calculate the discriminant (D)

[tex]D = b^2 - 4ac[/tex]

Where

[tex]a = 8;\ \ \ b =11\ \ \ c = 8[/tex]

So, we have:

[tex]D = 11^2 - 4 * 8 * 8[/tex]

[tex]D = 121 - 256[/tex]

[tex]D = -135[/tex]

The above value implies that:

[tex]D<0[/tex]

When [tex]D<0[/tex], the solution of the equation is: complex roots

Answer:

C) 143

D) 37

E) 74

Step-by-step explanation:

C) 180 - 37 = 143

D) 180 - 143 = 37

E) 180 - 37 - 69 = E

Answer:

[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]

Step-by-step explanation:

Given

[tex]\tan A = 2/3[/tex]

Required

[tex]\sec\ A[/tex]

First, we have:

[tex]\tan A = \frac{x}{y}[/tex]

Where

[tex]x \to oppo site\\[/tex]

[tex]y \to adja cent[/tex]

[tex]z \to hypotenuse[/tex]

So:

[tex]\tan A = \frac{x}{y} =\frac{2}{3}[/tex]

By comparison:

[tex]x = 2; y =3[/tex]

Using Pythagoras, we have:

[tex]z^2 = x^2 +y^2[/tex]

[tex]z^2 = 2^2 +3^2[/tex]

[tex]z^2 = 13[/tex]

[tex]z = \sqrt{13[/tex]

[tex]\sec A =\frac{z}{y}[/tex]

[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]

Answer:

We know that:

H(x) = |1 - x^3|

and:

We want to write H(x) as  f( g(x) ) , such that for two functions:

So we want to find two functions f(x) and g(x) such that:

f( g(x) ) = |1 - x^3|

Where neither of these functions can be an identity function.

Let's define g(x) as:

g(x) = x^3 + 2

And f(x) as:

f(x) = | A - x|

Where A can be a real number, we need to find the value of A.

Then:

f(g(x)) = |A - g(x)|

and remember that g(x) = x^3 + 2

then:

f(g(x)) = |A - g(x)| = |A - x^3 - 2|

And this must be equal to:

|A - x^3 - 2| =  |1 - x^3|

Then:

A = 3

The functions are then:

f(x) = | 3 - x|

g(x) = x^3 + 2

And H(x) =  f( g(x) )

Answer:

80 degrees

Step-by-step explanation:

the angles in a triangle all add up to 180 degrees

Answer:

Let the third angle be [tex]{x°}[/tex]

Since the sum of all three angles of a triangle is 180°,

We have

40°+60°+[tex]{x}[/tex] = 180°

→ 100+[tex]{x}[/tex] = 180°

[tex]{x}[/tex] = 180-100 = 80°

The measure of the third angle is 80°

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: \: 1 \frac{1}{15} \:(or) \: 1.0667}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{4}{5} \div \frac{3}{4} [/tex]

= [tex] \: \frac{4}{5} \times \frac{4}{3} [/tex]

= [tex] \: \frac{4 \times 4}{5 \times 3} [/tex]

= [tex] \: \frac{16}{15} [/tex]

= [tex] \: 1 \frac{1}{15} [/tex]

( OR )

= [tex] \: 1.0667[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35\:♨}}}}⋆[/tex]

Step-by-step explanation:

[tex] \frac{4}{5} \div \frac{3}{4} \\ = \frac{4}{5} \times \frac{4}{3} \\ = \frac{16}{15} \\ thank \: you[/tex]

Answer:

Carrier A is 2,104 feet and Carrier B is 2,094 feet.

Step-by-step explanation:

Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:

(4,198 - 10) / 2 = X

4.188 / 2 = X

2,094 = X

2,094 + 10 = 2,104

2,094 + 2,104 = 4,198

Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.

Answer:

[tex]y < - 1[/tex]

Step-by-step explanation:

[tex]y < - 4 + 3[/tex]

[tex]y < - 1[/tex]

[tex] \sf \: y < - 4 + 3 \\ \sf \: y < - 1[/tex]

[tex] \sf \: Just \: add \: - 4 \: and \: 3 \: and \: you \: \\ \sf will \: get \: the \: inequality \: in \: the \: simplest \: form.[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]k=-\frac{1}{42}[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Given the equation [tex]y=14x+2[/tex], we can identify the slope (m) to be 14. This means that the slope of a perpendicular line would have to be [tex]-\frac{1}{14}[/tex] since that is its negative reciprocal.

In the equation [tex]y=k*3x+2[/tex], the slope would be 3k. 3k would be equal to [tex]-\frac{1}{14}[/tex]:

[tex]3k=-\frac{1}{14}[/tex]

Divide both sides by 3 to solve for k

[tex]k=-\frac{1}{42}[/tex]

I hope this helps!

Answer:

18% and 0.18

Step-by-step explanation:

converting fraction 9/50 as a percent leaves u with 18%

Answer:

78

Step-by-step explanation:

[tex]nC_k = \frac{n!}{k!(n-k)!}[/tex]

[tex]13 C_{11} = \frac{13!}{11! \times (13-11)!}[/tex]

        [tex]= \frac{13!}{11! \times 2!}[/tex]

       [tex]= \frac{ 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10\times 11 \times 12 \times 13}{(1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10\times 11 )\times ( 1 \times 2)}[/tex]

        [tex]=\frac{12 \times 13}{2} \\\\= 6 \times 13\\\\=78[/tex]

Answer:

B

Step-by-step explanation:

the slope is 0

the y intercept is ( 0,4 )

Answer:

13km per day

Step-by-step explanation:

If this does not involve complex rules then we can calculate the rate just by dividing 52 with 4 which results 13km per day

Goodluck

Use the following property below:

[tex] \large \boxed{ \sqrt[n]{a} \times \sqrt[n]{a} \times \sqrt[n]{a} = { (\sqrt[n]{a}) }^{3} }[/tex]

Therefore,

[tex] \large{ \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} = { (\sqrt[7]{x}) }^{3} }[/tex]

Then we use next property.

[tex] \large{ \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } }[/tex]

Hence,

[tex] \large{ \sqrt[7]{ {x}^{3} } = {x}^{ \frac{3}{7} } }[/tex]

Answer

Answer: 33.4

Step-by-step explanation:

Answer:

The quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].

Step-by-step explanation:

Parabolae are defined by second order polynomials, that is, a polynomial of the form:

[tex]y = a\cdot x^{2} + b\cdot x + c[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a, b, c[/tex] - Coefficients.

By Algebra, we know can calculate the set of all coefficients based on the knowledge of three distinct points. According to the graph, we have the following points: [tex](x_{1}, y_{1}) = (2, 0)[/tex], [tex](x_{2}, y_{2}) = (4, 0)[/tex] and [tex](x_{3}, y_{3}) = (6, 8)[/tex], and the resulting system of linear equations is:

[tex]4\cdot a + 2\cdot b + c = 0[/tex] (2)

[tex]16\cdot a + 4\cdot b + c = 0[/tex] (3)

[tex]36\cdot a + 6\cdot b + c = 8[/tex] (4)

The solution of the system of linear equations is:

[tex]a = 1, b = -6, c = 8[/tex]

Hence, the quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].