Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-20y=-160

Answer: -5+6i

Step-by-step explanation:

Answer:

D.  x = 6

Step-by-step explanation:

Given equation:

[tex](x-2)^{\frac{1}{2}}+4=x[/tex]

Subtract 4 from both sides:

[tex]\implies (x-2)^{\frac{1}{2}}+4-4=x-4[/tex]

[tex]\implies (x-2)^{\frac{1}{2}}=x-4[/tex]

Square both sides:

[tex]\implies \left( (x-2)^{\frac{1}{2}}\right)^2=(x-4)^2[/tex]

[tex]\implies x-2=(x-4)^2[/tex]

Expand the brackets on the right side:

[tex]\implies x-2=(x-4)(x-4)[/tex]

[tex]\implies x-2=x^2-8x+16[/tex]

Subtract x from both sides:

[tex]\implies x-2-x=x^2-8x+16-x[/tex]

[tex]\implies -2=x^2-9x+16[/tex]

Add 2 to both sides:

[tex]\implies -2+2=x^2-9x+16+2[/tex]

[tex]\implies 0=x^2-9x+18[/tex]

[tex]\implies x^2-9x+18=0[/tex]

Factor the left side of the equation:

[tex]\implies x^2-6x-3x+18=0[/tex]

[tex]\implies x(x-6)-3(x-6)=0[/tex]

[tex]\implies (x-3)(x-6)=0[/tex]

Apply the zero-product property:

[tex]\implies x-3=0 \implies x=3[/tex]

[tex]\implies x-6=0\implies x=6[/tex]

Therefore, the solutions of the quadratic equation are:

[tex]x=3, \quad x=6[/tex]

Input both solutions into the original equation to check their validity:

[tex]\begin{aligned}x=3 \implies (3-2)^{\frac{1}{2}}+4&=3\\(1)^{\frac{1}{2}}+4&=3\\1+4&=3\\5&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=6 \implies (6-2)^{\frac{1}{2}}+4&=6\\(4)^{\frac{1}{2}}+4&=6\\2+4&=6\\6&=6\end{aligned}[/tex]

Therefore, the only valid solution to the given equation is x = 6.

Answer:

The answer is D. 6

Step-by-step explanation:

Add both sides:

(x - 2)^1/2 + 4 + (-4) = x + (-4)

(x - 2)^1/2 = -4

Solve exponent:

(x - 2)^1/2 = x - 4

((x - 2)^1/2)^2 = (x - 4)^2

x − 2 = x^2 − 8x + 16

x − 2 − (x^2 − 8x + 16) = x^2 − 8x + 16 − (x^2 − 8x + 16)

−x^2 + 9x − 18 = 0

(−x + 3)(x − 6) = 0

−x + 3 = 0 or x − 6 = 0

x = 3 or x = 6

Check the answers: (Plug them in to see what will work.)

x = 3 (won't work)

x = 6 (does work)

Therefore,

x = 6

Solution

Part a

Part b

For this case we can do this:

Fx= 585 N* cos 80= 101.58 N

Fy= 585N * sin 80= 576.11 N

Then the best answer is:

B. (102, 576) N

Answer:

whats the problme?

Step-by-step explanation:

The cost of a membership for 1 year is 490

The equation of the membership is given as

c(m) = 40m + 10

From the question, we understand that:

m represents the number of months

For the cost of a membership for 1 year, the number of months is 12

i.e. m = 12

Substitute the known values in the above equation

So, we have

c(12) = 40 * 12 + 10

Evaluate

c(12) = 490

Hence, the cost is 490

Read more about linear equation at

https://brainly.com/question/4074386

#SPJ1

One of the forms we can write the equation of a line is like this:

y - y1 = m(x - x1)

Where (x1, y1) is a point where the line passes through, and the value of m, the slope of a line is given by the following formula:

Then, for the first line (line q), we can take the points (-9, 0) and (-3, 18), then we get:

By replacing the value of the slope and the coordinates of the point (-9, 0), we get:

y - 0 = 3(x - (-9))

y = 3(x + 9)

y = 3x + 27

y - y = 3x + 27 - y

0 = 3x + 27 - y

-27 = 3x + 27 - 27 - y

-27 = 3x - y

For line v, we can take the points (-4, 10) and (0, 8), then we get:

By taking -1/2 for the slope and the coordinates of the point (0,8), we gat:

y - 0 = -1/2(x - 8)

y = -1/2x + 4, multiplying both sides by 2:

2y = -x + 16

2y + x = -x + x + 16

2y + x = 16

Then, the system represented by the lines q and v is option G

1 nickel is worth 5 cents and 1 quarter is worth 25 cents.

So, if he has 4 nickels, this is worth 4 times 5 cents and if he has 11 quarters, this is worth 11 times 25 cents.

Both are worth the sum of these, so:

So, he has 295 cents.

If he has n nickels and q quarters, he has 5 times n plus 25 times q worth, so he has:

The correct option b: 49° because the angles are supplementary to angle d.

For the given question.

∠d = 131 degrees.

∠d + ∠f = 180  (supplementary angle)

∠f = 180 - 131

∠f = 49 degrees

Now,

∠f = ∠g = 49 degrees (vertically opposite angles)

∠f = ∠c = 49 degrees (alternate interior angles)

Thus, the angle d is supplementary to angle f, c and g.

To know more about the supplementary angles, here

https://brainly.com/question/12919120

#SPJ13

Step 1: Use the formula below to find the future value:

Fv = P + Prt

P = present value or initial deposit

r = rate in %

t = time in years

Step 2: List the given data

P = $7900

r = 6.5% = 0.065

t = 4 years

Step 3: Substitute the values of P, r and t to find the future value.

FV = P + Prt

= 7900 + 7900 x 0.065 x 4

= 7900 + 2054

= $9954.00

Stop 4: Final answer

Future value = $9954.00

Answer:

slope = 5/4

Step-by-step explanation:

What is the slope of a line that passes the points (-1,4 ) and ( 3,9 ) ?

slope = change in y ÷ change in x

slope = (9-4) ÷ (3 - (-1))

slope = 5/4

Answer:

x = 2

Step-by-step explanation:

Hello!

Let the unknown number be x. The product of 6 and that number can be represented by 6x. And since we are adding 5, we can use 6x + 5 to represent that expression.

This equation is equal to the difference of 9x and 1, or 9x - 1.

The value of x is 2.

EXPLANATION:

Given;

We are given two points which are shown below;

Required;

We are required to calculate the slope.

Step-by-step solution;

To calculate the slope given two points, we shall use the following formula;

Where the variables are;

We can now substitute these values and solve;

Therefore.

ANSWER:

The sum of the interior angles of any triangle is always 180º:

Use the equation above and the given data to find C:

Law of sines:

Use the pair of ratios for a and b to solve a:

Use the pair of ratios for b and c to solve c:

ANSWER :

The answer is 5/33 or 0.15

EXPLANATION :

From the problem, we have a total of 5 number of species.

Using the given Biodiversity Index formula :

Answer:

the slope is -5/3

Step-by-step explanation:

it is that because to find slope u do y2-y1/x2-x1

Answer:

geometric, neither, arithmetic, and neither

Step-by-step explanation:

right on edg 2023

We can determine the slope using the following expression:

Now, using the two points given, we have:

From this, we have that the slope(m) equals -1/5.

Answer:

Qualitative data is the data that is not represented by numbers, for example, favorite food or country.

On the other hand, the quantitative data is represented by numbers and it is classified as discrete and continuous. The discrete data is the data that only can take specific values, for example, the number of people is always a whole number, there can't be 5.5 people. The continuous data is the data that can take decimal values, for example, the mass of an object can be 4.06 kg.

After solving the equation, If both A and B of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.

Two mathematical expressions' values are said to be equal in an equation, which is a statement of this fact. A mathematical formula declares that two things are equal.

The equals sign ('=') is used to indicate it.

Let the work completed be W

For A

W = 5hours = 1/8 days

1 hour =  1/8 days ÷ 5

1 hour = 1/40 days

For B

W = 6 hours = 1/10 days

1 hour = 1/60 days

Add both the equation

1 hours + 1 hours = 1/40 days + 1/60 days

2 hours = 5/120 days

2 hours = 1/24days

If both of them worked for 1 hour a day

1 hour = 1/48 days

If both of them worked for 8hour a day

8 hours = 1/48 × 8

             = 1/6 days

Thus, if both of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.

Learn more about equations

https://brainly.com/question/2972832

#SPJ9

2.

3.

Answer:

Explanation:

Given:

To fully understand how we get the given answer, we simplify the equation first:

Next, we apply the rule:

So,

Then, we also apply the radical rule:

For

Therefore the x-values are: x=4i, x=-4i. The i on the answer means imaginary number. It is a number that, when squared, has a negative result.

Given data:

The given expression for the points is,

Thus, the expression or

Answer:

A. a chorus

Step-by-step explanation:

There are 126 ways to choose a committee of five from a group of nine people using combinations; one of them must include JONES.

So, we have a comiitte of 5 be chosen from 9 people and JONES must be one of them -

Therefore, there are a total of 126 ways in which we can decide that JONES must be on it.

Know more about combinations here:

https://brainly.com/question/28065038

#SPJ9

Answer:

Given that,

Circle with a diameter whose endpoints are (8,17) and (4, - 15).

To find the equation for the circle

we know that,

Equation of the circle is of the form,

where r is the radius and (h,k) is the center of the circle.

If the end points of the diameter is given, then the equation of the circle is,

Substitute the points we get,

On simplifying this we get,

Divide 31 into 32 and then multiply the result by 100 to get the percent:

Given

Solution

Recall : SOHCAHTOA

The final answer

Option A

1) In order to convert from the standard version to the vertex form we'll need to find the vertex of that parabola:

We can find the vertex, using these formulas:

So this is the vertex of that parabola at point (-3,-10)

2) Now, note that the coefficient a = 1, and with the vertex, we can now rewrite that equation into the vertex form:

Since the triangle is equilateral, all of its interior angles have a measure of 60º.

Substract the area of the triangle from the area of a circular sector with radius 7cm enclosed by an angle of 60º to find the area of the shaded region.

The area of an equilateral triangle with side length L is:

The area of a circular sector of radius r enclosed by an angle of θ degrees is:

Replace θ=60 and r=7cm to find the area of the circular sector:

Replace L=7cm to find the area of the triangle:

Then, the area of the shaded region is:

Therefore, the area of the shaded region to 3 significant figures, is:

Step 1

Given;