Find the equation of the line that goes through the points (4, –1) and (2, –5).

Use slope formula,equation,to find the slope of a line that passes through the points.

m =
Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.

b =
Write the equation in slope-intercept form, y = mx + b.

Answer:

subtract 3 from both sides

Step-by-step explanation:

Given

2x + 3 = 11 ( subtract 3 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

a) -5/2.

Step-by-step explanation:

Try substituting (-5/2) into f(x):

6(-5/2)^4 + 5(-5/2)^3 - 33(-5/2)^2 - 12(-5/2) + 20

= 234.375 + -78.125 - 206.25 + 30 + 20

= 0.

So it is -5/2.

Answer:

a) [tex]x= -5/2[/tex]

Step-by-step explanation:

We substitute in the function the values given in the options to confirm whether they are roots or not

a) [tex]x= -5/2[/tex]

the function will be:

[tex]f(-\frac{5}{2} )=6(-\frac{5}{2} )^4 + 5(-\frac{5}{2} )^3-33(-\frac{5}{2} )^2-12(-\frac{5}{2})+20[/tex]

simplifying:

[tex]f(-\frac{5}{2} )=6(\frac{625}{16} )-5(\frac{125}{8} )-33(\frac{25}{4} )+30+20[/tex]

[tex]f(-\frac{5}{2} )=234.375-78.125-206.25+50\\f(-\frac{5}{2} )=0\\\\[/tex]

since the function when [tex]x= -5/2[/tex] is equal to zero, this is an actual root of f(x).

Answer:

An imaginary number is a number that does not exist pretty much. It is usually written as "i", and, when squared = -1. However, you cannot root -1 to get a number, so i is the term that is given to be the answer.

Note:

i² = -1

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Answer:

1 ticket equals to $2.50. Since x number of tickets are sold, the total amount raised will be $2.50 multiply by x, which is 2.5x. Since y represents the total amount of money raised, 2.5x equals to y

Answer:

35

Step-by-step explanation:

We know that the general formula for arithmetic sequence is  

a_n=a_0+(n-1)d

Using the general formula, we can make equations for 6th term and 9th term

a_6=a_0+(6-1)d

a_6=a_0+5d

101=a_0+5d Eqn 1

For 9th term

a_9=a_0+(9-1)d

a_9=a_0+8d

83=a_0+5d   Eqn 2

Subtracting equation 2 from equation 1

101-83=a_0+5d-(a_0+8d)

18=a_0+5d-a_0-8d  

18=-3d

d= -6

Putting d=-6 in Eqn 1, we get:

101=a_0+5(-6)

101=a_0-30

a_0=101+30

a_0=131

Now that we have values of a_0, and d we can find the 17th term

a_17=a_0+(17-1)d

=131+(16)(-6)

=131-96

=35

So the 17th term is 35 ..

Answer:

∠2 = 18°

Step-by-step explanation:

∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2

∠WXZ = 3∠2 + ∠2, that is

72 = 4∠2 ( divide both sides by 4 )

18 = ∠2, that is

∠2 = 18°

Answer:

The answer is B.

e^a=55

Taking log on both sides,

lne^a = ln 55

a lne= ln55

a= ln55.

The value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

We solve the value of this expression using the basic logarithm,

[tex]\rm{log_ab=c[/tex]

Similarly,

[tex]\rm{log_e55=a[/tex]

we know that the log base of exponent is natural log, therefore,

[tex]\rm ln\ 55=a[/tex]

Therefore, the value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).

Learn more about Logarithm:

https://brainly.com/question/163125

[tex]77500[/tex]

In this case, the digit in the hundredths place is a [tex]5[/tex].  We need to take a look at the next digit to the right, which is a [tex]4[/tex].

Since it is [tex]4[/tex] or less, we can simply replace the [tex]4[/tex] and the rest of the digits to the right with [tex]0[/tex]s to round it.

If the [tex]4[/tex] was [tex]5[/tex] or more, we would round the [tex]5[/tex] up to [tex]6[/tex] and replace the remaining digits to the right with [tex]0[/tex]s.

Answer:

77500

Step-by-step explanation:

To round something to the nearest hundred, we first look to the 10s digit. It is 4. Since 4 is less than 5, then we keep the same hundreds place. So we get 77500.

Answer:

A) 32y³ + 24y² - 12y - 9

Step-by-step explanation:

(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)

                           = 32y³ + 24y² - 12y - 9

The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:

               [tex]32y^3+24y^2-12y-9[/tex]

We are asked to find the product of the two expressions which are given by:

[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]

i.e.

we are asked to find the product of a quadratic and a linear polynomial.

We are asked to find the result of:

[tex](-8y^2+3)\cdot (-4y-3)[/tex]

Hence, on using the distributive property we have:

[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]

The correct answer is: Option: A

Answer:

$3.80

Step-by-step explanation:

We are given a graph showing the location of 3 houses where you had to do lawn work today, with the distances from your house.

Given that one truck gets 8 miles per gallon of gasoline and gas costs $1.52 per gallon, we are to find the total cost of the gas used.

Total distance = 7 + 3 + 4 + 6 = 20 miles

Gallons of gas used = 20 / 8 = 2.5

Total cost of gas used = 2.5 * 1.52 = $3.80

Answer:

The correct answer option is E) No solution.

Step-by-step explanation:

We are given the following quadratic equation which we are to solve for x when the value of y is 0:

[tex]y = x ^2+ 6x +12[/tex]

[tex]x ^2+ 6x +12=0[/tex]

Using the quadratic formula since there are no factors:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac }}{2a}[/tex]

Substituting the values in the formula to get:

[tex]x=\frac{-6 \pm \sqrt{6^2-4(1)(12) }}{2(1)}[/tex]

[tex]x=-3+\sqrt{3}i[/tex] or [tex]x=-3-\sqrt{3}i[/tex]

There are no real number solutions to this quadratic equation.

Answer:

B) 8 over 35 plus 8 over 35 equal 64 over 1225

Step-by-step explanation:

There are 8 yellow tiles out of 35 tiles.

Its not A because she replaces.

Its not C or D because you would only add when it says and

Answer:

8 over 35 multiplied by 8 over 35 equal 64 over 1225

Step-by-step explanation:

I got it right on my test. Give the other person brainliest.

Answer:

see below

m = males = 50

e = females = 25

a = adults = 7

Step-by-step explanation:

Givens

Let the adults = a

let the males students = m

lef the female students = e

Equations

a + m + e = 82                                  

m = 7*a + 1

e = 1/2 * (7a + 1)

Solution

a + 7a + 1 + 1/2(7a + 1) = 82                 Remove the brackets on the left.

a + 7a + 1 + 3.5*a + 1/2 = 82                Combine the like terms on the left.

11.5a + 1.5 = 82                                    Subtract 1.5 from both sides.

11.5a + 1.5 - 1.5 = 82 - 1.5                     Combine

11.5a = 80.5                                          Divide by 11.5

a = 80.5/11.5

a = 7                  

The number of adults = 7

===============================

m = 7a + 1

m = 7*7 + 1

m = 50

===============================

e = 1/2 m

e = 1/2 * 50

e = 25

Answer:

-y(7+y) =0

Step-by-step explanation:

-7y - y^2 = 0

Factor out a -y

-y(7+y) =0

Using the zero product property

-y =0  and 7+y =0

y=0     7-7+y = 0-7

y=0    y = -7

Answer:

(a)(b²)√a

Step-by-step explanation:

√(a³b⁴)

Root both variables. Note that pairs of the same variables can be brought out of the root.

√(a³) = √(a * a * a) = a√a

√(b⁴) = √(b * b * b * b) = b²

(a)(b²)√a is your answer.

Answer:

C. parallel lines

Explanation:

If two straight lines be at right angles to the same plane, the straight lines would be parallel.

Answer:

United Kingdom , France,  Soviet Union , and China  

Step-by-step explanation:

United Kingdom , France,  Soviet Union , and China  was an ally of the United States durning World War II.

Answer:

Yes,a similar formula is used to find all the products

Step-by-step explanation:

The formula applied in this case is;

(a+b)²=   (a+b) (a+b)= a(a+b)+b(a+b) = a²+ab+ab+b²= a²+2ab+b²

In the first one;

[tex](x+3)^2= (x+3) (x+3) = x(x+3)+3(x+3) = x^2 +3x+3x+9  = x^2 +6x +9[/tex]

In the second one;

[tex](x+4)^2 = (x+4) (x+4) = x(x+4)+ 4(x+4) = x^2 +4x+4x+16 = x^2 +8x+16[/tex]

⇒This is the same for the third and fourth product.

Answer:

3rd option is right

Step-by-step explanation:

Answer:

29.74 degrees.

Step-by-step explanation:

Tan(theta) = opposite / adjcent.

opposite = 8

adjacent = 14

Tan(theta) = 8/14

Tan(theta) = 0.5714

theta = tan^-1(0.5714)

theta = 29.74 degrees

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = [tex]e^{2x}[/tex] - 4

let f(x) = y

y = [tex]e^{2x}[/tex] - 4

Switch x and y and solve for y, that is

x = [tex]e^{2y}[/tex] - 4 ( add 4 to both sides )

x + 4 = [tex]e^{2y}[/tex]

Take the ln of both sides

ln(x + 4) = ln [tex]e^{2y}[/tex] = 2y [tex]ln_{e}[/tex] = 2y

Divide both sides by 2

y = [tex]\frac{ln(x+4)}{2}[/tex], that is

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

The value of x that is not in the domain is x = 7.

which of the following values of X is not in the domain of f(x)?

Remember that in math we can't divide by zero, so any value that makes the denominator equal to zero can't be in the domain.

Here the rational function is:

f(x) = (x + 3)/(x - 7)

When x = 7, the denominator becomes zero, so x = 7 is not in the domain.

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

Look at the picture.

We have

center at (3, 5) → h = 3 anf k = 5

radius r = 8

Substitute:

[tex](x-3)^2+(y-5)^2=8^2\\\\(x-3)^2+(y-5)^2=64[/tex]

Answer:

  x = 1

Step-by-step explanation:

The graph is shown below. The solution is x = 1.

___

√x +2 = 3x . . . . given

√x = 3x -2 . . . . . subtract 2

x = 9x^2 -12x +4 . . . . square both sides

9x^2 -13x +4 = 0 . . . . subtract x to put in standard form

(x -1)(9x -4) = 0 . . . . . factor the quadratic

x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero

The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.

The solution is x=1.

Answer:

= 135 m²

Step-by-step explanation:

First we divide the kite into 2  isosceles triangles

The bigger triangle has base angles = 45°

We can use these angle as follows to find the common base of the two triangles.

Cos 45=adjacent/9√2

Adj=9√2×cos 45

=9

common base =9×2=18

We can use the angle 45° above to find the height of the bigger triangle.

Tan 45°=opposite/adjacent

Opposite = adjacent×Tan 45

=9 tan 45=9

Area =1/2BH+1/2Bh where B is the common base H is the height of the big triangle, h represents the height of the smaller triangle.

A=1//2× 18 × 9 +1/2× 18 × 6

= 135 m²

Answer:

Answer:

X

The given statement is true.

Step-by-step explanation:

An inverse function can be defined as  a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x.

Examples are x+2 and x-2

WE get f(x) = x+2

Apply g(x) = g(f(x))=g(x+2)

=x+2-2=x

Thus by applying composiiton g f or fg in any order we get the answer as x

THis is the property of any inverse function

Step-by-step explanation:

Answer:

X

Step-by-step explanation:

It was corrected on E2020.

Answer:

x = 8

Step-by-step explanation:

Step 1: Write an equation

2x - 9 = 7

Step 2: Use the Addition Property of Equality

2x = 16

Step 3: Use the Division Property of Equality

x = 8

Answer:

number = 8

Step-by-step explanation:

Let "number" = x. Set the equation.

"product of 2 and number" = 2(x)

"nine less" = -9

"equal to 7" = "= 7"

2x - 9 = 7

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 9 to both sides.

2x - 9 (+9) = 7 (+9)

2x = 7 (+9)

2x = 16

Divide 2 from both sides.

(2x)/2 = (16)/2

x = 16/2

x = 8

8 is your answer.

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Answer:

D. 21

Step-by-step explanation:

Hope I helped!

Your answer is for this question is 21

1.) To find 70% percent of 30 you simply multiply both. To do that you gotta first change the percent into a decimal by moving the point two types to the left.

70 = 70.0

2.) As you can see we change the percent into a decimal.

70% = .70

3.) Now we can multiply 30 by .70 which will give us an answer of 21.

Hope this helps!!!

Please Mark as Brainliest!!!

Answer:

Option 1 is correct

Step-by-step explanation:

Given expression is:

[tex](3x^3y^{-2})^2\\[/tex]

Putting the values

[tex]= [3 (-2)^3 (5)^{-2}]^2\\We\ have\ to\ make\ the\ powers\ positive\\= [{\frac{3(-2)^3}{5^{2}} }]^2\\= \frac{[{3(-2)^3}]^2}{(5^2)^2} \\Applying\ outer\ power\\= \frac{3^2(-2)^6}{5^4} \\[/tex]

Hence option one is correct ..

Answer:

the ninth root of 3

Step-by-step explanation:

3 to the 2 over 3 power, to the 1 over 6 power rewritten as a radical expression is ''the ninth root of 3''.

Hope this helps!

Answer:

kk

Step-by-step explanation: