factor the GCF: 12a^3b + 8a^2b^2 — 20 ab^3

Answer:

[tex]y + 2 = - (x - 4)[/tex]

Step-by-step explanation:

The graph passes through: (0,2) and (2,0)

The slope is

[tex] \frac{0 - 2}{2 - 0} = - 1[/tex]

The equation of the line in point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

The graph passes through (4,-2).

We substitute the slope and this point to get:

[tex]y - - 2 = - 1(x - 4)[/tex]

[tex]y + 2 = - (x - 4)[/tex]

The first option is correct

[tex]\bf \begin{array}{ccll} x&y\\ \cline{1-2}\\ 2&\stackrel{2\cdot 7}{14}\\\\ 4&\stackrel{4\cdot 7}{28}\\\\ x&x\cdot 7 \end{array}~\hspace{7em}y=7x[/tex]

Answer:

y = 7x

Step-by-step explanation:

A direct variation is of the form

y = kx where k is the constant of variation

We have the point (2,14)

Substituting this in

14 = k*2

Divide each side by 2

14/2 =2k/2

7 =k

The direct variation equation is y = 7x

Answer:

d (-5,0)

Step-by-step explanation:

x-coordinate moves a point left or right from the origin.

y-coordinate moves a point down or up form the origin.

So we don't want any down or up, so we want y to be 0.

If a point is located on the x-axis, then the y-coordinate is 0.  

d is the only point that sits on the x-axis. I know this because it's y-coordinate is 0.

(0,8) is actually a point sitting on the y-axis.

Answer:

(D) (-5,0)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Person A bought 3 tickets for 191

The price per ticket is 191/3 =63.67

Person B bought 5 tickets for 309

The price per ticket is 309/5 =61.80

Person C bought 8 tickets for 435

The price per ticket is 435/8 =54.38

The lowest price per ticket is 54.38

Person C paid the lowest price per ticket

Answer:

x1/2

Step-by-step explanation:

Simplify the following:

(3 x1)/6

Hint: | In (x1×3)/6, divide 6 in the denominator by 3 in the numerator.

3/6 = 3/(3×2) = 1/2:

Answer:  x1/2

For this case we have the following expression:

[tex](x ^ {\frac {1} {6}}) ^ 3[/tex]

We have that by definition of properties of powers it is fulfilled that:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Now we have to, by applying the property:

[tex](x ^ {\frac {1} {6}}) ^ 3 = x ^ {\frac {3} {6}}[/tex]

Simplifying:

[tex]x ^ {\frac {3} {6}} = x ^ {\frac {1} {2}}[/tex]

Answer:

[tex]x ^ {\frac {1} {2}}[/tex]

the name of the plane is C. plane EGF

Answer:

1)all numbers less than -5 and greater than 5

Step-by-step explanation:

We are given

x<-5

and

x>5

So

Looking at both the inequalities one by one, The solution will consist of all the numbers that are less than -5 and greater than 5. The numbers between -5 and 5 will be excluded from the solution..

Hence,

1)all numbers less than -5 and greater than 5

is correct ..

The intersection of the sets {X|X<-5} and {x|x>5}, which represents numbers that fulfill both conditions, results in no real numbers, or the empty set.

The solution set of the given intersection of the two sets {X|X<-5} and {x|x>5} is defined as the set of numbers that fulfill both conditions: numbers less than -5 and numbers greater than 5.

However, there are no real numbers that can be both less than -5 and greater than 5 at the same time. Therefore, when these two sets intersect, the result is an empty set.

https://brainly.com/question/15513632

#SPJ3

Answer:

29.97 square feet

Step-by-step explanation:

Given

The length of rectangle = 9 ft

The width of rectangle = 40 in

We have to bring the length and width in same unit. As the area is required in square feet so we will convert width in feet

The width will be divided by 12 to be onverted into feet

So,

Width = 40/12 = 3.33 feet

Now

Area = Length * width

= 9 * 3.33

= 29.97 square feet ..

Answer:

Area of rectangle = 30 square feet

Step-by-step explanation:

We are given that a rectangle is 9 feet long and 40 inches wide and we are to find its area in square feet.

For this, we will covert the width of the rectangle to feet and then find the area.

We know that:

[tex]\frac{1 foot}{x} =\frac{12 inches}{40}\\x=3.3 feet[/tex]

So width in feet is 3.3 feet.

Area of rectangle = [tex]9 \times 3.33[/tex] = 30 square feet

The expression will be    [tex]\[ (-125) \cdot c^3 \][/tex]

The exponential form of the expression [tex]\((-5)(-5)(-5) \cdot c \cdot c \cdot c\)[/tex] can be calculated as follows:

First, simplify the multiplication of the negative numbers:

[tex]\[ (-5)(-5)(-5) = (-125) \][/tex]

Next, simplify the multiplication of the variables:

[tex]\[ c \cdot c \cdot c = c^3 \][/tex]

Now, combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

The final exponential form of the expression is:

[tex]\[ (-125) \cdot c^3 \][/tex]

Here's a step-by-step explanation of the calculation:

1. Multiply the negative numbers:

[tex]\[ (-5)(-5) = 25 \][/tex]

  Multiply 25 by -5 again:

[tex]\[ 25 \cdot (-5) = -125 \][/tex]

2. Multiply the variables:

[tex]\[ c \cdot c = c^2 \]\\ Multiply \(c^2\) by c again:\\ \[ c^2 \cdot c = c^3 \][/tex]

3. Combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

That's the final exponential form of the given expression.

Complete Question:

What is the exponential form of the following expression

(-5)(-5)(-5) •c•c•c

Answer:

10 ≥ ⅛c + ¼d

Step-by-step explanation:

They budgeted up to 10 gallons of water, meaning that it CANNOT exceed 10. When turned around, you will see that everything is less than or equal to 10.

I am joyous to assist you anytime.

Complete question:

A small kennel has budgeted to provide 10 gallons of water for its animals. Each cat receive one eight of a gallon per day and each dog receives one fourth of a gallon per day . Which inequality correctly represent the scenario.

a. 10 < -1/8c - 1/4d

b.  10 ≤  1/8c + 1/4d

c  10 ≥ -1/8c - 1/4d

d. 10 ≥ 1/8c + 1/4d

Answer:

d. 10 ≥ 1/8c + 1/4d

Step-by-step explanation:

The kennel was budgeted to provide 10 gallons of water for its animals. The cat receives  1/8 of a gallon per day and each dog receive 1/4 of a gallon per day.

Since 10 gallons was budgeted for the animals the sum of the a gallon per day for the cat and dog will most likely not exceed 10 gallons. The animals will most likely consume less than the budgeted value or equals to the budgeted value.    

note that the sum of 1/8 of a gallon  for the cat and 1/4 of a gallon for the dog should be either less than 10 or equals to 10. This means  10 ≥ 1/8c + 1/4d .

Answer:

22

Sarah's age is best represented by M-24 or as the question used x-24 where the mother's age is best represented by M where the question used x.

Step-by-step explanation:

We are given that Sarah (S) is 24 years younger than her mother (M).

So S=M-24.

We are given that Sarah (S) and her mom's age adds up to 68.

So S+M=68.

We are going to solve this system by substitution since one of the variables is solved for. I'm going to plug first equation into second like so:

(M-24)+M=68   I replaced S with M-24.

M+M-24=68      Put like terms together.

2M-24  =68       Combined the like terms.

2M      =  92      Added 24 on both sides.

 M      = 92/2    Divided 2 on both sides.

 M      = 46        Simplified the 92/2.

So her mother's age is 46.

We know that S=M-24 so S=46-24=22.

Sarah is 22 years old.

Answer:

33

Step-by-step explanation:

Line 1: 2

Line 2: 2 * 2 - 1 = 3

Line 3: 2 * 3 - 1 = 5

Line 4: 2 * 5 - 1 = 9

Line 5: 2 * 9 - 1 = 17

Line 6: 2 * 17 - 1 = 33

Answer:

$60 a month is the answer

Step-by-step explanation:

$200 down payment leaves you with $300's to pay still. Divide the $300's by 5 and that leaves you with $60 a month.

Answer:

Isolate the variables in all cases. Note the equal sign, what you do to one side, you do to the other.

a) 3x = 18

Isolate the variable, x. Divide 3 from both sides:

(3x)/3 = (18)/3

x = 18/3

x = 6

b) 2x = 9

Isolate the variable, x. Divide 2 from both sides:

(2x)/2 = (9)/2

x = 9/2

x = 4.5

c) (x/5) = 7

Isolate the variable, x. Multiply 5 to both sides:

(x/5)(5) = (7)(5)

x = 7 * 5

x = 35

d) x/2 = 6.5

Isolate the variable, x. Multiply 2 to both sides:

(x/2)(2) = (6.5)(2)

x = 6.5 * 2

x = 13

~

a) 3x = 18

x = 6

____________

b) 2x = 9

x = 4.5

____________

c) (x/5) = 7

x = 35

____________

d) x/2 = 6.5

x = 13

____________

Have a great day!

Answer:

[tex]f( - 10) = 2(-10)+1[/tex]

which is then equal to-19

[tex]f(2)=2^2 \\ [/tex]

which is then equal to 4

[tex]f(-1)=1^2 \\ [/tex]

which is then equal to 1

[tex]f(8)=3-8 \\ [/tex]

which is then equal to -5

Answer:

In the explanation:

Step-by-step explanation:

f(-10) means we need to find the piece so that x is also satisfied.

So we have x=-10 here.  Which of your pieces satisfy that?

Well [tex]-10 \le -5[/tex] so the first piece.  

[tex]f(-10)=2(-10)+1=-20+1=-19[/tex].

f(2) means we find the piece so that x is also satisfied.

So we have x=2 here. Which of your pieces satisfy that?

Well [tex]-5<2<5[/tex] so the second piece.

[tex]f(2)=(-2)^2=4[/tex].

f(-5) means we use the piece that satisfied x=-5.

-5 equals -5 and the equals -5 part is included in the first piece.

[tex]f(-5)=2(-5)+1=-10+1=-9[/tex]

f(-1) means use the piece so that x=-1 is satisfied.

-1 is between -5 and 5 so use [tex]x^2[/tex]

[tex]f(-1)=(-1)^2=1[/tex]

f(8) means use the piece so that x=8 is satisfied.

9 is greater than 5 so we use the third piece.

[tex]f(8)=3-8=-5[/tex]

It looks like you have all the answers and you are trying to figure out why.

Let's do another problem.

What piece would you use if I asked you to evaluate:

f(-2)?

x=-2 satisfies the [tex]-5<x<5[/tex] so we use the [tex]x^2[/tex]

[tex]f(-2)=(-2)^2=4[/tex]

f(-6)?

x=-6 satisfies the [tex]x \le -5[/tex] so we use the [tex]2x+1[/tex]

[tex]f(-6)=2(-6)+1=-12+1=-11[/tex]

f(7)?

x=7 satisfies [tex]x \ge 5[/tex] so we use [tex]3-x[/tex]

[tex]f(7)=3-7=-4[/tex]

I will post the answers here after you had time to think about it.

Answer:

y^18

Step-by-step explanation:

(y^2)^5 x y^8

Assuming the x is multiplication

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

Assuming the x is a variable

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

This is multiplies by x

x y^18

Answer:

[tex]\Huge \boxed{xy^1^8}[/tex]

Step-by-step explanation:

Exponent rule: [tex]\displaystyle (a^b)^c=a^b^c[/tex]

[tex]\displaystyle y^2^\times^5[/tex]

Multiply.

[tex]\displaystyle 2\times5=10[/tex]

[tex]\displaystyle y^1^0^+^8[/tex]

Add.

[tex]\displaystyle 10+8=18[/tex]

[tex]\large \boxed{xy^1^8}[/tex], which is our answer.

Answer:

[tex]f^{-1}[/tex] (x ) = [tex]\frac{x+6}{5}[/tex]

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject, that is

y = 5x - 6 ( add 6 to both sides )

y + 6 = 5x ( divide both sides by 5 )

x = [tex]\frac{y+6}{5}[/tex]

Change y back into terms of x

[tex]f^{-1}[/tex] (x ) = [tex]\frac{x+6}{5}[/tex]

Answer:

[tex]\large\boxed{C.\ 75<x<110\ and\ 0<y\leq50}[/tex]

Step-by-step explanation:

x - the temperature

y - the number of people

the temperature is between 75 degrees and 110 degrees:

75 < x < 110

the room for 50 people:

0 < y ≤ 50

Answer:

C

Step-by-step explanation:

We know x is more than 75

75<x

and there is room for 50 people and we have to use y

0<y<110

  _^

The only possible answer is C hope this helps :)

Answer:

A) x greater than or equal to −3

Step-by-step explanation:

We have the following inequality:

7 − 9x − (x + 12) ≤ 25

Solving the inequation, we have:

7 − 9x − x - 12 ≤ 25

-10x ≤ 30

-x ≤ 3

x≥-3

Therefore the result is option A) x greater than or equal to −3

Answer:

B.

Step-by-step explanation:

7-9x - (x+12) ≤ 25

7 - 9x - x - 12 ≤ 25

-10x - 5 ≤ 25

-10x ≤ 25 +5

x ≥ 30/-10

x ≥ -3.

So, the incorrect answer is B.

Step-by-step explanation:

A = P (1 + r)^t

Given that P = $1,200,000, r = 0.1037, and t = 5:

A = $1,200,000 (1 + 0.1037)^5

A = $1,965,334.41

Round as needed.

Answer:

The forecasted sales for 2004 is $1965281.

Step-by-step explanation:

The annual sales in 1999 were = $1,200,000

Let geometric mean growth rate = r

we have now p = $1,200,000,

r = 10.37% or 0.1037

t = 5:

We have the formula Amt= [tex]p(1+r)^{t}[/tex]

Amt =[tex]1200000(1+0.1037)^{5}[/tex]

Solving this we get;

[tex]1200000\times1.63777=1965324[/tex]

A = $1,965,324

Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (6, 9)

m = [tex]\frac{9-4}{6-2}[/tex] = [tex]\frac{5}{4}[/tex]

Answer:

y = - 10x - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here slope m = - 10, hence

y = - 10x + c ← is the partial equation

To find c substitute (- 1, 4) into the partial equation

4 = 10 + c ⇒ c = 4 - 10 = - 6

y = - 10x - 6 ← equation of line

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 2^{\frac{3}{4}} \right)^2\implies 2^{\frac{3}{4}\cdot 2}\implies 2^{\frac{3}{2}}\implies \sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}[/tex]

Answer:

(5/2 ,  3/2)

or

(2.5  , 1.5)

(These are the same point; just one is in fraction form and the other in decimal)

Step-by-step explanation:

I could be wrong but I think you want to solve the system

x+y=4

x-y=1

The cool thing about this system it is already set up for elimination (some people call it linear combination).  This means when you add the equations together, a variable will get eliminated allowing you to solve for the other.

x+y=4

x-y=1

----------Add equations.

2x+0=5

2x    =5

 x     =5/2

 x     =2.5

So plug in your x into either one of the equations and solve for y.

x+y=4

2.5+y=4

y=4-2.5

y=1.5

So the solution is (2.5 , 1.5)  or (5/2, 3/2).

Answer:

The measure of angle A is 51 degrees

Answer:

The measure of an angle A=[tex]1^{\circ}[/tex].

Step-by-step explanation:

We are given that an angle [tex]95^{\circ}[/tex] and two sides are 7  in and 9 in in a given figure.

We have to find the value of measurement of angle A.

To find the measurement of angle A we apply sine law.

Sine law:[tex]\frac{a}{sin \alpha}=\frac{b}{sin\beta}=\frac{c}{sin \gamma}[/tex]

Where  side a is opposite to angle [tex]\alpha[/tex]

Side b is opposite to angle [tex]\beta[/tex]

Side c is opposite to angle[tex] \gamma[/tex]

We are given an angle 95 degrees and opposite side of given angle is 9 in and the angle A is opposite to side 7 in.

Substituting the values then we get

[tex]\frac{9}{sin 95^{\circ}}=\frac{7}{sin A}[/tex]

[tex]\frac{9}{0.683}=\frac{7}{sin A}[/tex]

[tex] sin A=\frac{7\times 0.683}{9}[/tex]

[tex] sin A=\frac{4.781}{9}=\frac{4781}{9000}[/tex]

[tex] sin A=0.531[/tex]

[tex] A= sin^{-1}(0.531)[/tex]

[tex] A=0.56^{\circ}[/tex]

[tex] A= 1^{\circ}[/tex]

Hence, the measure of an angle A=[tex]1^{\circ}[/tex].

Answer:

45

Step-by-step explanation:

Here are two ways of solving this problem.

Method 1:

Term 1 is 2.

Term 2 is 3.

Term 3 is 4.

Each term is 1 more than the term number.

The 44th term is 45.

Method 2:

Using the hint

Find the common difference: 5 - 4 = 1

The common difference is 1.

1st term + (common difference)(desired term - 1)

2 + 1(44 - 1) = 2 + 43 = 45

Answer: 45

Answer:

1/6

Step-by-step explanation:

(1/2)/3

To solve, note that there are 2 denominators in all. To solve, multiply the denominators together:

(1/2)/3 = 1/(2 * 3) = 1/6

1/6 is your answer.

~

Answer:

0.16

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact form: 1/6

Decimal form: 0.16

Answer:

2.5 gallons

Step-by-step explanation:

We need to go 100 miles

Write the proportion

Picking a point on the graph (40 miles, 1 gallon)

100 miles         40 miles

-------------- = -------------

x gallons         1 gallon

Using cross products

100 * 1 = 40 *x

Divide each side by 40

100/40 = 40x/4

2.5 =x

We need 2.5 gallons to go 100 miles

Answer: Based on the graph, the car requires 2.5 gallons of fuel to travel 100 miles.

Look at the picture below for help. The blue dot represents were the two points meet. We are trying to figure out how many gallons are for the 100 miles, 100 miles would be on the side that says distance (miles). That is were you start. Find point 100 on the distance (miles) side and just draw a straight line, stopping when you hit the black line on the graph. Once done, draw another line going straight down from the black line, and you get your answer of 2.5

Answer: 2.5

Hope it helps!

Answer: I know you prob don't need this answer anymore but this is for the people who look it up and need it.

Step-by-step explanation:

It's 2.1*10^-3

[tex]2.1 \times 10^{-3[/tex] is the scientific notation of the given number.

To write in scientific notation,

So, in scientific notation, 0.0021 is written as [tex]2.1 \times 10^{-3[/tex].

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ6