Jack is driving from his house to the airport. At 9:00 AM, he is 150 miles from the airport. At 10:30 AM, he is 75 miles from the airport. What is Jack’s average driving speed between 9:00 AM and 10:30 AM?

______ miles/hour

Answer:

Equation: 7n = 8.61

Solution: n = $1.23

Step-by-step explanation:

7 binders = $8.61

1 binder = $n

The price of one binder is seven times the price of 7 binders.

7n = The price of 7 binders

The price of 7 binders is $8.61

7n = $8.61

Divide both sides of the equation by 7

n = $1.23

Answer:

x³ - 4x² - 16x + 24

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² + 2x - 4) - 6(x² + 2x - 4) ← distribute both parenthesis

= x³ + 2x² - 4x - 6x² - 12x + 24 ← collect like terms

= x³ - 4x² - 16x + 24

A. x³ - 2x² - 16x + 24

To multiply 2 polynomials, apply the distributive property by using each term in 1 polynomial to multiply every in the other polynomial.

(x – 6)(x² + 2x – 4)

x(x² + 2x – 4) -6(x² + 2x – 4)

x³ + 2x² - 4x - 6x² - 12x + 24

Combine like terms

x³ - 2x² - 16x + 24

(x – 6)(x² + 2x – 4) equals: A. x³ - 2x² - 16x + 24

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[tex]n[/tex] - 4-digit number

[tex]q[/tex] - quotient

[tex]131q+112=n\\132q+98=n\\\\131q+112=132q+98\\q=14\\\\131\cdot14+112=n\\\boxed{n=1946}[/tex]

The four-digit number which has the remainder of 112 when divided by 131 is 1946.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, number which has the remainder of 112 when divided by 131.

Let n be the number and q be the quotient.

We know that, Dividend = Divisor × Quotient + Remainder

Now, n=131×q+112 ------(i)

The remainder of 98 when divided by 132.

That is, n=132×q+98 ------(ii)

From equation (i) and (ii), we get

131×q+112=132×q+98

131q+112=132q+98

132q-131q=112-98

q=14

Substitute q=14 in equation (i), we get

n=131×14+112

n=1946

Therefore, the four digit number is 1946.

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Answer:

The answer is C) 57.46cm2

Step-by-step explanation:

To find the area of a trapezoid you add together the parallel lines and times the answer by the height. Then you divide it by 2.

Answer:

The answer is B, 160 cm2

Step-by-step explanation:

To find the area of a trapezoid we have to use the following equation:

A= 0.5*(b1*b2)*h

a= area

b1: base 1

b2: base 2

h: height

Then,

A= 0.5*(14cm+18cm)*10cm = 160 cm2.

Answer:

(-7,3)

Step-by-step explanation:

Given that point (-7,1) is on the graph of f(x), means that

[tex]f(-7)=1[/tex]

To find the corresponding point for the function y=3f(x), you have to find the value of the function at x=-7.

Substitute x=-7 into the function's expression:

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

Since f(-7)=1, we have that

[tex]y=3\cdot 1=3[/tex]

Hence, the corresponding point has coordinates (-7,3)

To find the corresponding point for the function 3f(x), multiply the y-coordinate of the given point by 3.

To find the corresponding point for the function 3f(x), we need to multiply the y-coordinate of the given point by 3.

Given that (-7,1) is on the graph of f(x), we multiply the y-coordinate by 3 to get (1*3) = 3.

Therefore, the corresponding point for the function 3f(x) is (-7,3).

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Answer:

Step-by-step explanation:

We know:

1. Diagonals of a rhombus are perpendicular.

2. Diagonals divide the rhombus on four congruent right triangles.

3. The sum of measures of acute angles in a right triangle is equal 90°.

Angles CAD and ACB are alternate angles. Therefore they are congruent:

m∠DAC = m∠ACB ⇒ m∠ACB = x°.

From 3. we have the equation:

(5x - 18) + x = 90

(5x + x) - 18 = 90              add 18 to both sides

6x = 108             divide both sides by 6

x = 18

Answer:

Option D

Step-by-step explanation:

In any Rhombus the diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.

So,

5x-18+x+90=180 ( Angles of a triangle add to 180 degrees)

Simplifying like terms:

6x+72=180

Subtracting  72 both sides :

6x= 108

Dividing by 6 both sides:

x=18.

Option D is correct.

Answer:

Cats: 28; Dogs: 13

Step-by-step explanation:

54-26=28

48-35=13

54+48=102

102-61=41

28+13=41

Answer:

Step-by-step explanation:

To find each answer, we just have to complete the table.

We know that there are 54 cats in total, and 26 belong to 8th grade. So, 7th grade would be 54-26=28.

Also, we know that there are 48 dogs in total, if 35 belong to 8th grade, then 7th grade would be 48-35=13.

Therefore, 7th grade students have 28 cats, 13 dogs, and 41 pets in total. Therefore, the right choice is the second one.

First you are going to multiply the number by the percent. 9,895 x 20= 197,900.

Now divide the answer by 100. 197,900 / 100= 1,979.

This means the car salesman should make 1,979 from the car sale.

Remember, multiply the number by the percent, then divide that answer by 100.

I hope this helps! :)

Answer:

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

  right column to find the corresponding function formula in the

  left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

 take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

Answer:

D) 8

Step-by-step explanation:

2^3 means 2 times itself 3 times:

2*2*2

2*2 is 4 so:

4*2

4*2 is 8 so the answer is D, 8!

D) 8

Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. example, 2 + 4 + 5 = 11 is an equation.

When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters

2^3 means 2 times itself 3 times:

2*2*2

2*2 is 4 so:

4*2

4*2 = 8

so the option is D, 8

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Answer:

[tex]\boxed{A=6}\checkmark[/tex]

The answer should have positive sign.

Step-by-step explanation:

First you do is divide by -6 from both sides of an equation.

[tex]\frac{-6(2+a)}{-6}=\frac{-48}{-6}[/tex]

Then, simplify and solve the problem.

[tex]-48/-6=8[/tex]

[tex]2+a=8[/tex]

Next, you switch sides.

[tex]a+2=8[/tex]

You subtract by 2 from both sides of an equation./

[tex]a+2-2=8-2[/tex]

Finally, solve/simplify.

[tex]8-2=6[/tex]

A=6 is the correct answer.

Hope this helps you!

Have a nice day! :)

Answer:

the first one is graph c and the second, graph b.

Step-by-step explanation:

They are both linear inequalities, so for both, you have to solve for x first. For the first one, since x is basically multiplied to 2 (2x), you have to divide both sides to get x by itself, and you get x>25. The graph has to have an opened circle, and the arrow should go to the right because all the numbers greater than 25 can be x. For the second one, you have to subtract 6 to both sides to get x by itself which then leaves you with ×<26. This one should also be an opened circle, and is going to the left, because all the numbers less than 26 can be x.

Answer:

first box c second box b

Step-by-step explanation:

[tex]|\Omega|=6^4=1296\\|A|=1\cdot1\cdot5\cdot5\cdot\dfrac{4!}{2!2!}=25\cdot6=150\\\\P(A)=\dfrac{150}{1296}\approx11.6\%[/tex]

Answer:

Height of parallelogram = 5.07 inches

Step-by-step explanation:

We are given Area of Parallelogram = 32 in^2

Height of Parallelogram = ?

Base of Parallelogram = 6.3 in

The formula to find the Area of Parallelogram is:

Area of Parallelogram = Base * Height

32 = 6.3 * Height

=> Height = 32/6.3

=> Height = 5.07 inches

So, height of parallelogram = 5.07 inches

The missing variable for this parallelogram is the height, which is 5.08 inches.

We begin with the formula for the area of a parallelogram:

We plug in all given information.  We know the area, 32 in², and we know the base, 6.3 in:

Next we solve for our variable, h.  Since 6.3 and h are beside each other, we know they have been multiplied.  To cancel this, we will divide both sides by 6.3:

This means that the missing variable, the height, is approximately 5.08 inches.

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Keywords: missing variables, missing measurements, area of parallelogram, missing side of parallelogram

Answer:

Simplify by combining like terms, she combined 1/2 and 1 which equals 3/2. Your answer is A.

Step-by-step explanation:

The missing step in Fiona's solution to the equation 1/2 - 1/3(6x - 3) = -13/2 was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2.

To find the missing step of Fiona's solution, we first need to simplify the equation. The given equation is 1/2 - 1/3(6x - 3) = -13/2. The missing step may be the distribution of the 1/3 onto the (6x - 3). This leads to 1/2 - (2x - 1) = -13/2.

Following this, we need to remove the fraction on the left side of the equation by multiplying the entire equation by 2. This gives 1 - (4x - 2) = -13. Finally, simplifying this further gives us -4x = -16, and solving for x we get x = 4.

Therefore, Fiona's missing step was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2 to get rid of fractions.

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Answer:

p^4 p^3 P^2

Step-by-step explanation:

Look at the numbers and put them in order from largest to smallest number.

Answer:Answer:

p^4 p^3 P^2

Step-by-step explanation:

Look at the numbers and put them in order from largest to smallest number.

Answer:

[tex]x=\frac{5}{3}[/tex]

Step-by-step explanation:

Let do algebra and figure out the value of x:

[tex]\frac{4}{x-3}+5=2\\\frac{4}{x-3}=2-5\\\frac{4}{x-3}=-3\\4=-3(x-3)\\4=-3x+9\\3x=9-4\\3x=5\\x=\frac{5}{3}[/tex]

Note: assuming that the problem is [tex]\frac{4}{x-3}+5=2[/tex]

Answer:

The answer is 5/3

Step-by-step explanation:

Answer:

1.59

Step-by-step explanation:

log (2x-3)= log (3-x) -2

log (2x-3)/(3-x) =-2

If we remove log,

2x-3/(3-x) = e^-2

2x-3= 3e^-2 -xe^-2

2x+ xe^-2 = 3e^-2+3

x(2+e^-2) = 3( e^-2+1)

If you use calculator you will get answer nearly equal to 1.59.

Answer:

$ 2.737

Step-by-step explanation:

The amount of tax is 6% of the purchase price

Solution

[tex]\frac{6}{100} *45.62=2.7372[/tex]

Amount of tax will be $2.737

The amount of tax is 6% of the purchase price

Solution

\frac{6}{100} *45.62=2.7372

Amount of tax will be $2.737

Multiply last years rainfall by the percent of increase.

26 inches x 0.15 = 3.9 inches more.

Round the answer as needed.

First, we need to find 15% of last years total rainfall to estimate next years. To do this, multiply last years rain by the decimal form of 15%.

26*.15=3.9

There will be 3.9 more inches of rain predicted to fall next year.

Hope this helps!

Answer:

yes

Step-by-step explanation:

You can perform the "line test." If it is a function, there will not be two x's of the same value. In this case, x is 2,6,-1. No number repeats, thus making a function.

Answer:

Function:

(7, -4) (0, 9), (2, -2)

(-6, 5), (-5,6), (8,2)

(2, 3), (6, -5), (-1,3)

Not a Function:

(1, 9), (-3, -2), (1, -4)

(0, 3), (0, 7), (4, 0)

Step-by-step explanation:

I got it right on edge lol

also none of the other answers for this question on here are right

Answer:

[tex]\cos (x-y)=\dfrac{1}{2}=0.5[/tex]

Step-by-step explanation:

Use formula:

[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y[/tex]

Since

[tex]\sin x=-\dfrac{1}{2}[/tex]

and angle x is in the fourth quadrant, then cos x is greater than 0 and is equal to

[tex]\cos x=\sqrt{1-\sin ^2x}=\sqrt{1-\left(-\dfrac{1}{2}\right)^2}=\sqrt{1-\dfrac{1}{4}}=\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt{3}}{2}[/tex]

Since

[tex]\cos y=\dfrac{\sqrt{3}}{2}[/tex]

and angle y is in the first quadrant, then sin y is greater than 0 and is equal to

[tex]\sin y=\sqrt{1-\cos ^2y}=\sqrt{1-\left(\dfrac{\sqrt{3}}{2}\right)^2}=\sqrt{1-\dfrac{3}{4}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}[/tex]

Hence,

[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y=\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{3}}{2}+\left(-\dfrac{1}{2}\right)\cdot \dfrac{1}{2}=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{1}{2}[/tex]

Answer:

38

Step-by-step explanation:

Range is the largest number minus the smallest number

The largest number is 55 and the smallest number is 17

55-17 = 38

Answer:

x=2

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Hello!

Answer:

[tex]\boxed{2y+11x}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

First, you switch sides. *Group like terms*

[tex]4y-2y+7x+4x[/tex]

Then, you add the similar to elements. You can also add the numbers from left to right.

[tex]4y-2y=2y[/tex]

[tex]2y+7x+4x[/tex]

[tex]7x+4x=11x[/tex]

[tex]\boxed{2y+11x}\checkmark[/tex], is the correct answer.

Hope this helps!

Have a nice day! :)

Answer:

2y + 11x

Step-by-step explanation:

Simplify the expression 4y+7x- 2y+4x​

To simplify any expression, combine the like terms by adding or subtracting

To simplify 4y+7x- 2y+4x​, combine the like terms

combine 4y and -2y, = 2y and

combine 7x and 4x = 11x

2y + 11x

The line of reflection between the two pentagons is the y-axis.

We can see this because all of the points in pentagon P'Q'R'S'T' have the same x-coordinate as their corresponding points in pentagon PQRST, but their y-coordinates are negated. For example, point P has coordinates (-4, 6), and its reflected image P' has coordinates (-4, -6).

The y-axis is the only line that passes through all of the midpoints of the segments connecting corresponding points in the two pentagons. Since reflection preserves distance, the line of reflection must be the perpendicular bisector of any segment connecting a point in one pentagon to its reflected image in the other pentagon.

Answer:

[tex]x=37.5[/tex]

Step-by-step explanation:

We need to find the solution to the following system of equations:

[tex]y = -\frac{4}{5} x[/tex] and [tex]y=-30[/tex]

By plugging the value of 'y' into the first equation we have that:

[tex]-30 = -\frac{4}{5} x[/tex] ⇒ [tex]30=\frac{4}{5} x[/tex]

Solving for 'x' we have:

[tex]x=37.5[/tex]

So, the solution to the system of equation is: (37.5, -30)

Answer:

b d e f

Step-by-step explanation: