Find the greatest common factor for each of the following expressions, then factor each expression. a. 4p – 4 = ? b. x4 + x3 + x2 = ? c. 8p2 + 9p2q = ? d. x2y2 + 3xy – 4x – 2x4y3 = ? Factor each of the following expressions. a. 4a3 + 28a2 + 4a + 28 = ? b. x3 + 3x2− 2x − 6 = ? c. 8x2− 4xy + 2x − y = ? Factor each of the following, using the difference of perfect squares where possible. a. u2 – 100 = ? b. 4a2 − 49 = ? c. 81 − y2= ? d. 16q4− 16 = ? e. 9c3− 9c = ? f. 48a2b − 12b = ?

Answer:

x = -6

Step-by-step explanation:

Hello!

2x - 15 = 3(2x + 3)

Distribute the 3

3 * 2x = 6x

3 * 3 = 9

2x - 15 = 6x + 9

Subtract 2x from both sides

-15 = 4x + 9

Subtract 9 from both sides

-24 = 4x

Divide both sides by 4

-6 = x

Hope this helps!

Answer:

6. No. See explanation below.

7. 18 months

8. 16

Step-by-step explanation:

6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.

Let's find the GCF of 85 and 99:

85 = 5 * 17

99 = 3^2 + 11

5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.

Answer: No because the GCF of 85 and 99 is 1.

7.

We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.

6 = 2 * 3

9 = 3^2

LCM = 2 * 3^2 = 2 * 9 = 18

Answer: 18 months

We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.

Month                Charlie          Dasha

1                          home             home

2                          home             home

3                          home             home

4                          home             home

5                          home             home

6                         trip                home

7                          home             home

8                          home             home

9                          home             trip

10                         home             home

11                         home             home

12                         trip               home

13                         home             home

14                         home             home

15                         home             home

16                         home             home

17                         home             home

18                         trip                 trip

Answer: 18 months

8.

First, we find the prime factorizations of 96 an 80.

96 = 2^5 * 3

80 = 2^4 *5

GCF = 2^4 = 16

Answer: 16

Answer:

t ≈ 5.1 days

Step-by-step explanation:

A 10 gram sample of a substance thats used to detect explosives has a k-value of 0.1356. Find the substances half-life in days. round your answer to the nearest tenth. N=N₀ e^-kt N₀= initial mass (at time t = 0) N = mass at time t k= a positive constant that depends on the substance itself and on the units used to measure time t=time in days

The initial condition is that, at time t = 0, the amount of substance contains originally 10 grams

Find the value of N₀

N=N₀ e^-kt

We substitute:

10 = N₀ {e^(-0.1356)*0}

10 = N₀ (e^0)

10=N₀(1)

10=N₀

N₀ = 10

When the substance is in half-life

That is, half of the original substance (5 grams)

Find t

N=N₀ e^-kt

5 = 10 e^(-0.1356*t)

0.5 = e^(-0.1356*t)

Bring down t by multiplying natural log on both sides

ln(0.5) = -0.1356*t

Divide both sides by -0.1356

t = -(ln(0.5) / 0.1356

t ≈ 5.11 days

To the nearest tenth

t ≈ 5.1 days

Answer:

5.1 days in Plato

Step-by-step explanation:

Answer:

LOOK BELOW

Step-by-step explanation:

I would not call the explanation a formula

All you have to do to solve mean or average is add all of the numbers up and divide by the total amount of numbers

so for example

0,2,4,0,2,3,2,8,6  <-------- lets find the mean/average

0+2+4+2+3+2+8+6= 27/amount of numbers

amount of numbers=9

(count the zeros too!)

27/9=3

3 is the mean or average!!!

Answer:

3x and 9y and -31 is the correct answer if you are bloviating.

Step-by-step explanation:

bloviate the factors of x and y.

Answer:

Question (i):

Reduce = 15% of Rs 40 = 0.15 x 40 = Rs 6

Price after reduced = Rs 40 - Rs 6 = Rs 36

Answer: Rs 36

-

Question (ii):

Reduce = 15% x 20.40 = 0.15 x 20.40 = Rs 3.60

Price after reduced = Rs 20.40 - Rs 3.60 = Rs 17.34

Answer: Rs 17.34

-

Answer:

28 - 10 - 15 - 3

=> 18 - 15 - 3

=> 3 - 3

=> 0

Another way:

=> 28 - 10 - 15 - 3

=> 28 - 25 - 3

=> 28 - 28

=> 0

Answer:

[tex]l = 28[/tex]

Step-by-step explanation:

Given

[tex]S = \sum (2k - 3); k = 4\ to\ l[/tex]

Required

What is l when S = 725

This can be solved using Sum of n terms of an AP;

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where

[tex]S_n = 725[/tex]

[tex]T_1 = first\ term[/tex]

To get T1; we substitute 4 for k in 2k - 3

[tex]T_1 = 2 * 4 - 3[/tex]

[tex]T_1 = 8 - 3[/tex]

[tex]T_1 = 5[/tex]

[tex]T_n = last\ term[/tex]

To get Tn; we substitute l for k in 2k - 3

[tex]T_n = 2 * l - 3[/tex]

[tex]T_n = 2l - 3[/tex]

n = the number of terms;

Since k = 4 to l, then

[tex]n = l - 4 +1[/tex]

[tex]n = l - 3[/tex]

Substitute these values in [tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]725 = \frac{l-3}{2}(5 + 2l - 3)[/tex]

Collect Like Terms

[tex]725 = \frac{l-3}{2}(2l + 5- 3)[/tex]

[tex]725 = \frac{l-3}{2}(2l + 2)[/tex]

Open the bracket

[tex]725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2[/tex]

[tex]725 = (l-3) * l + (l-3)[/tex]

[tex]725 = l^2-3l + l-3[/tex]

[tex]725 = l^2-2l -3[/tex]

Subtract 725 from both sides

[tex]725 - 725 = l^2-2l -3 - 725[/tex]

[tex]l^2-2l -3 - 725 = 0[/tex]

[tex]l^2-2l - 728 = 0[/tex]

[tex]l^2 + 26l - 28l - 728 = 0[/tex]

[tex]l(l + 26) - 28(l + 26) = 0[/tex]

[tex](l - 28)(l + 26) = 0[/tex]

[tex]l - 28 = 0[/tex] or [tex]l + 26 = 0[/tex]

[tex]l = 28[/tex] or [tex]l = -26[/tex]

But l must be positive;

Hence, [tex]l = 28[/tex]

Answer:

9:50

Step-by-step explanation:

Given the following information :

First meeting = 4:30

Second meeting = 5:20

Third meeting = 6:30

Fourth meeting = 8:00

Frim careful observation of the meeting times :

Difference between the ;

Second and first meeting:

5:20 - 4:30 = 50 minutes

After that 20 minutes is added to the subsequent meetings as observed from the third and fourth meetings

6:30 - 5:20 = 70 minutes

8:00 - 6:30 = 90 minutes

Therefore, next meeting time :

(90 + 20) minutes = 110 minutes

8:00 + 110 minutes = 9:50

Answer:

6 scarves

Step-by-step explanation:

So we know that 3/4 yd. = 1 (scarf)

We have 4 2/3 material to make the scarves

=> convert to an improper fraction 4 2/3 = 14/3

=> Divide material by needed amt.

=> 14/3 x 4/3 = 56/9

56/9 = 6 2/9

But 6 2/9 is not our answer. Since we need a full amt. of scraves, we round down to our final answer of 6 scarves.

Hope this helps!

Answer:

Number of push up = 8 + 2x

Step-by-step explanation:

Keenan can do 8 push ups each day. He plans to do 2 extra day until he is doing 30 push ups. Each day he does an additional 2 push up, on the first day he does 8 + 2 = 10 push up, on the second day he does 10 + 2 = 12 push ups. This can be represented by the expression:

Number of push up = 8 + 2x

where x is the number of days.

To do 30 push ups, we can calculate the number of days needed:

30 = 8 + 2x

2x = 30 - 8

2x = 22

x = 11

Answer:

8+2x its from khan academy

Step-by-step explanation:

give person above brainliest :)

Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Answer:

the slope of the line x+y = 6 is -1.

Step-by-step explanation:

slope = - coefficient of x

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

coefficient of y

slope = -1 /1

slope = -1

Answer:

A: -1

Step-by-step explanation:

Answer:

The vertex is (3,4)

Step-by-step explanation:

f (x) = x^2 - 6 x + 13

Completing the square

-6/2 = -3 and squaring it = 9

    = x^2 -6x +9 +4

   = ( x-3) ^2 +4

The equation is now in vertex form

a( x-h) ^2 +k

where the vertex is ( h,k)

The vertex is (3,4)

Answer:

C on edge

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

From the question, we are told that:

Time required to drive a fixed distance varies inversely as the Speed

T ∝ 1/S

k = proportionality constant hence,

T =k × 1/S

T = k/S

Step 1

Find k

It takes 2 hr at a speed of 200 km/h to drive a fixed distance

T = 2 hours, S = 200km/h

T = k/S

2 = k / 200

k = 2 × 200

k = 400

Step 2

How long will it take to drive the same distance at a speed of 80 km/h?

S = 80km/h

T = k/S

k = 400

T = 400/80

T = 5

Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr

Answer:

        4hx - 8x - 3h - 4

k  =  ------------------------

                  5

            8x + 5k + 4

h  =  ------------------------

              4x - 3

Step-by-step explanation:

4 (hx - 1) - 3 (x + h) = 5 (x + k)

4hx - 4 - 3 (x + h) = 5 (x + k)

4hx - 4 - 3x - 3h = 5 (x + k)

4hx - 4 - 3x - 3h = 5x + 5k                   add 3h both sides

4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h   simplify

4hx - 4 - 3x = 5x + 5k + 3h                   add 4 both sides

4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4       simplify

4hx - 3x = 5x + 5k + 3h + 4                  subtract 5x from both sides

4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x   simplify

4hx - 8x = 5k + 3h + 4                          

4hx - 8x - 3h - 4 = 5k  

      4hx - 8x - 3h - 4

k  =  ------------------------

                5

solving for h;

4hx - 3h = 8x + 5k + 4

h(4x - 3) = 8x + 5k + 4

          8x + 5k + 4

h  =  ------------------------

            4x - 3

The value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively

Given:

4 (hx - 1) -3 (x +h) ≡ 5 (x + k)

open parenthesis

4hx - 4 - 3x - 3h = 5x + 5k

4hx - 4 - 3x - 3h - 5x - 5k = 0

4hx - 8x - 3h - 5k - 4 = 0

For k

4hx - 8x - 3h - 4 = 5k

[tex]k = (4hx - 8x - 3h - 4) / 5[/tex]

For h

4hx - 8x - 3h - 5k - 4 = 0

4hx - 3h = 8x + 5k + 4

h(4x - 3) = 8x + 5k + 4

[tex]h = (8x + 5k + 4) / (4x - 3)[/tex]

Therefore, the value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively

Read more:

https://brainly.com/question/21406377

Answer:

-3.5

Step-by-step explanation:

The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5

Answer:

[tex]\large\boxed{-3.5}[/tex]

Step-by-step explanation:

(y - z) ÷ z          y = -2 and z = 4/5

Substitute in the given values for y and z into the equation

(y - z) ÷ z  

(-2 - 4/5) ÷ 4/5

Subtract inside the parenthesis (-2 - 4/5)

-2.8 ÷ 4/5

Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)

4/5 = (4 * 20) / (5 * 20) = 80 / 100

80 / 100

Divide numerator and denominator by 10

8/10 = 0.8

Substitute into previous equation

-2.8 ÷ 4/5 = -2.8 ÷ 0.8

Divide

[tex]\large\boxed{-3.5}[/tex]

Hope this helps :)

Answer:

16. 1 miles

Step-by-step explanation:

Using Pythagorean Theorem,

a^2 + b^2 = c^2

Since the road that goes from his home to work directly is c^2...

Plug in the rest of the numbers

16^2 + 2^2 = c^2

256 + 4 = c^2

260 = c^2

The reverse square of 260 is

16. 1 miles

Answer:

The total duration of the trip is 48 hours.

Step-by-step explanation:

Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:

[tex]v =\frac{\Delta s}{\Delta t}[/tex]

Where:

[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.

[tex]\Delta t[/tex] - Time, measured in hours.

[tex]v[/tex] - Speed, measured in kilometers per hour.

Now, each stage is represented by the following expressions:

Outbound trip

[tex]v = \frac{700\,km}{\Delta t}[/tex]

Return trip

[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]

By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:

[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]

[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]

[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]

[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]

This equation can be solved by means of the Quadratic Formula, whose roots are presented below:

[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]

Only the first roots offers a physically resonable solution. Then, total duration of the trip is:

[tex]t_{T} = 28\,h +20\,h[/tex]

[tex]t_{T} = 48\,h[/tex]

The total duration of the trip is 48 hours.

Answer:

122

Step-by-step explanation:

5!=5 x 4 x 3 x 2 x 1 = 120

2!=2 x 1 = 2

120+2=122

Answer: -10 points

Step-by-step explanation:

She lost 110,so that loss -the gain(100) is the total score at the end of three games

Answer:

v = -54

Step-by-step explanation:

27= -v/2

Multiply each side by -2

27 *-2= -v/2 *-2

-54 = v

Answer:

-54

Step-by-step explanation:

[tex]27=\frac{-v}{2}[/tex] .... Equation to start with

[tex]27 x 2= \frac{-v}{2} x2[/tex] ..... Cancelling out the denominator and multiplying on the other side

[tex]54 = -v[/tex] .... Multipling

[tex]-54 =v[/tex] ..... Solving for v, not -v, so bring the negative over to the other side

Hope you understood:)

Answer:

31° change

Step-by-step explanation:

If we want to find the change between two numbers, we need to imagine it like a number line.

<-------------0------------->

Let's plot -7 and 24 on this number line.

<----------[tex]-7[/tex]--0------------24>

If we want to get from -7 to 0, we increase by 7. To get from 0 to 24, we increase by 24.

So the total change is [tex]7 + 24 = 31[/tex].

Hope this helped!

Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

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

Explanation:

Refer to the diagram below.

In order for triangle TOP to be isosceles, the missing side x must be either 5 or 7. This way we have exactly two sides that are the same length.

--------

If TP = 5, then the value of y could be either 5 or 11 to ensure that triangle TIP has exactly two sides the same length.

If TP = 7, then y = 7 or y = 11 for similar reasons.

--------

Therefore, the possible lengths for segment TO are 5, 7, and 11.

Answer:

7, 11

Step-by-step explanation:

its right- trust me-

Answer:

A.  [tex]Claire = 20250[/tex]

B.   [tex]Richard = 9350[/tex]

C.    Height = 3.2 feet

D. Charges = $760

Step-by-step explanation:

Given

[tex]Claire = 50x^2 + 250[/tex]

[tex]Richard = 40x^2 + 350[/tex]

Solving (a): Claire's 20ft charges

In this case, x = 20

Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(20)^2 + 250[/tex]

[tex]Claire = 50(400) + 250[/tex]

[tex]Claire = 20000 + 250[/tex]

[tex]Claire = 20250[/tex]

Solving (b): Richard's 15ft charges

In this case, x = 15

Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(15)^2 + 350[/tex]

[tex]Richard = 40(225) + 350[/tex]

[tex]Richard = 9000 + 350[/tex]

[tex]Richard = 9350[/tex]

Solving (c): Height which they both charge the same;

This implies that

[tex]50x^2 + 250 = 40x^2 + 350[/tex]

Solving for x [Collect Like Terms\

[tex]50x^2 - 40x^2 = 350 - 250[/tex]

[tex]10x^2 = 100[/tex]

Divide both sides by 10

[tex]x^2 = 10[/tex]

Take square roots of both sides

[tex]x = \sqrt{10}[/tex]

[tex]x = 3.2ft[/tex]  (Approximated)

Hence; Height = 3.2 feet

Solving (d): How much they charge when the charge the same amount.

Substitute 3.2 for x in any of the given equation

[tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(3.2)^2 + 250[/tex]

[tex]Claire = 50*10.24 + 250[/tex]

[tex]Claire = 512 + 250[/tex]

[tex]Claire = 762[/tex]

[tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(3.2)^2 + 350[/tex]

[tex]Richard = 40 * 10.24 + 350[/tex]

[tex]Richard = 409.6 + 350[/tex]

[tex]Richard = 759.6[/tex]

The reason for the difference is due to approximation

Hence, they both charge approximately 760

Answer:

The answer is below

Step-by-step explanation:

From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³

While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25

The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

Volume of the flask = The volume of the cylinder  + The volume of the sphere = 2.36 + 47.71 = 50.07 in³

If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025

The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

New Volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125

The resulting volume would be 0.125 times the original volume

Answer:

50.07 and 8 times

Step-by-step explanation:

1) Calculate volume of each figure using according formulas.

You should get:

Sphere: 47.71in^3

Cylinder: 2.36in^3

Now let's add, and you should get 50.07.

2) Let's dilate the dimensions/flask by 2 (multiply by 2)

4.5 * 2 = 9

1 * 2 = 2

3 * 2 = 6

Now with these dimensions you should get:

Sphere: 381.7in^3

Cylinder: 18.85in^3

This should add up to 400.55in^3

Divide new by original. 400.55 / 50.07 = 8

So it is 8 times larger.  

Answer:

-3

Step-by-step explanation:

-7+4=-3

The absolute value of -3 is 3

The negative sign in front of the absolute value bracket makes it -3

Hi there! :)

Answer:

[tex]\huge\boxed{x = 3}[/tex]

Given the equation:

[tex]3(11)^{x} = 3993[/tex]

Divide both sides by 3:

[tex](11)^{x} = 1331[/tex]

Rewrite both sides of the equation with a base of 11.

[tex]1331 = 11^{3}[/tex], therefore:

[tex](11)^{x} = 11^{3}[/tex]

x = 3.

Answer:

121

Step-by-step explanation:

121 x 33 = 3993