Prove that the value of the expression: (3^5 - 3^4)(3^3 + 3^2) is divisible by 24. Answer format: The value of the expression is 24 • __

Answers

Answer 1

Step-by-step explanation:

(3^5 - 3^4) (3^3 + 3^2)

= (243 - 81) (27 + 9)

= (162) (36)

= 5832

24 = 8*3

since 832 is divisible by 8 and 5+8+3+2 = 18 is divisible by 3

5832 is therefore divisible by 24

check:

5832/24 = 243


Related Questions

Help,anyone can help me do quetion,I will mark brainlest.​

Answers

Answer:

Area of a triangle=1/2×base x height

Let y represent the height

50cm²=1/2×20cm×y

50cm²=10cm×y

50cm²/10cm=10cm×y/10cm

5cm=y

therefore the height of the triangle is 5cm

Area of a trapezoid=1/2×a+b×height

let h represent the height

42cm²=(1/2×14cm+7cm)×h

42cm²=1/2×21cm×h

42cm²=21cm×h/2

42cm²×2=21cm×h(cross multiply)

84cm²=21cmh

84cm²/21cm=21cmh/21cm

4cm=h

Therefore the height is 4cm

The graph below have the same shape. What is the equation of the graph?

Answers

Answer:

C

Step-by-step explanation:

The graph has been translated down 4 units and moved to the right 2 units

so correct answer is C (x-2)^2-4.

Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4.
What is the average rate of change?

Answers

Answer:

5

Step-by-step explanation:

You divide the change in the output value by the change in the input value.

  Input: 0 |  4

Output: 1  |  21

20/4= 5

How do I find the m and b from number 1 and what would the area be for 2

Answers

Hopefully that’s right, sorry if it’s not

Answer:

Step-by-step explanation:

compare with y=mx+b

m=-1

b=4

(b)

area of triangle=1/2×4×4=8 square units.

A car is sold for $7560 at a loss of 10%. What is the original cost of the car?

Answers

Answer:

car(c.p)=$8400

Step-by-step explanation:

L%=(c.p-s.p)100%

c.p

10%=(c.p-7560)100%

c.p

10c.p=100c.p-756,000

(10-100)c.p= -756,000

-90c.p= -756,000

-90 -90

c.p=8400

lines b and c are parallel. no links.

Answers

Answer:

Value of x:

[tex]{ \tt{(13x + 9) + (5x + 9) = 180 \degree}} \\ { \tt{18x + 18 = 180 }} \\ { \tt{18x = 162}} \\ { \tt{x = 9}} \\ [/tex]

Angle m‹6:

[tex]{ \boxed{ \tt{m \angle6 = (5x + 9) \degree}}} \\ { \tt{m \angle6 = (5 \times 9) + 9}} \\ { \tt{m \angle6 = 54 \degree}}[/tex]

Answer:

B. 54 degrees

Step-by-step explanation:

Set up an equation that equals 180 degrees because a line is 180 degrees:

(13x+9)+(5x+9)=180

Solve for x:

x=9

Substitute 9 in 5x+9:

5(9)+9

Solve.

54

Since angle 6 is complementary, it is the same as the 7th angle.

So the answer is B, 54 degrees.

Hope this helps!

which of the following numbers has the least number of positive divisors if a=50^(100) . choose: 1)25a 2)4a 3)3a 4)26a 5)10a​

Answers

Answer:

the answer would have to be B

Step-by-step explanation:

Write 48596 in standard form​

Answers

Answer:

forty-eight-thousand five-hundred and ninety-six

Real number: 48596
Standard form: 48596X10^4

help I need help with my homework no link please BTW its 9th grade work I need help with number 1 a) I still need help with it​

Answers

Answer:

you need to learn how to "prime factor" numbers....

primes are 2,3,5,7,11,13,17....

they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.

take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...

15 = 3 * 5

24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6

thus   [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex]  now just cancel all the SAME numbers from to to bottom

"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top

result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]

~~~~~~~~~~~~~~~~~~~~

[tex]\frac{21}{35}[/tex]

21= 3 * 7

35= 5* 7

[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]

Step-by-step explanation:

How do you work out the volume of a cube

Answers

Answer:

V=a cubed

Step-by-step explanation:

in need help
Relationships in Triangles

Answers

Answer: x = 17

Step-by-step explanation: Since ray SQ bisects <TSR, we know

that the m<TSQ ≅ m<QSR by the definition of an angle bisector.

So we can setup the equation (3x - 9) + (3x - 9) = 84

using the angle addition postulate.

Simplifying on the left gives us 6x - 18 = 84.

Now add 18 to both sides to get 6x = 102.

Now divide both sides by 6 so x = 17.

I hate this, I’m not sure how to do these

Answers

Answer:its B....sorry i didnt read the qn properly earlier

Answer:

tanθ = 9/40

Step-by-step explanation:

Which graph below shows the solutions for the linear inequality v2-3x+1?
A
B
10, 1)
(0.1)
с
D
10.1)
16,-1)
16,-1)

Answers

Answer:

A. Graph D

Step-by-step explanation:

y >= -1/3x + 1

this means all the y values that are bigger (= above) than the line definition.

and because it says ">=", the line is included.

Refer to pictures above

Answers

Answer:

6.9

Step-by-step explanation:

Cos ∆ = Adjacent/Hypotenuse

therefore x=12Cos55°

=6.88

=6.9 to the nearest tenth

Four graphs are shown below:

Scatter plot A shown with data points that move in an upward direction and are located at 1 and 0.3, 2 and 1, 3 and 2, 4.1 and 4, 5.2 and 6.1, 5.9 and 9.5. Additional points are located at 4.6 and 5, 5.8 and 7.4, 5.2 and 7.1. Scatter plot B is shown with data points that move in an upward direction and are located at 1 and 3, 2 and 4, 3 and 5, 4 and 6, 5 and 6, 6, and 7, 7 and 8, 8 and 9. Scatter plot C is shown with data points that move in a downward direction and are located at 1 and 8.7, 4 and 5.6, 5 and 4.3, and 6 and 0.5. Additional points are located at 5.9 and 1.5, 5.5 and 3.5. Scatter plot D is shown with data points that move in a downward direction and are located at 0 and 7, 1 and 6, 2, and 5, 3 and 4, 4 and 3, 5 and 4, 6, and 5.

Which graph represents a negative linear association between x and y?

Graph A
Graph B
Graph C
Graph D

Answers

Answer:

graph D

Step-by-step explanation:

because d it at 0 then moves

Answer:

a

Step-by-step explanation:

parallel to y - 2x = 4 and passes through (0,5)

Answers

Answer:

y=2x+5

Step-by-step explanation:

y=2x+4 means that the slope is m1=2

A parallel line shall have the same slope so

m2=m1=2

Therefore, the equation of the new line will be

y=2x+q

where q is the y-intercept, that is 5 because the line must pass in (0,5), so

q=5

and

y=2x+5

PLEASE HELP! Use the substitution method to solve the system of equations.

A. (-30,11)

B. (5,-3)

C. (10,-5)

D. (0,1)

Answers

Hello,

[tex]\left\{\begin{array}{ccc}2x+5y&=&-5\\x+3y&=&3\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\6-6y+5y&=&-5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\y&=&11\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&-30\\y&=&11\\\end{array}\right.\\\\[/tex]

Answer A

Can someone help me with this

Answers

Answer:

a = 17

c = 9

Step-by-step explanation:

2a + 3c = 61

3a + 5c = 96

3a = 96 - 5c   (solve for 'a'. Then you can substitute)  

a = 32 - [tex]\frac{5}{3}[/tex] c

2(32 - [tex]\frac{5}{3}[/tex]c) + 3c = 61     (Substitute)

64 - [tex]\frac{10}{3}[/tex]c + 3c = 61        ([tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]. So subtracting, adding a negative, leaves [tex]\frac{-1}{3}[/tex])

-[tex]\frac{1}{3}[/tex] c= -3  

c = 9

2a + 3(9) = 61

2a + 27 = 61

2a = 34

a = 17

What is the scale factor from abc to xyz?

Answers

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

What is a scale factor?

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

To know more about scale factors follow

https://brainly.com/question/25722260

#SPJ2

Evaluate –3 2nd power + (2 – 6)(10).

Answers

Answer:

-49

Step-by-step explanation:

-3^2=-9

(2-6)*10=-40

(-9) + (-40) = -49

-31
9 + (-4) (10)
9+ (-40)
-31

If a class has a total of 3400 points I can earn how many points would I need to get in total to get at least a 90?

Answers

hi wassup yo k bye daddy

Answer:

are you asking how many points are needed to get 90% in

a class that has a total of 3400 points ?

id so that is : 3060

Step-by-step explanation:

Drag each shape to the correct category. Identify which shapes are similar to shape A and which are not.

Answers

I need to see the photo

Find the measure of the indicated angle.

Answers

2x + 40 = 180

2x = 140

x= 70

answer is 70

represent the following additions on a number line 3+5=8 3+(-5)

















Answers

Answer:

8 &-2

Step-by-step explanation:

<-------------------------->

-2-1 0 1 2 3 4 5 6 7 8

________________

-2<8 and 8>-2

Find the value of the following​

Answers

Answer:

110.01 (aprox)

Step-by-step explanation:

x + (1/x) = 5

x(x + (1/x)) = x(5)

x*x + x*1/x = 5x

x² + 1 = 5x

x² - 5x + 1 = 0

x = {-(-5)±√((-5²) -(4*1*1))} / (2*1)

x = {5±√(25-4)} / 2

x = {5±√21} / 2

x = {5±4.5826} / 2

x₁ = {5-4.5826} / 2 = 0.4174/2 = 0.2087

x₂ = {5+4.5826) / 2 = 9.5826/2 = 4.7913

Comprobación:

x₁

0.2087 + 1/0.2087 = 5

0.2087 +  4.7913 = 5

x₂

4.7913 + 1/4.7913 = 5

4.7913 + 0.2087 = 5

Respuesta:

x₁

(0.2087)³ + 1/(0.2087)³ = 0.0091 + 1/0.0091 = 0.0091 + 110.0101 = 110.019

x₂

(4.7913)³ + 1(4.7913)³ = 110 + 1/110 = 110 + 0.01 = 110.01

Robert took 8 minutes to complete his 12 worksheets. What is his unit rate of completing worksheets

Answers

Answer: 40 seconds per worksheet

Step-by-step explanation:

From the information given in the question, we are informed that Robert took 8 minutes to complete his 12 worksheets.

Based on this, his unit rate of completing worksheets will be given as:

= 8 minutes / 12

= 480 seconds / 12

= 40 seconds per worksheet

Note 1 minute = 60 seconds

8 minutes = 8 × 60 = 480 seconds

0.2(x + 20) – 3 > –7 – 6.2x

Answers

Answer:

x > - 1.25

Step-by-step explanation:

0.2(x + 20) – 3 > –7 – 6.2x

0.2x + 4 - 3 > - 7 - 6.2x

0.2x + 1 > - 7 - 6.2x

Collect like terms

0.2x + 6.2x > -7 - 1

6.4x > -8

x > - 8/6.4

x > - 1.25

Note:

The > didn't change because you didn't divide by a negative value

Inequality signs changes when divided by a negative value

Answer:

Step-by-step explanation:

-1.25

If EF = 117 , FG = 100, EG = 94, IJ = 40 , and HJ = 37.6 , find the perimeter of HIJ. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answers

Answer:

124.4

Step-by-step explanation:

Perimeter of ∆HIJ = IJ + HJ + HI

IJ = 40

HJ = 37.6

HI = ?

Let's find HI

∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.

Thus:

EF/HI = FG/IJ

EF = 117 (given)

HI = ?

FG = 100 (given)

IJ = 40 (given)

Plug in the values

117/HI = 100/40

117/HI = 2.5

117 = HI*2.5

117/2.5 = HI

HI = 46.8

✔️Perimeter of ∆HIJ = IJ + HJ + HI

= 40 + 37.6 + 46.8

= 124.4

(6x-5)/7-(2x-1)/3=2?

Answers

x=25/2 or 12.5 hope this helps!

Work out the area of the shaded shape.

Answers

Answer:

65 m²

Step-by-step explanation:

Area 1 :-

A = 3m * 9m A = 27 m²

Area 2 :-

A = (12-3-2) m * (9 - 5) m A = 7m * 4 mA = 28 m²

Area 3 :-

Area = 2m * 5 m A = 10 m²

Total Area :-

A = ( 27 + 28 + 10 ) m²A = 65 m²
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