Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.

hope it will be helpful.......

Answer:

Step-by-step explanation:

160 = 2 × 2 × 2 × 2 × 2 × 5

Hope this helps

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The number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

A prime number factor is any prime number that can be multiplied by the original number to get the factor.

The prime factors of the numbers will be:-

160 = 2 × 2 × 2 × 2 × 2 × 5

Therefore, the number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5.

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Answer:  proof below

Step-by-step explanation:

Use the Difference formula for sin:

  sin (A - B) = sin(A)·cos(B) - cos(A)·sin(B)

sin (180° - θ) = sin(180°)·cos(θ) - cos(180°)·sin(θ)

                    =       0  · cos(θ)    -      -1  · sin(θ)

                    =              0           -           -sin(θ)

                    =                         + sin(θ)

sin (180° - θ) = sin(θ)  [tex]\checkmark[/tex]

I’m guessing number 32 is true, since it asks you to round to the nearest integer.

To solve this problem, use the Pythagorean Theorem, which is a^2 + b^2 = c^2, where c is the hypotenuse. The hypotenuse of the triangle is always the longest side, meaning the hypotenuse would be 15.23.

To ensure these measurements can be used in order to make a right triangle, substitute the numbers into the Pythagorean Theorem.

6^2 + 14^2 = 15.23^2.

36 + 196 = 231.9529

232 = 231.9529

Because we were asked to round, that makes the equation 232 = 232, meaning the answer is true.

Answer: 2077

There are 31 terms.

S₃₁ = 31(a₁+a₃₁)/2 = 31(7+127)/2 = 2077

Answer:

Correct option: E

Step-by-step explanation:

The group must have 1 man and 1 woman.

So, for the woman slot, we have 4 possible choices, because we have 4 women and 1 slot to occupy.

For the man slot, we have 2 possible choices, because we have 2 men and 1 slot to occupy.

So the number of different groups we can make is the product of the number of possibilities for each slot:

Number of groups = 4 * 2 = 8

Correct option: E

Answer:

120°

Step-by-step explanation:

all exterior angles of any polygon add up to 360 therefore 4 x 60 = 240

360 - 240 = 120

The measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have:

If four of the exterior angles of a convex pentagon measure 60°

The sum of the total interior angles = 360

The sum of the four of exterior angles = 4(60) = 240 degrees

The measure of the fifth exterior angle = 360 - 240 = 120 degrees

Thus, the measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.

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Answer:

Area of rectangle = H × B

Area of rectangle = 10(H)

Step-by-step explanation:

Given:

Base (B) = 10

Height = H

Find:

Area of rectangle

Computation:

Area of rectangle = Height × Base

Area of rectangle = H × B

So,

Area of rectangle = H × B              [Base (B) = 10]

⇒ Area of rectangle = H × 10

⇒ Area of rectangle = 10(H)

Answer:

The expression that represents the area of this rectangle is 8b

When b = 10, the area of the rectangle is 80 square units.

Step-by-step explanation:

The rectangle’s base is b units, and its height is 8 units. The area of the rectangle is the product of its base and height, which is 8b.

To find the area of the rectangle when b = 10, substitute 10 for b in the expression:

8b= 8(10)

    =80

Answer:

  120

Step-by-step explanation:

n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.

n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.

The least common multiple of 6 and 40 is 120.

The smallest positive integer n is 120.

_____

Check

120^2/18 = 800

120^3/640 = 2700

Answer:

solution,

[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]

Use negative power rule:

[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]

[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]

Simplify:

[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]

Use this rule:

[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]

[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]

Since, 4*4=16 ,the square root of 16 is 4

[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]

Simplify:

[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The average speed for his journey from York to Blackpool is 61.4 KM/H

Step-by-step explanation:

Answer:

x = 1/9

Step-by-step explanation:

8x + 2 = 3 - x

Add x to both sides.

9x + 2 = 3

Subtract 2 from both sides.

9x = 1

Divide both sides by 9.

x = 1/9

Answer:

x = 1/9

Step-by-step explanation:

We are given the equation:

8x + 2 = 3 - x

In order to solve for the variable x, we need to isolate it; in other words, we need to combine all the x terms and move everything else to the other side.

First, add x to both sides:

8x + x + 2 = 3

9x + 2 = 3

Now subtract 2 from both sides:

9x = 3 - 2 = 1

Divide both sides by 9:

x = 1/9

The answer is thus 1/9.

~ an aesthetics lover

Answer:

$42.88

Step-by-step explanation:

Let's create a proportion using the following setup:

cost/pounds=cost/pounds

We know that it costs $20.42 for a 10 pound turkey.

$20.42/10 pounds= cost/pounds

We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.

$20.42/ 10 pounds= $x/ 21 pounds

20.42/10=x/21

We want to find x, by getting x by itself.

x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.

21*(20.42/10)=(x/21)*21

21* 20.42/10=x

21*2.042=x

42.882=x

Round to the nearest cent, or hundredth.

42.88=x

x= $42.88

A 21 pound turkey costs $42.88

Answer:

Step-by-step explanation:

The number of sets that can be generated from the given set is determined by calculating the power of the set. Power of a set is expressed as 2ⁿ where:

n represents the number of elements in the set.

Given the set S = {0,1,2,3,4,5,6,7,8,9}.

n(S) = 10

The Power of the set = 2^n(S)

Power of the set = 2^10 = 1,024

This means that 1,024 different sets can be formed from the given set including the empty set.

Answer:

39600

Step-by-step explanation:

8! - 3!(5!)

Evaluate.

40320 - 6(120)

40320 - 720

= 39600

Answer: 39600

Step-by-step explanation:

8!=40320

3!=6

5!=120

40320 - 6(120)

120*6=720

40320 - 720

= 39600

Answer: y = (5)(2)x-10

Step-by-step explanation:

Answer:

561

Step-by-step explanation:

an = dn - (a-d)

The difference is 3.

The first term is 12.

an = 3n - (12-3)

an = 3n - 9

Put n as 1, 2, 3, 4, 5 ....22.

3(1) - 9 = -6

3(2) - 9 = -3

3(3) - 9 = 0

3(4) - 9 = 3

3(5) - 9 = 6

...

3(22) - 9 = 57

Add the first 22 terms.

-6+-3+0+3+6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57

= 561

Answer:

C

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given (h, k ) = (5, - 3 ), then

y = a(x - 5)² - 3 and with a = - 3, then

y = - 3(x - 5)² - 3 ← is a possible equation

Answer:

2

Step-by-step explanation:

The question, is basically asking for the order of rotational symmetry for the parallelogram. This is 2, which means while spinning the parallelogram around its centre point 360 degrees, it looks exactly the same, or matches with its original at 2 points

Answer: hope this helps

Step-by-step explanation:

7kg of nuts = £10

350g nuts into bags= 75p

convert 7kg into g which is 7000g

then do 7000 divide by 350 which is 20

so then you do 0.75 times 20 which is £15.00

so your answer is £15.00 hope it helps

Answer:

10 inches

Step-by-step explanation:

Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?

Hence, L1/L2 = W1/W2

∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches

Answer:

Terri’s speed can be calculated like this:

her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

An experimental probability is the number of times an event occurred when actually attempted.

So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:

60-50 = 10.

So, the probability of picking a painted ball = 10/60 = 1/6

Hope this helps

Answer:

false

Step-by-step explanation:

the constant term is 3 not 8

hope this helps

Answer:

-9 + 4 = 4 - 9 = -5

-5 + 8 = 8 - 5 = 3

3 is the answer

Step-by-step explanation:

8+[4+(-9)]

-9 + 4 = 4 - 9 = -5

-5 + 8 = 8 - 5 = 3

3 is the final answer.

Answer:

The cost of a loaf of bread in 1983 to the nearest cent is  $0.89  

Step-by-step explanation:

The cost of the loaf of bread in 1983 can be computed using the below formula:

cost of a loaf of bread in 1983=$2.89/current CPI *100

cost of a loaf of bread in 1983=$2.89/323*100=$ 0.89  

It is obvious that the cost of a loaf of bread in the year 1983 is $0.89  

Answer:

£60

Step-by-step explanation:

Let the original cost be x.

x × (1 - 20%) = 48

0.8x = 48

x = 48/0.8

x = 60

The original cost was £60 before the sale.

Answer:

£57.60

Step-by-step explanation:

find 20% of £48, which is £9.60

then add that to £48, which will give you the answer of £57.60

Answer:

a. -5 + 3x = -41

3x = -36

x = -12

b. 7x - 4 = -2x + 11

9x = 15

x = 15/9 = 1 and 2/3

c. (-4x) / 5 = 8

-4x = 40

x = -10

d. x / 3 - 1/2 = 1/4

4x - 6 = 3 (multiply by lcm of 3, 2 and 4 which is 12)

4x = 9

x = 9/4 = 2 and 1 / 4

e. -4(6x + 1) + 3 = 11 + 2(x + 2)

-24x - 4 + 3 = 11 + 2x + 4

-24x - 1 = 2x + 15

-26x = 16

x = -8/13