❗️10 points❗️
5. simplify the expression.
pleasseee

Answer:

The expression a^b

means that we multiplicate the number a by itself b times.

So x^2 means that we multiplicate the number x by itself 2 times:

x^2 = x*x

and 2^x means that we multiplicate the number 2 by itself x times

2^x = 2*2*2*....*2 (if you count them, you should see x times the number 2)

for example, if x = 4, we will have

2^4 = 2*2*2*2

Answer:

The last choice:   log 25  Over  log 8

Step-by-step explanation:

Because the change of base formula says:

log (subscript 8)  of 25  =    log (25)  /  log (8)

let  log be the Common Log  without subscripts

The change of base formula used by Devonte to approximate the logarithm expression log₈ 25 is log 25 / log 8.

Using logarithm theorem,

logₐ b = logₓ b / logₓ a

Therefore,

log₈ 25  can be express as follows;

Recall that the natural base is base 10

Therefore,

log₈ 25  =  log 25 / log 8.

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Answer:

boii put the diagram then put the question

Step-by-step explanation:

Answer:

21 square inches

Step-by-step explanation:

Given: The  length of a gift shop was 12 yards and the width was 7 yards. 25% of the gift shop will be dedicated to the cashier and employees.

To find: area dedicated to just the employees and cashier

Solution:

Length of a gift shop (rectangle) = 12 yards

Breadth of a gift shop (rectangle) = 7 yards

Area of a gift shop (rectangle) = Length × Breadth = 12 × 7 = 84 square inches

Area dedicated to the employees and cashier = 25% of the gift shop

=[tex]\frac{25}{100}(84)=21[/tex]  square inches.

The problem involves using trigonometry to find the height of a mast given the hypotenuse of a right-angled triangle and an angle. The sine function is used in this case, providing an approximate mast height of 30 meters.

This question involves the application of trigonometry. The wires form right-angled triangles with the mast and the ground, and the measure provided, 57m, is the hypotenuse of these triangles. The question asks for the height of the mast (opposite side) and the angle provided is 32° with the horizontal.

To solve this, the function of sine can be used, where the sine of an angle is equal to the opposite/hypotenuse. This can be rearranged to the formula: Opposite (height of the mast) = Hypotenuse * Sin(angle).

Therefore, the height of the mast =  57 meters * sin(32°) = 29.96 meters, approximately 30 meters mast height.

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Final answer:

Using the tangent function with the given angle of 32 degrees and the distance from the base of the mast to the attachment points of the wires (57 metres), the height of the mast is calculated to be approximately 35.64 metres.

Explanation:

To find the height of the mast, we can use trigonometry, specifically the tangent function, because we have an angle and the opposite side, which in this case is the distance from the ground to the point where the wire is attached to the mast. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side (tan(θ) = opposite/adjacent).

In this scenario, we have the angle (32°) and the adjacent side (57 metres), and we want to find the opposite side, which is the height of the mast. The formula we will use is:

height = adjacent × tan(angle)

Let's put the values we know into this formula:

height = 57 × tan(32°)

To calculate the height, you will need a calculator that can compute the tangent of an angle. The height will then be found as follows:

height = 57 × 0.6249 (tan(32°))

height = 35.6393 metres, which can be rounded to 35.64 metres.

The mast is therefore approximately 35.64 metres tall.

Answer:

65 cm =? m

1m =100cm

1cm=1/100m

65cm=65/100m

65cm =0.65m

Answer:

9 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Equating to 1260 gives

180° (n - 2) = 1260 ( divide both sides by 180 )

n - 2 = 7 ( add 2 to both sides )

n = 9

Thus a polygon with 9 sides

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain. The correct option is C.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of all the interior angles of an 'n' sided polygon is given by the formula,

Sum of all the interior angles = (n-2) × 180°

Given that the sum of the interior angle is 1260°. Therefore, the number of sides n can be calculated as,

1260° = (n-2) × 180°

7 = n - 2

n = 7 + 2

n = 9

Hence, the number of sides the given polygon has is 9.

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Answer: 6+(-15)

Step-by-step explanation:

6+(-15) = -9

Answer:

6+(-15)

Step-by-step explanation:

:)

Answer:

The polynomial is irreducible.

Step-by-step explanation:

The polynomial 3p²-15pq+20q² can be factored as (p-2q)(3p-10q).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

The polynomial is given as follows:

3p²-15pq+20q²

It is required to find the factorization of the given polynomial.

The greatest common factor (GCF) of the coefficients (3, -15, 20), is 3.

Rewrite the polynomial using the GCF of 3. We get:

3(p²-5pq+6q²)

We need to find two numbers that multiply to 6q² and add to -5pq.

The numbers are -2q and -3p.

Combine the factored quadratic expression with the GCF of 3.

3(p-2q)(p-3q)

Therefore, the correct factorization of the polynomial 3p²-15pq+20q² is 3(p-2q)(p-3q).

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Answer:

24

Step-by-step explanation:

Answer:

probably 27 H

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

[tex]\frac{-3}{4}\div\frac{2}{-8}=[/tex]

[tex]\frac{-3}{4}\times \frac{-8}{2}=[/tex]

[tex]\frac{-3\cdot -8}{4\cdot 2}=[/tex]

[tex]\frac{24}{8}=[/tex]

[tex]\boxed{3}[/tex]

Hope this helps!

Answer:

C. 5/12 = 2/x

Step-by-step explanation:

There's no explanation, you have to study the proportion

Answer:

Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.

Step-by-step explanation:

The department store was adding sales tax to the bill. Sales tax is a tax on goods and services purchased and is normally a certain percentage added to the buyer's cost.

Solution: 2.36 ÷ $32.00 = 0.0735. Sales tax was charged by the department store at a rate of 7.375%.

Answer: Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.

Sales tax rates vary from state to state. Retail sales tax rates are set by the individual states in the United States and vary from 0 to 9% of the sales price. Sales tax is usually the responsibility of the merchant to collect and submit to the state, and stated separately (or implicitly added at the time of the sale) to consumers.

The additional amount Mr. Smith paid is tax.

The amount was determined by calculating 7.4% of the items bought.

Mr Smith. should pay $34.36.

Tax is an amount of money levied by the government or an agency of the government on certain goods and services. Taxes increases the price of a good or service.

In order to determine the tax paid, divide the additional amount paid by the total cost of items purchased.

(2.36 / $32) x 100 = 7.4%

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Answer:

multiply the value of x by 8

Answer: r = 18 ft

Step-by-step explanation: To get the radius, divide 36ft by 2.

The radius of the circle is 18 ft.

A circle is a round shape that has all points in the plane equidistant from a single point known as Center.

The diameter is a line segment which has one end on the circumference of the circle and passes through the center connecting to the second point of the circle on its circumference.

Radius =  Diameter /2

It is given in the question that

diameter of circle = 36ft

Radius = ?

Radius = 36/2

Radius = 18ft

Therefore the radius of the circle is 18 ft.

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Answer:

80% of the students would vote for Tammy.

Step-by-step explanation:

To find Kimberly's best estimate, we need to use the sample the surveyed.

From the sample of 30 students, 24 said that they would vote for Tammy, so to generalize this sample, we need to find the percentage of students in the sample that would vote for Tammy:

Percentage = 24 / 30 = 0.8 = 80%

So the best estimate Kimberly can make is that 80% of the students would vote for Tammy.

Answer:

a. 1007.27

b. 2895.29

c. 2714.34

d. 111.84

Step-by-step explanation:

Answer:

789 Siberian tigers

Step-by-step explanation:

2030 = 40 years after 1990, so...

215 * e^(.0325*40) =

215 * e^1.3 =

788.89878405, which is approx. 789

Step-by-step explanation:

Putting value of y

6x + 8(-5) = - 22

6x - 40 = - 22

6x = - 22 + 40

6x = 18

x = 18 / 6

x = 3

Answer:

answer is 2:3

Step-by-step explanation:

i solved it including a calculator

Answer:

0.45 second

Step-by-step explanation:

The number of seconds it takes a dropped object to fall d feet on Earth is given as:

E(d)=0.25√d

the number of seconds it takes a dropped object to fall d feet on the sun is given as:

S(d)=0.2⋅E(d)

Therefore

S(d)=0.2 × 0.25√d = 0.05√d

Given that it take a dropped object to fall 80 feet on the sun (i.e d = 80 feet), to calculate the time in seconds we use:

S(d) = 0.05√d

S(d) = 0.05 × √80 = 0.05 × 8.944 ≈ 0.45 s

It takes 0.45 second for a dropped object to fall 80 feet on the sun

Answer:

x = [tex]\frac{-1}{3}[/tex]

Step-by-step explanation:

The bold side will be the "first side" and the italics will be the "second side."

3x + 2x + 7 = 8x + 8

First, you add the variables from the first side of the equal sign together.

3x + 2x = 5

Now the equation becomes: 5x + 7 = 8x + 8

Then you're going to take the 7 from the first side and subtract it from the 8 on the second side.

8 / 5 x + 1

8-7 = 1

Now the equation becomes: 5x = 8x + 1

Subtract 8x from both sides

-3x = 1

Divide both sides by -3

x = [tex]\frac{-1}{3}[/tex]

Answer:

use the area of a rectangle to calculate for the total area of the rectangular grass plot

area = length × width

Step-by-step explanation:

The grass plot in Nathan's backyard has a rectangular shape. The dimensions of the sides are in meters . The width and the length are in metres . Since the grass plot is rectangular , the area of the plot can be computed using the formula for area of a rectangle.

Area of a rectangle = L × W

where

L = length

W = width

The area of a rectangle is the width multiplied by the length. For example if the width of the grass plot is 100 meters and the length is 200 meters .The area of the grass rectangular plot will be

area = L × W

area = 200 × 100

area = 20000 m²

The unit of the area will be in square meters (m²)

Answer:

the correct answer is B on edge

Step-by-step explanation:

Answer:

x+4

Step-by-step explanation:

x² + 8x² +16 = x² + 2*4x +4² = (x+4)²

Area of a square = side²

So, the length of  one side of the given square is (x+4).

The expression that represent the length of one side of the square is x+4.

Since the equation is

[tex]= x^2 + 8x^2 +16[/tex]

So, we can write as the

[tex]= x^2 + 2\times 4x +4^2 \\\\= (x+4)^2[/tex]

Now we know that

Area of a square = side²

hence, we can say that  the expression that represent the length of one side of the square is x+4.

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Answer:

m > - 6

Step-by-step explanation:

Given

5 - 3m < 23 ( subtract 5 from both sides )

- 3m < 18

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

m > - 6

Answer:

4 ounces.

Step-by-step explanation:

There is 16 ounces in a pound.

1/4 ounces means there is one pound that was cut into 4 pieces and you want to find how many ounces is in one of those pieces.

Since the pound is divided into 4 pieces, we have to do the same with the 16 ounces in that one pound.

16 ounces divided by 4 is 4 ounces.

1/4 of a pound converted into ounces is 4 ounces.

I hope this helped you! :)