A question on an exponents and logarithms sheet that I need help with

When multiple of the same number are multiplied together, this can be represented as an exponent. An exponent is a way to write repeated multiplication of a number by itself. In your case, 7 multiplied by itself 3 times (7*7*7) can be written using exponents as 7^3.

In mathematics, when you multiply the same number multiple times, you can express that multiplication as an exponent. An exponent tells you how many times to multiply the number, or the base, by itself. For example, in your question, the number 7 is multiplied by itself 3 times (7*7*7), so this multiplication can also be written with exponents. The correct way to express this multiplication using exponents is 73.

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Answer:

The value of b is 12.9 cm

The value of a is 15.3 cm

Step-by-step explanation:

see the attached figure to better understand the problem

Find the value of b

we know that

in the right triangle ABC

The function sine of angle of 40 degrees is equal to divide the opposite side to the angle of 40 degrees (AC) by the hypotenuse (AB)

so

[tex]sin(40\°)=AC/AB[/tex]

Solve for AC

[tex]AC=(AB)sin(40\°)[/tex]

substitute the given value

[tex]AC=(20)sin(40\°)[/tex]

[tex]AC=12.9\ cm[/tex]

therefore

The value of b is 12.9 cm

Find the value of a

we know that

in the right triangle ABC

The function cosine of angle of 40 degrees is equal to divide the adjacent side to the angle of 40 degrees (BC) by the hypotenuse (AB)

so

[tex]cos(40\°)=BC/AB[/tex]

Solve for BC

[tex]BC=(AB)cos(40\°)[/tex]

substitute the given value

[tex]BC=(20)cos(40\°)[/tex]

[tex]BC=15.3\ cm[/tex]

therefore

The value of a is 15.3 cm

Answer:

a=2B/d-l

Step-by-step explanation:

da-la=2B

1) Factor out an a from (da-la):

a(d-l)=2B

2) Divide both sides by (d-l):

a=2B/d-l

Answer:

2.058 x 10 to the -1st

Step-by-step explanation:

Answer:

A is the answer. 2(n+2)

Answer:

A

Step-by-step explanation:

The sum of a number n and 2 is n + 2

Twice this sum is

2(n+ 2) → A

Answer:

A. x radians

Step-by-step explanation:

The circumference of the unit circle is

[tex]2\pi r=2\pi \cdot 1=2\pi[/tex]

The full rotation angle has the measure [tex]2\pi[/tex] radians.

So,

[tex]\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}[/tex]

Write a proportion:

[tex]\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}[/tex]

Cross multiply:

[tex]2\pi x=2\pi \theta\\ \\\theta=x[/tex]

Answer:

Part a) and Part b) see the explanation

Step-by-step explanation:

Part a)  Illustrate both girls’ solutions

Carly

Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children

so

1) Each child receive first 2 whole cereal bars

the remaining is

[tex]7-(2+2+2)=7-6=1\ cereal\ bar[/tex]

2) Divides the remaining cereal bar among the 3 children

Each child receive 1/3 cereal bar

3) Each child receive in total

[tex]2+\frac{1}{3}=2\frac{1}{3}\ cereal\ bar[/tex]

Gina

Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.

so

1) Divide the total bars by 3

Each child receive

[tex]\frac{7}{3}\ cereal\ bar[/tex]

Part b) Explain why they are both right

Compare the results

Carly ----> [tex]2\frac{1}{3}\ cereal\ bar[/tex]

Gina ----> [tex]\frac{7}{3}\ cereal\ bar[/tex]

Convert mixed number to decimal number

[tex]2\frac{1}{3}\ cereal\ bar=2+\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}\ cereal\ bar[/tex]

so

[tex]2\frac{1}{3}\ cereal\ bar=\frac{7}{3}\ cereal\ bar[/tex]

therefore

Carly and Gina are right

Answer: 36

Step-by-step explanation:

5x has to equal 180 and 180 divided by 5 equals 36. This means that x=36 and 4x=144

Answer: B. 36

Step-by-step explanation:

Look at the answer choices. The one that is an obtuse angle, 144, is going to be divided by 4. Your answer is B. 36

Answer:

Step-by-step explanation:

[tex]n,\ n+1-\text{two consecutive numbers}\\\\535-\text{the sum}\\\\\bold{EQUATION:}\\\\n+(n+1)=535\\\\n+n+1=535\\\\2n+1=535\qquad\text{subtract 1 from both sides}\\\\2n+1-1=535-1\\\\2n=534\qquad\text{divide both sides by 2}\\\\\dfrac{2n}{2}=\dfrac{534}{2}\\\\n=267[/tex]

Answer:

The estimate of the product is about 35 answer C

Step-by-step explanation:

- We use rounding to estimate the product of two fractions

- The mixed number has whole number and fraction

- To round the mixed number we look to the fraction

- If the numerator is half or greater than half the denominator, then we

  add the whole number by 1 and cancel the fraction

- If the numerator is less than half the denominator, then we keep the

  whole number as it and cancel the fraction

- Ex: If the mixed number is [tex]2\frac{3}{4}[/tex], 3 is more than

 half 4 then we will add 2 by 1 and cancel the fraction part, the

 mixed number [tex]2\frac{3}{4}[/tex] after rounding is 3

- Ex: If the mixed number is [tex]5\frac{1}{4}[/tex], 1 is less than

 half 4 then we will keep 5 as it and cancel the fraction part, the

 mixed number [tex]5\frac{1}{4}[/tex] after rounding is 5

* Lets solve the problem

∵ In the part [tex]4\frac{3}{4}[/tex] 3 is more than half 4

∴ The rounding value of [tex]4\frac{3}{4}[/tex] is 5

∵ In the part [tex]7\frac{2}{17}[/tex] 2 is less than half 17

∴ The rounding value of [tex]7\frac{2}{17}[/tex] is 7

∴ [tex]4\frac{3}{4}*7\frac{2}{17}=5*7=35[/tex]

* The estimate of the product is about 35

Answer:

(-4,0)(-7,0)

Step-by-step explanation:

The x axis is crossed when y = 0.

That happens in two places.

x +4=0 is one place

x = - 4 when it does.

x + 7 =0 is the other.

x = - 7

Answer:

j = (h-4) / k

Step-by-step explanation:

Unless there is more information given about this question somewhere else in the assignment, I'm assuming you are being asked to solve this equation for j.

If so, then its just a matter of rearranging the equation so that it is in the form

j = (expression containing other variables)

(h-4) / j = k   (multiply both sides by j)

(h-4) = jk  (divide both sides by k)

j = (h-4) / k

[tex]\bf 3\div \cfrac{3}{4}\implies \cfrac{3}{1}\div\cfrac{3}{4}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\cdot \cfrac{4}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 4[/tex]

Answer:

you got to draw a line cutting the shapes in half, then add the permiters or area of both squares

Step-by-step explanation:

Answer:

The midpoint is 5

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two numbers is

[tex]M=(\frac{x1+x2}{2})[/tex]

we have

[tex]x1=-2, x2=12[/tex]

substitute

[tex]M=(\frac{-2+12}{2})[/tex]

[tex]M=(\frac{10}{2})[/tex]

[tex]M=5[/tex]

therefore

The midpoint is 5

Answer:

72.5 miles/hour

Step-by-step explanation:

When we say "miles per hour" in English this just is simply the question "If Bailey drove for only one hour, how far did she go?". Now mathematically we can find this very easily by simply dividing 290 by 4, which is equal to 72.5. So Bailey travels 72.5 miles every hour.  

If it is confusing about why we do this, think about splitting up 290 miles evenly between 4 hours, how many miles does each hour 'get'. Each would 'get' 72.5 miles. So for every hour Bailey drives she travels 72.5 miles which is the same as saying that she drove at 72.5 miles per hour.

Hope this helps!  

Answer:

206.

Step-by-step explanation:

100x2 = 200

3x2 = 6

200+6 = 206

Answer:

206

Step-by-step explanation:

multiplying anything by 2 is basically adding the exact same number to the original number. So basically: 103 +103

which equals 206

Answer:

6 x 6 x 6

Step-by-step explanation:

Six to the third power means to multiply 6 by itself 3 times.

The standard exponential function is expressed as y = ab^x. The value for the simplified form of 6 to the third power is 216

The standard exponential function is expressed as y = ab^x

Given the following parameters

6 to the third power

This can be expressed as 6^3

6^3 = 6 * 6 * 6

6^3 =36 *6

6^3 = 216

Hence the value for the simplified form of 6 to the third power is 216
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Answer:

Mixture 1 and Mixture 2 will create the same color

Step-by-step explanation:

we know that

If two mixtures create the same color, then the proportion of the painting in the mixtures must be the same

Let

x ----> the ounces of a red paint in the mixture

y ----> the ounces of a blue paint in the mixture

Verify the proportion of the paints in each mixture

Mixture 1) x=2, y=1

[tex]\frac{2}{1}=2[/tex]

Mixture 2) x=7, y=3.5

[tex]\frac{7}{3.5}=2[/tex]

Mixture 3) x=4.5, y=2

[tex]\frac{4.5}{2}=2.25[/tex]

Mixture 4) x=5.5, y=2.5

[tex]\frac{5.5}{2.5}=2.2[/tex]

therefore

Mixture 1 and Mixture 2 will create the same color, because have the same ratio

Answer:

Mixture 1 and Mixture 2

Step-by-step explanation:

It is given that Raj is mixing different colors (blue and red) of paint to make a new color.

If two mixtures have same ratio of red and blue color, then that will create the same color.

The ratio of red and blue color in each mixture is shown below:

Mixture 1: [tex]\frac{Red}{Blue}=\frac{2}{1}=2:1[/tex]

Mixture 2: [tex]\frac{Red}{Blue}=\frac{7}{3.5}=\frac{2}{1}=2:1[/tex]

Mixture 3: [tex]\frac{Red}{Blue}=\frac{4.5}{2}=\frac{9}{4}=9:4[/tex]

Mixture 4: [tex]\frac{Red}{Blue}=\frac{5.5}{2.5}=\frac{11}{5}=11:5[/tex]

From the above calculation it is clear that the ratio of red and blue color in mixture 1 and mixture 2 is same.

Therefore, Mixture 1 and Mixture 2 will create the same color.

Answer:

C. [tex]h(x)=x-3[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=x+3[/tex]. We are asked to find the inverse of the given function.

First of all, we will replace [tex]f(x)[/tex] by y as:

[tex]y=x+3[/tex]

Now, we will interchange x and y variables as:

[tex]x=y+3[/tex]

Solve for y:

[tex]x-3=y+3-3[/tex]

[tex]x-3=y[/tex]

Switch sides:

[tex]y=x-3[/tex]

Therefore, the inverse function for the given function would be [tex]h(x)=x-3[/tex].

Answer:

C

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

If you do 5/ 3/5 what youre really doing is just doing two division problems which by the way equals 5/0.6 or 8.3333333

But one thing i realized when i was doing division by fractions is that if you flip the fraction then you can multiply and you get the same exact answer. SO lets try: 5/3 = 1.6666

1.6666*5=8.3333333

So you can use that trick when dividing a whole number by fractions. It makes it a lot easier.

The official answer is instead of dividing 5 by 3/5 you can instead multiply 5 by 5/3 and get the same answer!

Answer:

4428

Step-by-step explanation:

Answer:

Step-by-step explanation:

:  I got A)90

          B)108

          C)333

              Hope that's right. I checked it 4 times.

Answer:

Step-by-step explanation:

A) 90

B) 108

C)333

Answer:

[tex]\boxed{39}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcc}& \textbf{Archery Sign Up} & \textbf{Total Campers}\\\textbf{Week 1} & 36 & 120\\\textbf{Week 2} & 45 & 150\\\textbf{Week 3} & ? & 130\\\end{array}[/tex]

Let x = Total campers

and y = Archery sign up

In a direct proportionality,

y = kx

1. Calculate the value of k

Substitute a pair of values for x and y

150 = k × 45

Divide each side by 45

k = 150/45 = 10/3

2. Calculate the value of x in Week 3

[tex]\begin{array}{rcl}130& = & \dfrac{10}{3}x\\\\390 & = & 10x\\x & = & \mathbf{39}\\\end{array}[/tex]

[tex]\boxed{\textbf{39 campers}} \text{ will sign up for archery in Week 3}[/tex]

The diagram is a graph of your proportionality. It shows that y = 130 when x = 39.