What is the area and perimeter? Show your work

Answer:

Question (a)

Given equation:

[tex]8^{2x} = 32^{x+3}[/tex]

8 can be written as [tex]2^3[/tex]

32 can be written as [tex]2^5[/tex]

Therefore, we can rewrite the equation with base 2:

[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]

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Question (b)

To solve:

[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]

Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]

[tex]\implies 2^{6x} = 2^{5x+15}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :

[tex]\implies 6x = 5x+15[/tex]

Subtract [tex]5x[/tex] from both sides:

[tex]\implies x = 15[/tex]

The Area of the shaded portion = area of 5 shaded squares = 80 in.².

Area of a square = s², where the edge length is s.

Edge length of each small square = 12/3 = 4 in.

Area of the shaded portion = area of 5 shaded squares = 5(s²)

s = 4 in.

Area of the shaded portion = 5(4²)

Area of the shaded portion = 80 in.²

Therefore, the Area of the shaded portion = area of 5 shaded squares = 80 in.².

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Answer:

Step-by-step explanation:

Answer:

11mi² = 28489869m²

Step-by-step explanation:

m² = mi² / 0.00000038610

graphed below:

[tex]\sf f(x)=3x^2-6x+5[/tex]

Answer:

Given function:    [tex]f(x)=3x^2-6x+5[/tex]

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  

(where [tex](h, k)[/tex] is the vertex)

Expand vertex form:

[tex]y=ax^2-2ahx+ah^2+k[/tex]

Compare coefficients of given function with expanded vertex form

Comparing coefficient of [tex]x^2[/tex]:

[tex]3=a[/tex]

Comparing coefficient of [tex]x[/tex]:

[tex]\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1[/tex]

Comparing  constant:

[tex]\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2[/tex]

Therefore, the vertex is (1, 2)

As the leading coefficient is positive, the parabola will open upwards.

Additional plot points:

[tex]f(0)=3(0)^2-6(0)+5=5[/tex]

[tex]f(2)=3(2)^2-6(2)+5=5[/tex]

(0, 5) and (2, 5)

Answer:

[tex]23n + 64[/tex]

Step-by-step explanation:

Hope this helps

Subtract to find how much was spent on coffee:

90 - 47.65 = 42.35

Divide what was spent by the price per pound:

42.35 / 8.47 = 5

They bought 5 pounds of coffee

Answer:

100.53m² area of carpet is left after putting the table in place.

Answer:

A = 5

I hope you have an amazing day!

First, you know that Jackson (let call her J) scored 42 more points than L (Leslie).  What we don't know is how many points L scored so we can use a variable that will be 'x'.

So the equation will be J=42+x.

We also know that the total points is 1,144.

To find out what x is we first subtract 1,144-42.  We then get 1,102.

We are now left with 2x and 1,102 so we divide 1,102 by 2 and get 551.

551=x so now we can plug that in.

J = 551 + 42

Jackson scored 593 points and Leslie scored 551 points

(You can use bar modeling to do solve this problem.  An example of bar modeling is shown below.  

Answer:

y-intersept is where the line crosses the y axis

on this one it is

(0,-3)

Hope This Helps!!!

Answer:

(0,-3)

Step-by-step explanation:

The y-intercept is where the equation of the line intersects the y-axis. In this case, by looking at the graph, we see that the y-intercept is (0,-3).

Hope this helps!!

Check the picture below.

Answer:

c

Step-by-step explanation:

because you can simplify 4/6 by 2.

2 goes into 4 twice and then 2 goes into 6 3 times

2/3

Answer: C. 125.66 in²

Step-by-step explanation:

      This is asking us to find the surface area of this cone. We can use the formula and solve.

A = πrl + πr²

A = π(4)(6) + π(4)²

A = π(4)(6) + π(4)²

A ≈ 125.66 in²

      It would take C. 125.66 in² of toilet paper to cover the surface of this cone.

Using the t-distribution, as we have the standard deviation for the samples, it is found that the data does not provide statistical evidence that there is a difference.

At the null hypotheses, it is tested if there is no difference in the means, that is, the subtraction is of 0, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypotheses, it is tested if there is a difference, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, they are given by:

[tex]\mu_1 = 1.82, s_1 = \frac{1.51}{\sqrt{100}} = 0.151[/tex]

[tex]\mu_2 = 1.65, s_2 = \frac{1.39}{\sqrt{100}} = 0.139[/tex]

Hence, for the distribution of differences, they are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 1.82 - 1.65 = 0.17[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.151^2 + 0.139^2} = 0.205[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Then:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{0.17 - 0}{0.205}[/tex]

[tex]t = 0.83[/tex]

Considering that it is a two-tailed test, as we are testing if the mean is different of a value, with 100 + 100 - 2 = 198 df and a significance level of 0.02, the critical value is of [tex]|t^{\ast}| = 2.3453[/tex].

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis, which means that the data does not provide statistical evidence that there is a difference.

More can be learned about the t-distribution at https://brainly.com/question/13873630

Answer:

Mixed Fraction: [tex]5\frac{1}{5}[/tex]

Improper Fraction: [tex]\frac{26}{5}[/tex]

Step-by-step explanation:

[tex]\mathrm{Rewrite\:as}[/tex]

[tex]=5+0.2[/tex]

[tex]\mathrm{Convert\;0.2\;to\;a\;fraction}:\frac{1}{5}[/tex]

[tex]=5+\frac{1}{5}[/tex]

[tex]=5\frac{1}{5}[/tex]

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

[tex]5\frac{1}{5}=\frac{5\cdot 5+1}{5}=\frac{26}{5}[/tex]

[tex]=\frac{26}{5}[/tex]

~lenvy~

Hello!

First, let's convert 5.2 into a fraction:

[tex]\bf{5\displaystyle\frac{2}{10} }[/tex]

Simplify:

[tex]\bold{5\displaystyle\frac{1}{5}}[/tex]

We turned this number into a mixed number.

That's why it's mixed - we have a whole number and a fraction.

Now, convert the mixed number into an improper fraction.

Step 1: Multiply the whole number times the denominator.

5×5=25

Step 2: Add the numerator.

25+1=26

The denominator stays the same.

Therefore, the answer is

[tex]\bold{\displaystyle\frac{26}{5}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning :-)

Answer:

slope = 7

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope, and b is the y-intercept)

Therefore, for the equation: y = 7x + 9/16

Step-by-step explanation:

i) linear

ii)2

iii) 1

iv) 1

v) -1/5

First one can u type the options in the comment

Answer:

3/10

Step-by-step explanation:

Hope this helped

Answer:

the value of n is -1.5

Step-by-step explanation:

I hope the question was to find the unknown.

Answer:

n= -3/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n=−32

Decimal Form:

n=-1.5

Mixed Number Form:

n=−112

Answer:

find the product of (4m-n)and(3m-2n)

Answer:

1

Step-by-step explanation:

the number of circles which can pass through three given non-collinear points is exactly one.

the reason is that the center of such a circle must be on the (perpendicular) bisectors of the lines between each pair of these points.

these bisectors intersect at one unique point which is the center of the circle and the distance of any point from the center is the radius. So given three non collinear points fixes the center and the radius thereby giving us one unique circle.

the same way we find the circumscribing circle of a triangle, which is exactly the same situation.

Answer:

D

Step-by-step explanation

A.96=6+576

B.576=96+6

C. 96=6×576

D. 576=96×6

Answer: 13.5 in

Step-by-step explanation:

The formula for the volume of a cone is: V = π*r^2*(h/3).

Therefore, when the given numbers are plugged in, it becomes:

1144.53 = (3.14)(9^2)(h/3).

Solving this for h, we get the answer of 13.5 in

Answer:

x = 9/10

Step-by-step explanation:

This problem features a ratio: 4x/3 = 6/5

By cross multiplying you get that 4x*5 = 3*6 or 20x = 18. By dividing both sides by 20, you get that x = 18/20, and when simplified, 9/10.

The solutions to the system of the equations graphed below are where the graphs intersect:

In this case, the two graphs intersect at (0,6) and (-3, -3)

So the solutions are (0,6) and (-3,-3)

Hope that helps!

The solution to the system of the equations below is: (0,6) and (-3,-3)

The solutions are where the two graphs of the equations intersect

Answer:

Yes they are similar

Step-by-step explanation:

Divide the length VW by ST

24 ÷ 16 = 1.333

Divide the length VU by SR

16 ÷ 12 = 1.333

→ As they have the same scale factor, they are similar.

Answer:

Step-by-step explanation:

First when triangles are similar angles are congruent and the side ratio are the same .

18/24=12/16=m/32

3/4=3/4=m/32

3/4=m/32

4m=96

m=24

The period of the given function is T = 2π

The period T of a function f(x) is such that:

f(x + T) = f(x).

In this case, our function is:

f(θ) = e^{iθ}

Remember that this can be written as:

f(θ) = cos(θ) + i*sin(θ)

So yes, this is in did a periodic function.

Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.

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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)

For any real value θ, we have:

[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

Functions which repeats their values after a fixed interval, are called periodic function.

For a function [tex]y = f(x)[/tex], it is called periodic with period 'T' if we have:

[tex]y = f(x) = f(x + T) \: \forall x \in D(f)[/tex]

where D(F) is the domain of the function f.

Suppose that, the period of the function [tex]f(\theta) = e^{i \theta}[/tex] be P, then we get:
[tex]f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex]

When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.

That means,

[tex]\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)[/tex] implies that:

[tex]\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)[/tex]

Also, we know that the period of sine and cosine function is [tex]2\pi[/tex]

Thus, we get:

[tex]P = 2\pi[/tex]

Thus, the period of the function [tex]f(\theta) = e^{i \theta}[/tex]  is P = 2π

Learn more about periodic functions here:

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Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}[/tex] or [tex]\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

[tex]\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}[/tex]

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as [tex]\displaystyle \large{a_{n-1} \cdot r = a_n}[/tex] meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

[tex]\displaystyle \large{r=\frac{a_{n+1}}{a_n}}[/tex]

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

Above should be applied for series that have common ratio not equal to 1.

[tex]\displaystyle \large{S_n=a_1 \cdot n}[/tex]

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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Answer:

x = 102.5°

Step-by-step explanation:

these two angles are adjacent and supplementary which means their sum must be equal to 180 degrees

create this equation to find 'x':

x + x-25 = 180

combine 'like' terms:

2x - 25 = 180

add 25 to each side:

2x = 205

x = 205/2 or 102.5°

Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.

Two examples of linear relationships that are useful are:

Changes of units:

These ones are used to change between units that measure the same thing. For example, between kilometers and meters.

We know that:

1km = 1000m

So if we have a distance in kilometers x, the distance in meters y is given by:

y = 1000*x

This is a linear relationship.

Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:

y = a*x

This is a linear relationship.

So linear relationships appear a lot in our life, and is really important to learn how to work with them.

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