How far is Town Center from Maple Station? (please look at attachment) 15 POINTS

4

2

5.83

5.57

The compound interest for 5 year is $3868.7.

Interest accrued on both the principal sum of money and the interest already earned.

The formula for compound interest is p(1+r/100)ⁿ - p

Where p is principal amount, r is rate and n is time.

Given that,

Principal = $20000,

Time = 5 years,

And rate of interest = 18/5 %

To find compound interest, use formula,

Compound interest =  p(1+r/100)ⁿ - p

Compound interest = 20000(1+18/(5×100))⁵-20000

Compound interest = 23868.7 - 20000

                                 = 3868.7

The compound interest for 5 years is $3868.7.

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Answer:

(1) B. f(x)->0  as x->∞, f(x)->∞  as x->-∞

(2) D. [tex]f(x)= 2^{-x}+5[/tex]

Step-by-step explanation:

[tex]f(x) = b^x[/tex]. Given 0<b<1

'b' is between 0  and 1  so b should be a fraction

'b' is a fraction, so for positive value of x , the value of f(x) cannot be negative.

the graph of f(x) will goes close to 0 but it never cross x  axis

So end behavior is f(x)->0  as x->∞

for negative values of x , the y value increases

So end behavior is f(x)->∞  as x->-∞

(2)  f(x) = 2^x

When graph reflects across y axis, x becomes -x

so [tex]f(x)= 2^{-x}[/tex]

For translating up by 5 units we add 5  at the end

so [tex]f(x)= 2^{-x}+5[/tex]

When 0 < b < 1, the graph of the function f(x) = [tex]b^x[/tex] is decreasing. This means that the values of f(x) will get smaller and smaller as x gets larger and larger.

In the limit as x approaches positive infinity, f(x) will approach zero. On the other hand, in the limit as x approaches negative infinity, f(x) will approach positive infinity.

The correct answer is g(x) = 2*+5.

The function g(x) = 2*+5 reflects the graph of f(x) = 2x across the y-axis and translates it up 5 units.

The reflection across the y-axis is achieved by multiplying the function by -1.

The translation up 5 units is achieved by adding 5 to the function.

The graph of g(x) is also shifted up 5 units.

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Answer: B

Step-by-step explanation:

4ˣ = 1024

1024 = 4ˣ

log⁴1024 = x

Answer:

the answer is D

Step-by-step explanation:

As per linear equation, since 8.8 rounds to 9 and 2.7 rounds to 3, so division rounds to 3. His answer of 4.14 rounds to 4. So, it is not reasonable.

A linear equation is an equation that contains one or multiple variable with the highest power of the variable is one.

Given expression is:

8.8 ÷ 2.7

≈ 9 ÷ 3

= 3

His answer is 4.14 ≈ 4.

Therefore, this is not a reasonable answer.

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Answer: 3 1/4 tons = 6500 tons

Step-by-step explanation:

3 tons is 6000 since 3 * 2000 = 6000

1/4 would be 25% of 2000 which would be 500

because if you take 500 four times it will be 2000

So here you go bud.

3 1/4 tons in pounds.

if 2000 pounds are 1 ton multiply 2000 to 3 tons.

You get 6000.

Then you move on to 1/4.

2000 divided by 4 is 500.

500 is your 1/4.

So 6500 is your answer.

Hope this helped!

2 pounds is equal to 908 grams (rounded to the nearest whole gram).

Started by converting 2 pounds to kilograms using the conversion factor 1 pound = 0.454 kilograms.

So, 2 pounds * 0.454 kilograms/pound = 0.908 kilograms.

Then, I converted 0.908 kilograms to grams using the conversion factor 1 kilogram = 1000 grams.

So, 0.908 kilograms * 1000 grams/kilogram = 908 grams.

Finally, I rounded 908 grams to the nearest whole gram, which is 908 grams.

Therefore, 2 pounds is equal to 908 grams (rounded to the nearest whole gram).

Question

1 pound = 0.454 kg 1 kg = 1000 g Using the conversions given, convert 2 pounds to grams (round to the nearest whole gram).

Answer:

24% chance

Step-by-step explanation:

First, find the total number of graduates in the table, that number is 2610, that will be your numerator.

You will look at the table for the total number of students, that is 10730, that will be the denominator.

Now divide the smaller number/numerator (2610) by the larger number/denominator (10730)

[tex]\frac{2610}{10730}[/tex] = 0.2432432...

Then, multiply by 100 to get the percentage: 24.32432...%

Now, round to the nearest percentage: 24%

Answer: D

Step-by-step explanation:

The orange color is represented by the bottom line, which is y > x - 2

The purple color is represented by the top line, which is y < x + 1

How do we know the equations of those lines?

The orange line:

The purple line:

Answer:

c is the correct answer i believe

Step-by-step explanation:

Because a triangle must have two equal sides

Final answer:

The sets of measurements that could be the side lengths of a triangle are c (9 cm, 4 cm, 4 cm) and d (7 cm, 10 cm, 8 cm), as they both satisfy the Triangle Inequality Theorem.

Explanation:

The question asks which set of measurements could be the side lengths of a triangle. To determine if three lengths can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Let's analyze each option:

Therefore, options c (9 cm, 4 cm, 4 cm) and d (7 cm, 10 cm, 8 cm) could be the side lengths of a triangle.

Answer:

The length of arc AB is 120 centimeters.

Step-by-step explanation:

Given information: O is the center of circle and radius of the circle is 4 centimeters. It is given that [tex]x=30^{\circ}[/tex].

Length of arc is

[tex]l=2\pi r(\frac{\theta}{360})=r\theta[/tex]

Since the radius of circle is 4 and [tex]x=30^{\circ}[/tex], therefore

[tex]AB=4\times 30=120[/tex]

Therefore the length of arc AB is 120 centimeters.

Answer:

2π/3 cm

Step-by-step explanation:

usatestprep

Answer:

a) -1 mult. 2 & 2 mult. 2

b) [tex]-a(x+1)^2(x-2)^2[/tex]

c) 4 at least (even degree could be 4, 6, 8, etc)

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -1,2

We can write them in intercept or factored form as (x+1) and (x-2).

Because the graph never crosses the x-axis each has an even multiplicity of at least 2.

The graph is facing down and is an upside down W so is negative. [tex]-a(x+1)^2(x-2)^2[/tex]

This means the function has a degree of 4 or higher with the degree being even.

Answer:

Angle 3 is 49 degrees

=============================

Explanation:

Angle 1 is 50 degrees and angle 2 is 48 degrees. Added up, they total to 98 degrees. This is angle DEF.

Angle DEF is congruent to angle ABC because they are alternate exterior angles and because lines m and n are parallel

We are told that angle ABC is bisected (aka cut in half) because of line s; which means that the angles labeled "4" and "5" are exactly half that of angle ABC = 98 degrees

Therefore, angle 4 is 98/2 = 49 degrees and so is angle 3 (due to angles 3 and 4 being vertical angles; angle 3 = angle 4)

I believe the answer is C because it is the only answer that proves helpfulness to the survival of a mole

Answer:

Which of the following situations describes a helpful adaptation for a mole?

Question 2 options:

A mole is blind and cannot see underground.

 A mole is bright and attracts the attention of predator birds.

A mole has a sensitive sense of smell to help it find food underground.

Step-by-step explanation:

Despite their very poor eyes, moles can hunt worms and insects thanks to their keen sense of smell and capturing vibrations of their prey with their whiskers.

The answer is: A mole has a sensitive sense of smell to help him find food underground.

Answer:

[tex]h>1600[/tex]

Step-by-step explanation:

We have been given that Matt is climbing a mountain. When his elevation is higher than 1600 meters, breathing is difficult for Matt.

We are asked to write an inequality that describes h, the elevation at which breathing is difficult for Matt.

We know when elevation (h) will be higher than 1600 meters Matt will face difficulty in breathing. We can represent this situation as:

[tex]h>1600[/tex]

Therefore, inequality representing the elevation at which breathing is difficult for Matt will be [tex]h>1600[/tex].

She nee to save $60 more so she can buy a new bike

The measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that Aliya lined up the interior angles of the triangle along line p .

We have to find the what happens to angle When the measure of angle A increases in the triangle.

An angle is the figure formed by two rays, called the sides of the angle, sharing

When the measure of angle A increases in the triangles, the measure of angle A on line p also increases.

Hence,  the measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.

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Answer:

The equation of this line is y - 7 = 4(x + 3)

Step-by-step explanation:

To find this, start with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the slope in for m and the two coordinates in for (x1, y1).

y - 7 = 4(x + 3)

Final answer:

The equation in Point-Slope form for the given point ( -3,7) and slope 4 is B. y - 7 = 4 ( x + 3 ). (Option B)

Explanation:

The correct equation in Point-Slope form for the given point and slope, where the point is ( -3,7) and the slope is 4, can be written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Substituting the given values, we obtain y - 7 = 4(x + 3).

Therefore, the correct equation in Point-Slope form is:

B. y - 7 = 4 ( x + 3 )

Answer:4

Step-by-step explanation:

76/19=4

Answer:

Anya rode at 8.5 miles per hour.

Step-by-step explanation:

We have been given that Taylor and Anya live 63 miles apart. One day they left their houses at 8 am and met at 11 am riding toward each other. Taylor rode at 12.5 miles per hour.

We can see that Taylor and Anya met after 3 hours as 11-8=3. This means that both rode their cycles for 3 hours.

Let us find distance covered by Taylor.

[tex]\text{Distance}=\text{Speed*Time}[/tex]

[tex]\text{Distance covered by Taylor}=12.5\frac{\text{Miles}}{\text{hour}}*3\text{ hours}}[/tex]

[tex]\text{Distance covered by Taylor}=12.5*3\text{ Miles}[/tex]

[tex]\text{Distance covered by Taylor}=37.5\text{ Miles}[/tex]

Therefore, Taylor covered 37.5 miles in 3 hours.

Let us find distance covered by Anya in 3 hours by subtracting distance covered by Taylor from total distance of 63 miles.

[tex]\text{Distance covered by Anya in 3 hours}=(63-37.5)\text{ Miles}[/tex]

[tex]\text{Distance covered by Anya in 3 hours}=25.5\text{ Miles}[/tex]

Now let us find speed at which Anya rode bike.

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Speed at which Anya rode the bike}=\frac{25.5\text{ Miles}}{3\text{ Hour}}[/tex]

[tex]\text{Speed at which Anya rode the bike}=8.5\frac{\text{ Miles}}{\text{ Hour}}[/tex]

Therefore, Anya rode the bike at the speed of 8.5 miles per hour.

Answer:

B C E

Step-by-step explanation:

Just did it on edg

The incenter of a triangle is the center of the triangle

The true statements are:

From the diagram (see attachment), we have the following observations.

The lines from points X, Y and Z to point A are perpendicular to lines DX, DY and EF.

This mean that, point A is the center of a circle that passes through points X, Y and Z.

Hence, (b) is true

Also it means  that:

[tex]\mathbf{AX \cong AY \cong AZ}[/tex] --- the radius of the circle.

Hence, (c) and (e) are true.

So, the true statements are: (b), (c) and (e)

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Answer:

SSS congruency

Step-by-step explanation:

Here’s an easy way to remember it. S stands for side so it is side side side congruency.

Answer:

7

Step-by-step explanation:

The remainder from division by (x+1) is the value of f(-1). That remainder is the number at the lower right of the synthetic division tableau, 7.

Answer:

f(-1) is 7

Step-by-step explanation:

When using synthetic division, the value of the function is the final value of the division.

f(-1) is 7

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Using SOH CAH TOA in right triangle,

[tex]sin 22=\frac{opposite}{hypotenuse}[/tex]

[tex]sin 22=\frac{689}{x}[/tex]

[tex]x=\frac{689}{sin 22}[/tex]

Plugging the value of sin 22

[tex]x=\frac{689}{0.3746}[/tex]

[tex]x=1839.29[/tex] feet

So the distance is 1839.29 feet.

[tex]time=\frac{distance}{speed}=\frac{1839.29}{130}[/tex]

time=14.15 minutes   :    Answer

Hope it will help :)

Answer:

Option C is correct.

288 degree measure could he have rotated the pentagon so that is mapped onto itself

Step-by-step explanation:

Given:  Patrik rotated the pentagon about its center.

A Rotational symmetry of a regular polygon is based on the number of vertices it has.

If the Pentagon figure is rotated [tex]360^{\circ}[/tex] about its center, each vertex lands exactly on the top of where it started.

Since you have 5 vertices, so your starting vertex can land in 5 different starting places and still come up with the same figure.

So if you take [tex]\frac{360}{5} = 72^{\circ}[/tex] rotations to each consecutive vertex.

⇒a rotation of 72 degree, 144 degree, 216 degree, 288 degree and 360 degree will result in the same figure.

Therefore, 288 degree measure could he have rotated the pentagon so that is mapped onto itself.

Answer: Yes option C

Step-by-step explanation:

Answer:

20 pages

Step-by-step explanation:

2 minutes is 1/2 of 4 minutes.

By proportion  number of pages he scans in 2 minutes = 1/2 * 40

= 20 pages

Final answer:

To calculate the number of pages a scanner can scan in 2 minutes, you divide the total pages scanned in 4 minutes by 4 to find the rate per minute, and then multiply by 2. The scanner can scan 20 pages in 2 minutes.

Explanation:

To find out how many pages a scanner can scan in 2 minutes if it can scan 40 pages in 4 minutes, we use proportion or unit rate since the scanning speed is constant. We start by determining how many pages are scanned in one minute. Since 40 pages are scanned in 4 minutes, we divide 40 by 4 to find the scanning speed per minute:

40 pages ÷ 4 minutes = 10 pages per minute.

Now we find out how many pages can be scanned in 2 minutes by multiplying the rate by the number of minutes:

10 pages per minute × 2 minutes = 20 pages.

Therefore, the scanner can scan 20 pages in 2 minutes at the given rate.

Answer:

Whole numbers are 1 and 2

Step-by-step explanation:

Given that a number 5 and we use the square root of 5.

We are to find two whole numbers that falls between square root of 5.

We know that whole numbers are 0,1,2.....

We know that square root of 5 is irrational approximately equal to 2.236.

Consider square root of 5.

Since square root of any number always has two solutions the solutions are

-[tex]\sqrt{5}[/tex] and [tex]\sqrt{5}[/tex]

We have to find two whole numbers lying between these values.

We see that  0, 1,2 are the whole numbers lying between these two values.

Let us select any two of them from these two.

Say 1,2

Then answer is 1,2.

Answer: C (0.391)

I'm pretty sure that's right.

Answer:

0.391

Step-by-step explanation:

Gradpoint

Solution:

Centroid: Point of intersection of Medians of Triangle which is drawn from opposite vertex.

Incenter : Point of intersection of Angle Bisectors drawn from opposite vertex of triangle.

Circumcenter : Point of intersection of Perpendicular bisectors of sides of triangle.

Orthocenter: Point of intersection of perpendiculars drawn from opposite vertex of triangle.

1.ABC Widget Company wants to build a central location for it’s new distribution center. They need the center to be equally located between their 3 stores. Which point of concurrency is needed to determine the best location?

Answer: Circumcenter , as it is equidistant from three vertices A, B and C.

2. Build it Furniture Company is designing a triangular pedestal table and need to determine the exact center of the table top. Which point of concurrency is needed to determine the exact location of the table top?

Answer: Centroid , it is located exactly inside the center of Triangle.

3. We could come up with a unique scenario for this point of concurrency but unfortunately this point is good for absolutely nothing.

Answer : Orthocenter,

4. Charleston is building a statue of Euclid to celebrate his influence in mathematics. The center of the park that they would like to build the statue of Euclid has a triangular walkway that borders the location for the statue. They want the statue to be the same distance from each side of the walkway. Which point of concurrency is needed to determine the best location within the triangular region?

Answer: Incenter, as it is a point which is equidistant from three sides of triangle.

Answer:

The correct option is (d)

domain= real numbers and Range= positive real numbers

Step-by-step explanation:

The given function is an exponential function in which the condition on the parameters are as follows-

f(x) = a^x

(1) Base condition is , a>0 and a≠1

(2) Domain = The value of x = x can take any value that is x∈ R

(3) Range = f(x)>0 that is f(x) can take positive values only.