(ASAP WORTH 10 POINTS) Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
72.5 in
75.5 in
83 in
96 in

Answer:

Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)

Part c) The scale factor is [tex]3[/tex]

Step-by-step explanation:

Part a) Write the similarity statement

we know that

If two figures are similar, then the ratio of its corresponding sides is equal so

[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

substitute the values

[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]

[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true

therefore

the figures are similar

Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)

Part c) we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z------> the scale factor

x-----> corresponding side of the image

y------> corresponding side of the original figure

so

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=A'B'=27\ units[/tex]

[tex]y=AB=9\ units[/tex]

substitute

[tex]z=\frac{27}{9}=3[/tex]

The scale factor is greater than 1

therefore

Is an enlargement

Simplifying

y = 0.25x + 2

Reorder the terms:

y = 2 + 0.25x

Solving

y = 2 + 0.25x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 2 + 0.25x

Answer:

12 minutes

Step-by-step explanation:

if it fills up in 4 minutes but empties in 6 minutes, that means there's a two minute gap of water sitting - meaning it would multiple attempts to get the bucket filled - taking 12 minutes to be exact - hope this helps!!

Is it 12 minutes good job

it is 3

4 time 3 plus 1.3 equals 13.3

Answer:

(x-7)  (x+4)

Step-by-step explanation:

x^2 - 3x - 28

What two numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

(x-7)  (x+4)

Answer:

on the top: -28

on the bottom: -3

on the sides: -7 and 4

(x-7)(x+4)

Step-by-step explanation:

Answer:

i think its .b.   sorry if im wrong

Step-by-step explanation:

Answer:

A) 5x -4y =1

B) 4x -2y = 8

Using Cramer's Rule of detrminants

a = 5 b = -4  e=1

c = 4 d = -2  f = 8

denominator = 5 * -2 -(4 *-4) = 6

x = 1 * -2 [-(8 *-4)] / denom = 30 / 6 = 5

y = 5 * 8 -(4 * 1) / denom = 36 / 6 = 6

Step-by-step explanation:

6.45$ for 3 divide 15.05

Answer:

4 feet or 4/15

Step-by-step explanation:

1. So first you have to multiply the top and bottom number of each fraction by the denominator of the opposite fraction to have the same denominator:

1/3 X 5/5 = 5/15

3/5 X 3/3 = 9/15

2. Then you compare the two fractions and subtract the smaller fraction from the bigger:

9/15 - 5/15 = 4/15

So Jimmy dived 4 feet deeper the second time

Answer:

The answer is 4/15 in fraction and 4 feet in whole number

Step-by-step explanation:

Answer:

y=1/6x+3

the slope has to be negative reciprocal and it passes though (6,4)

Answer:

I believe the answer is 10/x.

Step-by-step explanation:

A quotient is a result obtained by dividing one quantity by another and sence we don't know what x is it will have to just be an algebraic equation like the question says.

Mark brainliest if you can thanks!

13^2-5^2=144 find the square root of that which is 12

Answer:

I think they both have the same amount walked, therefore they are both considered as they have walked the same distance

Step-by-step explanation:

Both walked the same distance.

Joelle walked 2/5 of the way from her house to school
Franco also walked 2/5 of the way from his house to school.

What is fraction?

Fraction is defined as the number of composition constitute the Whole.

The question is incomplete so we assume that Joelle and Franco are the neighbors. and school is equally distance from the both the houses

so if Joelle walked for 2/5 and Franco also walked for 2/5
implies both have walked the same distance.

Thus, Both walked the same distance.  

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Answer:

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Its really easy, count backwards 16 from 9 and go into negatives.

Here is the answer counting backwards: 9,8,7,6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-7

Answer: -7

Step-by-step explanation:

If you write out the expression it looks like this, x+16=9. All you have to do is solve for x, which would make the answer -7 because 16 more than -7 is 9.

Mark brainliest please!

The answer is 360in,hope this help!

The answer is:

b. [tex]g(x)=x^{2} +3[/tex]

To find what's the equation of the red graph, first, we need to find a function that intercepts the y-axis at 3 and its vertex is located at (0,3)

We must remember that the constant value in a quadratic equation (c) will tell us where the function intercepts the y-axis, so, we are looking for an equation which has a constant value equal to 3, it discards the options a, c and d, so the correct option would be the option b.

Option b function:

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

Where,

[tex]a=1\\b=0\\c=3[/tex]

Let's check if the option b is the correct option:

First, let's find the axis intercepts:

Y-axis intercept

[tex]f(x)=x^{2}+3\\f(0)=0^{2}+3\\y=3[/tex]

X-axis intercept

[tex]0=x^{2}+3\\x=\sqrt{-3}[/tex]

There is no x-axis intercepts since the square roots of negative numbers does not exists in the real numbers.

Finding the vertex coordinates:

The x coordinate of the vertex can be found using the following equation:

[tex]x=-\frac{b}{2a}=-\frac{0}{2*1}=0[/tex]

The x coordinate of the vertex is located at x=0, so to find the y-coordinate we must substitute the x value into the parabola equation, so

[tex]y=x^{2}+3=0^{2}+3=3[/tex]

So, the y coordinate of the vertex is located at y=3

Therefore, the vertex of the function is (0,3)

Hence, the calculated values of the option b match with the given graph.

The correct option is: b. [tex]g(x)=x^{2} +3[/tex]

Have a nice day!

Answer:

Domain= how many boxes there are from each circle to the other, and the range is basically the height. In this case, Domain= 8, Range=2

Answer:

= 0.583

Step-by-step explanation:

Changing 7/12 as a decimal

we could use long method or convert to percentage

such that;

7/12 ×  100 = 700/12

                 =58.333%

This is equivalent to; 58.333/100

= 0.58333 ; to the nearest thousandth

= 0.583

Answer:

The correct answer is option A.    0.583

Step-by-step explanation:

It is given a fraction 7/12. This fraction is a proper fraction.

proper fraction :- Numerator is less than denominator

We have to convert this fraction into decimal number.

we can convert all proper fractions into decimal.

Convert 7/12 into decimal

7/12 = 0.58333333...

It is a non terminating rec-curing decimal number.

Therefore we can write, 7/12 = 0.583

The correct answer is option A.    0.583

Answer:

The proportion is true.

Step-by-step explanation:

We are given the following proportion and we are to determine whether it is a true proportion or not:

[tex] \frac { 15 } { 3 } = \frac { y } { 7 } [/tex]

Finding the value of y:

[tex]y = \frac{15}{3} \times 7[/tex]

[tex]y=35[/tex]

So now we have [tex] \frac { 15 } { 3 } = \frac { 35 } { 7 } [/tex]

Checking if it is a true proportion:

[tex] \frac { 15 / 3 } { 3 / 3 } = \frac { 5 } { 1 } [/tex]

[tex] \frac { 35 / 7 } { 7 / 7 } = \frac { 5 } { 1 } [/tex]

Since the simplified fractions are equivalent, therefore the proportion is true.

The given expression, 15/3 = y/7, is a true proportion. Solving for y, we find y = 35.

The given expression, 15/3 = y/7, is a proportion. In a proportion, the product of the means (15 and 7) is equal to the product of the extremes (3 and y). To check if the given proportion is true, we can cross-multiply and check if the products are equal.

Cross-multiplying, we have 15 * 7 = 3 * y. This simplifies to 105 = 3y. Solving for y, we divide both sides of the equation by 3, obtaining y = 35.

Therefore, the proportion is true, and y = 35.

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We know that the line is tangent at the point (2,8)

The derivative of the function at x=2 is

[tex]f'(x) = 6-2x \implies f'(2) = 6-4=2[/tex]

So, the tangent line passes through the point (2,8) and has slope 2. The equation is

[tex]y-8 = 2(x-2) \iff y = 2x+4[/tex]

This line crosses the x axis where y=0:

[tex]0 = 2x+4 \iff 2x = -4 \iff x = -2[/tex]

The coordinates of point P where the tangent to the curve y=6x-x² cuts the X-axis can be found by finding the x-value when the derivative of the curve is equal to zero. In this case, the x-coordinate of point P is 3, so the coordinates of point P are (3, 0).

In this question, we are asked to find the coordinates of point P on the X-axis where a tangent to the curve y=6x-x² cuts the X-axis. The equation of the curve is given as y = 6x - x². A tangent line to the curve intersects it at exactly one point. The equation of this tangent line can be written in slope intercept form y = mx + b. When the tangent line cuts the X-axis, y=0.

The first step is taking the derivative of the curve, which gives us the slope of the tangent line. The derivative of y = 6x - x² is y' = 6 - 2x. This gives us the slope of the tangent line.

The second step is finding the x-coordinate of point P where the tangent line intersects the X-axis. This is where the y-coordinate is zero, or when y = 6x - x² is equal to zero. Solving for x, we get x = 0 or x = 6. However, because the curve y = 6x - x² intersects the X-axis at the x-coordinate of 0 and 6, the x-coordinate of point P must be a different value.

The final step is to solve for the x-coordinate when y' = 0, or when 6 - 2x = 0. Solving this equation gives us x = 3. So, the tangent line will cut the X-axis at point P(3, 0).

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Answer:

A- 4 2/3 miles

Step-by-step explanation:

We are given that one of the hiking trails at a state park is [tex] \frac { 14 } { 3 } [/tex] miles long.

We are to determine whether which of the given answer options shows the length of the hiking trail in mixed number.

Basically, we need to divide 14 by 3 to get: [tex] 4 \frac { 2 } { 3 } [/tex]

So the correct answer option is A. [tex] 4 \frac { 2 } { 3 } [/tex].

Answer:

A- 4 2/3 miles

Step-by-step explanation:

To find the mixed fraction, we divide the numerator with the denominator to get a whole number and a remainder. the remainder becomes the numerator of the proper fraction included in the improper fraction.

14÷3=4 remainder 3.

Therefore our fraction becomes,4 2/3 miles.

Answer:

44

Step-by-step explanation:

substitute k = 1, 2, 3, 4 into 2k² - 4 and sum the terms

k = 1 : 2(1)² - 4 = 2 - 4 = - 2

k = 2 : 2(2)² - 4 = 8 - 4 = 4

k = 3 : 2(3)² - 4 = 18 - 4 = 14

k = 4 : 2(4)² - 4 = 32 - 4 = 28

sum = - 2 + 4 + 14 + 28 = 44

Heya!

--------------------

Things to know before we solve:

The "4" at the top means that the the sequence only goes to the 4th term.

k = 1 represents that the sequence starts with the 1st term.

(2k² - 4) represents the rule of the sequence, we can substitute 1, 2, 3, and 4 to solve for the terms of the sequence.

--------------------

Solving for each term:

1st term:

2(1)² - 4

2(1) - 4

2 - 4

-2

2nd term:

2(2)² - 4

2(4) - 4

8 - 4

4

3rd term:

2(3)² - 4

2(9) - 4

18 - 4

14

4th term:

2(4)² - 4

2(16) - 4

32 - 4

28

--------------------

Simplifying:

Write these terms in expanded form:

(-2) + 4 + 14 + 28

Find the sum of the series:

(-2) + 4 + 14 + 28 = 44

--------------------

Answer:

The sum of the series is 44

--------------------

Best of Luck!

Answer:

Part a) The ratio of the perimeters is [tex]3[/tex]

Part b) The ratio of the areas is [tex]9[/tex]

Step-by-step explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

[tex]z=\frac{x}{y}[/tex]

we have

[tex]z=3[/tex]

substitute

[tex]\frac{x}{y}=3[/tex]

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=3[/tex]

substitute

[tex]\frac{x}{y}=3^{2}[/tex]

[tex]\frac{x}{y}=9}[/tex]

Answer:

Part a) The ratio of the perimeters is 3

Part b) The ratio of the areas is 9

Here's how you solve this problem.

1) find how many kilometers equals 1 mile (16/10=1.6).

2) Divide 100 (from 100 km/h) by 1.6 (1.6×100=62.5).

3) solve for mph.

The answer is 62.5mph.

5/5 and then convert this to 100. so, you would multiply it by 20 which would equal 100/100. it’s a whole number, so it’d just be 100%.

On a number line, a point that is 10 units away from 5 can be either 15 (if you move right) or -5 (if you move left). Both these points are 10 units away from 5.

In mathematics, if the value 5 is plotted on the number line, you can plot another point that is 10 units away from 5 by moving 10 places towards either the right or left on the number line. If you move to the right, 10 places ahead of 5 is 15. So, you can plot a point on 15. On the other hand, if you move to the left, 10 places behind 5 is -5. So, you can plot a point at -5. Either of these points (15 or -5) are 10 units away from 5.

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The number obtained when it is added with 9, multiplied by 3, subtracted by 16 and then added with 7 is 3.

Suppose the number is x

An addition of  9 to x = 9+x

Multiplication of 9+x and 3 = 3(9+x)

According to the question

3(9+x)-16+7 = 27

By solving the above equation we will get x

An equation is a statement that equates to two expressions.

So, 3(9+x) = 36

9+x=12

x=3

So, the number is x=3

Thus, the required number that satisfies the question is 3.

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Answer:

Part A. = 2,000,000,000

Step-by-step explanation:

To find the first measurements solve the equation.

10^3 = 1,000

So now 1,000 multiplied by 4

4 x 1,000 = 4,000

for the second side or measurement solve again.

10^5 = 100,000

5 x 100,000 = 500, 000

with both measurements 4,000 and 500,000 to find area we need to multiply both sides

4,000 x 500,000 = 2,000,000,000

See if you can solve the other one, if you can't I'll help!

Hope this helps!

Please mark as brainliest answer!! THanks!!

A cosine function is simpler to model the situation of the changing tides because it starts at an extremum, aligning with the low tide occurring at t=0 (12:00 am). By calculating the amplitude, midline, and period, we can construct an approximate model for the tidal heights using a cosine function without a phase shift.

The phenomenon of tidal movements can be modeled through periodic functions, such as sine or cosine functions, which are suitable for representing recurring events over time.

In this scenario, since the low tide occurs at t=0 (12:00 am) and reaches the same low tide level at t=12.5 (12:30 pm), a cosine function would be more appropriate as it inherently starts at a maximum or minimum value.

On the other hand, a sine function starts from the middle of its range, making it necessary to introduce a phase shift in the function for accurate modeling of the tides in this case.

A simple cosine model for the tidal heights would look like: Depth(t) = A * cos(B * (t - C)) + D, where A represents the amplitude, B is related to the period of the tide cycle, C is the phase shift (in this model C would be zero), and D adjusts the midline to fit the average between high and low tides.

Considering the given data:

Amplitude (A): (High tide depth - Low tide depth) / 2 = (5.5m - 2.5m) / 2 = 1.5m

Midline (D): (High tide depth + Low tide depth) / 2 = (5.5m + 2.5m) / 2 = 4m

Period (Related to B): Since there are two high and two low tides every 24 hours, the period would be 12 hours. We would then find B by using the formula 2 * pi / period, yielding B = 2 * pi / 12.

So, the model would be approximately Depth(t) = 1.5 * cos((pi / 6) * t) + 4, accurately reflecting the transition from low to high tides and back over a 12-hour cycle.

Answer:

A cosine function would be a simpler model for the situation.

The minimum depth (low tide) occurs at t = 0. A reflection of the cosine curve also has a minimum at t = 0.

A sine model would require a phase shift, while a cosine model does not.