In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length AC is 850 meters. Which angle of this triangle has the greatest measure?

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We are asked to simplify the expression [tex]\large\pmb{7x^2-x^2}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

That's exactly what we need to do - combine like terms.

So, we subtract:

[tex]\star~\large\pmb{7x^2-x^2}[/tex]

Which gives us:

[tex]\star~\large\pmb{6x^2}[/tex]

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The area of the smallest side of the right triangle is 25 ft².

A triangle having two sides at an angle of 90 degrees is called the right-angle triangle.

Note:- The figure is missing in the question I am attaching the complete figure with the answer below for calculation.

Given that:-

The hypotenuse = 169 ft ²  = 13 ft

The side with area 144 ft²   = 12 ft

Using Pythagoras' identity to find the third side x ( smallest )

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = 5

Thus the area of the smallest side will be calculated as:-

A =  5²

A =  25 ft²

Therefore the area of the smallest side of the right triangle is 25 ft².

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Answer:

see below

Step-by-step explanation:

There are two points where y = -3

   at x = -2   and x = 1

   when x = 0    f(0) = 1

The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression option is A x⁹y⁶z⁸. Hence, the correct option is A.

Usually, simplification involves proceeding with the pending operations in the expression.  

Simplification usually involves making the expression simple and easy to use later.

The expression is given as

(x⁵y³z²) and (x⁴y³z⁶)

Then, the product of the expression will be

= (x⁵y³z²) (x⁴y³z⁶)

= x⁵x⁴y³y³z²z⁶

= x⁵⁺⁴y³⁺³z²⁺⁶

= x⁹y⁶z⁸

Hence, the correct option is A x⁹y⁶z⁸.

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The value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.

To calculate the polynomial expression below, we use the technique below.

From the question,

Given:

To find f(4) we substitute 4 as the value of x in equation 1

To find 3[f(t)] we multiply equation 1 by 3

Hence, the value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.

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Answer:

$97.875

Step-by-step explanation:

interest = 750 * 4.35% * 3

= $97.875

Answer:

51 guests

Step-by-step explanation:

150+30x

1700=150+30x

1550=30x

x=1550/30=51

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

Given that;

First, we determine the mark price.

Since the Furniture Store marks up all furniture by 45%.

Mark up price = mark up × purchase price

Mark up price = 45% × $113.00

Mark up price = 0.45 × $113.00

Mark up price = $50.85

Now, the selling price will be;

Selling price = Purchase price + mark up price

Selling price = $113.00 + $50.85

Selling price = $163.85

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

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One of the best things about box plots is that they include all of the measures of central tendency in one convenient package.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The typical value of a set of data is known as the central tendency. We can measure central tendency in three different ways: mean, median, and mode.

Thus, one of the best things about box plots is that they include all of the measures of central tendency in one convenient package.

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The equation of the line of fit and the data shows that the number of hats will be 48.

From the information, x games is won as y hats are sold. Therefore, the equation is given as:

y = 3.75x + 13.75

y = 3.75(9) + 13.75

y = 47.5

y = 48.

Therefore, the number of hats sold is 48.

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Answer:

45

Step-by-step explanation:

how many number you rolled 3 times how many times its rolled 15 x 3 +45

Therefore,the answer would be 45

Answer:

it will cost $48

Step-by-step explanation:

30/10 = 3

3x6 = 18

18 + 30 = 48

Answer:

$48

Step-by-step explanation:

30/10 equals to 3/1 3 x 16 is 48

Answer:

4 only play piano

Step-by-step explanation:

12 + 16 = 28

32 - 28 = 4

Answer:

No

Step-by-step explanation:

21 = 3p - 5

Step 1 : Add 5 on both sides

21 + 5 = 3p

26 = 3p

3p = 26

Step 2 : Divide 3 on both sides

p = 26/3

Hence, the solution of the given equation is 26/3, not 9.

The options B and E are the correct answer.

We have given that,

A group of students is collecting books to add to their library.

The table shows the number of books in the library after 1, 3, and 5 days. if the relationship between days and books continues to be linear

We have to determine which ordered pairs could appear in the table.

The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation.

If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.

B and E are the correct answer. Because (2,23) and (7,48) are linear.

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Answer:

It is 49. You will know it is right down here:

Step-by-step explanation:

1323 when factorised = 3 *3*3*7*7

Therefore it is to be divided by 7*7 = 49

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Answer:

Correct (192)

Step-by-step explanation:

The formula for a parallelogram's area is just base times height. 16x12 is equal to 192, so you are correct.

A parallelogram can be:

Therefore we calculate the rectangle of a square, which is a parallelogram.

To start solving, we obtain the following data:

The formula to calculate the area is:

[tex]\bf{a=b*h }[/tex]

To calculate the area, multiply the base by the height (which is represented in "h")

We clear formula, calculate the area:

[tex]\bf{A=(16 \ cm)(12 \ cm) \ \ \ ==== > \ Multiply }[/tex]

[tex]\bf{A=192 \ cm^{2} }[/tex]

Answer: The area of the parallelogram is 192 cm2. So if you're right, it was a rectangle.

Answer:

a) 12/18

b) 6

Step-by-step explanation:

If adding 6 white balls doubles the probability then the original amount of balls is 6 and with the new amount of 18, the likelihood of picking a white ball becomes 12/18.

Answer:

Step-by-step explanation:

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{0}{k})}\qquad \stackrel{radius}{\underset{7}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-0 ~~ )^2~~ = ~~7^2\implies x^2+y^2=49[/tex]

The age of Jennifer is 16.

Let Jennifer's age be represented with x

Jonathan's age would be 2x

The sum of their ages would be 48

2x + x = 48

3x = 48

x = 48 /3 = 16

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Answer:  Jennifer is 16

Step-by-step explanation: 2x+y=48, divide by 3 then multiply by 2

Answer:

A and C

Step-by-step explanation:

Exponent from biggest to lowest

Part 1

V = pi*r^2*h .... volume of a cylinder

250 = pi*r^2*h

h = 250/(pi*r^2)

Plug this into the surface area of a cylinder equation

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )

SA = 2*pi*r^2 + 500/r

Now replace every copy of r with x to get this function

f(x) = 2*pi*x^2 + 500/x

x = radius

y = f(x) = surface area

Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.

Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).

The coordinates of that local min point will show up and they are (3.414, 219.689)

We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689

This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.

Use this value of r to find h

h = 250/(pi*r^2)

h = 250/(pi*3.414^2)

h = 6.828

Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.

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Part 2

Answer:

Step-by-step explanation:

The experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, total multiple choice quiz = 5 questions

          Each question contains 5 choices in which 1 choice is correct and remaining 4 are incorrect.

Possibility of first wrong choice = 4/5

Possibility of second wrong choice = 4/5

Possibility of third wrong choice = 4/5

Possibility of fourth wrong choice = 4/5

Possibility of fifth wrong choice = 4/5

Overall probability for Zero correct answer=(4X4X4X4X4)/(5X5X5X5X5)

                                                                        = (4/5)⁵

Thus, the experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵

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