lateral surface for a triangular prism l=8 w=4 h=6

The complete question is

"In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. Triangle N Q L has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, Q M, and L P. The length of line segment N S is x + 10 and the length of line segment S R is x + 3.

What is RS?

4 feet, 7 feet, 10 feet, 14 feet"

Answer:

The Length of RS would be 7 ft. so the correct option is B.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Based on the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR,

NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3)

Solve for x

x + 10 = 2x + 6

x - 2x = -10 + 6

-x = -4

x = 4

SR = (x + 3) ft (SR is same as RS)

substitute the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Hence, The Length of RS would be 7 ft. so the correct option is B.

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Answer: B, 7 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]8.6 + 5.6x - 1.5 = 40.7\\5.6x = 33.6\\x=6[/tex]

Answer:

Step-by-step explanation:

solve for x

8.6 + 5.6x - 1.5 = 40.7

5.6x = 40.7 - 8.6 + 1.5

5.6x = 33.6

x = 33.6 : 5.6

x = 6

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

check

8.6 + 5.6 * 6 - 1.5 = 40.7

40.7 = 40.7

the answer is good

The attached graph represents the piecewise function h(x)

Which of the following is the graph of the piecewise function

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The function is given as:

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The above means that the piecewise function has 3 domains

Next, we plot the graph using a graphing tool

See attachment for the graph of the piecewise function h(x)

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The slope of the line in its simplest form is 3.

The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].

We need to find the slope of the line in its simplest form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.

Select any two points on the line like A and B.

From the below figure it is clear that

Rise = Change in y = -2-(-5) = 3

Run = Change in x = 9-0 = 9

Now, [tex]\frac{9}{3} =3[/tex]

Therefore, the slope of the line in simplest form is 3.

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Answer:

[tex]\fbox {B. CA}[/tex]

Step-by-step explanation:

Picture the line segment :

⇒ A ---------------- C ------------------ B

Then :

⇒ CA + CB = AB

Answer:

C. m∠1 = m∠4

Step-by-step explanation:

A. m∠2 + m∠4 = 180°

∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.

Hence, it's a false statement.

B. m∠2 + m∠3 = 180°

∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.

It's a false statement.

C. m∠1 = m∠4

∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.

Therefore, it's a true statement.

D. m∠1 = 90°

As clearly visible in the diagram;

It's a false statement.

Answer: 450 Minutes

Step-by step explanation:

135-x)/5 = hours connie runs

x/7 = hours Bonnie runs

(135-x)/5 + x/7 = 24

135-x + 5x/7 = 120

945-7x+5x = 840

-2x = -105

x = 52.5 miles = distance of Bonnie

52.5 miles / 7 m/hr = 7.5 hours = 450 minutes

Answer:

7

Explanation:

Use the distance formula to find the answer

Answer:

7 units

Step-by-step explanation:

since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.

LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7

or

LM = | - 3 - 4 | = | - 7 | = 7

Answer:

  (b)  y = 18/x; y = 9/4

Step-by-step explanation:

Different kinds of variation are generally described by the equation ...

  y = k·( ) . . . . . . . where k is the constant of proportionality

__

What goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.

The value of k can be found by solving the variation equation with given values of the variables.

__

The variables x and y are said to vary inversely, so the appropriate equation is ...

  y = k(1/x) = k/x

Using the given values, we can find k:

  9 = k/2

  9·2 = k = 18

So, the equation is ...

  y = k/18

__

Using the above equation, the value of y for x=8 is ...

  y = 18/8 = 9/4

Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.

Answer:6.76 cm2

Step-by-step explanation:

You have multiply 2.6 by 2.6 and then you have to square the cm so it will be 6.76 cm2

Answer: A. 6.76 [tex]cm^2[/tex]

Step-by-step explanation:

Area is just length times width.

The length is 2.6 cm and the width is 2.6 cm, so just multiply the two.

2.6 x 2.6 = 6.76 [tex]cm^2[/tex]

Make sure you don't forget the squared in questions that ask for area.

Answer: [tex]133^{\circ}[/tex]

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary, so:

[tex]4x+5+x+15=180\\\\5x+20=180\\\\5x=160\\\\x=32[/tex]

This means that [tex]m\angle A=4(32)+5=\boxed{133^{\circ}}[/tex]

Answer:

5 blue marbles

10 Red marbles

3 Green marbles

Step-by-step explanation:

5 times 2 = 10

then 5-2 =3

Add 5+10+3

=18 Marbles in total

Step-by-step explanation:

please mark me as brainlest

The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

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Answer:

x2

Step-by-step explanation:

x2

Answer:

54

Step-by-step explanation  

(area of mat subtracted from area of room)-center of mat to wall

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

Explanation:

She has already ran 8 miles, so she has 26-8 = 18 miles left to go.

She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.

I used the equation distance = rate*time, and solved for time to get time = distance/rate.

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

Another approach:

Here's how you can use algebra.

x = time she has left in hours

7.5x = distance covered in those x hours

7.5x+8 = total distance

7.5x+8 = 26

7.5x = 26-8

7.5x = 18

x = 18/(7.5)

x = 2.4

Answer:{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

Step-by-step explanation:

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

Random sampling is the method of selecting the subset from the set to make a statical inference.

Utilizing two six-sided number solid shapes, each named with the numbers 1 through 6.

The number of the total events will be given as,

Total events = 6²

Total events = 6 x 6

Total events = 36

The total sample is given below.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

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The area of the swimming pool on the scale drawing will be 300 sq. centimeters.

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,

40 meters = 40/2 centimeters = 20 centimeters

The width of 30 meters one scale drawing will be equal to,

30 meters = 30/2 centimeters = 15 centimeters

Now, the area of the swimming pool on the scale drawing will be,

Area= 20 centimeters × 15 centimeters = 300 sq. centimeters

Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.

The complete question is:

A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?

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Answer:

if a and b are both negative numbers, the product is a positive number

Answer:

Function

Step-by-step explanation:

Yes, the graph is a function. For each x value, there is a unique y value that corresponds with it.

A graph can also be tested as a function by using the popular "vertical-line test".

If the 72% of its original amount of C-14. Then the number of years will be 3285.

The complete question is attached below.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.

Then the function is given below.

[tex]\rm N= N_0 \ e^{-kt}[/tex]

Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.

[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]

We have N = 0.72N₀, the time will be

[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]

Take log on both side, then we have

ln 0.72 = -0.001 × t × ln e

  -0.33 = -0.001 × t

         t = 3285 years

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Answer:

Sam is correct

Step-by-step explanation:

6 divided by 1/4.

This is asking how many times can 1/4 go into 6?  This might be a calculation needed if Sam brought 6 pies to the party of 24 people.  How should Sam cut the pies so that each person gets an equal share, and there is none left over.  This is a serious issue because Sam only knows how to cut pies into quarters.  He always gets confused when having to split a pie into 5, 6, 7, 8 or even 9 equal pieces.  Sam decided that if he cuts the pies into quarters, that he'll have exactly 24 pieces of pie, all equal in size, and exactly enough to feed everyone.

Sam says 24 is wrong.  I don't see the figure that Sam has in mind, but it apparently is not 24.

When a pie is cut into quarters, it will serve 4 people.  If one has 6 pies, and everyone takes only one slice, then there would be 4 x 6 or 24 pieces of pie, exactly what is needed:  one for each person.

Answer:

No, the table does not represent a function.

Step-by-step explanation:

By definition, a function will not have 2 or more results for the same input.

The table shows two values of y for the same x:  (2,1) and (2,4).  The same input, 2, results in two different values, 1 and 4.

See attached image.

Answer:

-5 + 12 i

Step-by-step explanation:

(2 + 3i)^2   = 4  + 6i  + 6i  + 9i^2

                 =   4   + 12 i   + 9(-1)

                     = - 5 + 12 i

A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The complete question is:

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is  16 feet. Round your answer(s) to the nearest hundredth.

The time at which the height of the ball is 16 feet can be found by,

h = 2 + 31t - 16t²

16 = 2 + 31t - 16t²

16 - 2 - 31t + 16t² = 0

16t² - 31t + 14 = 0

[tex]t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\[/tex]

t = 0.717 , 1.221

Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

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[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]

Generally, the equation for the function is mathematically given as

f(x) = -5x + 11 + 10

Therefore

When x >= -1, the function decreases because f(x) = -5(x+1)+10.

This means that the function is dropping throughout this range[tex](-1,\infty).[/tex]

b)

A look at the graph reveals a decreasing trend in the function over the timeframe (-2,2).

In conclusion, The number line will represent

Using the point where the intervals with decreasing functions overlap

[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]

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Answer:

see photos

Step-by-step explanation:

Plato/Edmentum

Answer:

add 2 to each side of the equation

Step-by-step explanation:

x-2=10

To solve for x, we need to add 2 to each side of the equation

x-2+2 = 10+2

x = 12