What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?



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[ ] units²

Check the picture below.

Answer:

Step-by-step explanation:

10 x 10 x 10 = 1000

10/3 = 3.333333

The value of the x-intercept is 6, the y-intercept is 75, and the value of the slope is -25/2.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The x-intercept from the graph(where y = 0)

The x-intercept = 6

The y-intercept from the graph(where x = 0)

The y-intercept = 75

The slope can be found using two points: (0, 75) and (2, 50)

[tex]\rm m =\dfrac{50-75}{2-0}[/tex]

m = -25/2

Thus, the value of the x-intercept is 6, the y-intercept is 75, and the value of the slope is -25/2.

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Answer:

20°

Step-by-step explanation:

Exterior angle property: The exterior angle of a triangle equals the sum of opposite interior angles.

  ∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

 10x - 5  = 3x + 3x + 17 + 2

  10x - 5 = 6x + 19

        10x = 6x + 19 + 5

        10x = 6x + 24

10x - 6x  = 24

        4x  = 24

         x   = 24÷ 4

           [tex]\sf \boxed{x = 6}[/tex]

∠WXY =  3x + 2

           = 3*6 + 2

          = 18 + 2

          = 20°

Solution:

Give the following below

To find the cosine function, we will apply the general formula for cosine function below

To find the value of b

Substitute the values of the variables into the general formula for cosine function

Applying a graphing tool,

The graph of one cycle of the function is shown below

Answer:

x = 2

Explanation:

The given expression is

7x - 4 - 3x = -3x + 10

First, we need to add the like terms on the left side

(7x - 3x) - 4 = -3x + 10

4x - 4 = -3x + 10

Add 4 to both sides

4x - 4 + 4 = -3x + 10 + 4

4x = -3x + 14

Add 3x to both sides

4x + 3x = -3x + 14 + 3x

7x = 14

Finally, divide by 7

7x/7 = 14/7

x = 2

Therefore, the answer is x = 2

Answer:

5y + x + 2 is one.

Step-by-step explanation:

Another one:  x + (2 + 5y)

6.72 liters per 100km

35 miles per gallon is 6.7204 liters per 100 kilometers

Here given ,

1 mile = 1.609km

1 gallon = 4.546 liters

We have to find 35 MPG to L/100km,

35 miles per gallon = 6.7204 liters per 100km

6.7204 to 3 significant figures = 6.72 liters per 100km

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The equation for the perpendicular bisector of the given line segment is y = 2x + 2.

Here, we are given a line segment with end points (3,−7) and (−9,−1)

Thus, the slope of the line can be calculated as-

(y1 - y2)/ (x2 - x1)

= (-1 + 7)/ (-9 - 3)

= 6/ -12

= -1/2

Now, since we the slope of 2 lines that are perpendicular to each other is negative of the reciprocal, thus-

slope of the perpendicular bisector = 2

Now, the midpoint of the given line segment will be-

{(x1 + x2)/2, (y1 + y2)/2}

= {(3-9)/2, (-7-1)/2}

= {-6/2, -8/2}

= (-3, -4)

Now, we can use the point slope form to find the equation of the perpendicular bisector-

(y- y1) = m(x - x1) where m is the slope and (x1, y1) is a point on the line.

⇒ (y+4) = 2(x+3)

y + 4 = 2x + 6

y = 2x + 2

Thus, the equation for the perpendicular bisector of the given line segment is y = 2x + 2.

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The fraction of the money the old girl gets is 7x/22 and the oldest gets 5x/11.

Given,

Oldest gets 5/11 of the share.

The older gets 7/12 of the remainder.

Solution:

Let x be the total amount.

Oldest share = 5/11*x

= 5x/11

Older share =( x - 5/11*x)*7/12

= (11x-5x/11)*7/12

= 6x/11*7/12

= 42x/132

= 21x/66

=7x/22

The fraction of the money the old girl gets is 7x/22 and the oldest gets 5x/11.

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Answer:

F

Step-by-step explanation:

The shape ABCD is reflected over the given line. If you were to fold the shape over to overlap the new figure FGHI, point A would correspond with point F

Answer:  F.

Step-by-step explanation:

because that's the answer.

Answer:

∠M

Step-by-step explanation:

∠M is the only vertex that does not already have an indicated angle. There are three vertexes, being 90° at ∠K (the box-like figure means it is a right angle, therefore 90°) , 61° at ∠N , and ∠M, which does not have a given angle.

The quantity which represents the dependent variable in this problem situation is: A. the number of cards sold.

In Mathematics, there are two (2) main types of variables and these include the following:

A dependent variable can be defined as the variable which signifies the effect of an independent variable and it is dependent on other factors because it's the part of an experiment that's being observed or measured.

Based on the information provided in this scenario, we can reasonably infer and logically deduce that the dependent variable is the number of greeting cards sold by Ben.

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Complete Question:

Ben sells greeting cards for $5 each in his online store. He also charges $1.99 for shipping. The total cost, y, of an order from Ben’s store is found using the equation y = 5x + 1.99, where x is the number of cards bought. Which quantity represents the dependent variable in this problem situation?

A. the number of cards sold

B. the total cost of an order

C. the cost of one card

Solving the simultaneous equation gives x as 2 and y as 3

From the information given, we have the equations as;

Now, substitute the value of y as x + 1 in equation (2) into the equation (1)

We have;

x² + (x + 1)² = 13

expand the bracket

x² + (x + 1)(x+1) = 13

x² + x² + x + x +1 = 13

collect like terms

2x² + 2x + 1 - 13 = 0

2x² + 2x - 12 = 0

Factorize the equation

2x² + 6x - 4x - 12 = 0

Factor the common terms

2x(x + 3) - 4(x + 3) = 0

2x - 4 = 0

x = 2

x = -3

Substitute x as 2 into equation (2)

y = x + 1

y = 2 + 1

y = 3

Hence, the values are 2 and 3

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The slope is -0.1 starting at 3.9, the GPA will decrease by 0.1 for each text sent in class.

Here we have to find the slope.

The equation given is:

y = 3.9 - 0.1x

As we know that the equation of a line is:

y = mx + c

Therefore we get that the slope is m = -0.1

Starting at 3.9 the GPA will decrease by 0.1 for every text sent in class ( for y = mx + b, a is the slope which is the coefficient of x)

Because the slope is less than 0, it is decreasing.

Therefore the slope is -0.1 and there is a decrease in GPA of 0.1.

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Simplifying the given expression, the passcode would be: CDOPWR.

To simplify an expression means to solve to find the value in its simplest form.

Simplify the given expression as explained below:

P. 1/2 + 2/3 - 4.25

= 1.17 + 4.25 [addition]

= 5.42

R. -7 * -4 + 3.5

28 + 3.5 [multiply before adding based on PEMDAS]

= 31.5

D. -5.6 + 2.7 - 3.2 = -6.1

W. 3/4 - 0.25 + 6.8

0.75 - 0.25 + 6.8 = 7.3 [apply PEMDAS]

C. -2 * 4.3 - 7.1 [apply PEMDAS]

= -8.6 - 7.1

= -15.7

O. 1/2 + 0.5 - 2/5 [convert all fractions to decimals]

0.5 + 0.5 - 0.4 = 0.6

From the least to the greatest, the passcode would be: CDOPWR.

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Answer:

8 visits

Step-by-step explanation:

x=# of visits
100=40+7.5x
60=7.5x
x=8

hope this helps :)

Answer:

A

tyler has a points card for a movie theater.

he receives 75 rewards points just for signing up.

• he earns 10.5 points for each visit to the movie theater.

he needs 180 points for a free movie ticket.

.

a

how many visits must tyler make to earn a free movie ticket?

Step-by-step explanation: hqwediywydgwq78d

For the given data set the frequency of the number in the range of 16 – 20 will be 6.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

It is given that frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.

Calculate the frequency of each class by counting the tally marks. The proportion of data items in a data class is its relative frequency.

The table shows the value and the frequency of all the numbers. It is obtained that the values occur in the range of 16 and 20 is 6.

Thus, for the given data set the frequency of the number in the range of 16 – 20 will be 6.

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The 20 in. by 20 in. cardboard used make the box by cutting out squares of length x from the corners gives;

The dimensions that will yield maximum volume are;

Length =

The dimensions of the cut square that gives the maximum volume is approximately 3.3 feet, while the dimensions of the box are;

Length; 13.3 feet

Width; 13.3 feet

Height; 3 feet

The maximum volume of the box is approximately 592.6 ft³

The maximum value of a function is the peak or highest point on the graph of the function.

The volume, V, of a box of Length, L, Width, W and Height, H, is given by the formula;

V = L×W×H

The length, width, and height of the box obtained by cutting a square of side length, x from the corners are;

Height of the box formed = x

Length of the cardboard box = 20 - 2•x

Width of the cardboard box = 20 - 2•x

The volume of the box is therefore;

V(x) = (20 - 2•x)•(20 - 2•x)•x = 4•x³ - 80•x² + 400•x

At the maximum point, we have;

V'(x) = (3×4)•x² - (2×80)•x + 400 = 0

V'(x) = 12•x² - 160•x + 400 = 0

Which gives;

3•x² - 40•x + 100 = 0

(3•x - 10)•(x - 10) = 0

Therefore;

[tex] \displaystyle{x = \frac{10}{3} }[/tex] and x = 10

When x = 10, we have;

V(10) = 4×10³ - 80×10² + 400×10 = 0

When x = 10/3, we have;

V(10) = 4×(10/3)³ - 80×(10/3)² + 400×(10/3) ≈ 592.6

Therefore, the dimensions of the box that gives the maximum volume is [tex] \displaystyle{x = \frac{10}{3} \approx 3.3}

The dimensions that yield maximum volume are therefore;

The maximum of the box is 592.6 ft³

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The length of the ribbon used for the craft project is 3 meters

The length of ribbon need for the craft project = 114 inches

So, the length of the ribbon need to be in meters .

Thus, we can convert inched to centimeter by

                  1 inches = 2.54 centimeters

We know that 1 cm = 0.01 m

Thus , 1 inch = 2.54 x 0.01 m

          1 inch = 0.0254 m

Then for length of 114 inch ,

      114 inch = 0.0254 x 114 meters

                    = 2.89

                   ≈ 3 meters

Therefore , the length of the ribbon is 3 meters

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(C): 3 meters.

Step-by-step explanation: The answer is 3 meters. The way to find this is relatively easy.

1. First, write 114 x 2.54.

2. Which is 289.56. Next, we convert 389.56 centimeters to meters.

3. That should give you 2.89. Because 8 is bigger than 4, we round up.

4. Now our answer is 3.

AFTER MESSAGE: I hope this helps! This is my first answer in a while, so forgive me if it is complicated. Also, give brainliest to other guy, he was here first.

Thank you!

Answer: 3 / 8 of the puppies have red collars

Answer:

Step-by-step explanation:

-1 + 14x = 12x + 17

    -12x    -12x

-1 + 2x = 17

+1          +1

2x = 18

x is equal to 9

hope this helps!

Answer:

(-9, 5)

Step-by-step explanation:

A midpoint is the point, or center at the middle of two given points.

The midpoint formula:

[tex](Xm, Ym)= (\frac{x1 + x2}{2}), (\frac{y1 + y2}{2})[/tex]        

X1, Y1  is an endpoint

X2, Y2 is an endpoint.

Explanation:

X1, Y1= (-8, 6)

X2, Y2= (-10, 4)

[tex]Xm, Ym= \frac{(-8)+(-10)}{2}, \frac{(6+(4)}{2}[/tex]

[tex]Xm, Ym= \frac{-18}{2}. \frac{10}{2} \\\\Xm, Ym= (-9, 5)[/tex]

The Midpoint is (-9, 5)

The number of different selections that a customer can make is of 210.

To calculate the number of different selections that the customer can make, we need to verify if the order of the selections matters or not, then:

In the context of this problem, the order does not matter, hence the combination formula is used.

The number of combinations, from a set of n elements, of x elements, is given according to the following rule:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, the number of selections is of 4 samples from a set of 10 samples, hence it is calculated as follows:

[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]

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Answer:

1. 14

2. 25

3. 22

4. 25

5. 8

Step-by-step explanation:

These are actually simple linear equations disguised as geometry.

Image 1.

the triangle is an isosceles triangle, so 2x = 50

sum in triangle is 180, so

5y+10 = 180 - 2*50

5y = 70

y = 14

Image 2.

the triangle is an isosceles triangle, so AB=BC

5x+5 = 7x-1

5 = 2x-1

2x = 6

x = 3

AC = 6x+7 = 18+7 = 25

Image 3.

the triangle is an isosceles triangle, so AC=AB

2x-24 = x-2

x-24=-2

x = 22

BC = x = 22

Image 4.

The triangle is an equilateral triangle, so AB=BC=AC

3x-5=2x+20

x-5=20

x=25

Image 5.

The triangle is an equilateral triangle, so every angle is 60 degrees

7x+4 = 60

7x = 56

x = 8

Answer:B 66.72

Step-by-step explanation:

complementary means if two angles are added up they will equal 90. we and eliminate d cause 23.28+23.28=46.56 so d is wrong now let's try c 46.56+23.28=69.84 so c is wrong cause it doesn't equal 90 now let's try a 156.72+23.28=180 its wrong since we are using complementary angles instead of supplementary angles Supplementary are angle two angles that add up to 180. so that just leaves b cause 23.28+66.72=90. i hope this helps and i made sure to explain it as best as i can have a great day

The solution is Option B.

The measure of the complementary angles are 66.72° and 23.28°

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

Let the first angle and second angle be a and b respectively such that

a + b = 90°

Given data ,

Let the first angle be represented as A

Now , the value of A is = 23.28°

Let the second angle be represented as B

Now , the value of B is = B

The angles A and B are complementary ,

So , A + B = 90°   be equation (1)

Substituting the values in the equation , we get

23.28° + B = 90°

On simplifying the equation , we get

Subtracting 23.28° on both sides of the equation , we get

B = 90° - 23.28°

B = 66.72°

Therefore , the value of B is 66.72°

Hence , the measure of the angle is 66.72°

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Answer:

20m

11m

20m2

5m

11m

8x8

11x2

Answer:

1. False. The only term is the number of miles traveled or z

2. True 1.50 is being multiplied so it is a coefficient of z

3. False. there is no division being done.