Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2

Answers

Answer 1

Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]

[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]

Related Questions

Question 21 of 25
f(x) = 3x + 2
What is f(5)?
OA. 17
OB. 15
OC. 10
01

Answers

Answer:

A. 17

Step-by-step explanation:

f(x) = 3x + 2

f(5) = 3(5) + 2

= 15 +2

= 17

The answer should be A.17
;)

Daniel used the formula to find the area of the following special trapezoid. His work is shown. Identify his error and correct it to find the area of the special trapezoid.

Answers

Daniel made an error in line 3. He wrongly divided the sum of sides and height. The area of the trapezoid is 42 cm².

What is the area of the trapezoid?

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.

Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height

Line 1: A = 1/2 x (6) + (7 + 7) Line 2: A = 1/2 (6) (14) Line 3 : 3 x 14 Line 4 : A = 42 cm²

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Find Median of 10,12,14 and 16

Answers

Step-by-step explanation:

the median is the value, where half of the other values is smaller (or equal), and the other half bigger (or equal).

with an even number of data points that is not directly possible to find.

in this case the 2 middle values are taken and their mean value is the median.

in our case, the 2 middle values are 12 and 14.

their mean value is

(12+14)/2 = 26/2 = 13

so,

13 is the median (even though if is not a data point itself).

A nuclear power plant has two independent safety systems. The probability the first will not operate properly in an emergency P (A) is 0.01, and the probability the second will not operate P (B) in an emergency is 0.03. What is the probability that in an emergency both of the safety systems will not operate?

Answers

Step-by-step explanation:

they are independent systems, so in case of an emergency both systems will activate.

this is like rolling 2 dice and asking for the probability that both will show 1.

the probability that both will fail is the product of the individual probabilities for failure :

0.01 × 0.03 = 0.0003

so, the third answer option is correct.

FYI - the probability for 2 dice to both roll 1 is

1/6 × 1/6 = 1/36

The equation of a circle is given below:

x squared minus 4 x plus y squared minus 6 y minus 7 equals 0

Identify the center and radius of the circle.

Group of answer choices

Center: left parenthesis 2 comma 3 right parenthesis
Radius: 20

Center: left parenthesis 4 comma minus 6 right parenthesis
Radius: 2 square root of 5

Center: left parenthesis negative 4 comma 6 right parenthesis
Radius: 20

Center: left parenthesis 2 comma 3 right parenthesis
Radius: 2 square root of 5

Answers

Given:

The equation of the circle is

We need to determine the center and radius of the circle.

Center:

The general form of the equation of the circle is

where (h,k) is the center of the circle and r is the radius.

Let us compare the general form of the equation of the circle with the given equation to determine the center.

The given equation can be written as,

Comparing the two equations, we get;

(h,k) = (0,-4)

Therefore, the center of the circle is (0,-4)

Radius:

Let us compare the general form of the equation of the circle with the given equation to determine the radius.

Hence, the given equation can be written as,

Comparing the two equation, we get;

Thus, the radius of the circle is 8

Use technology or a z-score table to answer the question.
The weights of boxes of rice produced at a factory are normally distributed with a
mean of 20 ounces and a standard deviation of 1.5 ounces. Consider a shipment of 1500 boxes of rice.
How many of the boxes will weigh 18 ounces or less?
138 boxes
154 boxes
632 boxes
781 boxes

Answers

The number of boxes will weigh 18 ounces or less will be 138. Then the correct option is A.

What is a normal distribution?

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The weights of boxes of rice produced at a factory are normally distributed with a mean of 20 ounces and a standard deviation of 1.5 ounces.

Consider a shipment of 1500 boxes of rice.

Then the number of the boxes will weigh 18 ounces or less will be

z = (18 - 20) / 1.5

z = -1.33

Then the probability will be

P(x ≤ 18) = P(z ≤ -1.33)

P(x ≤ 18) = 1 - P(z > -1.33)

P(x ≤ 18) = 1 - [1 - P(z < -1.33)]

P(x ≤ 18) = P(z < -1.33)

P(x ≤ 18) = 0.091211

Then the number of the boxes will weigh 18 ounces or less will be

⇒ 0.091211 x 1500

⇒ 136.8

approximately 138 boxes.

Then the correct option is A.

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11. 6.2 m B 1.8m Calculate the value of x. NOT TO SCALE

Answers

Answer:

24.19

Step-by-step explanation:

[tex] \tan(x) = \frac{6.2}{13.8} \\ x = { \tan}^{1} \frac{6.2}{13.8} \\ x = 24.19320899[/tex]

or the value of x can be 24.20

If f(x)=3x+5/x, what is f(a + 2)?

a. 3a + 5/a + 2

b. 3(f(a)) + 5/f(a)+2

c. 3(a+2) + 5/a+2

Answers

Answer:

Answer C is correct

Step-by-step explanation:

1. We replace x as (a + 2)

2. Then we just rewrite this function with the new value

3. Result: 3(a+2) + 5/(a+2)

please answer thank you!

Answers

Answer:

1. Median:70, Range:12, IQR: 8

2. Median: 59, Range: 48, IQR: 31

Step-by-step explanation:

Hello, the answers I have are just approximations because I can not tell the specific number in between each mark.

The median is the middle vertical line of the box. The range is you maximum subtracted from your minimum. You can find these at the lines that extend out of the box. The interquartile range is the ends of the box subtracted from each other, meaning quartile 3 subtracted from quartile 1.

Hope this helps.

Can someone help with number 4. I will reward brainliest.

Answers

Answer:

theta = pi/6 and

theta = 5pi/6

Step-by-step explanation:

see image. Factor the expression. Solve for sin theta. Then use a calculator or unit circle to solve for theta. See image.

Let's simplify the problem down a little:

⇒ set 'sin(θ)' as x

⇒ the new equation looks like: [tex]2x^2+5x-3=0[/tex]

Now let's solve this equation as a quadratic:

[tex]2x^2+5x-3=0\\(2x-1)(x+3)=0\\\\2x-1=0\\x = \frac{1}{2} \\\\x+3 = 0\\x=-3[/tex]

Now set the x value of '1/2', to sin(θ)

it can't be -3, because trig functions can't equal a negative number

sin(θ) = 1/2

θ = π/6, which is between the range given

Answer: π/6

Hope that helps!

11/12 - 7/9
5/36
5/72
25/36
25/72

Answers

Step-by-step explanation:

P and q are two arithmetic sequences. The first four terms of sequence P are 2,6,10,14. The nth term of sequence Q is 145-3n. The rth term of sequence P has the same values as the rth term of sequence Q. Work out the value of r.

Answers

Answer:

r = 21

Step-by-step explanation:

nth of sequence P :

[tex]T_{n} = 4n -2[/tex]

[tex]r^{th} term[/tex] : [tex]4r-2=145-3r\\4r+3r=145+2\\7r=147\\r=21[/tex]

Help! I need to finish but I'm stuck! Will give brainliest!
The shaded figure below is composed of a trapezoid and a semicircle on a coordinate plane.

Which of the following expressions represents the area of the shaded figure?

2(18 + π)
2(12 + π)
4(9 + 2 π)
8(3 + π)

Answers

Answer:

2(12 + π)

Step-by-step explanation:

This will get you about 30and even by just counting squares you will get the closest to this answer.

Suzie's Slushes has increasing profits each week during the hot summer months. Suzie finds that each week during the summer her profits increase by 30% over what they were the previous week. In her first week of business, her profits were $300. How much money will she make in all over 4 weeks

Answers

The amount of money that Suzie will make over the four weeks is; $1856

How to find amount of profit made?

Suzie will make a profit of:

The first week = $300

The second week = (300 * 30%) + 300 = $390

The third week = 390 * (1430%) = $507

The fourth week: 507 × (1430%) = $659.1

Thus, Sum of profit = $300 + $390 + $507 + $659.1

Sum of Profit = $1856.1 ≈ $1856

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Find the value of x in the given
right triangle.
7
X
10
x = [ ? ]

Answers

The value of x in the given right triangle is approximately 7.14

How to find unknown side in a right triangle?

Hypotenuse = 10opposite = xAdjacent = 7

Hypotenuse² = opposite² + adjacent ²

10² = x² + 7²

100 = x² + 49

100 - 49 = x²

51 = x²

x = √51

x = 7.14142842854284

Approximately,

x = 7.14

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Which expression is equivalent to -6(-2+2x)?
O −4-12%
O −4+2%
O 4-12%
O 4+12%

Answers

-6(-2+2x)

Use distributive law

a(b+c)=ab+ac

-6(-2)-6(2x)12-12x12(1-x)

Evaluate -6y - 5 for y = 1/2

Answers

Answer:

Step-by-step explanation:

-6y-5

Substitute 1/2 for y.

-6y-5

-6(1/2)-5

-3(-5)

if the point D (8, -5) is reflected over the x-axis, the coordinates of D’ would be

Answers

The image of the point after the reflection across the x-axis is (8,5)

How to determine the image of the point?

The point is given as:

D = (8,-5)

The rule of reflection across the x-axis is:

(x,y) -> (x,-y)

So, we have:

D' = (8,5)

Hence, the image of the point after the reflection across the x-axis is (8,5)

Answers

Step-by-step explanation:

-2g(1+g)

-2g - 2g²

(-2)g - (2)g²

Which of the following best describes AD?
OA. Angle bisector
OB. Perpendicular bisector
OC. Median
OD. Altitude
B
17
D
17
C

Answers

Answer:

see the attachment photo!

just comment here if you need help

The best description about the line AD is,

⇒ Perpendicular bisector

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC is shown in figure.

Now, We have by figure;

BD = 17

DC = 17

Hence, We can say that;

Line AD is Perpendicular bisector of line BC.

Thus, The best description about the line AD is,

⇒ Perpendicular bisector

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A study was conducted about the number of miles that a sample of automobiles in New York City drive within a year. The sample was taken in front of an apartment complex and included 20 taxicab drivers and 40 of the building’s residents. Which is a reasonable explanation for the large gap in the histogram?

Answers

The histogram includes data from a voluntary response sample which is not representative of the population.

How to interpret Histograms?

A histogram is a chart that represents numerical data using bars. The dataset is split into intervals, each interval is represented by a bar, and the number of variables in each interval makes up the frequency for that interval.

From the histogram attached, we can see that there is a huge gap from around 17000 miles to 32500 miles.

Now, when we have this kind of gap it means that the histogram includes data from a voluntary response sample which is not representative of the population.

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DILATE TRIANGLES URGENTTTTTT
photo is inserted so work from that, the original triangle is the one in blue.

Answers

The Dilation is 0.76

What is dilation?

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.

Dilation or scale factor= Dimension of new shape/ dimension of old shape

= Perimeter of new triangle(green)/ Perimeter of old Triangle (blue)

= 8.3/10.9

= 0.76

Hence, the scale factor is 0.76.

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complete the proof and tell me how to come up with the answer please ASAP

Answers

Step 4 is the reason SSS

10 more than w is equal to 40 what is the expression

Answers

Answer:

w + 10 = 40

Step-by-step explanation:

10 more than w is w + 10 is equal to 40 is =40

w + 10 = 40

Please mark as brainliest.

Answer:

10 + w = 40

Step-by-step explanation:

10 more than w is equal to 40 what is the expression

10 + w = 40 is the expression

w = 40 - 10

w = 30 is the solution

pls help me I can,t do this

Answers

15.75 square inches

Seleccione el número que se puede
describir mejor como enteros.

Answers

the second one

Step-by-step explanation:

After arguing for two weeks, melissa convinced her parents to have her birthday party at flyzone trampoline park. as soon as she gets there, melissa spends time practicing flips on the trampolines. then, she spends 1/2 of an hour eating birthday cake with her friends. in all, melissa spends 1/4 hours at flyzone.

Answers

The amount of time that Nora practices flips is; t = 1 ¹/₄

How to Solve Algebra problems?

We are told that;

Nora spends time practicing flips on the trampolines. Let this be t.

Then, she spends 1/2 of an hour eating birthday cake with her friends.

Thus, total amount of time spent on flips and eating with her friends is;

t + ¹/₂ = 1 ³/₄

t = 1 ³/₄ - ¹/₂

t = 1 ¹/₄

Complete Question is;

After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?

Solve this equation for (t) to find the amount of time Nora practices flips

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Kellie thinks of a number, then doubles the number, and then multiplies the result by 3. If her final number is 65 more than her original number, then what was her original number I will give 70 points pls

Answers

Kellie's original number given the analogy and corresponding equation is 13

How to write and solve equation?

let

the unknown number = x

(x × 2) × 3 = x + 65

2x × 3 = 65 + x

6x = 65 + x

6x - x = 65

5x = 65

divide both sides by 5

x = 65/5

x = 13

check:

6x = 65 + x

6(13) = 65 + 13

78 = 78

Therefore, the unknown number, x is 13

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Which of the following statements is true concerning ABC below?
10
B
с
OA. ZA is the smallest angle.
OB. ZB is the largest angle.
C. Bis the smallest angle.
OD. ZA is the largest angle.
2

Answers

Answer:

see the attachment photo!

Use the function to predict the minimum target heart rate for a person 20 years old. beats per minute

Answers

The minimum target heart rate for a person 20 years old is 120 beats per minute

How to predict the minimum target heart rate?

The equation of the function is given as:

y = -0.6x + 132

Where x represents the age, and y represents the minimum target heart rate

From the question, we have:

x = 20

Substitute x = 20 in y = -0.6x + 132

This gives

y = -0.6 *20 + 132

Evaluate

y = 120

Hence, the minimum target heart rate for a person 20 years old is 120 beats per minute

Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9). A= units^2

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Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2