Plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area.
A=(-2,11) B = (4.6) C=(-1,0)
Choose the correct graph below that shows points A, B, C, and triangle ABC.
D.
ОА.
Ов.
Q
a
a
To show that the triangle is a right triangle, show that the sum of the squares of the lengths of two of the sides (the legs) equals the square of the length
of the third side (the hypotenuse).
Sum of the squares of the lengths of the legs of the triangle =
Square of length of the hypotenuse of the triangle =
Find the area of the triangle.
square units
Area =
?
Click to select your answer(s).
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Answers
Answer:
Step-by-step explanation:
AB=√[(4+2)²+(6-11)²]=√61
BC=√[(-1-4)²+(0-6)²]=√61
AC=√[(-1+2)²+(0-11)²]=√122
AC²=AB²+BC²
So it is a right angled triangle.
The area of the triangle is (8/5)sqrt(1199) square units.
We are given that;
Coordinates= A=(-2,11) B = (4.6) C=(-1,0)
Now,
we can plug in one point on line AB, such as A(-2, 11), and solve for b:
y = mx + b 11 = (-5/6)(-2) + b 11 = (5/3) + b b = 11 - (5/3) b = (28/3)
Hence, the equation of line AB is:
y = (-5/6)x + (28/3)
Now we can set y equal to 0 (the y-coordinate of C) and solve for x:
y = (-5/6)x + (28/3)
0 = (-5/6)x + (28/3) (-5/6)
x = -(28/3)
x = -(28/3)/(-5/6)
x = (56/15)
Therefore, point D has coordinates (56/15, 0). To find the height of the triangle, we need to find the distance between points A and D using the distance formula:
[tex]h = AD = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) h = sqrt((56/15 - (-2))^2 + (0 - 11)^2) h = sqrt((136/15)^2 + 121) h = sqrt(18496/225 + 121) h = sqrt(45121/225) h = (3/15)sqrt(5024)[/tex]
Now we can plug in the values of b and h into the area formula and simplify:
[tex]A = (1/2)bh A = (1/2)(sqrt(61))((3/15)sqrt(5024)) A = (1/10)sqrt(61)sqrt(5024) A = (1/10)sqrt(307584) A = (1/10)(16)sqrt(1199) A = (8/5)sqrt(1199)[/tex]
Therefore, by the given triangle answer will be (8/5)sqrt(1199) square units.
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Related Questions
Find the quotient if the dividend is 2.26 · 108 and the divisor is 0.013.
a.5.75 × 10 -11
b.2.938 × 10 6
c.1.738 × 10 10
d.1.738 × 10 6
Answers
Answer:
17.38*10^8
Step-by-step explanation:
Step one:
given data
The dividend is 2.26*10^8 (i rewrote the given data, i hope it was mearnt to be so)
divisor is 0.013.
Step two:
Hence the quotient is the whole number gotten when the dividend is divided by the divisor
quotient= 2.26*10^8/0.013.
quotient= 17.38*10^8
Select the correct answer from each drop-down menu. f(x) = x2 − 8x + 15 g(x) = x − 3 h(x) = f(x) ÷g(x) h(x) = . The domain of h(x) is U .
Answers
Answer:
h(x) = x-5 . The domain of h(x) is (- infinity,3) U (3, infinity)
Step-by-step explanation: plato/edmentum
The domain of h(x) is (-∞ , 3 ) ∪ (3,∞) .
What is domain?The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.
According to the question
f(x) = [tex]x^{2}[/tex] − 8x + 15
g(x) = x − 3
h(x) = f(x) ÷ g(x)
i.e,
h(x) = [tex]\frac{ x^{2} -8x + 15}{x-3}[/tex]
now,
x ≠ 3
[tex]h(x) = \frac{(x-5)(x-3)}{(x-3)}[/tex]
so,
Domain or x ∈ (-∞ , 3 ) ∪ (3,∞)
Hence, The domain of h(x) is (-∞ , 3 ) ∪ (3,∞)
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Suppose a normally distributed set of data with 4800 observations has a mean of 195 and a standard deviation of 12. Use the 68-95-99.7 Rule to determine the number of observations in the data set expected to be below a value of 231. Round your result to the nearest single observation.
Answers
Answer:
The number of observations in the data set expected to be below a value of 231 is of 4793.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 195
Standard deviation = 12
The normal distribution is symmetric, which means that 50% of the observations are above the mean and 50% are below.
Proportion of observations below 231:
231 = 195 + 3*12
So 231 is three standard deviations above the mean.
Of the 50% of observations below the mean, all are below 231.
Of the 50% of observations above the mean, 99.7% are between the mean of 195 and three standard deviations above the mean(231).
So, the proportion of observations below 231 is:
[tex]P = 0.5*1 + 0.5*0.997 = 0.9985[/tex]
Out of 4800:
0.9985*4800 = 4793
The number of observations in the data set expected to be below a value of 231 is of 4793.
A coordinate grid with 4 lines. Line A passes through (0, 5) and (4, 3.75). Line B passes through (3.75, 0) and (0, negative 5). Line C passes through (0, negative 5) and (negative 3.75, 0). Line D passes through (negative 3.75, 0) and (0, 5).
Which line represents the linear equation
–3y = 15 – 4x?
The equation –3y = 15 – 4x rewritten in slope-intercept form is
.
The y-intercept is
and the slope of the line is
.
Line
is the graph of the line –3y = 15 – 4x.
Answers
Answer:
Step-by-step explanation:
Line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
What is a Line??
A line can be defined by the shortest distance between two points is called as a line.
Given the expression of the line,
–3y = 15 – 4x
Now by putting every given point of the lines given with their passing points in –3y = 15 – 4x , it is found that point (3.75, 0) and (0, -5) lies on the line.
Hence, the expression –3y = 15 – 4x represents line B.
Now, the slope and y-intercept of the equation.
Rearrange the equation into standard form,
y = 4/3 x - 5
Now compare the above equation with the standard form line
y = mx +c
m = 4/3 and c = -5
Thus, line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.
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Find the missing angle
Answers
Sorry if wrong :) I hope this help
Allen weighs 44 kg. Miller weighs half as much as Allen, and James weighs 3 kg more than Miller.
What is their weight all together?
Answers
Answer:
91
Step-by-step explanation:
there are 30 students in Ms. jones's class. if 10% of the students are left-handed, how many students are left-handed? explain
Answers
Answer:
3
Step-by-step explanation
So, you need to find 10% of 30
10/100 (fraction form of 10%) x 30
of = multiply
10/100 x 30 = 300/100 = 3
Ken used 1 3/8 cupe of walnuts and 1 3/4 cups of raid in to make trail mix did he make
Answers
Answer:
3 1/8
Step-by-step explanation:
Add the 1 3/8 cups of walnuts to the 1 3/4 cups of raisins. You will have to make your denominators the same to add the fraction.
1 3/8. 1 3/8
+1 3/4. 3 x 2 = 6. +1 6/8
_____ 4 x 2 = 8. ______
2 9/8 reduce 3 1/8
Please help! I've been stuck on these questions for awhile!
Answers
Y = 2x - 2
For a line to be perpendicular to another line the 2 gradients multiplied have to equal -1. Therefore the gradient of the new line is -1/2.
Y = -1/2x + c
Now sub in -4 for x and 5 for y.
5 = (-1/2 x -4) + c
5 = 2 + c
c = 3
So the equation of the line:
Y = -1/2x + 3
There are 44 students in the band . If eleven of them own their own instrument, what percent do NOT own their own instrument?
Answers
Answer:
75%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
You can tell since it is 11/44 as a fraction and if there are 4 11's, it will be 44 and a percent that is equal to 100 but has four "places" is 25%
Luis rides his bicycle 3/4 mile in 5 minutes along the bike trail.
Assuming he rides at a constant rate, what is his speed, in miles per hour? Use the table to help find the answer.
Enter your answer in the box.
Answers
Answer: 3 mph.
Because....
3/4 of a mile is 0.75 miles.
0.75 miles = 15 minutes
X = 15 * 1 / 0.75
X = 20 minutes takes a mile to travel
20 minutes = 1 mile
60 minutes = X
Clearing X would give:
X = 60/20
X = 3 miles per hour.
Luis rides 3 miles per hour.
* Hopefully this helps:) Mark me the brainliest!!!
What is the scientific notation of 0.000000000012
Answers
Answer:
1.2x10^-11
You never start with a zero so you move the decimal 11 spots the right which makes it negative
Wwhich expression has the greatest value when x=3?
A) 2x^3
B) 2x^3 + 5
C) (2x)^3
D) (x-1)^3
Answers
Answer:
C!
a=54
b=59
c=216
d=8
Step-by-step explanation:
Marco bought a 64 ounce bag of popcorn.
He ate 5% of the bag with his lunch. How
much popcorn did he eat at lunch?
Answers
Answer:
3.2 ounces.
Step-by-step explanation:
Divide 5 percent by One Hundred,
5/100 = 0.05
Multiply 0.05 by 64
0.05x64= 3.2
Answer:
3.2
Step-by-step explanation:
Find 5% of 64
10% = 6.4 (64 divided by 10)
5% = 6.4÷2= 3.2
Write each expression in exponential form.
Answers
p2-q2=7 and p-q=2. Find the value of p + q.
Answers
Answer:
p + q = 13/4
Step-by-step explanation:
p² - q² = 7
p - q = 2
Use substitution.
p = 2 + q
(2 + q)² - q² = 7
Expand (2 + q)² with FOIL - first, outer, inner, last
(2 + q)(2 + q)
4 + 2q + 2q + q²
4 + 4q + q²
Subtract q².
4 + 4q + q² - q² = 7
4 + 4q = 7
Combine like-terms.
4q = 3
Divide by 4 to isolate q.
q = 3/4
Plug q into the equation to find p.
p - q = 2
p - (3/4) = 2
Add 3/4 to both sides.
p = 11/4
Add p and q.
11/4 + 3/4
= 13/4
how do you solve the problem 2247 divided by 7?
Answers
Answer:
321
Step-by-step explanation:
2247÷7=321
Answer:
321
Step-by-step explanation:
Shown in picture attached.
Which equation represents the graph shown?
A.) y=x
—
35
B.) y=x-35
C.) y=x+35
D.) y=35x
Answers
I need help please it so confusing can somebody anyone break it down
Answers
Answer:
[tex]a=\sqrt{63}[/tex]
Step-by-step explanation:
When we solve for this we should always remember this formula [tex]a^2+b^2=c^2[/tex] and since we already know b and c we can plug that in tho find out what a could be but we won't actually solve it.
[tex]a^2+b^2=c^2\\a^2+9^2=12^2\\a^2+81=144\\a^2=63\\\sqrt{a^2}=\sqrt{63}[/tex]
So a would equal whatever the square root of 63 is.
Please help me with this question
Answers
9514 1404 393
Answer:
A∪B = (-7, -2)
Step-by-step explanation:
It can be helpful to draw a picture. It shows that set B is completely contained within set A, so the union of the two sets is simply set A.
A∪B = (-7, -2)
Connor drove 340 miles on 8 gallons of gas. How many miles did his car travel per gallon of gas?
Answers
Answer:
42.5
Step-by-step explanation:
calculatour
Using the formula A = 6s2, solve when s = 2?
Answers
Answer:
When s=2, A=24
Step-by-step explanation:
We are given the formula [tex]A = 6s^2[/tex]
We need to solve and find value of A , when s=2
So, putting value of s in the given formula we can find value of A
The formula given is:
[tex]A=6s^2\\Put\:s=2\\A=6(2)^2\\A=6(4)\\A=24[/tex]
So, by putting s= 2, We get A=24
The following are the weights of 10 young dogs, in pounds: 7, 5, 11, 8, 14, 19, 16, 15, 13, 27 What proportion of the measurements lie in the interval LaTeX: \bar x \pm 2sx
Answers
Answer:
0.9
Step-by-step explanation:
Given that data:
x : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27
Mean = Σx / n
Using calculator :
Mean (m) = 13.5
Standard deviation (s) = 6.433
Proportion that lies in mean ± 2s
Lower = Mean - 2s
13.5 - 2(6.433) = 0. 632
Upper = Mean + 2s
13.5 + 2(6.433) = 26.376
Mean ± 2(sd) = (0.632, 26.276)
The only digit from the data which falls outside the defined range = 27
Proportion within interval = 9 / n
Proportion which falls within range = 9/10 = 0.9
Tim earns $31 after 2 hours, $46.5 after three hours,
and $62 after four hours. Write an equation that
represents the amount of money Tim makes.
Answers
Answer:
Equation: y = 15.5x
Step-by-step explanation:
Given that:
Time earns $31 for 2 hours
$46.5 for 3 hours
$62 for 4 hours
We will find unit rate first.
Unit rate = [tex]\frac{31}{2}[/tex] = $15.5 per hour
Now,
Let,
x be the number of hours
y be the total money earned by Tim
Total earning = Per hour rate * Number of hours
y = 15.5x
Hence,
Equation: y = 15.5x
If Brenda has 10 math problems to solve and she can solve one math problem per minute how long will it take her to solve all 10 problems
Answers
Solve the inequalities by graphing. Identify the graph that shows the following equations.
3x – 2y <1
y > 3
Answers
Answer:
its 9
Step-by-step explanation:
What is the value of the
underlined digit?
56
Answers
Hope this helps
What is an equation of the line that passes through the point (-4,-6)and is
paralel to the line 2x-y=6
Answers
Answer:
Step-by-step explanation:
2x - 7y = -6.
What is the distance between the points (-1, 8) and (5, 8) in the coordinate plane?
Answers
Explain the pattern that you notice when dividing by 10, 100, and 1,000
Answers
Answer:
when you divide by 100 it is .1 but when you divide by 1000 it is .01 so every time you divide you move the decimal up by one
I hope this helps:
