Find the area, in square units, of ABC plotted below.
A(0,7)
B(7,-2)
D(2, -3)
C(-3,-4)
Answers
So A=52 square units
And the brackets was absolute value
The area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
What is the distance between two points ( p,q) and (x,y)?The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The coordinates of the points A, B, C, and D in the given figure are:
A(0, 7)B( 7,-2)C(-3, -4)D(2, -3)Finding the length of the line segments AD and CB, which will be the distance between A and D, and C and B respectively.
Thus, we get:
Length of line segment AD = |AD| = distance between A and D = [tex]\sqrt{(0-7)^2 + (7-(-2))^2} = \sqrt{7^2 + 9^2} = \sqrt{130} \: \rm units.[/tex]
Similarly, we get:
|CB| = [tex]\sqrt{(-3-7)^2 + (-4-(-2))^2} = \sqrt{10^2 + 6^2} = \sqrt{136} \: \rm units.[/tex]
If we take CB as the base of ABC triangle, then as AD is perpendicular on CB, and touches the peak of the triangle ABC from its base, so AD is height of the triangle.
Thus, as we know know that:
Height's measurement of ABC = |AD|= [tex]\sqrt{130} \: \rm units[/tex]Base length of ABC = |BC| = [tex]\sqrt{136} \: \rm units[/tex]Thus, the area of the triangle ABC is:
[tex]A = \dfrac{base \times height}{2} = \dfrac{\sqrt{130} \times \sqrt{136}}{2} \approx 66.5 \: \rm unit^2[/tex]
Thus, the area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
Learn more about distance between two points here:
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Related Questions
Luca had a large container of yogurt with 1 and StartFraction 5 Over 8 EndFraction pounds of yogurt left in it. If a serving of yogurt is StartFraction 3 Over 8 EndFraction of a pound, to the nearest whole serving, how many servings of yogurt are in the container?
Answers
Answer:There are 4 serving in the container.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Took Edge 2020 Fraction Multiplication and Division Test
Here is a set of signed numbers: 7, -3, 1/2, -0.8, 0.8, -1/10, -2
Order the numbers from least to greatest.
first gets brainllest
Answers
Answer:
7, 0.8, 1/2, -0.8, -1/10, -2, -3,
Step-by-step explanation:
accidently put greatest to least just flip it i still want brainliest tho
What are the terms on the expression 2x-4y+8
Answers
The regular price of a bathing suit is $89.99. Estimate the sale price of the 25 points
bathing suit at 70% off regular price.
$27.00
$82.99
$19.99
Answers
what is the best classification for angle 1 and angle 3?
Answers
Answer:
C not adjacent because adjacent angles are right next to each other. And <1 and <3 are not right next to each other.
Step-by-step explanation:
They are not vertical angles this is what vertical angles look like ><
They are not adjacent or a linear pair.
So it is C.
Kindly help me with this question. (Chapter - Complex Numbers)
Answers
Answer:
z1(z2 + z3) = z1 z2 + z1 z3 ⇒ verified down
Step-by-step explanation:
∵ z1 = 4 + 3i
∵ z2 = 3 - 2i
∵ z3 = i + 5
→ Find the left side
∵ z1(z2 + z3) = (4 + 3i)[3 - 2i + i + 5]
∴ z1(z2 + z3) = (4 + 3i)[(3 + 5) + (-2i + i)]
∴ z1(z2 + z3) = (4 + 3i)(8 - i)
∴ z1(z2 + z3) = (4)(8) + (4)(-i) + (3i)(8) + (3i)(-i)
∴ z1(z2 + z3) = 32 - 4i + 24i - 3i²
→ Remember that i² = -1
∴ z1(z2 + z3) = 32 - 4i + 24i - 3(-1)
∴ z1(z2 + z3) = 32 - 4i + 24i + 3
→ Add the like terms
∴ z1(z2 + z3) = (32 + 3) + (-4i + 24i)
∴ z1(z2 + z3) = 35 + 20i
→ Find the right side
∵ z1 z2 + z1 z3 = (4 + 3i)(3 - 2i) + (4 + 3i)(i + 5)
∴ z1 z2 + z1 z3 = [(4)(3)+(4)(-2i)+(3i)(3)+(3i)(-2i)] + [(4)(i)+(4)(5)+(3i)(i)+(3i)(5)]
∴ z1 z2 + z1 z3 = [12 -8i + 9i -6i²] + [4i + 20 + 3i² + 15i]
→ Replace i² by -1
∴ z1 z2 + z1 z3 = [12 -8i + 9i -6(-1)] + [4i + 20 + 3(-1) + 15i]
∴ z1 z2 + z1 z3 = [12 -8i + 9i + 6] + [4i + 20 - 3 + 15i]
→ Add the like terms
∴ z1 z2 + z1 z3 = [12 + 6 + 20 - 3] + [-8i + 9i + 4i + 15i]
∴ z1 z2 + z1 z3 = 35 + 20i
∵ The left side = 35 + 20i
∵ The right side = 35 + 20i
∴ The left side = the right side
∴ z1(z2 + z3) = z1 z2 + z1 z3
Undefined slope, (0,-8)
Answers
G
Which fraction is equivalent to 6?
12 / 2
3
2 2+1 3
7, because
6 6+17
mo
2 1 1 3
because 6 - 3 and
39
2 /
3
12
2 1
because =
6 3 and
2
nd 3 -
3
12
2 1
8.
because 6 2
2+1 3
6+28
Answers
Answer:
what is the question
Step-by-step explanation:
i don't understand what you're trying to say
Answer please so hard
Answers
Answer:
b s=3w
Step-by-step explanation:
when graphed its a straight line and it goes through the orgin so its proportional
Which statement describes the inverse of m(x) = x^2 – 17x?
a. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
b. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
c. The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
d.The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
Answers
Given:
The function is
[tex]m(x)=x^2-17x[/tex]
To find:
The inverse of the given function.
Solution:
We have,
[tex]m(x)=x^2-17x[/tex]
Substitute m(x)=y.
[tex]y=x^2-17x[/tex]
Interchange x and y.
[tex]x=y^2-17y[/tex]
Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,
[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]
Add [tex]\dfrac{17}{2}[/tex] on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]
Substitute [tex]y=m^{-1}(x)[/tex].
[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]
We know that, negative term inside the root is not real number. So,
[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]
[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]
Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].
Hence, option D is correct.
Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.
Answer:
C on edu
Step-by-step explanation:
Which two numbers have a product of −18 and a sum of −7?
Answers
Answer:
2 and -9
Step-by-step explanation:
2 times -9 is -18
2 plus -9 is -7
Hope this helped!
8. Fay Teng's expenditures for the past 3 months were: August,
$1,735.50; September, $1,829.42; and October, $1,793.88.
What is her average monthly expenditure?
9. You use the utility company's budget plan for paying your
home heating bills. You pay $75 a month for 9 months. Your
actual bills are: September, $28.95; October, $16.15; November,
$68.46; December, $109.34; January, $115.26; February. $94.19;
March $75.66; April, $51.97; and May, $49.16. Compute the
average for the 9 months.
ght The McGraw-e Companies, Inc. All rights
Answers
=$75.66 all in all and $67.99 dollars
Eight more than.twice an number is four less than the same number
Answers
Answer:
2x+8=x-4
Step-by-step explanation:
I think that's right, let me know if it's wrong and I'll delete
someone help please!!
Answers
Answer:
1
Step-by-step explanation:
PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
Answers
Pls Help :( 15 points
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation please.
Answers
Answer:
(108-27)/3 =27
Each bus has 27 students, because 108-27=81, 81/3=27
Step-by-step explanation:
Hope this helps! <3
The original price for a jacket is $124.95. It is on sale for 20% off. Which of the following gives the best estimate of the savings?
Answers
Answer:
24.99
Step-by-step explanation:
We first must figure out the current price of the jacket, we need to multiply the original price (124.95) times .80 (1.00 - .20). Doing so we get a total of 99.96. In order to find the savings, we subtract the original price by the new price. 124.95-99.96 = a savings of 24.99
Answer:
You would be saving 24.99 dollars
Step-by-step explanation:
Find 20% of 124.95 using P(percentage in decimal form) times X(original number) and you should have your answer.
Hope this helps!
variation does not depend on that of another.
#6 THE SOLUTION FOR F(X) = 3X + 2 WHEN F(X) IS 2 IS
Answers
Answer:
0
*see below incase you worded it wrong
Step-by-step explanation:
then we substitute 2 for f(x)
2 = 3x + 2
0 = 3x
x = 0
UNLESS you mean f(2) is what then that is:
f(2) = 3(2) + 2 = 8
hope that helps!
Kenya went to the convenience store to buy some candy bars for her friends. She spent a total of $6.00 on candy bars. Each candy bar cost $1.50.
How many candy bars did Kenya buy?
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Find the equation of the line passing through the points (-2,-4) and (7,23)
Answers
Answer:
y=−5.4x
Step-by-step explanation:
Slope -5.4
Intercept -14.80
How is 5 represented in 6.75
Answers
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
Please look at the pic and help it got marked wrong
Answers
Answer:
although it is true that could be -(1/4)^4
if you multiply the answer can also be -1/256
Heya!!
your answer is!
-1/256
To solve the problem -9 + 18 what is the first step?
a. KCO (keep change fli[p)
b. Subtract 18 - 9
c. Subtract 9 - 18
d. Add 9 + 18
Answers
Answer:
Step-by-step explanation:
Help the pic is right here
Answers
Answer:
i think its C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
its just division tbh
a bowl contains 4 yellow marbles, 5 red marbles, 1 blue marbles, and 3 green marbles. find the probabilityof the given outcome
Answers
Answer:
bowl of colorful marbels
Step-by-step explanation:
bowl+marbels
what is 32221 x444444444444
Answers
Answer: 1.43
Step-by-step explanation:
Answer:
1.432044444444301e+17
Step-by-step explanation:
Store B sells a set for $27.00 and offers a 20% discount
Answers
Answer:
22.50
and you can pleasent do 22.50
Step-by-step explanation:
5 1/5- 1 3/4 fractions
Answers
Answer:
3 9/20
Step-by-step explanation:
first find a common demonator and change the denomators and what ever you did to the bottom you do to the top, then subtract them.
help with this immediately
Answers
Answer:
c
Step-by-step explanation:
%gggggyyhhttbu6gnmk8tg
Which shows another way to write 9.54?
O 0.5 + 0.04
O 9+ 0.4 + 0.05
O (9 * 1) + (5 x 0.1) + (4 x 0.01)
O (9 x 0.1) + (5 x 0.01) + (4 x 0.001)
Answers
Answer:
It would be C
Step-by-step explanation: