Given:
The vertices of a right triangle are:
[tex](-3,4),(3,4),(3,-4)[/tex]
To find:
The length of the hypotenuse of the given right triangle.
Solution:
Let the vertices of the right triangle are [tex]A(-3,4),B(3,4),C(3,-4)[/tex].
The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(3-(-3))^2+(4-4)^2}[/tex]
[tex]AB=\sqrt{(3+3)^2+(0)^2}[/tex]
[tex]AB=\sqrt{(6)^2+0}[/tex]
[tex]AB=\sqrt{36}[/tex]
[tex]AB=6[/tex]
Similarly,
[tex]BC=\sqrt{(3-3)^2+(-4-4)^2}[/tex]
[tex]BC=\sqrt{(0)^2+(-8)^2}[/tex]
[tex]BC=\sqrt{64}[/tex]
[tex]BC=8[/tex]
And,
[tex]AC=\sqrt{(3-(-3))^2+(-4-4)^2}[/tex]
[tex]AC=\sqrt{(6)^2+(-8)^2}[/tex]
[tex]AC=\sqrt{36+64}[/tex]
[tex]AC=\sqrt{100}[/tex]
[tex]AC=10[/tex]
Now, taking sum of squares of two smaller sides, we get
[tex]AB^2+BC^2=6^2+8^2[/tex]
[tex]AB^2+BC^2=36+64[/tex]
[tex]AB^2+BC^2=100[/tex]
[tex]AB^2+BC^2=AC^2[/tex]
By the definition of the Pythagoras theorem, AC is the hypotenuse of the given triangle.
Therefore, the length of the hypotenuse is 10 units.
Allison invested $70,000 in an account paying an interest rate of 6.2%
compounded continuously. Assuming no deposits or withdrawals are made,
how long would it take, to the nearest year, for the value of the account to
reach $223,200?
Answer: 19
Step-by-step explanation: j trust me
smeone invests £800 at a rate of 2% simple interest per year. Work out the amount of interest she receives after three years.
Answer:
£48
Step-by-step explanation:
I=Prt
I=(800)(0.02)(3)
I = 48
Answer:
the simple interest earned was £48.
Step-by-step explanation:
the appropriate simple interest formula is i = prt, where r is the annual interest rate as a decimal fraction. Here, with prt = (£800)(0.02)(3 yr), we find that the simple interest earned was £48.
I WILL GIVE BRAINLIEST IF YOU ANSWER ALL OF THEM!!!!!!!! but you dont have to do all of them but if you dont then i wont give brainliest
Answer:
-6, -1, 1, 6, 10-8.2, -2.5, 0.4, 2.4-7.1, -5.2, 0.5, 0.9-3.75, -2.4, 0.2, 9.5-7.4, -4 3/8, 0.2, 7.4-3.3, -3, 0.3, 3.3><>><>Select the Phrase that goes with the Expression:
a + b
A. The Product of a and b.
B. The total of a and b.
C. b fewer than a
D. The difference of a and b.
Use the long division method to find the result when 9x^3+18x^2+20x+169x 3 +18x 2 +20x+16 is divided by 3x+43x+4.
Given:
Dividend = [tex]9x^3+18x^2+20x+16[/tex]
Divisor = [tex]3x+4[/tex]
To find:
The quotient and remainder by using the long division method.
Solution:
Using the long division method, divide the polynomial [tex]9x^3+18x^2+20x+16[/tex] by [tex]3x+4[/tex] as shown below:
[tex]3x+4 |\overline{9x^3+18x^2+20x+16}|3x^2+2x+4\\[/tex]
[tex]9x^3+12x^2\\\underline{(-)\quad (-)\quad \quad \quad}[/tex]
[tex]0+6x^2+20x[/tex]
[tex]6x^2+8x\\\underline{(-)\quad (-)\quad \quad \quad}[/tex]
[tex]0+12x+16[/tex]
[tex]12x+8\\\underline{(-)\quad (-)}[/tex]
[tex]\underline{\quad 0\quad}[/tex]
Therefore, the quotient is [tex]3x^2+2x+4[/tex] and the remainder is 0.
i need help solving the paint questions
For S if the ratio is 2:7 and you use 20 drops of red paint you multiply 2 by 10 which is 20 so you also multiply 7 by ten to get 70 (So the answer for S is 70 drops) and for L you multiply 2 by 20 to get 40 so you multiply 7 by 20 and you get 140 (The answer for L is 140 drops) For T you multiply 2 by 1.5 to get 3 so you multiply 7 by 1.5 which is 10.5 ( so the answer for T is 10.5 drops)
3. Find the slope between the two points (-3,3) and (3,-1) Your Answer:
At what rate per cent will the intrest on Rs. 2520 add up to Rs. 84 in 8 months
Answer:
The rate of percent is 5%
Step-by-step explanation:
HELP ASAP!!!!!
ABCD is a parallelogram. AB = 2x, AD = 4y - 6, BC = 3x. If the perimeter of ABCD is 180, find the values of x and y
Answer and Step-by-step explanation:
AB = DC = 2x
AD = BC = 4y - 6 = 3x
180 = 2x + 2x + 3x + 3x = 10x
18 = x
4y - 6 = 3(18)
4y = 54 + 6
4y = 60
y = 15
18 = x
15 = y
2(18) + (4(15) - 6) + 3(18) + 2(18) = 36 + 36 + 54 + 54 = 180
#teamtrees #PAW (Plant And Water)
The marked price of a stove was $520. A worker bought the stove on hire purchase by making a down payment of $100, and twelve monthly payments of $40 each.
How much could she have saved if she had bought the stove for the marked price?
A) $40
B) $60
C) $100
D) $140
Sue bought a total of 12 candy bars at the store. Some cents cost 50 cents each and the rest cost 75 cent each. Write an expression to represent. a. The number of 75 cent bars if she bought y 50 cent bars b. The total cost, in cents, for all of the bars.
Answer:
According to this, the answer is:
a. x=(c-0.50y)/0.75
b. c=0.75x+0.50y
Step-by-step explanation:
With the information provided, the total cost in cents is equal to the result of the price of the 75 cent bars for the amount of bars plus the price of the 50 cent bars for the amount of bars, which would be:
c=0.75x+0.50y, where:
x is the amount of the 75 cent bars
y is the amount of the 50 cent bars
Now, you can solve for x to determine the expression that represents the number of 75 cent bars if she bought y 50 cent bars:
c-0.50y=0.75x
(c-0.50y)/0.75=x
x=(c-0.50y)/0.75
According to this, the answer is:
a. x=(c-0.50y)/0.75
b. c=0.75x+0.50y
helllohello help please if you want -
Hey Hey! It's me again!
Answer:
The variable u divided by the variable x.
Question 10 of 20. POOS The dimensions of a right rectangular prism are shown below. 1 in. How many cubes with side lengths of inch are needed to fill the prism without gaps or overlaps? 36 cubes 91 cubes 216 cubes 546 cubes
Answer:
546
Step-by-step explanation:
From the attached picture ;
Volume of a rectangular prism = (width * length * height)
Volume = 2 1/6 * 1 1/6 *1
Volume =. 13/6 * 7/6 * 1
Volume = 91 / 36 in³
Side length, a of cube = 1/6
Volume of cube = a³ = (1/6)^3 = 1/216
(91/36) ÷ 1/216
91/36 * 216/1
91 * 6 = 546
Answer:
546
Step-by-step explanation:
Two snails climbed up a tree at a constant rate. A person measured and recorded their respective distances above the ground. • Snail A was 12.5 inches above the ground at 10 minutes and 16 inches above the ground at 24 minutes. • Snail B started at 3 inches above the ground and climbed 0.3 inch per minute. The snails continued at the same speeds. • Determine the amount of time, in minutes, it took for the two snails to be the same distance above the ground. • Include an equation to represent each snail's distance above the ground, y, in terms of x, the minutes elapsed since the measurement started. Show your work or explain your answer.
Answer:
140 minutes
Step-by-step explanation:
Using m = (y₂ - y₁)/(x₂ - x₁) , we find the rate at which Snail A moves which is also the gradient of the line with which it moves. Given that Snail A was 12.5 inches above the ground at 10 minutes and 16 inches above the ground at 24 minutes, x₁ = 10 min, y₁ = 12.5 inches, x₂ = 24 min and y₂ = 16 inches.
So, m = (y₂ - y₁)/(x₂ - x₁)
m = (16 - 12.5)/(24 - 10) = 3.5/14 = 0.25
Also, the equation of the line,
(y - y₁)/(x - x₁) = m
(y - 12.5)/(x - 10) = 0.25
cross-multiplying, we have
y - 12.5 = 0.25(x - 10)
expanding the bracket, we have
y - 12.5 = 0.25x - 2.5
adding 12.5 to both sides, we have
y - 12.5 + 12.5 = 0.25x - 2.5 + 12.5
y = 0.25x + 10
Since Snail B started at 3 inches above the ground and climbed 0.3 inch per minute. The snails continued at the same speeds, its distance y moved is y = 0.3t + 3
We now find the time x it takes the snails to cover the same distance by equating both expressions. So,
0.25x + 10 = 0.3x + 3
collecting like terms, we have
10 - 3 = 0.3x - 0.25x
7 = 0.05x
0.05x = 7
x = 7/0.05
x = 140 minutes
Calculate this please and you will get the brainlist
Step-by-step explanation:
1. kinetic energy = 1/2 mass× velocity²mass= 5.2. velocity =2.4
thus, 1/2 × 5.2×2.4×2.4
= 14.97joule2. potential energy = mass× acceleration × heightmass=5.2. height=5.8 g=9.8
=5.2×5.8×9.8
= 295.5 joule3. mechanical energy = potential energy + kinetic energy= 295.5+14.97
=310.47 joulehope it helps :)
If a shirt originally cost $30 and was on sale for 20% off, how much was the sale price?
plzzzzz help me with this math plzzzz
Answer:
c i know just took it
Step-by-step explanation:
Answer:
C) -1(x+8)(x+7)
Step-by-step explanation:
[tex]-x^{2} -15x-56\\-1(x^{2} +15x+56)\\-1(x+8)(x+7)[/tex]
-1 factors through the entire equation.
8+ 7 = 15 and 8 x 7 = 56 (so 8 and 7 are our factors.)
pls help me fill this one out
Answer:
x=1
Step-by-step explanation:
Just look at the x axis and see where the coordinate lands on and it's 1
Can I please get help!!
Just answer the questions please
Help PLEASE 10pts CMON PEOPLE I NEED TO FINISH THIS TODAY
Answer:
1. 103
2. 67
3. 15
4. 44
Step-by-step explanation:
subtracting the sum of two given angles from 180.
Step-by-step explanation:
Sum of interior angles is always 180.
5) x + 40 + 37 = 180
x + 77 = 180
x = 180 - 77
x = 103
6) x + 41 + 72 = 180
x + 113 = 180
x = 180 - 113
x = 67
7) x + 137 + 28 = 180
x + 165 = 180
x = 180 - 165
x = 15
8) x + 84 + 52 = 180
x + 136 = 180
x = 180 - 136
x = 44
I need help with this math question.
Tyrese is making a map of his neighborhood using a coordinate plane.
Help help help help help help help
solve
¾.(z to the 3rd power . 4)=
Answer:
In the number 75, 5 is the base and 7 is the exponent. Solution: False. Example 7: 4. 3 a. a a a a b. b b b. + + +. = + +. Solution:.
What is L'L?
O 5 units
07.5 units
O 10 units
O 12.5 units
Answer:
12.5
Step-by-step explanation:
The value of LL' is 5 units.
Option A is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
ML' = 2.5
Triangle JKL dilated to Triangle J'K'L' with a scale factor of 1/3.
This means,
LL' = (2.5 x 3) - 2.5
LL' = 7.5 - 2.5
LL' = 5
Thus,
LL' is 5 units.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ2
Calculate simple interest :
a) P = 2500, rate 8% PA, T = 1 year
b) P = 4200, rate 6% P.A, T = 3 year
Nhen 6 added to a number gives 13
Answer:
the simple interest in both cases is 200 and 756 respectively
Step-by-step explanation:
The computation of the simple interest is shown below:
As we know that
Simple interest = P × r% × t
So
a. Simple interest is
= 2,500 × 8% × 1
= 200
b. The simple interest is
= 4,200 × 6% × 3
= 756
Hence, the simple interest in both cases is 200 and 756 respectively
HELP PLEASE QUICKLY
How many solutions does this system of equations have? Explain.
y = x + 1
y = 2x + 2
The system of equations has ... solution.
The equations have ... slopes, so the lines intersect at ... point.
Convince Me!
The equations of a system have the same slopes. What can you determine about the solution of the system of equations?
Answer:
The system of equations has one solution. The equations have different slopes, so the lines intersect at one point.
If a system of equations have the same slope, then the lines will run parallel to each other and never cross, leading to no solution being possible. Or if they have the same slope and same y-intercept (therefore being equations for the same line), they will have an infinite number of solutions.
Step-by-step explanation:
The solution to a system of equations is the point where the lines intersect. Looking at this question if we remember the slope-intercept form y=mx+b where m is slope and b is the y-intercept. We can see m=1 for the first equation and m=2 for the second equation. Anytime two equations have different slopes it is guaranteed they will intersect at some point leading to one solution.
The ratio of red to blue marbles in a bag is 2:5. If there are 65 blue marbles in the bag, how many red marbles are there? Let x represent the number of red marbles. Set up a proportion and cross multiply to solve.
Answer:
first get the total ratio; 2 + 5 = 7
so the fraction of blue marbles is 5/7
then assume the number of total marbles to be k
then use the expression;
5/7*k = 65
7*5/7 * k = 65*7
5k =455
5/5k = 455/5
k = 91
then calculate the number if red marbles from;
x = 2/7*91
x = 26
Therefore there are 26 red marbles.
Which statement is true about the purpose of trend lines in scatterplots? A trend line must pass through the largest data point. A trend line must pass through the smallest data point. A trend line can be used to make predictions in real-world situations. A trend line shows the exact data points collected.
Answer:
a trend line can be used to make predictions in real-world situations (the third option)
Explanation:
the first & second options are wrong because it is not a requirement for a trend line to pass through any given data point.
the fourth option is wrong because a trend line shows the general upward/downward trend of the data, and may not necessarily touch all of the data points.
the third option is correct because a trend line helps to roughly estimate the trend (hence the name) of the graph, which allows us to make predictions in real-world situations.
i hope this helps! :D
Answer:
C just took the test edge 2020
Step-by-step explanation:
Jahan bought 2/3 pounds of peanuts and 1/4 pound of walnuts. Did Jahan buy more peanuts or more walnuts
Answer:
Peanuts
Step-by-step explanation:
Johan bought 4/6 pounds of peanuts and 2/6 pounds of walnuts.
The obvious answer is Johan bought more peanuts.