Answer:
The scale factor of the dilation is 2
Step-by-step explanation:
The given vertices the ΔFGH are;
F(2, 1), G(4, 1), and H(4, -1)
The lengths of the sides of the triangle ΔFGH are;
The length of segment FG = √((4 - 2)² + (1 - 1)²) = 2
The length of segment FH = √((4 - 2)² + ((-1) - 1)²) = 2·√2
The length of segment GH = √((4 - 4)² + ((-1) - 1)²) = 2
After a dilation with the center of dilation = (0, 0), to give the ΔF'G'H', we have;
The given vertices the ΔF'G'H' are F'(4, 2), G'(8, 2), H'(8, -2)
The length of segment F'G' = √((8 - 4)² + (2 - 2)²) = 4
The length of segment F'H' = √((8 - 4)² + ((-2) - 2)²) = 4·√2
The length of segment G'H' = √((8 - 8)² + ((-2) - 2)²) = 4
The length of the sides of ΔFGH = 1/2 × The length of the sides of ΔF'G'H' or the length of the sides of ΔF'G'H' = 2 × The length of the sides of ΔFGH
Therefore, the scale factor of the dilation is 2.
Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not.
Answer:
The equation of a linear function is:
[tex]y = 2x+4[/tex]Step-by-step explanation:
Given the table
x y
-10 -16
-3 -2
1 6
2 8
Determining the slope between the points (-10, -16), (-3, -2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]
[tex]m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (-3, -2), (1, 6)
[tex]m=\frac{6-\left(-2\right)}{1-\left(-3\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (1, 6),(2, 8)
[tex]m=\frac{8-6}{2-1}[/tex]
[tex]m = 2[/tex]
As the slope between the points is the same. Thus, the table represents the linear function.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 2 and any point let say (1, 6)
[tex]y - 6 = 2(x-1)[/tex]
[tex]y-6 = 2x-2[/tex]
[tex]y = 2x-2+6[/tex]
[tex]y = 2x+4[/tex]
Therefore, the equation of a linear function is:
[tex]y = 2x+4[/tex]can someone help me please !!!!!!
Answer: From top to bottom of the chart: -13, -6, 1, 8, 15
Step-by-step explanation:
You can solve the equation by putting the numbers in the graph (under the letter x) into the equation. Meaning when it says "-2", you can write 7(-2)+1, or 7 times negative 2 minus one, which equals -13. Do the same thing with the rest :]
Solve the following equation for the
variable (a). -3a = 15
a = 5
a = 12
a = -5
a = 18
Write an
explicit formula for the sequence 6,2,-2,-6-10, ... Then find the 1st term.
Answer:
Step-by-step explanation:6232821
A package of notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.
Answer:
24
Step-by-step explanation:
Given that:
Number of yellow notepads = 6
Number of Blue notepad = 6
Number of green notepads = 6
Number of pink notepads = 6
Samole space for experiment :
(Number of different distinct notepads * Number of notepads in each)
(4 * 6) = 24
Find the percent increase. Round to the nearest percent.
From 95 books to 139 books.
The percent increase is __%
(I just need the answer, no need for explanation)
Answer:
32%
Step-by-step explanation:
at least twenty caters long
(26+5)•2-15
Please show with step
Answer:
47
Step-by-step explanation:
(26+5) • 2-15
Follow Pemdas
P.E.M.D.A.S
Parenthesis first
31•2-15
Multiplication next
62-15
47
A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
I need help with this plz percent equations the question is blank % of 35 = 21
Answer:
60%
Step-by-step explanation:
Derive the equation, in the
form y = mx + b, for the line. (Look at the photo.)
Answer:
y=2x+1
Step-by-step explanation:
y=mx+c
y-intercept is 1
y=mx+1
gradient= rise/run= 2/1= 2
y=2x+1
According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event F) is 0.2805. The probability that the driver is 24 years old or less (event A) is 0.1759. The probability that the driver is female and is 24 years old or less is 0.0424. Answer parts (a) through (d) below.
(a) Find the probability of FUA. P (FUA)Round to four decimal places as needed.)
(b) Find the probability of F'UA. P(FUA) (Round to four decimal places as needed.)
(c) Find the probability of FnA'
Question d:
(D) Find the probability of F'nA'
Answer:
0.4140
0.7619
0.2381
0.9576
Step-by-step explanation:
Given that :
Female in fatal accident P(F) = 0.2805
Driver is 24 years or less P(A) = 0.1759
Driver is female and 24 years or less P(FnA) = 0.0424
A.) Find the probability of FUA.
P(FUA) = P(F) + P(A) - P(FnA)
= 0.2805 + 0.1759 - 0.0424
= 0.4140
(b) Find the probability of F'UA.
P(F'UA) = 1 - P(F) + P(FnA)
= 1 - 0.2805 + 0.0424
= 0.7619
C.) P(FnA') = 1 - P(F'UA)
= 1 - 0.7619
= 0.2381
(d) Find the probability of F'nA'
P(F'nA') = (FnA)' = 1 - (FnA)
= 1 - 0.0424
= 0.9576
2.) Jennifer bought a shirt at Forever 21 for $21.50 after a 3% sales tax. What was the original price of the shirt?
Pls answer and expplain how you got it
Answer:
$20.87
Step-by-step explanation:
Divide 1.03 into 21.50
Find the hypotenuse, c, of the triangle.
А
4
B.
C С
12
Answer:
A.
Step-by-step explanation:
Mrs. Garcia borrowed some money at the rate of 4% per annum for the first year, at the rate of 6% pe r annum for the next 2 years, and at the rate of 7.5% per annum for the period beyond 3 years. If he pays a total interest of ₱ 15 750 at the end of 5 years, how much money did he borrow?
Answer: ₱40,909.1
Step-by-step explanation:
Given data:
Rate for first year = 4%
Rate for next two years = 6%
Rate for the next 3 years = 7.5%
Interest paid back after 5years = ₱ 15,750
Solution:
How much did she borrow.
= let the sum borrowed be P
= P * 4 / 100
= 4P/100
= 1P/25.
For the next two years
= P* 6 * 2/100
= 12P/100
= 3P/25
For the next 3years
= P* 7.5*3/100
= 22.5P/100
= 9P/40.
1P/25 + 3P/25 + 9P/40 = 15750
77P/200 = 15750
P = 15750 * 200 / 77
P = 315,0000/77
P = ₱40,909.1
The amount borrowed is ₱40,909.1
What is the solution for x in the
system of the following
equations?
3x+4 y= 31
3x-4 y=-1
Answer:
5
Step-by-step explanation:
Here a easy question for yall.
Hannah has 10 apples and she gave her friend 5 out of it. how much does hannah has now?
Easy~ UwU
Answer:
5
Step-by-step explanation:
The answer is 5 because it just is
Answer:
5Step-by-step explanation:
__________________________________________________________
Hannah gave her friend 5, so now she has 5!
__________________________________________________________
We can solve this by subtracting!
__________________________________________________________
10 - 1 = 9
10 - 2 = 8
10 - 3 = 7
10 - 4 = 6
10 - 5 = 5
__________________________________________________________
Hope this helps! uwu
__________________________________________________________
√ 25 –2√3 + √27 +2√ 9 Express in simplified radical
Answer:
The expression in simplified radical form is:
√ 25 –2√3 + √27 +2√ 9 = 11 + √3
Step-by-step explanation:
Given the expression
√ 25 –2√3 + √27 +2√ 9
as
√ 25 = 5
√27 = 3√3
2√9 = 6
so the expression becomes
√ 25 –2√3 + √27 +2√ 9
= 5 - 2√3 + 3√3 + 6
= 11 + √3
Thus, the expression in simplified radical form is:
√ 25 –2√3 + √27 +2√ 9 = 11 + √3
solve the following equation: 8x^2 = 2x
Answer:
x = 0, x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given
8x² = 2x ( subtract 2x from both sides )
8x² - 2x = 0 ( factor out 2x from each term )
2x(4x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
4x - 1 = 0 ⇒ 4x = 1 ⇒ x = [tex]\frac{1}{4}[/tex]
HELPPP FASTTT PLEASE
Answer:
(3,-2)
Step-by-step explanation:
I used a graphing calculator to get the solution, attached is what I got with the graphing calculator.
hope this helps.
rob is asked to graph this system of equations: 6x + 2y = 5; y + 3x =2; how many times will the lines intersect? A. there is no way to tell without graphing the lines first. B. the lines will not intersect, cuz the system only has one system. C. the lines will intersect once. D. the lines will intersect more than once.
Answer:
C
Step-by-step explanation:
A and B are wrong and with D they wouldn't be lines so imma go with C.
Sorry if it's wrong.
Which of these equations represents a line parallel to the line 2x + y = 6?
A) y= 2X+3
B) y -2X=4
C) 2X -y=8
D) y= -2X+1
Answer:
D) y= -2X+1
Step-by-step explanation:
All of the lines are perpendicular to the line 2x+y=6 except for D) y= -2X+1.
An earthquake wave travels through 55 km of rock in 25 seconds . Which equation represents the relationship between t, the number of seconds, and d, the total distance the wave travels?
Answer:
2.2 m/s
Step-by-step explanation:
Step one
Given data
An earthquake wave travels through 55 km
hence distance = 55 km
time taken = 25 seconds
Required
the expression relating t and d
Step two:
we know that velocity is
Speed= distance/time
speed= 55/25
Speed= 2.2 m/s
I really need help :(
plsssssss help 5/6 x 7/8
A taxi in myrtle beach charges $2 per mile and $1 per person. If a taxi cab ride for 2 people cost $12, how far did the taxi cab travel ( don’t include units (miles) in the answer)
Answer:
I belive the answer is 5
Step-by-step explanation:
$12- $2 for ppl= $10
$10÷$2 per mile = 5
Find the x and y intercept of the line below
2x + 5y = 10
Answer:
x - intercept = 5
y- intercept = 2
Step-by-step explanation:
2x + 5y = 10
Write the equation in [tex]\frac{x}{a}+\frac{y}{b}=1[/tex] form
So, divide the equation by 10
[tex]\frac{2x}{10}+\frac{5y}{10}=\frac{10}{10}\\\\\frac{x}{5}+\frac{y}{2}=1[/tex]
x - intercept = 5
y- intercept = 2
Answer:
(5,0) and (0,2)
Step-by-step explanation:
Basically, all we need to do is enter 0 for both variables. We can do this because the y-value of an x-intercept will always be 0, and the x-value of a y-intercept will always be 0.
So, to find the x-intercept we can set y equal to 0 and then solve for x.
[tex]2x+5(0)=10\\2x=10\\x=5[/tex]
So the x-intercept will be (5,0).
We can do the same thing to find the y-intercept.
[tex]2(0)+5y=10\\5y=10\\y=2[/tex]
The y-intercept is (0,2)
Hope this helps!
Help me please and thank you
Possibly B but i'm not sure..
Item 19 A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate? The store donates basketballs. Item 19 A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate? The store donates basketballs.
Answer:
28 soccer balls.
Step-by-step explanation:
Let there are 7x basketball and 6x soccer balls.
A sports store donates basketballs and soccer balls to the boys and girls club.
The store donates 24 soccer balls.
It means,
6x = 24
x = 4
No of basketballs = 7x
= 7(4)
= 28
Hence, the store denote 28 soccer balls.
At the market, Meyer buys a bunch of bananas for $0.65 per pound and a frozen pizza for $4.99. The total for his purchase was $6.94, without tax. How many pounds of bananas did Meyer buy?
Answer:
Well, 6.94 - 4.99 = 1.95 also that divided by 0.65 = 3 So it is 3 pounds of bananas
Step-by-step explanation:
P.S can I have brainliest?
x⁴+x²+1+x⁴64445555555555555555
Answer:
2x⁴ + x² + 64445555555555555556