When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).
What is a intercept theorem?The intercept theorem, also referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem, is a crucial concept in basic geometry that discusses the ratios of different line segments that are produced when two intersecting lines are intercepted by a pair of parallels.
It is equivalent to the ratios in similar triangles theorem. It is typically credited to the Greek mathematician Thales. Despite the fact that its first known demonstration may be found in Euclid's Elements, it was known to the ancient Babylonians and Egyptians.
Similarity and the intercept theorem go hand in hand. It is equivalent to the idea of similar triangles in that it may be used to demonstrate both the qualities of similar triangles and the intercept theorem.
Hence, When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).
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find the x-intercepts of y= x^2+4x+8 using the quadratic formula.
Answer: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
Step-by-step explanation: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
+
2
√
3
,
0
)
,
(
2
−
2
√
3
,
0
)
y-intercept(s):
(
0
,
8
)
20) If the area of a rectangular playground is
p^2 -6p - 7 square feet, what is the perimeter of the
playground?
Answer:
Explanation:
Write an equation to solve the problem.
Area of rectangle = L(w)
Assuming that the width measures x meters, the length measures x + 5 meters.
500 = x(x + 5)
500 =
x
2
+ 5x
0 =
x
2
+ 5x - 500
As you may already know, a trinomial of the form
a
x
2
+ bx + c, a = 1, you must find 2 numbers that multiply to c and that add to b. Two numbers that multiply to -500 and add to +5 are +25 and -20
0 = (x + 25)(x - 20)
x = -25 and 20
Since a negative length is impossible, the width mesures 20 meters and the length measures 25 meters.
Practice exercises:
A rectangle has a perimeter of 90 meters. Find the maximum area.
The area of a right triangle is 120
m
2
. The base measures half the sum of the height and one. Find the perimeter.
Find the area and perimeter of a right triangle the has a height that is 2 more than the double of the width and that has a hypotenuse that measures
√
68
meters.
Good luck!
Step-by-step explanation:
Question 4 (1 point)
The image shows quadrilateral ABCD.
Find the area of ABCD. Explain or show your reasoning.
Answer:
25
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the side length of each side.
a^2 + b^2 = c^2
=> 3^2 + 4^2 = x^2
=> 9 + 16 = x^2
=> x = 5
By applying the same formula for each side, we will get that each side is 5 units.
So, the area = 5*5 = 25
The quadrilateral is a square and the area of square is 25 square units.
What is a quadrilateral?
A quadrilateral is 2-dimensional geometric closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
For the given situation,
The quadrilateral ABCD has points A(0,4), B(3,0), C(7,3), D(4,7).
The distance these points can be found by
[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
AB = [tex]d=\sqrt{(3-0)^{2}+(0-4)^{2} }[/tex]
⇒ [tex]AB = \sqrt{3^{2}+4^{2} }[/tex]
⇒ [tex]AB=\sqrt{9+16}[/tex]
⇒ [tex]AB=\sqrt{25}[/tex]
⇒ [tex]AB=5[/tex]
BC = [tex]d=\sqrt{(7-3)^{2}+(3-0)^{2} }[/tex]
⇒ [tex]BC=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]BC=5[/tex]
CD = [tex]d=\sqrt{(4-7)^{2}+(7-3)^{2} }[/tex]
⇒ [tex]CD=\sqrt{(-3)^{2} +4^{2} }[/tex]
⇒ [tex]CD=5[/tex]
DA = [tex]d=\sqrt{(4-0)^{2}+(7-4)^{2} }[/tex]
⇒ [tex]DA=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]DA=5[/tex]
Since AB = BC = CD = DA, the quadrilateral is a square.
The formula of area of quadrilateral is
[tex]A=(side)^{2}[/tex]
⇒ [tex]A=5^{2}[/tex]
⇒ [tex]A=25[/tex]
Hence we can conclude that the quadrilateral is a square and the area of square is 25 square units.
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A triangle has one side that is 5 inches long and another that is 7 inches long. How many different lengths, in inches,are possible for the last side of the triangle?
Answer:
2 < c < 12
Step-by-step explanation:
Let the last side of the triangle = c
The sum of any two sides must be greater than the third side. Let's say we have triangle ABC, where a = 5 inches and b = 7 inches
a + b > c (1)
a + c > b (2)
b + c > a (3)
From (1);
a + b > c
7 + 5 > c
c < 12
From (2):
a + c > b
7 + c > 5
7 - 5 < c
c > 2
From (3):
b + c > a
5 + c > 7
c > 7 - 5
c > 2
So the possible lengths of c are: 2 < c < 12
What are the roots of this equation x^2-2x+3=0
Step-by-step explanation:
hope it's help.
see answer attached
A quality control expert at a drink bottling factory took a random sample of 9 bottles from a
production run of over 1,000 bottles and measured the amount of liquid in each bottle in the
sample. The sample data were roughly symmetric with a mean of 505 mL and a standard
deviation of 6 mL.
Based on this sample, which of the following is a 95% confidence interval for the mean
amount of liquid per bottle (in mL) in this production run?
Answer: It's in the screenshot
Step-by-step explanation:
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.
The other parameters are given as follows:
[tex]\overline{x} = 505, s = 6, n = 9[/tex]
Hence:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 505 - 2.306\frac{6}{\sqrt{9}} = 500.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 505 + 2.306\frac{6}{\sqrt{9}} = 509.61[/tex]
The 95% confidence interval for the mean amount of liquid per bottle (in mL) in this production run is (500.39, 509.61).
More can be learned about the t-distribution at https://brainly.com/question/16162795
Please helppp
The function ƒ(x) = 2x − 1 indicates:
a downward shift of 1 unit.
a shift of 1 unit to the left.
an upward shift of 1 unit.
None of these choices are correct.
Answer:
It is a downward shift of one unit
8.8C
What value of x makes this equation true?
12x - 15 = 6 - 3x
How may candies did Thad get all together? Pls help quickly
Answer:
all together there is 141 candies in all
Which of the following functions translates the graph of the parent
function f(t) = x² horizontally left 6 units?
Answer:
shawty us bad with the scratchers in
What is the distance between points A (3,-5) and B(-8,2) on the coordinate plane?
Answer:
[tex]\sqrt{-51}[/tex]
or aprox 7.14
hopefully this helps
What are the zeros of f(x) = x2 + 3x - 10?
A. X= -5 and x = 2
B. x= -5 and x = -2
C. X= 5 and x = -2
D. x = 5 and x = 2
Answer:
(x+5) (x-2)
SO -5 and 2 option A
Step-by-step explanation:
factor it. and set equal to zero.
Bounty paper towels cost $8.49 for 8 rolls. Brawny paper towels cost $13.99 for 12 rolls. Which is the better buy?
Answer:
Bounty Paper Towels is the better deal
Step-by-step explanation:
8.49 divided by 8 = 1.06125 ($1.01)
13.99 divided by 12 = ~1.16583 ($1.16)
The Brawny is more expensive per roll, so Bounty would be a better deal
What is the slope, m, of the line through (-9, -17) and (-9, 12)?
Express the slope as a fraction in lowest terms.
If the slope is undefined, enter undefined into the text box.
m =
Answer:
m = undefined
Step-by-step explanation:
(-9, -17) and (-9, 12)
Slope:
m=(y2-y1)/(x2-x1)
m=(12+17)/(-9+9)
m=29/0
Since 0 is the denominator, the slope is undefined
Find the total length of rope that is brought on the trip.
A. 25 3 4 yards
B. 29 3 4 yards
C. 33 3 4 yards
D. 37 3 4 yards
i have the quiz before and the answer is D: 37 3/4 yards
:)
what is the value of d?
How can I Solve this problem Solve. for g.
18 = 3g
g
Answer:
[tex]g = 6[/tex]
Step-by-step explanation:
1) Diving both sides by 3.
[tex] \frac{18}{3} = g[/tex]
2) Simplify 18/3 to 6.
[tex]6 = g[/tex]
3) Switch sides.
[tex]g = 6[/tex]
Therefor, the answer is g = 6.
Find the missing length. The triangles in each pair are similar.
Answer:
........................................
I can choose and create diagrams to help me compare two situations.
SOMEONE PLEASE HELP MY TEACHER WANTS TO PUT ME IN SUMMER SCHOOL SO I NEED TO GET MY HW DONE ASAP SO PLEASE REPLY WITH AN ANSWER PLSS!!!
Answer:
blurred poate
Step-by-step explanation:
blurred po ate
Karolyn puts 4,500 into a life insurance policy that pays 7.5% annual interest. If no additional investment is made into the policy how much accumulated interest should Karolyn expect at the end of 10 years?
Answer: $4,774.64
Step-by-step explanation:
The amount after 10 years assuming 7.5% compound interest is:
= Amount * ( 1 + rate) ^ no. of years
= 4,500 * ( 1 + 7.5%)¹⁰
= $9,274.64
The accumulated interest is:
= Amount after 10 years - Present amount
= 9,274.64 - 4,500
= $4,774.64
135 is 90% of what number
Answer:
150
Step-by-step explanation:
0.90x=135
x=135/0.90
x=150
need help
problem/question in image below
Answer:
Option A would be the correct answer
I don't have an explanation to type but you can trust me :)
Please mark as brainliest for further answers :)Find the value of a. Round your answer to the nearest tenth.
Answer:
Polly do you know the formula for law of Cosines?
find it if you don't
Step-by-step explanation:
a = sqrt( b^2 +c^2 - 2bcCos(A) )
a = sqrt( 100 + 62.41 -34.197)
a = sqrt(128.213)
a = 11.323
a = 11.3 ( to the nearest tenth )
please help!!No links
Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3. (2 points)
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
fraction 1 over 4 of 10 times the sum of 5 and 3, minus 3
3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
10 times fraction 1 over 4 plus 3 and 5, minus 3
Answer:
10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3
plz mark as brainliest
hope it helps
Answer:10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 2
Step-by-step explanation:
what's the answer to this problem?
[tex]5x + 35 = 45[/tex]
Answer:
5x+35=45
5x=45-35
5x=10
x=2
The dollar store buys a hat for $0.80. Then they mark up the price by 20%.
How much will they sell the hat for?
Answer:
$0.96
Step-by-step explanation:
20% of 0.80 is 0.16
0.80 + 0.16 = 0.96
Answer:
$0.96
Step-by-step explanation:
Multiply 0.80 times 0.2
0.80 x 0.2=0.16
Then add up 0.16 and 0.80 to get your answer
0.80 + 0.16=0.96
Hope it helps
Alternate interior angles are always congruent. TRUE OR FALSE
Answer:
false
Step-by-step explanation:
Answer:
False.
Step-by-step explanation:
Alternate interior angles are congruent only when the two lines intercepted are parallel.
PLEASE HELP I WILL MARK YOU BAINLIEST AND SHOW YOUR WORK PLEASE
A school is raising money to build a new auditorium! It costs $6,500 to hire a worker to put in new floors in the auditorium. The other information about the cost of the project is below:
The teachers have already raised $500.
There are twelve teachers trying to help the school raise money and each teacher raises the same amount of money.
The teachers organize a car wash and earn $10 for each car they wash.
How many cars must each teacher wash to raise enough money to complete the new auditorium?
Answer:
54
Step-by-step explanation:
6500/12=541....
540/10
54
Which expression is equivalent to (3x2+3x−3)−(6x2−4x−2)?
A
−3x2+7x−1
B
−3x2−x−5
C
−3x2+7x−5
D
−3x2−x−1
Answer:
A. -3x^2+7x-1
Step-by-step explanation:
(3x^2+3x-3)-(6x^2-4x-2)
3x^2+3x-3-6x^2+4x+2
-3x^2+7x-1