What is a rule that describes the reflection that mapstriangle EFG onto triangle E’F’G’?
Answers
The formula for a reflection around a vertical line is given by the following expressions:
\(\begin{gathered} x^{\prime}=-x+2\cdot C \\ y^{\prime}=y \end{gathered}\)Where (x',y') are the new coordinates of the point and C is the coordinate of the vertical line. For this problem the vertical line is located in -2. So the rules are:
\(\begin{gathered} x^{\prime}=-x+2\cdot(-2)=-x-4 \\ y^{\prime}=y \end{gathered}\)\(\begin{gathered} F^{\prime}=\text{ -(-3)+2}\cdot(-2)=3-4=-1 \\ G^{\prime}=\text{ -(-5)+2}\cdot(-2)=5-4=1 \\ E^{\prime}=-(-4)+2\cdot(-2)=4-4=0 \end{gathered}\)Related Questions
The value of Maggie's car decreased by 15% since last year, when she bought it. If the car is now worth $13,000.00, how much was the car worth when she bought it?
A.
$14,950.00
B.
$15,294.12
C.
$16,250.00
D.
$14,444.44
Answers
The car is now worth 85% of its value. (100-15=85)
Solve the equation:
.85x= 13000
x= 15294.12
Determine the whole number of standard deviations from the mean that include all
data values.
The mean price of the nonfiction books on a best-sellers list is $25.07; the standard
deviation is $2.62.
$26.95, $22.95, $24.00, $24.95, $29.95, $19.95, $24.95, $24.00, $27.95, $25.00
Answers
The number of standard deviations from the mean that include all
data values is two.
Standard Deviation could be a live that shows what proportion variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean.it's a well-liked live of variability as a result of it returns to the initial units of live of the information setFrom the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)
Use the given values of mean \(\overline x\) and normal deviation (σ) to notice the worth of "a".
\(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)
On rounding off we get a = 2
Checking another inequality
\(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)
Thus , 2 standard deviation include the all values from the given set of data .
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Find an equation of the line that has a slope of 5 and a
y
-intercept of
(
0
,
8
)
. Write your answer in the form
y
=
m
x
+
b
.
Answers
Which description is paired with its correct expression?
four less than the quotient of a number cubed and seven, increased by three; 4-2+3
five times the difference of a number squared and six; 5(6-n²)
nine more than the quotient of six and a number cubed, decreased by four; 8+²-4
9+
O twice the difference of nine and a number squared; 2(9-n²)
Answers
The correct pairings are:
a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
b) Five times the difference of a number squared and six: 5(n² - 6)
c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
d) O twice the difference of nine and a number squared: 2(9 - n²)
The correct pairings of descriptions and expressions are as follows:
Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.
Five times the difference of a number squared and six: 5(n² - 6)
This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.
Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.
O twice the difference of nine and a number squared: 2(9 - n²)
This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.
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Lily loves 2.5 miles farther from school than Dante Dante lives 16.25 miles from school how many miles from school does Lily live
Answers
Answer:
18.75
Step-by-step explanation:
Just add 2.5 and 16.25 :)
Answer:
Lily must live 18.75 miles away
Step-by-step explanation:
If Lily lives 2.5 miles further from school than Dante then the equation is
16.25+2.5 = x
Add them together and you get 18.75
Find the surface area of the square pyramid (above) using its net (below)
Answers
Answer:
7 votos
Answer:12Step-by-step explanation:For each of the four triangles you multiply the base (2) by the height (2) and then divide it by 2 which equals 2.
Solve for x to make A||B
Answers
Answer: x = 50
Step-by-step explanation:
In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.
prove that a square matrix and its transpose have the same characteristic polynomial, and therefore the same set of eigenvalues. g
Answers
The eigenvalues of a matrix are roots of its characteristic polynomial using this we prove that a square matrix and its transpose have the same characteristic polynomial.
What is a matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.
Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.
Hence if the matrices A and A Transpose have the same characteristic polynomial, then they have the same eigenvalues.
So we show that the characteristic polynomial pA(t)=det(A−tI) of A is the same as the characteristic polynomial p\(A^T\) (t)=det(A ^T−tI)of the transpose \(A^T\).
We have,
p\(A^T\)(t)=det(\(A^T\) −tI) =det(\(A^T\) −tI T )
=det((A−tI) \(A^T\) )
=det(A−tI)
=pA(t)
Since I ^T =I
Since det(\(B^T\) )=det(B)for any square matrix B
Therefore, we obtain p\(A^T\) (t)=pA(t), we conclude that the eigenvalues of A and \(A^T\) are the same.
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Stretched 1 cm beyond its natural length, a rubber band exerts a restoring force of magnitude 2 newtons. Assuming that Hooke's Law applies, answer the following questions:
(a) How far will a force of 3 newtons stretch the rubber band?
(b) How much work does it take to stretch the rubber band this far?
Answers
A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m
B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J
How to solve Hooke's Law?
From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.
F = Ke
Where;
F = force
K = force constant
e = extension
Thus, for a restoring force of magnitude 2 newtons ;
2 N = K(1 × 10⁻²) m
K = 2 N /(1 × 10⁻²) m
K = 200 N/m
a) For a force of 3 newtons, we have;
3N = 200 N/m × a
Where a is the extension in meters
a = 3N/200 N/m
a = 0.015 m
b) The formula to find the work done is;
P.E = ¹/₂Ke²
P.E = ¹/₂ * 200 * 0.015²
P.E = 0.0225 J
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Consider the function f(x)=2x−−√−8. If f−1(x) is the inverse function of f(x), find f−1(2)
Answers
\(f^(-1)(2) = 6\), which is consistent with our earlier result.
What is inverse function?A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.
Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?
Solution:
To find f^(-1)(2), we need to find the value of x such that \(f(x) = 2\) . We can set up an equation:
\(f(x) = \sqrt(2x - 8) = 2\)
Squaring both sides, we get:
\(2x - 8 = 4\)
\(2x = 12\)
\(x = 6\)
Therefore, \(f^(-1)(2) = 6.\)
We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:
\(f(f^(-1)(x)) = x\)
We can substitute x = 2 and solve for f^(-1)(2):
\(f(f^(-1)(2)) = 2\)
\(f^(-1)(2) = (f(6))^(-1)\)
f(6) = √(2(6) - 8) = √4 = 2
Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.
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PLEASE HELP WILL GIVE BRAINLIST
Answers
Answer:
greater than or equal to
Step-by-step explanation:
In Jayce's favorite video game, he collects stars to earn points. Today, he collected 80 silver stars and earned 160 points. He also collected 30 gold stars and earned 150 points. How many more points per star does Jayce earn from gold stars?
Answers
Jayce earns 3 more points from gold stars than from silver stars.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Jayce collected 80 silver stars and earned 160 points.
He collected 30 gold stars and earned 150 points.
Therefore,
The points per star Jayce earns from silver stars
160/80=2,
The points per star Jayce earns from gold stars
150/30=5
Hence, Jayce earns 3 more points from gold stars than silver stars.
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Alisa uses her cell phone to search how many pounds of sand will is required to fill 1 cubic foot and finds out the answer is 100 pounds. Choose 1 of the brands and compute how much it will cost Alisa to purchase enough sand to fill the court. Sand A - 12 dollars per 150 lb, Sand B - 5 dollars per 60 pounds. BRO PLEASE HELP, THIS THING IS DUE IN A WEEK AND IM ABSOLUTELY CLUELESS
Answers
Using proportions, the cheapest option for Alisa to purchase enough sand to fill the court is Option A, which will cost $8.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
For each option, the cost per pound is
Option A: 12/150 = $0.08.Option B: 5/60 = $0.0833.Option A is cheaper, hence the total cost for 100 pounds is:
$0.08 x 100 = $8.
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Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
Answers
Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
Solve for x
2x + 10 = -3x - 15
A -5
B -7
C -4
D -2
Answers
Answer:
A. x = -5
2(-5) + 10 = -3(-5) - 15
0 = 0
What is the measure of angle c?
Answers
Answer:
65
Step-by-step explanation:
Angle A=70
Angle B=180-135=45.
70+45=115. A triangle has 180 degrees.
Angle C=180-115=65
Hope I helped!
Here are 10 numbers. 3 7 2 4 7 5 7 1 8 8 what is the median
Answers
Answer: 7
Step-by-step explanation:
234577788
^
the number in the middle is 7
Explain why 8 x ¾ is the same as adding ¾ + ¾ + ¾ + ¾ + ¾
Answers
8 x ¾ is the same as adding ¾ + ¾ + ¾ + ¾ + ¾
because, when you are adding 3/4
8 times, you are 3/4 plus itself,
eight times,
so you are doing 3/4*8
8×¾ = ¾+¾+¾+¾+¾+¾+¾+¾
8×¾ = (1+1+1+1+1+1+1+1)×¾
= ¾+¾+¾+¾+¾+¾+¾+¾ distributive rule
PLEASE HELLP ASAP!!!
Answers
The quadratic function graphed is defined as follows:
y = x² - 10x + 9.
How to define the function?We are given the roots for each function, hence the factor theorem is used to define the functions.
The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
From the graph, the roots are given as follows:
x = 1 and x = 9.
Hence the function as a product of it's linear factors is defined as follows:
y = a(x - 1)(x - 9)
y = a(x² - 10x + 9).
When x = 5, y = -16, hence the leading coefficient a is obtained as follows:
-16 = a(5² - 10(5) + 9)
-16a = -16
a = 1.
Thus the function is:
y = x² - 10x + 9.
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Deborah bikes 2.2 miles in 8 minutes. Her friend Caleb bikes 3.5 miles in 12 minutes. Who bikes at a faster speed?
Answers
Answer:
Caleb.
Step-by-step explanation:
Deborah's speed = 2.2 / 8 = 0.275 miles / minute.
Caleb's speed = 3.5/12 = 0.292 miles / minute.,
Rewrite the equation by completing the square.
x^{2}+10x+21 = 0
(x+__)^2=__
Answers
Answer:
Step-by-step explanation:
x²+10x+21=0
x²+10x+(10/2)²-(10/2)²+21=0
x²+10x+25-25+21=0
(x+5)²-4=0
(x+5)²=4
(x+y)²=(x+y)(x+y)=x(x+y)+y(x+y)=x²+xy+xy+y²=x²+2xy+y²
(x+y)²=x²+2xy+y²
coefficient of x=2y
y²=[(coefficient of x)/2]²=(2y/2)²=y²
Is there an option for no solution?
h(t) = − 4.9 t^2 + 226t + 283
Answers
The Maximum height of the object is 2888.9 feet which is at 23.06 seconds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let h represent the height of an object after t seconds. Given that:
h(t) = -4.9t² + 226t + 283
The maximum height is at h'(t) = 0, hence:
h'(t) = -9.8t + 226
-9.8t + 226 = 0
9.8t = 226
t = 23.06 s
h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9
Maximum height is 2888.9 ft
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A plastic liner for a landfill is 50 millimeters thick. How many meters is this equal to?
Answers
1000 milimeters ---> 1 meters
50 milimeters ------> x
\(\begin{gathered} 1000x=1\times50 \\ 1000x=50 \\ \frac{1000x}{1000}=\frac{50}{1000} \\ x=0.05 \end{gathered}\)answer: 0.05 meters
k) v=u+ax make x the subject
Answers
Answer:
x = (v - u) / a
Step-by-step explanation:
v = u + ax.
subtract u from both sides:
v - u = ax.
divide both sides by a:
(v - u) / a = x.
so x = (v - u) / a.
this can also be written v/a - u/a
A solid rectangular right prism is 10 inches long, 9 inches high, and 9 inches deep. At one square base of the prism, a 2 inch high square pyramid is cut from the prism. At the opposite square base of the prism, a square pyramid measuring 3 inches high is added. The bases of the pyramids are the same size as the square bases of the rectangular prism.
What is the volume of the composite figure?
Enter your answer in the box.
in³
Answers
The pyramid that is cut from the prism has a volume of (1/3) x base area x height = (1/3) x 9 in² x 2 in = 6 in³.
The pyramid that is added to the opposite base has a volume of (1/3) x base area x height = (1/3) x 9 in² x 3 in = 9 in³.
The composite figure is formed by removing a pyramid with volume 6 in³ from the rectangular prism and adding a pyramid with volume 9 in³ to the opposite base. The resulting figure is still a rectangular prism, with the same length and width, but a slightly different height.
The height of the rectangular prism is reduced by 2 inches (the height of the pyramid that was cut), and then increased by 3 inches (the height of the pyramid that was added). So, the new height of the rectangular prism is:
9 in - 2 in + 3 in = 10 in
The volume of the composite figure is then:
Volume = length x width x height = 10 in x 9 in x 10 in = 900 cubic inches.
Therefore, the volume of the composite figure is 900 cubic inches.
Answer:
837
Step-by-step explanation:
At an amusement park, 15 riders ride the race cars every 20 minutes and 35 riders ride the ferris wheel every 60 minutes. Which ride has the greater ratio of riders?
Answers
Answer: the Ferris Wheel
Step-by-step explanation:
Please help me solve this.
Answers
\(\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions\)
A high school is voting on a new mascot. Lion Eagle Bee Ninth Grade 45% 32% 23% Tenth Grade 36% 40% 24% Eleventh Grade 50% 28% 22% Twelfth Grade 40% 25% 35% Match the two-way table to the segmented bar graph.
Answers
The steps to create a bar graph are explained below.
To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.
Here is how we can match the two-way table to the segmented bar graph:
For the Lion mascot option, the segmented bar graph would have the largest segment for 11th grade, followed by 9th grade, 10th grade, and 12th grade.For the Eagle mascot option, the segmented bar graph would have the largest segment for 10th grade, followed by 11th grade, 9th grade, and 12th grade.For the Bee mascot option, the segmented bar graph would have the largest segment for 12th grade, followed by 9th grade, 10th grade, and 11th grade.By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.
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The employee benefits manager of a medium size business would like to estimate the proportion of full-time employees who prefer adopting plan A of three available health care plans in the coming annual enrollment period. A reliable frame of the company's employees and their tentative health care preferences are available. Using Excel, the manager chose a random sample of size 50 from the frame. There were 17 employees in the sample who preferred plan A. Construct a 99% confidence interval for the proportion of company employees who prefer plan A. Assume that the population consists of the preferences of all employees in the frame. The lower boundary is 0.172
Answers
Answer:
it's a because I did this test
Divide 240 grams in the ratio 5 : 3 : 4
Answers
Answer:
48
80
60
Step-by-step explanation:
240 ÷ 5 = 48
240 ÷ 3 = 80
240 ÷ 4 = 60
Answer:
100g, 60g, 80g
Step-by-step explanation:
Total of ratio 5+3+4=12
(240×5)÷12=100
(240×3)÷12=60
(240×4)÷12=80
verification 100g+60g+80g=240g