Answers
Answer:
Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.
Step-by-step explanation:
For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.
For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.
Answer:
ASArigidStep-by-step explanation:
Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.
Sides and anglesThe segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.
When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.
Motion"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.
Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.
__
Additional comment
The rigid motions include ...
translationrotationreflection.<95141404393>
Related Questions
Subtract the expressions.
Pls help asap
(8.21n − 5.3) − (7 + 11.8n)
−3.59n − 12.3
−35.90n − 4.8
13.51n − 4.8
20.01n + (−12.3)
Answers
Answer:
I will gladly help (see explanation)
Step-by-step explanation:
1. 8.21n−5.3−(7+11.8n)
Distribute the Negative Sign:
=8.21n−5.3+−1(7+11.8n)
=8.21n+−5.3+(−1)(7)+−1(11.8n)
=8.21n+−5.3+−7+−11.8n
Combine Like Terms:
=8.21n+−5.3+−7+−11.8n
=(8.21n+−11.8n)+(−5.3+−7)
=−3.59n+−12.3
(Hope his helped, Good Luck! )
Answer:
-3.59 - 12.3
Step-by-step explanation:
Algebraic ExpressionsAlgebraic Expressions are similar to numerical expressions but instead of just numbers, alphabet variables are being used as well.
Note: BODMAS rule applies to Algebraic Expressions as well.
Eg. 7x + 4 + 5y + 4x = 11x + 5y + 4
SolutionGiven from the question:
(8.21n - 5.3) - (7 + 11.8n)
= 8.21n - 5.3 - 7 - 11.8n
= 8.21n - 11.8n - 5.3 - 7
= -3.59n - 12.3
Therefore, the answer is -3.59 - 12.3.
quadratic equation in standard form:
17=5-6 z-z²
Answers
Answer:
i think z would be 17
Step-by-step explanation:
Two friends take a 4000-mile cross-country trip together, but they drive their own cars. Car A has a 10-gallon gas tank
and averages 30 miles per gallon, while car B has a 20-gallon gas tank and averages 20 miles per gallon. Assume
both drivers pay an average of $2.65 per gallon of gas.
a. What is the cost of one full tank of gas for car A? For car B?
b. How many tanks of gas do cars A and B each use for the trip?
c. About how much do the drivers of cars A and B each pay for gas for the trip
Answers
Answer:
a.
Car A: $26.50
Car B: $53.00
b.
Car A: 13 1/3
Car B: 10
c.
Car A: $353
Car B: $530
Step-by-step explanation:
Car A: 10 gal, 30 mpg
Car B: 20 gal, 20 mpg
a.
Car A: 10 gal × $2.65/gal = $26.50
Car B: 20 gal × $2.65/gal = $53.00
b.
Car A: 1 full tank will drive 10 gal × 30 mpg = 300 miles
4000 miles / 300 miles = 13 1/3
Car B: 1 full tank will drive 20 gal × 20 mpg = 400 miles
4000 miles / 400 miles = 10
c.
Car A: 13 1/3 × 10 gal × $2.65/gal = $353
Car B: 10 × 20 gal × $2.65/gal = $530
A psychologist is studying the self image as measured by the self image score for a personality
Answers
The minimum sample size needed for the desired margin of error of the confidence interval is given as follows:
44.
How to obtain the sample size needed?The sample size needed is obtained using the z-distribution, as the standard deviation for the population is known.
The equation that gives the margin of error for a z-distribution confidence interval is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given as follows:
z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The known measures in this problem are given as follows:
[tex]M = 20, \sigma = 80, z = 1.645[/tex]
Then the desired sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.645\frac{80}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.645 \times 80[/tex]
Simplifying by 4, we have that:
[tex]\sqrt{n} = 1.645 \times 4[/tex]
[tex](\sqrt{n})^2 = (1.645 \times 4)^2[/tex]
n = 43.3.
Rounding up, as a sample size of 43 would have a margin of error slightly above 20, the sample size needed is of 44.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Question 1 of 10
What is the value of x?
35⁰
70⁰
Answers
⇒Sum of interior angles of a triangle is 180°
⇒ The above statement means that
[tex]70+35+x=180[/tex]
⇒Solving for x :
[tex]105+x=180\\x=180-105\\x=75[/tex]
∴ x=75°
Option D is the answer.
Criteria: I can explain what happens to lines and angles in a dilation.
Triangle DEF is a scaled copy of Triangle ABC}, answer the following question equations that could be used to solve for x.
Answers
7 ÷ x = 1.5 is the equation used to solve for x.
Given,
Triangle DEF is a scaled copy of triangle ABC.
We have to find the equation to solve for x.
Scaled Copy;-
A scaled copy is a representation of a figure in which each length from the original representation has been multiplied by the same amount. Triangle ABC, for instance, is a scaled version of triangle DEF. Triangle DEF's side lengths were calculated by multiplying each side length from triangle ABC by 1.5.
Here,
Length of side AB = 6
Length of side DE = 4
Let y be the value used for scaling.
Then,
6 = 4y
y = 6/4 = 1.5
So,
Length of side BC ÷ x = 1.5
7 ÷ x = 1.5
7 = 1.5x
x = 7/1.5
x = 4.67
That is,
The equation used for getting the value of x is 7 ÷ x = 1.5
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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 27 seconds, the elevator for the miners begins to descend. What position of each elevator relative to the surface after 17 seconds? At that time, which elevator is deeper?
Answers
1. The position (distance covered) of each elevator relative to the surface after additional 17 seconds is as follows:
The equipment elevator descended 176 feet from the surface.The miners' elevator descended 255 feet from the surface.2. After 17 seconds, the miners' elevator is deeper by 79 feet than the equipment elevator.
How are the distances computed?Distance is a function of speed and time.
This implies that distance is the product of speed and time.
The descent speed of the equipment elevator = 4 feet per second
The total time in seconds the equipment elevator descended = 44 seconds (27 + 17)
The descent distance covered in 44 seconds = 176 feet (44 x 4)
The descent speed of the miners' elevator = 15 feet per second
The total time in seconds the miners' elevator descended = 17 seconds
The descent distance covered in 17 seconds = 255 feet (17 x 15)
Thus, the difference in the descent distance between the equipment elevator and the miners' is 79 feet (255 - 176).
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Sandy wants to graph the equation y=2x^2+4x-6. What set of key points can she use to graph the equation?
Answers
The key points of option (B) are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
What are graphs?Write the equation in the form y = MX + b to determine the slope m and the y-intercept.
This will allow you to graph the equation using the slope and y-intercept (0, b). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
y=2x^2+4x-6
Now, plot this equation in the graph as follows:
(Refer to the image attached below)
x-axis: (1, 0)
y-axis: (-3, 0)
Vertex: (-1, -8)
Therefore, the key points of option (B) which are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
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five apple pies were shared equals by 12 people. How much pie did each pie
Answers
Answer:2.4
Step-by-step explanation:20 - 8.99 = 2.4
PLEASEE HURRY
Frank is wanting to create a scale model of the Eiffel Tower. The real Eiffel Tower is 984 feet tall and 328 feet wide at its base. If Frank's model is 12 inches tall, how wide (in inches) must his scale model be?
Answers
Answer:
4 Inches.
Step-by-step explanation:
To find the width of Frank's scale model, we need to first determine the scale of the model. This can be done by dividing the height of the real Eiffel Tower by the height of Frank's model. Since the real Eiffel Tower is 984 feet tall and Frank's model is 12 inches tall, the scale of the model is 984 / 12 = 82 feet per inch.
Next, we can use this scale to determine the width of the model. Since the real Eiffel Tower is 328 feet wide at its base, and the scale of the model is 82 feet per inch, the width of the model must be 328 / 82 = 4 inches.
Therefore, the width of Frank's scale model of the Eiffel Tower must be 4 inches.
Find x in this equation
Answers
Answer:
5
Step-by-step explanation:
[tex]\triangle HBK \cong \triangle NBK[/tex] by SAS. Using CPCTC, [tex]3x=x+10 \implies 2x=10 \implies x=5[/tex].
Convert 97°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=(F-32)
9
F ==C+32
5
97 °C
= F
Answers
Answer: 97 degrees Celsius is 206.6 degrees Fahrenheit.
hi everyone, I'm studying for a math test. I just have one specific question: are all equations in the format y=mx+b linear equations? Or do I still need to graph it and check if it is a straight line first??
Answers
Yes, all equations in the format y=mx+b are linear equations. In this format, "m" represents the slope of the line and "b" represents the y-intercept, which is the point where the line intersects the y-axis. This means that all equations in this format will produce a straight line when graphed.
However, it is always good practice to graph the equation to confirm that it is a straight line. This will also allow you to see the slope and y-intercept of the line, and check if they match the values of "m" and "b" in the equation.
write an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1
Answers
An equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
What is a slope-intercept form?When the line to be examined slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula. In order to make it simple to identify the slope and y-intercept of a line, its equation can be written in the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is referred to as the slope.
Perpendicular line slopes are reciprocals with a negative sign. In the slope-intercept form, y = mx + b, where m is the slope, the supplied line, y = 3x+1, is already in the slope-intercept form.
The line in the example has a slope of 3.
The negative reciprocal of three, or -1/3, is the slope of the perpendicular.
Y = -1/3x + b is the equation for the line that we are looking for.
We must track down b. We solve for b by using the x and y coordinates of the provided location as x and y in the equation above.
y = -1/3x + b
5 = (1/3)(2) + b
5 = (2/3) + b
b = -5-(2/3)
b= -17/3
B is now substituted for in the equation
y = -1/3x-17/3 as we know that b =-17/3.
Therefore, an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
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Write an equation of a line with the given slope and y-intercept.
m = 1, b = 4
Answers
Answer: " y = x + 4 ".
Step-by-step explanation:
We shall write the equation of a line written in slope-intercept format;
that is, " y = mx + b " ;
in which y is isolated as a single variable on the 'left-hand' side of the question, and with no "coefficient"—
{except for the implied coefficient of 1 }; and:
m refers to the slope of the line—and is the coeffcient of x ;
and b refers to the y-intercept—or more specifically, the value of the y-coordinate when "x = 0" [i.e. the value of the y-coordinate where the line crosses the x-axis].
So: We can plug the given values: m = 1 ; and b = 4 ; into the equation:
" y = mx + b " ; as follows:
→ y = 1x + 4 ; Note: By convention, we often omit the 1 as the coefficient of x —since the 'stand-alone' variable, x ; has an implied coefficent of x ; and we can write the equation:
→ y = x + 4 ; which is our answer.|
______
Hope this is helpful to you! Best wishes!
______
Find the slope for the answer
Answers
The Equation for the given line in the graph is x+ y = 3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
From the Graph take two points (0, 3) and ( 3, 0)
So, slope for the line
= ( 0-3 ) ( 3-0)
= -3/3
= -1
So, the Equation of line is
y[tex]- y_1[/tex] = m(x[tex]-x_1[/tex])
y- 3 = (-1)(x- 0)
y- 3 = -x
y+ x = 3
x+ y = 3
Hence, the Equation line is x+ y= 3.
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Which of the following equations has a maximum at (9,7)?
A.
y = -x2 − 14x − 58
B.
y = -x2 − 18x − 88
C.
y = -x2 + 14x − 40
D.
y = -x2 + 18x − 74
Answers
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
What is an equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 4x + 6 = 15 consists of the two equations 4x + 6 and 15, which are separated by the 'equal' sign.
How do you find the maximum value of an equation ?The graph's transition from increasing to decreasing must be identified in order to determine the maximum. We look at the second derivative and see when the value changes from positive to negative to determine the rate at which the graph goes from increasing to decreasing.
According to the given information
[tex]y = -x^{2} + 18x-74[/tex]
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
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If you good w functions come help me out
Answers
Answer: Number one is a function
Number two is not a function
Number three is a function
Step-by-step explanation:
An easy way to determine functions in situations like these is to look and see if there are multiple outputs for the same X. If there are it is not a function. There can be multiple X values that go to the same Y value however.
Is 70/100 equal to 7/10?
Answers
Answer:
Yes
Step-by-step explanation:
A simple way to know is by simplifying them.
70/100 divided by 10 is 7/10
First divide 70 by 10: you get 7
Then divide 100 by ten: you get 10
Question 1: Find the percent of change to the nearest tenth of a percent for Centerville
Question 2: Which town had the greatest percent of change
Question 3: What was the percent of change? (From your answer in Part B) Do Not Include 'Increase' or 'Decrease.' Round to the nearest whole percent.
Answers
Answer:
Sorry just trying to get points
If 2 sides of a triangle are 10 and 20, what is the possible range of the 3rd side?
Answers
Answer:10<x<30
Step-by-step explanation:
According to the triangle side theorem all you need to do is this.
Difference of the two sides<x<Sum of the two sides.
That will give you the range your looking for. For the difference always remove the smaller number from the bigger number so you can always have positive integers.
Answer: 10<x<30
Step-by-step explanation: The third side of the triangle has to be greater than the difference of the other two sides and smaller than the sum of the other two sides.
2 times 50 find the product or quotient
Answers
Answer:
product is the answer good luck on your test
If random samples are drawn from two independent populations where we draw samples of size 51 from population A which has mean 20.1 and standard deviation 5.49, and samples of size 76 are drawn from population B with mean 27.3 and standard deviation 5.06, what is the standard error for the sampling distribution? Round to four decimal places.
Answers
the required standard error is 6.9 for the sampling distribution.
The standard error of the sampling distribution is given by the formula SE = sqrt( (SD1² / n1) + (SD2² / n2) )
As per the question, we are given that samples of size 51 are drawn from population A with a standard deviation of 5.49, and samples of size 76 are drawn from population B with a standard deviation of 5.06.
Substituting these values into the formula, we get:
SE = √( (5.49² / 51) + (5.06² / 76) )
SE = √( (30.11) + (17.93) )
SE = √(48.04)
SE = 6.9
Therefore, the required standard error is 6.9 for the sampling distribution.
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A school is arranging a field trip to the zoo. The school spends 778.88 dollars on passes for 28 students and 4 teachers. The school also spends 241.64 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answers
The total money spent on a pass and lunch for each student is $850.14.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.
Total number of person = 28 + 4
= 32
Cost per pass = 778.88 / 32
= $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14
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HELP ASAP PLS AND USE THE ANSWERS GIVEN!
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
−13.16
−9.89
0.49
20.11
Answers
The value of the given Fraction expression is -6.93.
What is Fraction?
A fraction is a mathematical expression that represents the division of a whole number or quantity into parts. It is written as two separate numbers, a numerator and a denominator, separated by a slash. The numerator represents the number of parts being considered, and the denominator represents the total number of parts. Additionally, fractions can also represent parts of a whole number. For example, the fraction 1/2 represents one part of a whole number that has been divided into two equal parts. Fractions can also be combined to create a sum of parts.
So, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Evaluate the quotient and the exponent
So, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Evaluate the product
-15 - 3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the value of the given fraction expression is -6.93 (none of the options is correct)
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My new dog! Wanted to show him off cause he’s adorable
Answers
Answer: So Cute!
Step-by-step explanation:
Answer:
Yes. I also think he is adorable.
describe the end behavior of the function y=-x^2+4
Answers
The end behaviour of the function [tex]y = -x^{2} + 4[/tex] is
f(x) → −∞, as x → −∞
f(x) → −∞, as x → +∞
The degree of the function is even, and the leading coefficient is negative.
End behaviour of a function:
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behaviour is determined by a polynomial function's degree and leading coefficient.
For very big or very small values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behaviour based on the sign of the leading coefficient.
To predict the end-behaviour of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
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4) Find 14.56 ÷ 2.8.
First, find an equivalent expression with a
whole number divisor.
1.456 = 28
14.56 28
145.628
1,456 ÷ 28
Answers
The value of the expression is 5.2.
The equivalent expression with a whole number divisor is 145.6/28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
14.56 ÷ 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
= 145.6 / 28
= 5.2
Thus,
The value of the 14.56÷ 2.8 is 5.2.
The equivalent expression is 145.6/28.
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Answer:
The expression answer is 5.2.
145.6/28 is the equivalent expression using a whole number divisor.
Explanation:
For the time being, we have:
14.56 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
For the time being, we have:
As a result, the value of 14.56 2.8 is 5.2.
145.6/28 is an equivalent expression.
-5 = t + 6 1/3 solve for t
Answers
Answer: t=-34/3 or -11 1/3
Step-by-step explanation:
isolate t
t+19/3=-5
subtract both sides with 19/3
t=-34/3 or -11 1/3
Answer:
-34/3
Step-by-step explanation:
-5=t+6 1/3
6 1/3= 19/3
-5=t+19/3
-t. -t
-5-t=19/3
+5. +5
-t=34/3
/-1. /-1
t= - 34/3
5. At Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair. How many cars needed both repairs? How many cars needed new brakes, but not a new exhaust system.
Answers
13 cars needed both repairs and 10 cars needed new brakes, but not a new exhaust system.
In the given question, at Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair.
(a) We have to find the how many cars needed both repairs.
Total inspected cars = 50
The cars needed new brakes = 23
The cars needed new exhaust systems = 34
The cars needed neither repair = 6
So the cars that needed repair = 50-6 = 44
Total cars that needed new brakes and new exhaust systems = 23+34 = 57
So, the cars that needed both repairs = 57-44
The cars that needed both repairs = 13
Hence, 13 cars needed both repairs.
(b) Now we have to find how many cars needed new brakes, but not a new exhaust system.
The cars needed new exhaust systems = 34
The cars that needed repair = 44
So, the cars needed new brakes, but not a new exhaust system = 44-34
The cars needed new brakes, but not a new exhaust system = 10
Hence, 10 cars needed new brakes, but not a new exhaust system.
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