Graph and label the image of the figure below after a dilation by a factor of 1/2.
Answers
M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)
see graph below
Explanation:Given:
The image of a quadrilateral on a coordinate plane
To find:
The coordinates of the new image after dilation of 1/2 have been applied to the original image.
Then graph the coordinates
First, we need to state the coordinates of the original image:
M = (3, -2)
F = (4, -2)
L = (1, -5)
W = (5, -5)
Next, we will apply a scale factor of 1/2:
[tex]\begin{gathered} Dilation\text{ rule:} \\ (x,\text{ y\rparen}\rightarrow(kx,\text{ ky\rparen} \\ where\text{ k = scale factor} \\ \\ scale\text{ factor = 1/2} \\ M^{\prime}\text{ = \lparen}\frac{1}{2}(3),\text{ }\frac{1}{2}(-2)) \\ M^{\prime}\text{ = \lparen}\frac{3}{2},\text{ -1\rparen} \\ \\ F\text{ = \lparen}\frac{1}{2}(4),\text{ }\frac{1}{2}(-2)) \\ F^{\prime}\text{ = \lparen2, -1\rparen} \end{gathered}[/tex][tex]\begin{gathered} L\text{ = \lparen}\frac{1}{2}(1),\text{ }\frac{1}{2}(-5)) \\ L^{\prime}\text{ = \lparen}\frac{1}{2},\text{ }\frac{-5}{2}) \\ \\ W\text{ = \lparen}\frac{1}{2}(5),\text{ }\frac{1}{2}(-5)) \\ W^{\prime}\text{ = \lparen}\frac{5}{2},\text{ }\frac{-5}{2}) \end{gathered}[/tex]The new coordinates:
M' (3/2, -1), F' (2, -1), L' (1/2, -5/2), W' (5/2, -5/2)
M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)
Plotting the coordinates:
Related Questions
Algebra Question, please provide a step-by-step explanation.
Answers
Answer:
4 seconds
Step-by-step explanation:
First I substitute the Y with 0 and then I move the 16x^2 to the left side of the equation and then I divide both sides with 16 leaving me with x^2 then I get the square root of both sides and then I evaluate it and then I got the answer x = 4
Answer:
4 seconds
Step-by-step explanation:
We have a quadtratic equation, that is, we have a function to the highest degree of x^2.
When solving this, we can either solve using the quadratic equation, or by solving for X which would be the easiest and quickest way to do it.
256 -16x^2=0
-16x^2=-256
x^2=16 (divide both sides by -16)
[tex]\sqrt{x} =\sqrt{16}[/tex]
Which leaves x=4 as your answer.
To check this, we can simply input 4 back into the equation, and we will find that it does indeed equal 0.
To further visualize this, when we solve the equation for x, we are finding where the x value that intersects the x axis. We are finding where x=0, or when it touches the ground.
Find the volume of this cone.Use 3 for T.10 ft=115 ftTr²hV=3Hint: The radius (1) is1/2 of the diameter.V ~ [?]ft3
Answers
Given:-
[tex]V=\frac{\pi r^2h}{3}[/tex]To find the volume of the cone.
From the given image it is clear,
[tex]h=5,r=5[/tex]So now we substitute the known values. so we get,
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{3(5)^25}{3} \\ V=5^3 \\ V=125 \end{gathered}[/tex]So the required volume is 125ft^3.
Ajay is working two summer jobs, making $8 per hour washing cars and $11 per hour
tutoring. Last week Ajay worked 2 more hours tutoring than hours washing cars and
earned a total of $60. Write a system of equations that could be used to determine
the number of hours Ajay worked washing cars last week and the number of hours he
worked tutoring last week. Define the variables that you use to write the system.
Let
Let
System of Fiquations
Answers
Using equation, the number of hours Ajay spent washing car and tutoring are 2 and 4 hours respectively.
How to represent system of equation?Ajay is working two summer jobs working $8 per hour washing cars and $11 per hour tutoring.
Last week Ajay worked 2 more hours tutoring than hours washing cars and earned a total of $60.
The system of equation that could be used to determine the number of hours Ajay worked washing cars last week and the number of hours he worked tutoring last week can be calculated as follows:
let
x = number of hours washing cars
y = number of hours tutoring
Therefore,
y = 2 + x
Hence,
8(x) + 11(2 + x) = 60
8x + 22 + 11x = 60
19x = 60 - 22
19x = 38
x = 38 / 19
x = 2
Therefore,
y = 2 + 2
y = 4
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Answer:
variables :
Let = w = The number of hours washing car.
let = t = The number of hours tutoring.
system of equations:
8w + 11t = 60
t = w + 2
Step-by-step explanation:
Make g the subjest of a=g+h/2
Answers
g = a - [tex]\frac{h}{2}[/tex]
PLS HELP 40 POINTS IF YOU GET THIS RIGHT AND BRAINLIST. PRETTY SIMPLE.
• Jackie made a mistake when he _________.
• The Triangle Congruence Postulate or Theorem that is easiest for me to use is ____ because _____.
• The Triangle Congruence Postulate or Theorem that is the most difficult for me to use is ____ because _____.
Answers
Answer:
12
Step-by-step explanation:
bla bla bla is not 12 and I know that thanks for my points is not 12 thanks
this is due now pls explain how u got the anser
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
I got the answer by plotting the points on a graph. Then count how many places you have to go from one point to the other to find the slope. To find the y - intercept, look at where the point passes or is on the y-intercept. Sorry if this isn't a good explanation.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Please use a picture to show where they are plotted if you can.
Answers
The slope of the line in the given diagram = rise/run = 1/2.
How to Determine the Rise and Run of a Line to Determine its Slope?The slope of a line is determined as the ratio of the rise of the line to the run of the line.
The rise of a line = change in y
The run of a line = change in x.
The red line in the image attached below shows the rise of the line which is, 1 units.
The blue line represents the run, which is, 2 units.
The slope of the line = 1 units/2 units = 1/2.
Therefore, we can state that the slope of the line = 1/2.
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irections: Find the missing endpa
D. R(-9, 4) and S(2, -1); Find T.
Answers
The coordinates of T are (13, -6) which s is the midpoint of rt r(-9,4) and s(2,-1).
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,
M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Assuming that S is the midpoint of the line segment RT, where point R's coordinates are (-9, 4) and S's coordinates are (2, -1).
We have to determine the coordinates of point T.
The midpoint is the average of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).
In this case, the midpoint is given by M = S(2, -1).
Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).
2 = (-9 + x₂)/2
-9 + x₂ = 4
x₂ = 13
-1 = (4 + y₂)/2
4 + y₂ = -2
y₂ = -6
Therefore, the coordinates of T are (13, -6).
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The question seems to be incomplete the correct question would be
Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T
Line g passes through points (2, 3) and (5, 2). Line h is perpendicular to line g. What is the slope of line h?
Answers
The slope of the line h is 3
Let m1 be the slope of line g and m2 be the slope of line h.
Line g passes through points (2, 3) and (5, 2).
Using the formula of slope,
m1 = (2 - 3)/(5 - 2)
m1 = -1 / 3
Line h is perpendicular to line g.
We know that the product of slopes of the perpendicular lines is -1.
m1 * m2 = -1
(-1/3) * m2 = -1
m2 = 3
Therefore, the slope of the line h is 3
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Which statement is true
A)Only graph A is a function
B)Only graph B is a function
C)Both graphs are functions
D)Neither graph is function
Answers
Answer:wish i could help
Step-by-step explanation:......
The domain for f(x) and g(x) is the set of all real numbers.
Let fix)=x²+1 and g(x) = 3x.
Find f-g-
A. x²+3x+1
B. 3x³ +3x+1
C. x² + 3x
D. x²-3x+1
Answers
The value of the composite function (f - g)(x) is x² - 3x + 1
How to evaluate the function?The functions are given as
f(x) = x² + 1
g(x) = 3x
The composite function definition is given as
(f - g)(x)
This composite function is calculated using the following composite function formula
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation
So, we have the following equation
(f - g)(x) = x² + 1 - 3x
Evaluate the like terms
(f - g)(x) = x² - 3x + 1
Hence, the composite function is (f - g)(x) = x² - 3x + 1
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How much would Haiti’s balance be from account two over 3.4 years round to two decimal place
Answers
Solution:
Given:
Account 2 details:
Assume a year is 365 days;
[tex]\begin{gathered} P=\text{ \$}8100 \\ t=3.4years \\ r=5.1\text{ \%}=\frac{5.1}{100}=0.051 \\ n=365days \end{gathered}[/tex]Using the compound interest formula to get the amount;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence, substituting the values;
[tex]\begin{gathered} A=8100(1+\frac{0.051}{365})^{365\times3.4} \\ A=8100(1+\frac{0.051}{365})^{1241} \\ A=9633.55 \end{gathered}[/tex]Therefore, the balance in account 2 will be $9633.55
y=-4x+12
6x+ 5y = 11
Answers
The value of x = 7/2 and y = -2, Given equation are linear.
What is a linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.
The equation are,
y=-4x+12 --------(i)
6x+ 5y = 11 --------(ii)
for eq(i),
y + 4x = 12
4x + y = 12
Now, put together both the equation and multiply with coefficient of x to make common value of x so that we can cut by opposite signs,
(4x + y = 12) * 6
(6x+ 5y = 11) * 4
After multiplying, we get
24x + 6y = 72
24x + 20y = 44
Now change the signs with + to - and - to +, like that
24x + 6y = 72
24x + 20y = 44
- - -
-----------------------
0 + 6y - 20y = 72 - 44
=> -14y = 28
=> y = 28/(-14)
=> y = -2
Put y = -2 in eq(i),
4x + y = 12
4x - 2 = 12
4x = 12 + 2
x = 14/4
x = 7/2
Hence, the values we get after solving given equation is x=7/2 and y= -2.
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Find the least common multiple of 3x and 3(x−2)
Answers
The least common multiple of the 3x and 3(x−2) is 9x(x - 2)
How to determine the least common multiple of the expressions?From the question, the expressions are given as
3x and 3(x−2)
The expressions do not have direct factors or multiples
So, we multiply both expressions to calculate the least common multiple
This above computation can then be represented as
Least common multiple = Product of the two expressions
Substitute the known values in the above equation
So, we have the following representation
Least common multiple = 3x * 3(x - 2)
Evaluate the product of 3x and x in the above equation
So, we have the following equation
Least common multiple = 9x(x - 2)
Hence, the least common multiple of the expressions is 9x(x - 2)
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in the given picture, the measure of x is __°
*no multiple choice*
Answers
Answer:
x = 52°
Step-by-step explanation:
Exterior Angle Theorem
The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ x + 90° = 142°
⇒ x + 90° - 90° = 142° - 90°
⇒ x = 52°
Let us assume that,
→ x + y + 90° = 180°
Now the required value of y is,
→ y + 142° = 180°
→ y = 180° - 142°
→ [ y = 38° ]
Then the value of x will be,
→ x + 38° + 90° = 180°
→ x = 180° - 128°
→ [ x = 52° ]
Hence, the value of x is 52°.
Determine the value of y in the inequality.
18 + 6y < 42
y < −7
y > −7
y < 4
y > 4
Answers
Answer:
y>-7
Step-by-step explanation:
Answer:
the answer is option 3
Step-by-step explanation:
18+6y<42
6y<42-18
6y<24
y<4
The division law of exponents says that if b is a non zero number and n and m are any numbers then bm/bn = bm-n true or false?
Answers
it is True that the division law of exponents says that if b is a non zero number and n and m are any numbers in the exponents of b then b^m/b^n = b^(m-n)
What is division law of exponents?This is the law that governs numbers that are have exponents or power.
According to the question b is the number while m and n represents the value of the exponents or the numbers for which number b is raised to their power say: b^m and b^n
The division law of exponents holds as:
= b^m ÷ b^n
= b ^ ( m - n )
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Write the following expression using the fewest possible terms.
(−2x − 13) + (19 + 5x)
3x + (−6)
7x + (−6)
7x + 32
3x + 6
Answers
There is nothing more we can do with these binomials, so we break them up and combine like terms.
-2x - 13 + 19 + 5x
5x - 2x + 19 - 13
3x + 19 - 13
3x + 6
Answer:
[tex]\boxed{\sf 3x+6}[/tex]
Step-by-step explanation:
[tex]\sf \left(-2x-13\right)+\left(19+5x\right)[/tex]
Simplify:-
[tex]\sf -2x-13+19+5x[/tex]
Combine like terms/Add numbers:-
[tex]\sf -2x+5x-13+19[/tex]
[tex]\sf (-2x+5x)=\bf 3x[/tex]
[tex]\sf (-13+19)=\bf 6[/tex]
[tex]\boxed{\sf 3x+6}[/tex]
Therefore, your answer is D. 3x + 6!!
_______________________
Hope this helps!
Have a great day!
Find the quotient of
30 x 10-24
5x10-24
Write the final answer in scientific notation.
Answers
Answer: The quotient of (30 x 10^-24)/(5 x 10^-24) is 6, which means that in scientific notation, it’s written as 6 x 10^0.
Factorise 12x raise to power of 2 and y raise to power of 2 +11xy-5
Answers
According to the solving the factorized value of the given equation is:
(4x-5). (3x+1).
What is factorization?Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.
Why do we factor?Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.
According the given data:Detailed explanation:
12x² - 11x-5
12x²+4x-15x-5
4x(3x+1) - 5(3x+1)
(4x-5). (3x+1)
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Yessenia works at The Buckle. She earns $350 per week plus 3% commission on her sales. If Yessenia sells $8,500 worth of clothing this week,
what would her hourly rate be if she worked 40 hours?
Answers
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The total amount earned in a week including the commission is $605 working for 40 hours.
The hourly rate is $15.125.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
The amount earned in a week = $350
Amount earned in commission = 3% of $8,500
= 3% of 8500
= 3/100 x 8500
= 3 x 85
= $255
The number of hours worked = 40 hours.
The hourly rate for the week:
= (350 + 255) / 40
= 605 / 40
= $15.125
Thus,
The hourly rate is $15.125.
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Give a real-life representation of loudness and sound using exponential function.
Answers
Using an exponential function, the sound intensity of a noise that is 130 dB is of I = 10 watts/m².
Sound levelThe sound level, in dB, of a sound of intensity given by I is given according to the following equation:
[tex]B = 10\log{\left(\frac{I}{I_0}\right)}[/tex]
In which [tex]I_0[/tex] is the smallest sound heard by the human ear, which is of [tex]I_0 = 10^{-12}[/tex] watts/meter.
Hence, for a sound of 130 db, the intensity I is found as follows:
[tex]130 = 10\log{\left(\frac{I}{10^{-12}}\right)}[/tex]
Isolating the logarithm, the equation is:
[tex]\log{\left(\frac{I}{10^{-12}}\right)} = 13[/tex]
The power of 10 and the logarithm are inverse functions, hence the power of 10 is applied to both sides of the equation to isolate the intensity creating the exponential function given as follows:
[tex]10^{\log{\left(\frac{I}{10^{-12}}\right)}} = 10^{13}[/tex]
[tex]\frac{l}{10^{-12}} = 10^{13}[/tex]
[tex]l = 10^{-12} \times 10^{13}[/tex]
Multiplying two terms with the same base and different exponents, we keep the base and add the exponents, hence the intensity is given as follows:
I = 10 watts/m².
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What is the slope of the linear relationship shown on the graph?
4/3
-4/3
3/4
-3/4
Answers
The slope of the linear graph is - 4 / 3.
How to find the slope of a linear graph?The slope of a linear graph is the change in the dependent variable with respect tot he change in the independent variable.
The slope is describe as rise over run.
Therefore, the slope can be represented mathematically, as follows;
Hence,
slope = y₂ - y₁ / x₂ - x₁
Therefore, using (0, -2) and (- 3 / 2, 0)
x₁ = 0
x₂ = - 3 / 2
y₁ = - 2
y₂ = 0
Therefore,
slope = 0 + 2 / - 3 / 2 - 0
slope = 2 ÷ - 3 / 2
slope = 2 × 2 / -3
Therefore,
slope = - 4 / 3
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How do yu solve this problem right here 25m^2 - 17= -1
Answers
Answer:
The answer will be 4/5
Step-by-step explanation:
25m^2-17=-1
25m^2=-1+71
√25m^2=√16
5m=4
m=4/5
plss someone help me asap!!
Answers
By analyzing the geometric system, the measure of the angle RSP is equal to 49°.
What are the variables behind the angles of the system of triangles and one of the internal angles
In this problem we find a geometric system formed by two triangles, in which the line segment QR is parallel to the line segment PS. Then, we can obtain the following system of linear equations:
Intern alternate angles between parallel line segments
m ∠ QRP = m ∠ RPS
5 · y + 14 = 8 · y - 13
27 = 3 · y
y = 9
Internal angles of a triangles
m ∠ RPS + m ∠ PRS + m ∠ RSP = 180°
(8 · y - 13) + 3 · x + (2 · x + 1) = 180
8 · y + 5 · x - 12 = 180
8 · y = 180 + 12 - 5 · x
5 · x = 192 - 8 · y
x = (192 - 8 · y) / 5
x = (192 - 8 · 9) / 5
x = (192 - 72) / 5
x = 120 / 5
x = 24
Finally, the measure of the angle RSP is:
m ∠ RSP = 2 · x + 1
m ∠ RSP = 2 · 24 + 1
m ∠ RSP = 49
The measure of the angle RSP is equal to 49°.
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(p+2) is a factor of (3p^3-4p^2-13p+14)
Answers
Answer:
true
Step-by-step explanation:
3p^3-4p^2-13p+14 = (p-1)(3p-7)(p+2)
PLEASE HELP!! PICTURE INCLUDED!!
Please explain how to find angle R!!
Answers
Answer:
∠ R = 75°
Step-by-step explanation:
you are correct with answers to a, b, c
d
the sum of the 3 angles in Δ QRS = 180° , that is
∠ Q +∠ R + ∠ S = 180° , so
55° + ∠ R + 50° = 180°
∠ R + 105° = 180° ( subtract 105° from both sides )
∠ R = 75°
The sides of a triangle are 7 cm, 18 cm, and 16 cm. Find the length of the longest side of a similar triangle whose shortest side is 14.7 cm.
Answers
The longest side of the other triangle is 37.8 cm
How to determine the longest side of the other triangle?From the question, the sides of the triangle are given as
Sides of a triangle = 7 cm, 18 cm, and 16 cmThe shortest side on a similar triangle is 14.7 cm.This means that
Ratio = Corresponding sides of the triangles
So, we have
Ratio = Longest sides : Shorters sides
Substitute the known values in the above equation
So, we have the following equation
18 : 7 = Longest side : 14.7
Multiply 18 : 7 by 2.1
So, we have
37.8 : 14.7 = Longest side : 14.7
So, we have
Longest side = 37.8
Hence, the longest side is 37.8 cm
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- Without looking, Jeff threw a small beanbag on a target with a radius of 20 cm. Adiagram of the target is shown below.10 cm 10 cmcIf the beanbag lands on the target, what is the probability it will land on the shadedarea?
Answers
To find the probability, we will need to first find the area of the whole circle and the area of the shaded part.
Area of the Big Circle
Given that the radius, R, is 20cm, the area is
[tex]\begin{gathered} A=\pi R^2 \\ =\pi\times20^2 \\ =400\pi \end{gathered}[/tex]Area of the Shaded Part
We can find the area of the shaded part by calculating the area of the small circle (r = 10cm) and subtract it from the big circle.
Hence
[tex]\begin{gathered} a=\pi r^2 \\ a=\pi\times10^2 \\ a=100\pi \end{gathered}[/tex]The area of the shaded portion is
[tex]\begin{gathered} A_s=A-a \\ A_s=400\pi-100\pi \\ A_s=300\pi \end{gathered}[/tex]Probability of landing on the shaded portion:
The probability is calculated by
[tex]\begin{gathered} P(A_s)=\frac{A_s}{A} \\ =\frac{300\pi}{400\pi} \\ P(A_s)=\frac{3}{4} \end{gathered}[/tex]Therefore, the probability that the ball will land on the shaded area is 3/4.
The FOURTH OPTION is correct.
2. A car is going 65 miles per hour down the highway.
a. How far does it travel in 1.5 hours?
b. How long does it take the car to travel 130 miles?
c. Mai wrote the equation y = 65x, with a representing
the time traveled, in hours, and y representing the
distance traveled, in miles. Explain why Mai's equation
matches the story.
C
t
a
m
e
th
d
d
Answers
a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
In this question, we have been given a car is going 65 miles per hour down the highway.
Part a.
A car is going 65 miles per hour.
This means, in 1 hour car traveled 65 miles.
Let car travels 'm' miles in 1.5 hours.
So, m = 1.5 × 65
m = 97.5 miles
Thus, a car travels 97.5 miles in 1.5 hours
Part b.
Suppose that it will take t hours to travel 130 miles.
We have been given 1 hour = 65 miles
So, we get an equation,
t = 130 / 65
t = 2 hours
This means, a car takes 2 hours to travel 130 miles.
Part c.
Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.
We know that the formula of speed.
speed = distance / time
⇒ distance = speed × time
here, speed = 65 miles per hour
⇒ distance = 65 × time
Assuming distance = y and time = x
y = 65x
This means, Mai's equation matches the story.
Therefore, a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
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