The coordinates of the vertices of △ABC are A(−4, 6) , B(−2, 2) , and C(−6, 2) .
The coordinates of the vertices of △A′B′C′ are A′(2, 6) , B′(0, 2) , and C′(4, 2) .
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △ABC to △A′B′C′ is a blank followed by a blank.
translation 2 units left
reflection across the x-axis
reflection across the y-axis
translation 2 units down
Answers
Answer-
The sequences of transformations that maps △ABC to △A′B′C′ are
Reflection across the y-axisTranslation 2 units leftSolution-
The coordinates of the vertices of ΔABC are
A = (−4, 6)
B = (−2, 2)
C = (−6, 2)
The coordinates of the vertices of ΔA′B′C′ are
A′ = (2, 6)
B′ = (0, 2)
C′ = (4, 2)
As all the y-coordinates of all the function are same, so the triangle is neither translated up or down (∵ (x, y) → (x, y±k)), nor reflected over x-axis(∵ (x, y) → (x, -y)).
As the signs of x-coordinate is changed, it might be reflected over y axis,
Rule for reflection over y axis is,
(x, y) → (-x, y)
so,
A" = (4, 6)
B" = (2, 2)
C" = (6, 2)
As the x-coordinates of vertices of ΔA′B′C′ are 2 units less than that of ΔA"B"C"
So it is then translated 2 units left.
Therefore, the sequences of transformations that maps △ABC to △A′B′C′ are
Reflection across the y-axisTranslation 2 units left
Answer:
Here is my test answer
Step-by-step explanation:
Related Questions
A 10-pound weight in a 2-pound weight are dropped from the same height at the same time which weight will hit the ground first
Answers
they would drop at the same time
Answer:
explained below
Step-by-step explanation:
when two object one of 10 pound weight and another of 2 pound is dropped from same height
condition 1 : when body fall In vaccum
When body fall in vaccum then there will be no effect of weight.
Both the body will hit the ground at the same time.
Condition 2 : when body falls in normal condition
When body falls in normal condition then in this condition the heavy weight object will fall first as the light weight object will have more air resistance than the heavy one.
Jorge is 1 year younger than his brother. The sum of their ages is no less than 25 years. Enter the youngest age Jorge's brother can be. Question 10 options:
12
13
14
15
Answers
The youngest age Jorge's brother can be is 13. This is derived from the given condition that the sum of their ages is no less than 25, by assigning Jorge's brother's age as an unknown 'x' and using algebraic principles.
Explanation:The subject question is a simple algebraic problem. Let's denote Jorge's brother's age as x, so Jorge's age would be x-1. The problem states that the sum of their ages is no less than 25, which would translate algebraically into x + (x-1) ≥ 25.
Then we simplify the equation by combining like terms, it turns into 2x - 1 ≥ 25. To isolate x, you first add 1 to both sides of the equation, which gives you 2x ≥ 26, and then divide both sides by 2, resulting in x ≥ 13.
Therefore, the youngest age Jorge's brother can be is 13.
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Solve 4/5m = -15 show you’re work please ;)
Answers
m = -15 (5/4)
m = -75/4
m = -18.75
(4m/5 = -15)
Multiply both sides by 5
(4m = -15 x 5)
simplify 15 x 5 to 75
4m = -75
divide both sides by 4
(m = 75/-4)
Answer: m = 75/-4
*The work in the parenthesis box is the work shown
* The words above the parenthesis box are the steps in order
* The text in bold is the answer.
John and Mary Billings own a condominium with an acid value of 110000 if the tax rate is 25 meals per dollar off the valuation how much tax do they pay
Answers
A mills is equal to 0.001
This means that the tax they pay is 25 x 0.001 = 0.025 per dollar of valuation.
Since the acid value is 110,000, therefore the amount of tax they pay can be calculated as follows:
amount of tax = 110,000 x 0.025 = $2,750 tax paid
Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have
Answers
Answer:
Dustin has 17 nickels and 32 quarters.
Explanation:
Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]
We can set up a system of equations based on the given information:
1. The total number of coins: [tex]\(n + q = 49\)[/tex]
2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]
We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]
From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]
[tex]\[n = 49 - q\][/tex]
Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):
[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]
[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]
Combine like terms:
[tex]\[0.20q + 2.45 = 8.85\][/tex]
Subtract 2.45 from both sides:
[tex]\[0.20q = 6.40\][/tex]
Now, divide both sides by 0.20:
[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]
So, Dustin has 32 quarters.
To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]
[tex]\[n + 32 = 49\][/tex]
[tex]\[n = 49 - 32\][/tex]
[tex]\[n = 17\][/tex]
So, Dustin has 17 nickels.
the base of a pyramid has n sides write an expression for the number of faces of the pyramid
Answers
This means that a pyramid always have the number of face which is one more than the number of sides of the base.
Therefore, given that a pyramid has n number of sides of the base, the expression for the number of faces of the pyramid is given by
number of faces = n + 1.
Find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1).
Answers
Your y1 value is -3 and your x1 value is -1.
Before we can solve the equation, we need the slope first. To find the slope of a line, we need to use the equation y2-y1/x2-x1.
That would be 1-(-3)/4-(-1) which translates to 4/5. Your slope is 4/5.
Now we can plug this into the point slope form.
y-(-3)=4/5(x-(1))
That would be y+3=4/5x+4/5. You must then subtract 3 from 4/5.
This would mean that y=4/5x-2.2
Hope this helps.
Evaluate 4x^3 + 2 for x
Answers
X=-1
Plug in x
4 (-1)^3+2
4 (-1)+2
-4+2
-2
Answer: -2 (D)
Check your work: -2=4x^3+2
-2 both sides
-4=4x^3
÷4 both sides
-1=x^3
(Square root by 3) both sides
X=-1
Answer is correct
= -4 + 2
= -2
Need Answer ASAP!!!!!!!Solve the equation using the zero product property. -n(5n-4)=0
Answers
-5n^2+4n=0
n(-5n+4)=0
n=0
-5n+4=0
-5n=-4
n=4/5
Answer:
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Step-by-step explanation:
We have been given an equation [tex]-n(5n-4)=0[/tex]. We are asked to solve our given equation using zero product property.
Zero product property states that the product of two expressions are zero, if and only if, one of them is zero.
Using zero product property, we will set each factor of our equation to zero as:
[tex]-n=0\text{ or }(5n-4)=0[/tex]
[tex]n=0\text{ or }5n-4=0[/tex]
[tex]n=0\text{ or }5n-4+4=0+4[/tex]
[tex]n=0\text{ or }5n=4[/tex]
[tex]n=0\text{ or }\frac{5n}{5}=\frac{4}{5}[/tex]
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Therefore, the solutions for our given equation are [tex]n=0\text{ or }n=\frac{4}{5}[/tex].
Find the Domain and Range (show work)
Answers
see attached picture for solutions:
Solving: your denominator cannot equal zero so solve this x + 4 ≠ 0
Range: (f(x) | f(x) ≥ 0} or [0, ∞)
Solving you can get zero because x = 0 gives you zero
but when you test other numbers in your domain like x = -2 and x = 2 you only get positive results. Therefore your range is all real non-negative numbers.
Shaylee is determining if 6 is the solution to the equation.
42 ÷ w = 7 for w = 6
First, Shaylee must substitute ( ) for ( ).
To simplify, Shaylee must divide ( ) by ( ) .
Answers
First, Shaylee must substitute (6) for (w)
To simplify,Shaylee must divide (42) by(6)
:)
6 is the solution of the equation 42 ÷ w = 7.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Shaylee is determining if 6 is the solution to the equation
42 ÷ w = 7 for w = 6
Forty two divided by w equal to seven for w equal to six.
First, Shaylee must substitute 6 for w.
To simplify, Shaylee must divide 42 by 6
42/6=7
So 6 is the solution of the equation.
Hence, 6 is the solution of the equation 42 ÷ w = 7.
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Curt just drank a cup of coffee to help him stay awake. The coffee had 130 milligrams of caffeine in it. If his body processes 7% of the caffeine every hour, how much will be left in 4 hours?
93
94
98
91
Answers
Answer:
After 4 hours, there will 91.31 miligrams of caffeine within his body.Step-by-step explanation:
Givens
Curt drank 130 miligrams of caffeine.His body processes 7% of caffeine everyhour.If Curt's body processes 7% every hour, we just need to that 7% after each hour. Also, we know that 7% equals 0.07.
First hour.
[tex]0.07(130)=9.1ml[/tex]
The first hour, his body processed 9.1 miligrams, so it remains
[tex]130-9.1=120.9ml[/tex]
There's still 120.9 miligrams in his body.
Second hour.
[tex]0.07(120.9)=8.46ml[/tex]
[tex]120.9-8.46=112.44ml[/tex]
Third hour.
[tex]0.07(112.44)=7.87ml[/tex]
[tex]112.44-7.81=104.63ml[/tex]
Fourth hout.
[tex]0.07(104.63)=7.32ml[/tex]
[tex]104.63-7.32=97.31ml[/tex]
Therefore, after 4 hours, there will 91.31 miligrams of caffeine within his body.
If a car travels 23 miles on 1.0 gal of gas, how many liters of gasoline are needed for a 135 mile trip?
Answers
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next
Answers
200
At Susie's school, 5/8 of all students play sports. Of the students who play sports, 2/5 play soccer. What fraction of the students in Susie's school play soccer?
Answers
5x + 2y = 8
x + y = 4
If you want to solve the system of equations by addition, which of the following could you do?
(A.) Multiply the second equation by 5 and add.
(B.) Multiply the second equation by 2 and add.
(C.) Multiply the second equation by -2 and add.
Answers
Answer: C. Multiply the second equation by -2 and add
Step-by-step explanation:
Answer:
Step-by-step explanation:
The solution is C
5x + 2y = 8
-2x -2y= -8
3x = 0
x = 0
2y = 8
y = 4
(0,4)
How to find an equation in slope intercept form given two points?
Answers
(1,2)(3,4)
first we find the slope by using the slope formula
slope = (y2 - y1) / (x2 - x1)
now we label our points..
(1,2)...x1 = 1 and y1 = 2
(3,4)...x2 = 3 and y2 = 4
now we sub and find the slope
slope = (4 - 2) / (3 - 1) = 2/2 = 1....so we have a slope of 1
now we use y = mx + b
slope(m) = 1
use either of ur points...(1,2)...x = 1 and y = 2
now we sub into the formula and find b, the y int
2 = 1(1) + b
2 = 1 + b
2 - 1 = b
-1 = b ....this is ur y int
and in y = mx + b form, the slope will be in the m position and the y intercept will be in the b position
y = mx + b
slope(m) = 1
y int (b) = -1
so ur equation in slope intercept form is : y = 1x + (-1) which can be written as : y = x - 1
This diagram of airport runway intersections shows two parallel runways. A taxi way crosses both runways. How are 6 and 2 related?
a)corresponding angles
b) alternate interior angles
c)same side interior angles
d) none of these
Answers
Refer to the diagram below.
Two angles are corresponding to each other when they are on the same line that crosses two parallel lines, one angle is inside the parallel lines, the other is on the outside.
The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.
Answers
[tex]a = l * w[/tex] [tex]a = 108[/tex]
You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:
Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
[tex]2's[/tex] [tex]cancel[/tex] [tex]out[/tex]
[tex] \frac{p}{2} = w + l[/tex]
Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
[tex]\frac{p}{2} - l = w + l - l[/tex]
[tex]l's[/tex] [tex]cancel[/tex] [tex]out[/tex]
p/2 - l = w
[tex]a = l * w[/tex]
You replace w with the equation above p/2 - l = w
[tex]a = l( \frac{p}{2} - l)[/tex]
Multiply out the L.
[tex]a = \frac{p}{2}l - l^{2}[/tex]
Plug in all your numbers a = 110 and p = 42
[tex]110 = \frac{42}{2}l - l^{2}[/tex]
[tex]110 = 21l - l^{2[/tex]
Move everything to the left side so [tex] l^{2} [/tex] would be positive (makes the equation easier when [tex] l^{2} [/tex] is positive).
[tex]l^{2} - 21l + 110 = 0[/tex]
Factor.
[tex](l -10)(l-11) = 0[/tex]
Make each parenthesis set equal to 0.
[tex]l-11=0[/tex] [tex]l-10=0[/tex]
Add.
[tex]l = 11[/tex] [tex]l = 10[/tex]
By doing this you solve for both the width and length so the answer is:
w = 11 L = 10
define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.
Answers
Whether or not a measurement gives the same results when it is repeated under the same conditions is an indication of the measurement’s _____
Answers
Which expression is the factored form of 2/3x+4 ?
A 2/3(x+6)
B 2/3(x+12)
C 2/3(x+4)
D 1/3(2x+6)
Answers
2/3x+4
4/(2/3)=6
2/3(x+6)
Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:
Answers
Final answer:
The 5% represents the annual interest rate on Loretta's investment in a simple interest account.
Explanation:
The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).
To find the interest rate, we can use the formula:
Interest = Principal * Rate * Time
Using the given information, we can plug in the values and solve for the rate:
100 = 1000 * Rate * 2
Simplifying the equation, we get:
Rate = 100 / (1000 * 2) = 0.05 or 5%
Therefore, the 5% represents the annual interest rate in this scenario.
|2y+10|=-4 solve for y
Answers
2y+10=-4
2y=-14
y=-7
The absolute value of something can never be negative.
Which lines must be parallel if angle 10 is supplementary to angle 11?
Answers
Analyze the function’s graph to determine which statement is true.
Over the interval [–2.5, 0.5], the local maximum is 2.
As the x-values go to positive infinity, the function’s values go to negative infinity. The function is decreasing over the interval (–1, 0.75).
The function is negative for the interval [–2, 0]
Answers
1. Over the interval [-2.5, 0.5], the local maximum is 2.
TRUE
2. As the x-values go to positive infinity, the function's values go to
negative infinity.
The opposite happens.
FALSE
3. The function is decreasing over the interval (-1, 0.75).
The function decreases in (-1, 0), but it increases in (0, 0.75).
FALSE
4. The function is negative for the interval [-2, 0].
The function is positive in [-2, -1). It is negative only in (-1, 0].
FALSE
The truth of the statements in the question can be verified by analyzing the function's graph over the stipulated intervals. Understanding concepts such as local maxima, the behavior of functions at infinity, an interval of decrease, and intervals where a function remains negative or positive are essential in this process.
Explanation:To determine which statement in the question is true, we need to analyze the function's graph. The statements included talk about specific behaviors of the function in different intervals of the x-axis.
The first statement mentions a local maximum of 2 over the interval [–2.5, 0.5]. You will need to locate this interval on the x-axis and see if 2 is indeed the highest y-value within this range. If there is a point on the function where the y-value is 2 and it is higher than all neighboring points, then this statement is true.
The second statement states that as the x-values go to positive infinity, the function's values go to negative infinity. This implies that as the function continues towards the positive direction on the x-axis, the y-values continuously decrease towards negative infinity. If the graph shows this, then this statement is true.
The third statement says the function is decreasing over the interval (–1, 0.75). This would mean that as x goes from –1 to 0.75, the y-values decrease. If you observe this on the graph, this statement is true.
The last statement asserts the function is negative for the interval [–2, 0]. If, for all x-values from –2 to 0, the corresponding y-values are below the x-axis (negative), then this statement is valid.
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Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?
Answers
Answer:
4:10 is smaller because when put into fraction form and making the denominators even, 12:20 comes out to be 6/10
Step-by-step explanation:
A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint
Answers
The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).
What are the coordinates of the midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m) / 2
and
y = (q+n) / 2
Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,
X- coordinate = (14+ 4)/2
= 18/2
= 9
Y- coordinate = (-8+12)/2
= 4/2
= 2
Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).
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Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?
Answers
9.75 / 1.25 = 7.8
10^6 - 10^2 = 10^4
= 7.8 x 10^4 greater
The expression 53 ( 1 − x) gives the discounted price of a pair of shoes, where x is the percent of the discount written in decimal form.
What does 1 − x represent in the expression?
A. percent of original price being paid
B. discount price of the shoe
C. percent of discount
D. original price of shoe