△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″.△DEF is reflected in the y-axis. Then it is translated along the vector ⟨3,−5⟩. Enter your answers as points using parenthesis and commas. Do not use any spaces.
Answers
the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)
Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows
the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)
The diagram below shows the transformation of triangle DEF
Related Questions
What are the possible values of x in x2 + 3x + 3 = 0?
Answers
[tex] x^{2} +3x+3=0[/tex]
The only way to solve this is to use the quadratic formula. When you do that you get a negative number under the square root sign which we all know is illegal, UNLESS you factor out the imaginary "i". So your roots would be this:
[tex]x= \frac{-3+ \sqrt{3}i }{2} ,x= \frac{-3- \sqrt{3}i }{2} [/tex]
Solve by taking square roots: x^2 - 40 = 9
Answers
The answer is x = 7, -7.
[tex] x^{2} = 49[/tex]
[tex] \sqrt{ x^{2} } = \sqrt{49} [/tex]
x = +7 or -7
Two lines are perpendicular. if one line has a slope of 0, what is the slope of the other line?
Answers
The length of a rectangle is twice its width. if the area of the rectangle is 162 cm2 , find its perimeter.
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Then, the length of the rectangle will be 2x
The area of the rectangle will be
2x(x)=2x^2
Since the area of the rectangle is 162cm2
2x^2=162
x^2=81
x=9
Width of the rectangle=9
Length of the rectangle=9x2=18
Perimeter of a rectangle
=2(width) + 2(length)
=2(9)+2(18)
=54cm
points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k
Answers
3-0 over 3-0 = 1
to get the perpendicular slope of a line, you must use the negative reciprocal therefore, the slope of a line that is perpendicular to k is equal to -1
The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
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Part A: Intersection at [tex]\((-13/4, -83/4)\)[/tex].
Part B: Two solutions for [tex]\( f(x) \): (0, -11) and (5, 14).[/tex]
Part C: Solve [tex]\( p(x) = g(x) \)[/tex] graphically for the Point of intersection
Part A: Solution to the Pair of Equations (p(x) and f(x)):
The solution to the pair of equations represented by [tex]\( p(x) \) and \( f(x) \)[/tex]is the point of intersection. From the information provided, it seems that the intersection point is [tex]\((-13/4, -83/4)\).[/tex]
Part B: Two Solutions for [tex]\( f(x) \)[/tex]:
1. [tex]\( (0, -11) \)[/tex]
2. [tex]\( (5, 14) \)[/tex]
Part C: Solution to [tex]\( p(x) = g(x) \)[/tex]:
To find the solution to [tex]\( p(x) = g(x) \), set \( p(x) = 7x + 2 \)[/tex] equal to [tex]\( g(x) = 1 + 1.5^x \). Solve for \( x \)[/tex] to determine the point of intersection between [tex]\( p(x) \) and \( g(x) \)[/tex]. The solution to this equation provides the [tex]\( x \)[/tex] coordinate, and substituting it into either [tex]\( p(x) \) or \( g(x) \)[/tex] gives the [tex]\( y \)[/tex] coordinate. The justification lies in the graphical intersection of the functions.
Note: It's essential to examine the graph for precise details, as visual inspection can help confirm the solutions.
For such more questions on point of intersection
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Find the value of X.
Answers
3x + 1 + 2x - 2 = 64
5x - 1 = 64
5x = 64 + 1
5x = 65
x = 65/5
x = 13 <==
What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)
Answers
Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3
Answer: [tex]y-11=-3(x+2)[/tex]
Step-by-step explanation:
Given points : (0, 5) and (−2, 11)
Slope of the line passing through given points .
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]
Thus, slope of line passing through given points m=-3
We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]
Thus, equation of a line passing through (−2, 11) with slope m=-3 will be
[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]
Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]
If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).
Answers
f'(7) = the slope of the tangent line : let A(7,4) B(0,3)
the slope is : (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4
Final answer:
To find f(7) and f'(7) of y = f(x) given a point on the tangent line passing through another point.
Explanation:
Given:
Equation of tangent line to y = f(x) at (7, 4) passes through (0, 3).
To find:
f(7) and f'(7).
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
what way do you shade in
Answers
2x - 6 > = 6x - 12 + 8...simplify
2x - 6 > = 6x - 4...subtract 6x from both sides
2x - 6x - 6 > = 6x - 6x - 4...simplify
-4x - 6 > = -4 ...add 6 to both sides
-4x - 6 + 6 > = -4 + 6...simplify
-4x > = 2...divide both sides by -4, change the inequality sign
x < = -2/4
x < = -1/2 or -0.5
so u would have a solid circle (because of ur equal sign) on -1/2...and the shading would go to the left (because less then goes to the left)
** the reason the inequality sign was changed is because when multiplying/dividing by a negative, u have to flip the sign...but dont forget to keep the = sign in there
Answer:
x < = -1/2 or -0.5
Step-by-step explanation:
that's the answer
Compare 9 ⋅ 104 to 3 ⋅ 102.
9 ⋅ 104 is 3 times larger than 3 ⋅ 102.
9 ⋅ 104 is 30 times larger than 3 ⋅ 102.
9 ⋅ 104 is 300 times larger than 3 ⋅ 102.
9 ⋅ 104 is 3,000 times larger than 3 ⋅ 102.
Answers
as, (9×10⁴)/(3×10²)=3× 10²
and the proper of writting powers in computer form is a×10^b
Answer:
9×10⁴ is 300 times greater than 3×10²
Step-by-step explanation:
guy above me's work. thanks to him we get this answer :)
Tony is four years younger than his brother josh, and two years older than his sister cindy. tony also has a twin brother, evan. all the ages of the children totaled together is 66. how old is tony?
Answers
To solve this problem, let us assign the variables. Let us say that:
x = age of Tony = which also the age of his twin brother Evan
x + 4 = age of Josh (since tony is 4 years younger, then josh must be 4 years older)
x – 2 = age of Cindy (since tony is 2 years older, then cindy must be 2 years younger)
There are a total of 4 children, therefore:
x + x + x + 4 + x – 2 = 66
4 x + 2 = 66
4 x = 64
x = 16
Therefore Tony is 16 years old.
To find Tony's age, we can set up an equation using the information given and solve for x. After solving the equation, we find that Tony is 16 years old.
Explanation:To solve this problem, we can assign variables to each person's age. Let's say Tony is x years old. Since Tony is four years younger than Josh, Josh's age can be represented as x + 4. Since Tony is two years older than Cindy, Cindy's age can be represented as x - 2. Since Tony has a twin brother, Evan, we can assign Evan's age as x as well.
According to the information provided, the sum of all their ages is 66, so we can set up the equation: x + (x + 4) + (x - 2) + x = 66. Simplifying the equation, we get 4x + 2 = 66. By subtracting 2 from both sides and dividing by 4, we find that x = 16.
Therefore, Tony is 16 years old.
2, -4, 8, -16, . . . find the next two numbers in the pattern and describe the pattern.
Answers
What would be the point of discontinuity in the following function f(x)=x^2+5x+6/x+3
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For the expression f(x)=x^2+5x+6/x+3, you see that there is a term 6/x. Therefore, the expression can be continuous when x=0 because 6/0 or any number divided by zero is undefined. To verify this, let's see the graph by assigning values of x and plotting them against their values of y. As you can see, the curves only approach zero but never touches zero. These are called asymptotes.
Solve the system using elimination. y – x = 13 7y + x = 11
Answers
7y + x = 11
---------------------add
8y = 24
y = 3
y – x = 13
3 – x = 13
-x = 10
x = -10
answer
x = -10 and y = 3
What is the remainder of (x3 - 6x2 - 9x + 3) ÷ (x - 3) A. -25 B. -52 C. -51 D. -17
Answers
BRAINLIEST PLS!!!
the correct answer in C. -51 hope this helps you
Write an inequality for the situation.
all real numbers y that are less than –3 or greater than 18
A) y < –3 or y < 18
B) y < 18 or y > –3
C) –3 < y < 18
D) y < –3 or y > 18
Answers
y<-3.
Next, it is greater than 18 which means the value of y is greater than 18;
y>18
Also, this is known as the compound inequality which you could write as: 1818. In conclusion, D is the only correct answer. Have a nice day!
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). The answe is x_ _= something
Answers
Next find the slope of the segment 1,0 and 5,-2 using rise over run or deltax / deltay which is a fancy way of saying change in x over change in y.
The slope is 4/2 or 2
When a line is perpendicular to another the slope is the negative reciprocal so the slope of our new line will be -1/2
Now plug in the coordinate (3, -1) to find the y-intercept and the equation of that line will be complete
so -1 = -1/2 (3) +b
-1= -1.5 +b
0.5 = b
The final equation will be -1/2x + 0.5 =y
hope this helps:)
the minute hand of a clock is 9.5cm long, How far does the tip of the hand travel in one day?
Answers
The formula for circumference of a circle (c) is:
c = πd = 2πr
So, for a circle with radius 9.5, the circumference is:
c = 2π(9.5)
= 19π cm
The tip travels 19π cm every hour, so in a day of 24 hours it will travel:
24 * 19π = 456π cm
(= 1432.566... ⇒ 1432.6 cm)
Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.
Answers
Answer
Hasim is the closest... I just took the test
Describe the graph of the function.y = |x – 4| – 7
Answers
(x-4)=0 ===> x=4,
so that now you have to plot 2 functions!
For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:
|x-4| = -(x-4)=4-x
Then:
for x<=4, y = -x+4-7 = -x-3
for x=>4, (x-4) is positive, so no changes:
y= x-4-7 = x-11,
Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11
In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:
x=4 and x= 3 for y=-x-3
And just x=5 for y=x-11
The reason is that the absolute value is continuous, so x=4 works for both:
x=4===> y=-4-3 = -7
x==4 ====> y = 4-11=-7!
abs() usually have a cusp int he point where it is =0
Hope it helps, despite being this long!
We are given a function as:
[tex]y=|x-4|-7[/tex]
We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.
The rule that holds in this transformation is:
It is a translation of the parent function 4 units to the right and 7 units down.
Also, the graph of the function is attached to the answer.
Which line is parallel to the line y=12x+5 and passes through the point (-2, 1)?
Answers
The equation of the line parallel to y=12x+5 that passes through the point (-2, 1) is y=12x+25.
Since the two lines are parallel, they will have the same slope. The slope of the given line is the coefficient of x, which is 12. Therefore, the line we are looking for also has a slope of 12.
To find the equation of the new line, we'll use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the given point and the slope into this form we get:
y - 1 = 12(x + 2)
Expanding and simplifying this, we have:
y - 1 = 12x + 24
Finally, adding 1 to both sides to solve for y, we get:
y = 12x + 25, which is the equation of the line that is parallel to y=12x+5 and passes through the point (-2, 1).
A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90
Answers
(125,100) and (120,120), from these we can find the slope or rate of change of customers as a function of price...
m=20/-5
m=-4
m=-4
c(p)=-4p+b, now we can use (125,100) to solve for b
100=-4(125)+b
100=-500+b
600=b, so our number of customers as a function of price is:
c(p)=600-4p
Revenue will simply be the number of customers times the price charged per customer...or p*c(p):
r(p)=600p-4p^2
We can find price that creates maximum revenue by finding when the derivative is equal to zero...
dr/dp=600-8p
dr/dp=0 only when
0=600-8p
8p=600
p=75
So the price that maximizes revenue is $75.
The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1.
A carpet cleaning business has 100 customers when they charge $125 for cleaning.
Research shows that every $5 reduction in price attracts another 20 customers.
Since a $5 decrease in price increases customers by 20, we can say that we have two options.
(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.
[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]
Then we have
[tex]\rm c(p ) = -4 p +b[/tex]
Now, we can use (125, 100) to solve for b
100 = -4(125) + b
b = 600
So our number of customers as a function of price is
[tex]\rm c(p) = 600 - 4p[/tex]
Revenue will simply be the number of customers times the price charged per customer will be
[tex]\rm r(p) = 600 p -4p^2[/tex]
We can find a price that creates maximum revenue by finding when the derivative is equal to zero.
[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]
WE know that for maximum,
[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]
So, the price that maximizes revenue is $75.
More about the linear system link is given below.
To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?
Answers
In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?
Answers
Answer:
its 6 i think
Explanation:
if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?
well u do CE x DE = AE x BE
(3)(4)= (2)(BE)
12=2x
12÷2= 6
Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4
Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:
f(t) = 200(0.976)t
Which statement best describes the rate at which Maureen's and Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.
Maureen's body eliminated the antibiotic at the same rate as Ken's body.
Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.
Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.
Answers
f(t) = 200(0.976)^1 = 195.2 mg
In the second hour,
f(t) = 200(0.976)^2 = 190.52 mg
In the third hour,
f(t) = 200(0.976)^3 = 186 mg
If you compare this with Maureen's data which is 150, 90 and 54 for the first, second and third hour, respectively, you will see that Maureen's rate is much faster. However, you cannot tell by what factor because the function is exponential, not a multiple. There is no constant difference between their rates. Therefore, we only know that Maureen's rate is much faster.
The answer is Maureen's body eliminated the antibiotic faster than Ken's body.
Answer:
(A)Maureen's body eliminated the antibiotic faster than Kens body
Step-by-step explanation:
We already have the table for Maureen, so lets figure out the table for Ken. We've been given the formula 200(0.976)^t.
we already know our starting point is 0, 200
first we substitute 1 into t, which would look like this 200(0.976)^1
So we would solve the power of 0.976 to the power of 1, which is just 0.976. so now we do 200 x 0.976 which results in 195.2. on the chart, the point would be (1, 195.2). now lets solve for the rest doing the same steps.
(2, 1905.5)
(3, 181.4)
(4, 135.5)
(5, 01.9)
Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15
Answers
y2*y3 = y5
z3 * z5 = z8
answer is 18x8y5z8
B
Answer:
18 x 8y 5z 8 witch is answer choice B
Step-by-step explanation:
The graph below shows a line segment PQ: graph of line PQ going through ordered pairs negative 1, 3 and 2, negative 3 Which of the following equations best represents the line segment PQ?A: y = −3x + 2B: y = −2x + 1C: y = −3x − 2D: y = −2x − 1
Answers
The most common way of writing linear equations is the slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
The slope is the ratio of the change of y to the change of x coordinates. Let's say point 1 is (-1,3) and point 2 is (2,-3). Then,
m = (-3-3)/(2-⁻1) = -2
Next, we use any of the given point to the standard equation along with the m to find b. Let's use (-1,3)
3 = -2(-1)+b
b = 1
Thus, the complete linear equation is y = -2x + 1. The answer is B.
Answer:
y = -2x + 1. The answer is B.
Step-by-step explanation:
State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.
Answers
Hypothesis test are generally used to test a validity of claim that is made about a population.This claim that's on trial in essence is called as a Null Hypothesis.
The p - values is a number between 0 to 1 and interpreted in following way:
A small p - value (<= 0.05) indicates the strong evidence against a null hypothesis , so you reject a null hypothesis.
A large p - value (>0.05) indicates weak evidence against a null hypothesis , so you fail to reject the null hypothesis.
The reason which include the p - value is prudent when you are reporting the result of a hypothesis test are given below:
1. It allows us for evaluating the strength of the evidence against the null hypothesis.
2. Allow us for assessing significance at any desired level . The null hypothesis can be rejected at any significance level larger than or equal to p - value and it can not be rejected at any significance level smaller than the p - value.
Which law would you use to simplify the expression (p/q)^3
Answers
Answer:
B. Power of quotient.
Step-by-step explanation:
We have been given an expression [tex](\frac{p}{q} )^3[/tex] and we are asked to choose the correct rule to simplify our given expression.
Since our given expression is a fraction raised to 3rd power. Power of a quotient rule states when a quotient is raised to an exponent, then the exponent is distributed to both numerator and denominator of the quotient.
Using power of a quotient rule, we will get,
[tex](\frac{p}{q} )^3=\frac{p^3}{q^3}[/tex]
Therefore, we can simplify our given expression using power of a quotient and option B is the correct choice.
The power of quotients is the law that would be used to simplify the expression.
What is the power of quotients?This is a mathematical rule that states that the power of a quotient is the same thing as the quotient that is gotten.
Given that the numerator p and the denominator q are raised to to the power expressed in the question separately.
The division is calculated after this has done
Read more on the power of quotient here:
https://brainly.com/question/2141690