Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this, we get
[tex]A(-1,-3)\to A'(-1,3)[/tex]
[tex]B(-4,-1)\to B'(-4,1)[/tex]
[tex]C(-6,-4)\to C'(-6,4)[/tex]
If a figure is shifting 10 units right, then
[tex](x,y)\to (x+10,y)[/tex]
Using this we get
[tex]A'(-1,3)\to A''(-1+10,3)[/tex]
[tex]A'(-1,3)\to A''(9,3)[/tex]
Similarly,
[tex]B'(-4,1)\to B''(-4+10,1)[/tex]
[tex]B'-4,1)\to B''(6,1)[/tex]
And,
[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]
[tex]C'(-6,-4)\to C''(4,4)[/tex]
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
I can’t solve plz help me ...
Your answer is in the attachment.
P,W,R & S form the vertices of a quadrilateral. PQR = 74 degrees
RSP = 121 degrees
Find the value of SPQ
Answer:
∠ SPQ = 75°
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Subtract the sum of the 3 angles from 360 for ∠ SPQ
∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°
g Kristina Karganova invites 17 relatives to a party: her mother, aunts, uncles, brothers, 1 male cousin, and female cousins. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows. (a) A brother or an uncle (b) A brother or a cousin (c) A brother or her mother (a) The total number of outcomes is nothing and the number of outcomes in the event is nothing.
Answer:
7 / 17 ;
10 / 17 ;
5 / 17
Step-by-step explanation:
Guests :
Mother = 1
Aunts = 3
Uncles = 3
Brothers = 4
Male cousin = 1
Female cousin = 5
_________________
Total guests = 17
Since each of the guests have an equal probability of arrival :
Probability that first guest to arrive :
Brother or uncle :
Number of brothers =4
Number of uncles = 3
P(brother or uncle) = required outcome / Total possible outcomes
Required outcome (number of brothers + uncles) = (4 + 3) = 7
Total possible outcomes = total guests = 17
P(brother or uncle) = 7 / 17
2.)
P(brother or cousin) :
Required outcome = (number of brothers + cousins) = (4 + 1 + 5) = 10
Total possible outcomes = total guests = 17
P(brother or cousin) = 10/17
3.)
P(brother or mother) ;
Required outcome = (number of brothers + mother) = (4+1) = 5
Total possible outcomes = total guests = 17
P(brother or mother) = required outcome / Total possible outcomes = 5 / 17
The graph shown below expresses a radical function that can be written in
17
the form f(x) = a(x + k)!
C. What does the graph tell you about the
value of k in this function
Answer:
C. [tex]k[/tex] is greater than zero.
Step-by-step explanation:
We know that graph is obtained from the function of the form [tex]f(x) = a\cdot (x+k)^{1/n} + c[/tex]. According to the graph and if [tex]x + k = 0[/tex], we find that:
[tex]x = -k[/tex] (1)
[tex]x < 0[/tex] (2)
By (1) and (2):
[tex]-k < 0[/tex]
[tex]k > 0[/tex]
Hence, correct answer is C.
Consider the generic chemical equation:
2 A + 3 B ------> 3 C
If 6 moles of A and 2 moles of B are reacted, what is the maximum number of moles of C that can be formed?
For this problem, you can see that a ratio exists between A, B, and C. Now you'll just have to find the constant k that satisfies this ratio using the proportional relationship formula.
After that, you can plug in the constant k to find the missing C value.
What are the values of (-2)4 and -24?
1. 8 and -8
2. -8 and -8
3. 16 and -16
4. 16 and 16
Answer:
2.
Step-by-step explanation:
(-2)×4=-8
-2×4=-8
~~~~~~~~
Answer:
16 and 16 is the correct answer
Use the following graph to evaluate f’(-5) and f’(-1).
Answer:
Bonsoir,
f'(-5)=-4/3
f'(-1) =3/4
Step-by-step explanation:
f'(-5) = ?
2 points : (-6,9) and (-3,5)
f'(-5)=(9-5)/(-6-(-3))=-4/3
f'(-1) = ?
2 points : (-3,5) and (1,8)
f'(-1)=(5-8)/(-3-1)=3/4
The lines are perpendicular
The derivative at the points -5 and -1 are:
f’(-5) = -4/3
f’(-1) = 3/4
What is derivative at a point on line?The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.
We consider the line on which where the x coordinate -5 lies.
It is the line with points (-3, 5) and (-6, 9).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]
f'(-5) = -4/3
We consider the line on which where the x coordinate -1 lies.
It is the line with points (-3, 5) and (1, 8).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]
f'(-1) = 3/4
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Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.
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Answer:
14.3%
Step-by-step explanation:
We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.
The APR is about 14.3%.
_____
The amount to be repaid is calculated using the simple interest formula:
A = P(1 +rt) = $4900(1 +0.08·4) = $6468
Then the required monthly payment (for 48 months) is ...
$6468/48 = $134.75
__
The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...
A = 4900(r/12)/(1 -(1 +r/12)^-48)
In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).
_____
Additional comment
The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.
We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.
A store is advertising a new DVD player for $189.00. If the sales tax rate is 7.25 percent,
Answer:
then what's the question???..
Find F(-3).
F(x) = 2x^2- 5x-8
Answer:
25
Step-by-step explanation:
F(x) = 2x^2- 5x-8
Let x=-3
f(-3) = 2 (-3)^2 -5(-3) -8
=2(9) +15 -8
=18+15-8
=25
what is the sign of x/y times 7y^3 when x<0 and y>0? A. Positive B. Negative C. Zero
X <0 means x would be negative.
For x/y, a negative divided by a positive would give a negative answer.
A negative multiplied by a positive would result in a negative.
The answer would be B. Negative
A wall that is 10 feet high and 16 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). If each window is 4 feet by 7 feet, determine the area of the space to be painted.
Answer:
104 square feet
Step-by-step explanation:
Total area of the wall: 10 x 16 = 160 square feet
Area of each window: 4 x 7 = 28
Since there are 2 windows, the total area that should not be painted is 28 x 2 = 56 square feet
160 - 56 = 104 square feet
To determine the area of the space to be painted on a wall with two rectangular windows, we need to calculate the total area of the wall and subtract the area of the windows.
First, let's calculate the area of the wall. The wall is 10 feet high and 16 feet wide, so the total area of the wall is: Area of wall = height × width = 10 feet × 16 feet = 160 square feet Next, let's calculate the area of each window. Each window is 4 feet high and 7 feet wide, so the area of each window is: Area of window [tex]= height × width = 4 feet × 7 feet = 28[/tex] square feet Since there are two windows, the total area covered by the windows is 2 times the area of one window,
Which is: Total area of windows [tex]= 2 × 28[/tex] square feet = 56 square feet Finally, we can calculate the area of the space to be painted by subtracting the total area covered by the windows from the total area of the wall: Area to be painted = Area of wall - Total area of windows = 160 square feet - 56 square feet = 104 square feet Therefore, the area of the space to be painted on the wall is 104 square feet.
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What is |1-8i|?
A.
B.
C
D
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Answer:
(b) √65
Step-by-step explanation:
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.
|1 -8i| = √(1² +(-8)²) = √(1+64) = √65
Find the value of x.
A. 6
B. 3
C. 5
D. 2
[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]
[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]
[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]
[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]
[tex]\\ \sf\longmapsto 3x=15[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
What is the domain of the function graphed below?
Answer:
A. x<7
Step-by-step explanation:
The point at x=7 is an open circle, so the sign is <, not ≤
Solve
0.9(7x + 14) = 1.5 - (x + 2)
[tex]\\ \sf\longmapsto 0.9(7x+14)=1.5-(x+2)[/tex]
[tex]\\ \sf\longmapsto 6.3x+12.6=1.5-x-2[/tex]
[tex]\\ \sf\longmapsto 63x+12.6=-x-0.5[/tex]
[tex]\\ \sf\longmapsto 63x+x=-0.5-12.6[/tex]
[tex]\\ \sf\longmapsto 64x=-13.1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-13.1}{64}[/tex]
[tex]\\ \sf\longmapsto x=0.2[/tex]
Jacob bought a magazine for $2.80 and three candy bars. Write an expression for how much Jacob paid.
Answer:
total = 2.8 + 3x
x is the price of the candy bars
Given that f(x) = 2x + 9, find the value that makes f(x) = 27.
Answer:
9
Step-by-step explanation:
f(x) = 2x+9
f(x) = 27
so, you get:
2x+9=27
2x=18
x=9
If 3x+2=5/9, what is the value of −3x+8?
Group of answer choices
Answer:
= 4
Step-by-step explanation:
first lets find the value of x in 3x+2=5/9
3x+2=5/9
3x = [tex]\frac{5}{9}[/tex] -2
3x = [tex]\frac{3}{9}[/tex]
3x = [tex]\frac{1}{2}[/tex]
x = [tex]\frac{1}{2 * 3\\ }[/tex]
x = [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] can also be written as [tex]6^{-1}[/tex]
−3x+8
-3 ([tex]\frac{1}{6}[/tex]) +8
[tex]\frac{-3}{6}[/tex] +8
= 4
Fill in this blank spaces (1,3,5,7,9 , 11, 13, 15) _+_+_=30
Step-by-step explanation:
Just till the number 9 upside down to make it 6 then
6+11+13=30
The sum of three odd numbers can never be even. so I did it in that way.
I HOPE THIS WILL HELP U
STAY SAFE, STAY HAPPY
If a runner jogs 3 miles west and then jogs 8 miles
north, how far is the runner from her starting point
if she plans to run straight back? Remember to
simplify your answer.
If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.
A^2+B^=C^2
3^2+8^3=C^2
9+64=C^2
Square root 73=C or 8.54=C (Miles)
The runner is 8.54 miles from her starting point if she plans to run straight back.
From the question, a runner jogs 3 miles west and then jogs 8 miles north.
An illustrative diagram for the journey is shown in the attachment below.
In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.
The cardinal points (North, East, West and South) are indicated beside the diagram.
Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.
The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.
The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.
In the diagram, hypotenuse = /ES/
∴ /ES/² = /SR/² + /RE/²
/SR/ = 3 miles
/RE/ =8 miles
/ES/² = 3² + 8²
/ES/² = 9 + 64
/ES/² = 73
/ES/ = [tex]\sqrt{73}[/tex]
/ES/ = 8.54 miles
Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.
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Please help!
It took Suki 127 minutes from start to finish to carve her pumpkin. Carving the pumpkin took her 13 fewer minutes than 10 times as long as it took her to pick the pumpkin out at the pumpkin patch. Write and solve an equation to find how long it took Suki to pick out her pumpkin.
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Answer:
14 minutes
Step-by-step explanation:
Let t represent the time it took Suki to pick out her pumpkin. The given relation is ...
10t -13 = 127 . . . . . equation for minutes to carve
10t = 140 . . . . . . . . add 13
t = 14 . . . . . . . . . . divide by 10
It took Suki 14 minutes to pick out her pumpkin.
HELP!!!!
Please help me!!
I need help!!
HELP!!!!
Answer:
Pretty sure it's A
Step-by-step explanation:
The x outside the parenthesis means that there's an x intercept at (0,0) and (x-3) means there's another one at (3,0)
A rocket is fired upward with an initial velocity v of 100 meters per second. The quadratic function S(t)=-5t^2+100t can be used to find the height s of the rocket, in meters, at any time t in seconds. Find the height of the rocket 7 seconds after it takes off. During the course of its flight, after how many seconds will the rocket be at a height of 450 meters?
The rocket will be at the height of 450metres at 13.16secs and 6.84secs
Given the expression modeled by the height S(t)=-5t^2+100t where
t is the time taken by the rocket to take off
s is the height traveled by rocket
In order to find the height of the rocket 7 seconds after it takes off, we will substitute t = 7 into the equation
S(7) = -5(7)²+100(7)
S(7) = -5(49)+700
S(7) = -245+700
S(7) = 455metres
Hence the height of the rocket 7 seconds after it takes off is 455metres
Given that S = 450m, we can also get the time taken by the rocket at this height.
Recall that S(t)= -5t²+100t
450 = -5t²+100t
Rearrange
-5t²+100t - 450 = 0
5t²-100t + 450 = 0
Divide through by 5
t²-20t + 90 = 0
On factorizing above equation;
t= 10+√10 or t=10−√10
t = 10+3.1623 or 10 - 3.1623
t = 13.16 and 6.84secs
Hence the rocket will be at the height of 450metres at 13.16secs and 6.84secs
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What are m and b in the linear equation, using the common meanings of m and b? 2 + 3x + 5 - 2x = y
y=mx+b is the general formula of linear equation
y=-2x+5+3x+2
y=1x+7
m=1
b=7
Linear equation given in the question is,
2 + 3x + 5 - 2x = y
To simplify this equation further,
Add like terms of the equation,(2 + 5) + (3x - 2x) = y
7 + x = y
Now compare this linear equation with the slope-intercept form of the linear equation,
y = mx + b
Here, m = slope of the line'
b = y-intercept
By comparing the equations,
m = 1
b = 7
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[tex]3^n^+^1+9/3^n^-^1+1[/tex]
how do i solve it?
Answer:
Hello,
Step-by-step explanation:
[tex]\dfrac{3^{n+1}+9}{3^{n-1}+1} \\\\=\dfrac{9*(3^{n-1}+1)}{3^{n-1}+1}\\\\=9\\[/tex]
Need help with precalc please! Thank you!
que es eso ._ .wooooooooo .
Reduce 20/60 to its lowest common denominator
Answer:
it is 1/4
Step-by-step explanation:
20/60=10/30=1/3
Answer:
20/60=1/3
Step-by-step explanation:
20/60
HCF=20,
20*1=20, 20*3=60
1/3
or,
Remove the zeros,
2/6
Divide by 2 on both,
1/3
or divide by any common factor on both and keep dividing until u cant no more
20/60=1/3
GIVING 15 POINTS PLS FAST
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
-24 8 + 30
131.87
28.98+(-52.22)
65
45%+39
-23.24
56.75 +75.12
Reset
Next
Next
Answer:
Hope this helps! All you needed to do was add and subtract. Go through the slides, I added the step by step explanation, as well as the final table which contains the answers.
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
We have,
Expressions:
-24(5/9) +30(7/9)
Simplifying the fractions.
This can be written as,
= (-24 + 30) +(-5/9 + 7/9)
= 6 + 2/9
= 6(2/9)
45(2/9) +39(3/9)
= (45 + 39) + (2/9 + 3/9)
= 84 + 5/9
= 84(5/9)
28.98 + (-52.22)
= 28.98 - 52.22
= -23.24
56.75 + 75.12
= 131.87
Thus,
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
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Need help!
given rectangle ABCD find m<CAB
Answer:
∠ CAB = 60°
Step-by-step explanation:
∠ CAD and ∠ BCA are alternate angles and congruent , so
∠ CAD = 30°
∠ BAD = 90° ( angle in a rectangle ) , then
∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°
The measure of the angle m∠CAB is 60.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The rectangle has 90 degrees on all the vertices.
So,
In ΔABC,
The sum of the angles = 180
So,
30 + 90 + m∠CAB = 180
m∠CAB = 180 - 120
m∠CAB = 60
Thus,
The measure of the angle m∠CAB is 60.
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