Answer:
The translation is left 1 unit, up 5 units ⇒ A
Step-by-step explanation:
Let us revise the rules of translation of a function
If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - kThe vertex form of the quadratic function is f(x) = ax² + bx + c, where a, b, and c are constant is f(x) = a(x - h)² + k, where h = [tex]\frac{-b}{2a}[/tex] and k = f(h)
You will use the vertex form to find the translation
∵ g(x) = x² + 2x + 6
∴ a = 1 and b = 2
→ use the rule of h to find it
∴ h = [tex]\frac{-2}{2(1)}=\frac{-2}{2}[/tex]
∴ h = -1
→ Use it to find k
∵ g(h) = k
∴ k = g(-1)
→ Substitute x by -1 in g to find k
∴ k = (-1)² + 2(-1) + 6 = 1 - 2 + 6
∴ k = 5
→ Substitute the values of h and k in the vertex form above
∴ g(x) = 1(x - -1)² + 5
∴ g(x) = (x + 1)² + 5
→ By using the 2nd and 3rd rules of translation above
∴ f(x) is translated 1 unit to the left and 5 units up
∴ The translation is left 1 unit, up 5 units
The translation that maps the graph is mathematically given as
"The translation as left 1 unit, up 5 units"
Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?Translation is simply defined as the communication of the meaning of source content into target-content.
Generally, the equation for the vertex form is mathematically given as
g(x) = x² + 2x + 6
Where
a = 1 and b = 2 and h=-1
g(h) = k
k = g(-1)
k = (-1)² + 2(-1) + 6
k= 1 - 2 + 6
k = 5
In conclusion
g(x) = (x + 1)^2 + 5
Giving the translation as left 1 unit, up 5 units
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1. Represent the following system with a matrix
-2x + 4y + z = 0
-X + 3y = 0
5x + y + 9z = 8
2. What linear system of equations does this matrix represent?
6 -1 112
-1 10
3. What is the solution of this system of equations? Use your calculator.
3a + 2b - C = 7
2a - C = 5
A-4b+c=.4
4. You manage a health food store and budget $80 to buy ingredients to make 30 pounds
of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, and granola
costs $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how
many pounds of each ingredient should you buy? Show as much work as necessary.
You will not get any credit for just writing answers.
Answer:why is it show glitchy
Step-by-step explanation:
a car decelerated from zero 40 mph to 0 mph what is the deceleration of thecar?
Answer:
40
Step-by-step explanation:
Deceleration means how much did it go down? It makes sense that 40 is correct! Let me know if I'm wrong.
What is the image of (3,-6) after a dilation by a scale factor of 4 centered at the origin?
Answer:
7,-10
Step-by-step explanation:
-6x+15=33 what is the first best step in solving for x?
Answer:
x= -3
Step-by-step explanation:
1) subtract 15 on both sides
should look like: -6x=18
2) divide the -6 on both sides
3) 18 divided by -6 is -3
A staircase has an angle of elevation of 28 degrees and covers a total distance of 17 feet. To the nearest foot, what is the vertical height h covered by the staircase?
Answer:
..
Step-by-step explanation:
Given m<12= 121 and m<6= 75, find the measure of each missing angle.
Answer/Step-by-step explanation:
Given:
m<12 = 121°
m<6 = 75°
a. m<1 = m<6 (vertical angles)
m<1 = 75° (substitution)
b. m<12 = m<1 + m2 (alternate exterior angles)
121° = 75° + m<2 (substitution)
121° - 75° = m<2 (subtraction property of equality)
46° = m<2
m<2 = 46°
c. m<1 + m<2 + m<3 = 180° (angles on a straight line)
75° + 46° + m<3 = 180° (substitution)
121° + m<3 = 180°
m<3 = 180° - 121° (subtraction property of equality)
m<3 = 59°
d. m<4 = m<3 (vertical angles)
m<4 = 59° (substitution)
e. m<5 + m<4 + m<6 = 180° (angles on a straight line)
m<5 + 59° + 75° = 180° (substitution)
m<5 + 134° = 180°
m<5 = 180° - 134° (Subtraction property of equality)
m<5 = 46°
f. m<7 = m<12 (vertical angles)
m<7 = 121° (substitution)
g. m<8 = m<4 (vertical angles)
m<8 = 59° (substitution)
h. m<9 = m<6 (Alternate Interior Angles)
m<9 = 75° (substitution)
i. m<10 + m<9 = 180° (Linear Pair)
m<10 + 75° = 180° (substitution)
m<10 = 180° - 75° (Subtraction property of equality)
m<10 = 105°
j. m<11 = m<8 (vertical angles)
m<11 = 59° (substitution)
k. m<13 = m<10 (vertical angles)
m<13 = 105° (substitution)
l. m<14 = m<9 (vertical angles)
m<14 = 75° (substitution)
The GCF of two whole numbers is the ________.
Translate each sentence to a equation
1. Six more than the quotient of a number
and 6 is -3.
2. Five more than twice a number is 27
3. Ten less than the quotient of a number and 2 is 5
Answer: (below)
Step-by-step explanation:
1) n/6 + 6 = -3
2) 2n + 5 = 27
3) n/2 - 10 = 5
is an ice cube melting into water a chemical change?
Answer:
No
Step-by-step explanation:
When an Ice Cube melts into water it is a physical change not a chemical change because no chemicals were used.
Hope this Helps!!! :)
Let me know if I should change anything or if it was helpful in the comments!!!
Brayden just lit a new candle and then let it burn all the way down to nothing. The
candle burned at a rate of 0.75 inches per hour and its initial length was 6 inches.
Write an equation for L, in terms of t, representing the length of the candle
remaining unburned, in inches, t hours after the candle was lit.
Answer:
L = -0.75t + 6
Step-by-step explanation:
L = length (this is what equation you are looking to solve for
-0.75t because the candle burns at 0.75 in per hour so the value decreases, hence the (-)
+6 because the candle has a positive value of 6 inches to begin with
The standard form of what you are writing is called slope intercept form y = mx + b, learn it because it is very important for future math.
The equation of the candle remaining unburned at any given time is L(t) = 6 - 0.75t.
What is a function ?A function is a set of values of the dependent variable for specified independent variable.
According to the given question Brayden just lit a new candle and then let it burn all the way down to nothing.
The candle burned at a rate of 0.75 inches per hour and its initial length was 6 inches we have to write an equation for L in terms of t where t represents time in hours and L(t) represents length of the candle remain unburned.
∴ L(t) = 6 - 0.75t.
At t = 0 the length of the unburned candle L(t) will be 6 inches and at t = 8 L(t) will be 0,So the candle can burn for 8 hours.
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Town M is 282 feet below sea level. Town R is 679 feet above sea level. How much higher, in feet, is Town R than Town M?
Answer:
397 feet
Step-by-step explanation:
All you have to do is subtract the feet of Town R from Town M. The equation would look like this.
679 - 282 =397
So Town R is 397 feet higher than Town M.
Hope that helps and have a great day!
Which expression uses the associative property to make it
easier to evaluate 6(1/3•7/5)
O A. (6.1/3)7/5
O B. (6•5/7)1/3
O C. 6(7/5•1/3)
OD 3(1/6•7/5)
Answer:
A
Step-by-step explanation:
Here, we want to select which of the expressions correctly use the associative property
The associative property deals with rearrangement
So for (a + b) + c
we can have (a + c) + b
In the case of this question, the associate property is the one that makes the evaluation easier
Thus;
we need to bring 1/3 and 6 together since 3 is a factor of 6
We have;
(6•1/3)7/5
Guys someone please help with this if you're good at math
Select the equation that is the inverse of the given function.
x
- 3
f(x) =
5
o
o
o
f-1(x) = 5x + 15
f-1(x) = 5x +3
f-1(x) = 3x - 5
-1(x) = x
wun
DONE
Answer: f-1(x) = 5x+3
Step-by-step explanation: just did the assignments
Which equation is written in slope-intercept form?
O y=3x-2
x=žy+8
2x+5y = 12
O 3y=8x-5
please help
Answer:
y=3x-2
Step-by-step explanation:
the slope intercept form formula is
y=mx+b
Can anyone help me? Worth 10 points!!!
Answer:
33
Step-by-step explanation:
Fabric for 1 pillow case: 1.5 ÷ 3 = 0.5Amount of pillow cases made with 16.5 yards of fabric: 16.5 ÷ 0.5 = 33I hope this helps!
Answer:
33 pillowcases
Step-by-step explanation:
16.5 yard of fabric/ 1.5 yards of fabric = 11 yards of fabric
Multiply 11 (yards of fabric) by 3 (# of pillowcases) to get the number of pillowcases you can make with 16.5 yards of fabric.
11 * 3 = 3 pillowcases
Henry is following the recipe to make a cake. He has 95 cups of flour. How many cakes can Henry make
Answer
31
Step-by-step explanation:
3 cups in a cake you have 95
95÷3=31 hole cups
Simplify 9 − (−4).
please help quickly
27 is 25% of __? plz helpppp me Thia is worth all my brainly points
Answer:
27 is 25% of 108.
Step-by-step explanation:
A question like this is quite easy. You can multiply 27 by 4 to get 108.
That's the answer, hope it helps
Please help ASAP!!!! Due in 5
Answer:Y=2
Step-by-step explanation:
Answer:
y =-1
Step-by-step explanation:
What are the real and imaginary parts of the complex number?
−7+8i
Enter your answers in the boxes.
Answer: The real part is -7, the imaginary part is 8i
Step-by-step explanation:
Answer: The Real Part: -7
The imaginary Part: 8i
Step-by-step explanation:
Please Dont Skip Over My Question, Please Help Me. ;(
Let f(x) = –7x + 9. Suppose you add 2 to the input of f to create a new function g, then multiply the output of function g by –3 to create function h. What are the slope and y-intercept of the graph of function h?
slope =
y-intercept =
Answer: slope = 21, y-int = 15
Step-by-step explanation:
f(x) = -7x + 9
g(x) = -7(x + 2) + 9 = -7x - 5
h(x) = -3(-7x - 5) = 21x + 15
slope = 21
y-intercept = 15
hope this helps (not sure if my answer is correct)
can someone please help me with this
Answer:
m<B=74°
Step-by-step explanation:
3x-23+2x-12=180
5x-35=180
5x=180+35
5x=215
x=215÷5
x=43
m<B=2x-12=2(43)-12=86-12=74
answer:
b= 10x i pretty sure
Step-by-step explanation:
Plsase help me with this question
a)
Isaac is purchasing two pairs of shoes-one pair for $37.00 and the second
pair for $42.00. The state sales tax applied to Isaac's bill is 7%. How much is Isaac's
total bill? Show your work. (2 points)
The answer is 84.53
Add both pair of shoes together. Then take that total and multiply by7% or.07
what is the approximate volume of the cone? use 3.14 for p? help immediately
Answer:
V=157
Step-by-step explanation:
Formula-
V=π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]
1.) Place height and radius in the formula.
V=π[tex]5^{2}[/tex][tex]\frac{6}{3}[/tex]
2.) Now all you have to do is simplify.
V=3.14 x 25 x 2
3.) Now solve.
V=157.07963
Answer:
I say 157 cubic centimeters
Step-by-step explanation:
Help me pls I am struggling In everything
Answer:
The answers are A, B, C, F
I RLLY NEED HELP BC THIS WAS DUE ALREADY!!! Answer ASAP thank you!
Answer:
10,560 yards
Step-by-step explanation:
5280 plus 5280 equals 10,560
Keiko runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
Answer:
4.8 miles
Step-by-step explanation:
Set up a ratio, Kelvin.
6/55 = x/44
55x = 6(44)
55x = 264
x = 264/55 = 4.8 miles
Find the slope of the line through (6, -7) and (4, -8)
Answer:
1/2
Step-by-step explanation:
Y2-y1
________
X2-x1
-7 - (-8) = 1
6-4=2
Slope is 1/2
The slope of the line through (6, -7) and (4, -8)
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
Given;
Two points; (6, -7) and (4, -8)
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m=(-8-(-7))/(4-6)
m=(-1)/-2
m=1/2
Therefore, the slope between the two given points will be1/2
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