Answer:
The resulting equation in the vertex form is [tex](y-4)=-(x-4)^2[/tex] having the vertex at the point (4,4).
Step-by-step explanation:
The given function is f(x) = -x² + 8x-7.
As the given function is translated 5 units down, so, subtract 5 units in the given function.
The resulting function, y = f(x) -5
[tex]\Rightarrow y= - x² + 8x - 7 - 5 \\\\\Rightarrow y = - x² + 8x - 12[/tex]
Now converting the obtained equation to vertex form,
[tex]y= - x² + 8x - 12 \\\\\Rightarrow y = -(x^2-8x+12) \\\\[/tex]
Adding and subtraction 4 as
[tex]y= -(x^2-8x+12+4-4) \\\\\Rightarrow y= -(x^2-8x+16-4) \\\\\Rightarrow y= -((x-4)^2-4) \\\\\Rightarrow (y-4)=-(x-4)^2[/tex]
The vertex of the above equation is (4,4).
Hence, on translating five units in the downwards direction, the resulting equation in the vertex form is [tex](y-4)=-(x-4)^2[/tex] having the vertex at the point (4,4).
On translating five units in the downwards direction, the resulting equation in the vertex form is (y-4)=-(x-4)² having the vertex at the point (4,4).
The given function is f(x)= -x²+8x-7.
A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other.
When the shape is moved down by k units, then replace y with y - k.
The function f(x) = -x² + 8x-7 is translated five units down.
That is, y=f(x)-5
y=-x² + 8x-7-5
y=-x² + 8x-12
Subtract 4 on both the sides of an equation, we get
(y-4)=-x² + 8x-12-4
(y-4)=-x² + 8x-16
(y-4)=-(x²-8x+16)
(y-4)=-(x-4)²
Hence, on translating five units in the downwards direction, the resulting equation in the vertex form is (y-4)=-(x-4)² having the vertex at the point (4,4).
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Jim works overtime to save $500 per month for a pickup truck. The savings account Jim uses earns him 5% interest, compounded monthly.
In two years, Jim will have___in savings. He will have earned ___
in interest on his savings.
Answer:
Blank1= C:12.593
Blank2= C:593
Step-by-step explanation:
First we need to remember the equation for future value of annuity
FV=C(((1+i)ⁿ-1)/i
PV is 500
i=0,05/12=0,004
n=24 months
FV=500((1+0,0041)²⁴-1)/0,004
FV=12.593
If the total of payments were 500x24=12.000
it means for interest is 593
hope it helps! please mark me brainliest
Merry Christmas good day ✌️
"Four more than a number is at least 22"
Answer:
4 + x < 22
that's what the equation is
Step-by-step explanation:
a number just means a variable ex: x, y
at least is this : <
so 4 + x < 22
A $1,000 savings bond earns simple interest at the rate of 3% each year. The interest is paid at the end of 3 month
Answer:
97
Step-by-step explanation:
88 + 8 = 97
8. Solve.
|(3x – 7) – (4x – 8) = -(10x – 6)
Answer:
x=5/9
Step-by-step explanation:
TRUST GOES A LONG WAY!
BRAINLIEST?
Choose the equation and the slope of the line that passes through (6, -1) and Is perpendicular to the x axlo. A. Equation: 4 B. Slope; undefined O C. Equation: y = -4 D. Slope: 0 E. Equation: x 6 O E Equation: 6
If a library has 3,000 nonfiction books how many books does it have in all?
Answer:
(3,002 joke answer) 3,000 books
Step-by-step explanation:
marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green
Answer:
What's the question??
Step-by-step explanation:
Answer:
what is the question...
If 4 gal of pure ethanol are added to 46 gal of 2% ethanol how much of the final solution do you have? How much ethanol is contained in the mixture? What is the strength (percentage) of ethanol in the mixture?
Answer:
100 i belive
Step-by-step explanation:
you add 4+46=50x2=100
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is 4 gal of pure ethanol is added to 46 gal of 2% ethanol.
In 46 gal of 2% ethanol, we have (46 x 0.02) = 0.92 gallons of pure ethanol.
When 4 gal of pure ethanol is added, total ethanol in the mixture = 4 + 0.92 = 4.92 gallons
Total mixture quantity in gallons = 46 + 4 = 50 gallons
The percentage of the ethanol in the mixture will be -
(4.92/50) x 100 = 9.84%
Therefore, the percentage of the ethanol in the mixture will be 9.84%.
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This is kind of off topic for math but I still need to know the answer, so I’ve finished all my math work and I know my work is also correct but for some reason my grades drop down. I don’t understand why...
Answer:
email or call or talk to your teacher and ask why
Step-by-step explanation:
please help, what is the domain of the graph?
Answer:
-3,-2,1,2
Step-by-step explanation:
this is the domaim
Markus has one
$I0 bil, three $5 bills, and one $I bill. Count
on to find how much money Markus has.
Answer:
26$
Step-by-step explanation:
10+ (5x3) +1= 26$
Answer:
26
Step-by-step explanation:
10+($5x3)+1
the first thing you would want to do is 3x5 because you have 3 5 dollar bills
and the answer for that is 15 then you add 10+15 which is 25 plus the 1 we have left which is 26
so 26 is your finally answer
Pythagorean theorem
a²+b²=c² is pythagorean theorem :)
Pythagorean theorem
in the right angle triangles there is a relationship that governs the length of the three sides. if we knows the length of any two sides, the third side may be calculated by the use of the Pythagorean theorem.
This theorem states that the square on the hypotenuse of a right angled triangle is equal to the sum of the squares on the remaining two sides.
we only use Pythagorean theorem to find the length of the missing side of a right angled triangle only.
What is the next step to solve this equation?
Answer:
Add 6 to both sides.
Step-by-step explanation:
Remember you are trying to isolate the variable
Describe how to find the mean, median and mode of a set of data. what does each mean
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Find the coordinates of midpoint F.
(Enter answer in simplified form.)
A(-3a, b)
B3a b)
F= ([?],[])
Midpoint Formula : M = ()
Ca 5b
Answer:
The coordinates are (0,b)
Step-by-step explanation:
Here, we want to find the coordinates of the midpoint F
as we can see, F is between A and B
we proceed to use the midpoint formula
The midpoint formula is;
(x,y) = (x1 + x2)/2, (y1 + y2)/2
(x1,y1) = (-3a, b)
(x2,y2) = (3a, b)
The substitution of these values will thus yield;
(-3a + 3a)/2, (b + b)/2
= (0/2), (2b/2)
= (0, b)
If x>0, then the expression ((x^3)^-2)^5
What is the equation of the graphed line written in
standard form?
Ox-4y = 4
Ox+4y = 4
(4,0)
Oy-x-1
Oy-1
45
o,-1)
Answer:
the third option is the answer, y= 1/4x-1
Step-by-step explanation:
graph line in standard form:
[tex]y = mx + c[/tex]
where m = slope and c = y-intercept
1) find the slope
slope formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
use the two coordinates given in the graph
i/ (0,-1)
x1 = 0
y1 = -1
ii/ (4,0)
x2 = 4
y2 = 0
substitute the values into the formula
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex] \frac{0 - ( - 1)}{4 - 0} [/tex]
[tex] \frac{1}{4} [/tex]
thus, m = 1/4
2) find the y-intercept
* y-intercept is the value of y that cuts through the y-axis
based on the graph, the y-intercept is -1
thus, c = -1
3) substitute the value of m and c into the standard form formula
[tex]y = mx + c[/tex]
[tex]y = \frac{1}{4} x - 1[/tex]
3
42 ➗ (15-2)
I don’t know know to do this
Answer:
Step-by-step explanation:
42/13=4
Please help asap please please I’ll give the brain thing if you give a correct answer + explain thanks :))
Answer:
i believe it would be 7
Step-by-step explanation:
7 times 1 is 7
7 times 4 is 28
7 times 12 is 84
and 7 times 15 is 105
Answer:
D. 7
Step-by-step explanation:
Divided 105 by 15 to get 7
15 x 7 = 105
12 x 7 = 84
4 x 7 = 28
1 x 7 = 7
Missing value = Multiply by 7
hope it makes sense
Which number is closest to √52?
Answer:
7
Step-by-step explanation:
Answer:
√52 = 2√13
Step-by-step explanation:
Which similarity transformation could map ADEF to AD'E'F'? dilation and reflection dilation and translation rotation and dilation o rotation and reflection
Answer:
The correct answer is indeed C. Rotation and dilation :)
The similarity transformation that maps ΔDEF to ΔDEF is rotation and dilation.
What is dilation?
Dilation involves scaling an object by multiplying the distance between all of its points and a fixed point, called the center of dilation, by a constant factor.
The factor can be greater than 1, in which case the object gets larger, or it can be between 0 and 1, in which case the object gets smaller.
The center of dilation can be located anywhere in the plane.
We have,
Rotation and dilation are both transformations in geometry that can be used to change the size and shape of an object.
Rotation involves rotating an object around a fixed point, called the center of rotation.
The object remains the same size and shape, but its orientation changes.
Dilation involves scaling an object by multiplying the distance between all of its points and a fixed point, called the center of dilation, by a constant factor.
Now,
We see that,
There is rotation and dilation on ΔDEF.
Thus,
The similarity transformation that maps ΔDEF to ΔDEF is rotation and dilation.
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PLEASE HELP ME PLSS ITS TIMED
Answer:
1 pound of blueberries cost $2.75 and 12 pounds of blueberries cost $33
Step-by-step explanation:
Divide $16.50 by 6, that's how you find out how much 1 pound of blueberries costs
The principal portion of the 20th payment of Ron an amortized loan is $ 340.95 and the principal portion of the 21st payment of R is $348.11. If there are 55 payments in total, what is R?
Answer: $720.47
Step-by-step explanation:
what is the slope of the linear function..........
Answer:
-1
Step-by-step explanation:
slope: change in y divided by change in x
y2-y1/x2-x1
-11-(-5)/4-(-2)
-11+5/4+2
-6/6
-1
Which of the following ratios will form a proportion with 2/3?
6/15
12/18
9/12
6/8
Answer:
12/18
Hope this helps!
Which inequality is represented by the graph below? Check all that apply
answer pls .
Answer
2nd and last
Step-by-step explanation:
19=10+3(7x-1)^((1)/(3))
Answer:
X = 4
Step-by-step explanation:
Please send help AsAp
Answer: 130
Step-by-step explanation: 1
how you could find the decimal that is equivalent to 3/15 without doing any long division.
Answer:
You could multiply both the numerator and the denominator by 2
Step-by-step explanation:
Juma earns $12.50 for each newspaper subscription he sells. He also earns a $50 base salary each week. If he wants to earn $400 next week, how many newspaper subscriptions does he need to sell? Write an equation and solve.
Answer: 400=12.50x+50
400-50=12.50x
350=12.50x
350÷12.50=x
28=x
Step-by-step explanation:
he needs to sell 28 newspaper subscriptions to earn $400 in the next week.
equation:
$400=50+12.50x
x=amount of newspaper subscriptions required to sell
