Answer:
f(x) = 6(x - 2)² + 3Step-by-step explanation:
f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)
"the parabola opens upward" means: a>0
"the parabola has x = 2 as an axis of symmetry" means: h = 2
so f(x) = a(x - 2)² + k
"the parabola contains the point (1, 9)" means:
9 = a(1 - 2)² + k
9 = a(-1)² + k
9 = a + k
k = 9 - a
"the parabola contains the point (4, 27)" means:
27 = a(4 - 2)² + k
so:
27 = a(2)² + 9 - a
27 = 4a + 9 - a
3a = 18
a = 6
and k = 9 - 6 = 3
Therefore the vertex form for this parabola is:
f(x) = 6(x - 2)² + 3
A rhombus is graphed
on the set of axes below.
Answer:
Step-by-step explanation:
reflection over y-axis
Option A is correct, 180 degree rotation counter clockwise about the origin is transformation which would carry the rhombus onto itself.
We need to consider the properties of a rhombus and how each transformation affects its shape and orientation.
A rhombus is a quadrilateral with all four sides of equal length. It also has opposite angles that are congruent. Based on this information, we can analyze each transformation option:
180-degree rotation counterclockwise about the origin is a transformation would preserve the shape and size of the rhombus since a 180-degree rotation does not change the lengths of the sides or the angles.
Therefore, it is a possible transformation that carries the rhombus onto itself.
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what is 3x+4/5 = 7-2x
Answer:
..jkbiuhlihuhiuuhi
Step-by-step explanation:
kguykguyufkyugyyguygyggkuy
solve : 3 under root a/b
Use intercepts to graph the line described by the equation 5x − 5y = 10.
Pls help me this is so hard can someone help me.
Answer: 4x+8=12
Step-by-step explanation: there is the 1st one im going to try and o the second one oh im a 7th grader
−3x+8<15 please help
Answer:x<-7/3
Step-by-step explanation:
Answer: X > -7/3
Step-by-step explanation:
-3x + 8 < 15
subtract 8 from both sides
-3x < 7
divide by negative 3
Also, when dividing or multiplying by a negative you flip the sign.
x > -7/3
Answer :)
Find the value of x. The diagram is not to scale.
a. x = 40
b. x = 23
c.x= 13
d. none of these
Answer:
d. none of these
Step-by-step explanation:
A sprinter travels a distance of 100 m in a time of 11.21 seconds.
What is the sprinter's average speed rounded to 4 sf?
Answer:
distance travelled by sprinter = 100 m
Time taken = 11.21sec
∵speed = distance/time taken
= 100/9.83
= 10.17 m/s
Now we know, 1 km/h = 1000/3600 m/s
so, 1 m/s = 3600/1000 km/h = 18/5 km/h
∴ 10.17 m/s = 10.17 × 18/5 = 10.17 × 18/5 = 36.612 km/h
Hence, average speed = 36.612 km/h
Step-by-step explanation:
Answer:
distance travelled by sprinter = 100 m
Time taken = 11.21sec
Hence, average speed = 36.612 km/h
Step-by-step explanation:
I need help plz like ASAP
I will give you a Brainist if you answer first
Answer:
Step-by-step explanation:
The proportion of x/y is 8/1. And to solve your question the value of y when x is 10 is 1.25 .
Complete Eduardo's definition of parallel lines: "If two coplanar lines are both perpendicular to a third line in the same plane, all of the angles formed between the two lines and the third line are "Explain your answer.
URGENT!! WILL MARK BRAILIEST! GOD BLESS. PLEASE SHOW ALL WORK. The age of Vicky and Krishna total 27 years. In 4 years, Krishna’s age plus twice Vickey’s age will be 43. What are Vickey and Krishna’s ages?
9514 1404 393
Answer:
Vickey is 4Krishna is 23Step-by-step explanation:
Let v represent Vickey's age now. Then Krishna's age now is 27-v. In 4 years, the sum of their ages is ...
(27 -v +4) +2(v +4) = 43
27 -v +4 +2v +8 = 43 . . . . eliminate parentheses
v +39 = 43 . . . . . . . . . . . . . collect terms
v +39 -39 = 43 -39 . . . . . . subtract 39 from both sides
v = 4 . . . . . . . . . . . . . . . . . simplify; this is Vickey's age
27 -v = 23 . . . . . Krishna's age
Vickey's age is 4; Krishna's age is 23.
How much will Ashley’s plan cost for the same number of texts as when Jumel’s costs $75? Show your work and write your answer in a sentence.
Please help me out
Answer: In order to begin figuring that out, we need to know how both of their plans work.
Find the length of side x in simplest radical form with a rational denominator
Answer:
The length of x=3/1
Step-by-step explanation:
Given the right triangle
Ф = 30
We know that
sin Ф = opposite/hypotenuse
The opposite of angle 30° = x
The hypotenuse is = 6
so
sin 30 = opposite/hypotenuse
1/2 = x/6 ∵ sin 30 = 1/2
1/2 × 6 = x
6/2 = x
3/1 = x
Therefore, the length of x=3/1
Which proportional relationship has the greatest rate of change?
Answer:
The answer is A.
Step-by-step explanation:
A- slope is 7
B- slope is 3
C- slope is 4
D- slope is 6
The first option, [tex]y=7x[/tex] has greatest rate of change.
Any relationship which have greatest slope, that relationship will also have greatest rate of change.
First option is, [tex]y=7x[/tex] , compare with y = mx
Slope = 7
Slope of option B is, [tex]=\frac{12}{4} =3[/tex]
Slope of option C is, [tex]=\frac{8}{2}=\frac{16}{4} =4[/tex]
Slope of option C is, [tex]=\frac{2}{1}=\frac{4}{2}=2[/tex]
From slope of all options , it is observed that function y = 7x has greatest slope.
Hence, first option y = 7x has greatest rate of change.
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What is the rate of change of y with respect to x for 25x - 4y = 50 ?
Answer:
25/4Step-by-step explanation:
The change of y with respect to x is known as the slope of the line. The standard form of the equation is y = mx+c where m is the slope.
Given the equation 25x - 4y = 50, we need to make y the subject of the formula before we get the slope as shown;
25x - 4y = 50
-4y = -25x+50
Divide through b y -4
-4y/-4 = -25x/-4 + 50/-4
y = 25/4 x - 25/2
Comparing with y = mx+c
mx = 25/4 x
m = 25/4
Hence the rate of change of y with respect to x is 25/4
The rate of change of y with respect of x for the given equation is [tex]\frac{25}{4}[/tex].
Given the equation:
[tex]25x - 4y = 50[/tex]
The rate of change = the slope of the line
To determine the slope of 25x - 4y = 50, rewrite the equation in slope-intercept form. i.e. [tex]y = mx + b[/tex]Where, slope = mThus,[tex]25x - 4y = 50[/tex]
Add 25x to both sides of the equation[tex]25x -25x - 4y = - 25x + 50\\\\-4y = - 25x + 50[/tex]
Divide both sides by -4[tex]\frac{-4y}{-4} = \frac{-25x}{-4}+ \frac{50}{-4}\\\\y = \frac{25}{4}x - \frac{25}{2}[/tex]
Therefore, the rate of change of y with respect of x for the given equation is [tex]\frac{25}{4}[/tex].
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The following triangle shows the length of each side using expressions.
2n +7
2n +7
3n
a. Write an expression in simplest form to represent the perimeter of the triangle above. Show all work.
b. If n = 8, find the perimeter of the triangle. Show all work.
In the equation a= 3/b is a positive, real number. As the
value of b is increased so it becomes closer and closer to
infinity, what happens to the value of a ?
Answer:
The value of a tends to zeroStep-by-step explanation:
Given the expression a = 3/b
as the denominator of the of the expression b increases the value of the output is known to be decreasing. if the value of b now goes so large to become an infinite, value then the value of a will goes to zero as shown;
If b = ∞
a = 3/∞
a = 0
Note that for any constant value a, the ratio a/∞ will always tends to zero
Giovanni justifies whether the expression -4x-8 is equivalent to -2(x+1)-2(x+3) by letting x=3 in both expressions. What is the value of each expression when x=3.
3 and -20
4 and 4
-20 and -20
3 and 4
Answer:
The value of each expression when x=3 will be -20 and -20.
Step-by-step explanation:
Given the expression
-4x-8
setting x=3
= -4(3)-8
=-12-8
=-20
Given the expression
-2(x+1)-2(x+3)
setting x=3
=-2(3+1)-2(3+3)
=-2(4)-2(6)
=-8-12
=-20
so we conclude that the value of both the expressions was -20 when we substituted the value x=3.
Therefore, the value of each expression when x=3 will be -20 and -20.
Plz help btw the second one has the same options .
What is the answer I got it wrong
Answer:
-1/2
Step-by-step explanation:
It’s y2 - y1 over x2-x1
- 2 - 3
— - -—-
6 - (-4)
= -5/10
= -1/2
Answer: 1/2
Step-by-step explanation:
I need someone’s help please I don’t know this that well
Answer:
raiz de 84 = 9.16
Step-by-step explanation:
la ubicacion que debes de poner es en la primera linea que te anexe en la linea
isolate the variable on the following problem. show your work.
11=c/5
quadratic formula:
3x^2+2x-4=0
Answer: i hope this helps!
Kevin wants to buy 2.5 pounds of chicken at $6.49 per pound. How
much will he pay?
Answer:
16.225
just times 2.5 times 6.49
At a basketball game 64% were supporting the visiting team. If total number of people attending h the e game was 2000, how many people were supporters of the home team
Answer:
720
Step-by-step explanation:
0.64 x 2000 = 1280
2000 - 1280 = 720
No. of people supporting the home team out of 2000 people is 720.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, At a basketball game, 64% were supporting the visiting team.
The percentage of people supporting the home team is
(100 - 64)% = 36%.
Now, Total number of people who came to watch is 2000.
∴ No. people supporting the home team is,
= (36/100)×2000.
= 36×20.
= 720 people.
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which expression is equal to 5/2? Write a situation that could represent the fraction above.
Answer:
3/2 + 2/2. A teacher has to give 2 pencils to one student. 1 student gives him 3 pencils, another student give him 2 pencils. How much pencils does the teacher have?
Step-by-step explanation:
All you do is you find a problem that would give you 5/2 then create a word problem.
Maria's plant grew 3 1/4 inches every month for 2 1/2 months. How many inches did Maria's plant grow during that time?
Answer: 8.125 inches
Step-by-step explanation: Ok so if the plant grew 3.25 inches every month, and there were 2.5 months, you need to multiply 3.25 by 2.5 to get the total amount of growth. So that would be 8.125
Last week at Best Bargain, 20% of the computers sold were laptops. If 70 computers were sold last week, how many were laptops?
Type only a number for your answer
Answer:
x = 80
Step-by-step explanation:
x + 30 = 110 (opposite sides are congruent/equal)
x = 110 - 30 (subtract the 30 from both sides to get X by itself)
x = 80 (simplify)
How much do you need to subtract from 43/10 to make 4?
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[tex] \frac{43}{10} - x = 4 \\ [/tex]
[tex] \frac{43}{10} - x = \frac{40}{10} \\ [/tex]
Subtract sides 43 / 10
[tex] - \frac{43}{10} + \frac{43}{10} - x = - \frac{43}{10} + \frac{40}{10} \\ [/tex]
[tex] - x = \frac{ - 43 + 40}{10} \\ [/tex]
[tex] - x = - \frac{3}{10} \\ [/tex]
Negatives simplifies
[tex]x = \frac{3}{10} \\ [/tex]
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Thus we need to subtract
[tex] \frac{3}{10} \\ [/tex]
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Answer:
83/10
Step-by-step explanation:
let x represent the number:
43/10 - x = 4
x = 4 + 43/10
simplifying the answer:
x = (4(10) + 43)/10
x = (40 + 43)/10
x = 83/10