Answers
Answer:
[tex]\textsf{a)} \quad y=(x+1)^2-4[/tex]
[tex]\textsf{b)} \quad y=2(x-4)^2-2[/tex]
Step-by-step explanation:
Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and [tex]a[/tex] is some constant)
Part aVertex = (-1, -4)Point on parabola = (1, 0)Substitute the vertex into the formula:
[tex]\begin{aligned}\implies y &=a(x-(-1))^2-4\\y & =a(x+1)^2-4\end{aligned}[/tex]
Substitute the point (1, 0) into the formula:
[tex]\begin{aligned}\implies a(1+1)^2-4&=0\\4a-4&=0\\4a &=4\\a &=1\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]y=(x+1)^2-4[/tex]
Part bVertex = (4, -2)Point on parabola = (6, 6)Substitute the vertex into the formula:
[tex]\begin{aligned}\implies y &=a(x-4)^2+(-2)\\y & =a(x-4)^2-2\end{aligned}[/tex]
Substitute the point (6, 6) into the formula:
[tex]\begin{aligned}\implies a(6-4)^2-2&=6\\4a-2 & =6\\4a &=8\\a &=2\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]y=2(x-4)^2-2[/tex]
Find a
a(x-h)²+k=ya(1+1)²-4=04a-4=04a=4a=1So
Vertex form
y=(x+1)²-4#2
(h,k)=(4,-2)passes through (6,6)Find a
a(6-4)²-2=64a=8a=2Vertex form
y=2(x-4)²-2Related Questions
Identify the Pre-Image in the diagram below. EXPLAIN your answer.
Answers
A transformation's preimage is the shape before the change. The image that is a pre-image is A'B'C', which is in blue colour.
What are an image and pre-image?We have a term for the shape before the transformation and another one for the shape after the transformation. The shape after a transformation is the image of the transformation. A transformation's preimage is the shape before the change.
In maths, the pre-image is the original figure. Therefore, the image that is a pre-image is ABC, which is in red colour.
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Yahaya, a Tailor started sewing an agabada dress at 9:45am. he completed the dress at 12:30pm. How long did he take to sew the dress
Answers
The swim team is sharing 6 pizzas. There are 36 players on the team. If each member has 1 slice, and each pizza has 8 slices, how much pizza in fraction form is left over?
Answers
Then take 36 and subtract that from 48 getting 12.
So there is 12 slices of pizza left over.
The amount of pizza left over in the fraction form will be 1/4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the swim team is sharing 6 pizzas. There are 36 players on the team. If each member has 1 slice, and each pizza has 8 slices.
Total slices = 8 x 6 = 48
Total players = 36
Left slices = 48 - 36 = 12
The portion in fraction left is,
L = 12 / 48
L = 1 / 4
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solve the system using elimination. show all work. write your answer in the form (x,y) 2x-3y=18 x+y=14
Answers
Answer:
x=12 y=2
Step-by-step explanation:
Due to fractions have screen shorted the steps in the image above
Chad is making trail mix for his next hiking club meeting. He mixes 2 pounds of peanuts, 2 pounds of raisins, and 1 pound of chocolate chips. His little sister asks him for a snack, so he gives her 5 ounces of the trail mix. Then, he portions out the rest for his meeting. If Chad splits the remaining trail mix evenly among 25 snack bags, how many ounces of trail mix will each bag have?
Answers
Answer:
3 ounces
Step-by-step explanation:
1 pound = 16 ounces
2(16) + 2(16) = 16 = 80 ounces of train mix - 5 from sister = 75 remaining
75 ounces of trail mix / 25 snack bags = 3 ounces of mix in each bag
fred buys a shipment of fruit that consists of only apples and oranges. for every 3 apples, there are 2 oranges. if there are 5 dozen pieces of fruit total, how many are oranges?
Answers
Answer:
24
Step-by-step explanation: 5 dozens = 60 so 3 +2=5 . 60 / 5 = 12 12 x 2 = 24
Rachael mixes 750 mL of mango juice 650 mL of orange juice and 325 mL pineapple juice she add sparkling water to fill the punch bowl that has a capacity of 2.5 L how many liters of juice does Rachel use show all work
Answers
Answer:
A. 1.725 L
B. 0.0775 L or 775 mL
Step-by-step explanation:
Part A
↓ Determine the liters of juice Rachel used ↓
750 + 650 +325 = 1,725
Rachel used 1,725 mL of juice. Convert the given mililiters to liters.
[tex]1725 \: ml \: \times \frac{1liter}{1000 \: ml} = 1.725 \: liters[/tex]
→ Rachel used 1.725 L of juice
Part B.
Determine the amount of sparkling water added to the punch bowl.
2.5 - 1.725 = 0.775 L
0.775 L was added tot he punch bowl. Convert liters to milliliters. ↓
[tex]0.775 \: \times \frac{1000 \: ml}{1 \: liters} = 775 \: ml[/tex]
Therefore, the answer is:
1.725 L & 775 mL
select the option for ? 3, 5, 12, 55, 648, ?
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Answer:
What option are you talking about for, is it for your quiz or for your classwork
What are the surface areas of these two prisms
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Can someone please help
Answers
Answer:
48
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180°.
We know one angle measures 42°.
Another angle is a right angle, so it measures 90°.
Only the angle labeled x is unknown.
42 + 90 + x = 180
132 + x = 180
x = 48
Answer: 48
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x4, but it is shifted to the right 3 units. What is its equation?
A. F(x) = - 3
O B. F(x) = (x-3)4
O C. F(x) = (x+3)4
O D. Fx) = 44+ 3
Answers
Answer: F(x) = 4x - 16
Step-by-step explanation: G(x) = 4x
if F(x) is the graph G(x) shifted over to the right by 4 then
F(x) = G(x-4) = 4(x-4) = 4x - 16
The general equation is f(x - amount_shifted)
The equation of the graph of the function F(x) is F(x) = (x - 3)⁴.
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given a function F(x) and G(x).
Given that,
F(x) has the same shape as the graph of G(x) = x⁴.
The difference is that F(x) is shifted to the right 3 units.
A function G(x) when shifted right to k units becomes G(x - k).
So the function F(x) is,
F(x) = G(x - 3)
= (x - 3)⁴
Hence the correct option is B.
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Can someone please help me with 4, 5, 6, 7, 8
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5) 2,1
6)2,1
7) 3,10
8)-3,8
5) x=2, y=1
6) x=2, y=1
7) x=3,y=10
8) x= -3, y= 8
Write a second degree polynomial with real coefficients and the given root; -2i
Answers
Answer: x^2+4
Work Shown:
x = -2i
x^2 = (-2i)^2
x^2 = 4i^2
x^2 = 4(-1)
x^2 = -4
x^2+4 = 0
Side note: Since -2i is one root, this means 2i is the other conjugate root.
[tex]\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0[/tex]
If x=5 and y=7, evaluate the following expression:
20−(3y−4x)
Answers
Answer:
[tex]\huge\boxed{\bf\:19}[/tex]
Step-by-step explanation:
Given,
x = 5y = 7Now, the expression is: [tex]20 - (3y - 4x)[/tex].
To solve this question we just need to substitute the values of x & y in the given expression. Then,
[tex]20 - (3y - 4x)\\= 20 - (3(7) - 4(5))\\= 20 - (21 - 20)\\= 20 - 1\\= \boxed{\bf\:19}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
find four consecutive whole numbers whose sum is 74
Answers
Answer:
17, 18, 19, 20
Explanation:
Let the numbers be x, x + 1, x + 2, x + 3
Their sum is equals to 74
x + x + 1 + x + 2 + x + 3 = 74 (group the variables)
x + x + x + x + 1 + 2 + 3 = 74 (simplify)
4(x) + 6 = 74 (subtract both sides by 6)
4x = 68 (divide both sides by 4)
x = 17
Other numbers:
x + 1 = 17 + 1 = 18
x + 2 = 17 + 2 = 19
x + 3 = 17 + 3 = 20
Answer:
17, 18, 19, 20
Step-by-step explanation:
Let four consecutive whole numbers be x, (x + 1), (x + 2) and (x + 3)According to the given condition:x + (x + 1) + (x + 2) + (x + 3) = 74-> 4x + 6 = 74-> 4x = 74 - 6-> 4x = 68-> x = 68/-> x = 17-> x + 1 = 17 + 1 = 18-> x + 2 = 17 + 2 = 19-> x + 3 = 17 + 3 = 20Thus, the four consecutive whole numbers are 17, 18, 19 and 20First round 0.676 to the nearest tenth.
Answers
Answer:
0.7
Step-by-step explanation:
Since 7 is above 5, you round 0.676 to 0.7
Answer: 0.7
Step-by-step explanation:
The nearest tenth is one decimal space after the dot. ex: 0.1234
Therefore, rounding 0.676, the 7 is ≥ 5, therefore we round the 6 up one number. This means the 0.6 becomes 0.7.
3. Given the geometric series 300 +360+432 +518.4+, what is the sum of the first 10 terms?
Answers
The sum of the first 10 terms of the given geometric series 300 +360+432 +518.4+..... is 7787.60.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , the multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
For the given geometric series, the common ratio is,
r = (360/300) = 1.2
Also, the first term of the series is 300. Therefore, the sum of the first ten terms of the series are:
Sum = a(rⁿ-1)/(r-1) = 300(1.2¹⁰-1)/(1.2-1) = 300(5.1917)/0.2 = 7787.60
Hence, the sum of the first 10 terms of the given geometric series is 7787.60.
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can anyone help without using reciprocal?
Answers
Answer:
x = -5/3
Step-by-step explanation:
-4 = [tex] \dfrac{20}{3}x[/tex]
-4×3 = 20 x
-12 = 20 x
[tex]x = \dfrac{-5}{3}[/tex]
PLEASE HELP ME I GIVE BRAINLIEST
Answers
Answer:
[tex]\frac{2\pi }{3} \ ,\ \pi \ ,\ \frac{4\pi }{3}[/tex]
Step-by-step explanation:
suppose cos(x) = y
Then
[tex]2\cos^{2} \left( x\right) +3\cos x+1=0\Longleftrightarrow \begin{cases}2y^{2}+3y+1=0&\\ y=\cos \left( x\right) \ \ \text{and} &0\leqslant x\leqslant 2\pi \end{cases}[/tex]
2y² + 3y + 1 = 0 ⇒ y = -1 or y = -1/2 (because 2-3+1=0)
y = -1 ⇔ cosx = -1 ⇒ x = π (because x∈[0,2π] )
y = -1/2 ⇔ cosx = -1/2 ⇒ x = 2π/3 or x = 4π/3
Final answer :
x = π or x = 2π/3 or x = 4π/3
pls help i need a good grade pls
Answers
Answer:
[tex]4*\frac{1}{6}[/tex]
Step-by-step explanation:
The number lines end points are 0 and 1 so the whole number line has a value of 1.
The number line is also broken up into 6 sections.
Then we have the pink rectangles that cover up each section. There are 4 of them and each cover 1/6 of the number line
So the expression that would represent the model would be 4 x 1/6
Answer:
4 * 1/6
Step-by-step explanation:
So to begin, I would find out what all the answers are equal to.
4 * 1/8 = 4/8 = 1/2
4 * 1/4 = 4/4 = 1
4 * 1/6 = 4/6 = 2/3
4 * 1/3 = 4/3
Next I would rule out all the answers bigger or equal to one, so 4 * 1/4 and 4 * 1/3.
Last, this fraction splits one into six parts, and 4 parts are highlighted. 4/6 is equal to 4/6. Your answer is 4 * 1/6
2x-y=-2 & x-2y=-16
It's due in an hour and I'm almost done :)
Answers
Step-by-Step Explanation:
We can solve it by Substitution Method,
=> 2x - y = -2 (Eq. 1)
=> x - 2y = - 16 (Eq. 2)
Therefore, from Eq. 2 :-
=> x = -16 + 2y (Eq. 3)
Substitute value of ‘x’ in Eq. 1 :-
=> 2x - y = -2
= 2(-16 + 2y) - y = -2
= -32 + 4y - y = -2
= -32 + 3y = -2
= 3y = -2 + 32 = 30
= 3y = 30
=> y = 30/3 = 10
Therefore, y = 10
Substitute value of ‘y’ in Eq. 3 :-
=> x = -16 + 2y
= x = -16 + 2(10)
=> x = -16 + 20 = 4
Therefore, x = 4 and y = 10
A circle with a radius of 9 millimeters.
Answers
Answer:
You didnt give us a question to answer, just a statement.
Step-by-step explanation:
If f(x) =1/x and g(x) = x - 2 what is f(g(x)) when X = 1
Answers
Answer:
f(g(x)) = -1
Step-by-step explanation:
[tex]f(x) = \frac{1}{x} \\ \\ g(x) = x - 2 \\ \\ \implies \: f(g(x)) = \frac{1}{x - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{1 - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{ - 1} \\ \\ \implies \: f(g(1)) = - 1[/tex]
Find the area of the composite figure below
Answers
Answer:
the answer is 25 hope it helps
A solid object was sliced to form two new objects. Each of the two new objects had a circular base. Which of the following solids may have been the original object? Select all that apply.
A: trapezoidal prism
B: cylinder
C: hexagonal prism
D: triangular pyramid
E: cone
Answers
Eric has 9 large pitchers for a sport drink at the soccer game. If he pours 4/7 of the sports drink into each pitcher will the total amount he lours into those pitchers be more or less than9 gallons?
Answers
Answer:
more because it is 9 pitchers and 4/7 of energy drink in each
hi! how do i do this?
Answers
Answer:
p = 2
Step-by-step explanation:
A rational function has a vertical asymptote where the denominator is zero.
__
Your function will have a denominator that is zero when ...
x -p = 0 ⇒ x = p
We are told there is a vertical asymptote at x = 2. That means ...
p = 2
Find the value of x in the triangle shown below.
=
२०
14
14
50°
18
Answers
Answer:
x = 87
Step-by-step explanation:
37 + 56 = 93
triangles always equal to 180
180 - 93 = 87
Please i really need help, i really need this i will give a brainliest to the people that answer correctly
Answers
Answer:
Graph B
Step-by-step explanation:
Replace y with x and vice versa.
y=1/2x+2 becomes x=1/2y+2
Then solve for y. Subtract 2 from both sides, then multiply by 2 which results in:
y=2x-4
Graph B is the one that has a y-intercept at -4 and a rise/run of 2.
Margo borrows $200, agreeing to pay it back with 8% annual interest after 7 months. How much interest will she pay?
Answers
Answer:
$9.33
Step-by-step explanation:
Interest = Principal × Rate × Time by 100
Therefore, I = 200×8×7/12 by 100
=16×7/12
=9.33
