Axis of sym: x =
Vertex: (
,
)
Do not do the domain
Range: Pick one: A. y≥4 B. y<4 C. y≤4 D. y≤−2 E. y<−2
The Range is
Zeros:
and
Equation:
Answers
Answer:
SEE BELOWStep-by-step explanation:
to understand thisyou need to know about:quadratic functionPEMDASlet's solve:vertex:(h,k)
therefore
vertex:(-1,4)
axis of symmetry:x=h
therefore
axis of symmetry:x=-1
to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0vertex form of quadratic equation:
y=a(x-h)²+ktherefore
y=a(x-(-1))²+4y=a(x+1)²+4it's to notice that we don't know what a is
therefore we have to figure it out
the graph crosses y-asix at (0,3) coordinates
so,
3=a(0+1)²+4
simplify parentheses:
[tex]3 = a(1 {)}^{2} + 4[/tex]
simplify exponent:
[tex]3 = a + 4[/tex]
therefore
[tex]a = - 1[/tex]
our vertex form of quadratic equation is
y=-(x+1)²+4let's simplify it to standard form
simplify square:
[tex]y = - ( {x}^{2} + 2x + 1) + 4[/tex]
simplify parentheses:
[tex]y = - {x}^{2} - 2x - 1 + 4[/tex]
simplify addition:
[tex]y = - {x}^{2} - 2x + 3[/tex]
therefore our answer is D)y=-x²-2x+3
the domain of the function
[tex]x\in \mathbb{R}[/tex]
and the range of the function is
[tex]y\leqslant 4[/tex]
zeroes of the function:
[tex] - {x}^{2} - 2x + 3 = 0[/tex]
[tex] \sf divide \: both \: sides \: by \: - 1[/tex]
[tex] {x}^{2} + 2x - 3 = 0[/tex]
[tex] \implies \: {x}^{2} + 3x - x + 3 = 0[/tex]
factor out x and -1 respectively:
[tex] \sf \implies \: x(x + 3) - 1(x + 3 )= 0[/tex]
group:
[tex] \implies \: (x - 1)(x + 3) = 0[/tex]
therefore
[tex] \begin{cases} x_{1} = 1 \\ x_{2} = - 3\end{cases}[/tex]
Related Questions
Cup G has a diameter of 4 in. and a height of 8 in. Find the volume of Cup G.
Answers
Answer:
32pi
Radius=1/2 Diameter
radius=2
Area of circle= pi*radius^2= 4pi
4pi*8=32 pi
(3.14)(32)
v=100.48
An expression is shown.
95-34
What is the value of the expression?
Answers
Answer:
61
Step-by-step explanation:
95
- 34
_______
61
1. The first bus stop on a bus route is 4 miles from school. How many yards is the first bus stop from school? A) 12 yards B) 1760 yards C) 5280 yards D) 7040
Answers
Answer:
D. 7040 yards
Step-by-step explanation:
What is 12 divided by 3/5
Answers
Answer:
20
Step-by-step explanation:
12 / 3/5
12 / 0.6
20
Answer:
12 divided by 3/5 = 20
In 2018, there were about 32 million teenagers (aged 13-17) in the United States. They each sent
an average of 1200 text messages per month. About how many text messages did all of the
teenagers in the United States send each month? Express your answer using scientific notation.
Answers
Answer:
About 38,400,000,000 text
thirty eight billion + four hundred million
Step-by-step explanation:
Let X and Y be the following sets:
X = {}
Y = {2,3, 5, 7, 11, 13}
Which of the following is the set X Y?
Answers
Answer: the answer is B
Step-by-step explanation:
2 1/2% as a simplified fraction
Answers
Answer:
Step-by-step explanation:
5/2% is in the fraction form
520 is the decimal form
hope this helps
NEED MAJOR HELP FAST GET HERE QUICK PLEASE
Answers
A 45 degree angle is 1/8 of a circle, so keep that in mind for later. You're looking for the circumference of that 1/8 fence, so you have to use the formula, circumference/diameter=pi. Now, the problem gives you half the diameter, a.k.a the radius, so double it to get 44 ft. then, you multiply that by 3.14 (pi) to get 138.16. Now take the 1/8, from before, of the circumfrence and you get your final answer, 17.27 ft!
A circle has a diameter of 7 inches. Find the radius
Answers
Answer:
radius= 3.5 in
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation:
The diameter is the length from one side of the circle to the other the radius is half that
A principal of $2900is invested at 3.25% interest, compounded annually. How much will the investment be worth after 9years? Use the calculator provided and round your answer to the nearest dollar.
Answers
Given:
Principal = $2900
Rate of interest = 3.25% compounded annually.
Time = 9 years.
To find:
The amount of investment after 9 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right){nt}[/tex]
Where, P is principal, r is rate of interest, n number of times interest compounded in an year and t is the number of years.
Substitute P=2900, r=0.0325, n=1 and t=9.
[tex]A=2900\left(1+\dfrac{0.0325}{1}\right)^{1\times 9}[/tex]
[tex]A=2900\left(1+0.0325\right)^{9}[/tex]
[tex]A=2900\left(1.0325\right)^{9}[/tex]
Using calculator, we get
[tex]A=3867.306[/tex]
[tex]A\approx 3867[/tex]
Therefore, the worth of the investment after 9 years will be $3867.
Recommendations
Skill plans
Math
Language arts
E Common Core
Seventh grade
> L.8 Solve percent equations: word problems JS6
You have prizes to reveal!
Learn with an example
The city council voted on a new tax. 27 council members voted in favor of the tax. The
council has 90 members. What percentage of the council members voted in favor of the tax?
Write your answer using a percent sign (%).
Submit
Answers
Answer:
Step-by-step explanation:
27 ÷ 90 = 0.3 = 0.30 = 30%
j varies directly with h and u
Answers
Answer:
Im sorry in order for us to answer this question you have to use real words and add details to your question and with complete sentences.
Thank You
I need these three and they shouldn’t be too hard.
Answers
Answer:
i dont know
Step-by-step explanation:
sorry my man my school is still just going into these kind of questions ):
A group of 140 students at an elementary school were asked if they prefer the color orange to the color green. The results are shown in the table below. Given that a randomly selected survey participant is a male, what is the probability that this student prefers the color green?
Enter your answer as a fraction.
Male Female Total
Orange 12 50 62
Green 5 73 78
Total 17 123 140
Provide your answer below:
$$
Answers
Answer:
1/28
Step-by-step explanation:
The probability that a male student picks green is 5 / 17
The randomly selected participant is a male which means that you should be looking at the probability that a male picks green not that a student picks green.
The probability that a male picks green is:
= Number of males who prefer green / Number of males in total
There are 17 males in total and 5 of them prefer green. Probability that a male picks green is:
= 5 / 17
In conclusion, the probability that a male picks green is 5 / 17.
Find out more at https://brainly.com/question/14682217.
A group of volunteers has been collecting toys to deliver to a local charity. Over the last 3 days, the volunteers have collected 324 toys. What has been their collection rate, in toys per day?
A.
110 toys per day
B.
105 toys per day
C.
107 toys per day
D.
108 toys per day
Answers
Answer:
D 108
Step-by-step explanation:
324/3=108
Answer: 108 toys per day
Step-by-step explanation: 324/3
For estimation purposes, the shape formed by the sectors is considered to be a parallelogram. Which statement is true?
A.The height is approximately r units, and the base length is approximately mr units.
B.The height is approximately r units, and the base length is approximately 2 units.
C.The height is approximately r2 units, and the base length is approximately it units.
D.The height is approximately 2r units, and the base length is approximately it units.
Answers
Answer:
Step-by-step explanation: B
Can someone help me please and show work thank you
Answers
Answer:
60% decrease
Step-by-step explanation:
To work out percentage change you takeaway the original number by the new number (New number-Original number) in this case 24-60=(-36), then divide the decreased amount by the original number and multiply the answer by 100 (Decrease amount ÷ Original number x 100) for this question you'd do (-36)÷60=(-0.6) then (-0.6)x100=(-60).
The minus shows its a decrease in percentage by 60%
(I hope this helps srry if it doesn't make sense)
Consider the following food chain:
Plants are eaten by grasshoppers, which are eaten by mice, which are eaten by snakes.
What will happen to the other members of the food chain if the grasshoppers are removed?
a.
the number of plants will increase, the number of mice will decrease, the number of snakes will decrease
b.
the number of plants will decrease, the number of mice will increase, the number of snakes will increase
c.
the number of plants will decrease, the number of mice will increase, the number of snakes will decrease
d.
the number of plants will increase, the number of mice will increase, the number of snakes will increase
Answers
Answer:
A
Step-by-step explanation:
the plant will increase because no grasshopper will be present to eat them without the grasshopper the mice cannot eat so the mice population will decrease....
If the grasshoppers are removed then the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
The correct answer is option a.
For the given Food chain:
If the grasshoppers are removed from the food chain, it will lead to a increase in the number of plants, as there will be no herbivores (grasshoppers) to consume them. This is because grasshoppers help control plant populations by feeding on them.
With the removal of grasshoppers, the mouse population is likely to decrease since their primary food source (grasshoppers) is no longer available.
As a consequence of the decreased mouse population, the snake population may also decrease because their primary food source (mice) has been affected.
Thus, the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
Thus, option a is correct.
Learn more about Food chain here:
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The yield of a chemical process is being studied. Fromprevious experience, yield is known to be normally distributedand 3. The past five days of plant operation have resulted inthe following percent yields: 91.6, 88.75, 90.8, 89.95, and 91.3.Find a 95% two-sided confidence interval on the true mean yield.
Answers
Answer:
(87.85 ≤ μ ≤ 93.11)
Step-by-step explanation:
Given the data:
91.6, 88.75, 90.8, 89.95, 91.3
Mean, m = Σx / n
n = sample size = 5
Mean = 452.4 / 5 = 90.48
Standard deviation, σ = 3
Zcritical at 95% = 1.96
Confidence interval :
Mean ± Error margin
Error margin = Zcritical*σ/sqrt(n)
Error margin = 1.96 * 3/sqrt(5)
Error margin = 2.630
Lower boundary : 90.48 - 2.630 = 87.85
Upper boundary : 90.48 + 2.630 = 93.11
(87.85 ; 93.11)
Use the unit price of gasoline at both gas stations to determine which gas station charges more for gasoline (gallons). Be sure to include the unit prices in your answer. Show or explain your work.
Answers
Answer: Gas station P
Step-by-step explanation:
When you plot gas station M on the graph all the values are under the line meaning it gas at station M costs less than station G.
Gas station P charges more than gas station M.
What is unit rate?A unit rate means a rate for one of something.
Given is a table and a graph,
When we compare each, we get,
Gas station P is charging $20 for 5 gallons, and gas station M charges $19 for same.
Hence, gas station P charges more than gas station M.
For more references on unit rate, click;
https://brainly.com/question/11258929
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If a video game cost $60 and it's on sale for 10% off, how much is the discount?
Answers
Answer:
$6
Step-by-step explanation:
Percentages have a cool little trick where they can be reversed :) 10% of 60 is a little tough, but we can switch it to 60% of 10, which is much easier. 60% of 10 is 6, so the discount is $6
Please let me know asap
Answers
Answer:
100
Step-by-step explanation:
Hello There!
∠4 and ∠8 are corresponding angles
corresponding angles are congruent so if ∠4 = 100 then ∠8 also equals 100
Six friends go to lunch and the total cost of lunch is $41.12. After using a $5 coupon to reduce the bill, the friends split the cost of lunch evenly. How much does each friend owe?
A $6.20
B $6.02
C $6.85
Answers
Answer:
6.02
Step-by-step explanation:
(41.12 - 5) / 6
= 6.02
If (×+1 ) and(×+2) are factors of the expressionx^4+ax^2+b , find the value of and b, with these value of and factorize completely.
Answers
Answer:
Step-by-step explanation:
(x⁴+ax²+b) ÷ (x+1) = x³-x²+(a+1)x-(a+1) remainder b+(a+1)
Since x+1 is a factor, b+(a+1) = 0.
(x³-x²+(a+1)x-(a+1)) ÷ (x+2) = x²-3x+(a+7) remainder -3a-15
Since x+2 is a factor, -3a-15 = 0
a = -5
b = 4
x⁴+ax²+b = x⁴ - 5x² + 4 = (x²-4)(x²-1) = (x+2)(x-2)(x+1)(x-1)
Find the area of the shape
Answers
Explanation:
To find the area, divide it up into sections, and find the area of each section before adding them all together like this:
HELPPPPPPPPPPP!! SMART People?
Answers
its $1.07 my bad XD :P
Step-by-step explanation:
Please help and will give brainliest
Answers
9514 1404 393
Answer:
12 m³
Step-by-step explanation:
The bottom platform has dimensions 2m × 4m × 3m, so a volume of ...
V = LWH
V = (2 m)(4 m)(3 m) = 24 m³
The top platform has dimensions 2m × 3m × 2m, so a volume of ...
V = (2 m)(3 m)(2 m) = 12 m³
The bottom platform has a larger volume by ...
24 m³ -12 m³ = 12 m³
The bottom prism has a 12 m³ larger volume.
Answer:
the answer is 12m squared
Which set of points on the graph represents equivalent ratios?
70
60
F
50
40
30
.
20
10
1
2 3
4
5
6 7
Х
points C, D, and F
O points B, C, and D
points B, C, and F
O points A, C, and D
Ο Ο Ο
Answers
Answer:
C or otherwise BCD
Step-by-step explanation:
right on edge
.5% of what number is 15.8?
Answers
Answer:
316 should be your answer
Step-by-step explanation:
Answer:
3160
Step-by-step explanation:
.5% of what number is 15.8?
Let the unknown number be x.
0.5% * x = 15.8
0.005x = 15.8
x = 15.8/0.005
x = 3160
What is 5^5 equal to
Answers
Answer:
5^5 is equal to 3125
Step-by-step explanation:
5×5×5×5×5=3125 Hope this helps!
the answer is 10 alangan