the roots of f(x)=-2x^2+8x+13 are __________and __________ the vertex of the parabola is at _________
Answer:
roots: 2 ± (1/2)√42
-8
axis of symmetry: x = -b/(2a) is x = ---------------- = 2
2(-2)
vertex: (2, f(2) ) = (2, -2(2)^2 + 8(2) + 13 ), or (2, 21)
Step-by-step explanation:
First, let's determine the roots of this quadratic, using the quadratic formula. Here the coefficients are -2, 8, 13.
Thus, the discriminant b^2 - 4ac is 8^2 - 4(-2)(13), or 64 + 104, or 168. Because the discriminant is positive, we know that there are two different real roots.
They are:
-8 ± √168 -8 ± 2√42
x = --------------------- or x = --------------------- = 2 ± (1/2)√42
-4 -4
If using the method of completing the square to solve the quadratic
equation x2 + 20x – 6 = 0, which number would have to be
added to "complete the square"?
Answer:
100
Step-by-step explanation:
20/2= 10 and 10 squared is 100 but you have to move the -6 to the opposite side
The number required to add to the equation x² + 20x - 6 is 106
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A = x² + 20x - 6 = 0
Now , to make the equation as a perfect square,
The number to be added to the equation is 106
Adding 106 to the equation , we get
A = x² + 20x - 6 + 106
On simplifying the equation , we get
A = x² + 20x +100
Now , the equation can be factorized as
A = ( x + 10 )²
A = 0
( x + 10 )² = 0
x = -10
Hence , The number required to add to the equation x² + 20x - 6 is 106 to make it a perfect square
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I need help with this
what do you need help with?
i would be happy to help you.
2 box plots. The number line goes from 175 to 450. For resort A, the whiskers range from 175 to 375, and the box ranges from 250 to 300. A line divides the box at 375. For Resort B, the whiskers range from 200 to 400, and the box ranges from 300 to 375. A line divides the box at 325.
What can be said about the data for the snowfall in each resort? Check all that apply.
Answer:
2 box plots. The number line goes from 175 to 450. For resort A, the whiskers range from 175 to 375, and the box ranges from 250 to 300. A line divides the box at 375. For Resort B, the whiskers range from 200 to 400, and the box ranges from 300 to 375. A line divides the box at 325.
Step-by-step explanation:
Answer:
ab 50 and ab 75
Step-by-step explanation:
The equation of the line shown in the graph is y = ?.
What is the equation of the line shown in the graph?
Answer:
-1/5
Step-by-step explanation:
I couldn't tell whether or not your question was asking for either the slope intercept form or just the slope.
Your answer would be: y = -1/5x + 3 [if your question is asking for the slope intercept form]
OR
Your answer would be: -1/5 [if your question is asking for just the slope]
1 ≥ x - 9
Find out what x means.
PLS HELP ME ASAP ILL GIVER BRAINliest
Answer:
Step-by-step explanation:
Sam's two new aquariums each hold exactly 200 gallons of water.One aquarium will hold small fish and the other will hold large fish. Now he needs new fish for his aquarium.He will buy 5 small fish for every 10 gallons of water in the aquarium.He will buy 8 large fish for every 40 gallons of water in the aquarium.What is the total number of fish Sam will have? What will be the ratio of Sam's small fish to large fish? Could the ration be 25 small fish for every 10 big fish?
Answer:
100 small fish will be in 200 gallons of water. 40 large fish will be in 200 gallons of water.
Step-by-step explanation:
200/10=20
20*5=100 small fish
200/40=5
5*8=40 large fish
100+40=140 total fish
small fish/large fish=100/40=10/4=5/2 is the ratio
Write a PARAGRAPH
explaining how the volume
of a sphere in real-world
and mathematical
problems.
Step-by-step explanation:
The volume of the mathematical cylinder is the amount of space what will fit inside. You can you can use the formula for the mathematical problems to find the amount. It's like, "Example" to find the volume of a cone, you need to plug in the measurement for the height of the cone and the radios of the base of the formula for the volume of the cone. The you just need to simply it to get your answer..................
In a school election, 100 students submit ed a ballot voting for either Patrick or Britney. After counting all the votes, Britney received 56 more votes than Patrick. How many students voted for Patrick?
Answer:
22 students
Step-by-step explanation:
Create a system of equations where p is the number of students that voted for Patrick, and b is the number that voted for Britney
p + b = 100
b = p + 56
Solve by substitution by plugging in p + 56 as b in the first equation
p + b = 100
p + p + 56 = 100
Solve for p:
2p + 56 = 100
2p = 44
p = 22
So, 22 students voted for Patrick
Patrick sold 22 ballots.
22+56=78
22+78=100
please help(if you could tell me why,that would be awesome)
1/2 4² - 6
find the value
Answer:
2
Step-by-step explanation:
(1/2) 4^2-6
(1/2) 16-6
8-6
=2
Solve for the value of t.
HELP!!
Answer:
28
Step-by-step explanation:
2x28 = 56 -7 = 49
my answer has to be 20 characters long so don't mind the sentence with words
Answer:
t= 27
Step-by-step explanation:
2t-7=49
+7+7
2t=56
t=27
I need help on 19 and 20. Please help me. Please don’t put a link. Please help me.
Answer:
19:
4 < third side < 14
20:
3 < third side < 13
Step-by-step explanation:
hint: go to http://www.17 28.org/trianinq.htm
(fix the space between 17 and 28)
you're welcome xx
PLEASE HELP ILL GIVE BRAINLIEST
SHOW WORK
Answer:
choice 1) $21.90
Step-by-step explanation:
30% of $72.99 = 0.3(72.99) = $21.90
Answer:
21.90
Step-by-step explanation:
Find the area and circumference of the circle. Use 3.14 for A.
4.5 in.
Area______
Circumference____
Answer:
A = 63.59
C = 28.26
Step-by-step explanation:
r = 4.5
Area of a circle:
A = πr²
A = 3.14(4.5²)
A = 3.14(20.25)
A = 63.59
Circumference:
C = 2πr
C = 2(3.14)(4.5)
C = 28.26
I have to find the missing angles
Answer:
Angle 3 = 115°
Angle 4 = 22°
Angle 5 = 43°
Angle 6 = 115°
Step-by-step explanation:
These two triangles are congruent by SSS. It is given that two sides are congruent already, and by the reflexive property, they share a side and therefore have a third congruent side.
By CPCTC, all of their angles and sides are also congruent. And by the triangles angle sum theorem, side 3 and 6 must equal 115°
~~~
Have a nice day. Feel Free to ask questions. Spread the love.
Step-by-step explanation:
4 = 22⁰
5 = 43⁰
3 and 6 are same
kite total angles = 360⁰
so, to find 3 and 6, we need to subtract all angles we have and devide it with 2 because we need to find 2 angles...
360-22-22-43-43= 230
3 and 6 = 230 ÷ 2
= 115⁰
The price of a shirt is $42. The sales tax is 6.5%. What is the final cost for the shirt?
$2.73
$44.16
$44.73
$2.16
If m 4 = 44, the m 8=
Answer:
I think it's 88.
Step-by-step explanation:
4 x 11 = 44
8 × 11 = 88
Hope that helped :)
The ratio table shows the costs for different amounts of bird seed. Find the unit rate in dollars per pound. The unit rate is $ per pound
Answer: The rate is $1.25 per pound.
Step-by-step explanation:
Ayuden porfa . Determine 4 ala potencia x + 4 la potencia -x si se sabe que 2 ala potencia x + 2 ala pontecia -x es igual a 3
Answer:
4ˣ + 4⁻ˣ es igual a 7
Step-by-step explanation:
4ˣ + 4⁻ˣ
Dónde;
2ˣ + 2⁻ˣ = 3
Nosotras tenemos
[tex]2^x + \dfrac{1}{2^x} = 3[/tex]
[tex]2^{2\cdot x} +1 = 3 \cdot 2^x[/tex]
[tex]2^{2\cdot x} - 3 \cdot 2^x +1 = 0[/tex]
Deje que 'a' represente 2ˣ, tenemos;
a² - 3·a + 1 = 0
a = (3 ± √(3² - 4 × 1 × 1))/2 = (3 ± √5)/2
∴ a = 2ˣ = (3 ± √5)/2
((3 ± √5)/2)^2 - 3×(3 ± √5)/2 + 1
x = ln(3 ± √5)/2/(ln(2))
4ˣ + 4⁻ˣ = 4^(ln((3 ± √5)/2)/(ln(2))) + 4^(-(ln((3 ± √5)/2)/(ln(2)))) = 7
∴ 4ˣ + 4⁻ˣ = 7.
The approximate areas of South Carolina and Perto Rico are listed below: South Carolina: 8.29 * 10 ^ 4 kilometers Puerto Rico: 5.33 * 10 ^ 3 square kilometers What's the difference between the areas of the two states? Express your answer using scientific notation.
Answer:
h if Shamus for steak FFS ah MI dj
Step-by-step explanation:
bight you gddjf SD NJ Gzgz SC jdd
Answer: 1.567x10^5
Step-by-step explanation: 2.2x10^5-5.33x10^3
220,000-5,330
214,670
2.1467x10^5
When converting a linear equation into Slope Intercept form, what is our main goal? Vour answer
Answer:
You have to make sure the y= is always on the left side and so it looks like ,y=mx+b. m=slope, x=independent variable and b = y intercept.
Step-by-step explanation:
Hope it helps :)
Solve it please 25 Points!
As part of a class project, Sarah and Geoffrey conducted a survey asking their peers whether they planned on taking a music class the next year.
of the 90 students they surveyed, 43 responded favorably. Sarah and Geoffrey calculated the margin of error for different confidence intervals.
Their work is shown.
Sarah
Geoffrey
95% confidence:
90% confidence
0.48(1 - 0.48
ME = 1.96 V
90
(8) 1 - 3
ME = 1.65V
133
Which student incorrectly found the margin of error and why?
O A Geoffrey incorrectly found the margin of error because he used the wrong critical value.
OB. Geoffrey incorrectly found the margin of error because he used the wrong sample size.
OC. Sarah incorrectly found the margin of error because she used the wrong sample proportion.
OD. Sarah incorrectly found the margin of error because she used the wrong critical value.
Answer:
Geoffrey incorrectly found the margin of error because he used the wrong sample size.
Please give me brainliest, I really need it.
There are 100 centimeters (cm) in every meter (m).
Complete each of the tables and find the constant of proportionality.
Answer:
sorry
where is the table
Step-by-step explanation:
plz send detailed question
The constant of proportionality of 100 cm in 1 meter is 0.01
How to determine the constant of proportionality?The statement is given as:
100 cm in 1 meter
Rewrite as:
x cm in y m
Express as ratio
100 : 1 = x : y
Express as fraction
100/1 = x/y
Divide
100 = x/y
Make y the subject
y = x/100
Divide
y = 0.01x
A direct proportion is represented as y = kx
Where k represents the constant of proportionality.
So, we have:
k = 0.01
Hence, the constant of proportionality is 0.01
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What is 0.44% of 625?
Answer:
2.75 i believe
Answer:
2.75
Step-by-step explanation:
[tex]625*\frac{0.44}{100} =2.75[/tex]
I need help with these question! Please do step by step-
Answer:
There are 47 Borogroves and 35 Mome raths
Step-by-step explanation:
Here, given the number of legs, we want to find the number of each type of animals
Let the number of borogoves be b and the number of mome raths be m
From the question, there are 82 creatures;
Thus;
m + b = 82 ••••••••(i)
the total number of legs by b borogroves will be b * 2 = 2b
the total number of legs by m mome raths will be m * 4 = 4m
the sum of all legs is 234
2b + 4m = 234 •••••••••(ii)
From equation 1, m = 82-b
Substitute this into equation ii
2b + 4(82-b) = 234
2b + 328 - 4b = 234
4b-2b = 328-234
2b = 94
b = 94/2
b = 47
Recall;
m + b = 82
m + 47 = 82
m = 82-47
m = 35
daniel uses a 20.00 bill to purchase an item that costs d dollars. Write an equation to represent the amount of chnage c that he should receive? Also, what is the solution?
Equation:
c = 20.00 - d
Solution:
c = 20.00 - 8.49
c = 11.51