The quadratic equation with the given characteristics is:
f(x) = (x + 3)*(x - 7).
How to get the quadratic equation?We know that the vertex must be (2, -25) and it passes through (7, 0).
For a quadratic equation:
y = a*x^2 + b*x +c
The x-value of the vertex is:
x = -b/2a
Then we have:
2 = -b/2a
We also have:
-25 = a*4 + b*2 + c
And because the function passes through (7, 0) we know that 7 is one of the roots, then:
0 = a*49 + b*7 + c
Then we have 3 equations to work with:
2 = -b/2a
-25 = a*4 + b*2 + c
0 = a*49 + b*7 + c
If we subtract the third and second equations we get:
25 = a*45 + b*5
Now, with the first equation we can rewrite:
a = -b/4
Replacing that in the other equation:
25 = a*45 + b*5
25 = (-b/4)*45 + b*5 = b*(-25/4)
25*(-4/25) =b = -4
Now we know the value of b.
2 = -(-4)/2a
a = 1
Now we need to find the value of c, we have that:
0 = 1*49 + -4*7 + c
0 = 49 - 28 + c
0 = 21 + c
Then c = -21
The equation is:
[tex]y = x^2 - 4x - 21[/tex]
It can be factorized to:
f(x) = (x + 3)*(x - 7).
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Which of the following is NOT equivalent to 16?
A:22 × 22
B:42
C:4(22)
D:(4 × 2)2
Answer:
D.(4x2)^2 = 64 not 16
What are the solving steps and two
solutions to this equation using the quadratic formula?
-x^2-10x-21=0
Answer:
-x² - 10x -21 = 0
x² +10x +21 = 0
x² + 7x + 3x + 21 = 0
x ( x+7) + 3 (x+7) = 0
(x+3) (x+7) = 0
when (x+3) = 0,
x = -3
Again,
(x+7) = 0
x = -7
Answer:
7 and 3
Step-by-step explanation:
-b +/- sqrt(b^2+4ac)/2a
10 +/- sqrt(100-84)/2
10 +/- 4/2
7 and 3
Which expression is equivalent to 5 sqrt 32x5y10z15?
The expression equivalent to 5 sqrt 32x5y10z15 is 2xy2z3
State the degree and dominant term of this polynomial
function. (2 marks)[tex]f(x)=2x(x-3)^3(x+1)(4x-2)[/tex]
The degree of the polynomial f(x) = 2x(x - 3)³(x + 1)(4x - 2) is 6, and the dominant term is - 216x²
The degree of the polynomial?The polynomial function is given as:
f(x) = 2x(x - 3)³(x + 1)(4x - 2)
To determine the degree, we simply add the multiplicities.
So, we have:
Degree = 1 + 3 + 1 + 1
Evaluate
Degree = 6
Hence, the degree of the polynomial is 6
The dominant term of the polynomialWe have:
f(x) = 2x(x - 3)³(x + 1)(4x - 2)
Expand
f(x) = 8x⁶ - 68x⁵ + 176x⁴ - 72x³ - 216x² + 108x
The term with the highest absolute value is - 216x²
Hence, the dominant term is - 216x²
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Pre-algebra Course challenge pls help
what’s the circumference, to this problem ?
Answer:
18.5 about
Step-by-step explanation:
2[tex]\pi[/tex]r
2[tex]\pi[/tex]3
= about 18.5
Answer:
circumference=2πr
2× 22/7×3=18.85
Find the slope of the line that passes through (5, 2) and (8, - 1)
Answer:
-1
Step-by-step explanation:
when the points are placed on a graph correctly, you would have to go down 6 and over 6; rise over run would make that -6/6 which is equal to -1
3. Convert the measure from radian to degree.
Answer:
Here is the answer...hope it helps
Carson needs to build a closed container out of sheet metal, but needs to minimize the amount of sheet metal used. The volume of Carson's container needs to be approximately 320 cubic Inches. Carson needs to select one of the following designs that meets his volume requirement, using the least amount of sheet metal. Which design should Carson choose? A. Rectangular prism with dimensions of 8 inches (in.), 8 in., and 5 in. B. Rectangular prism with dimensions of 10 in., 8 in., and 4 in. C. Cylinder with a radius of 5 in. and height of 5 in. D. Square pyramid with a base length of 10 in., height of 10 in, and slant height of approximately 14 in.
Carson needs to select one of the following designs that meet his volume requirement, using the least amount of sheet metal which is the first option. Rectangular prism with dimensions of 8 in, 8 in., and 5 in.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
[tex]V = a\times b \times c \: \: unit^3[/tex]
Carson needs to build a closed container out of sheet metal but needs to minimize the amount of sheet metal used.
The volume of Carson's container needs to be approximately 320 cubic Inches.
Carson needs to select one of the following designs that meets his volume requirement, using the least amount of sheet metal.
If we consider the Rectangular prism with dimensions of 8 inches (in.), 8 in., and 5 in.
Then the volume would be
[tex]V = 8 \times 8 \times 5\\\\V = 320[/tex]
This satisfies the given volume so it could be the correct answer.
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Can someone help me on this i am stuck on it thanks
Answer:
36
Step-by-step explanation:
Given:
A kitchen shop sells bowls in sizes small, medium and large.Draw a Venn diagram with 3 intersecting circles. Label each circle:
S = small bowlsM = medium bowlsL = large bowls----------------------------------------------------------------------------------------------
Given:
5 people bought all three sizes of bowl.Enter "5" in the central overlapping section of the Venn diagram.
----------------------------------------------------------------------------------------------
Given:
7 people bought a small bowl and a large bowl.We know that 5 people bought all 3 bowls, so to find the number who bought a small and large bowl (but not a medium bowl):
⇒ 7 - 5 = 2
Enter "2" in the section S and L but not M.
----------------------------------------------------------------------------------------------
Given:
In total, 27 people bought a small bowl, of which 12 also bought a medium bowl.First, calculate the number of people who bought only a small and medium bowl (but not a large bowl). We know that 5 people bought all 3 bowls, so subtract 5 from 12.
Enter "7" in the section S and M but not L
A total of 27 people bought a small bowl, so to find the number who bought a small bowl only (not a medium and/or large bowl), subtract the other found numbers from 27:
⇒ 27 - 5 - 2- 7 = 13
Enter "13" in the S only section.
----------------------------------------------------------------------------------------------
Given:
In total, 66 people bought a medium bowl, of which 15 also bought a large bowl.First, calculate the number of people who bought only a large and medium bowl (but not a small bowl). We know that 5 people bought all 3 bowls, so subtract 5 from 15.
Enter "10" in the section M and L but not S
A total of 66 people bought a medium bowl, so to find the number who bought a medium bowl only, subtract the other found numbers:
⇒ 66 - 5 - 7 - 10 = 44
Enter "44" in the M only section.
----------------------------------------------------------------------------------------------
Given:
On a given day, 100 people each bought at least one bowl from the shop.To find "L only" subtract all the known numbers from 100:
⇒ 100 - 5 - 2 - 7 - 13 - 10 - 44 = 19
Enter "19" into the L only section.
----------------------------------------------------------------------------------------------
Finally, to work out the total number of people that bought a large bowl, add up the numbers in the L circle:
⇒ 2 + 5 + 10 + 19 = 36
Use the given values of n and p to find the minimum usual value μ- 20 and the maximum usual value μ+20. Round your answer to the nearest hundredth unless otherwise noted.
n=713, p= 4/5
Answer:
μ - 2σ = 549.04μ + 2σ = 591.76Step-by-step explanation:
Given the parameters of binomial distribution
n = 713, p = 4/5We need to find the mean μ and the standard deviation σ to calculate required values
Follow the steps below1. Find the mean
μ = n·p = 713*(4/5) = 570.42. Find the variance
σ² = np(1 - p) = 713*(4/5)*(1 - 4/5) = 114.083. Find the standard deviation
σ = √114.08 = 10.68 (rounded)Find the minimum usual value
μ - 2σ = 570.4 - 2*10.68 = 549.04Find the maximum usual value
μ + 2σ = 570.4 + 2*10.68 = 591.76Answer:
Min:549.04; Max:591.76
Step-by-step explanation:
easy points..........
Answer:
38°; 142°; 308°Step-by-step explanation:
The solution of each question is self-explanatory.
Used properties
Vertical angles are congruentAngle sum property of circleCentral angle is same as intercepted arc measure#8mED = mAB = mAC - mBC = 90° - 52° = 38°#9mEA = mBCD = mBC + mCD = 52° + 90° = 142°#10mBDC = 360° - mBC = 360° - 52° = 308°Answer:
38°; 142°; 308°
Step-by-step explanation:
belive me
Find the distance between the points F And K
Answer:
is it 6?! eu n sei a pergunta
Brooke baked 7 batches of cookies with x cookies in each barch. She then ate 5 cookies, How many cookies does Brooke have left? Write your answer as an expression.
Answer
(7*x) -5
Step-by-step explanation:
What is the sum of 7 1/12 + 8 1/12 + 3 1/12?
Answer:
8,064 I'm sure that's is answerWhat is 10% of 79,775
Answer:
7977.5
Step-by-step explanation:
.10 times 79775 =7977.5
Identify the measure of arc AD◠.
Answer:
36
Step-by-step explanation:
18*2 = 36
Question
One hundred grams of radium are stored in a container. The amount R (in grams) of radium present after t years can be modeled by R=100e−0.00043t. After how many years will only 5 grams of radium be present? Round your answer to the nearest whole year.
It will take about ??
years for only 5 grams of radium to be present.
The number of years it would take for radium to be 5 grams is 6967 years.
After how many years will only 5 grams of radium be present?
The formula that is used to represent continuous compounding or continuous decay is:
FV = A x [tex]e^{-t}[/tex] x N
Where:
A= amounte = 2.7182818N = number of yearsr = interest rate5 = 100 x e^−0.00043 x t.
In order to determine the value of t, take the following steps:
Divide both sides by 100
5/100 = e^−0.00043 x t.
Then take the In of both sides
= 6967 years
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D 2. Is it true to say, between any 2 distinct integers, there always exists a national numbers.
Answer:
i would say no
Step-by-step explanation:
Between any two distinct integers not necessary to be one integer.
Hope This Helped
Please help me. I’m stuck on it
Answer:
y = 6
x = -16
Step-by-step explanation:
[tex]\left \{ {{x + 4y = 8} \atop {3x + 8y = 0}} \right.[/tex]
[tex]x + 4y = 8\\ - 4y -4y\\x = 8 - 4y\\substitution\\3(8 - 4y) + 8y = 0\\ 24 - 4y = 0\\-24 -24\\-4y = -24\\\frac{-4x}{-4} = \frac{-24}{-4}\\y = 6 \\plug \\x = 8 - 4y\\x = 8 - 4(6)\\x = -16\\y = 6, x = -16[/tex]
please solve for me. please be right
Answer:
It would be 60
Step-by-step explanation:
So 3(3*5 + 5) so 3*5 would be 15, 15+5=20, and 20*3=60
This is really simple if you can't figure this out, you might as well go back to 1st grade and below
pls try before asking
F(x, y, z) = yzi 9xzj exyk, c is the circle x2 y2 = 9, z = 1
The value of curlF.dS is 72π if the F(x, y, z) = yzi 9xzj exyk, c is the circle x2 y2 = 9, z = 1
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have:
[tex]\rm F(x, y, z) = yzi+ 9xzj+ e^{xy}k[/tex]
And curl is x²+y²= 9 and z =1
In the parametric form:
[tex]\rm \vec{r}(t) = 3cost \vec{i}+3sint \vec{j}+\vec{k}[/tex] 0 ≤ t ≤ 2π
First two component represent the circle and last one represent the z =1
Using Stoke's theorem:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = \int\limits_C {\vec{F}} \, .d\vec{r } = \int\limits^{2\pi}_0 {\fec{F}(\vec{r}(t)).\vec(r)t} \, dt[/tex]
Here:
[tex]\rm \vec{F}(\vec{r}(t)) = 3sint \vec{i}+27cost \vec{j}+e^{cost.sint}\vec{k}[/tex]
Now calculate the dot product of curl F and dS we get:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = \int\limits^{2\pi}_0 (-9sin^2t+81cos^2t)dt[/tex]
After solving the above integral, we will get:
[tex]\rm \int\limits\int\limits_S {curl \ \ve{F}.d\vec{S}} = 72\pi[/tex]
Thus, the value of curlF.dS is 72π if the F(x, y, z) = yzi 9xzj exyk, c is the circle x2 y2 = 9, z = 1
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omg i keep mixing up the questions I JUST NEED HELP ON PART A THATS IT
Answer:
1/557
Step-by-step explanation:
The scale factor on a map is the ratio of one unit to the distance that unit measures!
Dion flips a coin 20 times and records if it comes up heads. if getting heads is a success, what is the probability of a success on each roll? 0.2 0.3 0.5 1.00
The probability of a success on each roll of the coin that is filipped by Dion is 0.5.
What is the probability?Probability is the likelihood that a stated event would occur. The odds the event occurs is 1 and the odds that the event does not happen is 0. If a coin is flipped, there is 50% chance of getting either a head or a tail.
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Answer:
its c
Step-by-step explanation:
.5 on edge! just took the test
which has the same ratio as 8 inches/1 foot?
Answer:
16 inches/2 feet
Step-by-step explanation:
We already have our ratio of 8:1, so we can multiply this ratio by any number of out choosing and the ratio will still be the same.
Emergency pls help: tisha is moving into her first apartment and ordered a large mirror for her room from a catalog. the catalog says the mirror is 7 feet tall. if she leans the mirror against the wall at a 76 degree angle, how far away from the wall will its base be, to the nearest hundredth of a foot?
Using the slope concept, it is found that the base of the mirror will be 1.75 feet from the wall.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, the vertical change is of 7 ft, with an angle of 76º, and the distance is the horizontal distance, hence:
tan(76º) = 7/d
d = 7/tan(76º)
d = 1.75.
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What is the area of a square that has a length of x-5?
Answer:
x^2 - 10x + 25
Step-by-step explanation:
(x-5) (x-5)
= x^2-10x+25
Answer:
Step-by-step explanation:
[tex]\text{Formula for the area of a square:}[/tex]
[tex]A=s^2[/tex] [tex](\text{"S" represents the side length} )[/tex][tex]\text{Given}[/tex]:
[tex]\text{The side length is x - 5, so we can plug that into the equation}[/tex][tex]\text{Solving}[/tex]:
[tex]A=s^2[/tex][tex]A=(x-5)^2[/tex][tex]A=x^2-10x+25[/tex]b) Work out the value of (2.92 × 106) + (4 × 10¯²) Give your answer in standard form.
Step-by-step explanation:
[tex]3.0956 \times {10}^{2} [/tex]
is correct answer
What is the sum of all positive values of x such that x^2 + 6x - 91 = 0?
Answer:
20
Step-by-step explanation:
x^2 + 6x - 91 = 0
or, x^2 + 13x - 7x -91=0
or, x(x-13) -7(x-13) =0
or, (x-13)(x-7)= 0
either,
x-13=0 ==> X= 13
x-7=0 ==> X = 7
sum of all positive values of x = 13 +7 = 20The sum of all positive values of x such that x² + 6x - 91 = 0 is 20
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given equation is x² + 6x - 91 = 0
x² + 13x - 7x -91=0
Take common terms
x(x-13) -7(x-13) =0
(x-13)(x-7)= 0
x-13=0
x= 13 and
x-7=0
x= 7
The two positive numbers are 13 and 7.
The sum of all positive values is 13 +7 = 20
Hence, the sum of all positive values of x such that x² + 6x - 91 = 0 is 20
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4 + 7 + 9 + 5 - 44? pls HELPPPPP!!!!!!!!!!!!!!!
Answer:
-19.
Step-by-step explanation:
4 + 7 + 9 + 5 - 44
Doing the adds first;
= 25 - 44
= -19.
