Answers
f(x) = 5x^2 + 25x + 30
============================================================
Explanation:
The roots, aka x intercepts, of this curve are x = -3 and x = -2. This is where the graph crosses the x axis.
Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.
So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get
y = (x+3)(x+2)
y = (-1+3)(-1+2)
y = (2)(1)
y = 2
But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)
Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)
Now let's expand everything out and simplify
y = 5(x+3)(x+2)
y = 5(x^2+2x+3x+6)
y = 5(x^2+5x+6)
y = 5x^2+5*5x+5*6
y = 5x^2 + 25x + 30
Choice C is the final answer
-------------------------
To check this, we can plug in x = -3 and we should get 0
y = 5x^2 + 25x + 30
y = 5(-3)^2 + 25(-3) + 30
y = 5(9) + 25(-3) + 30
y = 45 - 75 + 30
y = -30 + 30
y = 0
This proves that x = -3 is a root of y = 5x^2 + 25x + 30
I'll let you check x = -2. You should also get y = 0 when plugging this x value in.
Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.
Related Questions
help me find x please
Answers
Answer:
[tex]3\sqrt{3}[/tex]
[tex]\left(\frac{\left(6\cdot \:\:\:sin\left(30\right)\right)}{sin\left(90\right)}\right)^2+x^2=36[/tex]
Step-by-step explanation:
The Coffee Counter charges $11
per pound for Kenyan French Roast coffee and $10
per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $10.60
per pound?
Answers
Answer:
12 pounds of Kenyan French Roast coffee
8 pounds of Sumatran coffee
Step-by-step explanation:
if you use x pounds of Kenyan French Roast coffee and y pounds of Sumatran coffee then you know that
11x + 10y = 10.6 * 20
x+y=20
10x+10y=200
11x+10y=212
x=12
y = 20-x = 20-12 = 8
so you want to use
12 pounds of Kenyan French Roast coffee
8 pounds of Sumatran coffee
14. What is the measure of angle wº? Show all work.
Answers
Answer:
100 degrees
Step-by-step explanation:
We can start by finding angle y, which is supplementary to 160.
180-160=20
angle y = 20 degrees.
With that, we can find angle w using the interior-exterior sangle theorem (or whatever name you use for it) which states that "the measure of an exterior angle of a triangle equals the sum of the measures of two remote interior angles". In other words:
angle w = angle y + 80
angle w = 20+80
angle w = 100.
The final answer is 100 degrees.
I hope this helped! :D
Answer:
Hello,
w=100
Step-by-step explanation:
y=180-160 (angles supplementaries)
y=20
w is a externel angle of the triangle is equal to the sum of non adjacents angles:
w=80+20=100
A baker used 12 cups of batter to make muffins. It took 2/3 of a cup of batter to make one muffin. How many did the baker make?
Answers
Answer:
8 cups
Step-by-step explanation:
1 cup = 2/3
so,2/3 x 12 = 8 cups
Answer:
8 cups
Step-by-step explanation:
Evaluate the expression
Answers
Answer:
3
Step-by-step explanation:
(5x -2y) / y
Let x = -4 and y = -4
(5*-4 - 2*-4) / -4
(-20 +8) / -4
-12/ -4
3
Hey there!
5x - 2y / y
= 5(-4) - 2(-4) / -4
5(-4)
= -20
(2)(-4)
= -8
= -20 - (-8) / -4
= -20 + 8 / -4
-20 + 8
= -12
= -12 / -4
= 3
Therefore, your answer is: 3
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
8a^3-36a^2+54a-27-64p^3
Answers
Answer:
8a^3-64p^3-36a^2+54a-27
Step-by-step explanation:
since it no common variable so it can not be further solved
Find the indicated side of the
triangle.
30°
a = [?]
help please quick
Answers
Answer:
SOH-CAH-TOA
TAN(30) = 3/x
[tex]x=3\sqrt{3}[/tex]
Step-by-step explanation:
Answer:
underoot 27....or 5.3(approx )or 3_/3
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Brainliest if you can help me!!
Answers
Step-by-step explanation:
I guess option 1 is correct answer
Use a graphing calculator or online application to find the solution to 3^-x = x^3 + x to the nearest tenth. The solution is approximately x = ?
the answer is not 0.5 or 0.48
Answers
Answer:
x = 0.5 to the nearest 1/10.
Step-by-step explanation:
3^-x = x^3 + x
y = x^3 - 3^-x + x = 0
Using a graphing calculator to draw the graph of the above:
The graph crosses the x-axis at x = 0.4798
Answer:
x≈ .5
Step-by-step explanation:
x ≈ 0.479822322350589
Rounding to the nearest tenth
x≈ .5
There is either an error in the equation or the solution key
Simplify this please
Answers
Answer:
4Step-by-step explanation:
[tex] \sqrt[3]{64} [/tex]
[tex] = \sqrt[3]{4 \times 4 \times 4} [/tex]
= 4 (Ans)
Answer:
Step-by-step explanation:
4. Find the index of algebraic expression 4x^6
Answers
Answer:
6
Step-by-step explanation:
"Index" is another name for exponent.
Chris drives 240 miles from his home in Atlanta, Georgia, at 60 miles per hour. How many minutes longer would the return trip take if he travels at 50 miles per hour
Answers
Answer:
48 minutes
240 at 60mph = 4 hrs.
240 at 50 mph = 4.8 hrs.
it would take an extra 60*.8 or 48 minutes
Step-by-step explanation:
The trip will be of 48 minutes longer when the speed is decreased by 10 miles per hour.
What is the formula for time?
The time is given by distance/speed. The unit of time is minutes or seconds.
What will be the time difference?When distance of 240 miles is cover by the speed of 60 miles per hour then the time take to travel this distance will be 240/60=4 hours
When distance of 240 miles is cover by the speed of 50 miles per hour then the time take to travel this distance will be 240/50=4.8 hours
The difference between 4.8 hours and 4 hours is of 0.8 hours or 0.8*60=48 minutes.
Therefore, the trip will be of 48 minutes longer.
Learn more: brainly.com/question/21061928
#SPJ2
Evaluate 10 + 8 ÷ 2 − 4
Answers
Step-by-step explanation:
we will solve this question according to BODMAS rule...
B for bracket
O for of
D for division
M for multiplication
A for addition
S for Subtraction
10+4-4
14-4
10 Answer..
Answer:
10
Step-by-step explanation:
Using order of operations as stated in PEMDAS , that is
division is performed before addition/ subtraction , then
10 + 8 ÷ 2 - 4
= 10 + 4 - 4
= 14 - 4
= 10
The supply station donated 115 notebooks to mrs.Michale to give to her class there are 28 students in her class mrs.Michale gives each student the same number of notebooks how many notebooks does she give each student
Answers
Answer:
4.107
Step-by-step explanation:
115/28=4.107
Which relation is not a function?
Answers
Answer:
A
For something to be a function every x value bust have at most 1 y value and in A 9 has 2 y values so it cant be a function
The triangular prism has a length of 40 centimeters, an end base of 5 centimeters, and an end height of 7 centimeters. What is the volume of this prism?
Answers
Step-by-step explanation:
volume of triangular prism= area of cross section *length
volume of triangular prism= area of cross section *lengthv=(1/2bh)l
volume of triangular prism= area of cross section *lengthv=(1/2bh)lv=?,b=5,h=40
volume of triangular prism= area of cross section *lengthv=(1/2bh)lv=?,b=5,h=40 =(1/2*5*7)40
volume of triangular prism= area of cross section *lengthv=(1/2bh)lv=?,b=5,h=40 =(1/2*5*7)40 =(35/2)40
=17.5*40
=700cm³
The volume of triangular prism is 700cm³
Answer:
The volume of triangular prism=700cm^3
Step-by-step explanation:
Good luck
-Sweety<3Need help ASAP!!!!Make sure you can explain your answer
Answers
Answer:
see below
Step-by-step explanation:
point A(x,y) becomes A'(-x,-y).
So point E (-3,-5) becomes E'( 3,5)
F (-1,-1) becomes F'(1,1)
and G (0,-5) becomes G'( 0,5)
For the Parabolay = (x + 7)2 – 3. the equation for the Line Of Symmetry is
Answers
Answer:
Hello
Step-by-step explanation:
Axis of symmetry is vertical:
x=-7 (since (-7,-3) is the vertex)
Answer:
x = -7
Step-by-step explanation:
y = (x+7)^2 -3
This is in vertex form
y =a(x-h)^2+k where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h
y = (x- -7)^2 -3
x = -7
make x the subject of the formula x(a-b)=a(b-x).
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]x(a-b)=a(b-x)\\\\x(a-b)=ab-ax\\\\x(a-b)+ax=ab\\\\x(a-b+a)=ab\\\\x(2a-b)=ab\\\\\\x=\dfrac{ab}{2a-b} \ if\ 2a-b\neq 0[/tex]
Answer:
[tex]{ \sf{x(a - b) = a(b - x)}} [/tex]
Open the brackets:
[tex]{ \sf{ax - bx = ab - ax}} \\ { \sf{2ax - bx= ab }}[/tex]
Factorise out x:
[tex]{ \sf{x(2a - b) = ab}} \\ { \sf{x(2a - b) = ab}} \\ { \sf{x = \frac{ab}{2a - b} }}[/tex]
Geometry, please answer question ASAP
Answers
Answer:
Step-by-step explanation:
D
Trigonometry help needed
help would be appreciated
Answers
Answer:
Step-by-step explanation:
Question 5
Part A
if Sin(x) = - 3/5 and tan(x) < 0
you are told 3 things
cos(x) must be plus because there are 4 quads. Everybody is plus in quad 1. Sin and tan are <0 so you must be in quad 4 where cos(x) => 0From sin^2(x) + cos^2(x) = 1, we get that cos(x) = 4/5Tan(x) = sin(x) / cos(x)tan(x) = Sin(x)/cos(x)
tan(x) = -3/5 // 4/5
Tan(x) = -3/4
Part B
cos(2x) = cos^2(x) - sin^2(x)
cos(2x) = (4/5)^2 - (-3/5)^2
cos(2x) = 16/25 - 9/25
cos(2x) = 7/25
Part B
x + y = 90
sin(x +y) = 1
Sin(x - y) =
Sorry can't do this part. I don't know what this is equal to.
Create a triangle of your choice on the grid. Measure the lengths of all the sides on the triangle and record them in the table.
Answers
Step-by-step explanation:
The program I used tells me the lengths, though I could use the law of cosines or Pythagoras's Therom for this.
AB: 2
BC: 3
AC: About 3.61
Also, point A is (-2, 4), point B is (-2, 2), and point C is (1, 2)
Hope this helps!
Pls help me it’s algebra
Answers
Answer:
x^2 + 13x + 2
Step-by-step explanation:
The perimeter is all of the sides added up.
11 + 3x + x^2 + 2 -(-6x+5) + 2/5(10x-15)
11 + 3x + x^2 + 2 + 6x -5 + 4x - 6
x^2 + 13x + 2
Basically, we combine like terms and you will get a final answer of:
x^2 + 13x + 2.
This is the simplified expression! I hope this helped.
I just need help with #15 … can someone please help me.. show step by step
Answers
Step-by-step explanation:
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The tax rate in a certain city is 10.25% Arnold makes a $310.50 purchase there. How much will Arnold pay in tax? How much will he pay in all?
Tax: $______
Total: $_____
Answers
Answer:
tax=31.83 and total=278.67
Step-by-step explanation:
310.50×10.25/100
Tax=31.83
Total=310.50-31.83
=278.67
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2
3
4
TIME REMAINING
55:50
In May, there were 14 days where the temperature was above 60°F and 17 days when it was below 60°F There were
also 19 days that were sunny. If a two-way table is made to represent the data, which could be the row and column
headings?
O column: sunny, below 60°F, row. not sunny, above 60°F
O column: above 60°F, below 60°F, row: sunny, not sunny
O column: above 60°F, sunny, row: below 60°F, not sunny
O column: sunny, month; row: not sunny, month
Mark this and return
Save and Exit
Next
Submit
Answers
A two-way table is such that has two categorical variables and as such, the data are presented in rows and columns.
The correct row and column headings for the given dataset are:
Column: above 60°F, below 60°F, Row: sunny, not sunny
Given that:
[tex]Above\ 60^oF=14[/tex]
[tex]Below\ 60^oF=17[/tex]
[tex]Sunny = 19[/tex]
The two-way table would have the following representations;
Above [tex]60^oF[/tex] and Below [tex]60^oF[/tex] as the column entriesSunny and not sunny as the row entriesThe following representations are also possible
Above [tex]60^oF[/tex] and Below [tex]60^oF[/tex] as the row entriesSunny and not sunny as the column entriesBase on the above representations, we can conclude that options (b) is true
Read more about two-way tables at:
https://brainly.com/question/20608299
paul leaves for school at 7:25 am he returned home at 3:15 pm how long was paul away from home?
Answers
Answer:
8 hours 10 minutes
I hope this answers your question
Answer: paul has been away from home for 7 hours and 50 minutes.
Step-by-step explanation:
. A cook buys six pumpkins. The mean mass of these pumpkins is 2,1 kg. The heaviest pumpkin, which has a mass of 3 kg, is used first. Calculate the mass of the remaining five pumpkins.
Answers
Answer:
9.6kg
Step-by-step explanation:
If the mean mass is 2.1 we can count the mass of these six pumpkins
the total mass of the pumpkins divided by the quantity of them is equal 2.1
TO find the mass multiply 2.1 by the quantity of them (6)
2.1*6=12.6 - the summary weight of six pumpkins
12.6-3=9.6 - the remainder after using the heaviest pumpkin
STEM The diagram shows the structure of a molecule of sulfur dioxide. The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. How many oxygen atoms (O) are there when there are 6 sulfur atoms (S)? Explain how you got your answer.
Answers
The ratios of oxygen atom and sulfur atom is an illustration of equivalent ratios.
There are 12 oxygen atoms, when the number of sulfur atom is 6.
From the diagram, we have:
[tex]S = 1[/tex]
[tex]O_x = 2[/tex]
So, the ratio is:
[tex]S : O_x = 1 : 2[/tex]
When there are 6 sulfur atoms, the equation becomes
[tex]6 : O_x = 1 : 2[/tex]
Express as a fraction
[tex]\frac{O_x}{6}= \frac{2}{1}[/tex]
Multiply both sides by 6
[tex]O_x = 2 \times 6[/tex]
[tex]O_x =12[/tex]
Hence, there are 12 oxygen atoms
Read more about equivalent ratios at:
https://brainly.com/question/18230617
PLEASE I JUST WANT A GOOD GRADE The spinner below shows 10 equally sized slices. Diane spun the dial 50 times and got the following results.
Outcome White Grey Black
Number of Spins 19 13 18
Fill in the table below. Round your answers to the nearest thousandth.
Answers
Part (a)
The experimental or empirical probability is based on the results shown in the table. There are 13 instances of grey out of 50 spins total. Therefore, we end up with an experimental probability of 13/50. This converts to the decimal form 0.26
Answer: 0.26===============================================
Part (b)
Since each slice is of equal size, this means theoretically each slice should have the same chance of being landed on. We have 3 grey slices out of 10 total. The probability of landing on a grey space is 3/10 = 0.3
Answer: 0.3===============================================
Part (c)
Answer: Choice A)As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
The theoretical probability is locked to 0.3 the whole time (only the experimental probability changes). This is according to the Law of Large Numbers.
