4. Describe the following graph completely
a. Where is the vertex of the parabola?
b. Is there a line of symmetry? If so, draw it in.
c. Are there any x-intercepts? If so, name them. d. Are there any y-intercepts? If so, name them.
Answers
Related Questions
Determine if this series converges or diverges. Find the sum if possible. 250, 50, 10...
Answers
Answer:
50
Step-by-step explanation:
Answer:
312.5
Step-by-step explanation:
We have the series: 250, 50, 10...
As we can see, each subsequent term gets smaller and smaller. Eventually, it will be infinitesimally small. So, our series converges.
We can also see this from our common ratio. Each term is 1/5 of the previous term. Since our r 1/5 is less than 1, our series will converge.
Since it converges, we can indeed find our sum. First, we can write our series using summation. This will be:
[tex]\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }[/tex]
We can use the following infinite geometric series formula:
[tex]\displaystyle{\sum_{n=0}^{\infty} ar^n=\frac{a}{1-r}[/tex]
So, let's substitute 250 for a and 1/5 for r. This yields:
[tex]\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=\frac{250}{1-\frac{1}{5}}[/tex]
Subtract:
[tex]\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=\frac{250}{\frac{4}{5}}[/tex]
Divide. So, our series converges to:
[tex]\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=312.5[/tex]
And we're done!
The weekly revenue for a company is r=−3p2+70p+102, where p is the price of the company's product. Use the discriminant to find whether there is a price for which the weekly revenue would be $1500.
Answers
Step-by-step explanation:
$1500 = 3p^2 + 70p + 102
0 = 3p^2 + 70p - 1398
0 = (x=12.87 or x=-36.2)
What is the equation of the line that passes through the point ( -2, 7) and has a slope of zero?
A) x = 7
B) y = - 2
C) x = - 2
D) y = 7
Answers
Answer:
D) y= 7
Step-by-step explanation:
y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.
Step-by-step explanation:
Given:
Let,
A ≡ ( x1 , y1 ) ≡ ( -2, 7 )
Slope = m = 0
To Find :
Equation of Line:
Solution:
What is an equation of the line that passes through the points (-6,5) and (6,7)
Answers
Answer:
y = 1/6 x + 6
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (7-5)/(6-(-6))
m = 2/12 = 1/6
Substitute x and y values with a pair of coordinates,
y = mx+c
7 = 1/6(6) + c
7 = 1 + c
c = 6
Thus, the equation is y = 1/6 x +6
Write a quadratic function in standard form with zeros -4 and -3
Answers
Answer:
y = x² + 7x + 12
Step-by-step explanation:
Given the zeros x = - 4 and x = - 3, then the corresponding factors are
(x - (- 4) ) and (x - (- 3) ), that is
(x + 4) and (x + 3)
The function is then the product of its factors
y = (x + 4)(x + 3) ← expand using FOIL
= x² + 7x + 12
i’ll give brainliest
Answers
The sum of three consecutive even integers is 138.Find the integers
Answers
Answer:
The 3 integers are 44, 46, 48
Step-by-step explanation:
The integers are:
Let the three consecutive even integers be denoted as :
x,x+2,x+4
x+x+2+x+4=138
3x+6=138
3x=138−6
3x=132
x=132/3
x=44
The integers are:
x=44
x+2=46
x+4=44+4=48
Complete the paragraph proof to prove the statement.
Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF
Prove: m∠ABC = m∠GHI
We are given that angle ABC and
are congruent, and that angle GHI and angle DEF are congruent. By the
, the measure of angle ABC is equal to the measure of angle DEF, and the measure of angle GHI is equal to the measure of angle DEF. By the substitution property, the measure of angle ABC is equal to
.
Answers
Answer:
1. angle DEF
2. definition of congruent angles
3. the measure of angle GHI
Step-by-step explanation:
The statement are
Angle DEFDefinition of congruent anglesAngle GHIWhat is Congruence?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Given:
∠ABC ≅ ∠DEF and
∠GHI ≅ ∠DEF
1. Angle ABC and angle DEF are congruent
2. By the definition of congruent angles, the measure of angle ABC is equal to the measure of angle DEF.
3. By the substitution property, the measure of angle ABC is equal to the measure of angle GHI.
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How do you solve a simple equation?
Answers
Answer:
Solving Simple Equations
When solving a simple equation, think of the equation as a balance, with the equals sign (=) being the fulcrum or center. Thus, if you do something to one side of the equation, you must do the same thing to the other side. Doing the same thing to both sides of the equation (say, adding 3 to each side) keeps the equation balanced.
Solving an equation is the process of getting what you're looking for, or solving for, on one side of the equals sign and everything else on the other side. You're really sorting information. If you're solving for x, you must getx on one side by itself.
Step-by-step explanation:
Addition and subtraction equations
Some equations involve only addition and/or subtraction.
Example 1
Solve for x.
x + 8 = 12
To solve the equation x + 8 = 12, you must get x by itself on one side. Therefore, subtract 8 from both sides equation
X+8=12
- 8 - 8
_____ _____
X = 4
To check your answer, simply plug your answer into the equation:
X+8=12
(4)+8=12
12=12
est
If f(x) = x2 - 1. find f(-1)
Answers
Answer:
f(-1) = 0
Step-by-step explanation:
Step 1: Define
f(x) = x² - 1
f(-1) is x = -1
Step 2: Substitute and Evaluate
f(-1) = (-1)² - 1
f(-1) = 1 - 1
f(-1) = 0
Robert earned $10, which was 4 less thank twice what Eric made, How much mint did Eric earn?
Answers
Answer:
12
Step-by-step explanation:
Answer:
$16
Step-by-step explanation:
First we would calculate twice of ten which is 20 then we subtract 4 from 20 which would be 16 and that is how you found your answer.
Hope this helps!! :)
All of the following numbers are rational except
O 25
O √17
O √121
O V1.44
Answers
In 2000, there were an estimated 5.28 million digital cable subscribers in the United States. The expected increase is 2.61 million by 2006. On average, over each of those 6 years how many new digital cable subscribers per year would be expected?
a.
1.315 million per year
c.
0.88 million per year
b.
0.435 million per year
d.
0.445 million per year
Answers
Answer:
D
Step-by-step explanation:
I am taking the practice.
Answer:
I just took the test and got the answer wrong, the CORRECT answer is B.0.435 million per year
Step-by-step explanation:
I hope this helps you out, because I got the answer wrong when I used the answer D. So the correct answer is B.
Have le good day.
what is the slope for a line that is parallel to the line y=2/5x-4
Answers
Answer:
2/5
Step-by-step explanation:
The slope of the line
y=2/5x-4
is 2/5 since it is in the form y = mx+b where m is the slope
Parallel lines have the same slope so a line that is parallel to y=2/5x-4 has a slope of 2/5
Write an expression that is equivalent to 7^3/4
Answers
Part 1:
What is the unit rate for this situation ?
Answers
Step-by-step explanation:
every bracelet that is made, 0.75 yards of string is used.
The center of an ellipse is (-9,3). One focus is (-6,3). The
major axis is 14 units long.
What is the equation of the ellipse in standard form?
Enter your answer by filling in the boxes.
Answers
Answer:
49 in first box, 40 in second box. I took the test.
The equation of an ellipse with center (-9, 3), focus (-6, 3) and major axis length of 14 units is [tex]\frac{(x+9)^2}{49} + \frac{(y-3)^2}{40}= 1[/tex]
The standard form of the equation of an ellipse is:
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}= 1[/tex]
The center of the ellipse, (h, h) = (-9, 3)
That is, h = -9, k = 3
The length of the major axis = 14 units
The length of the major axis = 2a
2a = 14
a = 14/2
a = 7
a² = 7²
a² = 49
The coordinates of the foci are [tex](h \pm c, k)[/tex]
One of the foci = (-6, 3)
h - c = -6
-9 - c = -6
c = -9 + 6
c = -3
[tex]c^2 = a^2 - b^2\\(-3)^2 = 7^2 - b^2\\9 = 49 - b^2\\b^2 = 49 - 9\\b^2 = 40[/tex]
Substitute a² = 49, b² = 40, h = -9, and k = 3 into the equation [tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}= 1[/tex]
[tex]\frac{(x+9)^2}{49} + \frac{(y-3)^2}{40}= 1[/tex]
The equation of an ellipse with center (-9, 3), focus (-6, 3) and major axis length of 14 units is [tex]\frac{(x+9)^2}{49} + \frac{(y-3)^2}{40}= 1[/tex]
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Which type of factoring is required to change x2 - 16 into factored form?
a.)Greatest Common Factor
b.) Difference of Squares
c.) Trinomial Factoring
Answers
Hopes this helps
what are the next 2 numbers in the pattern -6,48,-24,12...
Answers
Answer:
-6,48,-24,12,-6, 3
What is the point slope form
Answers
Answer:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Step-by-step explanation:
Answer: y - 2 = -6/5(x - 0)
You use the equation (y - y1) = m(x - x1)
Where y1 and x1 are coordinates of a point on the equation.
If the y intercept is 2, then the point (0, 2) is on the equation.
There are 100 bolts in 5 bookcases. What is the unit rate in bolts per bookcase?
Answers
Answer:
20/1
Step-by-step explanation:
The unit rate in bolts per bookcase is 20bolts per bookcase
What is unit rate?There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.
We are Given that 100 bolts in 5 bookcase
We need to find the unit rate in bolts per bookcase
Number of bolts in 5 bookcases= 100
Number of bolts in 1 bookcases= 100/5
= 20
So, it will be 20 bolts everyday
Thus, the unit rate is 20bolts/sec
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he ratio of pens to pencils in Mrs. Bosworth's desk is 3:1. What does this mean?
A.
There are 3 more pens than pencils.
B.
There are 2 more pens than pencils.
C.
For every 3 pencils, there is 1 pen.
D.
For every 3 pens, there is 1 pencil.
Answers
Help me solve this problem please
Answers
What two elements have properties that are most similar
Answers
Answer:
Lithium and Magnesium
Step-by-step explanation:
Answer: Sodium and Potassium.
Step-by-step explanation: Both are alkali metals and are in group 1 of the periodic table.
11)
What is the perimeter of a square with an area of 529 cm??
A)
92 cm
138 cm
x
C)
184 cm
D)
256 cm
Answers
Answer:
92
Step-by-step explanation:
What is the midpoint between the ordered pairs (10,-4) and (-9, 11)?
0 (0.5,3.5)
O (10.5,3.5)
O (-0.5, -0.5)
O (-10.5, -0.5)
Answers
Answer:
The answer would be (-0.5, -0.5)
Step-by-step explanation:
This is because when you solve for a mid-point you it's like solving for an average. You would take x1 and x2 and you would find the difference between them. Which would be -0.5. You do the same with y1 and y2. Which would be 3.5.
Jessica wants to earn at least a B this grading period, which is an average of an 85. So far Jessica has earned a 90, 75, and 88 on three tests. What is the least grade she can score on the fourth test to reach her goal?
Answers
Answer:
87
Step-by-step explanation:
i think please dont get mad if im wrong
What is the value of 5 in 28,251
Answers
Answer:hundredths
Step-by-step explanation:
Just know
Answer:
I think it’s 10
Step-by-step explanation:
what is 710,000 to the neareast ten thousand
Answers
Answer:
710,000
Step-by-step explanation:
can someone plz ezplain this step by step im ready behind
Answers
Answer:
It would be B and C I'm pretty sure
Step-by-step explanation:
Answer:
-2.5z+5y-8
Step-by-step explanation: