The axis of symmetry of a parabola is the line x = 6. What is the x-coordinate of the vertex of the parabola?
Answer:
x-coordinate of the vertex: h = 6.
Step-by-step explanation:
The axis of symmetry is an imaginary line that divides the graph of a parabola into two congruent parts. The vertex of a parabola, (h, k) is the point where the graph intersects the axis of symmetry.
In the standard form of quadratic equation, y = ax² + bx + c:
[tex]\large \sf{axis\:of\:symmetry:\:x\:=\:\frac{-b}{2a}}[/tex]
In the vertex form of quadratic function, y = a(x - h)²+ k:
[tex]\large \sf{axis\:of\:symmetry:\:h\:=\:\frac{-b}{2a}}[/tex]
Hence, the axis of symmetry is the point where x = h.
Given these definitions, we can infer that the x-coordinate of the axis of symmetry is the same as the x-coordinate of the vertex, where h = 6.
Ms. Mary spent $192 less than Ms.Mona on supplies for their class. Together they spent a total of $988. How much did each person spend?
Answer:
Ms. Mona and Ms. Mary spent $590 and $398 respectively.
Step-by-step explanation:
Total spent= $988
Ms. Mary +Ms. Mona= $988
Since Ms. Mary spent $192 less than Ms. Mona,
(Ms. Mona -$192) +Ms. Mona= $988
2(Ms. Mona)= $988 +$192
2(Ms. Mona)= $1180
Amount Ms. Mona spent
= $1180 ÷2
= $590
Since Ms. Mary spent $192 less than Ms. Mona,
amount Ms. Mary spent
= $590 -$192
= $398
Alternatively, since the total spending is $988,
amount Ms. Mona spent
= $988 -$590
= $398
Which graph represents a proportional relationship?
Answer: The first graph
Step-by-step explanation:
A proportional graph always goes through the origin
Answer:
The first graph
Step-by-step explanation:
Determine the intercepts of the line.
Do not round your answers.
y = 4r +7
Answer:
(-7/4, 0) (0, 7)
Step-by-step explanation:
I'm assuming r is x
0=4r+7
r=-7/4
y=0r+7
y=7
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y2; about y = 1
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.
Procedure - Determination of the volume of a solid of revolutionLet [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].
The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:
[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)
After substituting on each function and simplifying terms we get the following integral:
[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]
[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]
And the volume of the solid of revolution is:
[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]
[tex]V = \frac{11\pi}{30} [/tex]
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]
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Answer:
24.3
Step-by-step explanation:
Answer:
The answer would be 24.3
Select the correct answer
Consider the given solids with the dimensions shown. Which solids are similar?
Aonly figure 1 and figure 2
B.only figure 2 and figure 3
c.only figure 1 and figure 3
D. all three figures
E none of the figures
only figure 1 and figure 3 are similar.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
In figure 1, two of the sides (16 and 9 ) are perfect square and third is not.
If we take the ratio of three side as
16:9:12
(4)²:(3)²:(2√3)²
Similarly, In figure 3 two of the sides (64 and 36 ) are perfect square and third is not.
If we take the ratio of three side as
64:36:48
(8)²:(6)²:(4√3)²
Comparing the ratios of both figure, the figure 3 has twice the measurement of figure 1 sides.
Hence, only figure 1 and 3 are similar.
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Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truck (not the least of which is that it runs). The new truck would cost $55,440. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,400. At the end of 8 years, the company will sell the truck for an estimated $27,700. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset’s estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company’s cost of capital is 8%.
The payback period of the investment is 6.6 years.
The net present value is $7,797.22.
The payback period calculates the amount of time it takes to recover the amount invested from the cumulative cashflows.
Payback period = Amount invested / cost saving
$55,440 / $8,400 = 6.6 years
Net present value is the present value of after-tax cash flows from an investment less the amount invested.
NPV can be determined using a financial calculator
Cash flow in year 0 = $-55440
Cash flow in year 1 to 7 = $8,400
Cash flow in year 8 = $8400 + $27,700
I = 8%
NPV = $7,797.22
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if y=x^3+3 find the value of y when x=2
Answer:
11
Step-by-step explanation:
Substitute [tex]x=2:[/tex]
[tex]y=x^3+3[/tex]
[tex]y=2^3+3\\ =8+3\\ =11[/tex]
f(x)=(1/7)^x then what is f(-3)
Answer:
[tex]f(-3)=343[/tex]
Step-by-step explanation:
[tex]f(x)=(\frac{1}{7} )^x[/tex]
Plug -3 into x and solve using the negative power rule:
[tex]x^{-a}=\frac{1}{x^a}[/tex]
[tex]f(-3)=(\frac{1}{7} )^{-3} \\\\f(-3)=\frac{1}{\frac{1}{7}^3 } \\\\f(-3)=\frac{1}{\frac{1}{343} } \\\\f(-3)=343[/tex]
Sorry, those fractions got very small. Let me know if I need to clarify anything there
Scores in the first and final round for a sample of 8 golfers who completed golf tournament as shown below. Golfer First Round Final Round 1 73 78 2 68 75 3 70 66 4 67 71 5 71 73 6 70 68 7 68 65 8 73 72 a. State any appropriate hypothesis that can be tested for the above data. Use 2% level of significance to test the stated hypothesis. Use p-value approach
Answer:
golfing is fun but not to fun
Step-by-step explanation:
What is the solution to
4
+ 5 = 2 ?
X-3
Answer:
what you men
Step-by-step explanation:
Answer:
This may not be right, but I tried! I believe its 6.
Step-by-step explanation:
Skajekjejejwjejekwjkekekekejeje
Answer:
Skajekjejejwjejekwjkekekekejeje!!!
Step-by-step explanation:
Answer: lollllll , ?????
Step-by-step explanation:
Please help! Will give 50 points!!
Answer:
- 5 | - 1 | 3 | 7Step-by-step explanation:
Given function:
y = 2x + 3Complete table by finding y values:
x = - 4 ⇒ y = 2*(-4) + 3 = - 8 + 3 = - 5x = - 2 ⇒ y = 2*(-2) + 3 = - 4 + 3 = - 1x = 0 ⇒ y = 2*0 + 3 = 0 + 3 = 3x = 2 ⇒ y = 2*2 + 3 = 4 + 3 = 7If the side of a square is increased by 25%, then by how much is its area increased?
Answer:
56.25%Step-by-step explanation:
If a variable X changes by A% and another variable Y changes by B%, then overall net change when the two variables are multiplied is given by :
A + B + AB/100
If the change is “increase” it is positive & if the change is “decrease” it is negative.
In the given question, A = B = 25% ( Both positive as length increase )
And area = Side x Side
Applying our versatile relation :
Net increase in area = 25 + 25 + (25x25)/100 = 56.25%
PLEASE HELP URGENT
use the graph to solve the equation. the topic is quadratic equations
pic attached with graph & equation
Answer:
3 and-2
Step-by-step explanation:
The point of intersection
Answer:
x=-2, x=3
Step-by-step explanation:
x²-x-6=0
x²-3x+2x-6=0
x(x-3)+2(x-3)=0
(x+2)(x-3)=0
In 20Pg how many choices are
there for the eighth batter for a
line-up of 9 out of 20?
A. 20
B. 14
C. 13
Answer:
13
Explanation-
It is 13 because it is the only one out of all of them that makes sense.
For the ²⁰ P ₉ the required number of choices are 6.0949324 x 10¹⁰.
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
In the given question,
In ²⁰ P ₉, the number of choices are to be found.
To find the choices,
Expand ²⁰ P ₉ by using a formula,
[tex]\rm ^nP_r = n!/(n-r)![/tex]
The number of choices
= 20!/ (20 -9)!
= 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11!/ 11!
= 6.0949324 x 10¹⁰
The required number of choices are 6.0949324 x 10¹⁰.
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The complete question is given below.
A company borrows $50,000 for 8 years at a simple interest rate of 13.5%. Find the interest paid on the loan and the total amount paid
The interest paid on the loan is $
The total amount paid is $
Answer:
13.5%×50000=6750
this is interest paid on loan 6750
50000+6750=56750
The total amount paid
An adult elephant eats about 300 pounds of food each day. Write an
expression to represent the number of pounds of food a herd of
12 elephants eat in/5 days.
Answer:
18000
Step-by-step explanation:
you multiply 12 by 300 which is 3600 then you would multiply by 5 and its 18000.
Hasan plans to choose a book from a section of the store where everything is 25%
off He writes the expression d 0.25d to find the sale price of the book if the original
price is d dollars.
Bella correctly writes another
expression. 0.75d, that will also find the sale price of the
book if the original price is
I/ dollars,
Use the drop-down menus to explain what each part of Hasan's and Bella's
expressions mean.
Hasan's Expression: d - 0.25d
d: Original price0.25: percent discount 0.25d: amount of discountd - 0.25d: sale price--------------------
Bella's Expression: 0.75d
0.75: percent of original priced: original price0.75d: sale price=============================================
Explanation:
The variable d stands for the original price. The store is offering a 25% sale, which means that Hasan will save 25% of the original price. This means 0.25d represents the amount he saves (aka the discount amount).
For instance, let's say d = 100 is the original price. 25% of this is 0.25d = 25 dollars. So if the book is originally $100, then he saves $25.
As you can probably guess, the 0.75 comes from 1 - 0.25 = 0.75; it indicates that if Hasan saves 25%, then he still has to pay the remaining 75%
Notice how d - 0.25d = 1d - 0.25d = (1-0.25)d = 0.75d which points to the sale price being 75% of the original price d.
Identify the set of perpendicular lines in this image.
A) AB, CD
B) CD, EF
C) AB, EF
D) AB, FE
Answer:
AB, CD
Step-by-step explanation:
there is ⊥ 90° angle sign between them AB and CD.
They are perpendicular
Which expression is equivalent to 4w (-6w)
0 -2w3
O-202
0-24w3
0-24w2
Step-by-step explanation:
4w(-6w)
= (4*6)(w.-w)
= 24 * -w²
= -24w²
4. Ms. Bragg is giving a test worth 100 points. The test contains a total of 40 questions. Some questions are worth 2 points and some questions are worth 4 points on the test. Write a system of equations to determine how many of each type of question are on the test. A) Define your variables. You can use any letters you want) B) Write your system of equations. (There should be 2 separate equations)
9514 1404 393
Explanation:
A)
Let t and f represent the numbers of two-point and four-point questions, respectively.
__
B) The number of points for each type of question is the product of the point-value per question and the number of questions of that type.
2t + 4f = 100 . . . . . the test is worth 100 points
t + f = 40 . . . . . . . . there are 40 questions on the test
_____
Additional comment
The test will have 30 two-point questions and 10 four-point questions.
Hello i need some help here the answer
A.x−3y=6 5x−y=10
B.3x−4y=24 2x+3y=−6
C.2x−9y=18 7x−2y=14
D.x−8y=16 5x+2y=20
9514 1404 393
Answer:
A. x −3y = 6; 5x −y = 10
Step-by-step explanation:
The first table gives the x- and y-intercepts, so you can write the equation for the line in intercept form as ...
x/a +y/b = 1 . . . . . . x-intercept = a; y-intercept = b
The x-value with y=0 is a=6; the y-value with x=0 is b=-2. So, the equation of the line for the first table is ...
x/6 +y/-2 = 1
Multiplying by 6 gives ...
x -3y = 6
The only matching equation is in answer choice A.
__
You can check that the second given equation in choice A matches the second table:
for (x, y) = (-3, -25), you have ...
5(-3) -(-25) = -15 +25 = 10 . . . . as required
The number 1000 has been rounded to the nearest 100. Find its lower and upper bounds.
The lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
What are the lower and upper bound?
The lower bound is the smallest value that would round up to the estimated value.
The upper bound is the smallest value that would round up to the next estimated value.
Here the number 1000 is rounded to the nearest 100 will be:
The Lower bound will be 950.
The Upper bound will be 1050
Hence the lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
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A family buys airline tickets online. Each ticket costs $208. The family buys travel
insurance with each ticket that costs $16 per ticket. The web site charges a fee of
$22 for the entire purchase. The family is charged a total of $1142. How many
tickets did the family buy
Answer:
5 tickets
Step-by-step explanation:
Each ticket costs $224 including the travel insurance and they are charged $22 regardless of the number of tickets they buy.
Therefore, the equation is 224x + 22 = 1142
First, you have to subtract the 22 from both sides to amount to 224x = 1120
Now, you divide 224 from 1120 to get 5
The family bought 5 tickets.
Mr. Walthour is building a storage in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth.
I need help with this :///
9514 1404 393
Answer:
f(x) = -3/2x +5
Step-by-step explanation:
The differences between the x-values are all 2.
The differences between the y-values are all -3.
When the ratios of the differences are constant, the function is linear. The slope is ...
m = Δy/Δx = -3/2
The y-intercept is given by the table value where x=0: b=5.
Then the slope-intercept equation is ...
f(x) = mx +b
f(x) = -3/2x +5
Given that m||n, find the value of x.
Answer:
[tex] \boxed{ \sf{x = 65 \degree}}[/tex]
Step-by-step explanation:
In the given figure we have two corresponding angles.
We know that corresponding angles are equal to each other
So,
2x+5 = 1352x = 135 - 52x = 130x = 130/2x = 65Therefore, x = 65°
Corresponding angles are same
[tex]\\ \sf\longmapsto 2x+5=135[/tex]
[tex]\\ \sf\longmapsto 2x=135-5[/tex]
[tex]\\ \sf\longmapsto 2x=130[/tex]
[tex]\\ \sf\longmapsto x=130/2[/tex]
[tex]\\ \sf\longmapsto x=65°[/tex]
25 points! Help (Vectors)
Answer:
[tex]7\cos(30^{\circ})[/tex]
Step-by-step explanation: