Answers
a. We can see that this parabola opens downward, as in this example,
b. The axis of symmetry equation of a parabola whose vertex is (h, k) and opens up/down is: x = h. Therefore, the equation is x = 1
c. The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. In this case, it is (1,9)
d. Intercepts,
The x -intercepts are the points at which the parabola crosses the x -axis. If they exist, the x -intercepts represent the zeros, or roots, of the quadratic function, the values of x at which y=0 .
Therefore, x-intercepts: -2,4
The y -intercept is the point at which the parabola crosses the y -axis.
Therefore, y-intercept: 8
Related Questions
A firm has the marginal-demand function where D(x)=-1400x÷√25-x² is the number of units sold at x dollars per unit. Find the demand function given that D=17,000 when x=3 per unit.
The demand function is D(x)=
Answers
The equation of the demand function is D(x) = 1400√(25-x²) + 11400
How to determine the demand function?From the question, we have the following parameters that can be used in our computation:
Marginal demand function, D'(x) = -1400x÷√25-x²
Also, we have
D = 17000, when the value of x = 3
To start with, we need to integrate the marginal demand function, D'(x)
So, we have the following representation
D(x) = 1400√(25-x²) + C
Recall that
D = 17000 at x = 3
So, we have
17000 = 1400√(25-3²) + C
Evaluate
17000 = 5600 + C
Solve for C
C = 17000 - 5600
So, we have
C = 11400
Substitute C = 11400 in D(x) = 1400√(25-x²) + C
D(x) = 1400√(25-x²) + 11400
Hence, the function is D(x) = 1400√(25-x²) + 11400
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The scale of a map says that 4 cm represents 5 km. I What distance on the map (in centimeters) represents an actual distance of 4 kilometers? cm Question 5B
Answers
Answer: 3.2 cm
Step-by-step explanation: 4 ÷ 5 = 0.8
0.8 × 4 = 3.2
Ismelda watches a soap bubble resting on a driveway. The bubble is in the shape of a hemisphere. When the bubble pops, the soap residue left behind is in the shape of a circle with the same diameter as the hemisphere. Ismelda measures the diameter of the bubble as 6 inches. What volume of air was in the hemisphere before the bubble popped? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is .)
37.7 cu. in.
56.5 cu. in.
113.0 cu. in.
904.3 cu. in.
Answers
Answer:
56.5 cu.in
Step-by-step explanation:
Diameter is 6 inches,then radius(r)=3 inches
volume of hemisphere=2/3πr^3
=2/3×3.14×3×3×3
=2×3.14×3×3
=2×3.14×9
=56.52 cu.in
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
Ay
F(-2,4) AO, 4)
N
E-2, 2)
B(2,0)
4 x
-4 -2
D(0, -2)
-C(2,-2)
The perimeter is about how many
units.
Answers
Perimeter of the given polygon is 16.94 units.
To measure the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the ex[pression,
Distance = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
By using this expression,
Distance between A(0, 4) and B(2, 0) = \(\sqrt{(0-2)^2+(4-0)^2}\)
= \(\sqrt{20}\) units
Distance between B(2, 0) and C(2, -2) = \(\sqrt{(2-2)^2+(0+2)^2}\)
= 2 units
Distance between C(2, -2) and D(0, -2) = \(\sqrt{(0-2)^2+(-2+2)^2}\)
= 2 units
Distance between D(0 -2) and E(-2, 2) = \(\sqrt{(0+2)^2+(-2-2)^2}\)
= \(\sqrt{20}\) units
Distance between E(-2, 2) and F(-2, 4) = \(\sqrt{(-2+2)^2+(2-4)^2}\)
= 2 units
Distance between F(-2, 4) and A(0, 4) = \(\sqrt{(-2-0)^2+(4-4)^2}\)
= 2 units
Perimeter of ABCDEF = AB + BC + CD + DE + EF + FA
= \(\sqrt{20}+2+2+\sqrt{20}+2+2\)
= \(8+2\sqrt{20}\)
= 16.94 units
Therefore, perimeter of the given polygon in the graph attached is 16.94 units.
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Answers
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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A 4-sided polygon is classified as a quadrilateral.
True
False
Answers
Answer:
TRUEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answers
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
Calc II Question
Find the volume of the solid obtained by rotating the region bonded bt the given curves about the specified line.
Y = e^-x
Y = 1
X = 2
About the Y = 2
Answers
Answer:
\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Step-by-step explanation:
This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution. I'll show how to do it with both:
Shell Method (Horizontal Axis)
\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)
Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)
Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))
Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)
Plugging in our integral, we get:
\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Washer Method (Parallel to x-axis)
\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)
Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))
Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))
Bounds: \([a,b]=[0,2]\)
Plugging in our integral, we get:
\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)
\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!
Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.
I ABSOLUTELY NEED HELP BY TOMORROW!!! I AM GIVING 100 POINTS
Answers
3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
How to Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:
3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup
Since there are 1 cup in each term, we can rewrite it as:
3 cups + (1/2) cup
Now, we can express each term as a multiplication expression:
3 cups = 3 * 1 cup = 3
(1/2) cup = (1/2) * 1 cup = 1/2
Putting it all together, the multiplication expression is:
3 * 1 cup + (1/2) * 1 cup = 3 + 1/2
Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
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what is the answer to this equation 21 x ___=7
Answers
Answer:
the answer is 3
Step-by-step explanation:
21 x 3 =7
hope it helps
Answer:
21/7
Step-by-step explanation:
Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3
You want to take out a $219,000 mortgage (home loan). The interest rate on the loan is 4.5%, and the loan is for 30 years. Your monthly payments are $1,109.64. How much will still be owed after making payments for 15 years? Round your answer to the nearest dollar.
Answers
After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.
To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:
Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)
where:
P = the initial loan amount (in this case, $219,000)
r = the monthly interest rate (which is the annual interest rate divided by 12)
n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)
b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)
First, we need to calculate the monthly interest rate:
r = 4.5% / 12 = 0.00375 = 0.375%
Next, we can plug in the values to get:
Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)
= $145052.36
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Answer please quickly
Answers
Answer:
x-intercept = 4
y-intercept = 2
Step-by-step explanation:
Answer:
y-intercept is 2
x-intercept is 4
slope -2/4
thats all i know sorry
Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is 7 inches wide in the drawing. The actual bakery is 42 feet wide. What is the scale of the drawing?
Answers
Answer:
1:72
Step-by-step explanation:
The scale of a drawing is the ratio of the length in the drawing to the real length.
Drawing length: 7 inches
Real length: 42 ft × 12 in. / ft = 504 in.
Scale:
7 in. to 504 in.
Divide both numbers by 7:
1 in. to 72 in.
Scale: 1:72
6 sin =5 solve to the nearest 0.1
Answers
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
How many website graphics can be created?
Answers
I do not understand what do you mean
the manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 350 dollars per month. a merket survey suggests thet, on average, one additional unit will remaon vacant for each 5 dollars increase in rent. similarly, one addiotional unit will be occupied for each 5 dollar decrese in rent. what is the monthly revenue function for the manager
Answers
Answer:
Rent = $230 maximizes revenue
Step-by-step explanation: I just know ;)
HELP MIDDLE SCHOOL QUESTION
Answers
Answer:
the answer is 5.5 thank me later
Answer:
5.5
Step-by-step explanation:
Suzi starts her hike at 285 feet below sea level. When she reaches the end of the hike, she is still below sea level at −140 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answers
Answer:
• Elevation is the difference between original length and final length
\( = 285 - 140 \\ \\ = { \underline{ \: \: 145 \: \: feet \: \: }}\)
Answer:
140 ftStep-by-step explanation:
Start point = -285 ftEnd point = - 145 ftChange in elevation:
End point - Start point = -145 - (-285) = 140 ftAn elevator in a tall building goes up 7 floors then down 9 floors down 4 floors up 8 floors and down 2 floors now it it in floor 14 on what floor did the elevator start
Answers
Answer: I'm pretty sure its 14.
Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14
The temperature at 2 a.m. was -10°C.
At an earlier time the temperature was
0°C. It changed by -2°C each hour
until 2 a.m. At what earlier time was
the temperature 0°C?
Answers
Answer:
-1
Step-by-step explanation:
Describe the difference between Western Europe and Eastern Europe after WW II
Answers
Answer:
Eastern Europe were Soviet controlled communist puppet governments while the West were American, French, and British backed capitalist governments. Hope this helps
Find one value of x for which h(x)=4 and find h (-2)
Answers
the solutions are:
h(x) = 4 for x = 0h(-2) = 2How to find the value of x for which h(x) = 4?The only information of h(x) that we have is the given graph.
To find the value of x, we need to go to the vertical axis and find y = 4, then we move horizontally to the left until we meet the curve.
That intersection will give the value of x for which h(x) = 4.
Doing that, we conclude that h(x) = 4 when x = 0 (on the vertical axis).
Now we want to find h(-2), and we can do that using the graph.
By finding x = -2 on the horizontal axis and then moving up until we intercept the graph, we can see that:
h(-2) = 2
Concluding, the solutions are:
h(x) = 4 for x = 0h(-2) = 2If you want to learn more about parabolas:
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Which expression is equivalent to (f + g)(4)?
Answers
Answer:
4f + 4g
Step-by-step explanation:
Simplify. Distribute 4 to all terms in the first parenthesis by multiplication:
4(f + g) = (4)(f) + (4)(g) = 4f + 4g
4f + 4g is your answer.
~
What is the 25th term of this arithmetic sequence?-7,-3,1,5, …
Answers
Answer:
Step-by-step explanation:
nˣ=a+(n-1)d25th=-7+(25-1)425th=-7+(24×4)25th=-7+9625th=89What is the volume of a hemisphere with a diameter of 60.9 in rounded to the nearest tenth of a cubic inch
Answers
The volume of the hemisphere with a diameter of 60.9 inches rounded to the nearest tenth is 59131.7 inches³.
Given that,
Diameter of a hemisphere = 60.9 inches
We have to find the volume of the hemisphere.
We know that, radius is half the measure of the diameter.
Radius of the hemisphere = 60.9 / 2 = 30.45 inches
Volume of a hemisphere is,
Volume = 2/3 π r³
Here r is the radius
Substituting,
Volume = 2/3 π (30.45)³
= 59131.7 inches³
Hence the volume is 59131.7 inches³.
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please hurry
The equation shows the relationship between x and y: y = −4x + 9 What is the slope of the equation? (5 points) −9 −4 4 9
Answers
Answer:
-4
Step-by-step explanation:
11 of 3011 of 30 Questions
Question
A baker makes peanut butter cookies and chocolate chip cookies.
She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?
Answers
The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.
Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."
From the given information, we can set up the following system of equations:
For the flour:
2x + 3y = 26
For the butter:
34x + y = 9
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 17 (to make the coefficients of x in both equations the same):
34x + 51y = 442
Now we have the system of equations:
34x + y = 9
34x + 51y = 442
Subtract the first equation from the second equation:
34x + 51y - (34x + y) = 442 - 9
50y = 433
Divide both sides by 50:
y = 433/50
Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.
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A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
Answers
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
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Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
Answers
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
the first part of the problem asks them to calculate the work done on the gas when the gas goes from the initial state to the final state shown. here is part of their dialogue: nora: the gas is compressed because the volume decreases. that means that there is work done on the gas, and the work is positive. bob: ok. that's right because we're using the first law with q w. we need to use that area thing to find the work. nora: yeah. we want the area under the line between the dots. bob: that line shows the process, right? nora: yup, that's the one. so the area is one-half times base times height. it's the area of that triangle. bob: but you have to add the area of that skinny rectangle below it, don't you? nora: i don't think so. that bottom dot for the final state tells you where the bottom of the area is. bob: why don't we ever agree? tell you what. we'll each try our own way and let webassign tell us who's right. nora: hmmm... i hope i get the big, green check mark!
Answers
To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.
When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.
You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.
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