Step-by-step explanation:
1.) 630
2.) 13020
3.) 361
4.) 244
Consider the parabola given by the equation: f(x) = 2x2 + 14.0 – 4
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two z intercepts of the parabola and write them as a list, separated by
commas:
It is OK to round your value(s) to to two decimal places.
Answer:
Step-by-step explanation:
f(x) = 2x² + 14x - 4
= 2(x² + 7x) - 4
= 2(x² +7x + 3.5²) - 2(3.5²) - 4
= 2(x+3.5)² - 28.5
vertex (3.5, -28.5) = (7/2, -57/2)
The vertical intercept is the y-intercept, i.e., f(0) = -4.
The x-intercepts are the values of x for which y=0.
2x² + 14x - 4 = 0
x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27
2. Write a polynomial function of least degree with rational coefficients so that P(x)=0 has the given root.
4 - 5i
Answer:
p(x) = x^2 - 8x + 41
Step-by-step explanation:
If a polynomial with rational coefficients has a complex root, then the roots come in complex conjugate pairs. If the polynomial we need to find has the root 4 - 5i, then it must also have its complex conjugate 4 + 5i as a root.
p(x) = [x - (4 - 5i)][x - (4 + 5i)]
p(x) = [(x - 4) + 5i][(x - 4) - 5i]
Now it's a difference of two squares.
p(x) = (x - 4)^2 - (5i)^2
p(x) = x^2 - 8x + 16 + 25
p(x) = x^2 - 8x + 41
Question
Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and
-8i
Answer:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Step-by-step explanation:
A standard polynomial in factored form is given by:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros.
We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.
First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.
Therefore, we acquire:
[tex]f(x)=a(x-(2))(x-(-8i))(x-(8i))[/tex]
Simplify:
[tex]f(x)=a(x-2)(x+8i)(x-8i)[/tex]
Expand the second and third factors:
[tex]=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64[/tex]
Hence, our function is now:
[tex]f(x)=a(x-2)(x^2+64)[/tex]
It equals 320 when x = 4. Therefore:
[tex]320=a(4-2)(4^2+64)[/tex]
Solve for a. Evaluate:
[tex]320=(2)(80)a[/tex]
So:
[tex]320=160a\Rightarrow a=2[/tex]
Our third-degree polynomial equation is:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Answer:
f(x)=2(x-2)(x^2+64)
Step-by-step explanation:
Last year, Jason's average in math was a 72. This year, his average is a 90. What is the percent increase in Jason's grade?
Answer:
20% increase
Step-by-step explanation:
All you have to do is divide 72 by 90n and it will give you .8, move the decimal two places to the right to give you 80 and subtract 80 from 100 to get 20
A boy standing on a vertical cliff, observed two buoys in line with him, whose angles of depression are 19 degrees and 26 degrees. If the distance between the buoys is 222m, find the height of the cliff
work out the circumference of this circle
give your answer in terms of pi and state its units
14cm
Answer:
43.96
Step-by-step explanation:
Well, the first step is finding out the diameter. And then the basic outline is d x 3.14. So I simply just punched in 14 x 3.14 in my calculator.
Answer:
14π cm
Step-by-step explanation:
Circumference of the circle
= 2πr
= 2π(14/2)
= 14π cm
Can someone help me plsssss
Answer:
Sorry I don't know this.
Step-by-step explanation:
Answer:
wheel: radius=3/2 diameter=3 circumference=3pi
propeller: radius=24 diameter=48 circumference=48pi
orange: radius=10/pi diameter=20/pi circumference=20
Step-by-step explanation:
5 members or 20% of the math league did not come to the meet. how many total members are there
5 = (20%) x (total)
5 = (0.20) x (total)
Divide each side by (0.20):
Total = (5 / 0.20)
Total = 25
Help please someone please
Answer:
i dont know im just doing this for the points
45633 seconds en heures minutes et seconds
Pls hurry I need an instant answer ASAP! Thank you
Answer:
A= -2
Step-by-step explanation:
Hope I helped!! Negitive 2
With a capacity of 6,300 people, Royal Caribbean’s Oasis of the Seas is the world’s largest cruise ship. The average beer consumption over 35 randomly selected seven-day cruises on the ship was 81,740 bottles. From historical data you know that the population standard deviation of beer consumption is 4,590 bottles. Royal Caribbean would like to estimate the average beer consumption to plan its beer inventory levels on future cruises. (The ship certainly doesn’t want to run out of beer in the middle of the ocean!)
A. Construct a 95% confidence interval to estimate the average beer consumption per cruise.
B. Verify this interval using excel.
C. What assumptions need to be made about this population?
Step-by-step explanation:
Mean = 81740
Standard deviation = 4590
Sample size = 15
Alpha level = 1-0.95 = 0.05
Df = 15-1 = 14
Critical value:
alpha/2 = 0.05/2 = 0.05
t0.025
t critical value = 2.145
Margin of error ME
2.145 x 4590/√15
2.145 x 4590/3.873
ME = 2542.09
Confidence interval
Lower CI = mean - ME
= 81740-2542.09
= 79197.91
Upper CI = mean + ME
= 81740+2542.09
= 84282.09
[ 79197.91, 84282.09]
B.
Using excel, exact answer for CI
Lower limit = 79198.142724212173
Upper limit = 84281.8572757827
C.
The assumptions to be made from the population are that
1. Samples are random
2. These samples are gotten from an approximately normal distribution
Here is a circle. Points A, B, C, and D are drawn, as
well as Segments AD and BC.
D.
What is the area of the circle, in square units?
Let event A = The animal is a bird
Let event B = The animal can fly.
Which outcomes are in A and B?
A. {penguin, robin, sparrow, pelican, bat)
OB. {robin, sparrow, pelican}
O C. (penguin, robin, sparrow, pelican}
O D. (robin, sparrow, pelican, bat)
Answer:
B. {robin, sparrow, pelican}
Step-by-step explanation:
hope it helps you...
The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Let event A = The animal is a bird
Let event B = The animal can fly.
Hence, We get;
The outcomes are in A and B in which animal is a bird and also can fly.
Thus, The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
Hence, The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
Write an equation of the line that passes through (-2, 0) and is perpendicular to the line y=-1/3x+3
Slope of y = -⅓x + 3 is -⅓ (on comparing with m of y = mx + c)
As the required line is perpendicular to this, slope of the required line = - 1 / (-⅓) = 3
Equation:
=> y - y1 = m(x - x1)
=> y - 0 = (3)(x - (-2))
=> y = 3(x + 2)
=> 3x - y + 6 = 0
Carl has 50 apps on his phone. Of these apps, 12 are music apps. What percent of Carl’s apps are music apps?
AANNSSWWEER
AASSAAPP
Answer:
12 50 I don't know
Step-by-step explanation:
When a trucker opens the back of a truck filled with candy bars,
he sees a wall 9 cartons high and 6 cartons wide with no room
left over. How wide is the back of a candy company truck?
Answer:6 cartons wide
Step-by-step explanation:
It is 6 cartons wide due to the fact that there is no room left over. Awnser achived through text.
Higher Order Thinking a carpenter plans to extend the length of rectangular desk by 7 feet. Let x represent the desk's original length. The expression 96 + 7) represents the area of the desk surface where 9 is the width, in feet, and () represents the extended length, in feet, of the desk. The carpenter thinks that the area of the extended portion of the desk is 16 square feet Which choice below includes the expanded form of the area expression for the deck's surface and the correct area of the extended portion of the desk's surface?
a. 10x + 16 and 10k square feet
b. 9x+63 and 9x square feet
c. 9x + 7 and 7 square feet
d. 9x + 63 and 63 square feet
Answer:
d. 9x + 63 and 63 square feet
Step-by-step explanation:
Given
Original
[tex]Length = x[/tex]
[tex]Width = 9[/tex]
Extended
[tex]Length = x + 7[/tex]
[tex]Width = 9[/tex]
[tex]Area = 9(x + 7)[/tex]
Required
Determine an expression and the value of the extended area
First, we calculate the area of the original desk
[tex]A_1 = x * 9[/tex]
[tex]A_1 = 9x[/tex]
From the given parameters, we have:
[tex]Area = 9(x + 7)[/tex] --- area of the new surface
Open bracket
[tex]Area = 9x + 63[/tex]
The area of the new surface is the summation of the area of the original desk and the area of the extended portion (E)
So:
[tex]Area = A_1 + E[/tex]
Make E the subject
[tex]E= Area - A_1[/tex]
[tex]E= 9x + 63 - 9x[/tex]
[tex]E= 63[/tex]
Hence, the area of the extended portion is 63
calculate the actual sales since the sales tax were rung up together. assume sales tax of 6% and total sales of $27,000. What is the actual sales? ( round your answer to the nearest cent.)
Answer:
$25471.7
Step-by-step explanation:
1.06*25471.7=27000.002
Hope this helps
A hipopótamos weight 1.5 tons what is its weight in ounces
Answer:
48000
Step-by-step explanation:
multiply the mass value by 32000
Answer:
48000
Step-by-step explanation:
.
Determine which lines, if any, are parallel? Explain.
PLEASE PLEASE HELP ME ASAP
Answer:
The 2 on the right because they don't cross and they are straight
Step-by-step explanation:
On a map, the distance of two inches is equal to ten miles. How many
miles does 4 inches represent on the map?
10
20
30
40
WILL GIVE BRAINLIEST
Answer:
[tex]\sqrt{65}[/tex] is the closest to 8
Step-by-step explanation:
[tex]\sqrt{61}=7.81 \\\sqrt{66}=8.12 \\\sqrt{65} =8.06\\\sqrt{62} =7.87[/tex]
I need help please help
Answer: 25.12
Step-by-step explanation: good luck
PLS HELP ASAP IM RUNNING OUT OF POINTS PLSS
Answer:
x = 35°
Step-by-step explanation:
180 - (40+40) = 2x+30
180 -80 = 2x+30
100 = 2x+30
2x = 100-30
x = 70/2
x = 35°
20 POINTS!!!! PLEASE HELP ME!!!!!!
Please do not tell me the answer tell me how to do it with showing my work
Answer:
Step-by-step explanation:
a)
2.64÷3.3 ( said 2.64 divided by 3.3)
3.3√2.64 ( yes I know it's not the division sign but it's as close as we can get)
2.64 / 3.3
All three representations are the same. each say divide 2.64 by 3.3. If you're thinking that last one looks more like a fraction, you're right, but.. that's also what that means. I'm showing these different ways to express the idea of division b/c it's part of what is involved with showing the work and understanding it.
so, to do the above let's move the decimal point to the right .. and do we want to move it one or two places. :? one because of 3.3 or two , because of 2.64, well we want to move it so we don't have to think about it in the problem... so move it the biggest amount that you need to, get the the decimil out of both numbers.. since the 2.64 needs two moves to the right of the decimal... use 100 times to move it 2 places, If you needed 3 then use 1000, 4 , 10,000 ect ect... see the pattern?
so
100(3.3 √ 2.64 )
move the decimal point in both 2 places right
330.0 √ 264.0
I put the extra zeros in, just so you can see the decimal easy. The zeros to the right of the decimal make no difference here.
now I'll know to put the number that I use to divde with above the zero, of 264.0 .. and i'll think about how many times 3 goes into 26 ,without going over. 3*8 = 24 so I want an 8
↓ ← ← ← 0.8
330.0 √ 264.0 ( multiply 8 * 330 = 2640 )
↓ → -264 .0 ( subtract 2640 from the number above )
0
you are done with that one, since there is zero left over and 0.8 is the answer
b)
0.324 ÷ 0.27
0.27 √ 0.324
0324 / 0.27
1000( 0.27 √ 0.324)
270 √ 324.0
↓ ← ← 1.2
270 √ 324.0
↓→ - 270 ( multiply by the 1 )
↓ = 54
↓→ - 540 (multiply by the 2 )
0
since there is zero left over you are done. The answer is 1.2
C)
0.32 ÷ 0.16
0.16 √ 0.32
100(0.32 / 0.16)
↓ ← 2
16 √32
↓→ -32 ( multiply 16 * 2 = 32 )
0
zero left over you are done. the answer is 2 :)
d)
16.92 ÷ 9.4
9.4 √ 16.92
100(16.92 / 9.4)
↓ ← ← 1.8
940 √1692.0
↓→→ - 940 (multiply by 1 )
↓ 7520
↓→ - 7520 (multiply by 8 )
0
since there is zero left you are done, The answer is 1.8
that was a lot, really nobody has talked or told you how to do this before?
where is your teacher? :/
Please help me in ASAP
Step-by-step explanation:
code:257 403 0731
Pass:HELLO
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g(x) = 2x
Find g(g(-3))
Can someone please give me the answer I will mark u brilliant
Answer:
p = 16.8
[tex] r \geqslant 5.5[/tex]
Step-by-step explanation:
12)
p + 2.1 = 18.9
p = 18.9 - 2.1
p = 16.8
13)
[tex]r \geqslant 5.5[/tex]
A school buys 1,950 pencils. The pencils are sold in boxes, with 30 pencils in each box. If each box costs $4.05, what is the total cost, in dollars, that the school will pay for the pencils?