Step-by-step explanation:
We have to expand,
[tex]\longrightarrow [/tex] (2x — 4)²
(a ― b)² = a² + b² ― 2ab[tex]\longrightarrow [/tex] (2x)² + (4)² ― 2(2x × 4)
[tex]\longrightarrow [/tex] 4x² + 16 ― 2(8x)
[tex]\longrightarrow [/tex] 4x² + 16 ― 16x
[tex]\longrightarrow [/tex] 4x² ― 16x + 16
Hence, solved!
Answer:
D is the correct answer (2x)2 – 2(2x)(4) + 42
Step-by-step explanation:
Use the distributive property to simplify
the equation below.
с
8(2a + 4b - c)
[? ]a + [ ]b - [
[ ]
Answer:
16a +32b - 8c
Step-by-step explanation:
8(2a + 4b - c)
Distribute
8*2a + 8*4b+ 8*(-c)
16a +32b - 8c
Answer:
16a + 32b - 8c
Step-by-step explanation:
You bring 8 inside the parenthesis and then multiply it with everything. so for a you put 16, b you put 32 and c you put 8
A painter can paint 36 feet of molding per hour. How many inches of molding can he paint per hour?
Answer:
432 inches
Step-by-step explanation:
We need to convert feet to inches
1 ft = 12 inches
36 ft * 12 inches/ 1 ft = 432 inches
Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm
0.08 cm/min
Step-by-step explanation:
Given:
[tex]\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}[/tex]
Find [tex]\frac{dr}{dt}[/tex] when diameter D = 20 cm.
We know that the volume of a sphere is given by
[tex]V = \dfrac{4\pi}{3}r^3[/tex]
Taking the time derivative of V, we get
[tex]\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}[/tex]
Solving for [tex]\frac{dr}{dt}[/tex], we get
[tex]\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})[/tex]
[tex]\:\:\:\:\:\:\:= 0.08\:\text{cm/min}[/tex]
I need help with the answer
Answer:
Option B, x ≈ -2.25
Step-by-step explanation:
3^x-2=(x-1)/(x^2+x-1)
or x ≈ -2.21166
so it's closest to the answer of the 2nd option
You take out a 60-day loan for $5000. At the end of the loan, you owe $73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
The PERCENTAGE ANNUAL RATE is 9.0% to the nearest tenth using the SIMPLE INTEREST FORMULA
The question is related to a SIMPLE INTEREST problem:
Loan period = 60 days
using 365 days a year ;
converting to years , 60 days = (60 / 365) years
interest on loan = 73.97
principal = 5000
Using the formula:
interest = (principal * rate * time)
73.79 = (5000 * rate * (60/365)
Rate = 73.79/(5000 * (60/365)) =8.977%
rate = 9%
Therefore, PERCENTAGE ANNUAL RATE is 9.0%
Learn more : https://brainly.com/question/3880193
The doubling time for an investment is 7.5 yeas. Find an exponential model for the growth of your money. Then find how long will take your investment to grow by factor of 5(Assume that you make an investment P)
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Given:
Doubling time,
= 7.5 years
As we know,
[tex]P(t) = P_oe^{rt}[/tex]
now,
⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]
[tex]2 = e^{r\times 7.5}[/tex]
[tex]r = \frac{ln2}{7.5}[/tex]
[tex]=0.092[/tex]
[tex]=9.2[/tex]%
then,
⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]
here,
[tex]P(t) = 5P_o[/tex]
hence,
⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]
[tex]e^{0.092t}=5[/tex]
[tex]t = \frac{ln5}{0.092}[/tex]
[tex]=17.414 \ years[/tex]
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Problem 2 find m<GEF
Answer:
m<GEF = 66°
Step-by-step explanation:
(72+60)/2
= 132/2
= 66
Answered by GAUTHMATH
*20 points*
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1: 4
Sample 2: 1
Sample 3: 9
How do the sample statistics compare to the population mean and standard deviation?
There will be about 6.25 sheep on each acre.
250/40 = 6.25
What is the equation of this graph
Answer:
y-1=x^2
Step-by-step explanation:
That is the equation of a parabola with vertex at (0,1). The equation is y-1=x^2.
Locate the points of discontinuity in the piecewise function shown below.
Answer:
Step-by-step explanation:
The given piecewise function i
From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.
For x=-1,
LHL:
Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.
For x=2,
LHL:
Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.
Therefore, the correct option is A.
Pencils are sold in a local store for 55 cents each. The factory has $1300 in fixed costs
plus 15 cents of additional expense for each pencil made. Assuming all
pencils manufactured can be sold, find the break-even point.
Break-even point:
Answer:
3250 pencils sold
Step-by-step explanation:
Let x represent the number of pencils.
The profit from the pencils sold can be represented by 0.55x, and the cost from making the pencils can be represented by 1300 + 0.15x.
Set these two terms equal to each other, and solve for x:
0.55x = 1300 + 0.15x
0.4x = 1300
x = 3250
So, the break even point is at 3250 pencils sold.
Which graph has the solutions -1 and 4?
a.
On a coordinate plane, a parabola opens up and goes through (negative 4.2, 0) and (0, negative 1).
c.
On a coordinate plane, a parabola opens up and goes through (negative 4, 0) and (1, 0).
b.
On a coordinate plane, a parabola opens up and goes through (0, negative 3) and (4.5, 0).
d.
On a coordinate plane, a parabola opens up and goes through (0, negative 1) and (4, 0).
Please select the best answer from the choices provided
A
B
C
D
Answer:
graph d
in graph d, the line intersects the x axis twice at (-1,0) and (4,0), so those two are the solutions of the graph
A geometric sequence is a sequence of numbers where the next term equals to
the previous term multiplied by a common factor (for example, (3, 6, 12, 24, ...)
is a geometric sequence with the first term ”3” and the common factor ”2”). If
the 5th term of a geometric sequence is 24 and the 7th term is 144, what is the
first term of the sequence?
(A) 2
(B) 3/2
(C) 2/3
(D) 1/3
(E) 1/4
Answer:
C
Step-by-step explanation:
Let the first term be a and the common ratio be r.
ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3
of a loaf of brown bread costs R6, how much will 4 halves cost?
Answer:
R12
Step-by-step explanation:
Answer: R12
Explanation:
Cost of 1 loaf = R6
Cost of 4 halves = 6/2×4
= 6 × 2
= R12
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Diana get a gift card with a value of $55, and her favorite drink cost $2.20. How many plain black coffee can she buy with the gift card
Answer:
Twouufyjughgyuioiu567uhu888
Answer:
55/2.20=25 so 25 black coffees
Step-by-step explanation:
What is the volume of the cylinder below?
Answer:
A
Step-by-step explanation:
v=πr2h
r=(3)²* 5
45π unit³
Which of the following is correctly written in Standard Form? −3x + 7y = 12, y = 3/7x + 6 ,5x − 4y = 9 ,3/7x + 2y =9
I need help ASAP please help me solve this math question
Answer:
b appears to be correct
Step-by-step explanation:
Hi i need help i have class in 30 min! <3
For what values of a are the following statements true:
Answer:
if I understand correctly, I hope this helps:
Answer to b: a< or equal to Zero.
Answer to d: a>or equal to -5
Your credit card has a balance of $3300 and an annual interest rate of 14%. You decided to pay off the balance over two years. If there are no further purchases charged to the card, you must pay $158.40 each month, and you will pay a total interest of $501.60. Assume you decided to pay off the balance over one year rather than two. How much more must you pay each month and how much less will you pay in total interest?
9514 1404 393
Answer:
$137.90 more each month$246.00 less total interestStep-by-step explanation:
The amortization formula is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
for the monthly payment on principal P at annual rate r for t years. Here, we have P=3300, r = 0.14, and t=1, so the monthly payment is ...
A = $3300(0.14/12)/(1 -(1 +0.14/12)^-12) ≈ $296.30
The payment of $296.30 is ...
$295.30 -158.40 = $137.90 . . . more each month
The total amount paid is 12×$296.30 = $3555.60, so 255.60 in interest. This amount is ...
$501.60 -255.60 = $246.00 . . . less total interest
Given the following coordinates complete the glide reflection transformation.
A(−1,−3)
B(−4,−1)
C(−6,−4)
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this, we get
[tex]A(-1,-3)\to A'(-1,3)[/tex]
[tex]B(-4,-1)\to B'(-4,1)[/tex]
[tex]C(-6,-4)\to C'(-6,4)[/tex]
If a figure is shifting 10 units right, then
[tex](x,y)\to (x+10,y)[/tex]
Using this we get
[tex]A'(-1,3)\to A''(-1+10,3)[/tex]
[tex]A'(-1,3)\to A''(9,3)[/tex]
Similarly,
[tex]B'(-4,1)\to B''(-4+10,1)[/tex]
[tex]B'-4,1)\to B''(6,1)[/tex]
And,
[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]
[tex]C'(-6,-4)\to C''(4,4)[/tex]
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
Find the remainder when f(x)=x3−4x2−6x−3 f ( x ) = x 3 − 4 x 2 − 6 x − 3 is divided by x+1
Answer:
The remainder is -2.
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (x - a), then the remainder of the operation will be given by P(a).
Our polynomial is:
[tex]P(x) = x^3-4x^2-6x-3[/tex]
And we want to find the remainder when it's divided by the binomial:
[tex]x+1[/tex]
We can rewrite our divisor as (x - (-1)). Hence, a = -1.
Then by the PRT, the remainder will be:
[tex]\displaystyle\begin{aligned} R &= P(-1)\\ &=(-1)^3-4(-1)^2-6(-1)-3 \\ &= (-1)-4(1)+(6)-3 \\ &= -2 \end{aligned}[/tex]
The remainder is -2.
Help me please, is it d?
Answer:
Yes D is the correct answer :)
Answer:
Yes, D
Step-by-step explanation:
10) Find three numbers whose product is -72. You may use integers from -10 to 10. Give two
examples
Answer:
Step-by-step explanation:
-8 * 9 * 1
If you are going to get - 72, you need to have an odd number of minus signs.
4 * 3 * - 6
You must be careful of the limits. You can't use something like 36 * 2 * 1 because the numbers don't fall within +/- 10
You could use 6*6*-2
What is lim j(x)?
X-3
9514 1404 393
Answer:
(b) 4
Step-by-step explanation:
The point (3, 4) is a "hole" in the graph. The function approaches the value y=4 from either direction, so that is the limit as x → 3.
[tex]\displaystyle\lim_{x\to3}f(x)=4[/tex]
What is the range of the function?
{(1.2, 11.6), (3.6, 11.5), (1.9, 11.4), (2.7, 11.5)}
Answer:
Range: 10.4
Step-by-step explanation:
Range = maximum(xi) - minimum(xi), where xi represents the set of values
= 11.6 - 1.2
= 10.4
Answer:
Range-
{
11.6
,
11.5
,
11.4
}
Step-by-step explanation:
What is the length of the arc of a circle with a radius of 4 by a central angle of 7pi/4?
9514 1404 393
Answer:
(b) 7π
Step-by-step explanation:
The arc length is the product of the radius and the central angle in radians.
s = rθ
s = (4)(7π/4) = 7π . . . units
Can someone please help with 25 , please put the way you got it. Please no links it’s serious
Answer:
X * 0.8 = $64
x = $80
Step-by-step explanation:
What is 20×10 to the third power equal
Consider the following. fourteen less than the total of a number and three Translate into a variable expression. (Use x for your variable. Do not simplify.)
9514 1404 393
Answer:
(x +3) -14
Step-by-step explanation:
The total of a number and 3 will be represented by (x +3). Fourteen less than that is ...
(x +3) -14 or -14 +(x +3)
