Answer:
Step-by-step explanation:
y= 4x + 5
y = 4x - 5
4x + 5 = 4x - 5
0 ≠ -10
no solution
At what point on the curve x = 6t2 + 6, y = t3 − 2 does the tangent line have slope 1 /2 ?
Answer:
Hello,
P=(30,6)
Step-by-step explanation:
[tex]x=6t^2+6\\y=t^3-2\\\\\dfrac{dx}{dt}= 12t\\\dfrac{dy}{dt}= 3t^2\\\\\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } =\dfrac{3t^2}{12t} =\dfrac{t}{4} \\\\\dfrac{t}{4} =\dfrac{1}{2} \Longrightarrow t=2\\\\\\x=6t^2+6=6*2^2+6=30\\\\y=t^3-2=2^2-2=8-2=6\\\\\\Tangence\ point=(30,6)\\[/tex]
The point on the curve x = 6t² + 6, y = t³ - 2 where the tangent line have slope 1/2 is (30, 6).
How to depict the point on the curve?From the information given, x = 6t² + 6, y = t³ - 2. We'll find the first order derivative of x and y which will be:
dx/dt = 12t
dy/dt = 3t²
Therefore, 3t²/12t = t/4, t = 2.
We'll put the value of t back into the equations.
x = 6t² + 6,
x = 6(2)² + 6
x = 24 + 6 = 30
y = t³ - 2.
y = (2)³ - 2
y = 8 - 2 = 6
In conclusion, the correct options is (30, 6).
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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
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
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%
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What is the volume of the cylinder below?
Answer:
A
Step-by-step explanation:
v=πr2h
r=(3)²* 5
45π unit³
What is the equation of a line that passes through the point (8,-2) and is parallel to the line whose equation is 3x+4y=15?
Answer:
y = -3x/4 + 4
Step-by-step explanation:
slope m = -3/4
-2=(-3/4)×8+b
or, b = 4
y = mx + b
y = -3x/4 + 4
Answered by GAUTHMATH
Solve for x.
5x - 3 = 12
A) X = 3
B) X = -3
C) X = -9/5
D) X = 9/5
Answer:
A. x = 3
Step-by-step explanation:
5x - 3 = 12
5x = 12 + 3
5x = 15
x = 15/5
= 3
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
find the quadratic equations whose roots are 3 and -4
Answer:
Hello,
Step-by-step explanation:
(x-3)*(x+4)=0 or x²+x-12=0
Answer:
Step-by-step explanation:
[tex]\displyastyle \Large \boldsymbol{} (x-x_1)(x-x_2) \ \ x_1 \ ; \ x_2 -roots \\\\(x-3)(x-(-4))=(x-3)(x+4)=\boxed{x^2+x-12}[/tex]
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:
*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
One number is eight less than a second number. Five times the first is 6 more than 6 times the second. Find the numbers.
The value of the first number is -
Answer:
-42/11
Step-by-step explanation:
x = y - 8
5x = 6 - 6y
So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5
Now...
x = y - 8
x = 6/5 - 6y/5
Now substitute first equation into the second and x is gonna be -42/11 or the first number
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. Which of the following correctly labels the population?
1–1020
01–1020
001–1020
0001–1020
I think its (B), 01-1020.
Answer:
Should be (B)
01-1020
ED2021
The correct label for the population is 1 - 1020,
Option A is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a number of population given.
Each items has an equal probability of being chosen.
We have,
The population in this case refers to the entire group of interest, which is the entire student body of the school.
The total number of students is 1,020.
The population is usually labeled with a range or interval that includes all the possible values of the variable of interest.
In this case, the variable of interest is whether or not a student has an opinion on parking.
The correct label for the population is 1-1020, as this range includes all possible student identification numbers at the school.
The other options (01-1020, 001-1020, and 0001-1020) are not correct because they suggest that there are leading zeros in the student identification numbers, which is not usually the case.
Thus,
The correct label for the population is 1-1020,
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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.
Help me please, is it d?
Answer:
Yes D is the correct answer :)
Answer:
Yes, D
Step-by-step explanation:
6. 5x = -25
a. X= 5
b. X=-5
c. x=2
Answer:
x = -5
Step-by-step explanation:
5x = -25
Divide each side by 5
5x/5 = -25/5
x = -5
Answer:
[tex]Option\ B,\ x = -5[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 5
[tex]5x = -25[/tex]
[tex]5x / 5 = -25 / 5[/tex]
[tex]x = -25/5[/tex]
[tex]x = -5[/tex]
Answer: [tex]Option\ B,\ x = -5[/tex]
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:
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.)
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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)
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.
I need help ASAP please help me solve this math question
Answer:
b appears to be correct
Step-by-step explanation:
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.
Problem 2 find m<GEF
Answer:
m<GEF = 66°
Step-by-step explanation:
(72+60)/2
= 132/2
= 66
Answered by GAUTHMATH
Describe what is contained in a credit report
Answer:
Your credit report contains personal information, credit account history, credit inquiries and public records. This information is reported by your lenders and creditors to the credit bureaus. Much of it is used to calculate your FICO® Scores to inform future lenders about your creditworthiness.
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
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
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:
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).
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.