54
What value of b will cause the system to have an
infinite number of solutions?
y = 6x - b
-3х+ 1/2y=-3
b=

Answer:

2π or 0π are the only points that satisfy the expression, but since the restriction is 0 <= x < 2π

the answer would be 0π

The solution of the equation on the interval [0,2π) is 0.

To find Solution of the equation.

A statement that the values of two mathematical expressions are equal.

The given equation is :

7secx-7=0 on the interval [0,2π)

7secx-7=0

7secx=7

sec x =1

∴ x=0

So, the solution of the equation on the interval [0,2π) is 0.

Learn more about equation here:

https://brainly.com/question/24366859

#SPJ2

Answer is in a box.

The bag contains 6 red marbles, 8 blue marbles and 9 green marbles, that is 23 marbles.

The probability that one of the 23 marbles will be picked is 1 or 100%, we are picking a marble for sure.

So what is the probability you will pick for example one of the 6 red marbles? It is 6 out of 23 but since we need percentages multiply by 100,

[tex]\frac{6}{23}\cdot100\approx26.09\%[/tex]

The probability to pick a blue marble is,

[tex]\boxed{\frac{8}{23}}\cdot100\approx34.78\%[/tex]

And the probability to pick a green marble is,

[tex]\frac{9}{23}\cdot100\approx39.13\%[/tex]

To check that everything is right you can sum all the probabilities; the probability that it will be either red, blue or green is 100% so the individual probabilities must sum to 100%, and they do,

[tex]26.09\%+34.78\%+39.13\%=100\%[/tex]

Hope this helps :)

The amount Beth would be able to withdraw quarterly from her inheritance over the next 20 years is Quarterly Payments ≈ $11,124.53

The given parameters in the question;

Present value of inheritance, PV = $500,000

The number of years of withdrawal, n = 20 years

Interest rate, i = 6.4%

The required parameter;

The amount Beth would be able to withdraw quarterly over the next 20 years to draw the account down to zero, given a quarterly interest rate of 6.4%

Method

The required parameter is given by the payment formula

The question is related with annuity given that withdrawals will be made quarterly

The question seeks to find how much she can withdraw so as to exhaust the balance in 20 years

The amount she can withdraw quarterly is given by the payment formula as follows;

[tex]\mathbf{PMT = PV \times \dfrac{i}{1 - \left(1 + i\right)^{-n}}}[/tex]

Where;

PMT = The amount of quarterly payments

PV = The present value of the investment = $500,000

i = The interest rate = 6.4%

n = The number of years = 20 years

Therefore, we get;

[tex]\mathbf{PMT = 500,000 \times \dfrac{\dfrac{0.064}{4} }{1 - \left(1 + \dfrac{0.064}{4} \right)^{-4 \times 20}} \approx 11,124.53}[/tex]

The amount she can withdraw quarterly for the next 20 years ≈ $11,124.53

Quarterly payment, PMT = $11,124.53

Learn more about annuity here;

https://brainly.com/question/20796802

Answer:

Two numbers differ by 9 and the sum of their square is 653. What are the numbers?

Well,that's a mathematical question from algebra and it's quite difficult to answer such questions by writing through the circumstances offered by apps like quora.

However,I have tried to answer your question in an understandable way.Hope you may not find it difficult to analyze.

Let the numbers be x and (9+x)

Therefore,according to given,

x^2 + (9+x)^2 =653

=>x^2 + (9)^2 + x^2 + 2×(9)×(x)=653 (Applying the formula of (a+b)^2)

=>x^2 + 81 + x^2 + 18x =653

=>2x^2 + 18x + (81-653)=0

=>2x^2 + 18x - 572=0

=>2x^2 + (44x - 26x) - 572=0

=>2x^2 + 44x - 26x - 572=0

=>2x(x + 22) - 26(x + 22)=0

=>(x + 22)(2x - 26)=0

But since the number can't be negative

Therefore, x=13

Hence,the required numbers are 13 and 22.

Step-by-step explanation:

in first hope you like it

Answer:

y=4/3x-3

Step-by-step explanation:

Answer:

gr,wrgñegetjj

Step-by-step explanation:

jyyjytjjttj

Answer:

at x-intercept, y = 0

4x = 28

x = 7

x intercept = (7,0)

at y-intercept, x = 0

y = 28

y intercept = (0,28)

Answer:

269/99

Step-by-step explanation:

Answer:

74.80

Step-by-step explanation:

First find the discount

88 * 15%

88*.15

13.2

Subtract the discount from the original price

88-13.2

74.80

Answer:

Step-by-step explanation:

Answer:

27,000,200

Step-by-step explanation:

Going by basic math you know a million has six 0's.

So; one million is represented as 1,000,000.

Hence twenty-seven million as 27,000,000.

Using you tens, hundreds and thousands you'll know 200 will fall into the last area.

9514 1404 393

Answer:

  $18,540

Step-by-step explanation:

When interest is compounded yearly, the amount of interest earned in one year is the same as the amount of simple interest earned. The account balance is ...

  A = P(1 +r) = $18,000(1 +.03) = $18,540

$560-$500

=$500

therefore, other roommate will be paying $500 per month

Answer:

114 cm²

Step-by-step explanation:

Surface area of the rectangular prism,

2×(wl+hl+hw)

=2×(3×8+3×8+3×3)

= 2×(24+24+9)

= 2×(57)

=114 cm²

Answer:

3

Step-by-step explanation:

Y is given by sin(theta). sin(-60)=-sqrt(3)/2

Step-by-step explanation:

Rounding number are important in world-problem. They help us in many ways like counting class, food, etc. It's the same thing as estimating.

Tens Place:

50-99: round to 100

100th place:

150-101: round to 100

There is still a lot I'm missing out on, but you could say does are the lowest group that can be round to 100. I'm not a expert, but I hope I could help! You can also ask for the other numbers, but it just depends on where you place or how you use the 100.

9514 1404 393

Answer:

  A.  T<-4, -8>

Step-by-step explanation:

To get the second equation, we had to replace x with x+4 (a translation left 4) and we had to add -8 to the function value (a translation down 8).

Left 4 and down 8 is the translation ...

  T<-4, -8>

Answer:

-1 8/9

Step-by-step explanation:

w + ( - x)

w = -5/9

z = 4/3

Input:

-5/9 + ( -4/3)

-5/9 - 4/3

-4/3 * 3/3 = -12/9

-5/9 - 12/9 = -17/9 = -1 8/9

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Let y be a solution to the given differential equation,

[tex]y' = xy[/tex]

where

[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]

Substituting these series into the DE gives

[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,

[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]

We have

[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]

so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while

[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]

and so on, with the general n-th coefficient being

[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]

Then the power series solution is

[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]

but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.

More concisely: let n = 2k for integers k ≥ 0. Then

[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]

and as a bonus, it's easier to get an exact solution for this DE,

[tex]y(x) = c_0e^{x^2/2}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

The 1-year interest is simply the invested amount times the interest rate.

Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...

  1400r + 900(r +.02) = 202

  2300r +18 = 202 . . . . . . . . . .simplify

  2300r = 184 . . . . . . . . . .subtract 18

  r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r

$1400 was invested at 8%.

$900 was invested at 10%.

Answer:

y=-2x+1

Step-by-step explanation:

The slope of the line is (y(2)-y(1))/(2-1)=(-3+1)/1=-2. The equation of the line is y=mx+(y intercept), y=-2x+1

The complete equation describes how x and y are related y=-2x+1.

We have given, the equation,

We have to determine the complete equation describing how x and y are related.

The slope of the line is(m)=y2-y1/x2-x1

Where m is the slope,

Therefore we get,

(y(2)-y(1))/(2-1)

=(-3+1)/1

=-2.

The equation of the line is y=mx+(y-intercept), y=-2x+1.

To learn more about the slope visit:

https://brainly.com/question/3493733

#SPJ2

Answer:

because this figure does not have two parallel sides

I'm Sorry for by bad English but I am italian

Answer:

1/3

Step-by-step explanation:

.444444444(repeating)- .111111111111(repeating)

.44444444......

-.11111111........

--------------------

.33333333........

Let x = .3333333.....

10x = 3.3333333.....

Subtract the first equation from the second

10x = 3.33333.....

-x =     .33333.....

--------------------------

9x = 3

x = 3/9

x = 1/3

---------------------------

Answer:

See below.

Step-by-step explanation:

Are you sure it's 4 liters to 250 miles, and not 4 liters to 250 milliliters?

If it is 4 liters to 250 miles, then it equals

0.016 liter : 1 mile

If it is 4 liters to 250 ml, then it is

4 liters : 250 ml

4 liters : 0.25 liter

16 liters : 1 liter

16 : 1

9514 1404 393

Answer:

  0.2332

Step-by-step explanation:

The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...

  e = (1 +r/n)^n -1

For weekly compounding, we have n=52, so ...

  e = (1 +0.21/52)^52 -1 = 0.2332 . . . . . . . about 23.32%

Answer:

657

Step-by-step explanation:

pemdas

The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

Hence option A is correct.

Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,

Let's break down the expression step by step:

First, let's simplify the expression inside the innermost parentheses:

8 - 2 x 3 = 8 - 6 = 2

Next, let's simplify the expression inside the brackets:

3 x 23 - 2 = 69 - 2 = 67

Now, let's substitute the simplified expression inside the brackets back into the original expression:

(300 - 70 ÷ 5) - 67

Next, let's simplify the expression inside the remaining parentheses:

70 ÷ 5 = 14

Now, let's substitute the simplified expression inside the parentheses back into the expression:

(300 - 14) - 67

Next, let's simplify the expression inside the remaining parentheses:

300 - 14 = 286

Now, let's substitute the simplified expression inside the parentheses back into the expression:

286 - 67

Finally, let's perform the subtraction:

286 - 67 = 219

Now, let's multiply the result by 3:

3 x 219 = 657

Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

Learn more about expression click;

https://brainly.com/question/28170201

#SPJ2