find the value of a and b

a^2 + b^2 = 400

Answer:

[tex]\displaystyle 5b^{-4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5b^{-4} = (-5a^4b^{-7})(-a^{-4}b^3) \\ \\ \frac{5}{b^4} = 5b^{-4}[/tex]

According to the Negative Exponential Rule [part II], you bring the denominator to the numerator WHILE ALTERING THE INTEGER SYMBOL FROM POSITIVE TO NEGATIVE:

[tex]\displaystyle b^{-n} = \frac{1}{b^n}[/tex]

I am joyous to assist you anytime.

In the figure, Blueline is Line AB and Redline is target line.

You can see that the target line does not pass through (18,-8)

Step-by-step explanation:

In the figure, Blueline is Line AB and Redline is target line.

You can see that the target line does not pass through (18,-8)

Taking a bottom-left corner of the graph as (0,0)

Given Line AB,

Point A is located as (4,9)

Point B is located as (16,1)

The slope of AB is

[tex]=\frac{Y1-Y2}{X1-X2}[/tex]

[tex]=\frac{9-1}{4-16}[/tex]

[tex]=\frac{8}{-12}[/tex]

[tex]=\frac{-2}{3}[/tex]

The question says "  Draw a line passes through C(13,12) and parallel to Line AB "

Now, Let the equation of the target line is y=mx + c

Where m=slope and c is the y-intercept

The target line is parallel to the line AB

The slope of the Target line = The slope of the Line AB [tex]=\frac{-2}{3}[/tex]

m=[tex]=\frac{-2}{3}[/tex]

We can write, the equation of the target line is

[tex]y=\frac{-2}{3}x + c[/tex]

Also, the Target line is passing through C(13,12)

Point C satisfies the equation

[tex]y=\frac{-2}{3}x + c[/tex]

[tex]12=\frac{-2}{3}13 + c[/tex]

[tex]12=\frac{-26}{3} + c[/tex]

[tex]12+\frac{26}{3}=c[/tex]

[tex]c= 12+\frac{26}{3}[/tex]

[tex]c= \frac{62}{3}[/tex]

Replacing the value

the equation of the target line is

[tex]y=\frac{-2}{3}x + c[/tex]

[tex]y=\frac{-2}{3}x +  \frac{62}{3} [/tex]

[tex]3y= -2x + 62 [/tex]

It is also asked that if a line is extended , would it passes through the (18,-8)?

If a line passes through the point (18-,8) then, that point must satisfy the equation of a line

the equation of the target line is  [tex]3y= -2x + 62 [/tex]

[tex]3(-8)= -2(18) + 62 [/tex]

[tex](-24)= (-36) + 62 [/tex]

[tex](-24)= (-36) + 62 [/tex]

[tex](-24)= 26 [/tex]

Left land side is not equal to right hand side.

Therefore. a line does not pass through the point (18,-8)

Answer:

12 km/h

Step-by-step explanation:

Given: Distance covered by boat downstream = 50 km

           Distance covered by boat upstream = 30 km

           Time taken by boat in down stream and upstream are equal.

           Speed of the stream = 3 km/h

Let x be the speed of boat in still water.

∴ Speed of boat in downstream [tex](s_1)[/tex] = [tex](x+3)\ km/h[/tex]

Speed of boat in upstream [tex](s_2)[/tex] = [tex](x-3)\ km/h[/tex]

As we know, [tex]Time = \frac{Distance}{speed}[/tex]

And time remain same for both upstream and downstream

∴ [tex]\frac{50}{(x+3)} = \frac{30}{(x-3)}[/tex]

Now, cross multiply both side

⇒  [tex]50\times (x-3) = 30\times (x+3)[/tex]

⇒ [tex]50x-30x = 150+90[/tex]

∴ [tex]x= 12\ km/h[/tex]

∴ Speed of boat in still water is 12 km/h

A function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}[/tex]

Given that  

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

[tex]=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052[/tex]

Similarly Amount earned by plant after three years [tex]=80 \times 1.05^{t}[/tex]

[tex]\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}[/tex]

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(t)=80 \times 1.05^{t}[/tex]

Answer:

Mr. Winking 87.9%

Ms. Sand 88.55%

Ms. Sand's class is better

Step-by-step explanation:

Step 1: Average in Mr. Winking's Class 87.9%

Convert each weight factor to a decimal.

Homework 10% = 0.1

Quiz 25% = 0.25

Test 45% = 0.45

Exam 20% = 0.2

Multiply your grades by the weight factors:

Homework 0.1 X 95% = 9.5%

Quiz 0.25 X 85% = 21.25%

Test 0.45 X 87% = 39.15%

Exam 0.2 X 90% = 18%

Add all of these values:

9.5% + 21.25% + 39.15% + 18%

= 87.9%

Step 2: Average in Ms. Sand’s Class 88.55%

Convert each weight factor to a decimal.

Homework 15% = 0.15

Quiz 20% = 0.2

Test 40% = 0.4

Exam 25% = 0.25

Multiply the weight factors by your grades:

Homework 0.15 X 95% = 14.25

Quiz 0.2 X 85% = 17

Test 0.4 X 87% = 34.8

Exam 0.25 X 90% = 22.5

All all these values:

14.25 + 17 + 34.8 + 22.5

= 88.55%

Step 3:

I would rather be in Ms. Sand's class. My average in her class would be 88.55%, whereas in Mr.Winking's Class, my average would be 87.9%. 88.55% is a higher mark than 87.9% and I want higher marks. Therefore, I would get higher marks in Ms. Sand's class.

Answer:

B.

Step-by-step explanation:

The total amount petra has to pay after 1 year is $ 209

The equation used is: Total amount to pay back = Amount Borrowed + Amount of Interest

Given that,

Petra borrowed $ 200 for 1 year with simple interest rate 4.5 %

We are asked to find the amount that petra has to pay back after 1 year

Total to Pay Back = Amount Borrowed + Amount of Interest

Let us first calculate the amount of interest Petra has to pay for 1 year

Given that simple interest rate = 4.5%

The simple interest is given as:

[tex]\text { simple interest }=\frac{\text { principal } \times \text {rate} \text { of interest } \times \text { number of years }}{100}[/tex]

[tex]\text { simple interest }=\frac{200 \times 4.5 \times 1}{100}=2 \times 4.5=9[/tex]

Thus the amount of interest = $ 9

Total to Pay Back = Amount Borrowed + Amount of Interest

Total to Pay Back = 200 + 9 = 209

Thus the total amount petra has to pay after 1 year is $ 209

Answer:

Step-by-step explanation:

The system of linear equations have:

one solution, infinitely many solutions or no solution.

One solution if the lines intersect.

Infinitely many solutions if the lines are the same (overlap)

There is no solution if the lines are parallel (they do not have a common point).

In the graph, two lines intersect. Therefore, the system of equations has one solution (0, 3).

There are no solution of System of equations

We have to given that,

System of equations are,

x+5y=4

3x+15y=-1

Now, We can use substitution method as,

x+5y=4  .(i)

3x+15y=-1  .. (ii)

From (i);

x = 4 - 5y

Put above value in (ii);

3 (4 - 5y) + 15y = - 1

12 - 15y + 15y = - 1

12 = - 1

Which is not possible.

Hence, There are no solution of System of equations

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Answer:

12.1

Step-by-step explanation:

76/2π

= 38/π

= 12

Answer: 12.1 ft

Step-by-step explanation:

Hi, to answer this we have to apply the circumference formula:

C= 2πr

Where:

C = circumference ( in this case is 76, since the dog can walk a distance of about 76 feet along the circumference.)

r = radius. (In this case the radius is the length of the rope, because the stake is in the center of the circumference)

Replacing with the values given and solving for "r":

76 = 2πr

76 /( 2π)= 12.0957= 12.1 ft

Answer: 90

Step-by-step explanation: You equation is 4(3*7) + 2(1*3). To solve this, you first solve what is on the inside of the parenthesis. so 3 times 7 is 21. And 1 times 3 is 3. So now your equation looks like this 4(21) + 2(3). 4 times 21 is 84 and 2 times 3 is 6. So now your equation is 84 + 6 which equals 90.

Answer:

90

Step-by-step explanation:

4(3*7)+2(1*3)=4(21)+2(3)=84+6=90

Answer:

198

Step-by-step explanation:

-511 + (+709) =

709 - 511 = 198

Answer:

-511 + 709 = 198

Step-by-step explanation:

-511+709 is the same as 709-511

Answer:

Amount of money Brain has is 11.84 after his shopping trip.

Step-by-step explanation:

Given:

cost of books = 15.99 each

Cost of 2 books = [tex]15.99\times 2 = 31.98[/tex]

Cost for DVD = 19.95

Cost of Magazine = 2.50

Money he gets return back for jacket = 42.59

Solution:

We will first find the total amount used for shopping.

Total Shopping done =  Cost of 2 books + Cost for DVD + Cost of Magazine = [tex]31.98+19.95+2.50= 54.43[/tex]

Now we will find the amount left after shopping which will be equal to the total amount used for shopping minus money he got in return for jacket.

Now net amount Left after shopping = Total Shopping done - Money he gets return back for jacket = [tex]54..43-42.59 =11.84[/tex]

Hence amount of money Brain has is 11.84 after his shopping trip.

The expression x=20-3D will present the amount Amy has left after buying D sodas.

Step-by-step explanation:

Given,

Total amount = 20 quarters

Cost of sodas = $0.75 = 0.75*100 = 75 cents

25 cents = 1 quarter

1 cent = [tex]\frac{1}{25}\ quarter[/tex]

75 cents = [tex]\frac{1}{25}*75[/tex] = 3 quarters

Amount of D sodas = 3D

Let x be the amount left with Amy.

Amount left = total amount - Amount of D sodas

[tex]x=20-3D[/tex]

The expression x=20-3D will present the amount Amy has left after buying D sodas.

Keywords: fractions, subtraction

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Answer:

Which is equal to 0.0865 hectometers?

86.5 millimeters

865 millimeters

8,650 millimeters

86,500 millimeters

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

Final answer:

By solving a system of equations, we find that the cost of one squash is $0.18 and the cost of one zucchini is $0.21.

Explanation:

The question involves solving a system of linear equations to determine the cost of each vegetable. Let's define x as the cost of one squash and y as the cost of one zucchini. We have the two equations based on the information provided:

We can solve this system using either substitution or elimination methods. For this example, I'll use the substitution method:

Therefore, the cost of one squash is $0.18 and the cost of one zucchini is $0.21.

Final answer:

To find the cost of each vegetable, a system of linear equations was set up and solved, revealing the cost of one squash to be $0.18 and the cost of one zucchini to be $0.21.

Explanation:

The cost of 5 squash and 2 zucchini is $1.32, and the cost of 3 squash and 1 zucchini is $0.75. To find the cost of each vegetable, we can set up a system of linear equations and solve for the unknowns.

Let 's' represent the cost of one squash and 'z' represent the cost of one zucchini. We can then create two equations based on the information given:

5s + 2z = $1.32

3s + 1z = $0.75

Now, we need to solve this system of equations. An effective way to do this would be using the substitution or elimination method. For simplicity, let's use the elimination method:

Multiply the second equation by 2 to align the coefficients of z:

6s + 2z = $1.50

Now subtract the modified second equation from the first:

(5s + 2z) - (6s + 2z) = $1.32 - $1.50

-s = -$0.18

s = $0.18

With the cost of one squash known, substitute 's' back into one of the original equations to find 'z':

3(0.18) + z = $0.75

0.54 + z = $0.75

z = $0.75 - $0.54

z = $0.21

So, one squash costs $0.18, and one zucchini costs $0.21.

Answer:

-1/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-(-3))/(-5-1)

m=(0+3)/(-6)

m=3/-6

simplify

m=-1/2

1) Find the solution to each equation.

A) 4(2x - 1) = -3x + 32

The solution to the equation 4(2x - 1) = -3x + 32 is x = 3.273

Need to find the solution of following equation

4(2x - 1) = -3x + 32

Let use BODMAS rule to solve the expression

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.

On opening the bracket of left hand side we get

[tex]4 \times 2x-4 \times 1=-3 x+32[/tex]

Now perform multiplication,

8x – 4 = -3x + 32

On bringing terms having variable x in left hand side and constant term on right hand side we get

8x + 3x = 32 + 4

=> 11x  = 36

On dividing both sides by 11, we get

[tex]\begin{array}{l}{\Rightarrow \frac{11 x}{11}=\frac{36}{11}} \\\\ {\Rightarrow x=\frac{36}{11}=3.273}\end{array}[/tex]

Hence solution of equation 4(2x - 1) = -3x + 32 is 3.273

Answer:

30 hours

Step-by-step explanation:

Let the small pipe take time "t" to fill up the tank alone

Since larger pipe takes 15 HOURS LESS, so it will take "t - 15" time to fill up the tank alone

Let the whole tank be equal to "1" and each pipe fills up a fraction of the tank.

Smaller Pipe fills up 10/t, and

Larger Pipe fills up 10/(t-15)

Totalling "1". So we can write:

[tex]\frac{10}{t}+\frac{10}{t-15}=1[/tex]

Now, we solve for t. First, we multiply whole equation by (t)(t-15), to get:

[tex]t(t-15)*[\frac{10}{t}+\frac{10}{t-15}=1]\\(t-15)(10)+10t=t(t-15)[/tex]

Now we multiply out and get a quadratic and solve by factoring. Shown below:

[tex](t-15)(10)+10t=t(t-15)\\10t-150+10t=t^2-15t\\20t-150=t^2-15t\\t^2-35t+150=0\\(t-30)(t-5)=0\\t=5,30[/tex]

Since, this time is for the smaller pipe (which takes longer than 15 hours), so we disregard t = 5 and take t = 30 as our solution. So,

Smaller pipe takes 30 hours to fill up the tank alone

The smaller pipe takes 30 hours to fill the tank on its own, determined by solving the equation derived from the combined and individual rates at which each pipe fills the tank.

Since they can jointly fill the tank in 10 hours, we can use the rates at which they fill the tank to set up the equation: 1/x + 1/(x - 15) = 1/10. To find the solution, we multiply each term by 10x(x - 15) to clear the denominators, which gives us 10(x - 15) + 10x = x(x - 15). This simplifies to 20x - 150 = x^2 - 15x. Rearranging the terms yields x^2 - 35x + 150 = 0, which can be factored into (x - 30)(x - 5) = 0. Thus, x could be either 30 hours or 5 hours. Since x - 15 must also be positive, x = 30 hours is the correct solution, meaning the smaller pipe takes 30 hours to fill the tank alone.

Answer:

d.every word in the first sentence of the first page of every chapter.

Step-by-step explanation

The solution of (2.3 x 10^3) + (6.9 x 10^3)​ is [tex]9.2 \times 10^3[/tex] that is 9200

Need to solve the following expression:

[tex]\left(2.3 \times 10^{3}\right)+\left(6.9 \times 10^{3}\right)[/tex]

There are two terms in given expression

Let’s find GCF for this two terms  

The greatest number that is a factor of two (or more) other numbers. When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.

[tex]\begin{array}{l}{2.3 \times 10^{3}=2.3 \times 10^{3}} \\\\ {6.9 \times 10^{3}=3 \times 2.3 \times 10^{3}}\end{array}[/tex]

[tex]\text {So GCF between two terms is } 2.3 \times 10^{3}[/tex]

Let’s bring GCF out of the bracket in expression for sake of simplicity.

[tex]\begin{array}{l}{=>2.3 \times 10^{3}(1+3)} \\\\ {=>2.3 \times 10^{3} \times 4} \\\\ {=>9.2 \times 10^{3}} \\\\ {=>9200}\end{array}[/tex]

Hence on solving the expression (2.3 x 10^3) + (6.9 x 10^3) the result we get is [tex]9.2 \times 10^3[/tex] that is 9200

Answer:

-4/5

Step-by-step explanation:

slope = m = (difference in y)/(difference in x) = (-3 - 1)/(3 - (-2)) =-4/5

Answer:

63 Inches.

Step-by-step explanation:

2 yards - 9 inches is equal to 1.75 yards and when converted to inches, equals 63 inches.

Answer:

63 inches

Step-by-step explanation:

2 yards - 9 inches = 1.75 yards and when converted is 63 inches

Answer:

The error Tara made is she rewrote incorrectly 3 3/8 as 17/8 and 4 1/9 as 13/9,

the corrected number can be rewrote as 3 3/8 as 27/8 and 4 1/9 as 37/9.

Step-by-step explanation:

To find the Product of:

[tex]3\frac{3}{8}\times 4\frac{1}{9}[/tex]

The Number can be rewrote as,

[tex]\frac{3\times8+3}{8}\times \frac{4\times9+1}{9}\\\\\frac{24+3}{8}\times \frac{36+1}{9}\\\\\frac{27}{8}\times \frac{37}{9}[/tex]

Tara made error here she rewrote the number incorrectly 3 3/8 as 17/8 amd 4 1/9 as 13/9.

Now multiplying the fraction we get

[tex]\frac{999}{72}[/tex]

Because she rewrote incorrectly which led her answer to multiplication of fraction, the product too was incorrect which she wrote as 221/72.

Answer:

400

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the distributive property:

a(b + c) = ab + ac

5(x + 9) = (5)(x) + (5)(9) = 5x + 45

The equation to represent Juan's pay is P = 2300 + 90N. If he sells 21 copies of the book, his total pay would be $4190.

Pay Calculation

Given that Juan's base salary is $2300 and he makes an additional $90 for every copy of Math is Fun he sells, we can write an equation relating P (total pay) to N (number of sales) by adding together his base pay and his earnings from selling the books. This can be written as P = 2300 + 90N. We can then use this equation to calculate Juan's total pay if he sells 21 copies of the Math is Fun book. By substituting N = 21 into our equation, we get P = 2300 + 90*21, which simplifies to P = 2300 + 1890 = $4190. So, if Juan sells 21 copies of Math is Fun, his total pay would be $4190.

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Answer:

30x+45

Step-by-step explanation:

5*6x=30x

5*9=45

Answer:

30x + 45

Step-by-step explanation:

We distribute the 5 to the variable 6x and the constant 9:

5(6x+9)

5 x 6x = 30x

5 x 9 = 45

The answer is 30x + 45

For this case we must simplify the following expression:

[tex](2x ^ 3 + 6x-1) + (3x ^ 2-7x)[/tex]

We eliminate the parentheses taking into account that:

[tex]+ * + = +\\+ * - = -[/tex]

So, we have:

[tex]2x ^ 3 + 6x-1 + 3x ^ 2-7x =[/tex]

We add similar terms taking into account that:

Different signs are subtracted and the sign of the major is placed:

[tex]2x ^ 3 + 3x^2-x-1[/tex]

Answer:

[tex]2x ^ 3 + 3x^2-x-1[/tex]