I need help I’ve been stuck on this problem for like 40 minutes already!!!

The numbers that are correctly written in scientific notation are:

Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.

The rules for correctly writing a scientific notation include the following:

Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.

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A) 42 x 10⁵

B) 1.1 x 10⁴

C) 7.0 x 20⁴

D) 6.01 x 10⁻⁴

E) 18.0 x 10³

The value of the side CB in the right angled triangle is found as 4√2 units.

For the given question,

The diagram is given;

AB = 7 units.

AG = 3 units.

GB = 7 - 3 = 4 units.

GC = 4 units.

In right angled triangle GCB, apply Pythagorean theorem.

CB² = GB² + GC²

CB² = 4² + 4²

CB² = 2(4)²

Taking square root both side.

CB = 4√2

Thus, the value of the side CB in the right angled triangle is found as 4√2 units.

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Answer:

9 quarters and 26 dimes

Step-by-step explanation:

your welcome :)

Answer:

x=17

Step-by-step explanation:

8x+20 is equal to 11x-31 because l parallel to m.

8x+20=11x-31

3x=51

x=17

Answer:

Step-by-step explanation:

L || m

[tex]\sf (8x+20)^o=(11x-31)^o[/tex]

[ Corresponding angles]

[tex]\sf 8x+20=11x-31[/tex]

[tex]\sf 8x-11x=-31-20[/tex]

[tex]\sf -3x=-51[/tex]

[tex]\sf \cfrac{-3x}{-3}=\cfrac{-51}{-3}[/tex]

[tex]\sf x=17^o[/tex]

__________________

Hope this helps!

Have a great day!

Answer:

9 days (round up)

Step-by-step explanation:

70 ÷ 8 = 8.75

           ≈ 9 (round up)

a) The coefficients are the costs of the respective shirts.

b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)

c) 3 solutions are:

(0, 25), (30, 0), (25, 4)

Here we know that:

And we have the linear equation:

10x + 12y = 300

The first coefficient is the one in the term "10x"

The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.

The second coefficient is on the term "12y"

And 12 means the cost in dollars of each long-sleeved shirt.

b) The graph of the linear equation can be seen on the image at the end.

The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.

The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.

c) 3 possible solutions can be seen on the graph, some examples are:

(0, 25), (30, 0), (25, 4)

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Answer:

y=5x+15

Step-by-step explanation:

the equation of a line is y=mx+b where b is the y-intercept and m is the slope.

if you look at the graph you will see that your line intecpts the y axes at b=15 or that would be your y value where the line touches the edge.

now you just have to find your slope. slope is y/x or rise/run

so by looking at the graph at where our line touches the corner of a square. we just need to find 2 of those. we can use (0,15) and (1,20) the distance from 15 to 20 is 5 so that is our rise or change in y. the distance from 0 to 1 is 1 so that is our change in x or run. now just put rise over run so 5/1 which is just 5.

lastly we fill out our equation y=mx+b

our slop m is 5 and our y-intercept b is 15 so y=5x+15

The number of square inches of the wrapping paper left over is 380 square inches

From the question, we have the following parameters that can be used in our computation:

Box:

Dimension = 8 inches by 9 inches by 10 inches

Rectangular-shaped wrapping paper

Dimension = 2 feet by 3 feet.

The surface area of the box is

Box = 2(lw + lh + wh)

So, we have

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10)

Evaluate

Box = 484 square inches

The surface area of the wrapping paper is

Wrapper = lw

So, we have

Wrapper = 2 * 3

Evaluate

Wrapper = 6 square feet

Convert to square inches

Wrapper = 864 square inches

The amount of square inches left is

Amount left = Wrapper - Box

Amount left = 864 square inches - 484 square inches

This  gives

Amount left = 380 square inches

Hence, the amount left is 380 square inches

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The functions g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, g(20) = -720 as a result of the mapping with the function g(x) = −2x² + 3x + 20

A function is a mapping whose codomain is the set of real numbers. It can also be defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

From the function g given as g(x) = −2x² + 3x + 20, by careful mapping we have the following;

put 0 for values of x

g(0) = -2(0)² + 3(0) + 20

g(0) = 20.

put -25 for values of x

g(-25) = -2(-25)² + 3(-25) + 20

g(-25) = -12.5 - 7.5 + 20

g(-25) = 0

put 4 for values of x

g(4) = -2(4)² + 3(4) + 20

g(4) = -32 + 12 + 20

g(4) = 0

put 0.75 for values of x

g(0.75) = -2(0.75)² + 3(0.75) + 20

g(0.75) = -1.25 + 2.25 + 20

g(0.75) = 21.125

put 20 for values of x

g(20) = -2(20)² + 3(20) + 20

g(20) = -800 + 60 + 20

g(20) = -720

Therefore, by proper mapping of the function g(x) = −2x² + 3x + 20, we derived g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, and g(20) = -720.

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Answer:

g(0) = 20

g(-2.5) = 0

g(4) = 0

g(0.75) = 21.125

g(20) = -720

Step-by-step explanation:

Hello!

We can evaluate each value by plugging the value inside the parenthesis into x in the equation [tex]-2x^2 + 3x + 20[/tex].

The values are, in order, 20, 0, 0, 21.125, and -720.

The freezing point of water in relation to the freezing point of acetone, is 169 °F

The difference between the freezing point of water (how much warmer the freezing point of water is) and the freezing point of acetone can be found by the formula:
= Freezing point of water - Freezing point of acetone

Freezing point of water = 32°F

Freezing point of Acetone = – 137°F

In relation to the freezing point of acetone, the degrees warmer that the freezing point of water is:

= 32 - (- 137)

= 32 + 137

= 169 °F

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Answer:

[tex]y_1=\boxed{-3}[/tex]

[tex]y_2=\boxed{-8}[/tex]

[tex]y_3=\boxed{-16}[/tex]

[tex]y_4=\boxed{-28.5}[/tex]

Step-by-step explanation:

Given:

Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:

[tex]y'=y-2x, \;\;y(3)=0[/tex]

at x = 3.5, 4, 4.5, 5.

Therefore:

[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]

Euler's Method

[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]

[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]

[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]

You can afford a car at a price of 13,016.79

What is the monthly payment formula?

The monthly payments are given by the equation presented as follows:

[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]

where R = r / 12

P is the initial amount , r is the interest rate , n is the number of payments.

Given data ,

A = $ 350

R = 6 %

r = 6 / 12 %

 = 0.5 %

 = 0.005

n = 5 years

  = 5 x 12 months

  = 60

Therefore , the maximum value of the car is calculated as

[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]

[tex]250=P\frac{0.005(1+0.005)^{60} }{(1+0.005)^{60}-1 }[/tex]

[tex]250=P\frac{0.0067}{1.3488501-1}[/tex]

[tex]P = \frac{250*0.348850}{0.0067}[/tex]

[tex]P=\frac{87.2125}{0.0067}[/tex]

P = 13016.79

Hence , you can afford a car at a price of 13,016.79

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Answer:5/6

Step-by-step explanation:

There are '5n' computers set up if they each set up the same number of computers.

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;

Ching and his 4 brothers set up computers at their family company.

Now,

Let the number of computers for each person = n

The total number of persons = 5

So, We can formulate;

⇒ The number of computers set up if they each set up the same number of computers = 5n

Thus, There are '5n' computers set up if they each set up the same number of computers.

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Answer:

  no, no, yes, yes

Step-by-step explanation:

You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.

The attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.

  (4, -5) . . . not a solution

  (-1, 8) . . . not a solution

  (7, 11) is a solution

  (0, -3) is a solution

Answer:

An arithmetic sequence occurs when the difference between each term and the next is constant. Therefore, only addition or subtraction is possible. Also, the amount (4, in this case) must remain the same when added to each successive term.

The amount to be credited, based on the invoice amount and the payment, is $612.24. The balance outstanding is $2, 387.76

Credit terms of 2/10, n/30 mean that if a buyer pays their payables in 10 days, they get a 2% discount. If they don't, then they'd have to pay the full thing in 30 days.

The days till the partial payment was made was:

= July 14 - July 5

= 9 days

The discount of 2% would apply on the payment of $600 so the amount to be credited is:

= 600 / (1 - 2%)

= $612.24

The balance would then be:

= Invoice amount - credited amount

= 3, 000 - 612.24

= $2, 387.76

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Answer:

25+10(4)= 65

Step-by-step explanation:

think of it as she makes 10 dollars an hour plus then she gets a 25 dollar bonus so you multiply the number of hours by 10 then and the bonus

Answer: $65

Step-by-step explanation:

25+10h h=4

25+10x4=

25+40=

65

Answer: 1/6

Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.

After 9 months each car will have the same number of miles on it.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here,

Let miles per month be x.

then, by a linear equation, we get

4298 + x(426) = 6129 + x(223)

203x = 1831

x = 9 months

Hence, after 9 months each car will have the same number of miles on it.

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Answer: [tex]x=\pm \sqrt{22}[/tex]

Step-by-step explanation:

[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]

Answer:

sqrt(22) = [tex]\sqrt{22}[/tex]

Step-by-step explanation:

we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem

log(x-1) + log(x+1) =  = [tex]log((x-1)(x+1))[/tex] = log(21)

this means that x^2 - 1 equals 21

xx-1 = 21

xx=22

x=sqrt(22)

The critical number are 0, 7 , -7.

Given function:

g(x) = [tex]\sqrt{49-x^{2} }[/tex]

first derivative is,

= -x/([tex]\sqrt{49-x^{2} }[/tex] )

-x = 0 or x = 0

[tex]\sqrt{49-x^{2} }[/tex] = 0

49 - [tex]x^{2} =0[/tex]

49 = [tex]x^{2}[/tex]

x = 7 , -7.

Therefore the critical number are 0, 7 , -7.

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Answer:

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

Answer:

-2/5

Step-by-step explanation:

the slope is change in y over change in x

formula for slope is

(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5

The equation of line with a slope of 3/2 which passes through point (-4,-2) is y = (3/2)x + 4.

The equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (-4, -2 )

First, we determine the y-intercept 'b'.

Plug the point and slope slope into the equation of line formula and solve for b.

y = mx + b

-2 = (3/2)(-4) + b

-2 = (3)(-2) + b

-2 = -6 + b

b = -2 + 6

b = 4

Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = (3/2)x + 4

Therefore, the equation of the line is y = (3/2)x + 4.

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Order of operation to simplify this expression as follows:

   [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]

⇒ [tex](1.125\times 1)\div2[/tex]

⇒ [tex]1.125\div 2[/tex]

⇒ [tex]0.5625[/tex]

What is order of operation?

The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.

The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.

PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.

Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])

Here, division is the highest priority ,

[tex]((0.25+7\div 8)\times 1)\div 2[/tex]

[tex]((0.25+0.875)\times 1)\div2[/tex]

and then we solve parathesis,

[tex](1.125\times 1)\div2[/tex]

now we do multiply,

[tex]1.125\div 2[/tex]

and the final answer will be [tex]0.5625[/tex]

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Answer:

below

Step-by-step explanation:

0.1

0.15

0.175

0.00125

1.13

2.02125

The given expression has a value of 2.5.

The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.

Given expression 6 x (2/3 divided by 2) + 0.5

To solve this expression, we must employ the BODMAS rule.

First 2/3 divided by 2

(2/3)/2

= 1/3

Now multiply 1/3 with 6

= 1/3 x 6

= 2

Now add both 2 and 0.5

= 2 + 0.5

= 2.5

Therefore the value of the given expression is 2.5

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The amount that is outstanding when Brett tallies up the transactions in his check.is $9.19.

From the information, Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72.

The amount that is outstanding will be the difference between the amount given. This will be:

= Bank statement - Total balance

= $257.72 - $248.53

= $9.19

This is the outstanding amount.

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Stock used to sell for $105.81 ten years ago.

[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]

Here, CAGR = Compounded Annual Growth Rate = -2.3%

               EV = Ending Value = x

               BV = Beginning Value = $83.80

                  n = No. of years = 10

Putting the values in the equation,

[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]

[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]

[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]

[tex]\frac{83.80}{x}=0.792[/tex]

[tex]x = \frac{83.80}{0.792}[/tex]

x = 105.81

Hence, the beginning value is $105.81.

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