Two parallel lines are cut by a transversal as shown below.
Suppose m2 = 97°. Find m5 and m<8

Expression as a single natural logarithm of -2 ln 2 is -1.386.

-2 ln 2

[tex]ln 2^{-2}[/tex] = - 1.386

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer: 2= -8+x

Step-by-step explanation:

Add eight to both sides to get

10=x

CHECK

then plug it in to get

2=-8+10

simplify

2=2

If you bought and then sold 300 shares at these prices, then the loss

would be $4,806.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

General Motors' stock fell from $41 per share in 2013 to $24.98 per share in 2016.

You bought and then sold 300 shares at these prices.

The price of 300 shares of General Motors stock in 2013 was:

300 x $41 = $12,300

The selling price of 300 shares of General Motors stock in 2016 was:

300 x $24.98 = $7,494

Therefore, the loss would be the difference between the purchase price and the selling price:

$12,300 - $7,494 = $4,806.

Therefore, the loss would be $4,806.

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The complete question;

General Motors' stock fell from $41 per share in 2013 to$24.98 per share in 2016. If you bought and then sold 300 shares at these prices, what was your loss?

Step-by-step explanation:

the common number of 4 and 8 is 8. You multiply 1/4 by 2 and it is equal to 2/8. 2/8+ 5/8= 7/8. 8-7=1. 1/8 of the houses are gray.

After five months, the percentage decrease in the daylight is 51.815%

As per the question, On the first day of June, there was 16.81 hours of daylight in a city and five months later, there was 8.10 hours of daylight. We are supposed to find the percent decrease in the daylight.

Percentage increases or decreases are calculated by setting the problem up proportionally.

We are trying to calculate at what percentage of 16.81 is 8.10 first

Let "x" be the percentage required percentage

therefore [tex]\frac{x}{100} =\frac{8.10}{16.81}[/tex]

[tex]x = \frac{8.10*100}{16.81} \\x=\frac{810}{16.81} \\x=48.185%[/tex]

8.10 is approximately 48.185% of 16.81.

So the percentage decrease is [tex]100 - 48.185=51.815[/tex]%

Hence the percentage decrease is 51.815%

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The coordinates of four points on each of the lines are:

6. (1, 4), (2, 9), (3, 14), (4, 19)

7. (1, 7), (2, 6), (3, 5), (4, 4)

8. (1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)

9. (1, -1.5), (2, 0), (3, 1.5), (4, 3)

10. (1, 4.5), (2, 5), (3, 5.5), (4, 6)

11. (0, -5), (3, -3), (6, -1), (9, 1)

12. (0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)

The equation of a line in slope-intercept form where m = slope and b = y-intercept is written as:

y = mx + b.

To find the coordinates, plug in x-values to find the corresponding y-values the equation of the line would give.

6. Slope (m) = 5

y-intercept (b) = -1

Equation of the line: y = 5x - 1

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 5(1) - 1

y = 4

y = 5(2) - 1

y = 9

y = 5(3) - 1

y = 14

y = 5(4) - 1

y = 19

The coordinates of four points on the line are:

(1, 4), (2, 9), (3, 14), (4, 19)

7. Slope (m) = -1

y-intercept (b) = 8

Equation of the line: y = -x + 8

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = -(1) + 8

y = 7

y = -2 + 8

y = 6

y = -3 + 8

y = 5

y = -4 + 8

y = 4

The coordinates of four points on the line are:

(1, 7), (2, 6), (3, 5), (4, 4)

8. Slope (m) = 0.2

y-intercept (b) = 0.3

Equation of the line: y = 0.2x + 0.3

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 0.2(1) + 0.3

y = 0.5

y = 0.2(2) + 0.3

y = 0.7

y = 0.2(3) + 0.3

y = 0.9

y = 0.2(4) + 0.3

y = 1.1

The coordinates of four points on the line are:

(1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)

9. Slope (m) = 1.5

y-intercept (b) = -3

Equation of the line: y = 1.5x - 3

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 1.5(1) - 3

y = -1.5

y = 1.5(2) - 3

y = 0

y = 1.5(3) - 3

y = 1.5

y = 1.5(4) - 3

y = 3

The coordinates of four points on the line are:

(1, -1.5), (2, 0), (3, 1.5), (4, 3)

10. Slope (m) = 1/2

y-intercept (b) = 4

Equation of the line: y = 1/2x + 4

Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:

y = 1/2(1) + 4

y = 4.5

y = 1/2(2) + 4

y = 5

y = 1/2(3) + 4

y = 5.5

y = 1/2(4) + 4

y = 6

The coordinates of four points on the line are:

(1, 4.5), (2, 5), (3, 5.5), (4, 6)

11. Slope (m) = 2/3

y-intercept (b) = -5

Equation of the line: y = 2/3x - 5

Substitute x = 0, 3, 6, and 9, into the equation to find their corresponding y-values:

y = 2/3(0) - 5

y = -5

y = 2/3(3) - 5

y = -3

y = 2/3(6) - 5

y = -1

y = 2/3(9) - 5

y = 1

The coordinates of four points on the line are:

(0, -5), (3, -3), (6, -1), (9, 1)

12. Equation of the line: y = 40x + 30

Substitute x = 0.1, 0.2, 0.3, and 0.4, into the equation to find their corresponding y-values:

y = 40(0.1) + 30

y = 34

y = 40(0.2) + 30

y = 38

y = 40(0.3) + 30

y = 42

y = 40(0.4) + 30

y = 46

The coordinates of four points on the line are:

(0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)

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Answer:

Step-by-step explanation:

flip 3/4 since we are dividing so we get 4/5 times 4/3 to get 16/15

So we get 1 1/15

Let me know if this was helpful

After evaluating the expression we get 2.

Given, x² ₋  x

Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.

A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.

substitute the value of x =2

2² ₋ 2

= 4 ₋ 2

= 2

hence we get the answer as 12.

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Based on the number of cups of flour and the number of teaspoons of cooking oil, if 1 cup of flour is used, the number of teaspoons of cooking oil needed is 2 / 5 teaspoons of cooking oil

When 5 cups of flour are used, then 2 teaspoons of cooking oil are needed by the recipe.

If there is only 1 cup of flour being used therefore, the number of teaspoons of cooking oil needed will be:

= Number of teaspoons needed for 5 cups / Number of cups of flour needed
= 2 / 5 teaspoons of cooking oil

First part of question is:
A recipe calls for 5 cups of four and 2 teaspoons of cooking oil.

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Paying monthly premium, at the end of 12 months Colin pays $1,155.36

Colin pays $95.36 more monthly than he would annually.

Colin pays (to the nearest percent) 8.99 % more by paying monthly premium than he would paying annually.

Premium is the amount of money one has to pay to insurance companies so that they provide us coverage at the time of need.

If we make payments monthly, the the premium is monthly.

If we pay the amount at the end of the year, then the premium is annual.

Given that Edmond has a $60,000 term life policy. The annual premium is $1,060. Colin pays $96.28 monthly.

Monthly premium of Edmond = $96.28

If he pays monthly, then total payment at the end of 12 months

= 12 *$96.28 = $1155.36

Then total payment at the end of 12 months is greater than the annual premium by = 1,156.36 - 1,060 = 95.36

Percentage of extra amount paid  when colin paid monthly

    = (extra payment made/ annual payment ) *100 = (95.36/1,060)*100             =8.99 %

Therefore, Colin pays 8.99 % more by paying monthly than he would paying annually.

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The length of the rectangular pool is 50 meters

The formula for perimeter of a rectangle is expressed as;

Perimeter = 2 ( l + w)

Where:

From the information given, we have;

Perimeter = 160 meters

Length = 20 + w

Substitute into the formula

160 = 2( 20 + w+ w)

expand the bracket

160 = 2(20 + 2w )

160 = 40 + 4w

collect like terms

160 - 40 = 4w

4w = 120

w = 120/ 4

w = 30 meters

But length = 20 + w = 20 + 30 = 50 meters

Thus, the length of the rectangular pool is 50 meters

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Answer: 10

Step-by-step explanation:

x = 2

y = 4

equation :

7x - y

after putting the values to the equation :

7(2x) - (4)

7*2 = 14

14 - 4 = 10

The answer is 10.

Answer:

170 ft²

Step-by-step explanation:

4ft = 48 in

You then multiply 48 by each given side.

48 in · 4.25in = 204 in

Divide by 12 to get answer in feet.

204 in ÷ 12 = 17

So the actual length of the side labeled 4.25 in is 17 ft.

48 · 2.5 = 120

Divide by 12 to get the answer in feet.

120 ÷ 12 = 10

The actual length of the side labeled 2.5in is 10 ft.

Area= L x W

Area= 17ft · 10ft = 170 ft²

The amount in a continuously compounded account is $ 565.2 .

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach.

The amount in the continuously compounded account is given as:

[tex]A=Pe^{rt}[/tex]

Where P is the principal amount, r is the interest rate, and t is the time period in years.

Now, we have

The principal amount, P = $500

Annual interest rate, r = 4.9 % = 4.9 / 100 = 0.049

Time = 2.5 years

Therefore, the amount in a continuously compounded account is:

[tex]\[A=Pe^{rt}\][/tex]

[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]

[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]

[tex]A = $500 \times e^{0.1225}[/tex]

A = $500 × 1.13031912007

A = $ 565.159

A = $ 565.2

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The two segments which have the same length are: D. segments YZ and VW.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

Next, we would determine the length of each segment as follows:

Length of segment WX is given by:

W (-2) and X (3)

WX = 3 - (-2)

WX = 3 + 2

WX = 5

Length of segment YZ is given by:

Y (10) and Z (18)

YZ = 18 - 10

YZ = 8

Length of segment XY is given by:

X (3) and Y (10)

XY = 10 - 3

XY = 7

Length of segment VW is given by:

V (-10) and W (-2)

VW = -2 - (-10)

VW = -2 + 10

VW = 8.

Therefore, segments YZ and VW are equal and have the same length.

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Complete Question:

Which two segments have the same length?  

A. segments WX and YZ

B. segments XY and YZ

C. segments VW and XY

D. segments YZ and VW

Step-by-step explanation:

a) Imagine folding the net into the shape. In this case, Net A can have both triangles fold up, and both rectangles fold in to make the above shape.

b) Side AB on this net is the height of the triangle, 3 inches.

   Side BC is the same as the hypotenuse (diagonal) on the triangle, which       .   is 5 inches.

   Side CD is the same as the length of the shape, which is 8.6 inches.

c) Surface area = area of all sides

Triangle = 1/2 bh

              = 2*3

              = 6 inches squared

There are two triangles, so that adds to 12 inches squared.

Now all of the rectangles:

Left most = 3*8.6

                = 25.8 inches squared

Middle = 4*8.6

            = 34.4

Right most = 5*8.6

                  = 43

Now we can add all of this:

43 + 34.4 + 25.8 + 12

= 115.2 inches squared.

This is the surface area of the prism.

Answer: 2.6 or 2 2/3

Step-by-step explanation:

3 1/4 = 3.25

3.25/5 = 0.65

0.65 x 4 = 2.6 or 2 2/3

The function rule after the given transformation is g(x) = -3x

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = 9x

Vertical compression = 1/3

Reflection in x-axis.

We know that when we compress a function f(x) by scale factor m

The new compress function is represented:

F(x) = m(f(x))

Reflection across the x-axis changes the sign of the new function.

Now,

With the vertical compression:

F(x) = 1/3 (f(x))

F(x) = 1/3(9x) = 3x

With the reflection in the x-axis:

g(x) = - F(x)

g(x) = -3x

Thus the function rule after the given transformation is g(x) = -3x

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The appropriate choice of ratio  will be given by

Polly got £30, Andy got £60, Phoebe got £180

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let Polly got £x

So Andy got £2x and Phoebe got £3(2x) = £6x

Total Amount = £(x + 2x + 6x)

                       = £9x

By the problem,

                         9x = 270

                           x = [tex]\frac{270}{9}[/tex]

                           x = 30

So Polly got £30,

Andy got £(2 * 30) = £60

Phoebe got £(6 * 30) = £180

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Reason:

The counting numbers, aka the set of natural numbers, is the set {1, 2, 3, 4, 5, ...} which is the set of positive integers

A value like 5 is the same as 5/1, which shows it is rational.

A rational number is any fraction of two whole numbers (eg: 2/3 and 4/7). The denominator cannot be zero.

Since we can rewrite the 5 as 5/1, it can be done with any counting number to show the natural numbers is a subset of the rational numbers.

Any counting number is rational, but not the other way around.

For continuous compounding, the effective annual interest rate is e^r - 1.

The following is the continuous compounding formula:

So,

Given: A(t) = a(1+r)^t and A(t) = a.e^rt.

Let the effective rate be R.

Then,  

Therefore, for continuous compounding, the effective annual interest rate is e^r - 1.

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Answer:

Im letting yall know rn that the answer actually 19 other guys wildn with 14

Step-by-step explanation:

Answer:

X=-5 :)

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

14+5=19, so -14+ -5= -19

The ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27

From the question, we are to solve the system of equations.

First, we will form the system of equations

Let x represent the ticket for a crab meal and y represent the ticket for a vegetarian meal

From the given information,

"One troop member sold tickets for 23 crab meals and 34 vegetarian meals, with total receipts of $1,930"

That is,

23x + 34y = 1930            -------------- (1)

Also,

"Another sold tickets for 20 crab meals and 38 vegetarian meals, bringing in a total of $1,906"

20x + 38y = 1906           -------------- (2)

Now, solve the equations simultaneously

Multiply equation (1) 20 and equation (2) by 23

20 × [23x + 34y = 1930

23 × [20x + 38y = 1906

460x + 680y = 38600

460x + 874y = 43838

Subtracting the resulting equations, we get

-194y = -5238

y = -5238/-194

y = 27

Substitute the value of y into equation (1)

23x + 34y = 1930

23x + 34(27) = 1930

23x + 918 = 1930

23x = 1930 - 918

23x = 1012

x = 1012/23

x = 44

Hence, the ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27

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Answer:

After 4 minutes

Step-by-step explanation:

After 1 min: Ant 1 is 9.75 mm underground. Ant 2 is 14.5 mm underground.

After 2 min: Ant 1 is 9.5 mm under. Ant 2 is at 14 mm under.

After 3 min: Ant 1 is 9.25 mm under.

After 4 min: Ant 1 is 9 mm under. Ant 2 is 13.5 mm under.

Ant 2 is now closer to the surface than Ant 1.

Answer:

Im pretty sure its A

Step-by-step explanation:

Total estimated cost for advertising= 30 +12x

The initial fees for ad is given= $30

And the fixed amount per click = 8 cents

Total number of click ad per day= 150

We know that,

$1= 100 cents

So 8 cents= $0.08

Now we will find the total estimated cost of advertising in dollars for x days.

Total estimated cost= The initial fees + charge per click ×total clicks ×total days

⇒ $30 + 0.08×150×x

⇒ 30+ 12x

Hence the answer is option( I) 30+12x.

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0.1678 is the probability that all the light bulbs work

Define probability?

Probability is a branch of mathematics and can be defined as the one which deals with the explanation of the possibility of an event to occur or take place. Probability has a range between 0 to 1. In probability, 0 indicates the impossibility of an event to occur and 1 indicates the certainty of that event to occur or take place.

As the light bulbs are not dependent on each other and work independently, the probability that all eight of the light bulbs will work can be calculated by multiplying the probability of each of the eight light bulbs.

As the probability of each of the eight light bulbs to work = 0.8

probability all the eight light bulbs work = 0.8^8

probability all the eight light bulbs work = 0.1678

Hence, 0.1678 is the probability that all the light bulbs work.

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