14 Jun 2018 · Norman is 12 years older than Michael. In 6 years, he will be twice as old as Michael. How old is Michael now? (A) 3 (B) 6 (C) 12

WE CAN USE THE GRAPH THAG CA HELP US IN THE PROBLEM

Lines a, b, c, and d are all straight lines in a two-dimensional coordinate system.

Line a has an equation of y=-x-2, which is the slope-intercept form of the equation of a line. This line has a slope of -1 and a y-intercept of -2. Line b is defined by two points (-6,1) and (3,-14), which can be used to find the equation of the line using the point-slope form of a line.

This line has a negative slope and passes through the points (-6,1) and (3,-14). Line c has two points (-1,8) and (4,11), which can also be used to find its equation using the point-slope form. This line has a positive slope and passes through the points (-1,8) and (4,11). Finally, line d has the equation -5x+3y=6, which is the standard form of the equation of a line. This line has a slope of -5/3 and a y-intercept of 2. These four lines are all different but all exist in the same two-dimensional coordinate system.

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The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.

If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.

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The triangles ΔIGH and ΔGFE are similar triangles. So, GJ / GE = HG / FG, then the side FE is parallel to the side HI.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the corresponding sides will be constant then the triangles will be similar triangles and the third sides of the triangles will be parallel.

GJ / GH = GK / GI, then the side KJ is parallel to the side HI.

In triangles ΔIGH and ΔGFE, then we have

∠IGH = ∠FGE        (Vertival angle)

∠1 = ∠2                         (Given)

Then the triangles ΔIGH and ΔGFE are similar triangles. Then we have

GJ / GE = HG / FG, then the side FE is parallel to the side HI.

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The height of the mountain using the angle of elevation is 3858.85 units.

The three basic categories of trigonometric functions are sine, cosine, and tangent. And from the basic functions, one can deduce the three cotangent, secant, and cosecant functions. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently.

Let the distance between the mountain and Matt = x.

Then the distance of Susie will be:

S = x - 1200

Matt measure the angle of elevation as 35 degrees.

Using the trigonometric function we have:

tan (35) = h / x

x = h/ 0.7.......(1)

For Susie:

tan(42) = h / x - 1200

0.9(x - 1200) = h

0.9x - 1080.48 = h .........(2)

Substitute the value of x in equation 2:

0.9 ( h/ 0.7) - 1080.48 = h

1.28h - 1080.48 = h

1.28h - h = 1080.48

0.28h = 1080.48

h = 3858.85

Hence, the height of the mountain using the angle of elevation is 3858.85 units.

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Answer:

x=120

Step-by-step explanation:

sum of angles is 540

given two right angles which is 90

90+90=180

540-180=360

360/3=120

All the values of y are calculated, the function table is complete. In this case, the final table looks like this

| x   | -2x | -2x-3 | y  |

| -2  | 4   | 1     | -3 |

| -1  | 2   | -1    | -5 |

| 0   | 0   | -3    | -3 |

| 1   | -2  | -5    | -7 |

| 2   | -4  | -7    | -9 |

The function y=-2x-3 is a linear equation. This means that the graph of the equation is a line with a constant slope. The slope of this line is -2 and the y-intercept is -3. The table above shows the output of the function for different values of x. To calculate the value of y for a given x, the first step is to calculate -2x. Then subtract 3 from the result to get the value of y. For example, for x=-2, -2*(-2)=-4 and -4-3=-3, so y=-3. For x=1, -2*(1)=-2 and -2-3=-5, so y=-5. In this way, the output of the function can be calculated for any given value of x.

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Probability of a successful call 0.3157 = 31.57%  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

A probability is the number of desired outcomes divided by the number of total outcomes.

The odds of making a sale on a single call are 6 to 13.

This means that in 6+13 = 19 calls, 6 are successful.

What is the probability of a successful call?

p = 6/19 =

0.3157 = 31.57% probability of a successful call.

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The 66 percent in the form of fraction representing the national average of the students graduating within six years from a private and non profit institution  is given by 33 / 50.

Percent of students graduating from private nonprofit institution within six years is equal to 66 percent

Value of one percent is equal to one part of  100

Percent in the form of fraction is given by :

⇒  1 percent = one part of hundred

⇒ 1 percent = ( 1 / 100 )

⇒ 66 percent  = ( 66 / 100 ) in fraction form

Simplify the fraction in more reduced form we get,

⇒ 66 percent  = ( 33 / 50 ) in fraction form

Therefore, the fraction form of the 66 percent students who have graduate within six years from private non-profit institution is equal to  ( 33 / 50 ).

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substitute y

3x - 2(6 + 4x) = 3

3x - 12 -8x = 3

-5x - 12 = 3

- 5x = 15

x = -3

The distance Danny travelled in 4 trips is 12 kilometres.

Danny cycled a total of 9 kilometres by making 3 trips to work. After 4 trips to work, the number of kilometres Danny would have cycled in total can be calculated as follows:

Using the proportional relationship,

3 trips = 9 kilometres

4 trips = ?

cross multiply

Distance cycled by Danny = 4 × 9 / 3

Distance cycled by Danny = 36 / 3

Distance cycled by Danny = 12 kilometres

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Answer:

C

Step-by-step explanation:

Plug (5, -2) into the equation

2(5) - (-2) =

10 + 2 =

12

C is the answer

(5, -2) is the answer

We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variables.

For the given inequality y > -x - 5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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The equivalent expressions are 7(2)^3x = 7(8)^x, 7(1/2)^x = 7(2)^-x, 7(4)^(3x + 1) = 7(2)^(6x + 2), 14(2)^x = 7(2)^(x + 1) and 14(2)^x = 14(4)^(x/2)

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

The expressions on the left and those on the right

To do this, we solve the expressions on the left and look for a match

Using the above as a guide, we have the following:

(a) 7(2)^3x

Evaluate the exponent

7(2)^3x = 7(8)^x

(b) 7(1/2)^x

Apply the law of indices

7(1/2)^x = 7(2^-1)^x

So, we have

7(1/2)^x = 7(2)^-x

(c) 7(4)^(3x + 1)

Apply the law of indices

7(4)^(3x + 1) = 7(2^2)^(3x + 1)

So, we have

7(4)^(3x + 1) = 7(2)^(6x + 2)

(d) 14(2)^x and (e) 14(2)^x

Without solving them, we have

14(2)^x = 7(2)^(x + 1)

14(2)^x = 14(4)^(x/2)

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Peter the rabbit have  51 carrots are left.

one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.

so total carrot is 84

and he ate one fourth on that day

so remaining are

84*1/4= 21

21 he eat on that the then remaining =

84 - 21  = 63

63 carrots are remain for next day and

he eat 12 carrot on next day

so remaining = 63 - 12 = 51

so 51 carrot left .

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The number of boards Mr.Kazoo should buy is given by the equation A = 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of boards Mr.Kazoo should buy be A

The total length of the board = 40 inches

The length of each board = 7 inches

So , the number of boards = total length / length of each board

Substituting the values in the equation , we get

The number of boards A = 40 / 7

The number of boards A = 5.71

The number of boards A = 6 boards

Hence , the number of boards is 6

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Answer:

To find a slope intercept in a table look what x is like this. ( 2,9) 2 is the x-intercept and 9 is the y-intercept. Furthermore, if you get a slope like 0,0 which is the origin put a dot on there.

Answer:

Step-by-step explanation:

use this equation

(y1-y2)/(x1-x2)

Turning 180° counterclockwise is essentially the same thing as a horizontal flip about the y axis.

That means C will find itself on the opposite side of the x axis, with negative inputs. However, it is still above the x axis, so it will have a positive y coordinate.

Your answer should be (-3,1)

Answer:

$19.29

Step-by-step explanation:

We know

Marisol buys a souvenir cup for $14.97 and a book of postcards for $4.32.

How much does Marisol spend?

14.97 + 4.32 = $19.29

So. Marisol spend $19.29

Answer:

-2x + 10

Step-by-step explanation:

When you add units you affect the y axis.

Knowing this you can translate it 14 units up by adding 14 + (-4).

The equivalent expression in expanded form of given function is -4x/4-4*3/4.

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We are given;

The expression of the function

=-1/4(-8x+12)

Now, to expand we take 4 common

=-1/4(-8x+12)

=-4/4(-1x+3)

=-4x/4-4*3/4

Therefore, the expression in expanded form will be -4x/4-4*3/4

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It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.

[tex]A = 325(1+0.047/12)^(12t)[/tex]

[tex]200 = 325(1+0.047/12)^(12t)[/tex]

[tex]200/325 = (1+0.047/12)^(12t)[/tex]

[tex]log_((1+0.047/12))(200/325) = 12t[/tex]

[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]

t = 8.75 years

It will take 9 years for the account to reach $200.

Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.

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If there are 15 boys and 17 girls in a math class then, the ratio of boys to girls is Option A. 15:17

The ratio of boys to girls in the math class is 15:17. This can be found by dividing the number of boys by the number of girls, which gives:

15/17

This ratio cannot be simplified because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls is 15:17.

The ratio of boys to girls in a math class is the relationship between the number of boys and the number of girls. The ratio is a way of expressing the comparison between two quantities. In this case, there are 15 boys and 17 girls in the class. To find the ratio of boys to girls, we divide the number of boys by the number of girls, which gives 15/17. This ratio cannot be simplified further because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls in the math class is 15:17. This means that for every 15 boys in the class, there are 17 girls.

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Answer:

We can start by finding the total number of learners who participate in jogging and cycling by multiplying the ratio by the total number of learners. Let's say x is the number of learners who jog. Then, the number of learners who cycle is 2x.

The total number of learners who jog and cycle is 125, so:

x + 2x = 125

3x = 125

x = 125 / 3

x = 41.67

Since x represents the number of learners who jog, there are 41.67 learners who jog. Since the number of learners who cycle is 2x, there are 2 * 41.67 = 83.33 learners who cycle.

Since these are whole numbers of learners, we round up to the nearest whole number to get 42 joggers and 83 cyclists.

The number of students participating in each of the sports will be 75 for jogging and 50 for cycling.

Solution:

Let's assume that the number of students who participated in jogging will be 3x and those in cycling will be 2x

Given,

3x + 2x = 125

5x = 125

So, x = 25

Therefore, the number of students in jogging will be 3*25 = 75 and in cycling will be 2*25 = 50

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Answer: bro just look it up fr fr

Step-by-step explanation:

The probability using the fair spinner to get P less than 4 is 3/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The total sections = 8.

The probability of less than 4 is:

P(less than 4) = Number of outcomes less than 4/ Total sections

P(less than 4) = 3/8

Hence, the probability using the fair spinner to get P less than 4 is 3/8.

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Answer: ITS 0.25!

Step-by-step explanation: i took the test

Answer:

Step-by-step explanation:

The formula to calculate the future value of an investment with compounded interest is:

Future value = Principal * (1 + rate/compoundings per year)^(number of years * compoundings per year)

In this case, the principal is $10,000, the interest rate is 2.5%, compounded annually, and the number of years is 20. So, the future value can be calculated as follows:

Future value = $10,000 * (1 + 2.5%/1)^(20 * 1)

Future value = $10,000 * (1.025)^20

Future value = $10,000 * 1.62897526

Future value = $16,289.75

Therefore, $10,000 deposited in an account earning 2.5% interest compounded annually would be worth $16,289.75 in 20 years.

The slope of this situation is equal to: C. 0.85.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = 10.20/12

Slope (m) = 0.85.

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By using Python to calculate the value of sin4 is a simple process that involves understanding the concept of radians and using the sine function available in Python's math module.

A radian is a unit of measurement for angles. It is defined as the angle formed when the arc length of a circle is equal to the radius of that circle. This means that an angle of 1 radian is equal to the angle formed by an arc length of 1 radius on a circle.

The sine function, denoted as sin(x), is a mathematical function that takes an angle x as input and returns the ratio of the opposite side to the hypotenuse in a right-angled triangle with an angle x.

Now, we can proceed to calculate the value of sin4 using Python. In Python, the sine function is available in the math module, so we will need to import this module at the beginning of our code. We will then use the sin() function to calculate the sine of 4 radians as follows:

import math

sin4 = math.sin(4)

Here, we are calling the sin() function and passing it the value of 4 as an argument. Since the sine function in Python accepts radians, we do not need to convert 4 to degrees.

Finally, we store the result of this calculation in a variable called sin4. This variable will now hold the value of the sine of 4 radians, which we can use in our program as needed.

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