Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-4, 3), (2,3)

Answer:

68.054

Step-by-step explanation:

I don't really have an explanation for this, it just is.

Sixty-eight (68) and fifty-four thousandths (.054, because the thousandths place is the third digit after the decimal point).

By using the graph we can see:

First, we want to find the value of x such that the graph touches (intercepts) the x-axis.

On the graph, we can see that it intercepts the x-axis at x = 0, so that is the x-intercept.

Now we want to find f(-2), this is the value of the function when x = -2, to find that we first need to find x = -2 in the horizontal axis.

f(-2) = 4

Now we want to find the value of x such that:

f(x) = 2

so now we need to find 2 in the vertical axis. we can see that the function is equal to 2 for x = -1.3 (approximation).

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As per the Simple interest concept, at 7% of rate the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly​ interest.

Simple interest.

Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

A financial planner has a client with 16000​$ to invest.

Here we need to calculate the rate does the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly​ interest when he invests $10,000 with the annual simple interest 12%.

Let us consider R represents the rate that remainder of money needs to be invested

Here we know that, $10,000 is invested at 12%

So, according to the formula the interest at 12% is evaluated as,

=> $10,000 * 0.12 * 1 = $1200

And the remaining $6000 is invested at R%

Then the interest at R%=$6000 * R * 1 = $6000R

Now we need to find that the two investments together need to yield at least $1620, so our equation to solve is:

$1620 = $1200 + $6000R

Now, we have to subtract $1200 from both sides, then we get,

$1620 - $1200=$6000R

Then collect similar terms

$420=$6000R

Now, divide both sides by $6000

R=0.07 or 7%

Therefore, the answer is 7%.

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Answer:

18 pi

Step-by-step explanation:

2xpixr d divided by 2 equals 9 pi x 2 x 9 =18

Answer:

Step-by-step explanation:

Givens

OF =     RF

OU = UR

Draw a line from U to F

UF = UF                              Reflexive property.

Solution

ΔOUF = ΔRUF                    SSS

<O = < R                              Congruent parts are congruent when the triangles are congruent.

Answer:

w - 20

Step-by-step explanation:

Remove the parenthesis by multiplying each term of (w + 5) by (-4)

-4(w + 5) + 5w = -4*w + 5*(-4) + 5w

                       = -4w - 20 + 5w

                       = -4w + 5w - 20

        Combine like terms. Like terms have same variable with same power.

                       = w - 20

SOLUTION

Solve the inequality.

divide both sides by -4

Answer:

2 points

Step-by-step explanation:

According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).

The height of the scale drawing in inches is 15.

As per the scale factor, the ratio of measurement in real is equal to the measurement to measurement of scale drawing. So, representing the two ratio -

3 inches : 2 feet = Height : 10 feet

Rearranging the formed ratio to find the height of bedroom in scale drawing is -

Height = (3 inches × 10 feet ) ÷ 2 feet

Performing division to find the height of bedroom in scale drawing

Height = 3×5

Performing multiplication to find the height of bedroom in scale drawing

Height = 15 inches

Therefore, scale drawing of 10 feet high bedroom will be 15 inches.

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The solution to the system of equation {x + y = 1, 3x - y = 7 } using augmented matrices is ( 2,-1 ).

Given the system of equation in the question;

x + y = 1

3x - y = 7

First, we write the system of equation in matrix form.

[tex]\left[\begin{array}{ccc}1&1&1\\3&-1&7\\\end{array}\right][/tex]

Next, we find the reduced row echelon form

Row operation R₂ = R₂ - 3R₁ to make the entry at 2, 1 a 0.

[tex]\left[\begin{array}{ccc}1&1&1\\3-3*1&-1-3*1&7-3*1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&-1\4&4\\\end{array}\right][/tex]

Next, multiply each element of R₂ by -1/4 to make the entry at 2, 2 a 1.

[tex]\left[\begin{array}{ccc}1&1&1\\-\frac{1}{4}*0 &-\frac{1}{4}*-4 &-\frac{1}{4}*4 \\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&1&-1\\\end{array}\right][/tex]

Now, perform the operation, R₁ = R₁ - R₂, to make the entry at 1,2 a 0.

[tex]\left[\begin{array}{ccc}1-0&1-1&1+1\\0&1&-1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&0&2\\0&1&-1\\\end{array}\right][/tex]

Using the result from the matrix, x = 2 and y = -1.

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The slope of the line above is -2.

The slope of a line can be defined as the change in y with respect to the change in x .

The slope can be regarded as rise over run.

The slope can be express in mathematical form as follows;

slope = m = y₂ - y₁ / x₂ - x₁

using the coordinates on the graph,

(0, 3)(3, - 3)

x₁ = 0

x₂ = 3

y₁ = 3

y₂ = - 3

Therefore,

slope = -3  - 3 / 3 - 0

slope = - 6 / 3

Hence,

slope = - 2

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The value of x is 6 degrees.

It is given in the question that:-

HI is parallel to JK and FG is the transversal intersecting HI at L and JK at M.

∠LMK = 115 degrees

∠MLI = (8x + 17) degrees

We have to find the value of x.

We know that,

Angles on the same side of the transversal sum up to 180 degrees.

Hence, we can write,

∠LMK + ∠MLI = 180 degrees.

115 + (8x + 17) = 180 degrees

8x + 132 = 180 degrees

8x = 180 - 132

8x = 48 degrees

x = 48/8 degrees

x = 6 degrees

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Answer:

1 91/100

Step-by-step explanation:

everything you need is in the picture

goodluck :)

Answer:The total cost is $41.04

Step-by-step explanation:

The rational number of 7¹/₃  as; a/b where a and b are integers.

A rational number is defined as any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero

Now, we are given the fraction as; 7¹/₃

This given number is expressed as a mixed fraction and so we convert it to improper fraction to get; 22/7

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pls tell me u understand the drawing

Step-by-step explanation:

Since right angles are 90°

11 = 90°

12 = 90°

13 = 90°

Step-by-step explanation:

I hope it will be helpful for you.

The minimum sample size of the given condition is 89.

In given condition,

For 95% confidence level, critical value of z is z* = 1.96

The margin of error given is E = 1

Standard deviation ( α ) = 4.8

Final required sample size is;

n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]

  = [tex](\frac{1.96 * 4.8}{1} )^2[/tex]

  = 88.51

n  ≅ 89

The minimum sample size of the given condition is 89.

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We want to find where to put the parentheses on each expression to make the expression true.

First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression

we have two symbols (+, *).

Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have

and

Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us

which coincides to the value we wanted.

In the second case, we have the following symbols / and -

This would give us two pairs for grouping, namely

and

as before, we will first evaluet the first option

If we try the second option, we woud get

which would give us the correct value.

The volume of the cylinder is 502.4m³

Volume of the cylinder:

Volume of the cylinder can be calculated by the product of the area of base and height.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

V = πr²h cubic units.

Given,

A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m.

Here we need to find the volume of the cylinder,

We know that the values of,

Radius = 4m

height = 10m.

Now we have to apply the value on the formula, then we get,

V = π x (4)² x 10

Apply the value of π as 3.14 then we get,

V = 3.14 x 16 x 10

V = 502.4

Therefore, the volume of the cylinder is 502.4 m³.

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If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Let the equation be

[tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]

Multiply both sides by 0.0375 / 12, and we get

[tex]$300000 \cdot \frac{0.0375}{12}=\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{\frac{0.0375}{12}} \cdot \frac{0.0375}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{1875}{2}=300\left(1+\frac{0.0375}{12}\right)^{12 t}$$[/tex]

Switch sides of the equation,

[tex]$300\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{1875}{2}$$[/tex]

Divide both sides by 300, and we get

[tex]$\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{300}=\frac{\frac{1875}{2}}{300}$$[/tex]

Simplifying the above equation, we get

[tex]$\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{25}{8}$$[/tex]

Apply exponent rules, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right)$$[/tex]

Solving the above equation, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right): \quad t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$[/tex]

[tex]$t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$$[/tex]

simplifying the above value of t, we get

t = 30.43236.

If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Therefore, the value of t = 30.43236.

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The number of millionaires Los Angeles should have will be equal to 5,065 millionaires.

Proportion may be defined as part or share of a complete unit compared with respect to the whole unit. A proportion is basically the equality of ratios. Two different ratios can be treated as equals if they are in proportion to each other. Now, the number of millionaires in Los Angeles will be equal to the Proportion of Millionaires in Dubai multiplied by the Population of Los Angeles that is

= 0.00124 × 4,085,014

= 5,065 millionaires

The Data and Calculations will be given as:

City                Millionaires     Population      Proportion

Los Angeles    11,560              4,085,014        0.00283 (11,560/4,085,014)

Casablanca     6,900              3,752,357        0.00184 (6,900/3,752,357)

Berlin               6,750              3,562,038         0.00189 (6,750/3,52,038)

Dubai               3,570              2,878,344         0.00124 (3,570/2,878,344)

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Complete Question:

City Millionaires Population

Los Angeles 11,560 4,085,014

Casablanca 6,900 3,752,357

Berlin

6,750

3,562,038

Dubai

3,570

2,878,344

Consider the chart of Millionaires and Population. If Los Angeles were

proportional to Dubai with respect to population, how many millionaires

should we expect Los Angeles to have? Round your answer to a whole number.

Answer:

(xy-6)(y-3)

Step-by-step explanation:

i don't know if you needed this, but if you need this i can explain step by step

xy(y-3)-6(y-3). we take the common ones out and than simplify as:. (xy-6)(y-3)

The population of the city in 5 years is 3430386 as the population is increasing 10% per year

What is percentage and how to calculate?

Percentage is the ratio which can be expressed as fraction of 100. And to calculate percentage we multiply by 100.

We are given that population of a city is 2130000

And the population is increasing at a rate of 10%

We are asked to find the population after 5 years

The equation can be given as (1.1)^x*2130000

We put x =5

We get

[tex](1.1)^5*2130000\\1.61051*2130000\\=3430386[/tex]

Hence the population will be 3430386 after 5 years at a rate of 10% increase per year

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Answer: 38 and 39

if you add them together you get 77

Answer:

38 & 39

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) = 77

→ 2x + 1 = 77

Now the value of x will be,

→ 2x + 1 = 77

→ 2x = 77 - 1

→ x = 76/2

→ [ x = 38 ]

Then the required integers are,

→ x = 38

→ x + 1 = 38 + 1 = 39

Hence, the integers are 38, 39.

The value that makes the triangle a valid triangle is x = 17

Angles are formed when two or more lines intersect.

This in other words means that angles is the measure of space between the intersection of rays or lines

The given parameters are

Shape = Triangle STU

Angle S = 6x - 15

Angle T = 2x - 2

Angle U = 4x - 7

The sum of angles in a triangle is 180 degrees

This means that

Angle S + Angle T + Angle U = 180

Substitute the known values in the above equation

So, we have the following:

6x - 15 + 2x - 2 + 4x - 7 = 180

Evaluate the like terms in the equation

So, we have the following:

12x = 180 + 15 + 2 + 7

Evaluate the like terms in the equation

So, we have the following:

12x = 204

Divide by 2

x = 17

Hence, the value of x is 17

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