Solve the inequality 8y- 5 < 3

Given from the number line:

D = -2 and F = 13

So, the distance DF = 13 - (-2) = 13 + 2 = 15

1) find E such that, DE : EF = 2 : 1

so,

so, x : (15 - x) = 2 : 1

x = 30 - 2x

3x = 30

x = 10

So, E = -2 + 10 = 8

=========================================================================

2) E is 4/5 of the distance from F to D

So, the distance from F = 4/5 * 15 = 12

So, E = 13 - 12 = 1

=====================================================================

3) the ratio of DE : EF = 2 : 3

So,

3x = 2 ( 15 - x)

3x = 30 - 2x

5x = 30

x = 30/5 = 6

E = -2 + 6 = 4

=================================================

4) E is 1/3 of the distance from D to F

So, the distance DE = 1/3 * 15 = 5

So, E = -2 + 5 = 3

=====================================================

As a summery:

1) E = 8

2) E = 1

3) E = 4

4) E = 3

Light house is located at (-5,2)

Lighthouese beacon will illuminate a distnce =12 km

Use the distance formula to find the equation :

Distance formula is expressed as :

Substitute the given values :

The most appropriate choice for area of rectangle will be given by -

Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

What is area of rectangle?

Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°

The total space taken by the rectangle is called area of the rectangle.

If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m

Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m

Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]

                               = [tex]\frac{187}{40}[/tex]

                               = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

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Explanation:

We have to find 5% of the original cost first:

And then add it to the original price:

Since it's a price, we have to round this result to the nearest hundredth

Answer:

The new price is $23.09

Step 1 : Let's review the information given to us to answer the problem correctly:

• Annual salary of the governor of New York = $ 1,790,000

• Annual salary of the governor of Tennessee = $ 940,000

Step 2: Let x to represent the annual salary of the governor of New York

and let's find the ratio of the salary of the governor of Tennessee, as follows:

940,000/1,790,000 = 0.525

Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:

• 0.525x = Annual salary of the governor of Tennessee

•

Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:

0.525x = 0.525 * 2,000,000 = 1,050,000

The annual salary of the governor of Tennessee woudl be 1,050,000

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:

y = kx

for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

From the given options, the baove property is satisfied by,

Thus, the correct option is A.

Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.

It is represented by the following expression:

Since P=24 when Q=3, we can substitute and solve for the constant k:

Then, the equation that represents the inverse variation would be:

It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.

There are two types of unitary methods because they result in two types of variations and those are given below:

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The quadrants of a coordinate plane are:

Then, we can say that the rectangle PQRS is in the first quadrant.

the rriangle is 3 4 5 triangle so 5×5 is 25

Answer:

The first option is correct

Explanation:

Two negatives makes a positive.

Figure 1 was enlarged to figure 2

Hence the side |AB| is corresspounding to the side |PQ|

Arjun applied the wrong laws of logarithms.

The question can be solved as shown below:

Step 1: Apply the addition rule of logarithm given as

Thus, we have:

Step 2: Apply the subtraction rule of logarithm given as

Thus, we have:

Therefore, the correct answer is:

Given,

The coordinates of the point is (-8, 0).

There are two methods of bearing is:

Compass bearing

True bearing.

The figure of the point is,

The bearing of the point with respect to anticlockwise from north is,

The bearing of point from west is 0 degree and from anticlockwise north is 90 degree.

The true bearing is,

SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating compound amount

where

A = final compounded amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

STEP 2: Write the given data

Semiannually means that n will be 2

STEP 3: Calculate the compound amount

Hence, the compounded amount after 4 years is $18,748.1972

In triangle PQR

Construction: Draw PX perpendicular to QR where x lies on QR

Since:

PX perpendicular to QR

In the 2 triangles PXQ and PXR

given

proved up

PX = PX ------- common side in the 2 triangles

Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency

As a result of congruency

PQ = PR ------- proved

Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft

This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.

In the question we have the following data

b = 250 feet

angles = 31 degrees, 29 degrees

for the top α = 31 degrees, β = 59

For the bottom α = 29 degrees, β = 61 degrees

We have the formula as

a /sin α = b / sin β = c

tan ∅ = opp / adj

for ΔOCA

h1 = 250 x tan 39 degrees

= 250 x 0.8098

= 202.45

h2 = OCB

= 250 x tan 23

= 250 x 0.4245

= 106.125

The height h = h1 + h2

= 202.45 + 106.125

= 308.58

The height of the tower is 308.58 ft

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The x intercept is the value of x when y = 0

Given that x intercept = - 1, the coordinate is (- 1, - 0)

The y intercept is the value of y when x = 0

Given that y intercept = - 2, the coordinate is (0, - 2)

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

x1 = - 1, y1 = 0

x2 = 0, y2 = - 2

Slope = (- 2 - 0)/(0 - - 1)

slope = - 2/1

slope = - 2

Given the triangle XYZ with the following parameters

The diagram of the triangle is shown below

To find the value of x, we will apply sum of interior angle of triangle theorem

Hence, the value of x is 9.2308°

Solution

- The first integral is bounded by the x-values of [6, 22]

- The second integral is bounded by the x-values of [6, 14]

- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.

- The extra values are from 14 to 22.

- Thus, we have:

Final Answer

The slope intercept form of a line can be expressed as,

Here, m is the slope of the line and c is the y intercept.

Comparing the above equation with the given equation of a line y=-5x+2, we get

m=-5.

The slope of a line perpendicular to line with slope m is -1/m.

Hence, the slope of line perpendicular to y=-5x+2 is,

The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).

The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,

Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,

To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

so we have the point (0,1).

If x=1, then:

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

so we have the point (0,-3)

If x=1, then:

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.

The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)

The inverse of a function that maps x into y, maps y into x.

The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)

To determine the domain of

[tex] {f}^{ - 1}( x)[/tex]

The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x

The reflection of the point (x, y) across the line y = x, gives the point (y, x)

The points on the graph of the inverse of the function, f(x), [tex] {f}^{ - 1} (x)[/tex] are therefore;

[tex]( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)[/tex]

[tex]( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)[/tex]

( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)

The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)

Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, [tex] {f}^{ - 1}( x)[/tex], which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;

The domain of the inverse of the function, [tex] {f}^{ - 1}( x)[/tex], using interval notation is; [-2, ∞)

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Given:

The quadrilateral PQRS is given.

The aim is to locate the given quadrilateral into first quadrant only.

The graph will be reflected across x=4 then the graph will not be located to the first quadrant.

Problem

Determine the functions value when x= -1?

a. g(-1) = -3

b. g(-1) = 0

c. g(-1) = 1

d. g(-1) = 27​

Solution

For this case we just need to find the value of g when x= -1 and if we look at the table we got:

g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8

g(-1)= -1 +6 -12+8 = 5-12+8= 1

And then the solution for this case would be:

c. g(-1) = 1

For supplementary angles, we can do the following equality

What we have to do, is to clear "x" to find its value.

In conclusion, the value of x is 33

The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:

Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):

So the price in August is $38.02.