What is the justification for each step in solving the inequality?

3x+5/8≥4x−1/2

Select from the drop-down menus to correctly justify each step.

3x+5/8≥4x−1/2 Given

3x≥4x−9/8 ?????

−x≥−9/8 ?????

−x/−1≥−9/8/−1 ?????

x≤9/8 ?????

Chose from
Multiplication or Division property of order
Distributive property
Addition or Subtraction property of order

Answer:

Width of the store = 15 feet.

Step-by-step explanation:

Area = length * width

Plugging in the given dimensions:-

325 =  21 2/3 * x

x = 325 / 21 2/3

= 325 /  65/3

= (325 * 3) / 65

= 15 feet    (answer)

Answer:

Let x be the number of mile.

Total cost is no more than 130.

As per the given statement: if the car rental 94 a week plus 12 cent a mile.

12 cent a mile means 12x

then the equation become:

[tex]94 + 12x \leq 130[/tex]

Subtract 94 to both sides we get;

[tex]94 + 12x-94 \leq 130-94[/tex]

Simplify:

[tex]12x \leq 36[/tex]

Divide both sides by 12 we get;

[tex]x \leq 3[/tex]

Therefore, 3 miles she drive  if the car rental 94 a week plus 12 cent a mile.

Answer:

89 feet

Step-by-step explanation:

First of all, we will make a diagram to demonstrate the given scenario as shown in the attached picture.

Now we will use similar triangles to set the ratios as shown below to figure out the height of the building.

[tex]\frac{x}{130} =\frac{5.5}{8}[/tex]

Now we will solve for x from this equation by cross multiplying.

[tex]8x=130\cdot5.5[/tex]

[tex]8x=715[/tex]

[tex]x=89.375[/tex]

Therefore, height of the building is approximately 89 feet.

The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex]     multiply both sides by 3

[tex]a=\dfrac{3}{2}=4.5[/tex]

[tex]\dfrac{b}{4}=\dfrac{3}{2} [/tex]   multiply both sides by 4

[tex]b=\dfrac{3}{2}\cdot4=6[/tex]

[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex]     multiply both sides by 6

[tex]c=\dfrac{3}{2}\cdot6=9[/tex]

[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex]    multiply both sides by 7

[tex]d=\dfrac{21}{2}=10.5[/tex]

The perimeter:

[tex]P=4.5+6+9+10.5=30[/tex]

Answer:

a) -1 mult. 2 & 2 mult. 2

b) [tex]-a(x+1)^2(x-2)^2[/tex]

c) 4 at least (even degree could be 4, 6, 8, etc)

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -1,2

We can write them in intercept or factored form as (x+1) and (x-2).

Because the graph never crosses the x-axis each has an even multiplicity of at least 2.

The graph is facing down and is an upside down W so is negative. [tex]-a(x+1)^2(x-2)^2[/tex]

This means the function has a degree of 4 or higher with the degree being even.

[tex]a_n=a_1+(n-1)d\\\\d=a_{n+1}-a_n[/tex]

[tex]a_1=-19;\ a_2=-14;\ a_3=-9;\ a_4=-4;\ a_5=1;\ ...\\\\d=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\d=-14-(-19)=-14+19=5\\\\a_n=-19+(n-1)(5)=-19+5n-5=5n-24\\\\a_{100}=5(100)-24=500-24=476\to\boxed{c.}[/tex]

Answer: A

Step-by-step explanation:

[tex]V = 32,000(.8)^{t}[/tex]

   [tex]= 32,000(.8)^{2}[/tex]

   [tex]= 32,000(.64)[/tex]

  = 20,480

Answer:

B C E

Step-by-step explanation:

Just did it on edg

The incenter of a triangle is the center of the triangle

The true statements are:

From the diagram (see attachment), we have the following observations.

The lines from points X, Y and Z to point A are perpendicular to lines DX, DY and EF.

This mean that, point A is the center of a circle that passes through points X, Y and Z.

Hence, (b) is true

Also it means  that:

[tex]\mathbf{AX \cong AY \cong AZ}[/tex] --- the radius of the circle.

Hence, (c) and (e) are true.

So, the true statements are: (b), (c) and (e)

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Answer:

 The population at the end  of 2017 is 65,550

Step-by-step explanation:

 step 1; find the  population   at the end  of 2016

if 60,000   increases by 15% therefore final % = 100 +15 =115%

Therefore  60,000   = 100%

                         ?      =    115%

by cross multiplication

={ (115 % x 60,000) /100}  =69,000

Step 2:  find the population at the end  of 2017  

if  69,000   decrease by 5% therefore the final% = 100 -5 =95%

Therefore 69000  = 100%

           ?    =  95%

by cross multiplication

= 69000 x 95/100 = 65,550

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Using SOH CAH TOA in right triangle,

[tex]sin 22=\frac{opposite}{hypotenuse}[/tex]

[tex]sin 22=\frac{689}{x}[/tex]

[tex]x=\frac{689}{sin 22}[/tex]

Plugging the value of sin 22

[tex]x=\frac{689}{0.3746}[/tex]

[tex]x=1839.29[/tex] feet

So the distance is 1839.29 feet.

[tex]time=\frac{distance}{speed}=\frac{1839.29}{130}[/tex]

time=14.15 minutes   :    Answer

Hope it will help :)

Answer:

An equation with a slope of -3 and an intercept of -4 is y = -3x - 4

Step-by-step explanation:

To find this we start with the base form of slope-intercept.

y = mx + b

Now we know that the slope goes in for m and the intercept goes in for b. Simply input those values.

y = -3x - 4

Answer:4

Step-by-step explanation:

76/19=4

Answer:600 miles apart

Step-by-step explanation: one inch is 100 miles multiply that by 6 you get 600 miles

Answer:

The equation of this line is y - 7 = 4(x + 3)

Step-by-step explanation:

To find this, start with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the slope in for m and the two coordinates in for (x1, y1).

y - 7 = 4(x + 3)

Final answer:

The equation in Point-Slope form for the given point ( -3,7) and slope 4 is B. y - 7 = 4 ( x + 3 ). (Option B)

Explanation:

The correct equation in Point-Slope form for the given point and slope, where the point is ( -3,7) and the slope is 4, can be written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Substituting the given values, we obtain y - 7 = 4(x + 3).

Therefore, the correct equation in Point-Slope form is:

B. y - 7 = 4 ( x + 3 )

Answer:

550

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. Since we know the population increased to 200% of last year and is 1,100.

[tex]\frac{200}{100}=\frac{1100}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

200y=100(1100)

200y=110,000

y=550

There was 550 rabbits last year.

By applying percentages and division, we find that there were 550 rabbits last year, as this year's population of 1,100 rabbits is 200% or twice the amount of last year's.

The rabbit population in a certain area is 200% of last year's population. This year, there are 1,100 rabbits. It means that 1,100 is double the population from last year because 200% is equal to 2 times the original number. To find the population of rabbits last year, we need to take this year's total and divide it by 2. So, 1,100 rabbits divided by 2 equals 550 rabbits. Therefore, last year, the population of rabbits was 550.

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The measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that Aliya lined up the interior angles of the triangle along line p .

We have to find the what happens to angle When the measure of angle A increases in the triangle.

An angle is the figure formed by two rays, called the sides of the angle, sharing

When the measure of angle A increases in the triangles, the measure of angle A on line p also increases.

Hence,  the measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.

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Answer: D

Step-by-step explanation:

The orange color is represented by the bottom line, which is y > x - 2

The purple color is represented by the top line, which is y < x + 1

How do we know the equations of those lines?

The orange line:

The purple line:

Answer:

10 5/6 ounces

Step-by-step explanation:

That is 65 / 6

= 10 5/6 ounces

Solution:

Centroid: Point of intersection of Medians of Triangle which is drawn from opposite vertex.

Incenter : Point of intersection of Angle Bisectors drawn from opposite vertex of triangle.

Circumcenter : Point of intersection of Perpendicular bisectors of sides of triangle.

Orthocenter: Point of intersection of perpendiculars drawn from opposite vertex of triangle.

1.ABC Widget Company wants to build a central location for it’s new distribution center. They need the center to be equally located between their 3 stores. Which point of concurrency is needed to determine the best location?

Answer: Circumcenter , as it is equidistant from three vertices A, B and C.

2. Build it Furniture Company is designing a triangular pedestal table and need to determine the exact center of the table top. Which point of concurrency is needed to determine the exact location of the table top?

Answer: Centroid , it is located exactly inside the center of Triangle.

3. We could come up with a unique scenario for this point of concurrency but unfortunately this point is good for absolutely nothing.

Answer : Orthocenter,

4. Charleston is building a statue of Euclid to celebrate his influence in mathematics. The center of the park that they would like to build the statue of Euclid has a triangular walkway that borders the location for the statue. They want the statue to be the same distance from each side of the walkway. Which point of concurrency is needed to determine the best location within the triangular region?

Answer: Incenter, as it is a point which is equidistant from three sides of triangle.

Answer:

130m

Step-by-step explanation:

Let the ocean be the origin (0,0)between the the bird flying and the shark swimming. If the distance between a bird flying and the ocean is 100m and the distance between the ocean above and a shark swimming below the sea is 30 m, the distance between the flying bird and the shark will be calculated by adding the two distances to give;

=(100-0)+(30-0)

= 100+30

= 130m

Note that the ocean serves ad the origin(0,0) therefore the distance between each animal and the sea will be known first and the two values will be added as shown above to get the distance between the two animals.

Answer:

The length of arc AB is 120 centimeters.

Step-by-step explanation:

Given information: O is the center of circle and radius of the circle is 4 centimeters. It is given that [tex]x=30^{\circ}[/tex].

Length of arc is

[tex]l=2\pi r(\frac{\theta}{360})=r\theta[/tex]

Since the radius of circle is 4 and [tex]x=30^{\circ}[/tex], therefore

[tex]AB=4\times 30=120[/tex]

Therefore the length of arc AB is 120 centimeters.

Answer:

2π/3 cm

Step-by-step explanation:

usatestprep

Answer:

SSS congruency

Step-by-step explanation:

Here’s an easy way to remember it. S stands for side so it is side side side congruency.

Answer:

The correct option is (d)

domain= real numbers and Range= positive real numbers

Step-by-step explanation:

The given function is an exponential function in which the condition on the parameters are as follows-

f(x) = a^x

(1) Base condition is , a>0 and a≠1

(2) Domain = The value of x = x can take any value that is x∈ R

(3) Range = f(x)>0 that is f(x) can take positive values only.

She nee to save $60 more so she can buy a new bike

Answer:

(1) B. f(x)->0  as x->∞, f(x)->∞  as x->-∞

(2) D. [tex]f(x)= 2^{-x}+5[/tex]

Step-by-step explanation:

[tex]f(x) = b^x[/tex]. Given 0<b<1

'b' is between 0  and 1  so b should be a fraction

'b' is a fraction, so for positive value of x , the value of f(x) cannot be negative.

the graph of f(x) will goes close to 0 but it never cross x  axis

So end behavior is f(x)->0  as x->∞

for negative values of x , the y value increases

So end behavior is f(x)->∞  as x->-∞

(2)  f(x) = 2^x

When graph reflects across y axis, x becomes -x

so [tex]f(x)= 2^{-x}[/tex]

For translating up by 5 units we add 5  at the end

so [tex]f(x)= 2^{-x}+5[/tex]

When 0 < b < 1, the graph of the function f(x) = [tex]b^x[/tex] is decreasing. This means that the values of f(x) will get smaller and smaller as x gets larger and larger.

In the limit as x approaches positive infinity, f(x) will approach zero. On the other hand, in the limit as x approaches negative infinity, f(x) will approach positive infinity.

The correct answer is g(x) = 2*+5.

The function g(x) = 2*+5 reflects the graph of f(x) = 2x across the y-axis and translates it up 5 units.

The reflection across the y-axis is achieved by multiplying the function by -1.

The translation up 5 units is achieved by adding 5 to the function.

The graph of g(x) is also shifted up 5 units.

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Answer:

7

Step-by-step explanation:

The remainder from division by (x+1) is the value of f(-1). That remainder is the number at the lower right of the synthetic division tableau, 7.

Answer:

f(-1) is 7

Step-by-step explanation:

When using synthetic division, the value of the function is the final value of the division.

f(-1) is 7

Answer:

20 pages

Step-by-step explanation:

2 minutes is 1/2 of 4 minutes.

By proportion  number of pages he scans in 2 minutes = 1/2 * 40

= 20 pages

Final answer:

To calculate the number of pages a scanner can scan in 2 minutes, you divide the total pages scanned in 4 minutes by 4 to find the rate per minute, and then multiply by 2. The scanner can scan 20 pages in 2 minutes.

Explanation:

To find out how many pages a scanner can scan in 2 minutes if it can scan 40 pages in 4 minutes, we use proportion or unit rate since the scanning speed is constant. We start by determining how many pages are scanned in one minute. Since 40 pages are scanned in 4 minutes, we divide 40 by 4 to find the scanning speed per minute:

40 pages ÷ 4 minutes = 10 pages per minute.

Now we find out how many pages can be scanned in 2 minutes by multiplying the rate by the number of minutes:

10 pages per minute × 2 minutes = 20 pages.

Therefore, the scanner can scan 20 pages in 2 minutes at the given rate.

Answer:

[tex]h>1600[/tex]

Step-by-step explanation:

We have been given that Matt is climbing a mountain. When his elevation is higher than 1600 meters, breathing is difficult for Matt.

We are asked to write an inequality that describes h, the elevation at which breathing is difficult for Matt.

We know when elevation (h) will be higher than 1600 meters Matt will face difficulty in breathing. We can represent this situation as:

[tex]h>1600[/tex]

Therefore, inequality representing the elevation at which breathing is difficult for Matt will be [tex]h>1600[/tex].