8. Part A The area A of the rectangle shown is described with the inequality100 ≤A≤1,000. Select the compound inequality for the area written in termsof x. Length is 4x width is 5. A. 100 ≤ 10 + 8x ≤ 1,000B. 100 ≤ 18x ≤ 1,000C. 100 ≤ 9x ≤ 1,000D. 100 ≤ 20x ≤ 1,000

Answers

Answer 1

Answer:

(D)100 ≤ 20x ≤ 1,000

Explanation:

Given that:

Length of the rectangle = 4x

Width of the rectangle = 5

Area of the rectangle = Length x Width

=4x x 5

=20x

Therefore, the compound inequality for the area written in terms of x is:

100 ≤ 20x ≤ 1,000

The correct choice is D.


Related Questions

ABCD is a parallelogram. Find the length of BC.
А
B
4a - 1
5a - 4
D
с

Answers

One property of a parallelogram is that opposite sides are equal in length

Hence,

[tex]\begin{gathered} BC=AD \\ 9z-42=3z-6 \\ 9z-3z=42-6 \\ 6z=36 \\ z=\frac{36}{6} \\ z=6 \end{gathered}[/tex]

Side BC is then calculated as:

[tex]\begin{gathered} 9z-42=9(6)-42 \\ =54-42 \\ =12 \\ \\ \text{Therefore, BC is 12 units} \end{gathered}[/tex]

which of the following should be set equal to (x+y)³ to form an identity?A) (x+y) (x²-xy+y²)B) x³-y³-3xy (x-y)C) x³+y³+3xy(x+y)D) (x-y) (x²+xy+y²)

Answers

the answer is because

Alex found the change of his stocks over the following months: -10.29 in June, -8.16 in July, +34.50 in August, and +3.12 in September. Estimate the change in his stocks by rounding to the nearest whole number A) + 20B) + 56C) - 56D) -20

Answers

We have

[tex]-10.29-8.16+34.50+3.12=19.17\approx20[/tex]

Answer: A. + 20

Tim is using proportions to make a scale model of the front face of his school  building. He uses small building bricks that are __12 inch tall and 1 inch wide. The  front of Tim’s school is 24 feet tall and 50 feet wide.   Tim made a scale drawing of his model on a sheet of drawing paper. The  sizes of paper available to Tim were 9 in. × 12 in., 12 in. × 16 in., and   15 in. × 20 in. If Tim’s drawing of the school has a height of 8 inches,   which paper size would he have used so that the entire drawing was   shown, but left the least amount of empty space on the page? Explain. 

Answers

The paper sizes he has for his drawing are the following sizes

[tex]\begin{gathered} 9\text{inch}\times12inch \\ 12inch\times16inch \\ 15inch\times20inch \end{gathered}[/tex]

His drawing has a height of 8inches. Therefore, the drawing paper that can contain the drawing and still have the least amount of empty space is 9 inch by 12 inch. Since we only know the height of tim's drawing of the school , we can use a drawing paper above the required height of the tim's drawing. The

in PQR, V is the centroid. If VS=9 find RS

Answers

Answer: 27

Step-by-step explanation:

Centroid divides a median in 2:1 ratio,

So, RV/VS=2/1

⇒RV = 2*9 = 18

So RS = RV + VS = 18 + 9 = 27

What is the real number component of the complex numbers 6-2i?

Answers

We have the following:

The real part of a complex number is the integer part, that is:

Therefore, the answer is 6

This year you earned $75,500 Laat year you earned $72,400. What was the rate of change on your earnings since last yeara. 4.28%b. 4.68%c. 4.92% d. 5.12%

Answers

This year you earned $75,500 Laat year you earned $72,400.

the rate of change on your earnings since last year

[tex]\begin{gathered} R=\frac{75500-72400}{72400}\times100 \\ R=\frac{3100}{72400}\times100 \\ R=4.28 \end{gathered}[/tex]

So the rate of change is 4.28%.

Describe the transformation that takes place on the graph of ƒ(x) = x√3x3 to create the graph above.

Answers

Given the following graph after being translated, and being able to transform the initial function y = ∛x, the equation that must be applied is:

[tex]\text{ y = }\sqrt[3]{\text{ x - 2}}[/tex]

It means the graph must be translated into 2 units in the positive direction.

Shown in the graph,

Therefore, the answer is letter B.

Find a formula for the inverse of the given function.f(x) = 6xy =

Answers

The given function is

[tex]f(x)=6x[/tex]

First, we express the function in terms of y

[tex]y=6x[/tex]

Then, we isolate x

[tex]\frac{y}{6}=x[/tex]

Now, we exchange the variable to have the inverse of f(x)

[tex]y=\frac{x}{6}[/tex]Therefore, the answer is[tex]y=\frac{x}{6}[/tex]

As a scuba diver dives deeper and deeper into the ocean, the pressure of the water on his bodysteadily increases. The pressure at the surface of the water is 14.7 pounds per square inch (psi). Thepressure increases at a rate of 0.445 psi for each foot you descend.A. Write an equation that represents the pressure P as a function of the depth d.

Answers

The form of the linear equation is

y = m x + b, where

m is the rate of change

b is the initial value

Since the presure at the surface is 14.7 pounds per square inch, then

b = 14.7

Since the rate of increase of the pressure is 0.445 pound per foot

m = 0.445

The equation is P(d) = 0.445 d + 14.7

what is the percent change from 30 to 15.

Answers

A decrease of 50%

1) Considering the first number to be 30 we can write out

30 ------100%

15 ------- x

2) Cross multiplying it, we have:

1500=30x

x=50

Since 15 is 50% then we can subtract 50% from 100% and the answer is

A decrease of 50%

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 5.2% interest per year. He will put some of the money into Fund A that earns 4% per year and the rest in Fund B that earns 10% per year. How much should he invest into each fund (in dollars) if he wants to earn 5.2% interest per year on the total amount

Answers

Let x = the amount in fund A.

Let y = the amount in fund B.

Interest fund A = 4% = 0.04

Interest fund B = 10% = 0.10

Then, according to the information given we have that:

x + y = 55000

And the formula for determining simple interest is given by:

[tex]I=PRT[/tex]

Where:

P = initial capital

R = interest rate

T = time

We have the following equation

[tex]\begin{gathered} 0.04x+0.10y=0.052(55000) \\ 0.04x+0.10y=2860 \end{gathered}[/tex]

Next, we solve the system of two equations.

From the first equation we clear x:

[tex]\begin{gathered} x+y=55000 \\ x+y-y=55000-y \\ x=55000-y \end{gathered}[/tex]

Substitute x in the second equation:

[tex]\begin{gathered} 0.04x+0.10y=2860 \\ 0.04(55000-y)+0.10y=2860 \end{gathered}[/tex]

Simplify

[tex]\begin{gathered} 2200-0.04y+0.10y=2860 \\ 2200+0.06y=2860 \end{gathered}[/tex]

Solve for y:

[tex]\begin{gathered} 2200+0.06y-2200=2860-2200 \\ 0.06y=660 \\ \frac{0.06y}{0.06}=\frac{660}{0.06} \\ y=11000 \end{gathered}[/tex]

Then, for x:

[tex]x=55000-y=55000-11000=44000[/tex]

Answer:

Fund A = $44000

Fund B = $11000

camel can compute his school project in x hours. what part of the job can be completed by camel after 3 hours?

Answers

Given:

The time taken by the camel to complete the work= x hours.

Let 1 be the total work(W).

So, the work done per hour by the camel(Efficiency) is,

[tex]\begin{gathered} Efficiency(E)=\frac{\text{ Total work(W)}}{\text{Time}} \\ E=\frac{W}{x} \\ E=\frac{1}{x} \end{gathered}[/tex]

So, the efficiency of camel is 1/x.

Efficiency is a constant.

Since Work =Efficiency x Time taken, the work done by camel in t=3 hours is,

[tex]\begin{gathered} w=E\times t \\ =\frac{1}{x}\times3 \\ =\frac{3}{x} \end{gathered}[/tex]

We have to find what part of the of the job can be completed by camel after 3 hours.

Since total work is W=1, the part of the job can be completed by camel after 3 hours is,

[tex]\frac{w}{W}=\frac{\frac{3}{x}}{1}=\frac{3}{x}[/tex]

Hence, 3/x part of the job can be completed by camel after 3 hours.

Convert 16 charms to trams, given 5 charms equal 4 hotts, 3 hotts equals = 1 bill, 8 bills equal 10 rings, 5 rings equal 2 trams. Keep as improper fraction

Answers

We will have the following:

[tex]16charms\ast\frac{4hotts}{5charms}\ast\frac{1bill}{3hotts}\ast\frac{10rings}{8bills}\ast\frac{2trams}{5rings}=\frac{32}{15}trams[/tex]

So, 16 "chrams" is equivalent to 32/15 "trams".

Can somebody tell me if this correct? Or I have to do something else?

Answers

Keep in mind that "a less than b" means the same as "a substracted from b". Both can be represented algebraically as the following expression:

[tex]b-a[/tex]

Then, the correct algebraic expression for the first phrase, is:

[tex]\begin{gathered} (6\times3)-5 \\ 5\text{ less than the product of 6 and 3} \end{gathered}[/tex]

The rest of the given expressions are correct:

[tex]\begin{gathered} 3\times(6-5) \\ 3\text{ multiplied by the difference of 6 and 5} \end{gathered}[/tex][tex]\begin{gathered} (6\times5)-3 \\ 3\text{ substracted from the product of 6 and 5} \end{gathered}[/tex]

which group of students below should she ask to get the most representative sample

Answers

Given:

Sample size = 24

Given that she wants to ask the students which of the 5 speakers they would most like to hear, let's select the group of students she should ask to get the most representative of the sample.

In this case, the best group will be selected randomly to prevent sampling bias.

Hence, from the list, the best group to select is:

4 students from each of grades 1 through 6 at the all school

at what age is Giraffe 2 taller than Giraffe 1

Answers

The height of the giraffes is discribed with a linear graph. This means that their height grows at a steady rate, for every month that passes they'll grow a little. To find the moment at which the height of the giraffe 2 is greater than the height of the giraffe 1, we need to look at the graph. The graph has two axis, the horizontal axis and the vertical axis. The horizontal axis has the age of the giraffes, while the vertical one has their heights, we need to find the month at which the line for the giraffe 2 is above the line for the giraffe 1. This happens at 8 months.

mp + p^2use m = 2 and p = -4

Answers

SOLUTION

All we need to do is to substitute the value of m and p respectively into the equation, This can be seen below.

[tex]\begin{gathered} mp+p^2 \\ Since\text{ m=2 and p=-}4 \\ \text{This gives} \\ =(2\times-4)+(-4)^2 \\ =-8+16 \\ =8 \\ \end{gathered}[/tex]

Therefore, the answer is 8

Unit 3The Abbott family got their energy bill from Trident Power Company which showed the following uses of energy: gas usage = 57 therms; electricity usage = 1,049 kwh; taxesand other charges = $14.36. Given the information below, what was the total energy bill for the Abbott family? Trident Power Company has the following rates for gas andelectricity usage: Gas: Baseline usage: 25 therms At or below baseline usage: $1.15 per therm Above baseline usage: $1.41 per therm Electricity: Baseline usage: 450 KwhAt or below baseline usage: $0.40 per kwh Above baseline usage: 90.56 per Kwh

Answers

The gas usage was 57 and the rate for gas is 25 therms At or below baseline usage: $1.15 per therm Above baseline usage: $1.41 per therm, so in this case we use the above baseline usage $1.41 per therm

57 * $1. 41 = $80.37

The Electricity usage was 1,049 kwh and the rate Baseline usage: 450 Kwh

At or below baseline usage: $0.40 per kwh Above baseline usage: 90.56 per Kwh. In this case 1,049 kwh is above for the baseline 450 kwh, so we use 90.56 per Kwh

1,049 kwh *$ 90.56 = $94997.44

Then we sum the gas, electricity and taxes to know the total energy bill

$80.37 + $94997.44 + $14.36 = $95092.17

Quadratics 10x^2+ 23x =42Solve for x

Answers

First, bring the equation to the form ax²+bx+c=0 :

10x² + 23x - 42 = 0

Let's use quadratic formula: quadratic formula:

x =( -b ± √(b² - 4a*c) )/2a

a = 10

b=23

c=-42

x = (-23 ± √((-23)² - 4*10*-42)/2*10

x = (-23 ± √2209)/20

x1 = (-23 + √2209)/20 = (-23+47)/20 = 6/5 = 1.2

x2 = (-23 - √2209)/20 = (-23-47)/20 = -7/2 = -3.5

help me out please how do i plot these on a coordinate plane

Answers

Problem Statement

The question asks us to plot the points given in the table.

Solution

To plot the points, locate the x-values of each row on the table and trace it to their corresponding y-values on the y-axis.

For example, we can take the point (x = 3, y = 1) from the 3rd row in the table.

This is shown in the figure below:

The figure above shows an example of how to plot the points, given the values on the table.

After plotting all the points on the graph, we have the following:

Final Answer

We can pass a curve through all the points as follows:

Rewrite the following equation in slope intercept form 8x - 2y = -15Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

The given equation is

[tex]8x-2y=-15[/tex]

To express it in slope-intercept form, we have to solve the equation for y.

[tex]\begin{gathered} -2y=-15-8x \\ 2y=15+8x \\ y=\frac{8x+15}{2} \\ y=4x+\frac{15}{2} \end{gathered}[/tex]Hence, the equation in slope-intercept form is[tex]y=4x+\frac{15}{2}[/tex]

Estimate the rate of change of f(x) = 35(0.7)^x at x = 0.

Answers

To find the rate of change we need to find the derivative of the function. The derivative of an exponential function is:

[tex]\frac{d}{dx}a^x=a^x\ln a[/tex]

Then in our case we have:

[tex]\begin{gathered} \frac{d}{dx}\lbrack35(\text{0}.7)^x\rbrack=35\frac{d}{dx}(0.7)^x \\ =35(0.7)^x\ln 0.7 \\ =35\ln 0.7(0.7)^x \end{gathered}[/tex]

Now we evaluate the derivative at the point x=0, then:

[tex]35\ln \text{0}.7(\text{0}.7)^0=-12.4836[/tex]

Therefore the rate of change is appoximately -12.4836.

Fill in each blank so that the resulting statement is true

Answers

We have a synthetic division of polynomials.

The divisor is 2x+3.

In the last step, (2x+3) was multiplied by 8 resulting in 16x+24.

This has to be substracted from the remaining of the polynomial, that is 16x+5.

If we perform this substraction we obtain:

[tex]\begin{gathered} (16x+5)-(16x+24) \\ 16x+5-16x-24 \\ (16-16)x+5-24 \\ 0x-19 \\ -19 \end{gathered}[/tex]

Answer:

Completing the step designated by the question mark ("?") obtains -19.

Thus, the quotient (the result from dividing the polynomial 6x²-7x+5 by the divisor 2x+3) is 3x-8 and the remainder is -19.

The answer to this long division problem is (6x^2-7x+5)/(2x+3) = 3x-8-19/(2x+3)

Which equation has a constant of proportionality equal to 1? Choose 1 answer: 10 y = 11 7 y = 32 3. C y = 15

Answers

the constant of proportionality is the constant that multiplies the variable x

as we can see in the different options the only equation that the constant of proportionality is 1 is the option D.

y=x

Usually, we don't put the constant 1 when it is a constant of proportionality that is why we don't see the number one in this case.

2 Given f(x) = 45x" - 41x + 4 and g(x) = 9x - 1, where g(x) = 0, find (x). .

Answers

As given functions are:

[tex]\begin{gathered} f(x)=45x^2-41x+4 \\ g(x)=9x-1 \end{gathered}[/tex]

Given that g(x)=0, So:

[tex]\begin{gathered} g(x)=0 \\ 9x-1=0 \\ x=\frac{1}{9} \end{gathered}[/tex]

Now put the value of x in f(x):

[tex]\begin{gathered} f(x)=45(\frac{1}{9})^2-41(\frac{1}{9})+4 \\ f(x)=45(\frac{1}{81})-\frac{41}{9}+4 \\ f(x)=\frac{5}{9}+4-\frac{41}{9} \\ f(x)=\frac{5+36-41}{9} \\ f(x)=\frac{41-41}{9} \\ f(x)=0 \end{gathered}[/tex]

So the value of f(x) is 0.

Cody spent 27 hours practicing piano last week That is three times longer than his sister practiced. How many hours (h) did his sister practice

Answers

Time Cody's sister spent practicing x

Time spent by Cody is 3 times x = 27 hours

Express Cody time mathematically and solve for x

[tex]\begin{gathered} 3\times x=27 \\ 3x=27 \\ x=\frac{27}{3} \\ x=9\text{hours} \end{gathered}[/tex]

Since the time Cody's sister spent is x

Hence, Cody's sister spent 9 hours

Write the equation of the line parallel to y=2/3x+1/3 that passes through the point (-1,1)

Answers

The equation of line parallel to y=2/3x+1/3 that passes through the point (-1,1) is y = (2/3)x + (5/3).

What is equation of line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We can easily know whether a given point lies on a line or not using the equation of any line.

The given equation in the question is:

[tex]y = \frac{2}{3}x + \frac{1}{3}[/tex]

The slope of the line represented by this equation is 2/3

we know that, parallel lines have equal slope.

So, let the required lines slope be m, and m = 2/3

The equation of a line can be written in the form:

[tex]y-y_1 = m(x-x_1)[/tex]

Here, m = slope

(x1, y1) is given in the question as (-1,1)

Putting the values in the above equation:

[tex]y-1 = \frac{2}{3} (x-(-1))[/tex]

[tex]y-1 = \frac{2}{3} (x+1)[/tex]

[tex]y = \frac{2}{3}x+ \frac{2}{3} + 1[/tex]

[tex]y = \frac{2}{3}x+ \frac{5}{3}[/tex]

Therefore, required equation is y = (2/3)x + (5/3)

To know more about equation of line, go to link

https://brainly.com/question/12131651

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a) P(heads, then P)b) P(tails, then a vowel)2. A coin is tossed, then aletter from the wordINDIANAPOLIS is selected atrandom. Find eachprobability.c) P(tails, then N)d) P(heads, then D or 1)

Answers

we are asked to determine the probability of getting heads and the letter "P" from the word "INDIANAPOLIS". To do that we will use the product rule of probabilities:

[tex]P(head\text{ and P\rparen= }P(heads)\times P(P)[/tex]

The probability of getting heads is 1 out of 2 since there are only two possible outcomes, therefore, we have:

[tex]P(heads)=\frac{1}{2}[/tex]

The probability of getting "P" is equivalent to the quotient between the number of "P's" and the total number of letters:

[tex]P(P)=\frac{1}{12}[/tex]

Now, we substitute in the product:

[tex]P(heads\text{ and P\rparen=}\frac{1}{2}\times\frac{1}{12}[/tex]

Solving the product:

[tex]P(heads\text{ and P\rparen=}\frac{1}{24}[/tex]

Therefore, the probability is 1/24.

The same procedure is used to determine the other probabilities.

6 A line goes through Paints (0,2) and (1,1). what is the x-coordinate of the intersection of this line with the line y=3x+3?

Answers

Given: A line goes through points (0,2) and (1,1). Equation of the line formed between these two points will be:

[tex]\begin{gathered} \frac{y-2}{x-0}=\frac{2-1}{0-1} \\ \frac{y-2}{x}=-2 \\ y-2=-2x \\ 2x+y=2 \end{gathered}[/tex]

Thus, the eqaution of the line formed through points (0,2) and (1,1) is 2x+y=2.

Now solve equations 2x+y=2 and y=3x+3 to find the x coordinate of the intersection of this line.

[tex]\begin{gathered} y=3x+3---(1) \\ 2x+y=2---(2) \end{gathered}[/tex]

Substitute equation (1) in equation (2).

[tex]\begin{gathered} 2x+3x+3=2 \\ 5x+3=2 \\ 5x=-1 \\ x=-\frac{1}{5} \end{gathered}[/tex]

Thus, the x coordinate of the intersection of this line is x=-1/5.

Other Questions
Given ABC with points A (-1,2) B(4,-3) and C (0,0) dilated about a center at the origin by a scale factor of 3, what are the coordinates of C'? Show all work. Define a function that transforms the parent root function with a horizontal compression by a factor of 3 and a downward shift of 15 units Jacob has an 8 gift certificate to use at a toy store. He decides to buy a toy airplane that costs 8.61 and 3 toy cars that' cost 2.85 each which of the following is false concerning bonds? group of answer choices mortgage bonds are secured by assets such as real estate. subordinated debentures are riskier than unsubordinated debentures. the indenture spells out the obligations of the bond issuer. debentures are secured by assets other than real estate. To make fruit punch, the recipe calls for 2 parts of orange juice, 3 parts of ginger ale, and 2 parts cranberry juice. If 24 ounces of orange juice is used, how much ginger ale should be used? Select the correct answer. Simplify 75 Alec lives in New York City; his cousin Bonnie lives in Los Angeles, California. It is 3 hours earlier in Los Angeles than in New York City. Alec went to the show at 8:50 p.m. and returned 23 hours later. What time was it in "L.A." when Alec called Bonnie after the show? 7. Look at the figure. What is another name for line m? A vehicle uses 3 gallons of gasoline to travel 19 1/2 miles. At this rate, how many miles can the vehicletravel per gallon of gasoline? The rate constant for the first-order reaction below is 0.0385 M/s.A - B3rd attempthd See Periodic Table SIf the reaction is begun with an initial concentration of A equal to 0.95 M, what is the concentration of A after 34.01 s?M hello I'm a 7th grader please help me with this word problem and explain it in a way that a 7th grader can understand .. I have a test tomorrow and this is the review I dont understand this.Question 4 The angle of incidence of a light ray on a mirrored surface is 55.2o. What is the angle between the incident and reflected rays? The base of a triangle is multiplied by 1/3. which of the following describes the effect of this change on the area? Help, Please! Solve the system of equations:x + 3y = 152x + 2y = 14Group of answer choicesx = 3, y = -4x = 4, y = 3x = -3, y = -4x = 3, y = 4 A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 1.80 cm diameter into the bottle, placing it in direct contact with the wine. He is amazed when he pounds the cork into place and the bottom of the jug (with a 18.0 cm diameter) breaks away. Calculate the extra force (in N) exerted against the bottom if he pounded the cork with a 120 N force. A cylinder has a height of 6 in ches and a radius of 4 inches find the Volume and the Surface area Compare color photography with black and white photography. Discuss their pros and cons. According to you, does color in a photograph work for or against the image? how do u get the molar mass of NH3 ?? 8. The speed of light is 3.0 x 10^10 cm/sec. Express this speed in mi/hr. (You have choices with the scientific notation: multiply scientific notation with the conversion rate, or change the scientific notation to the standard numberbut count your zeros very carefully.)I need this in step by step, Id like explanations to understand too if possible