The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2
The y-intercept is g(0) = 4The end behaviour is [tex]\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:[/tex]From the question, we have the following parameters that can be used in our computation:
The 5 functions of g(x)
To determine the key features of the function g(x), we make use of the first
g(x) = (x + 2)(x − 1)(x − 2)
So, we have
Zeros
This is when the function equals 0
(x + 2)(x − 1)(x − 2) = 0
Evaluate
x = -2, 1 and 2
The y-intercept
This is when the value of x in the function equals 0
g(0) = (0 + 2)(0 − 1)(0 − 2)
Evaluate
g(0) = 4
End behaviour
This is the behavior of the graph of the function as it approaches the ends of the x-axis
So, we have
[tex]\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:[/tex]
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find the area of the circle, which is circumscribed about the isosceles right triangle with area 8
Answer:8π
Step-by-step explanation:
To find the area of the circle circumscribed about an isosceles right triangle, we first need to determine the length of the hypotenuse of the triangle.
Given that the area of the isosceles right triangle is 8, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Since the triangle is isosceles and right-angled, the base and height are equal. Let's denote the base and height as 'x'.
8 = (1/2) * x * x
16 = x^2
x = √16
x = 4
Therefore, the length of the hypotenuse of the triangle is 4√2 (using the Pythagorean theorem).
Now, the diameter of the circle is equal to the hypotenuse of the triangle. So, the diameter of the circle is 4√2.
The radius of the circle is half the diameter, so the radius is (4√2)/2 = 2√2.
The area of a circle is calculated using the formula:
Area = π * radius^2
Plugging in the value of the radius, we get:
Area = π * (2√2)^2
Area = π * 4 * 2
Area = 8π
Therefore, the area of the circle circumscribed about the isosceles right triangle with area 8 is 8π.
which expression is a cube root of -2i?
The cube root of -2i,
⇒ ∛2[ cos(π/6) + i sin(π/6) ]
We can represent -2i in polar form as,
r(cosθ + i sinθ)
by computing its magnitude and angle.
The magnitude of -2i is 2
Since the absolute value of any imaginary number is equal to its magnitude.
To find the angle θ,
We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case,
The opposite side is -2 and the adjacent side is 0.
Therefore, we have tanθ = -2/0, which is undefined.
However,
We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.
So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).
Now, we need to find the value of θ/3. Since θ is undefined,
we will represent it as π/2 + 2πn,
where n is any integer.
So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.
Therefore, the cube root of -2i is equal to
⇒ ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]
Now put n = 0
⇒ ∛2[ cos(π/6) + i sin(π/6) ]
This is the final form of the cube root of -2i in the required form.
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part 1:
Oliver spends $200 to produce some pineapples. He is able to sell one for $6. If represents the number of pineapples he must sell to make a profit write an inequality and solve for p. Do not round your answer 6p>200
Part 2:
To make a profit Oliver must sell enough to cover the cost of producing 50 pineapples. If he sells each fruit at $6, how many of them must he sell to cover the cost of producing all 50. To make a profit he must sell more than $200 worth of fruit.
Part 1: Oliver must sell more than 33 pineapples to make a profit.
Part 2: Oliver must sell at least 33 pineapples to cover the cost of producing 50 pineapples and make a profit.
How to solvePart 1:
The inequality is 6p > 200.
To solve for p, we divide both sides of the inequality by 6. This gives us p > 33.33.
Therefore, Oliver must sell more than 33 pineapples to make a profit.
Part 2:
To cover the cost of producing 50 pineapples, Oliver must sell at least 50 * $6 = $300 worth of fruit.
Since he must sell more than $200 worth of fruit to make a profit, he must sell at least 200 / 6 = 33.33 pineapples.
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QUESTION 1 Determine the general solution of: 2 sin x. cos x = COS X
Starting with the given equation: 2 sin x cos x = cos x
By dividing both sides by cos x, we may simplify: 2 sin x = 1
Dividing both sides by 2:
sin x = 1/2
The values of x that fulfil sin x = 1/2 must now be found, and they are:
x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.
Therefore, the general solution is:
x = π/6 + 2πn or
x = 5π/6 + 2πn, where n is any integer.
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The students in Mrs. Barnett's first-grade class sit down in a circle for show-and-tell. The circle they form has a diameter of 4 meters. What is the circle's radius?
Answer:
Step-by-step explanation:
If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.
Can anyone explain how to solve this parallelogram question (CORRECT ANSWERS ONLY)
Answer:
x = 155° , y = 25° , z = 155°
Step-by-step explanation:
in a parallelogram
• opposite angles are congruent
• consecutive angles sum to 180°
then
x + 25° = 180° ( subtract 25° from both sides )
x = 155°
y = 25°
z = 155°
Can some one solve these three questions
(I WILL MARK BRAINLIEST)
The value of x and y is x ≈ 7.87 and y ≈ 25.38, the correct option is B.
We are given that;
Hypotenuse is 27 base is y and height is x the angle between base and hypotenuse is 17 degree
Now,
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
To find x and y, we can use the Pythagorean theorem and the trigonometric ratios for a right triangle. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The trigonometric ratios relate the angles and sides of a right triangle.
Using the Pythagorean theorem, we can write:
y^2 + x^2 = 27^2
y^2 + x^2 = 729
Using the trigonometric ratios, we can write:
sin(17°) = x/27
cos(17°) = y/27
Solving for x and y, we get:
x = 27 sin(17°) ≈ 7.87
y = 27 cos(17°) ≈ 25.38
Therefore, by pythagoras theorem answer will be x ≈ 7.87 and y ≈ 25.38.
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Need help with this math problem I don't understand it
The cost to manufacture a unit of energy drink, the selling price and the fixed monthly cost, indicates;
a. C(x) = 1.20·x + 8,000
b. R(x) = 2·x
c. Please find attached the graph of the Revenue and Cost functions showing the break-even point, created with MS Excel.
d. 10,000 units
e. $20,000
What is a cost function?The cost function is an function that describes the cost of producing a specified number if units of a services or goods.
a. The cost of production = The variable cost + The fixed cost
The variable cost = The cost per unit × The number of units produced
The cost per unit = $1.20
The fixed cost per month = $8,000
Let x represent the number of units produced per month, we get;
Cost of production, C(x) = 1.20·x + 8,000
b. The revenue function, R(x) = The selling price per item sold × The number of items sold
The selling price per energy drink = $2
Let x represent the number of units sold, we get;
Therefore, the revenue function is; R(x) = 2·x
c. Please find attached the graph for the Revenue and Cost functions, showing the break-even point, created with MS Excel
d. The coordinates of the break-even point on the graph is; (10,000, 20,000), therefore, the number of energy drinks the manufacturer has to sell to break even is; x = 2,000 units of the energy drinks.
e. The revenue the manufacturer has to take to break-even is equivalent to the cost at the same number of units sold, which is $20,000
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Find the equation of a line perpendicular to y=5x-3 and which passes through (-3,4)
Answer: Hope this helps :)
Step-by-step explanation:
The slope of the given line y = 5x - 3 is 5. The slope of a line perpendicular to it would be the negative reciprocal of 5, which is -1/5. Using the point-slope form of a line, we can find the equation of the line perpendicular to y = 5x - 3 that passes through the point (-3,4) as follows: y - y1 = m(x - x1), where (x1,y1) is the point (-3,4) and m is the slope -1/5. Substituting these values into the equation gives us: y - 4 = (-1/5)(x + 3). Simplifying this equation gives us: y = (-1/5)x - 3/5 + 4, or y = (-1/5)x + 17/5.
Answer:
To find the equation of a line perpendicular to y=5x-3 and which passes through (-3,4), we first need to find the slope of the line y=5x-3. The slope of this line is 5.
Since we want to find the equation of a line that is perpendicular to y=5x-3, we know that the slope of this new line will be the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.
Now that we know the slope of the new line, we can use the point-slope form of a line to find its equation. The point-slope form of a line is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.
Using the point (-3,4) and the slope -1/5, we get:
y-4=-1/5(x-(-3)
y-4=-1/5(x+3)
y-4=-1/5x-3/5
y=-1/5x+23/5
Therefore, the equation of a line perpendicular to y=5x-3 and which passes through (-3,4) is y=-1/5x+23/5.
Plot the polar coordinates: (-5, 5pi/4)
*The pictures attached are the graphs that are available to choose from.*
Plotting the polar coordinates: (-5, 5pi/4) matched with the image at
C (image plotted is attached)
What are polar coordinates?Polar coordinates are a coordinate system used to describe the position of a point in a two-dimensional plane.
Unlike rectangular coordinates (x, y), which use Cartesian coordinates to represent a point's position as distances along the x and y axes, polar coordinates represent a point's position using a distance from the origin (r) and an angle from the positive x-axis (θ).
The graph calculator showed the graph matching with the option C
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BRAINLIEST!!!!!! HELP PLSSSS. Ms. Browning has a box with 1 red marker, 1 blue marker, and 1 yellow marker in it. She will reach into the box without looking, select a marker, use it, and put it back. She will do this a second time. All of the possible combinations that Ms. Browning could select are shown in the tree diagram below. What is the probability that Ms. Browning will select a blue marker both times?
1/3
1/6
1/9
1/2
The probability that Ms. Browning will select a blue marker both times is 1/9.
To calculate the probability that Ms. Browning will select a blue marker both times, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Ms. Browning has 3 markers in the box: 1 red, 1 blue, and 1 yellow. Since she selects a marker, uses it, and puts it back, the total number of possible outcomes for the first selection is 3.
For each outcome of the first selection, Ms. Browning again has 3 markers to choose from for the second selection.
Therefore, the total number of possible outcomes for the second selection is also 3.
To calculate the probability of selecting a blue marker both times, we need to determine the number of favorable outcomes. There is only 1 blue marker in the box, and Ms. Browning needs to select it twice.
Therefore, the number of favorable outcomes is 1.
The probability of an event is given by the ratio of favorable outcomes to total outcomes.
In this case, the probability of selecting a blue marker both times is:
Probability = (Number of favorable outcomes) / (Number of total outcomes)
= 1 / (3 × 3)
= 1 / 9
Therefore, the probability that Ms. Browning will select a blue marker both times is 1/9.
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Students at Central Middle School were polled about their activities. The poll
showed that 68% of students play an instrument, and 24% of students play an
instrument and are on a sports team. What is the probability(in percent) that a
student is on the sports team, given that the student plays an instrument? Give
your answer as a percent rounded your to 1 decimal place.
The probability that a student is on the sports team, given that the student plays an instrument, is approximately 35.3% when rounded to one decimal place.
To find the probability that a student is on the sports team given that the student plays an instrument, we can use conditional probability.
Let's denote:
A = Event that a student plays an instrument
B = Event that a student is on the sports team
We are given the following information:
P(A) = 68% = 0.68 (probability of a student playing an instrument)
P(A ∩ B) = 24% = 0.24 (probability of a student playing an instrument and being on a sports team)
The conditional probability P(B|A) represents the probability of event B occurring given that event A has already occurred. It is calculated as:
P(B|A) = P(A ∩ B) / P(A)
Substituting the given values:
P(B|A) = 0.24 / 0.68 ≈ 0.3529
To express the probability as a percentage, we multiply by 100:
P(B|A) ≈ 0.3529 * 100 ≈ 35.3%
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The odds of an event happening are 7/3
What are the odds against the event happening?
A. 7/3
B/3/7
Need Help!!! Please and thank you. See the attached image to see the question.
Answer: It is around 3000 dolallars for you
Step-by-step explanation:
I am a Tax Preitor
Write the resulting matrix after the stated row operation is applied to the given matrix.
Replace R_2 with R_2+(3) R_3.
Please answer with a matrix written.
The resulting matrix is shown below:
3 0 1 1
4 20 2 20
3 -2 0 6
What is a matrix?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
We can write resulting matrix after replacing R2 with R2 + 3R3 as:
3 0 1 1
4 2 2 2
3 -2 0 6
We Perform the row operation:
R2 = R2 + 3R3
3 0 1 1
4 2 2 2 + 3(6) = 20
3 -2 0 6
In conclusion, the resulting matrix is:
3 0 1 1
4 20 2 20
3 -2 0 6
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( PLEASE I NEED HELP AASP!!)
Answer:
2/3 * 660
Step-by-step explanation:
If we convert 65% to a decimal, we get 0.65.
First, it will helpful to find exactly what is 65% of 668:
0.65 * 668 = 434.2 and thus 65% of 668 is exactly 434.2.
Similarly, if you convert 2/3 to a decimal, you get 0.66 repeating.
2/3 * 660 = 440 which is only 10.2 units larger than 434.2. Thus, 2/3 * 660 is the most accurate estimate of 65% of 668.
3x+10=8x pzz solve
I will pay u enough
The solution to the equation 3x + 10x = 8x is x = 2
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
3x + 10x = 8x
Collect the like terms
So, we have
8x - 3x = 10
When the like terms are evaluated, we have
5x = 10
Divide both sides by 5
x = 2
Hence, the solution to the equation is x = 2
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Mr. Tobata has needed funds due to a family emergency, as there has been a medical situation in the family. The doctor quoted K85,800 as the total expenditure. Mr. Tobata didn't have much savings and medical insurance was covered to the tune of K20000, and the rest had to be borne by Mr. Tobata. hence Mr.Tobata approached the bank and the bank was ready to give him a personal loan, Which would charge a rate of 17%; he agreed to the same and his tenure will be 12 years. Based on the same information you are required to calculate the monthly installment amount and the excess amount in the form of interest.
The excess amount in the form of interest is K58,784.92.
To calculate the monthly installment amount and the excess amount in the form of interest, we can use the loan amount, interest rate, and tenure.
Loan amount: Total expenditure - Medical insurance coverage
Loan amount = K85,800 - K20,000
Loan amount = K65,800
Interest rate per month: 17% / 12 months = 1.42%
Tenure: 12 years × 12 months
= 144 months
Monthly interest rate = 1.42% = 0.0142
Number of months = 144
Monthly installment = (K65,800 × 0.0142) / (1 - (1 + 0.0142)⁻¹⁴⁴)
Monthly installment = K763.43
So, the monthly installment amount is approximately K763.43.
To calculate the excess amount in the form of interest, we can subtract the total interest paid from the loan amount.
Total interest paid = (Monthly installment × Number of months) - Loan amount
Total interest paid = (K763.43 × 144) - K65,800
Total interest paid= K58,784.92
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simplify each algrebraic expression. drag tiles to correct boxes to complete the pairs.
-5x-2 5x+2 5x-2 -5x+2
(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.
(b) The algebraic expression, 5x -2 - (5x + 2) is simplified as -4.
What is the simplification of the algebraic expression?The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.
The given algebraic expressions are;
-5x - 2 + 5x + 2
5x -2 - (5x + 2)
The first algebraic expression is simplified as follows;
-5x - 2 + 5x + 2
collect similar terms;
(-5x + 5x) + (-2 + 2)
= 0 + 0
= 0
The second algebraic expression is simplified as follows;
5x - 2 - (5x + 2)
= 5x - 2 - 5x - 2
collect similar terms;
= (5x - 5x) + (-2 - 2)
= 0 - 4
= - 4
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Question 13 of 25
A sample of 64 was taken from a population, with the mean of the sample
being 42 and the standard deviation of the sample being 5. What is the 95%
confidence interval for the mean of the population?
A. (40.75, 43.25)
OB. (37,47)
OC. (41.375, 42.625)
OD. (37.25, 46.75)
User Identify the change in the parent function that will produce the related function shown as a dashed line move to the right and downward . f(x)=|x|
The transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units
How to describe the graph of g(x)From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we can see that
f(x) = |x|
g(x) = |x + 5| - 3
So, we have
vertical difference = 0 - 3 = -3
horizontal difference = 5 - 0 = 5
This means that the transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units
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Triangle J′K′L′ shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation:
Which scale factor was used to create triangle J′K′L′?
4
2
one quarter
one half
The scale factor of triangle J'K'L is determined as 2.
What is dilation of triangle?Dilation is a technique for creating similar figures. It is also a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors.
In the given diagrams of triangle, we can conclude the following;
consider triangle JKL, the height of the triangle = (6 - 3.5) = 2.5
consider triangle J'K'L', the height of the triangle = (12 - 7) = 5.0
The scale factor of triangle J'K'L is calculated as follows;
S . F = New height / old height
S. F = 5.0 / 2.5
S. F = 2
Thus, the scale factor of triangle J'K'L is calculated from the ratio of the new height to the old height.
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Answer:
The answer would be 2
Step-by-step explanation:
The coordinates of JKL
J (8,12)
K (4,8)
L (12,6)
and Prime J'K'L'
J' (4,6)
K' (2,4)
L' (6,3)
have a similar factor 2
for example, if we were able to multiply J' aka (4,6) by 2 then we would get the pre image coordinates aka J (8,12). And vice versa, if we divided the coordinates of J (8,12) by the scale factor 2 we would end up geting the prime numbers, J' (4,6).
Thanks for letting me answer <3
7. Use the diagram to find the value of the median of the trapezoid.
A. 4
B. 14
C.7
D. 28
The value of the median of the trapezoid is, 14 units
In the given diagram a trapezoid has been given with two bases,
AB = 7 units and CD = 21 units
We have to find, the median of the trapezoid.
Since, We know that median of a trapezoid is half of the sum of bases.
So, We get;
median of ABCD = 1/2 (AB + CD)
= 1/2 ( 7 + 21 )
= 1/2 ( 28 )
= 14 units.
Thus,. The value of the median of the trapezoid is, 14 units
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Paul designed a patio for his backyard. The patio will cost
$3 per square foot to construct. His design and the scale
he will use to build the patio are both shown below.
How much will Paul spend constructing the patio?
Scale
1 cm = 3 ft.
5 cm
4 cm
8 cm
dollars
6.4 cm
Paul will spend $1382.4 constructing the patio.
To calculate how much Paul will spend constructing the patio, we need to determine the area of the patio and then multiply it by the cost per square foot.
Looking at the scale provided, we can see that 1 cm represents 3 ft. We can use this scale to find the dimensions of the patio in feet.
The length of the patio is given as 8 cm, so the actual length in feet would be:
Length = 8 cm × 3 ft/cm = 24 ft.
Similarly, the width of the patio is given as 6.4 cm, so the actual width in feet would be:
Width = 6.4 cm × 3 ft/cm = 19.2 ft.
Now, we can calculate the area of the patio in square feet by multiplying the length and width:
Area = Length × Width = 24 ft × 19.2 ft = 460.8 sq ft.
The cost to construct the patio is $3 per square foot, so we can calculate the total cost by multiplying the area by the cost per square foot:
Total Cost = Area × Cost per square foot = 460.8 sq ft × $3/sq ft.
Total Cost = $1382.4.
Therefore, Paul will spend $1382.4 constructing the patio.
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A machine shop has 100 drill presses and other machines in constant use. The probability
that a machine will become inoperative during a given day is 0.002. During some days, no
machines are inoperative, but on other days, one, two, three, or more are broken down.
What is the probability that fewer than two machines will be inoperative during a
particular day?
Answer:
Math mode activated
Step-by-step explanation:
The number of machines that become inoperative during a given day follows a binomial distribution with parameters n = 100 (the number of machines) and p = 0.002 (the probability that a machine will become inoperative).
The probability that fewer than two machines will be inoperative during a particular day is the sum of the probabilities that zero or one machine will be inoperative. This can be calculated using the binomial probability mass function as follows:
P(X < 2) = P(X = 0) + P(X = 1)
= (100 choose 0) * (0.002)^0 * (1 - 0.002)^100 + (100 choose 1) * (0.002)^1 * (1 - 0.002)^99
= 1 * 1 * 0.817 + 100 * 0.002 * 0.818
= 0.817 + 0.164
= 0.981
Therefore, the probability that fewer than two machines will be inoperative during a particular day is approximately 0.981.
which of the following is an equation of the line tangent to the graph y= x+2/x at the point of where x=1
Answer:
input 1 : output 3
Step-by-step explanation:
For the graph y = x+2/x where x = 1, y = 3. So find which equation when input 1, outputs 3.
I need an equation for the line graph
The equation of the line on the graph passing through the points (-3, 3) and (3, -1) is [tex]y = -\frac{2}{3}x + 1[/tex].
What is the equation of the line passing through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
From the image, the line runs through points (-3, 3) and (3, -1).
First, we determine the slope (m) using the given points:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1} \\\\m = \frac{-1 - 3}{3-(-3)} \\\\m = \frac{-4}{3+3} \\\\m = \frac{-4}{6} \\\\m =-\frac{2}{3}[/tex]
Now, plug a point (-3,3) and the slope m = -2/3 into the point-slope form and solve for y:
y - y₁ = m( x - x₁ )
[tex]y - 3 = -\frac{2}{3}( x - (-3)) \\\\y - 3 = -\frac{2}{3}( x + 3) \\\\y - 3 = -\frac{2}{3}x - 2\\\\y = -\frac{2}{3}x - 2+3\\\\y = -\frac{2}{3}x + 1\\[/tex]
Therefore, the equation of the line is [tex]y = -\frac{2}{3}x + 1[/tex].
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Select the correct answer.
Which is the minimum or maximum value of the given function?
A.
ST 0
-11
-2
The function has a minimum value of 1.
The function has a maximum value of -2.
The function has a minimum value of -2.
3
The function has a maximum value of 1
The function has a maximum value of 1
Option D is the correct answer.
We have,
The y-coordinate on the graph is the function value.
Now,
From the graph of the function,
The maximum is at the point = (-2, 1)
This means,
1 is the maximum value.
And,
From the graph of the function,
The minimum value can be calculated because the graph is infinitely down the graph.
Thus,
The function has a maximum value of 1
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What is the m∠J, to the nearest tenth? JLK is right angle triangle. The length of JL is 9.4 and length of LK is 15.1. explaination?
The angle m∠J in the right angle triangle is 58.1 degrees.
How to find the angle of a triangle?One of the angle of a right tangle triangle is 90 degrees. The sum of
angles in a triangle is 180 degrees.
Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.
Hence,
tan ∠J = opposite / adjacent
tan ∠J = 15.1 / 9.4
∠J = tan⁻¹ 1.60638297872
∠J = 58.0909229196
Therefore,
m∠J = 58.1 degrees
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Most cats have shoulder heights between 8 and 12 inches. The
following compound inequality relates the estimated shoulder height
(in inches) of a cat to the internal dimension of the skull x (in cubic
inches):
8s 1.03x-32.4 ≤ 12
Which compound inequality represents the range for the skull size of
cats? Answer choices are rounded to the nearest hundredth.
The compound inequality representing the range for the skull size of cats is: 39.32 ≤ x ≤ 43.01.
To find the compound inequality that represents the range for the skull size of cats, we need to solve the given compound inequality:
8 ≤ 1.03x - 32.4 ≤ 12
Let's solve it step by step:
Add 32.4 to all parts of the compound inequality:
8 + 32.4 ≤ 1.03x - 32.4 + 32.4 ≤ 12 + 32.4
40.4 ≤ 1.03x ≤ 44.4
Divide all parts of the compound inequality by 1.03 (the coefficient of x):
40.4/1.03 ≤ (1.03x)/1.03 ≤ 44.4/1.03
39.32 ≤ x ≤ 43.01
Therefore, the range for the skull size of cats can be represented by the compound inequality:
39.32 ≤ x ≤ 43.01
Rounded to the nearest hundredth, the compound inequality representing the range for the skull size of cats is:
39.32 ≤ x ≤ 43.01
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