The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question
Answers
Okay, here we have this:
Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:
[tex]\begin{gathered} Width=\frac{Area}{Length} \\ Width=\frac{9h^2+45h+36}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3\left(h+4\right)} \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}[/tex]Now, to know if the width is greater or less than the length, we will subtract it, then we have:
[tex]\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}[/tex]Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B
Related Questions
HELP I DONT UNDERSTAND THEIS QUESTIIONS
Answers
1) f(x)-3
[tex]\begin{gathered} f(x)=2x-4 \\ \Rightarrow f(x)-3=2x-4-3 \end{gathered}[/tex]Therefore, f(x)-3=2x-4-3
2) f(x-3)
[tex]\Rightarrow f(x-3)=2(x-3)-4[/tex]Thus, f(x-3)=2(x-3)-4
3) f(-3x)
[tex]f(-3x)=2(-3x)-4[/tex]Then, f(-3x)=2(-3x)-4
4) -3f(x)
[tex]-3f(x)=-3(2x-4)[/tex]Hence, -3f(x)=-3(2x-4)
What is 1/8 as a Decimal
Answers
The linear function
M= 10- 1.44p represents the amount m (in dollars)
of money that you have after printing p photographs.
(See Example 5.)
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.
Answers
Considering the given linear function, it is found that:
a)
The intercept is of 10, meaning that initially you have $10.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44.b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.
c) The graph of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule given below:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).The amount of money you have remaining after printing p photographs is modeled by the following function:
M(p) = 10 - 1.44p.
Hence the coefficients are as follows:
The intercept is of b = 10, meaning that initially you have $10 to spend on printing photos.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44, that is, for each photo you print, you are going to lose $1.44 from your amount.The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.
You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:
{0, 1, 2, 3, 4, 5, 6, 7}.
Considering the above domain, the graph of the function is given by the image at the end of the answer.
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RCX)=2VX SCx) = x(RSX4=
Answers
Given the two functions:
[tex]\begin{gathered} R(x)=2\sqrt[]{x} \\ S(x)=\sqrt[]{x} \end{gathered}[/tex]We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:
[tex](RoS)(x)=2\sqrt[]{\sqrt[]{x}}[/tex]When we plug in "4", into "x", we have:
[tex]\begin{gathered} (RoS)(x)=2\sqrt[]{\sqrt[]{x}} \\ (RoS)(4)=2\sqrt[]{\sqrt[]{4}} \\ =2\sqrt[]{2} \end{gathered}[/tex]are all angles are congruent to one another
Answers
Answer:
Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
5. Higher Order Thinking Linda wants to show
skip counting by 5s from a number to get to
1,000. Write the numbers she should put on
her number line below. How do you know?
1,000
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The numbers that Linda should put on her number line are 5,10,15,20...1000 .
Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.
The numbers are skip counted. so each number differs from the preceding number by 5.
let us take the number counting starts from 0. so the second number will be 5+5=10
The third number 10+5 = 15 and so on and so forth.
Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.
A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.
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PLEASEEE HELP ME
find the inverse of f(x)=1/x+5 -1 and it’s domain
Answers
Answer:
C
Step-by-step explanation:
HOPE IT HELPS MARK BRAINLEIST PLS
help meeeeeee pleaseee !!!!
Answers
The linear equation that passes through the two points (0, 360) and (10, 560) is:
y = 20*x + 360
How to find the linear equation?Remember that the slope-intercept form of a linear equation is:
y = a*x + b
Where b is the y-intercept and a is the slope or rate of change.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Here the line must pass through (0, 360) and (10, 560), so the slope is:
[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]
And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:
y = 20*x + 360
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Solve 3x - 2y = - 6 if the domain is {-2, -1, 0, 2, 3).
Write your answer as ordered pairs.
Answers
The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.
Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,
At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.
These are the values of outputs, and the ordered pair will be expressed as
{0, 3/2, 3, 6, 15/2}.
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In an apartment 40%read the nation 25%read the standard 5%read both .if a random resident is selected calculate the probability that
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Astronomers discover an exoplanet (a planet of a star other than the Sun) that has an orbital period of 3.95 Earth years in its circular orbit around its sun, which is a star with a measured mass of 3.97×1030kg . Find the radius of the exoplanet's orbit.
Answers
The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.
How to calculate the radius of the exoplanet's orbit?In order to calculate the radius of the exoplanet's orbit, we would apply Kepler's Third Law of planetary motion.
Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:
T² = 2π√(r³/GM)
Where:
T represents the orbital period.M represents the mass.G represents the universal gravitational constant.r represents the radius.Making radius (r) the subject of formula, we have:
Radius, r = ∛(GMT²/2π)
Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².
Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds
Substituting the given parameters into the formula, we have;
Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)
Radius, r = 4.71 × 10¹¹ meters.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
The correct option is True, there is enough information given to say that both line are parallel.
What is termed as as the supplement angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.For the given question.
The two lines are given with angles measure from 1 to 8.
Where,
∠4 = 89°∠3 = 91°As, the sum of the angles is;
∠4 + ∠3 = 91° + 89°
∠4 + ∠3 = 180° (supplementary angles)
Thus, we can say that both lines are parallel to each other.
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Two trains for Palwal leave Kanpur at 10 am and 10:30 am and travel at the speeds of 60Kmph and 75Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Answers
Answer:
150 km
Step-by-step explanation:
You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.
SetupAt t hours after 10 am, the distance of the first train from Kanpur will be ...
distance = speed × time
distance = 60t
At t hours after 10 am, the distance of the second train from Kanpur will be ...
distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am
These distances will be equal when ...
60t = 75(t -1/2)
SolutionThe time at which the trains meet will be the solution to the above equation.
60t = 75t -37.5 . . . . eliminate parentheses
0 = 15t -37.5 . . . . . . subtract 60t
0 = t -2.5 . . . . . . . . . divide by 15
2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves
The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:
60t = 60(2.5) = 150 . . . . km
The two trains will be together 150 km from Kanpur.
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯¯
K
M
.
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Answer L
Order from least to greatest5/6 4/50.82
Answers
Okay, here we have this:
Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:
Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:
Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.
A football team has a 60% chance of winning a league trophy each season it competes. What would be its probability of winning two times in three consecutive seasons?
Answers
Answer:
P(X = 2) = 43.2%
Step-by-step explanation:
P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)
P(X = 2) = 54/125
P(X = 2) = 0.432
P(X = 2) = 43.2%
Please!!Find the value of each variable. Write theequations and solve showing ALL the work.If an answer is not a whole number, leaveit in simplest radical form.
Answers
The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:
• For the larger triangle and the triangle on the left
[tex]\frac{z}{9}=\frac{5}{z}[/tex]From this equation, we can solve for z, to get:
[tex]\begin{gathered} \frac{z}{9}\times z=\frac{5}{z}\times z \\ \frac{z\times z}{9}=5\times\frac{z}{z} \\ \frac{z^2}{9}=5\times1 \\ \frac{z^2}{9}=5 \\ z^2=5\times9 \\ z^2=45 \\ z=\sqrt[]{45} \\ z=3\sqrt[]{5} \end{gathered}[/tex]Then, z equals 3√5
• Similarly, with the larger triangle and the one on the right:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \end{gathered}[/tex]From this expression, we can solve for x, like this:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \frac{x^2}{9}=4 \\ x^2=4\times9 \\ x^2=36 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Then, x equals 6
• With the triangles on the right and on the left:
[tex]\frac{y}{4}=\frac{5}{y}[/tex]Solving for y, we get:
[tex]\begin{gathered} \frac{y}{4}=\frac{5}{y} \\ \frac{y^2}{4}=5 \\ y^2=5\times4 \\ y^2=20 \\ y=\sqrt[]{20} \\ y=2\sqrt[]{5} \end{gathered}[/tex]Then, y equals 2√5
2.Graph and complete the t-chart for the function y=2/3 x +5.
Answers
Recall that to complete the table we have to evaluate the given function at every value of x:
[tex]\begin{gathered} y(-3)=\frac{2}{3}(-3)+5=-2+5=3, \\ y(3)=\frac{2}{3}(3)+5=2+5=7, \\ y(6)=\frac{2}{3}(6)+5=4+5=9. \end{gathered}[/tex]Answer:
Table:
Graph:
find the perimeter of the hallway
Answers
Answer: 17x - 39
Step-by-step explanation:
1) Find all sides of the hallway.
P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1
2) Add it together
P= 17x - 39
What happens to the surface area of a sphere if the radius is doubled?b. What happens to the surface area of a sphere if the radius is tripled?
Answers
Given:
a) The radius is doubled.
b) The radius is tripled.
To find:
The changes to the surface area of a sphere
Explanation:
Let us take the original radius as r.
The surface area of the original sphere is,
[tex]A=4\pi r^2[/tex]a) The new radius will be,
[tex]R=2r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes four times the original surface area if the radius is doubled.
b) The new radius will be,
[tex]R=3r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is tripled.
Juan rides the bus to school each day. He always arrives athis bus stop on time, but his bus is late 80% of the time.Juan runs a simulation to model this using a randomnumber generator. He assigns these digits to the possibleoutcomes for each day of the week:• Let 0 and 1 = bus is on time• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is lateThe table shows the results of the simulation.
Answers
B. 2/10 = 20%
Explanations:The total number of weeks shown in the simulation = 10
By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3
The number of weeks that Juan was late everyday = 2
The estimated probability that Juan will be late evryday of next week = 2/10 = 20%
The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. i think its 12
Answers
Answer: Correct! The answer is 12.
Step-by-step explanation:
1) Draw the triangle.
Drawing a triangle usually helps you see the problem better!
| \
| \ 13 cm
| \
|______\
5 cm
2) Solve the other leg
To find the other leg, we need to use the Pythagorean theorem. Which goes like this
[tex]a^2+b^2=c^2[/tex]
We will then substitute the numbers into the equation
[tex]5^2+b^2=13^2[/tex]
Simplify
[tex]25+b^2=169[/tex]
Set the variable on one side
[tex]b^2=144[/tex]
Get rid of the squared in the b by square rooting both sides.
[tex]b=12[/tex]
The answer is 12.
A worker in an assembly line takes 7 hours to produce 31 parts. At that rate, how many parts can she produce in 28 hours?
Answers
Answer:
124
Step-by-step explanation:
Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.
[tex]31(4)=124[/tex]
Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
Answers
1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.
2. The balance in Tammy's investment account at the end of last year was $7,585.
What is the percentage?The percentage is the proportion of a value in relation to another.
Percentages show how much a variable is contained in another.
The percentage gives the fractional value of the decrease in the investment account.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.
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5. Given the following lengths, determine if the shape is a RIGHT triangle: 14, 16, 18 (2 points: 1 point for the correct answer, 1 point for showing your work) Your answer
Answers
To be able to determine if the figure is a right triangle.
The given length must satifies the given conditions,
a.) The sum of the two sides must always be lesser than the other side. We get,
[tex]\text{ a + b }>\text{ c ; b+ c }>\text{ a ; a + c }>b[/tex]Given: a = 14 ; b = 16 ; c = 18
Let's check,
a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria
b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria
a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria
b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,
[tex]\begin{gathered} \text{ c}^2=a^2+b^2 \\ 18^2=14^2+16^2 \\ 324\text{ = }196\text{ + }257 \\ 324\text{ }\ne\text{ 457} \end{gathered}[/tex]Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.
Let's take a look at (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2). While Beeker believes that these two expressions are equal for all real numbers x and y Clod believes they are not! Let's get to the bottom of this!
a) Evaluate (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2) for x = 7 and y = 11
b) For which values of x and y does (x + y)^2 (x - y)^2 equal (x^2 + y^2)(x^2 - y^2)? For which values of x and y does (x + y)^2 (x - y)^2 not equal (x^2 + y^2)(x^2 - y^2)?
Answers
From the given expression, it is found that:
a) When x = 7 and y = 11, the numeric values are given as follows:
(x + y)²(x - y)² = 5184.(x² + y²)(x² - y²) = 12240.b) They will only have the same numeric value when x = y.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.
The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.
In the context of this problem, the expressions are given as follows:
(x + y)²(x - y)².(x² + y²)(x² - y²).When x = 7 and y = 11, the numeric values are given as follows:
(11 + 7)²(11 - 7)² = 5184.(11² + 7²)(11² - 7²) = 12240.The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.
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Calculate the mean of the electric bills for Family A. Round your answer to the nearest cent.
Month Family A Family C
January
February
March
April
May
June
July
August
September
October
November
December
$
Answers
Answer:
78.59$
Step-by-step explanation:
Find the height h of the solid. h I B = 147 cm2 Volume 1323 cm h= cm
Answers
Answer:
h = 9 cm
Explanation:
The volume of the solid can be calculated as:
[tex]V=B\cdot h[/tex]So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:
[tex]1323cm^3=147cm^2\cdot h[/tex]Then, dividing by 147 into both sides, we get:
[tex]\begin{gathered} \frac{1323cm^3}{147cm^2}=\frac{147cm^2\cdot h}{147cm^2} \\ 9\text{ cm = h} \end{gathered}[/tex]Therefore, the height h of the solid is 9 cm.
74/5+1 9/10 what is the the lowest denominata to use to solve?
Answers
A lowest denominator to solve the given equation is 10.
What are fractions?
Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.
We are given a equation
[tex]\frac{74}{5}+1\frac{9}{10}[/tex]
Upon solving we get the following
[tex]\frac{74}{5}+\frac{19}{10}[/tex]
If we multiply both numerator and denominator of the first term by 2 we get
[tex]\frac{148}{10}+\frac{19}{10}[/tex]
Hence after this we can add
Hence A lowest denominator to solve the given equation is 10
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( – 5q–1)–( – 2q–8)
help meeeee
Answers
The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.
As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.
Value of expression = (-5q - 1) + 2q + 8
Rearrange the expression
Value of expression = - 5q + 2q - 1 + 8
Performing addition of numerals written with q and subtraction of constant values
Value of expression = - 3q + 7
Thus, the value of expression mentioned in question is -3q + 7.
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