Answer:
1.5 hours
As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.
Write a function in any form that would match the graph shown below.
taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2. Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).
[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]
Check the picture below.
(b) Evan also has a bag of apples that weighs 3.545 pounds. The value of the digit 5 in the tenths place of 3.545 is how many times the value of the digit 5 in the thousandths place? Explain.
The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Evan has a bag of apples that weighs 3.545 pounds.
The value of the digit 5 in the tenths place of 3.545 is 0.500
The value of the digit 5 in the thousandths place of 3.545 is 0.005
Take the ratio of both values:
tenths place value/thousandths place value = 0.500/0.005
tenths place value/thousandths place value = 100
tenths place value = 100(thousandths place value)
Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.
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Helppp
The functions f and g are defined as follows:
#a
[tex]\\ \rm\Rrightarrow f(-4)[/tex]
[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]
[tex]\\ \rm\Rrightarrow -12+2[/tex]
[tex]\\ \rm\Rrightarrow -10[/tex]
#b
#1
[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]
Interchange x,y[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]
Find y
[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]
Inverse is
[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]
#2
[tex]\\ \rm\Rrightarrow gof(x)[/tex]
[tex]\\ \rm\Rrightarrow g(f(x))[/tex]
[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]
If we factor out
[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]
[tex]\\ \rm\Rrightarrow 2x+1[/tex]
#c
[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]
[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7[/tex]
[tex]\\ \rm\Rrightarrow x=-1[/tex]
Answer:
Given functions:
[tex]f(x)=3x+2[/tex]
[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]
Part (a)
[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]
Part (b)(i)
[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]
Part (b)(ii)
[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]
What is the volume of a cone with base diameter 14 and height 16?
Answer:
Your answer is 3282.34
Step-by-step explanation:
1/3 x 3.14 x 14 ^2 x 16
this is all you have to do really.
Which three side lengths best describe the triangle in the diagram?
A. 6 cm, 8 cm, and 10 cm
B. 3 cm, 4 cm, and 5 cm
C. 5 cm, 8 cm, and 10 cm
D. 6 cm, 8 cm, and 9 cm
Please help me
The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.
What is a Triangle?A triangle is a shape that has three sides. The sides can be measured using a ruler.
The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.
Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.
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Given: p || q, and r || s.
Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark.
Prove: ∠1 and ∠14 are supplementary angles.
Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16.
What is the next step in the proof? Choose the most logical approach.
See below for the proof that ∠1 and ∠14 are supplementary angles
How to prove that ∠1 and ∠14 are supplementary angles?The attached diagram represents the missing information in the question.
The given parameters are:
∠1 and ∠2 are supplementary angles∠2 = ∠6The next step in the proof is as follows:
∠2 and ∠14 are corresponding angles.
This means that:
∠2 = ∠14
Recall that:
∠1 and ∠2 are supplementary angles
This means that:
∠1 + ∠2 = 180
Substitute ∠2 = ∠14
∠1 + ∠14 = 180
Supplementary angles add up to 180
Hence, ∠1 and ∠14 are supplementary angles
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Answer:
Step-by-step explanation:
the answer is D
What is the slope of the line with this equation y = 7x - 3 ? Explain.
Answer:
7
Step-by-step explanation:
y=mx+bm=pendiente
por lo tanto:
pendiente=7
Hii!
__________________________________________________________
Answer:
Slope = 7! ^^
Step-by-step explanation:
Note that the equation is given to us in slope intercept form.
The slope intercept formula is y=mx+c.
m denotes the slope
c denotes the y intercept.
/--------------\
The slope of the line that we are working with is 7.
Remember how I said that the slope of the line y=mx+c is m?
Similarly, the slope of the line y=7x-3 is 7! ^^
--
Hope that this helped! Best wishes.
--
PLEASE HELPP
Solve for x
Answer:
x = 29.44
Step-by-step explanation:
[tex]tan31^{o} =\frac{x}{49}[/tex]
[tex]x=49tan31^{o}[/tex]
[tex]x=29.44[/tex]
Hope this helps
for what value of x is the rational expression below equal to zero?
3x+15
———
6-x
[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]
Answer:
the answer= -5
Fred bought a fancy lawnmower, paying $4,599.00. (Because $4,600.00 would have been just too much to spend!) One
year later he took it back to the dealer with the intention of trading it in on a newer, fancier model. The dealer offered him
$3,000 to trade it in. Fred still owed $4,000 on the mower, so he decided to keep it. Now he wants to create a
mathematical model to estimate the value of the mower t years after he originally purchased it. He knows an exponential
growth/decay model is appropriate. Which of the following equations can Fred use to find the appropriate growth/decay
constant?
A) 4599 4000e^k
B) 3000 4599e^k
C)4000 = 3000e^k
D 3000 4000e^k
E 4599 3000e^k
The equation that can be used to find the exponential decay is 3000 = 4599e^k.
What is the equation that can be used to find the decay constant?
The lawn mower is decreasing in value, thus it is the decay constant that would be found.
The formula that can be used to find the value of an asset that decays exponentially is:
Future value = present value x (e^k)
3000 = 4599e^k.
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NEED HELP FOR A TEST, PLEASE :) (30 POINTS)
Match each condition to the number of triangles that can be constructed to fit the condition.
condition A: one side
measuring 4 inches,
another side measuring
8 inches, and a third
side measuring 10 inches
condition B: one angle
measuring 60°, another
angle measuring 40°, and
a third angle measuring 90°
condition C: one side
measuring 4 inches,
another side measuring
8 inches, and the angle
between them measuring 70°
condition D: one side
measuring 5 inches,
another side measuring
7 inches, and a third
side measuring 12 inches
condition E: one angle
measuring 30°, another
angle measuring 80°,
and the length of the
included side measuring
8 inches
condition F: one angle
measuring 40°, another
angle measuring 80°, and
a third angle measuring 60°
-no triangles
-one triangles
-many triangles
Answer:
Hey!
Your Answer Is,
No Triangles: A, C
One Triangle, F, D
Many Triangles: B,E
I hope this helps you!
Step-by-step explanation:
The distance from the top of the cone to the edge is 15 feet. The height of the cone is 6 feet. What is the radius of the cone? Round to the nearest tenth.
Answer: 13.7 ft
Step-by-step explanation:
Use Pythagorean theory to find radius
C^2 - B^2 = A^2
We know the hypotenuse (cone to edge) is 15
We will call that C
We know the height is 6
We will call that B
We are looking for A or radius
15^2 - 6^2 = A^2
225 - 36 = A^2
189 = A^2
Take square root of both sides
13.7 = A (radius)
what is the length of AC
Check the picture below.
Make sure your calculator is in Degree mode.
Question 18
A wholesale grocery supplier shipped x2-pound blocks of cheese and y3-pound blocks of cheese to a caterer. The total weight of the cheese in the shipment was 44 pounds, and
the shipment consisted of 18 blocks of cheese. Which of the following systems of linear equations best represents this situation?
z+y=18
A
3z +2y=44
z+y=18
2x + 3y = 44
z+y=44
3z + 2y = 18
z+y=44
2z+3y=18
B
C
D
Imported (1)
The G
The system of linear equations that best represents the situation are:
z+y=18
3z +2y=44
What are the linear equations?In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.
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What value of g makes the equation true?
0.25 (g+1.5) = 2
• -1
• 2
• 6.5
• 9.5
Answer:
g= 6.5
Step-by-step explanation:
O.25(g+1.5) = 2
(g+1.5) = 2/0.25 divide both sides with 0.25
g+1.5 = 8
g = 8-1.5
g = 6.5
It is estimated that 75% of all young adults between the ages of 18 and 35 do not have a landline in their homes and only use a cell phone at home. What is the probability that everyone in a simple random sample of 100 young adults owns a landline
Using it's concept, it is found that the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:
[tex]p = (0.25)^{100}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 25% of the adults own a landline, and the probabilities for each adult are independent, hence the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:
[tex]p = (0.25)^{100}[/tex]
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Question 4 multiple choice answer for me
Answer:
B
Step-by-step explanation:
the symbol in the x < 0 has a line under it meaning it is a closed circle, and the other equation does not, so it is an open circle. And since the question has (or) in it, it means that the arrows should be facing away from eachother.
I need help please I’m just trying to pass
Answer:
a
Step-by-step explanation:
What is the quotient? startfraction 3 y 2 over 3 y endfraction divided by startfraction 6 y squared 4 y over 3 y 2 endfraction
The quotient of the expression [tex]\frac{3y+2}{3y} divided \frac{6y^{2} + 4y}{3y + 2}[/tex] is 3y + 2 / 6y
How to find quotient of an expression?
The quotient of the expression can be found as follows:
3y + 2 / 3y ÷ 6y² + 4y / 3y + 2
Therefore,
3y + 2 / 3y × 3y + 2 / 6y² + 4y
Hence,
3y + 2 / 3y × 3y + 2 / 2y(3y + 2)
Therefore,
1 / 3y × 3y + 2 / 2
Hence,
3y + 2 / 2(3y)
3y + 2 / 6y
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The gutierrez family and the kim family both have pools. the gutierrez family is filling their
pool, which is modeled by the equation y = x+1. the kim family is draining their pool,
which is modeled by the equation y = -1.25x + 5. in both equations, x represents the time in
hours and y represents the depth of the water in the pool in feet. these two situations can be
described by the following system of equations:
y
22+1
= -1.25x + 5
a) what is the rate of change for the kim family's pool, and what does it represent in the
context of the problem?
b) looking at the equation for the gutierrez family's pool, what does the 1 represent in the
context of the problem?
The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The Gutierrez family and the Kim family both have pools.
The Gutierrez family is filling their pool, which is modeled by the equation
y = x + 1
The Kim family is draining their pool, which is modeled by the equation
y = -1.25x + 5
In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.
These two situations can be described by the following system of equations:
Then the rate of change for the Kim family's pool will be
Rate of change = -1.25
The negative of 1.25 represents 1.25 feet is drain every hour.
Looking at the equation for the Gutierrez family's pool.
y = x + 1
The number 1 represents 1 foot of water that is already present in the pool.
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In triangle PQR,PQ=13 cm ,QR=18 cm and PR = 11 cm. Find the size of the largest angle.
Answer: ~96.83°
Step-by-step explanation:
1) It's obvious that the largest angle is the opposite to the largest side.
▪︎ QR = 18 (the largest side)
=> <QPR is the largest angle
2) Cosine Rule:
▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)
▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)
▪︎ 324 = 169 + 121 - 286*cos(QPR)
▪︎ 34 = -286*cos(QPR)
▪︎ cos(QPR) = -34/286
▪︎ <QPR = arccos(-34/286) = 96.827...°
The graph represents f(x) = [x]+3.
5
44
034
2-
1
3-2-1₁
-2
-3
--4-
-5
+
you
2 3 4 5
What is f(-2.2)?
O-2
0 0
O 1
02
Answer:
[tex]\large\text{$ f(-2.2)=1 $}[/tex]
Step-by-step explanation:
Given function:
[tex]\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}[/tex]
This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.
When graphing a Ceiling Function:
open dot means "not including"solid dot means "including"The Ceiling Function gives us the nearest integer up.
So the ceiling of x = -2.2 is -2, as the greatest integer that is more than (or equal to) -2.2 is -2
Therefore:
[tex]\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}[/tex]
This is confirmed when using the graph to solve.
To find f(-2.2), locate x = -2.2 on the graph.
Trace up vertically until a step is reached.
The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.
Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.
Therefore, f(-2.2) = 1
Let's see
[tex]\\ \rm\Rrightarrow f(x)=[x]+3[/tex]
[tex]\\ \rm\Rrightarrow f(-2.2)[/tex]
[tex]\\ \rm\Rrightarrow [-2.2]+3[/tex]
[tex]\\ \rm\Rrightarrow -2+3[/tex]
[tex]\\ \rm\Rrightarrow 1[/tex]
So
f(-2.2)=1Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the
fraction bar(s).
A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to the cost of
printing, the border should have an area of 48 square inches. The width of the border needs to be uniform around the entire menu. She has
already determined that her food listings will fit within a 13-inch by 9-inch rectangular area.
13 in
9 in
The area of the decorative border can be modeled by the following equation, where x represents the width of the decorative border.
x²+
X=
Is it reasonable for the border to be 2.5 inches wide?
(yes/no)
The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have an area of border 48 square inches.
Menu dimensions without border = 13-inch by 9-inch
The area of the border can be expressed by the equation:
area of border = area of rectangle with border—area of rectangle without
border
48 = (13 + 2x)(9 + 2x) - 13×9
[tex]\rm 48=4x^2+44x[/tex]
After simplification:
[tex]\rm 4x^2+44x-48=0[/tex]
or
x² + 11x = 12
Find the solution of the above quadratic equation:
x = 1 or x = -12(width cannot be negative)
Width should be 1 inches.
We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.
Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.
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What is the diameter of a circle that has a circumference of 120 pi
Answer:
38.1971
Step-by-step explanation:
The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971
Martin order a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in area of the two pizzas?
A - 50 inches
B - 113 inches
C - 201 inches
D - 452 inches
Answer:
B. -113 inches
Step-by-step explanation:
First you have to find the radius of the two pizzas. The radius is half of the diameter. So, the first pizza would have a radius of 8 inches, since 8 is half of 16. The second pizza would have a radius of 10 inches, since 10 is half of 20. Then you would use the area formula to find the area of the two pizzas. The area formula is A=3.14R^2. The area of the first pizza is 201.06. The area of the second pizza is 314.16. Then you subtract those two numbers to get -113.1. The answer is -113 inches.
choose the best answer
Answer:
1.B
2.A
3.B
4.(not sure)
5. C
Step-by-step explanation:
Give brainliest please!
Hope this helped :)
Solve the following system of equations. Show all work and solutions.
y = 2x^2 + 6x + 1
y = −4x^2 + 1
Answer: (0, 1), (-1, -3)
Given two equation's:
y = 2x² + 6x + 1y = −4x² + 1Solve them simultaneously:
[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]
[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]
[tex]\sf 6x^2 + 6x = 0[/tex]
[tex]\sf 6x(x + 1) = 0[/tex]
[tex]\sf 6x = 0, \ x + 1 = 0[/tex]
[tex]\sf x = 0, \ x = -1[/tex]
(a) When x = 0, y = −4(0)² + 1 = 1
(b) When x = -1, y = -4(-1)² + 1 = -3
Solution: (x, y) → (0, 1), (-1, -3)
Answer:
System of equations
[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]
To solve the given system of equations, use the substitution method:
[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]
Therefore the x-values of the solutions are:
[tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]
Substitute the found values of x into the second equation to find the y-values:
[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]
Therefore, the solutions of the system of equations are:
(-1, -3) and (0, 1)
4. The function A(r) = πr² gives the area of a circle with radius r. What is the context domain?
I only need help with #4 pls
Answer:
Domain = [0 , +∞)
Step-by-step explanation:
since r is the radius of a circle
Then
r must be a positive number.
Then
r ≥ 0
NOTE : if r = 0 ,then the circle reduces to a point .
Which of the following could not be the value of sin(0)
The ratio of any side and hypotenuse is always less than 1.
The question seems incomplete
The options are not given the options are
a. 1
b. 0.5
c. 2
What is the sin ratio?[tex]sin\theta=\frac{Opposite side}{hypotenuse}[/tex]
Therefore, the ratio of any side and hypotenuse is always less than 1. Now, in the case of 0 or 90 degrees, the figure is no longer a triangle because one of the sides ceases to exist while the other side coincides with the hypotenuse.
This is the reason that in these extreme cases, sin and cosine take values 0 or 1.
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One of the roots of the equation x^2-13x+q=0 is 12. Find the other root in the value of the coefficient Q.
Considering that 12 is a root of the function, the value of coefficient Q is of 12.
What does it means that x is a root of a function f(x)?
It means that f(x) = 0.
In this problem, the function is given by:
f(x) = x² - 13x + q.
Since 12 is a root, we have that f(12) = 0, hence:
12² - 13 x 12 + q = 0
q - 12 = 0.
q = 12.
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