the relation is 3x + y = 3
so,
y = 3x - 3
the domain is the values of x
so, substitute with each value of {-2,2,4} at the last equation of y
when x = -2 , y = 3*-2 - 3 = -6 - 3 = -9
when x = 2 , y = 3 * 2 - 3 = 6 - 3 = 3
when x = 4 , y = 3 * 4 - 3 = 12 - 3 = 9
so, the range will be {-9 , 3 , 9}
The correct answer is option a. (-9,3,9)x
What is the effect on the volume of a cylinder if the radius is doubled while the height is halved?A. The volume is halved.B. The volume remains the same.C. The volume is multiplied by 4.D. The volume is doubled.
Given that
There is a cylinder and we have to find the change in its volume if the radius is doubled and the height is halved.
Explanation -
Let the Initial radius be r and the height be h. Then the initial volume will be
[tex]v=\pi\times r^2\times h-----------(i)[/tex]Now applying the given changes,
new radius = 2 x r
new height = h/2
Then the new volume will be V,
[tex]\begin{gathered} V=\pi\times(2r)^2\times\frac{h}{2} \\ \\ V=\pi\times4r^2\times\frac{h}{2} \\ \\ V=2\times\pi\times r^2\times h \\ \\ On\text{ substituting v = }\pi\times r^2\times h \\ \\ V=2\times v \end{gathered}[/tex]Hence volume will be doubled. And option D is correct.
Final answer -
Therefore the final answer is OPTION D.What is the value of this expression
Plug in the values in the right positions. And simplify.
[tex] = \frac{1}{2} (12 \times \frac{1}{4} ) - \frac{1}{2} \\ = \frac{1}{2} (3) - \frac{1}{2} \\ = \frac{3}{2} - \frac{1}{2} \\ = \frac{2}{2} \\ = 1[/tex]
OPTION C IS THE ANSWER .
in the diagram below the lager angle is 4 times bigger than the smaller angle.find larger angle
Let the smaller angle be
[tex]=x[/tex]The larger angle is 4 times bigger than the smaller angle means
[tex]\begin{gathered} \text{larger angle =y} \\ \text{Therefore,} \\ y=4\times x \\ y=4x \end{gathered}[/tex]Concept:
The sum of two or more angles on a straight line is always 180°
Therefore,
[tex]x+y=180^0[/tex]By substituting the value of y=4x in the equation above, we will have
[tex]\begin{gathered} x+4x=180^0 \\ 5x=180^0 \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{180^0}{5} \\ x=36^0 \end{gathered}[/tex]substitute the value of x= 36° in y=4x to find the value of the bigger angle
[tex]\begin{gathered} y=4x \\ \text{when x=36} \\ y=4\times36 \\ y=144^0 \end{gathered}[/tex]Hence,
The larger angle is =144 °
OPTION D IS THE CORRECT ANSWER
what is the angle between west and north west
Answer:
the angle between west and Northwest is 90°
has being supplementry angles
hope it helps
Answer:
45°
Step-by-step explanation:
the angle between north and west is 90°
northwest is situated centrally between north and west at an angle of 45°
The average change in a company's sales income was $9 million over 3 moths. Determine the average change in sales income per month.
The average change in sales income per month is $ 3 million.
What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.
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Question 1
Order from smallest to largest by selecting the dropdown beside each option. Mark the smallest with number 1.
• Number of pennies in a stack that is 1 ft high [Select]
• Number of books in a stack that is 1 ft high [Select]
• Number of dollar bills in a stack that is 1 ft high [Select]
• Number of slices of bread in a stack that is 1 ft high [Select]
.
Question 2
The order from smallest to largest is a book, bread, penny, bills
In decreasing size, they are a book, a loaf of bread, a penny, and a bill.
The following details must be taken into account;
The least number of books was thought to be necessary to reach one foot, followed by bread and then pennies.Finally, there should be bills.We can infer from the facts above that the smallest to largest items are books, bread, pennies, and cash.
Hence, The order from smallest to largest is a book, bread, penny, bills.
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2(x + 7) = 6x + 9 - 4x
EXPLANATION
Given the equation:
2(x+7) = 6x + 9 -4x
Applying distributive property:
2x + 14 = 6x + 9 -4x
Adding similar terms:
2x + 14 = 2x + 9
Subtracting -2x to both sides:
14 ≠ 9
--->The equation hasn't got solution.
Question 2 of 6
A truck rental company charges $50 plus $10 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 4, and what does it represent?
Of(h) 50h + 10
=
$210, which is the total charge in dollars for renting 4 trucks
Of(h) = 50 - 10h
$40, which is the total charge in dollars for renting a truck for 4 hours
f(h) = 50h - 10
$190, which is the total charge in dollars for renting 4 trucks
Of(h) = 50+ 10h;
$90, which is the total charge in dollars for renting a truck for 4 hours. PLEASE HELP
Select the correct answer.
Which graph shows a function and its inverse?
A. The first graph
B. The second graph
C. The third graph
D. The last graph
Answer:
B
Step-by-step explanation:
It is asking which graph show (x,y) for one line and (y,x) for the other line.
For example, the blue line shows (0,2) as a point and the red line shows ( 2,0) and so on and so on.
Petra must write a report with more than 1,000 words forher history class. So far, she has written 684 words. Writeand solve an inequality to find how many more wordsPetra needs to write for her report.
Step 1: Let the remaining number of words be X.
The inequality equation becomes:
[tex]\begin{gathered} X+684>1000 \\ X>1000-684 \\ X>316 \end{gathered}[/tex]Hence, the number of words Petra has to write to have more than 1000 words should be greater than 316 words.
what is 4 2/3 + 1 3/4?
Answer: 6 5/12
Step-by-step explanation: You could do 3x4 = 12
so, 2x4 = 8, also 3x3 = 9 which would be 4 8/12 + 1 9/12, then just add.
Answer:
6 5/12
Step-by-step explanation:
We can first begin by separating the whole number and the fraction:
4 + 2/3 + 1 + 3/4
After reordering, it becomes:
4 + 1 + 2/3 + 3/4
5 + 2/3 + 3/4
Now, we must find the common denominator for the fractions so that we may add them:
The common denominator is 12.
5 + 2(4)/3(4) + 3(3)/4(3)
5 + 8/12 + 9/12
5 + 17/12
Simplifying the improper fraction gives us:
5 + 1 + 5/12
And the final answer is:
6 + 5/12
6 5/12
Hope this helped!
The snail travels 10 cm in 4 min. How far does a snail travel in 6 min?
Given.
The distance covered by the snail in 4 minutes is 10 cm.
The speed of snail is,
[tex]\begin{gathered} Spe\text{ed=}\frac{dis\tan ce}{time} \\ =\frac{10}{4}\frac{cm}{\min } \\ =2.5\text{ cm/min} \end{gathered}[/tex]The distance covered by snail in 6 minute is,
[tex]\begin{gathered} \text{Distance}=\text{speed }\times time \\ =2.5\times6 \\ =15\text{ cm} \end{gathered}[/tex]Hence, the distance covered by the snail is 15 cm.
Speed :
Speed is defined as the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.
Hence , speed can be calculated by using the formula,
Speed = [tex]\frac{Distance-travelled}{Time-taken}[/tex]
Given data :
Distance travelled by the snail = 10 cm = 0.1 m
Time taken by the snail to travel a distance of 10 cm = 4 min = 240 s
Then , speed of the snail = [tex]\frac{10}{4}[/tex] = 2.5 cm/min = 0.0004 m/s
If the time taken by the snail is 6 min = 360 s
Then, the distance travelled by the snail in 6 min
= speed x time taken
= 2.5 cm/min x 6 min
= 15 cm = 0.15 m.
Therefore, the snail travels a distance of 15 cm in 6 min.
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Match each equation to one of the lines
5x + 3y = 20
The graph of the linear function 5x + 3y = 20 is given at the end of the answer.
How to graph a linear function?To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.
In this problem, the function is:
5x + 3y = 20.
The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:
5x = 20
x = 20/5
x = 4.
Meaning that point (4,0) is on the graph of the function.
The y-intercept is the value of y when x = 0, hence:
3y = 20
y = 20/3
y = 6.67.
Meaning that point (0, 6.67) is on the graph of the function.
The graph is plotted with a line passing through the points (4,0) and (0, 6.67).
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1/3 divided by 2 (1/2)^3
please help me
Answer:
1/24
Step-by-step explanation:
.........................
Answer:
I'll assume that "2 (1/2)^3" means 2*(1/2)^3.
Step-by-step explanation:
(1/3)/(2*(1/2)^3)
(1/3)/(1)^3
= (1/3)
===========================
If "2(1/2)^3" means (2+1/2)^2:
((5/2)^2 = (25/4)
--
(1/3)/(25/4)
(1/3)*(4/25) = 4/75 or 0.05333
Help in this asap due soon
Answer:
Q4) 20
Q5) 48%
hope this helps
Use the function f(x) = 2-5x to fill out the table.
X | f(x)
——————
-2 |
-1 |
0 |
1 |
2 |
Answer:
Step-by-step explanation: f(x) =2-5x
2-5(-2)=12
2-5(-1)=7
2-5(0)=2
2-5(1)= -3
2-5(2)-8
I hope this helps. All you have to do is plug in the numbers in the equation for x and then solve!
Which of the following statements is true about the graph shown?
The equation y = 4.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (3, 13.5).
The graph is incorrect and the line should go through the point (4.5, 4.5).
The graph does not show a proportional relationship
Answer: A
Step-by-step explanation:
Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
[tex]-3a=-3(3,2)\text{ = (-9,-6)}[/tex]Also, vector b = (-5, 6), then;
[tex]2b=2(-5,6)=(-10,12)[/tex]Then, -3a + 2b = (-9, -6) + (-10, 12)
[tex]\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}[/tex]The answer is (-19,6)
Miyako is building a raised garden bed the garden is a right rectangular prism with the dimensions shown how many cubic feet of soil does miyako need to fill the garden bed
Answer:
Step-by-step explanation 10:
Which logical argument could you use to prove that triangle ABC is congruent to triangle DEF?
A. SSS Postulate
B. HL Theorem
C. SAS Postulate
D. ASA Postulate
i cn T FING THIS HELPPPPPPPP
The equation which describes Riya's graph is:
a). C(t) = -3t + 24.
We can easily find out the equation by concentrating on the axes.
For example,
Just look from the graph the value of C when t = 0.
We can conclude that C should be equal to 24 when t is equal to 0.
Now, let us put this value of t ( which is 0) in the equations one by one:
a). C(t) = -3t + 24
=> C(0) = -3 (0) + 24
=> C(0) = 24.
So, equation a). satisfies the given criteria.
Similarly, b) also qualifies but c) and d) are not equal to 24 when t = 0.
So, remove them.
Now, let's look at the value of t when C=0.
We can see that t should be equal to 8.
Let's put this value in equations,
a). 0 = -3t + 24
=> 3t = 24
=> t = 8.
Now, we can see that equation a). satisfies all the given conditions for the graph.
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a container full of marbles has a ratio of orange marbles to black marbles of 5 : 12. a what does this ratio mean . b . if a container held 72 black marbles, how many oranges are in the container?
The ratio 5:12 means that we have 5 orange marbles for 12 black marbles (5 to 12) and the orange marbles will be 30 if the container has 72 black marbles.
According to the question,
We have the following information:
A container full of marbles has a ratio of orange marbles to black marbles of 5:12.
It means that we have 5 orange marbles when the number of black marbles is 12.
Now, let's take the number of orange marbles to be 5x and the number of black marbles to be 12x.
Now, we have the number of black marbles as 72.
So ,we have:
12x = 72
x = 72/12
x = 6
Now, we will put the value of x in 5x to find the number of orange marbles:
5x
5*6
30
Hence, the number of orange marbles in the container when it has 72 black marbles is 30.
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5. suppose waiting time until the next failure of oil pump system is exponentially dis tributed, with mean of 37 hours. the pump is continuously in operation. what is the probability that the system does not fail for 2 days?
The Probability that the system does not fail for 2 days is 0. 053
Given ,
Mean (u) = 37 hours .
Step 1 : Calculate the rate parameter, λ.
λ = 1/ mean
λ = 1/ 37 = 0.02703
Step 2 : Find the probability that the system does not
fall for two days, P ( x[tex]\leq[/tex]2 )
P ( x[tex]\leq[/tex]2 ) .= 1 - e power (lamda(x))
= 1 - e - 2(lamda)
= 1 - e power -2(0. 02703 )
By solving,
P ( x[tex]\leq[/tex]2 ) = 0.05263
P ( x[tex]\leq[/tex]2 ) = 0. 053 [ upto three decimals]
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two people dined at the la fiesta grill where the food cost was $36.54 to that a tax of 4.12 was added what ha the percentage of this tax round your answer to the nearest tenth
The percentage of the tax is 11.26%
Percentage:
Percentage is defined as the number or ratio that can be expressed as a fraction of 100. If you want to calculate percent of a number, divide the number by the whole and multiply by 100.
Given,
Two people dined at the la fiesta grill where the food cost was $36.54 to that a tax of 4.12 was added .
Here we need to find the tax in percentage.
Let us consider x be the percentage of tax has been added to the food.
The the given details, we have identified the following details,
Amount of the food = $36.54
Tax amount = $4.12
So, it can be written as,
x% of $36.54 = $4.12
Here we need the percentage value so we have to move the other to the right side, then we get,
x% = $4.12/36.54
x% = 0.1126
To convert it into percentage, then we have to multiply it by 100, then we get,
x = 11.26
Therefore, the tax percentage is 11.26%.
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Home NaviarStudent and Parent...Grades and Attenda...If DE is parallel to PQ and DE is parallel to XY,which statement must be true?A. PQ and XY are perpeAdicular lines.B. PQ and XY are parallel lines.C. PQ and XY are skew lines.D. PQ and XY are oblique lines.
The line DE is parallel to line PQ and line DE is parallel to XY.
If any one line is parallel to any other line and any of one line (from two parallel line) is parallel to third line then all three line are parallel to each other.
So line PQ, line XY and line DE all three parallel to each other.
Option B is correct.
Algebraically solve for x: 7/2x-2/x+1=1/4
Step-by-step explanation: Check the photo
Answer:
x = -2
Step-by-step explanation:
7/(2x) - 2/x + 1 = 1/4
7/(2x) - 4/(2x) + 1 = 1/4
(7-4)/(2x) = 1/4 - 1
3/(2x) = 1/4 - 4/4
3/(2x) = - 3/4
3 = (-3/4)(2x)
3 = -6x/4
3*4 = -6x
12 = -6x
12/-6 = x
-2 = x
Check:
7/(2*-2) - 2/-2 + 1 = 1/4
7/-4 + 1 + 1 = 1/4
-7/4 + 2 = 1/4
-7/4 + 8/4 = 1/4
Describe how the equations for an ellipse, circle, hyperbola and parabola differ from one another. Include an example of each in your description.
See explanation below
Explanation:An ellipse has a standard equation formula written as:
[tex]\frac{(x^{}-h)^2}{a^2}+^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]When the sign between the x^2 and y^2 terms is positive, then it is a ellipse
[tex]\begin{gathered} \text{example of an ellipse:} \\ \frac{(x-3)^2}{9}\text{ + }\frac{(y\text{ - 8})^2}{25}\text{ = 1} \end{gathered}[/tex]An hyperbola has a standard equation written as:
[tex]\frac{(x^{}-h)^2}{a^2}-^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]when the sign between the parenthesis of x^2 and y^2 terms is minus, then it is an hyperbola
[tex]\begin{gathered} \text{example of a hyperbola:} \\ \frac{x^2}{64}\text{ - }\frac{y\text{ }^2}{49}\text{ = 1} \end{gathered}[/tex]A circle has a general formula written as:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where vertex = (h, k)} \\ r\text{ = radius} \end{gathered}[/tex]The terms x^2 and y^2 are not divided by a constant. Also the left side of the equation represents the square of the radius
[tex]\begin{gathered} An\text{ example of a circle} \\ (x-1)^2+(y-3)^2\text{ = }10 \end{gathered}[/tex]Parabola has a vertex form of equation written as:
[tex]\begin{gathered} y=a(x-h)^2+\text{ k} \\ \text{where a = constant} \end{gathered}[/tex][tex]\begin{gathered} An\text{ example:} \\ y\text{ = 2(x - 1})^2\text{ + }3 \end{gathered}[/tex]Here, we only have term x^2, no y^2. y has an exponent of 1. Also a constant of a
What is the y-intercept in the equation y = 45x + 65?
Answer:
The y intercept is : 65
Step-by-step explanation:
The y intercept is 65 as it is in the form of y=mx+c.
The c is the y intercept, being 65
find a polynomial f(x) of degree 3 with real coefficients and the following zeros -1, 3-i
The least polynomial that contains the roots - 1 and 3 - i is x³ - 5 · x² + 4 · x + 10.
What is the least polynomial that contains a given set?
In this case we need to find a polynomial that contains a set of roots, a real root and a complex root. In accordace to the quadratic formula, the root 3 - i must be accompanied by its conjugate, that is, 3 + i to guarantee that all coefficients of the polynomial are real.
Then, the factor form of the cubic equation is:
f(x) = (x + 1) · (x - 3 + i) · (x - 3 - i)
f(x) = (x + 1) · [x² - (3 - i) · x - (3 + i) · x + (3 - i) · (3 + i)
f(x) = (x + 1) · (x² - 3 · x + i x - 3 · x - i x + 9 - i²)
f(x) = (x +1) · (x² - 6 · x + 10)
f(x) = x³ - 6 · x² + 10 · x + x² - 6 · x + 10
f(x) = x³ - 5 · x² + 4 · x + 10
The least polynomial is x³ - 5 · x² + 4 · x + 10.
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