The equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1) is y = (-1/2)x + 1.
What is perpendicular line?
The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared.
[tex](y-1) = -\frac{1}{2} (x-0)[/tex]The equation of the line given in the question is:
y = 2x+7
On comparing with the equation y = mx + a
where, m is slope
we get slope of the line as m = 2.
Since the line we have to find is parallel to given line, they have equal slope.
Now, we know that the equation of perpendicular line is given by:
[tex](y-y_1) = -\frac{1}{m} (x-x_1)[/tex]
given points are (0,2) which is represented by (x1,y1)
On putting the value in the equation, we get
[tex](y - 1) = -\frac{1}{2}(x-0)[/tex]
After simplifying it we get the final equation as:
[tex]y = -\frac{1}{2} x + 1[/tex]
Above equation is the equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1).
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Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much
water as Elena. Lin drank twice as much water as Jada.
1. How much water did Jada drink?
2. How much water did Lin drink?
liters
liters
A spherical balloon is inflated so that its volume is increasing at the rate of 12 cubicfeet per minute. How fast is the radius of the balloon increasing when the radius is 6feet?
Given:
The rate of change in volume = 12 cubic feet per minute.
We need to find the rate of change of radius at radius = 6 feet.
Consider the formula to find the volume of the sphere.
[tex]V=\frac{4}{3}\pi r^3[/tex]Differentiate with respect to t.
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\times3r^2\times\frac{dr}{dt}[/tex][tex]\text{ Substitute }\frac{dV}{dt}=12\text{ and r=6 in the formula.}[/tex][tex]12=\frac{4}{3}\pi\times3(6)^2\times\frac{dr}{dt}[/tex][tex]12=144\pi\times\frac{dr}{dt}[/tex]Dividing both sides by 144pi, we get
[tex]\frac{12}{144\pi}=\frac{dr}{dt}[/tex][tex]\frac{dr}{dt}=\frac{1}{12\pi}[/tex][tex]\frac{dr}{dt}=\frac{1}{37.68}=0.0265\text{ feet per minute}[/tex]Hence the radius of the balloon increases by 0.03 feet per minute.
The steps at the right show cam's works in solving an equation. Circle the line where he makes a mistake. Then, find the correct solution to the equation.
The correct solution to the equation is -13.
-12x + 12 = -3(5x + 8)
Split the right-hand side,
-12x + 12 = -15x + 24 (This line have error, instead of + there will be - )
Shifted the values of x to the left-hand side and the constant values to the right-hand side,
3x + 12 = 24
3x = 12
x= 4, which is the incorrect value of x.
The correct solution to the equation,
-12x + 12 = -3(5x + 8)
Split the right-hand side,
-12x + 12 = -15x - 24
Shift the values of x to the left-hand side and the constant values to the right-hand side,
3x = -36
The final value of x,
x = -13
Therefore, the value of x is -13.
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PLEASE HELP DUE IN 4 MINUTES, THANK YOU!!
Answer:
A 100% increase in a total means the final amount is 200% of the initial amount.
A 100% decrease in a total means the final amount is 0% of the initial amount.
Error means that you were a way off from the real value
Step-by-step explanation:
Kara currently makes $12 per hour. If she receives a
50% raise, what is her new rate?
What would a 75% raise be equal to????
K
TO
160
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a textbook store sold a combined total of 392 biology and psychology textbooks in a week. the number of psychology textbooks sold was 48 less than the number of biology textbooks sold. how many textbooks of each type sold?
Number of biology book sold are 223.
Number of psychology books sold are 183.
What is equation?In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given Data
A textbook store sold a combined total of 392 biology and psychology textbooks in a week. the number of psychology textbooks sold was 48 less than the number of biology textbooks sold.
Let number of biology books sold be x
Let number of psychology books sold be (x- 48)
Total book sold = 392
392 = x + x - 48
392 + 48 = 2x
446 = 2x
x = 223
Number of biology book sold are 223.
Number of psychology books sold are 183.
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f(x)= 3x; translation up 5 units
After applying the given translation we get the function as 3x + 5
Graph translation is the process of converting an equation or existing graph into a new graph.
One common type of algebraic issue is changing algebraic equations.
A parent function's graph is altered by a translation. The three different types of translation are dilations, reflections, and translations.
A function can have its y-values modified vertically or its x-values changed horizontally (affects the x-values).
We are aware that the x- and y-coordinates must be modified to reflect the translation by the specified amount.
f( x ) = 3x is translated 5 units upwards.
Therefore the required graph is f ( x ) = 3x + 5 .
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Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
What is difference between fraction and mixed number?
Single fraction is represented as [tex]\frac{p}{q}[/tex] form where p is numerator and q is denominator and value of q can't be zero. Example [tex]\frac{5}{9}[/tex] .
Mixed number contains two part one is an integer and other is fractional part. It is represented as N [tex]\frac{p}{q}[/tex]. Example 5[tex]\frac{1}{2}[/tex] .
According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.
There are three shaded circle and a circle with 7 sector shaded.
So, Total shaded area in single fraction = 1 + 1 + 1+ [tex]\frac{7}{10}[/tex] = [tex]\frac{37}{10}[/tex]
and total shaded area in mixed number = 1 + 1 + 1 + [tex]\frac{7}{10}[/tex] = 3 + [tex]\frac{7}{10}[/tex] = 3[tex]\frac{7}{10}[/tex] .
Hence, shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
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Find the Properties to graph this Rational Expression. DO NOT GRAPH. If an answer is "none" type in "none" for the answer blank. Make sure to type in your Asymptotes correctly(x=y=)F(x)=-4x+8/x^2-x-2Need to answer:Hole:(___,___)Vertical asymptote:______X-intercept:(___,___)Y-intercept:(___,___)Horizontal asymptote:____
Given data:
The given expression is f(x)= (-4x+8)/(x^2 -x-2).
The hole of the graph is x=2.
The expression for the vertical asymptode is,
[tex]x=-1[/tex]The expression for the horizontal asymptode is,
[tex]y=0[/tex]There is no x-intercept, and y-intercept is,
[tex](0,\text{ -4)}[/tex]Thus, the
Need help solving these questions!! thank you :)
Answer:
1. 25+5c
2. -8y-16
3. (m+1)^9
4. -6a-15
5. 4y+12z
6. (2a+3b)^4
7. 23c
8. 8y+7x
9. 14a+16
10. 16m+16n
The cost of manufacturing a cake is directly proportional to the volume of the cake.
The baker makes a 70% profit when he sells a large rectangular cake.
The baker sells a large rectangular cake for £6.80 The baker decides to sell smaller rectangular cakes.
The length, width, and height of the smaller cakes are all half of those of the large rectangular cake.
He sells a pack of 6 of the smaller cakes for £6.50
How much profit does he make on the pack of smaller cakes?
Answer:
The baker makes £3.50 profit on smaller cakes================================
GivenLarge cake:
Price = £6.80,Profit = 70%Small cake:
Number = 6,Price = £6.50,Dimensions = each side is 1/2 of the large cakeSolutionThe profit is the difference of the cost and selling price.
Find the cost x of large cake:
x + 70% = 6.801.7x = 6.80x = 4Find the volume of the pack of smaller cakes, taking the volume of the large cake as a unit:
6*(1/2)³ = 6*1/8 = 3/4Cost of the pack of smaller cakes is proportional to the volume:
4*3/4 = 3Profit made on smaller cakes:
6.50 - 3 = 3.5048,384 - 2,904 divided by 48,384 multiplied by 100
How can you justify that the function is
exponential?
Answer:
Since the y axis is increasing at an exponential rate. You can see that it goes from 0.06 to 0.125 to 0.25. If you were to graph that it would be a exponential curve. You can see that it jumps alot.
0.0625 to 0.0625*2 to 0.0625*2*2 to 0.0625*2*2*2
A study on students drinking habits wants to determine the true average number of alcoholic drinks all uf greek students have in a one week period. We know from preliminary studies that the standard deviation is around 6. 3. How many students should be sampled to be within 0. 5 drink of population mean with 95% probability?.
Number of students need to be sampled = 610
A study to determine the true average number of alcoholic drinks consumed by Greek students is conducted.
Standard Deviation, σ = 6.3
Margin Error of population mean, E = 0.5
Probability = 95% = 0.95
The p-value corresponding to 0.95 probability = (1+0.95)/2 = 0.975
The z-score corresponding to this p-value = 1.96 [from the z-tables]
Now, The margin error, E = zσ/√n, where n is the sample size
⇒ n = (zσ/E)²
⇒ n = (1.96 x 6.3/0.5)²
⇒ n ≈ 610
Hence 610 students need to be sampled.
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Find the future value, using the future formula and a calculator. (Round your answer to the nearest cent.)$901 at 3.5% compounded semiannually for 6 years
To calculate the future value we need to use the compound formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the principal, r is the interest rate in decimal form, n is the number of times the interest is compound in any given time t.
In this case we have that P=901, r=0.035 and since the interest is compound semiannually this means that n=2. Finally t=6. Plugging this values into the equation above we have that:
[tex]\begin{gathered} A=901(1+\frac{0.035}{2})^{2\cdot6} \\ A=1109.53 \end{gathered}[/tex]Therefore the future value would be $1109.53
What’s the answer plss
The length of the opposite side XY = 15.2cm
How to calculate the opposite side XY?
From the right- triangle XYZ,
[tex]sin \theta =\frac{opposite}{hypotenuse}\\\\sin 61 ^\circ=\frac{XY}{XZ} \\\\XY = sin 61 ^\circ *XZ\\\\XY = 0.875* 17.4 \\\\XY = 15.2cm[/tex]
The length of the opposite side XY = 15.2cm
What is opposite side of a right-triangle?
From a particular angle, the opposite side is across. The legs of a right triangle are its adjacent and opposite sides, together, they make up the triangle. The opposing (shorter) side is the side that is shorter and perpendicular to the angle from which you are observing it.The angle from which we are looking does not include this side.An opposite side in a right triangle is the one that is across from a given angle, while an adjacent side is the one that is next to a given angle and the hypotenuse is the longest side in a right triangle.To learn more about opposite side, refer:
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Riley and Paul go to the driving range. Together, they hit 75 balls. Riley hit 17 more than Paul. How many
balls did each of them hit?
Riley hit 46 balls and Paul hit 29 balls at the driving range.
According to the question, let
Number of balls hit by Riley be x
Number of balls hit by Paul be y
Together Riley and Paul hit 75 balls
∴x+y=75 (1)
Riley hit 17 more balls than Paul
∴x= y + 17 (2)
Now we have to solve these simultaneous linear equations (1) and (2)
Replacing the value of x from equation (2) into equation (1) we get,
y+17+y=75
⇒2y + 17 = 75
⇒2y = 75 - 17
⇒2y = 58
⇒y = 58/2 (dividing both sides by 2)
⇒y = 29
∴No. of balls hit by Riley = x = y +17 = 29 + 17 = 46 (from equation (2))
Therefore, Riley hit 46 balls and Paul hit 29 balls at the driving range.
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Darlene has 6 3/4 gallons of gasoline. Every time she mows her lawn, she uses 3/8 gallon. How many times can she mow her lawn before she needs more gas?w
The number of times Darlene mow her lawn before she needs more gasoline is equal to 18times.
As given in the question,
Total gasoline with Darlene is equal to 6 3/4 gallons
Convert mixed fraction into proper fraction:
6 3/4 = 27/4 gallons
Every time amount of gasoline used to mow her lawn = 3/ 8gallon
Number of times Darlene mow her lawn before she needs more gasoline
= (27 / 4) ÷ (3 /8)
= (27 /4) × (8/3)
= 18 times
Therefore, the number of times Darlene mow her lawn before she needs more gasoline is equal to 18times.
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Convert to a percent: 0.341 A. 0.341% B. 341% C. 3,410% D. 34.1%
Answer:
34.1%, D
Step-by-step explanation:
To convert a number into a percent, you multiply it by 1, or more precisely, 100%. 100% can be thought of as 100 * 1%
0.341 * 100 * 1 % = 34.1%
Answer:
Step-by-step explanat
In ΔTUV, UV = 14, VT = 19, and TU = 9. Which statement about the angles of ΔTUV must be true?
In ΔTUV, UV = 14, VT = 19, and TU = 9, The statement about the angles of ΔTUV that must be true is [tex]m \angle U > m \angle T > \angle V[/tex] Option 5
This is further explained below.
What are angles?Generally, A triangle's angle is a measurement of the length of the side that is perpendicular to it.
This indicates that if one of the sides is longer in length, then the measure of the angle opposite to it will also be longer.
The angles in the triangle TUV are denoted by the symbols T, U, and V.
The side that is UV, TV, and T U correspondingly is the side that is opposite to these angles.
The length of the opposing sides will immediately determine the measure of the angles, which will be directly proportionate to those angles.
since V T>U V>T U, the arrangement of angles will correspond to this as follows: [tex]m \angle U > m \angle T > \angle V[/tex] Option 5
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CQ
In $\triangle T U V$, UV $=14, V T=19$, and $T U=9$. Which statement about the angles of $\triangle T U V$ must be true?
$\mathrm{m} \angle V>\mathrm{m} \angle T>\mathrm{m} \angle U$
$\mathrm{m} \angle T>\mathrm{m} \angle U>\mathrm{m} \angle V$
$\mathrm{m} \angle U>\mathrm{m} \angle V>\mathrm{m} \angle T$
$m \angle V>m \angle U>m \angle T$
$m \angle U>m \angle T>m \angle V$
$\mathrm{m} \angle T>\mathrm{m} \angle V>\mathrm{m} \angle U$
y + 8 < -9 solve for y please i need help im a smart student i just need a bit of help
Answer:
the answer is y<-17
Step-by-step explanation:
This is actually just like algebra.
y+8<-9
y<-9-8
y<-17
slope -4; passes through (2, 3)
Answer: y = -4x + 11
Step-by-step explanation:
y = mx + b
3 = -4(2) + b
3 = -8 + b
11 = b
8+2x3²
= 8+6²
= 8+36
= 44
What are his mistakes?
how long does it take ella to run 7.5 kilometers
HELP ASAP NEEDS TO BE TURNED IN TONIGHT
Answer:
y= 2x + 9
Step-by-step explanation:
3 Violet's Videos
clients. One week after launching the website, she had posted a total of 6 videos. At the end
Violet is a yoga instructor who regularly posts new exercise videos on a website for her
of week 2, she had a total of 10 videos. At the end of week 3, she had a total of 14 videos. At
the end of week 4, she had a total of 18 videos.
Find the Term Value
The completed table is:
Term Number 1 2 3 4 5 6
Term Value 6 10 14 18 22 26
What are the term values?In order to determine the term values, the rate of increase in the number of videos that Violet has at the end of each week has to be determined.
Rate of increase in the number of videos can be determined by dividing the change in the number of videos per week by the change in the number of weeks.
Rate of increase = change in the number of videos / change in the number of weeks
(10 - 6) / (2 - 1)
4 / 1 = 4 videos per week
Number of videos in week 5 = 18 + 4 = 22
Number of videos in week 6 = 22 + 4 = 26
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Rotate the shape as described.
The ordered pair for A' is
. The ordered pair for B' is
. The ordered pair for C' is
. The ordered paid for D' is
By applying a rotation of 90° clockwise to square ABCD, we have the following:
The ordered pair for A' is (5, -3).The ordered pair for B' is (-2, 7).The ordered pair for C' is (8, 8).The ordered pair for D' is (10, 4).What is a rotation?A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise direction.
In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (y, -x).
By applying a rotation of 90° clockwise to square ABCD, the coordinate of the image of square A'B'C'D' is given by:
(x, y) → (y, -x)
Points at A = (-3, 5) → Points at A' = (5, -(3)) = (5, -3)
Points at B = (-7, -2) → Points at B' = ((-2), -(-7)) = (-2, 7).
Points at C = (-8, 8) → Points at C' = (8, -(-8)) = (8, 8).
Points at D = (-4, 10) → Points at D' = (10, -(-4)) = (10, 4).
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please help ill give uu crown to the first person who is right
Answer:
No
Step-by-step explanation:
Using a graph typing in 9x and looking at the table, (2,1) is not on the table, so (2,1) is not a solution to 9x
Answer:
No
Step-by-step explanation:
to determine if (2, 1 ) is a solution, substitute the x- coordinate into the equation and if the result is equal to the y- coordinate then it is a solution.
y = 9x ( substitute x = 2 )
y = 9 × 2 = 18 ≠ 1
then (2, 1 ) is not a solution to the equation.
(2x - y)² =
(3x-1)(3x+5)=
Please help simplify both problems !
Answer: 4x^2 - 4xy + y^2 and the second one 9x^2 + 12x - 5
I hope this helps
Evaluate : (12.5)³
find the answer
Answer:
1953.125
Step-by-step explanation:
(12.5)³
= 12.5 × 12.5 × 12.5
= 1953.125
Answer: 1953.125
(12.5)³
so 12.5 multiplied to itself thrice
12.5x12.5x12.5
which is 1953.125