step 1
Find the slope
we take the points
(5,-30) and (8, -48)
m=(-48+30)/(8-5)
m=-18/3
m=-6
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-6
point (5,-30)
substitute
-30=-6(5)+b
-30=-30+b
b=0
therefore
y=-6xMay get help I am terribly bad at these equations.
The distance Rhea travelled is the perimeter around the triangle.
The first step in finding the perimeter is finding the side lengths and for that, the following distance formula is used.
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.
The distance between L(-1,6) and M(-4,2) is
[tex]d=\sqrt[]{(_{}-1--4)^2+(6_{}-2_{})^2}[/tex][tex]d=5[/tex]Similarly, the distance between L(-1,6) and K(2,2) is
[tex]d=5[/tex]And the distance between M(-4, 2) and L(2,2) is
[tex]d=6[/tex]Therefore, the perimeter of the triangle is
[tex]5+5+6=16[/tex]Hence, Rhea travelled 16 km.
4. 5.26 x 1031.37 x 10-1Which of the following pairs of numbers are between the two numbers shown?A. 294 and 0.0294B. 7,338 and 0.7388C. 5,007 and 0.5007D. 6,152 and 0.06152
Answer:
C. 5,007 and 0.5007
Explanation:
Given the two numbers:
[tex]\begin{gathered} 5.26\times10^3=5260 \\ 1.37\times10^{-1}=0.137 \end{gathered}[/tex]From the given options:
[tex]5260>5007>0.5007>0.137[/tex]All other options do not satisfy the condition.
The correct choice is C.
Describe the key features of the graph of the quadratic functionf(x) = -5x^2+5.A. Does the parabola open up or down?B. Is the vertex a minimum or a maximum?C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
The graph of the function will be something like this.
To make the graph correctly we can give values to x to find points in the plane
[tex]\begin{gathered} f(x)=-5x^2+5 \\ x\text{ | f(x)} \\ -2|-5(-2)^2+5=-15 \\ -1|-5(-1)^2+5=0 \\ 0|-5(0)^2+5=5 \\ 1|-5(1)^2+5=0 \\ 2|-5(2)^2+5=15 \end{gathered}[/tex]Then the graph passes by the points
[tex]\begin{gathered} (-2,15) \\ (-1,0) \\ (0,5) \\ (1,0) \\ (2,15) \end{gathered}[/tex]From this, you can draw the points in a cartesian plane.
Once we have the graph we can answer the question.
The parabola open down.
the vertex of the parabola is a maximun since all the other points are below it.
Finally, we see that the axis of symmetry is the y axis. Since the left part of the the graph is the reflection of the right part.
the vertex of the parabola is the point (0,5).
the y intercept of the parabola is 5. we see that from the point (0,5).
how many liters of paint must you buy to paint the walls of a rectangular prism shaped room that is 20m x 15m, with a ceiling height of 8m.. if 1 Liter of paint covers 40m^2? the amount of paint needed is ____ liters. (Round up to the nearest integer as needed)
For this question, we compute the superficial area of a rectangular prism without including the ceiling area nor the floor area. We will use the following formula:
[tex]A=\text{ }(\text{rectangle perimeter)}\cdot\text{ height}[/tex]The rectangle perimeter is 2*(20m+15m)=70m. Substituting in the equation above we get:
[tex]A=\text{ 70m}\cdot8m=560m^2[/tex]Therefore, the amount of paint needed is
[tex]\frac{560}{40}\text{liters}=14\text{liters}[/tex]Answer: 14 liters.
Answer: 14
Step-by-step explanation:
In the year 2016, Ethan was single and had a total income of $58,000. He took a deduction of $9,000 and had a tax credit of $1,500. Calculate the tax owed by Ethan. (Refer to the 2016 Tax Table for Singles for tax rates.)
The tax owed by Ethan is $6,521.25.
Ethan's total income was $58,000. There was a deduction of $9,000. Ethan's net income is $49,000. The tax table is attached below. Now we will calculate the tax as per the table.
From $0 to $9,275, the tax is 10%, i.e., $9,27.5.
From $9,276 to $37,650, the tax is 15%, i.e., $4,256.25.
From $37,651 to $49,000, the tax is 25%, i.e., $2,837.5.
The payable tax is the sum of the above calculated taxes. The payable tax is $8,021.25. There is a tax credit of $1,500. The tax owed is the difference between the payable tax and the tax credit. The tax owed is $8,021.25-$1,500 = $6,521.25.
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The graph below describes the distance from home over a period of time. What is the rate of change from 70 seconds to 100 seconds?
According to the given graph, after 70 seconds it ran 40 units of distance, after 100 seconds it ran 160 units of distance. So, the points we are going to use to find the rate of change are: (70, 40) and (100, 160).
Now, we use the following formula.-
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]r=\frac{160-40}{100-70}=\frac{120}{30}=4[/tex]Therefore, the rate of change from 70 seconds to 100 seconds is 4.7) Solve the system graphically.y = -X-4y=x² – 2x - 6
Ok, so
We have the next system of equations:
The first equation is a line, and the second one is a parable.
If we graph, we would get the following:
Then, we notice that there's two intersection points between both graphs.
These points are located at ( -1 , -3 ), and ( 2 , -6)
Therefore, there are two solutions for this problem.
x = -1 and y = -3,
x = 2, and y = -6
Now, how to graph each equation?
First one, take the line y = -x-4
Notice that this equation tells us that the line given has its intersection with y-axis at ( 0 , -4 )
We also know that a line is formed with two points, so we could replace by any "x" number and see which value "y" takes.
For example:
If x = 1,
y = -1-4, which is y = -5
So we got other point: ( 1, -5).
Now, we just join both points and we get the line, like this:
And that's how you can graph the line.
Now, how could we graph the parable?
We know that we have to take three points to join to graph a parable. So, first, we would find its intersections with x - axis, if we equal the equation to zero.
x² – 2x - 6 = 0
If we solve this equation, we obtain that x could take two different values.
To solve it, we use the next equation:
x = 1 - √7 or
x = 1 + √7.
Then, we actually have two points.
Now, finally, we could find its vertex.
If we find the vertex of the parable, we notice that it is located in (1,-7)
Now, we just join these three points as this:
And if we put these graphs together, we obtain the first graph I drew, and notice that the solution for the system is the intersection between both functions.
scale factor and dilations
The scale factor here is 3 : 2.
What is meant by scale factor and dilations?The scale factor is defined as the difference between the new image's and the old image's sizes. A fixed point in the plane is the center of dilation. The definition of the dilation transformation depends on the scale factor and the center of dilation.
A stretched image results from a scale factor of higher than 1.
The image shrinks when the scale factor falls between 0 and 1.
The resulting image is consistent with the source image if the scale factor is 1.
As a result of the dilation modifications, the following characteristics of forms don't change:
The figure's angles are all identical.
The figure's midpoints on its sides and the midpoint of the dilated shape are both preserved.
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Suppose sin(A) = 1/4 Use the trig identity sin^2(A)+cos^2(A)=1 to find the cosine in quadrant II. round to ten-thousandth.0.1397-0.9682-0.85720.4630
To find the value f rthe cosine function we will us the identity:
[tex]\sin^2A+\cos^2A=1[/tex]We know that the sine of A i 1/4 then we have:
[tex]\begin{gathered} (\frac{1}{4})^2+\cos^2A=1 \\ \cos^2A=1-\frac{1}{16} \\ \cos A=\pm\sqrt{\frac{15}{16}} \\ \cos A=\pm0.9682 \end{gathered}[/tex]Now, we need to determine which sign to choose. Since the sinA lies in th second quadrant thismeans that tehe coosine als lies in the quadrant; furthermore, we know that the cosine is negative in the second and thirsd quadrants whichmeans that we need to use the negative sign. Therefoore:
[tex]\cos A=-0.9682[/tex]Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $21.50
10 $25.00
15 $32.50
WILL GIVE BRAINLIEST TO FIRST ANSWER
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
The meaning of the y-intercept in this situation is that: D. when the cab travels 0 miles, the total fee will be $10.00.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the table, we have the following parameters:
Points (x, y) = (2, 5) and (13.00, 17.50)
Next, we would calculate the slope as follows:
Slope = (17.50 - 5)/(13.00 - 2)
Slope = 12.50/11.
Slope = 1.14.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
Where:
x and y represents the points.m represents the slope.b represents the y-intercept.Substituting the given parameters into the standard equation, we have;
y - 13.00 = 1.14(x - 2)
y - 13.00 = 1.14x - 2.28
y = 1.14x - 2.28 + 13.00
y = 1.14x + 10.72
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(08.01 LC)A cylinder has a height of 2 meters and a diameter that is 5 timesthe measure of the height. Using 3.14 for pi, which of the followingcan be used to calculate the volume? (6 points)
Let's begin by identifying key information given to us:
This figure is a cylinder. The formula for its volume is:
[tex]V=\pi r^2h[/tex]Height (h) = 2 m,
Diameter (d) = 5 × h = 5 × 2 = 10 m; radius (r) = d/2 = 10/2 = 5 m
pi = 3.14
The volume of the cylinder is calculated as shown below:
[tex]\begin{gathered} V=3.14\times5^2\times2 \\ V=3.14\times25\times2=157 \\ V=157m^3 \end{gathered}[/tex]2x + 4y=8
graphing in standard form
Answer:
slope = -1/2
Y-intercept = (0,2)
Step-by-step explanation:
Given the following table of values for f(x), find f(9).x−5−42489f(x)4124058
We have a table of values which contains different x-values and their related f(x).
We are searching for f(9), then we have to observe the value of the function f(x) when x=9.
In the table of values we can observe when x=9, then f(x)=8.
So f(9)=8
Step-by-step explanation:
please write the question properly
The sum of three consecutive numbers is 111. What is the smallest of the three numbers? please help show work
The sum of three consecutive numbers is 111.
Consecutive Numbers: Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let the three consecutive numbers are : x , x + 1, x +2
Since the sum of three consecutive number is 111
x + (x +1 ) + (x +2) = 111
Simplify :
x + x + 1 + x + 2 = 111
x + x + x + 1 + 2 = 111
3x + 3 = 111
3x = 111 - 3
3x = 108
x = 108/3
x = 36
So, the first number is x : x = 36
Second number is : x + 1= 36 + 1 = 37
Third Number is : x + 2 = 36 + 2 = 38
Numbers are : 36, 37, 38
Smallest number in 36, 37 & 38 is 36
Smallest number = 36
Answer : 36
jon drove an average of 250 miles a day for three days he drove 400 miles on the first dat 125 miles on the second day
Answer:
225 miles on 3rd day
Step-by-step explanation:
400 + 125 + x /3 = 250
multiply each by 3 to get 400 +125 +x = 750
subtract 525 each to get x = 225
PeriodNameDateUsing Tables to Graph Quadratic Functions1. Match the four graphs to the corresponding table.AB10TO105СD105-10D351055-10х-1х-2-101y47014у34.30-5NOХ-3-2-101у-3-4-3AWN-TOXo/w/tw/okalow2
In order to match each plot with its corresponding table, consider the positive and negative values of y respect to the positive or negative values of x.
For example, in the first case (plot A), all values of y-coordinate are positive. The only table with all positive y values if the first one.
Hence, plot A matches with the first table.
For plot B, you can notice that for x=0, y=4. The only table in which you have this result is the second one.
Hence, plot B matches with the second table.
For plot C, you can observe that x=0 for y=0. Moreover, if y=0, x = 4. The only table with this result is the fourth table.
Hence, plot C matches with the fourth table.
Finally, plot D matches with the third table.
At soccer practice, 35 minutes are spent playing and 5 minutes are spent on a water break. What percentage of practice time is spent playing?
Answer: 87.5%
Step-by-step explanation:
35/40 = x/100
40 times 2.5 gives you 100 so to find what x is you multiply 35 by 2.5.
x 1 2 3 y 16 32 48 Write an equation that represents the proportional relationship. y = 16x y = 2x y equals 1 over 16 times x y equals 1 over 2 times x Question 6(Multiple Choice Worth 2 point
Please HELP ME I WILL GIVE BRAINLYNEST
The equation which represents the proportionality relationship is:
y=16x.
Given, we have the pairs as:
(1,16),(2,32) and (3,48)
calculate the value of y/x for the ordered pairs:
For (1,16), the value of y/x is = 16/1 = 16
For (2,32), the value of y/x is = 32/2 = 16
For (3,48), the value of y/x is = 48/3 = 16
now, compare ratios:
for each ordered pair, y/x = 16
Since, k=y/x, you know that the constant of proportionality , k is 16.
Substitute 16 for k in the equation for a proportional relationship.
y = kx
y = 16x
Hence we get the equation as y=16x.
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Use algebra to solve each problem. If a diagram is not given, you MUST sketch one.Show your calculations for each question. Place your answer in the space provided.Yis between X and Z on segment XZ. XY = x + 7, XZ - 152, and YZ - 2XY. Find x to thenearest tenth.xX
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |XY|=x+7 \\ |XZ|=152 \\ |YZ|=2|XY|\Rightarrow|XZ|=|XY|+|YZ| \\ But\colon|YZ|=2|XY|\Rightarrow|XZ|=|XY|+2|XY|\Rightarrow|XZ|=3|XY| \\ |XZ|=3|XY| \\ But\colon|XY|=x+7,|XZ|=152 \\ 152=3(x+7)\Rightarrow152=3\cdot x+3\cdot7\Rightarrow152=3x+21 \\ 152=3x+21 \\ \text{Subtract 21 from each side, we have:} \\ 152-21=3x+21-21\Rightarrow131=3x\Rightarrow3x=131 \\ 3x=131 \\ \text{Divide each side by 3, we have:} \\ \frac{3x}{3}=\frac{131}{3}\Rightarrow x=43\frac{2}{3}\approx43.667\cong43.7 \\ x=43.7(ToNearestTenth) \end{gathered}[/tex]4-(-3/5) is equivalent to
Subtracting a negative number is the same as adding that number. In this case,
[tex]4-(-\frac{3}{5})=4+\frac{3}{5}[/tex]The point (x,y) is proportional to the point (2, 5).Select all the true statements.5(x, y) is a solution to y=3x:0 (x, y) is a solution to y=x+3.The ratio of is equivalent toPoint (x,y) is the same point as (5,2).A straight line through points (2,5) and (x, y) will pass through the origin.
Since all the points proportional to (2,5) follow the equation 2y = 5x, (x,y) is a solution to y=5/2x
Accordingly 2y= 5x is the same as y/x = 5/2 . Since the equation y = 5/2x is a line with y-intercept equal to 0 , there is a line which passes through points (x,y) and (2,5). The true statements are: first, third and fifth statements.
Help me please help me out please please
Answer:
The answer is it is true.hope the day is saved
6 Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff didnot spend more than $14 on the hot dogs and the bottle of water. Which inequality canbe used to find h, the number of hot dogs that Jeff could have bought?F 3h - 2 s 14G 3h + 2 S 14H h - 2 2 14J 3h + 2 2 14
SOLUTION
Step1: Write out the parameters in the question
Let the number of hot dogs be h
The cost of a hot dog is $3
The cost of the bottle of water is $2
The total amount spent by jeff is $ 14
Step2: Write the inequality
The total amount spend should be less than or equal to the total amount
then
The cost of the hot dog is
[tex]3\times h=3h[/tex]The inequality will be the sum of the cost of the hot dog and the bottle of water
[tex]3h+2\leq14[/tex]Hence option G is the correct op
pottery studio gives three-hour and four-hour ceramics classes for $36 an hour. If the studio has collected $4428 for a total of 32 classes, how many three hour classes and how many four-hour classes were paid for?
Answer:
5 three hour classes and 27 four hour classes
Step-by-step explanation:
Convert these words into equations
Since one hour is 36, we can write two expressions for the 2 different classes: 108x and 144y (the amount of money from those classes)
x is the number of 3 hour classes, y is the number of 4 hour classes
Since the amount of money the studio makes is 4428, 108x+144y=4428
Since there are a total of 32 classes, x+y=32
So we now have the equations x+y=32 and 108x+144y=4428
Solve for x in the first equation (in order to substitute it into the second one)
we get x=32-y
plugging this into the second equation gives
108(32-y)+144y=4428
3456-108y+144y=4428
Combining like terms gives 36y=972
y=27
So there are 27 four hour classes, and 5 three hour classes( because 32-27=5)
Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer.
What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters?
If he initially had 30 liters of fuel, and his car's fuel efficiency is cubic centimeters per kilometer. The calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters is: 30- 100/1000×120
How to determine the estimated volume?Given data:
Distance = 120 kilometers
Liters of fuel = 30 liters
Using this formula to find the remaining volume
Remaining volume = I - E × D
Where:
I = Initial volume
E = Fuel efficiency
D = Distance
First step is to formula an equation that will be use to find the remaining volume
Equation = 30- 100/1000 ×120
Now let use the formulated equation to find the remaining volume
Remaining volume = 30- 100/1000 × 120
Remaining volume = 30- 12
Remaining volume = 18
Therefore 30- 100/1000×120 can be used to determine the remaining volume.
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3/5 of the students in the band play the flute, and another 1/5 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet?
The fraction of the students in the band that play either the flute or the clarinet is 4/5.
We are given the fraction of the students that play a certain musical instrument.The fraction of the students in the band that play the flute is 3/5.The fraction of the students in the band that play the clarinet is 1/5.We need to find the fraction of the students in the band that play either the flute or the clarinet.The fraction of the students in the band that play either the flute or the clarinet is the sum of the individual fractions of the students in the band that play the flute and the students in the band that play the clarinet.The fraction of the students in the band that play either the flute or the clarinet is 3/5 + 1/5.The fraction of the students in the band that play either the flute or the clarinet is 4/5.To learn more about fractions, visit :
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For this problem, write the numbers in standard form.
19. 1.49 x 102 (1 point)
14.9
149
0 1,490
Answer:
1.49 × 101.
100+40+9
1.49 × 103.
Step-by-step explanation:
is this Right?
Write the vector v in terms of i and j whose magnitude and direction angle are given.
The magnitude, r, of the vector, v , is given to be 4/5.
The direction angle is given to be 114 degrees.
A vector component is written in the form of:
[tex]V=ai+bj[/tex]We are going to use the given magnitude and direction angle to obtain the values of a and b.
Thus, we have:
[tex]\begin{gathered} \text{The magnitude, r, of a vector with i and j component is given as:} \\ r=\sqrt[]{a^2+b^2} \\ \frac{4}{5}=\sqrt[]{a^2+b^2} \\ \text{square both sides;} \\ (\frac{4}{5})^2=a^2+b^2 \\ \frac{16}{25}=a^2+b^2 \\ \frac{16}{25}-b^2=a^2 \\ a^2=\frac{16}{25}-b^2 \\ a=\sqrt[]{\frac{16}{25}-b^2}\text{ ----eqn i)} \end{gathered}[/tex][tex]\begin{gathered} \text{The direction angle, }\theta,\text{ of a vector is given as;} \\ \text{Tan }\theta=\frac{b}{a} \\ \text{Tan 114=}\frac{b}{a} \\ -2.2460=\frac{b}{a} \\ b=-2.2460a\text{ -----eqn }ii) \end{gathered}[/tex]Substitute for b into eqn i); thus we have:
[tex]\begin{gathered} From\text{ eqn i)} \\ a=\sqrt[]{\frac{16}{25}-b^2} \\ \text{Put b=-2.2460a into the equation, we have:} \\ a=\sqrt[]{\frac{16}{25}-(-2.2460a)^2} \\ a=\sqrt[]{\frac{16}{25}-(5.0447a^2)} \\ \text{square both sides;} \\ a^2=\frac{16}{25}-5.0447a^2 \\ a^2+5.0447a^2=\frac{16}{25} \\ 6.0447a^2=0.64 \\ a^2=\frac{0.64}{6.0447} \\ a^2=0.1058 \\ a=\sqrt[]{0.1058} \\ a=0.325 \end{gathered}[/tex]Substitute for a= 0.325 into any of the equations, we have:
[tex]\begin{gathered} \text{From eqn }ii) \\ b=-2.2460a \\ b=-2.2460(0.325) \\ b=-0.729 \end{gathered}[/tex]Hence, the vector, v, in terms of i and j is:
[tex]\begin{gathered} v=0.325i-0.729j \\ \text{This can also be written as:} \\ v=\frac{13}{40}i-\frac{729}{1000}j \end{gathered}[/tex]Help needed! please help math
Answer:
Step-by-step explanation:
Point J is on line segment IK. Given IK=15 and IJ=13, determine the length of segment JK.
Line segment IK includes Point J. The length of the segment IK=15 and IJ=13. The length of the segment JK is 2.
Given that,
Line segment IK includes Point J.
We have to determine the length of segment JK.
We have length of the segment IK=15 and IJ=13.
Two unique points on a line define the boundaries of a line segment. A line segment is also known as a part of a line that connects two locations. A line and a line segment vary in that a line has no ends and can continue indefinitely in any direction.
We can write as,
IK=IJ+JK
15=13+JK
JK=15-13
JK=2
Therefore, The length of the segment JK is 2.
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