Answer:
5a^6,-3x^3-1
Step-by-step explanation:
we subtract the base and add the exponent
Find the equation of the parallel to the line 3x-2y=5 and passing through the midpoint of the line segment joining the points (-4,2) and (2,4).
Given:
The equation of parallel line is:
[tex]3x-2y=5[/tex]
The required line passing through the midpoint of the line segment joining the points (-4,2) and (2,4).
To find:
The equation of required line.
Solution:
Midpoint of line segment joining the points (-4,2) and (2,4) is:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-4+2}{2},\dfrac{2+4}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-2}{2},\dfrac{6}{2}\right)[/tex]
[tex]Midpoint=\left(-1,3\right)[/tex]
It means the required line passes through the point (-1,3).
The slope of line [tex]Ax+By=C[/tex] is:
[tex]m=\dfrac{-A}{B}[/tex]
The given equation is:
[tex]3x-2y=5[/tex]
Here, A=3 and B=-2. So, the slope of the line is:
[tex]m=\dfrac{-3}{-2}[/tex]
[tex]m=1.5[/tex]
Slope of parallel lines are same. So, the slope of the required line is 1.5.
The required line passes through the point (-1,3) with slope 1.5. So, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-3=1.5(x-(-1))[/tex]
[tex]y-3=1.5(x+1)[/tex]
[tex]y-3=1.5x+1.5[/tex]
Adding 3 on both sides, we get
[tex]y=1.5x+1.5+3[/tex]
[tex]y=1.5x+4.5[/tex]
Therefore, the equation of the required line is [tex]y=1.5x+4.5[/tex].
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Answer:
Step-by-step explanation:
Which is the correct calculation for the volume of the prism?'
3 units
5 units
4 units
O 3 + 5 + 4 = 12 units
O3(4) + 5 = 17 units?
3(4) = 12 units
3(5)(4) = 60 units
Step-by-step explanation:
V = l.W.H
3(5)(4) = 60 units
The volume of rectangular prism is given by the product of its dimensions hence the correct option is 3(5)(4) = 60 units
What is volume?A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere. Different shapes have different volumes.
Given that, we need to determine the correct calculation for the volume of the prism,
We know that, the volume of a rectangular prism is the product of its dimensions = length x width x height
Therefore, the correct formula is 3(5)(4) = 60 units
Hence, the correct option is 3(5)(4) = 60 units
Learn more about volumes, click;
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Answer:
12 cm
Step-by-step explanation:
OP = √(15² - (18/2)²)
=√(225- 9²)
=√(225-81)
=√144
= 12
Answer the statistical measures and create a box and whiskers plot for the following set of data.
1, 1, 6, 10, 12, 13, 13, 14, 16, 19
Min:
Q1:
Med:
Q3:
Max:
Answer:
min 1
Q1 = 6
med = 12.5
Q3 = 14
Max = 19
Step-by-step explanation:
Min simply refers to the smallest value and that is 1
Q1 is the first quartile and the formula is;
Q1 = (n+ 1)/4
where n is the number of terms which is 10
Q1 = (10 + 1)/4 = 2.75
This is approximately 3 and the 3rd term is 6
med is the median value and that is 12 + 13 = 25/2 = 12.5
Q3 is the third quartile
Q3 = 3(n+ 1)/4 = 8.25 and that is the 8th term which is 14
Max is simply the highest in value and that is 19
What is the area of the kite?
Answer:
1.125 ft²
Step-by-step explanation:
Take the height and the diagonals, multiply, and then divide by 2
A movie theater sells small and large boxes of popcorn. A small box of popcorn costs $1.50. A large box of popcorn costs $4.00. A total of 25 boxes of popcorn were sold totaling $75.00.
Below. What is m∠1?
m∠1 =
Given:
The figure of a triangle.
To find:
The measure of angle 1.
Solution:
Exterior angle theorem: In a triangle, the measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.
Using Exterior angle theorem, we get
[tex]101^\circ =31^\circ +m\angle 1[/tex]
[tex]101^\circ -31^\circ =m\angle 1[/tex]
[tex]70^\circ =m\angle 1[/tex]
Therefore, the measure of angle 1 is 70 degrees.
Caitlyn recorded the height of each plant after she exposed each plant to a set amount of darkness daily. The scatterplot shows her results after 2 weeks of exposing each plant to the amount of darkness.
A graph titled Plant Growth has hours of darkness on the x-axis, and height of plant (inches) on the y-axis. Points are grouped closely together and decrease. Point (17, 12) is above the cluster.
Which statement about the scatterplot is true?
The point (17, 12) could cause the description of the data set to be overstated.
The point (17, 12) could cause the description of the data set to be understated.
The point (17, 12) shows that there is no relationship between the number of hours of darkness and the height of the plant.
Although (17, 12) is an extreme value, it should be part of the description of the relationship bet
Answer:
B. The point (17, 12) could cause the description of the data set to be understated.
Step-by-step explanation:
All other points on the scatter plot except point (17, 12), all follow a similar trend showing the negative relation between height of plants and darkness. If we are to consider just point (17, 12) alone when describing the data set, we might likely understate the relation between both variables.
Therefore, the statement that is true about the scatter plot is "B. The point (17, 12) could cause the description of the data set to be understated."
Answer:
hello love! your answer is B :)
Step-by-step explanation:
i got a 100%
The given circle has radius r = 22. If \thetaθ = 141 degrees, what is the area of sector L?
Answer:
[tex]595.54[/tex]
Step-by-step explanation:
The formula for a sector of a circle with angle [tex]\theta[/tex] is [tex]\frac{\theta}{360}\cdot r^2\pi[/tex].
Substituting given values, we have:
[tex]\frac{141}{360}\cdot 22^2\pi\approx \boxed{595.54}[/tex]
what is the y intercept of this quadratic function
Answer:
the y-int is at the point (0,3)
Step-by-step explanation:
Answer:
(0,3)
Step-by-step explanation:
f(x)=x²+2x+3
x=0
f(0)=0²+2×0+3
f(0)=3
y=3
(0,3)
SOMEONE HELP ME PLEASE !! THANK YOU
A rectangle has a a perimeter of 68 ft. The length and width are scaled by a factor 1.5.
The perimeter of the resulting rectangle is ___ ft.
Answer and Step-by-step explanation:
Here is the equation for finding the sides (just to show):
68 = (2L + 2W)
We multiply L and W by 2 because there are two of the lengths and 2 of the widths.
Now, we add the scale factor to the outside, but on both sides of the equation.
68 × 1.5 = 1.5(2L + 2W)
Multiply 68 by 1.5.
102 = 1.5(2L + 2W)
The answer is 102.
The perimeter of the resulting rectangle is 102 ft.
#teamtrees #PAW (Plant And Water)
Given the exponential function A(x)= P (1+r)^x, what value for r will make the function a decay function
Answer:
negative value for r
Step-by-step explanation:
Given data
Given the exponential function A(x)= P (1+r)^x
A negative value for r will make the function a decay
Hence the decay function will look like
A(x)= P (1-r)^x
write in point-slope form (-4,-3) m=-1
Answer:
Point-slope form: y + 3= -1(x + 4)
Slope-intercept form: y = -1x - 7
y = m * x + b,
where:
m is the slope; and
b is the intercept of the y-axis.
\Six times a larger number is equal to the sum of a smaller number and 18. The difference of twice the larger number and the smaller number is 6. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?
y = 6 x + 18. y = 2 x minus 6.
y = 6 (x + 18). Y = 2 (x minus 6).
y = one-sixth x + 3. y = one-half x + 6.
y = one-sixth x + 3. y = one-half x + 3.
Answer:
last option: y = 1/6x+3; y = 1/2x+3
Step-by-step explanation:
6y = x + 18
Solve the above for 'y' to get:
y = 1/6x + 3
2y - x = 6
Solve the above for 'y' to get:
2y = x + 6
y = 1/2x + 3
A simple impact crater on the moon has a diameter of 15 kilometers. A complex impact crater has
a radius of 30 kilometers. How much greater is the circumference of the complex impact crater than
the simple impact craters?
Answer:
141.3 km
Step-by-step explanation:
First crater has the radius (that is, half the diameter) of 7.5 km; the circumference of this crater is C = 2(pi)r, or 2(3.14)(7.5 km) = 47.1 km;
Second crater radius is C = 2(pi)(30 km) = 188.4 km
The circumference of the complex (larger) impact crater is
(188.4 - 47.1) km greater than the circumference of the simple (smaller) crater:
141.3 km
Given the following table, what is the quadratic equation?
X
у
1
2
2
5
10
3 4
17
O A 2x2 + 1
o B. x2 + 1
o C. 4x2 + 1
OD. 2x2 + x + 1
Answer:
Answer B.
x² + 1
Step-by-step explanation:
x=1
Input x= 1 into x²+1 to get y
(1)²+1 = 2
when x=2
(2)²+1 = 5
when x = 3
(3)² + 1 = 10.
when x=4
(4)² + 1 = 17
Hence Option B
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Answer:
it will decrease
Step-by-step explanation:
if theres not enough food water, ect for all 55 to survive and only enough to support 40 wolves they will die down
Answer:
It will decrease
Step-by-step explanation:
There are 55 wolves means the wolf population will decrease as the place have only sufficient resources to 40 wolves and will eventually die.
I think this is the answer.
please HELPPPP me !!!!!
Answer:
[tex]y = 4x - 3\\Slope \ m_1 = 4[/tex]
EQUATION OF LINE PERPENDICULAR
[tex]Lines \ are \ perpendicular => m_1 \cdot m_2 = -1\\[/tex]
[tex]slope, m_2 = \frac{-1}{4}[/tex]
[tex]equation \ of \ the\ line \ passing \ through \ (-2, 2) \ slope ,m_2 :\\(y - y_2) =m_2(x - x_2)\\ (y - 2) = \frac{-1}{4} (x -(-2))\\\\y - 2 = \frac{-1}{4} (x +2)\\\\y = \frac{-1}{4}x - \frac{1}{2} + 2\\\\y = \frac{-1}{4}x + \frac{3}{2}[/tex]
EQUATION OF LINE PARALLEL
[tex]Lines \ are \ parallel => m_1 \cdot m_3 = 1\\slope, m_3 = \frac{1}{4}[/tex][tex]Equation \ of \ the \ line \ through \ (-2, 2) \ and \ slope, m_3:\\(y - y_3) =m_3(x - x_3)\\\\(y-2) = \frac{1}{4} (x - (-2))\\\\y-2 = \frac{1}{4}(x+2)\\\\y = \frac{1}{4}x + \frac{1}{2} +2\\\\y = \frac{1}{4}x + \frac{5}{2}[/tex]
The radius of a circular stage is 15 feet. Katie wants to lay down tile to cover the stage. If Katie pays $12.50 per square foot of tile, how much would it cost to tile the entire stage floor? Round to the nearest whole dollar.
Answer:
$8835.75
Step-by-step explanation:
The equation to use for this is for the area of a circle which is:
π r^2
So by plugging in 15 feet:
π 15^2,
π 225,
~706.86 ft^2.
Next, multiply this by the $12.50 per square foot.
706.86 * 12.50 = $8835.75
All done!
I will give brainiest
Answer:
A is equal to 20.
Step-by-step explanation:
To find the missing side we have to square both 21 and 29.
Because 21 x 21 = 441, and 29 x 29 = 841, all we have to do is subtract 841 from 441 and we have 400.
Now we have to find the square root of 400, since 20 x 20 = 400, that means 20 is our answer.
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In function graphing, if there is no amplitude change (mainly looking for tangent), what do you write? 1?
Answer:
The period of the tangent function is π because the graph repeats itself on intervals of kπ where k is a constant. If we graph the tangent function on −π2 to π2 , we can see the behavior of the graph on one complete cycle.
The tangent function does not have an amplitude because it has no maximum or minimum value. The period of a tangent function, y=atan(bx) , is the distance between any two consecutive vertical asymptotes..
so its not 1 but 2.
hope its right.
Leslie invested in an account that paid 2% annual interest compounded continuously. After 40
years, her investment was worth $6231.51. To the nearest dollar, what was the value of
Leslie's original investment?
Mrs. Murphy by balloons garlands paper lanterns and banners to decorate a school party she got three times as many bags of balloons as paper lanterns seven more garlands than paper lanterns and for banners she paid $5.25 for each banner $6.50 for each paper lantern five dollars for each bag of balloons and $3.50 for each garland how many of each kind of decoration did she purchase if she paid $145.50 please help
Answer:
Mrs. Murphy bought 4 packages of paper lanterns, 12 bags of balloons, 11
garlands and 4 banners
Step-by-step explanation:
I'm not really sure how I got this but it hope it helps!
i’m so bad at this someone please help me lol!
Answer:
It's B
Step-by-step explanation:
B makes the most sense to me
4. My son's age is of my wife's age, my wife's age is of my age, and my age is of my father's age. Find
age of my son, if my father is 50 years old
Answer:
50?
Step-by-step explanation:
Answer:
The age of son is 50.THANK YOU.
Can somebody help me with this im pretty bad with coordinates ty in advance!
Answer:
5 units
Step-by-step explanation:
4^2 + 3^2 = 25
sqr root 25 is 5
Answer:
The distance from P to Q is
D. 5 units
The debate team bought 20 matching T-shirts to split among its members. Each member of the team will get t T-shirts. Write an expression that shows how many people are on the debate team.
Answer:
20/t members are on the team
Step-by-step explanation:
From the question, we want to get the number of people on the team
20 T-shirts were bought
each of the team members got t T-shirts
To know the number of people on the team, we have to divide the number of shirts bought by the number of shirts gotten by each team member
We simply have this as 20/t
the florida gators football team recorded the following yardage in seven plays, 9, -3, -5, 0, 12, 20, and -4, order these from greatest to least
HELP ME REALLY FAST
I WILL MARK BRAINLIEST
Please help!!! I’ll give you the Brainly mark
Answer:
4
Step-by-step explanation:
just look at the graph and find where y is -5 the correlating point is 4