Step-by-step explanation:
first find the answer of 7^2 and swap it then it will be 1 over 49 multiply with 1 over 7^6
given: ∆abc with vertices a(-3,0), b(0,6), and c(4,6) Find the equations of the three perpendicular bisectors in abc.
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
What are the equations of the perpendicular bisectors of the triangle ABC?
Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.
First, determine the midpoints of each side:
Side AB
M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)
M₁(x, y) = (- 1.5, 0) + (0, 3)
M₁(x, y) = (- 1.5, 3)
Side BC
M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)
M₂(x, y) = (0, 3) + (2, 3)
M₂(x, y) = (2, 6)
Side AC
M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)
M₃(x, y) = (- 1.5, 0) + (2, 3)
M₃(x, y) = (0.5, 3)
Second, determine the slope of the perpendicular bisectors:
Side AB
m = (6 - 0) / [0 - (- 3)]
m = 2
m' = - 1 / m
m' = - 1 / 2
Side BC
m = (6 - 6) / (4 - 0)
m = 0
m' = - 1 / m
m' = NaN (Vertical line)
Side AC
m = [4 - (-3)] / (6 - 0)
m = 7 / 6
m' = - 1 / (7 / 6)
m' = - 6 / 7
Third, derive the equations of the bisectors:
Side AB
b = 3 - (- 1 / 2) · (- 1.5)
b = 9 / 4
y = - (1 / 2) · x + 9 / 4
Side BC
x = 2
Side AC
b = 3 - (- 6 / 7) · (0.5)
b = 24 / 7
y = - (6 / 7) · x + 24 / 7
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
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98!/100! x 10 (! = the number times every number before it and it) ex: 4! = 1 x 2 x 3 x 4
The value of the factorial expression is 99/10
How to evaluate the factorial expression?The expression is given as
98!/100! x 10
The above expression implies that we multiply 10 by the quotient of 98! and 100!
This can be done directly using a calculator, and it can be solved step by step
The step by step procedure is as follows
Expand the denominator
98!/100! x 10 = 98!/100 * 99 * 98! x 10
Evaluate the quotient
98!/100! x 10 = 1/100 * 99 x 10
This gives
98!/100! x 10 = 1/10 * 99
Evaluate the product
98!/100! x 10 = 99/10
Hence, the value of the factorial expression is 99/10
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Noah is buying a pair of jeans and using a coupon for 10% off.
The total price is $56.70, which includes $2.70 in sales tax.
Noah's purchase can be modeled by the equation:
`x-0.1x+2.70=56.70`
What does the solution to the equation mean in this situation?
Answer: The answer to this equation is 53.91
prove that the sum of the squares of two consecutive even numbers is a multiple of 4
Answer:
Since the final answer has a factor of 4, it is a multiple of 4.
Step-by-step explanation:
Let the smaller even number be 2n.
The next greater even number is 2n + 2.
(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)
Alan deposits $10 per month into his savings account. Which expression could represent the amount he saves, in dollars, in y years?
Answer:
in 1 year Allan would save 120 dollars, this is because, 10x12=120
Step-by-step explanation:
to find out what he would save I 2 years just multiply 120 by 2, 120x2=240, and for 3 years multiply 120 by 3, and so on.
Please help!:)))))))))))
Answer:
one way to name the symbol is our and another way to name the symbol is rco
Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y ' = y 2xy, y(2) = 1. (round the answer to four decimal places.) y(2.5) =
y(2.5) = 15.9389 is Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem.
What is euler's method?
First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.
f(x,y) = 3y+2xy
So, starting at t0 = 2, repeat the above sequence until t0>2.5
a) m = f(2,1) = 3(1)+2(2)(1) = 7
b) y1 = y0 + hm = 1+0.1(7) = 1.7
c) t1 = t0 + h = 2.1
d) show t1 and y1
e) t0 = t1 = 2.1
f) y0 = y1 = 1.7
2nd iteration
a) m = f(2.1,1.7) = 3(1.7)+2(2.1)(1.7) = 5.1 + 7.14 = 12.24
b) y1 = y0 + hm = 1.7+0.1(12.24) = 1.7 + 1.224 = 2.924
c) t1 = t0 + h = 2.2
d) show t1 and y1
e) t0 = t1 = 2.2
f) y0 = y1 = 2.924
This is what I got for all iterations from a simple program x y
2.1 1.7
2.2 2.924
2.3 5.08776
2.4 8.9544576
2.5 15.938934528
y(2.5) = 15.9389
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please help with this question and determine a,b,c,d and e
Answer:
a=7
b=8
c=12
d=33
find e by adding up all numbers in the Venn diagram then subtract the total amount of people by total from the Venn diagram to find e
HELP Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 467) and (10, 647)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (647 - 467)/(10 - 2)
Evaluate
Rate = 22.5
This means that the rate of change is $22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 22.5
So, we have
y = 22.5(x - x1) + y1
Using one of the points, we have
y = 22.5(x - 6) + 467
Set x = 0
So, we have
y = 22.5(0 - 6) + 467
Evaluate
y = 332
Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
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Find the eighth term of each geometric sequence. -30,7.5,-1.875, . . . . .
The eighth term of the given geometric sequence is: 0.00183.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: -30, 7.5, -1.875, ....
Here, [tex]\frac{7.5}{-30}=\frac{-1.875}{7.5}=-0.25[/tex]
That is, the given geometric sequence has a₁ = -30 and r = -0.25
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, [tex]a_8=(-30)(-0.25)^7[/tex] ≈ 0.00183
Hence, The eighth term of the given geometric sequence is: 0.00183.
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Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of
ΔABC
∆ABC
under the dilation with scale factor 3 and the origin as the center of dilation. Label the image
ΔA'B'C'
∆A′B′C′
. Make sure to include the coordinates of A’, B’, and C’.
(b) Draw the image of
ΔDEF
∆DEF
under the dilation with scale factor
−12
−12
and the origin as the center of dilation. Label the image
ΔD'E'F'
∆D′E′F′
. Make sure to include the coordinates of D’, E’, and F’.
Answer:
Answer:
(b) Draw the image of
ΔDEF
∆DEF
Step-by-step explanation:
A new community sports vs complex is being built in Erie. the perimeter of the rectangular playing field is 232 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
The dimensions of the rectangular playing field are:
length = 92 yards and
width = 24 yards.
Given, the perimeter of the rectangular field is : 232 yards.
From the given question, length of the field is 4 yards less than quadruple the width.
hence, let the width of the field be x yards.
Length of the field = 4x - 4 yards.
we know that perimeter of the rectangle = 2(l+w)
therefore, substitute the values in the above formula:
2(4x - 4 + x) = 232
2(5x - 4) = 232
multiply the terms.
10x - 8 = 232
arrange the constants on one side.
10x = 232 + 8
10x = 240
x = 240/10
x = 24
hence we get the width as x = 24 yards.
Now substitute the value of x to find out the value of the length.
therefore, l = 4x - 4
l = 4(24) - 4
l = 96 - 4
l = 92
Therefore length and width of the rectangular field is 92 and 24 yards respectively.
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A pair of parametric equations is given. x = 2t, y = t 5 (a) sketch the curve represented by the parametric equations. use arrows to indicate the direction of the curve as t increases.
Refer to the image attached.
What are parametric equations?Parametric equation uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used.
Now,
In order to plot the graphs of the given parametric equations, we will be sketching a table, in which, the values of the equations will be found at various values of the parameter.
=> Refer to the table in the image attached.
For the values so found of the parametric equations for the respective parameter, a graph will be plotted for both the equations:
Refer to the graph in the image attached.
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Negative 3 times negative 8
Answer:
Step-by-step explanation:
-24
the question is shown in the picture
Answer:
Final Cost of 3 pounds: 7.25
Final cost of p pounds: 3.50p
Step-by-step explanation:
3.50p - 3.25 = ?
3.50(3) - 3.25 = ?
10.50 - 3.25 = $7.25
Write an expression of the cost to buy at least one pound of chicken.
3.50p
I hope this helps!
Please help me I need help
The question is What is the slope of a line perpendicular to the line whose equation is 5x-2y= -10. Fully simplify your answer
Answer:
x=−2+2y/5
Step-by-step explanation:
Add 2y to both sides of the equation.5x=−10+2y
Divide each term in 5x=−10+2y by 5 and simplify.
Divide each term in 5x=−10+2y by 55x5=−105+2y5Simplify the left side
. Cancel the common factor of 5
Cancel the common factor.5x5=−105+2y5Divide x by1.x=−105+y5
Simplify the right side.
Divide
−10 by 5
Solve the inequality. Graph the solution -3s<11s+1
[tex]-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}[/tex]
===========================
[tex]\textcopyright ELIZA[/tex]
How many solutions does the equation have?
5(n–2)=5n–10
Answer:
Infinite solutions, regardless of the value of n.
Step-by-step explanation:
[tex]5\left(n-2\right)=5n-10\\5\left(n-2\right)\\5n-5\cdot \:2\\5n-10\\5n-10=5n-10\\5n - 10+10=5n-10 + 10\\5n = 5n\\5n-5n=5n-5n\\0=0\\\mathrm{\:for\:n = \infty,-\infty}[/tex]
Hello! Please help me with this. I'm very desperate lol. Its 16. Ill give brainliest
Answer:
You showed the right work and got the right answer!
x = 6
Step-by-step explanation:
Since B is in the middle of A and C, AB + BC = AC
So,
2x - 11 + 8 = x + 3
x - 3 = 3
x = 6
Write an equation in slope-intercept form for the line that has a slope of -5 and passes through the point (-3, -8).
Answer:
[tex]y = -5x - 23[/tex]
Step-by-step explanation:
To write an equation in the slope-intercept form for a line, given the coordinates of a point on the line as well as the line's slope, we use the following formula:
[tex]\boxed{y - y_1 = m(x - x_1)}[/tex],
where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] are the given coordinates of a point.
In this question, we are told that the slope is -5 and the coordinates of a point passing through the point are (-3, -8).
Therefore, using the above formula, we can write:
[tex]y - (-8) = -5(x - (-3))[/tex]
⇒ [tex]y + 8 = -5(x + 3)[/tex]
⇒ [tex]y + 8 = -5x - 15[/tex] [Distributing -5 into the brackets]
⇒ [tex]y = -5x - 15 - 8[/tex] [Subtracting 8 from both sides]
⇒ [tex]y = -5x - 23[/tex]
This means that the equation for the slope-intercept form of the line is [tex]y = -5x - 23[/tex] .
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Julian is trying to decide on a future career. He has narrowed down his choices to orthodontist, sound engineering technician, police officer, or editor. The following table represents the total employment numbers for 2006 and projected employment numbers for 2016.
Orthodontist
Sound engineer technician
Police officer
Editor
2006
9,206
16,125
648,982
122,273
2016
10,214
17,864
719,041
124,135
Which profession is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016?
a.
Orthodontist
b.
Sound engineer technician
c.
Police officer
d.
Editor
The profession that is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016 is B. sound engineer technician.
How to calculate the percentage?The increase in percentage for orthodontist will be:
= (10214 - 9206) / 9206 × 100
= 1008 / 9206 × 100
= 10.95%
The increase in percentage for sound engineer will be:
= (17864 - 16125) / 16125 × 100
= 1739/16125 × 100
= 10.79%
The increase in percentage for police officer will be:
= (719041 - 648982) / 719041 × 100
= 70059/719041 × 100
= 9.74%
The increase in percentage for editor will be:
= (124135 - 122273)/124135 × 100
= 1862/124135 × 100
= 1.5%
Therefore, the sound engineer has the greatest percentage increase.
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Answer:
sound engineer
Step-by-step explanation:
A store sells a water blaster for $26. They bought it for $20. What is the markup percent?
The markup percent of the water blaster in the store is 30%
How to calculate the markup percent of the water blaster ?The store sells a water blaster for $26
They bought it for $20
New price is $26
Original price is $20
The markup percent can be calculated as follows
26-20/20 × 100
= 6/20 × 100
= 0.3 × 100
= 30%
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PLEASE HELP ME WITH THIS!!!!
At a convention, 192 speakers gave one or more presentations of varying lengths. The histogram
summarizes the total presentation time, in hours, of each speaker.
Number of speakers
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7
Total presentation time (hours)
What interval contains the 25th percentile for this data?
The 25th percentile of the data is represented by the 0 to 1 hour range.
48 speakers, or around 25% of the total of 192 speakers, are present.
According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.
This means that 48 is between0 and1.
A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.
A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.
Therefore, the 0 to 1 hour period contains the data's 25th percentile.
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Solve p3 = −512.
pls help due in 1 hour
Answer:
-170 2/3
Step-by-step explanation:
Divide both sides by 3 to get p by itself
p = -512/3
Simplify
- 170 2/3
Answer:
p=−8
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] \rightarrow \sf \: p {}^{3} =−512[/tex]
Step 1: Take cube root.
[tex] \sf p={(−512) }^{ ( \frac{1}{3} )}[/tex]
[tex] \sf \: p=−8[/tex]
whta slope line goes through (4,5) &(-1,-5)
Answer:
y = 2x - 3
Step-by-step explanation:
1) Find the slope
The slope of any function, if given the coordinates of at least two of the points it crosses, is given by the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
We are given the points (4, 5) and (-1, -5), therefore, we can substitute their values:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-1)} = \frac{10}5 = 2[/tex]
2) Find the line's equation
We can find the line's equation by substituting one of the given points and the slope we just found into the formula [tex]y - y_1 = m(x - x_1)[/tex]:
[tex]y - 5 = 2(x - 4) \\ \to y - 5 = 2x - 8 \\ \to y = 2x - 3[/tex]
Answer: 2x - 3.
Step-by-step explanation: I took the test.
I need help in those questions please
The other root of the given quadratic equation is a = ± 3/√2.
Given that, x=2 and x²+ax+12=0.
What are the roots of quadratic equations?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Now, put x=2 in x²+ax+12=0 and find the value of a.
That is, 2²+2a+12=0
⇒4+12+2a=0
⇒16+2a=0
⇒2a=-16
⇒a=-8
So, the value of a is -8.
Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.
That is, 6=2(0)²+b(0)+c
⇒ c=6
6=2(4)²+b(4)+c
⇒ 6 = 32+4b+c
⇒ -26 = 4b + 6
⇒ 4b = -32
⇒ b = -8
So, the value of b is -8 and the value of c is 6.
Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.
That is, 2a²+a/a -9 = 0
⇒ 2a² - 9 = 0
⇒ a²=9/2
⇒ a = ± 3/√2
Therefore, the other root of the given quadratic equation is a = ± 3/√2.
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Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 3,6,12,24,48, .......
The next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
According to the given question.
We have a sequence 3, 6, 12, 24, 48, ..
Since, the first term of the sequence is 3.
The second term of the sequence is 6.
The third term of the sequence is 12.
Here, we can say that the next term is twice the previous term.
So, the next two terms of the given sequence, i.e.
Sixth term = 48 × 2 = 96
Seventh term = 96 × 192
Therefore, the formula for the nth term of the sequence is given by
[tex]T_{n+1} = 2T_{n}[/tex].
Hence, the next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
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(question in the in image above the other side if angle Q is 113
Find x
Answer:
x = 85
Step-by-step explanation:
the exterior angles of a polygon sum to 360°
note the exterior angle at P = 180° - 90° = 90°
sum the 4 exterior angles and equate to 360
x + 72 + 113 + 90 = 360
x + 275 = 360 ( subtract 275 from both sides )
x = 85
In a bag of gum balls 30% are blue. There are 21 blue gum balls in the ball how many gum balls are there in all
Answer:
70
Step-by-step explanation:
21 is 30 % so multiply 21 by 3 which is 63 and then divide 21 by 3 which is 7 and add the 7 to 63
