Answer:
Mean (Average) 19.142857142857
Median 19.5
Step-by-step explanation:
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Find the equation of a line perpendicular to y = 4 + x that passes through the
point (-3, 3).
Answer:
y=-1/4x+9/4
Step-by-step explanation:
Get slope of the line first (to find slope that is perpendicular, get the negative reciprocal)
4 turns into -1/4
To get the y-intercept, plug in the given coordinate values into this formula:
y=mx+b
3=-3(-1/4)+b
3-3/4=b
b=9/4
b is our y-intercept
9/4 is our y-intercept
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = 4 + x\implies y = \stackrel{\stackrel{m}{\downarrow }}{1}x+4\qquad \impliedby \begin{array}{|c|ll}\cline{1-1}slope-intercept~form\\\cline{1-1}\\y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}}\\\\\cline{1-1}\end{array}[/tex]
so therefore
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies\cfrac{1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{1}\implies -1}}[/tex]
so we're really looking for the equation of a line whose slope is -1 and passes through (-3 , 3)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-3=-(x+3)\implies y-3 = -x-3\implies y = -x[/tex]
A trapezoid has an area of 36 square feet. If its height is 8, and one base is 4, what is the length of the other base?
Answer:
5
Step-by-step explanation:
A=a+b/2 x h
4 = a
5 = b
8 = h
4 + 5 / 2 = 4.5
4.5 x 8 = 36
So the other base length is 5
Help x^2+10x=24 solve and simplify
Answer:
x= 2, x= -12
Step-by-step explanation:
cuz i said so
first move the 24 to the other side of the equation by subtracting it from both side's
now the equation looks like this
x^2+10x-24
then find values that add to equal 10 and that also multiply to equal -24
this works out to (x-2) (x+12)
which means that x is equal to 2 and -12
Peter says, If you subtract 16 from my number and multiply the difference by −6, the result is −84. What is Peters number?
Answer:
30
Step-by-step explanation:
[tex] - 6(x - 16) = - 84[/tex]
[tex]x - 16 = 14[/tex]
[tex]x = 30[/tex]
I need help with this question. Question is in image below.
Answer:
A. Answer is 2263.
Checkpoint 1 is -86 Checkpoint 4 is 2177
Subtract -86 from 2177....2177-(-86)
=2263
2263 is how much higher checkpoint 1 (-86) is from checkpoint 4 (2177)
B. 239 FEET.
the altitude of the hill must be subtracted by the depth of the ckeckpoint(2)(-189)
therefore the altitude of the hill comes out to be 428-189=239feet.
therefore,the actual altitude of the hill is 239 feet.
A committee of four is chosen at random from a group of 8 women and 5 men. Find the probability that the committee contains at least one man. Answer:
A race car is equipped with jets that can make it go from 0 to 64 mph (about 28 m/s) in 4 seconds. What is the acceleration of the car using its jets?
Answer:
So that it can run faster
Answer:
[tex]a = change \: in \: v \div time[/tex]
Step-by-step explanation:
Change in V =28-0
=28
time =4 sec
Therefore acceleration =28 ÷4
7m/s^-2
A cone has a base with a diameter of
12 inches and a height of 15 inches. What
is the volume of the cone in
cubic inches
using 3.14 for 77?
Answer:
452.16 in^3
Step-by-step explanation:
Volume of a cone = 1/3 pi r^2 h
= 1/3 (3.14)(6^2) (12)
Can someone help me with this problem?
Answer:
yes
Step-by-step explanation:
4:8 and 3:6 when simplified gives the same result which is 1:2
Answer:
A.) Yes, they do catch fish at the same rate.
Daniel:
4 : 8
Lester:
3 : 6
Both of these ratios have a rate of 1 catfish for every 2 trout. Daniel has just caught 1 more catfish and 2 more trout.
4 - 1 = 3
8 - 2 = 6
Both have a rate of catching 1 catfish for every 2 trout.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Evita is solving the system of equations shown using the elimination method. first equation: 3x+8y=20 second equation: 5x−2y=4 what operation will eliminate one of the variables?
a. multiply the first equation by 2
b. multiply the first equation by 4
c and multiply the second equation by 2
d. multiply the second equation by 4
Answer:
d. multiply the second equation by 4
The lengrh of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the function W(x) = 2x^2 - 4x + 13. Which of the following shows the area of the rectangle in terms of x?
Step-by-step explanation:
just multiply the 2 together to get the area
it would just be
[tex](5x) \times (2{x}^{2} - 4x + 13)[/tex]
use the distributive property
[tex]10 {x}^{3} - 20 {x}^{2} + 65[/tex]
unless you want to simplify the answer, this would be the answer
simplified, it would be
[tex]5(2{x}^{3} - 4 {x}^{2} + 13)[/tex]
SOMEONE PLEASE HELP ME WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER
IMAGE BELOW
Answer:
[tex]\sqrt{51[/tex]
Step-by-step explanation:
6^2 + 8^2 = y^2 (Pythag)
100 = y^2
10 = y
7^2 + x^2= 10^2
49+ x^2 = 10^2
x^2 = 51
Find the root of the equation 2x (x -8)=(x + 1)(2x – 3).
Answer: 1/5
Step-by-step explanation:
The root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4. To find the root of the equation 2x(x - 8) = (x + 1)(2x - 3), we need to solve for the value of "x" that makes both sides of the equation equal.
First, let's expand both sides of the equation:
2x(x - 8) = (x + 1)(2x - 3)
[tex]2x^2 - 16x = 2x^2 - x - 3x + 3[/tex]
Now, combine like terms on the right-hand side:
[tex]2x^2 - 16x = 2x^2 - 4x + 3[/tex]
Next, subtract [tex]2x^2[/tex] from both sides to get the x terms on one side:
-16x = -4x + 3
Now, bring all the x terms to one side by subtracting -4x from both sides:
-16x + 4x = 3
Simplify the left-hand side:
-12x = 3
Finally, solve for x by dividing both sides by -12:
x = 3 / -12
x = -1/4
So, the root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4.
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nearest whole number of
3÷80.81
Answer:
0.04
Step-by-step explanation:
3÷80.81= 0.037
to the nearest whole number = 0.04
last year the hiking club had 19 members. this year there are 37 members in the club. estimate the percetnage change in the number of club members
Two prisms are similar if the ratio of the base if the two prisms is 49:196 what is the ratio of the volumes of the prisms
Answer:
1:8
Step-by-step explanation:
First, you must find the scale factor. Because you are given the area of the base, you must take the square root of 49 and 196. That leaves you with 7:14, and that simplifies to 1:2. To find the ratio of the volumes, you must cube both. That leaves you with a 1:8 ratio.
Jill Barley obtained a 25-year, $145,117 mortgage loan from University Savings and Loan Association. The
interest rate is 6 percent. The monthly payment is $1,800.00. For the first payment, what is he interest?
Answer:
175,424.02
Step-by-step explanation:
multiply 145,117 by 106%
multiply 1800 by 12 (months in a year)
add 21600 to 153,824.02
Find the volume of a right circular cone that has a height of 8.9 ft and a base with a radius of 14.3 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
1905.9 cubic feet
Step-by-step explanation:
Use the formula for a volume of a cone - 1/3 * pi * radius^2 * height
Find volume of a cone - 1/3 * pi * 14.3^2 * 8.9 = 1905.8587024733 cubic feet
Round to nearest tenth - 1905.9 cubic feet
:)
6 1/2 + 5 7/8 what is the answer?
Answer:
12 3/8
Step-by-step explanation:
6 1/2 + 5 7/8 =
= 6 4/8 + 5 7/8
= 11 11/8
= 11 + 8/8 + 3/8
= 11 + 1 + 3/8
= 12 3/8
BIG QUESTION, 100 POINTS
Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.
Find the slope of line q.
Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)
Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)
Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b. Show your work.
Answer:
[tex]\textsf{Slope of line q}: \quad 3[/tex]
[tex]\textsf{Slope of line p}:\quad -\dfrac{1}{3}[/tex]
[tex]\textsf{Equation of line p in slope-point form}: \quad y+5=-\dfrac{1}{3}(x-6)[/tex]
[tex]\textsf{Equation of line p in slope-intercept form}: \quad y=-\dfrac{1}{3}x-3[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]y = mx + b[/tex]
(where m is the slope and b is the y-intercept)
Given:
line q: y = 3x + 5Therefore, the slope of line q is 3.
As line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q.
Therefore, the slope of line p is -1/3
Equation of line p, using the point-slope form, the slope of -1/3 and the point (6, -5):
[tex]\begin{aligned}y-y_1 &=m(x-x_1)\\\implies y-(-5) &=-\dfrac{1}{3}(x-6)\\y+5 &=-\dfrac{1}{3}(x-6)\end{aligned}[/tex]
Simplify to slope-intercept form:
[tex]\implies y=-\dfrac{1}{3}x-3[/tex]
Slope of q:-
m=3Perpendicular line's have slopes negative reciprocal to each other
Slope of p
-1/3Passes through (6,-5)
Equation in point slope form
y+5=-1/3(x-6)3y+15=-x+63y=-x-9y=-1/3x-3Answer two questions about Equations A and B:
A. 5x2+x= x=4
B.
5x + x = x - 4-
1) How can we get Equation B from Equation A?
2) Are these equations equivalent?
Answer:
Equation B is the same as Equation A + 2
Step-by-step explanation:
To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.
Equation B: 5x+x=x-4.
Equation A: 5x-2+x=x-4.
Simplifying equation A to be in the form of equation B:
5x -2 + x = x - 4
Adding 2 to both sides:
5x + x -2 + 2 = x - 4 + 2
5x + x = x - 4 + (+2)
= equation A + 2
But 5x+x=x-4 = equation A
Therefore Equation B is the same as Equation A + 2
Complete the statement using <, >, or =.
55% of 60 __ 60% of 65
Answer:
Less than(<)
55% of 60 is 33
60% of 65 is 39
when solving problems with percentage, always multiply x, your decimal form of the percentage, by y, the often whole number part you are multiplying the percentage by.
[tex]0.55 * 60 = 33\\0.60 * 65 = 39[/tex]
note that if the percentage is for example 30%, it will be 0.3, while if it were 3%, it would be 0.03 to avoid confusion.
That said, the answer is less than.
Can someone please give me the (Answers) to this? ... please ...
I need help….
Answer:
AB is chord
GF is tangent
DE is diameter
HJ is secant
C is center of the circle
DC is radius
K is point of tangency
AB is arc
Step-by-step explanation:
Solve the system of equations.
Answer:
1) {y,x}={-3,-23}
2) {x,y}={7,-9/2}
Step-by-step explanation:
Required:
Solve systems of equations1) y - x = 20, 2x - 15y = -1
Equations Simplified or Rearranged :
[1] y - x = 20
[2] -15y + 2x = -1
Graphic Representation of the Equations :
x + y = 20 2x - 15y = -1
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = x + 20
// Plug this in for variable y in equation [2]
[2] -15•(x +20) + 2x = -1
[2] - 13x = 299
// Solve equation [2] for the variable x
[2] 13x = - 299
[2] x = - 23
// By now we know this much :
y = x+20
x = -23
// Use the x value to solve for y
y = (-23)+20 = -3
Solution :
{y,x} = {-3,-23}
2) 25-x=-4y,3x-2y=30
Equations Simplified or Rearranged :
[1] -x + 4y = -25
[2] 3x - 2y = 30
Graphic Representation of the Equations :
4y - x = -25 -2y + 3x = 30
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 4y + 25
// Plug this in for variable x in equation [2]
[2] 3•(4y+25) - 2y = 30
[2] 10y = -45
// Solve equation [2] for the variable y
[2] 10y = - 45
[2] y = - 9/2
// By now we know this much :
x = 4y+25
y = -9/2
// Use the y value to solve for x
x = 4(-9/2)+25 = 7
Solution :
{x,y} = {7,-9/2}
Convert the units to the nearest tenth.
Enter the correct answer in the box.
Show Hints
kilometers = 50 miles
Answer:
80.5
Step-by-step explanation:
The Board of directories has 13 members. How many ways are there to elect a Chair and a Vice-Chair if the bylaw has a rotation rule: Chair and Vice-Chair cannot keep their positions for two years in a row
The number of ways to elect a Chair and a Vice Chair is 156.
Amount calculationGiven that the Board of directories has 13 members, to determine how many ways are there to elect a Chair and a Vice-Chair, the following calculation must be made:
13 x 12 = X156 = XAs the rule does not affect, because in the two years that have elapsed a different election will be held, the number of ways to elect a Chair and a Vice Chair is 156.
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Answer:The number of ways to elect a Chair and a Vice Chair is 156.
Step-by-step explanation:
please help fast I dont know the answer
What is this question asking and how do I solve it?
Answer:
the question is asking what it is the segment between HB,HG and CG
Step-by-step explanation:
If x^2 - 6xy = z - 9y^2, make x the subject of the formula
[tex]~~~~x^2-6xy=z-9y^2\\\\\implies x^2- 2\cdot x\cdot 3y + (3y)^2 - (3y)^2 = z-9y^2\\ \\\implies (x-3y)^2 -9y^2 = z-9y^2\\\\\implies (x-3y)^2 = z\\\\\implies x - 3y =\pm\sqrt z\\\\\implies x = 3y\pm\sqrt z[/tex]
Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005. The table gives the number of tickets sold for each
concert. Select the points that represent this data.
Year
Tickets Sold
(thousands)
10
2000
2001
10
2002
20
2003
40
2004
55
2005
70
90
80
70
(so
The points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on graph.
How to read the data from the table?Table is a way to represent the data of the two or more variable. To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.
Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005.
The table gives the number of tickets sold for each concert. Select the points that represent this data.
Tickets Sold (thousands) Year 10 200010 200120 200240 200355 200470 2005The graph which represent the data in the data is attached below year wise.
For the first point, select the value 10 on graph vertically at year 2000. Similarly, select all the points on the graph for the table.
Thus, the points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on the graph.
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