The equation of line is y = -3x + 8
What is slope?Slope is the ratio of the change in the y coordinates to the change in the x coordinates.
Analysis:
slope (m) = y2 - y1 / x2 - x1
m = 14 -5 / -2-1 = 9/-3 = -3
when y = 5, x = 1
y = mx + c
5 = -3(1) + c
5 = -3 + c
c = 5+3 = 8
Y = -3x + 8
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Find the interquartile range (IQR) for the following data set: 52, 60, 24, 36, 48, 52, 72
Answer:
24
Step-by-step explanation:
The interquartile range defines the difference between the third and the first quartile.
Let's put this data set in ascending order:
24, 36, 48, 52, 52, 60, 72
The median is 52. The median of both the lower (1st quartile) and upper half (3rd quartile) of the data is 36 and 60.
Now we can subtract the first quartile from the third quartile (60 - 36) to get the interquartile range of 24.
Hope this helped! :)
Write the following expression without negative exponents and without parentheses.
(9x)^-1
Answer:
1/9x
Step-by-step explanation:
The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.
(9x)^-1
= 1/9x
To be clear, this is a 1 one top and a 9x on the bottom of a fraction.
For the first 6% of Bianca's salary, her employer matches 100% of her 401(k)
contributions, and from 6% to 12%, Bianca's employer matches 50% of her
401(k) contributions. Bianca's salary is $50,000, and last year, she contributed
$6000 to her 401(k) plan. What was her employer's contribution to the
401(k)?
OA. $7200
OB. $4500
OC. $6000
OD. $3000
Answer:
B
Step-by-step explanation:
6% of her salary is .06 * 50000 = 3000 <===== matched 100%
from 6- 12% is another 3000 <=====matched 50% = 1500
3000 + 1500 = 4500 dollars matched
(she put in 6000 and her employer put in 4500 = 10500 total)
The article What is i* if I =o
questions:you have been offered a scholarships to further your studies in Australia
write a diary entry sharing your experience about it
can you simplify 8/15+1/6
Answer:
Yes and the answer is 16/5
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 1/6 : 6/1
Now, multiply it with the dividend
8/15 ÷ 1/6 = 8/15 × 6/1
And after that you get 48/15 but after reducing the fraction, the answer is 16/5. ( In mixed form, 3 1/5 )
I hope this helps and I am a middle school student answering this question.
Answer:
7/10Step-by-step explanation:
can you simplify 8/15+1/6
8/15 + 1/6 =
(16 + 5)/30 =
21/30 =
semplify (21:3 and 30:3)
7/10
A circular swimming pool has a radius of 28 ft. There is a path all the way around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path.
A circle has a radius of 28 feet. A larger circle goes around the smaller circle that is 4 feet wide.
About how many feet of fencing are needed to go around the pool path? Use 3.14 for Pi.
88 ft
100 ft
176 ft
201 ft
The number of feet of fencing that is needed to go around the pool path is D. 201 ft.
How to calculate the number of feet?
We have a pool with a radius of 28 feet. The radius of the outer edge of the pool path would be equal to the radius of the pool plus the width of the path.
= (28 + 4) feet
= 32 feet
The circumference of the outer edge of the pool path would be equal to the perimeter.
p = 2 * pi * r
p = 2 * 3.14 * 32
p = 200.96 feet
p = 201 feet
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What is the equation of a line that is parallel to -x + 3y = 6 and passes through the
point (3, 5)?
1.y=1/3x + 4
2.y = 3x + 4
3.y = -1/3x-4
4.y = -3x - 4
Answer:
Two lines are parallel if and only if they have the same slope.therefore the original line y=1/3x+2
so option 1 is the answer
Given matrix A below, and that A = B, find the value of the elements in B.
A =
9 −2 3
2 17 0
3 22 8
b11 =
9
b12 =
17
b13 =
b21 =
b22 =
b23 =
b31 =
b32 =
b33 =
The value of Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
Given : Matrix A = Matrix B
matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex]
The matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex] (according to the question)
Since it is given A=B
and substituting the given values of elements of B
matrix B=[tex]\left[\begin{array}{ccc}9&17&?\\?&?&?\\?&?&?\end{array}\right][/tex]
According to the property of equality of matrices,
When the matrices are given to be equal, their corresponding elements are also equal
so
b13 = 3
b21 = 2
b22 = 17
b23 = 0
b31 = 3
b32 = 22
b33 =8
Substituting the found out values in place of the question marks,
Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
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Answer:
b11 =
9
b12 =
-2
b13 =
3
b21 =
2
b22 =
17
b23 =
0
b31 =
3
b32 =
22
b33 =
8
Step-by-step explanation:
Which phrase best describes this polygon?
concave octagon
concave nonagon
convex nonagon
convex octagon
Answer:
Concave octagon
Step-by-step explanation:
Concave octagon:
This polygon has 8 sides. So it is a octagon. If one interior angle measures more than 180, then it is concave polygon.So, this is a concave octagon
Solve. 5/8 +3/4 over -2/3 - 5/6
The solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12
How to solve fractions5/8 + 3/4 ÷ -2/3 - 5/6
(5+6) / 8 ÷ (-4-5) / 6
= 11/8 ÷ -9/6
= 11/8 ÷ -3/2
= 11/8 × 2/-3
= 22/-24
= -11/12
Therefore, the solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12
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20. THOUGHT PROVOKING There are 100 coins in a bag.
Only one of them has a date of 2010. You choose
a coin at random, check the date, and then put the
coin back in the bag. You repeat this 100 times. Are
you certain of choosing the 2010 coin at least once?
Explain your reasoning.
Answer:
yes
Step-by-step explanation:
yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.
Nell is analyzing a quadratic function f(x) and a linear function g(x) will they intersect
The area of a rectangular shop in the mall is 160 square meters. The perimeter is 52 meters. What are the dimensions of the shop?
Answer:
width = 10 m
length = 16 m
Step-by-step explanation:
Formula
[tex]\textsf{Area of a rectangle} = wl[/tex]
[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]
(where [tex]w[/tex] is width and [tex]l[/tex] is length)
Given:
Area = 160 m²Perimeter = 52 mSubstituting the given values into the formulae to create two equations:
[tex]\textsf{Equation 1}: \quad wl=160[/tex]
[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]
Rearranging Equation 1 to make w the subject:
[tex]\implies w=\dfrac{160}{l}[/tex]
Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:
[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]
[tex]\implies \dfrac{160}{l}+l=26[/tex]
[tex]\implies 160+l^2=26l[/tex]
[tex]\implies l^2-26l+160=0[/tex]
[tex]\implies l^2-10l-16l+160=0[/tex]
[tex]\implies l(l-10)-16(l-10)=0[/tex]
[tex]\implies (l-10)(l-16)=0[/tex]
[tex]\implies l=10, 16[/tex]
According to Equation 1:
If length = 10 m ⇒ width = 16 mIf length = 16 m ⇒ width = 10 mAs width < length, the dimensions of the shop are:
width = 10 mlength = 16 mAndrew is showing his work in simplifying -4.5 + 4.2 + 5.6 - 7.3. Identify
any errors in his work or in his reasoning. Write feedback to Andrew
explaining the mistake he made and how to correct his work.
Answer:
hence the answer for given problem is -2, but andrew get -21.6 which is wrong
Step-by-step explanation:
45°
x 100°
y = [? ]º
Answer:
55
Step-by-step explanation:
For 95% of all randomly selected samples of n = 130 students, the mean amount of sleep will be between? Use the empirical rule.
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between [tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex].
What is the empirical rule?According to the empirical rule, also known as the 68-95-99.7 rule.
The percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between can be
[tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex]
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Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
I NEED THIS ANSWER FAST PLEASE
Fill in the missing coordinates of the x-intercept of the line defined by the equation y = x – 4
Answer:
the answer might be (-4,0) for x coordinates
Just need some help with this question.
A northbound train left at noon. Two hours later, a southbound train left the same station. At five o'clock the two trains were 210 miles apart. Find the rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train.
The rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train 26 miles per hour.
what is speed?
Speed is the time rate at which an object is moving along a path
Let the speed of southbound train is x miles/hour
so, northbound train has speed of x+10 miles/hour.
then, Speed of both train = Total distance/ total time
(x+10+x)=210/5
2x+10= 210/5
2x+10= 42
2x= 32
x= 16 miles per hour (southbound train)
northbound train: 16+10=26 miles per hour
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A fruit stand has to decide what to charge for their produce. They need \$10$10dollar sign, 10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put this information into a system of linear equations.
Can we find a unique price for an apple and an orange?
Answer:
no
Step-by-step explanation:
The prices are inconsistent, so there is no unique price that can be set for either an apple or an orange that will give the total prices indicated.
__
The first relation can be written as ...
$10 = 4A +4O
$10 = 4(A +O) . . . . factor out 4
$2.50 = A +O . . . . divide by 4
The second relation can be written as ...
$12 = 6A +6O
$12 = 6(A +O) . . . . factor out 6
$2 = A +O . . . . . . . divide by 6
These two relations give different prices for 1 apple and 1 orange. There is no price that can be set for either fruit that will give this result.
No unique prices can be assigned.
What is the total number of different 9-letter arrangements that can
be formed using the letters in the word Projector?
Help please and thank you
Answer: 9
Step-by-step explanation:
By the geometric mean theorem, [tex]\frac{x}[6} =\frac{6}{4} \longrightarrow x=\left(\frac{6}{4} \right)(6)=\boxed{9}[/tex]
41 is a prime number found in the middle of a list of 7 consecutive numbers. find the 7 consecutive numbers
Answer: 29, 31, 37, 41, 43, 47, 53.
Step-by-step explanation:
The table shown below lists the time, in days, that it takes for
a package to be delivered based on its mode of transport and
whether it is international or domestic. Some additional
information is provided.
1. The cost per package by air is $100; by train, $50; by
truck, $10; and by boat, $20.
2. Fragile packages cannot be transported by air.
3. Shipping fragile packages costs an extra $20.
4. Shipping international packages costs an extra $30.
Tim needs to transport a fragile package, and he needs it to
arrive as soon as possible. He is shipping domestic. Which of
the following shipping methods should he use?
Answer:gotchu g there it is
Step-by-step explanation:
Answer:sike gtf
Step-by-step explanation:
Prove that for a triple element x, y, z the distributive law is always satisfied if one of the elements equals 0 or 1, or if two of the elements are equal.
The distributive law is satisfied if the numbers 1,2, and 3 are used as multyplying factors.
What is the distributive law?This is basic mathematical law that states:
A multiplied by (b+c) equals (a x b) + (a x c)Is this law satisfied if there are three numbers involved?The law is always satisfied if one of the numbers is 1. Here is an example
2 x (1+2+3) = 2 x 6 = 12or
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A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t*2 + 88t +6. How long will it take the rocket to reach its maximum height? What is the maximum height?
Question content area bottom
Part 1
The rocket reaches its maximum height at ? second(s) after launch.
Answer:
Step-by-step explanation:
Find the value of each trigonometric ratio. 18) cos X Y 24 24 25 24 A) C) 25 B) D) 24 25 25
Answer:
Step-by-step explanation:
what are the prime factors of 30
Step-by-step explanation:
Stay safe, stay healthy and blessed.Have a good day !Thank you♡ #jennifer ♡
Solve the radical equation.
√x − 1 + 5 = 9
Answer:
17
Step-by-step explanation:
square root of x-1 +5=9
square root of x-1 = 4multiple by power of 2 because square root is cancled by 2.
x-1=16,x=17
Which is the graph of y = [X] - 2?
Answer:
Top right graph
Step-by-step explanation:
Graph is in attached image.