Answers
Answer:
7k - 7
Step-by-step explanation:
- k - (- 8k + 7) ← distribute parenthesis by - 1
= - k + 8k - 7 ← collect like terms
= 7k - 7
Related Questions
can someone help me!!
Answers
In his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month. What is the total distance that he biked in his first month of training?
Answers
Taking into account the change of units, the total distance that he biked in his first month of training is 55.8 miles.
Rule of threeIn first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Total distance that he biked in his first month of trainingIn his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month.
So you can apply the following rule of three: if for each workout Landon biked 3.1 miles, in 18 workouts he biked how far?
1 workout ⇒ 3.1 miles
18 workouts ⇒ total distance
So: [tex]total distance=\frac{18 workoutsx3.1 miles}{1 workout}[/tex]
Solving:
total distance= 55.8 miles
In summary, the total distance that he biked in his first month of training is 55.8 miles.
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Answer:
9
——- =
-2.1
Answers
Answer:
-9/2
In alternate forms -4•5,-4 1/2
30 A club of 12 people would like to choose people for the offices of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office?
Answers
1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.
How many different ways are there to select the officers so that only one person holds each office?Total number of people in the club = 12
total number of positions = (president, vice president, secretary) = 3
From 12 people 3 people are taken at a time.
That is, using the formula for permutation we get,
ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]
Here n = 12 and x = 3
P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320
Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.
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You want to retire on the equivalent of $50,000 per year in today's money. inflation is expected to be 3%. you will retire in 30 years. you will earn 10% annually on your investments from not till retirement and you will earn 8% during retirement (which is expected to last 20 years). how much do you need to save per month in order to fund this retirement?
Answers
$662.18 needs to be saved per month.
$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.
i.e. $218,454 is required in retirement years (for 20 years)
Calculating the PV of these payments at 7% is calculated as below.
FV = 0
1/y = 7%
n=20; PMT = 218454; calculate PV = $2,314,305
Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.
FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT = $662.18
So $662.18 needs to be saved per month.
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Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answers
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
Help please!!! Write an equation that represents the line.
Use exact numbers.
Answers
The slope is increasing the number will be positive and since it goes up six and over five that would be the fraction of the slope and 5 is the point on line Y
simplify the expression 2^m/n * 2^n/m
Answers
what is the value of x
find the value of f
Answers
Answer:
x = 20°
f = 40°
Step-by-step explanation:
4x + 5x = 180°
because a straight line is 180°
so 9x = 180°
1x = 180 ÷ 9
1x = 20
all angles in a triangle add together is 180°
so 7x + f = 180°
1x = 20
7x = 20 × 7
7x = 140°
f = 180° - 140 °
f = 40°
Answer:
x = 20 , f = 40
Step-by-step explanation:
4x and 5x are a linear pair and sum to 180° , then
4x + 5x = 180
9x = 180 ( divide both sides by 9 )
x = 20
then
5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
5x is an exterior angle of the triangle , then
f + 3x = 5x , that is
f + 60 = 100 ( subtract 60 from both sides )
f = 40
Order the number from least to greatest square root of 1, 1/3,2.5,square root of 2
Answers
The required order of the number from least to greatest square root is
1/√3 < √1 < √2 < √2.5
Which number is greatest in value:
In the above numbers 1, 1/3 and 2.5 do not have square roots.
So, we will write 1, 1/3 and 2.5 inside the square root as shown below.
√1 = 1
√(1/3) = 1/√3 = 0.577350269
√2.5 = 1.58113883
√2 = 1.414
Arranging these numbers according to their value, we get the order as-
0.577350269 < 1 < 1.414 < 1.581138831
Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.
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Which of the following are factor pairs for 12?
1. 1 and 12
2. 2 and 4
3. 2 and 6
3. 3 and 4
4. 3 and 5
NEED ANSWER QUICK PLEASE!!
Answers
Answer:
FACTOR pairs are a set of two integers that when multiplied together gives a particular product.FACTOR pairs of 12 are :1 and 12 because 1 x 12 = 122 and 6 because 2 x 6 =123 and 4 because 3 x 4 = 12Hope you understandHope this helps.Good luck ✅.Find the missing side length of the triangle.
Answers
Answer:
a = 1.5 in.
Step-by-step explanation:
Use the Pythagoras Theorem:
1.7^2 = a^2 + 0.8^2
a^2 = 1.7^2 - 0.8^2
= 2.25
a = 1.5 in.
Answer:
a = 1.5 in.
Explanation:
Using Pythagoras theorem:
a² + b² = c²
insert values
a² + 0.8² = 1.7²
a² = 1.7² - 0.8²
a² = 2.89 - 0.64
a² = 2.25
a = √2.25
a = 1.5
Select one or more expressions that together represent all solutions to the equation.
Your answer should be in radians.
Assume n is any integer.
30 cos (30x) + 14 = -16
Choose all answers that apply:
Answers
Answer:
D. π/30 + n(π/15)
Step-by-step explanation:
The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.
Solution30cos(30x) +14 = -16
30cos(30x) = -30 . . . . . . subtract 14
cos(30x) = -1
This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:
30x = π +2nπ
x = π/30 +n(π/15) . . . . . odd multiples of π/30
__
Additional comment
The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.
BRAINLIEST TO PERSON WHO HELPS
Mrs. Lindy is purchasing notebooks for her students. She spends $52 on n notebooks. Each notebook costs $3.25
Select the equation that matches this situation.
Answers
Answer:
B. 52= 3.25n
Step-by-step explanation:
Unit price multiplied by quantity equals total. So, each notebook cost $3.25 and she buys 'n' notebooks.
She totally spends $52.
In conclusion, 3.25 (unit price × n [quantity]) = 52.
And that is.. 52 = 3.25n.
<3
Answer:
B
Step-by-step explanation:
Let's think about what does the given info mean.
Because of n notebooks, she spent $52
One notebook is $3.25.
So 3.25n = 52
Take it this way if you don't understand
Let's say I spent 4$ on two (2) pens
What's the value of one pen?
We want to find the value of one pen and then multiply it by 2, to get 4$
So we normally would do 4/2
However, to set up an equation, we would create
v (value of one pen) x 2 (pens) = 4$ (cost)
v = 4$/2 = 2$
Help me solve this problem on arithmetic and geométrica sequences
Answers
Answer:
math math math math math math math math math math
The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
Answers
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
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you can afford to invest $150 per month in an annuity that earns 4% per year, compounded monthly. How long will it take before your investment is worth $6000?
Answers
The time it will take before your investment is worth $6000 = 7 years
Calculation of simple interestThe amount of money invested per month = $150
Therefore the amount principally invested yearly;
= 12 × 150 = $1,800
Simple interest = $6000
Rate = 4%
Time = ?
Using the formula for Simple interest (SI)= P×T×R/100
Make T the subject of formula,
T = SI × 100/P×R
T = $6000×100/1800×4
T = 600000/7200
T= 83 months/ 12 = 7 years
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When researching for a business report, you should find reliable sources whose information is accurate, unbiased, and .
Answers
Answer:
Creditable
Step-by-step explanation:
Could also be:
up-to-date
Refreshment we’re set up in one area of the gym . hot pretzels were a dollar lemonade was 50 cents, fruit was 35 cents , and cookies were a quarter . if you purchase two of each . How much money would you needed
Answers
Answer:
$4.20
Step-by-step explanation:
1+1+.50+.50+.35+.35+.25+.25=4.20
Drag each tile to the correct box.
Each function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
Answers
The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .
There are some rules for transformation of graph of various functions which are as follows :-
For F(x) →f(−x) = Reflection about the y-axisFor F(x) → f(ax) = It will depend upon value of a chosenIf |a|>1 then f(ax) is f(x) squashed horizontally by a factor of aIf 0<|a|<1 then f(ax) is f(x) is stretched horizontally by factor of aIf a<0 then is f(ax) is f(x) also reflected in the y-axisBy keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.
Thus the first graph represents sin(2x), the second graph represents
sin(-x) and the third graph represents sin(x/2)
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Select the correct answer from the drop-down menu.
Compare the steps for constructing a perpendicular line to line ABthrough point C using a reflective device and using paper.
.C
A
When using paper to construct the perpendicular line, the paper is folded so that
line ABwill lie exactly on top of each other.
When using a reflective device to construct a line perpendicular to line AB, set one end of the device to coincide with
then swing the other end of the device so the reflection of line ABcoincides with
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and the two sides of
and
Answers
The C is perpendicular to AB
When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.
When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB
The question is incomplete hence the complete question is shown here
Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line through point using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line coincides with.
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Answer:
I toke the test, I think the first one is A and B coincide
Step-by-step explanation:
A man left savings of the 2 50,000 to his wife, 2 daughters and a son. find the value of the shares that each received.q
Answers
Answer:
62,500
Step-by-step explanation:
250,000 ÷ 4 = 62,500
∴ Each member would receive 62,500.
if m = 2 and n = 5 then find the value of 6m+5n
Answers
Answer:
37
Step-by-step explanation:
6m+5n
plug in your given values
6(2) + 5(5)
12+25
=37
Answer:
37
Step-by-step explanation:
6m + 5n
6*2 + 5*5 = 12 + 25
= 37
A local farmer built a rectangular pen for her chickens using 12 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 12 meters of fence. She then build a rectangular pen for her pigs using 16 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the chicken pen. The width of her pen was 1 meter more than the width of the chicken pen. How much larger is the pig pen than the chicken pen
Answers
The pig pen is 14 sq. meters larger than the chicken pen built by the former.
What are the perimeter and area of a rectangle?Consider a rectangle with length 'L' and width 'W'.
So, its perimeter = 2(L + W) units and area = L × W sq. units.
Calculating the dimensions of the rectangular pen for chicken:It is given that a farmer built a rectangular pen for chickens.
The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.
So,
L + 2W = 12
⇒ L = 12 - 2W
Then its area is calculated as below:
Area = L × W
= (12 - 2W) W
= 12W - 2W²
Consider A' = 0 for finding the larger area.
So, differentiating the area w.r.t W,
dA/dW = 12 - 4W
0 = 12 - 4W
⇒ 4W = 12
∴W = 3 meters
Then,
L = 12 - 2W = 12 - 2(3) = 6 meters
So, the area of the chicken pen = 6m × 3m = 18 m²
Calculating the dimensions of the rectangular pen for the pig:It is given that,
The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2
The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1
On substituting L and W values to find the dimensions of the pig pen,
L' = 6 + 2 = 8m
W' = 3 + 1 = 4m
Then,
Area = L' × W'
= 8m × 4m
= 32 m²
Finding how much larger is the pig pen than the chicken pen:
Area of the pig pen - Area of the chicken pen
⇒ 32 m² - 18 m² = 14 m²
Therefore, the pig pen is 14 m² larger than the chicken pen.
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ProblemSolving One leg of an isosceles
right triangle has endpoints (1, 1) and (6, 1). The other
leg passes through the point (6, 2). Draw the triangle
5 on the coordinate plane below. Then show how you
can use the Distance Formula to find the length of the
hypotenuse. Round your answer to the nearest tenth.
Answers
The length of the hypotenuse of the isosceles triangle is 7.1 units.
We can use the distance formula to find the length of ST (base) and TU(perpendicular). Further, using these lengths, we can find the hypotenuse of the isosceles triangle.
The distance formula is given as follows,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Here, d is the distance between the two points (x₁, y₁) and (x₂, y₂)
As shown in the drawn isosceles triangle STU,
The length of the base ST is given as,
ST = √(x₂ - x₁)² + (y₂ - y₁)²
Here,
x₁ = 1 and y₁ = 1
x₂ = 6 and y₂ = 1
∴ ST = √(6-1)² + (1-1)²
ST = √5²
ST = 5 units
Similarly, for TU as the other leg passes through the point(6,2) and is of length 5 units ( STU being isosceles triangle), we have,
x₁ = 6 and y₁ = 1
x₂ = 6 and y₂ = 6
Also, TU = 5 units
Now, using Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
(SU)² = (ST)² + (TU)²
(SU)² = (5)² + (5)²
(SU)² = 50
SU = √50
SU = 7.071 units
SU ≈ 7.1 units (after rounding of to the nearest tenth)
hence, the hypotenuse of the isosceles triangle is of 7.1 units.
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(3.2x10 to the power of 5)(5.7x10 to the power of -2)
Answers
Answer:
1.320000
2. 0.057
Step-by-step explanation:
im stuck on this one
Answers
The value of X is 2/3 and -3/2.
According to the statement
we have given equation is 6x^2+5x-6 =0
and we have to find x by the factorization.
Factorization defines the the operation of resolving a quantity into factors.
So, by factorization method the equation is written as
6x^2+5x-6 =0
After forming factors the equation becomes
6x^2+9x-4x-6 =0
3x(2x+3) -2(2x+3) =0
By taking common
(3x-2) (2x+3) = 0
Now equate values equal to 0. and after that the output will get in the form of value of X.
Here the value of x is 2/3 and -3/2
So, the value of X is 2/3 and -3/2.
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During a very cold winter, water pipes sometimes burst because:
Answers
The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.
Bursting of Water Pipes During a Very Cold Winter
The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.
As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.
The pressure that the ice builds up inside the pipes could rupture the pipe walls.
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Determine the period.
Answers
Answer:
[tex]5 \cos( \frac{2\pi x}{7} ) [/tex]
The period of the given graph is 2π.
A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods. In other terms, a periodic function is one whose values recur after a specific interval.
This specific time span indicated above is the function's period.
The length of one function wave is referred to as the period.
The sine and cosine functions have a period of 2π radians, or 360 degrees. The period of the tangent function is π radians, or 180 degrees.
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Identify an equation in point slope form for the line parallel to y=-2/3×+8 that paases through (4,-5)
Answers
Answer:
y=-2/3x-7/3
Step-by-step explanation:
a parallel line has the same slope but different y intercept
so we need to solve for y=-2/3x+b
since it passes through 4,-5 we can plug it in for x and y
-5=-2/3(4)+b
-5=(-8/3)+b then add 8/3 to both sides
-5 is also -15/3
-7/3=b
so answer is y=-2/3x-7/3