Using linear functions, it is found that:
1. The functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.2. They will have the same elevation after 18.4 minutes.
3. At that time, the elevation is of 18,150 feet.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The initial heights are the intercepts.The rates are the slopes, climbing positive and descending negative.Hence the functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.They will have the same elevation when:
E1(t) = E2(t)
28270 - 550t = 5270 + 700t
1250t = 23000
t = 23000/1250
t = 18.4.
They will have the same elevation after 18.4 minutes.
This elevation will be of:
28270 - 550(18.4) = 18150.
At that time, the elevation is of 18,150 feet.
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Can you think of any other shapes that are always similar? If you can explain why they are always similar.
Answer:
Step-by-step explanation:
All you need is angles that are the same in each shape.
For example, all squares are similar. They all have 4 ninety degree angles.
All polygons with equal angles are similar. All regular hexagons have interior angles of 120 degrees. So all regular hexagons are similar.
All regular octagons are similar. All regular octagons (8 sides) have interior angles of 135 degrees.
To get more, just look up the names of all regular polygons from 3 to 10. I've given you three of them.
. Write down the first five terms of the AP with first term 7 and common difference 7.
The arithmetic sequence is 7,14,21,28,35,48
In an arithmetic progression (AP) sequence of numbers, the difference between any two consecutive integers is always the same. It is also known as an arithmetic sequence.
There are two definitions for an arithmetic sequence. Each term in an arithmetic sequence is created by adding a predetermined number (positive, negative, or zero) to its preceding term. It is a "series where the differences between every two following terms are the same."
Given,
first term, a = 7
common difference d = 7
n = 2
a+(n-1)d = 7+( 2 - 1 )7
= 7 + 7
= 14
n = 3
a+(n-1)d = 7+(3-1) 7
= 7+14
= 21
n = 4
a+(n-1)d = 7+(4-1) 7
= 7+ (3)7
= 28
n = 5
a+(n-1)d = 7+( 5-1 ) 7
= 7+ (4)7
= 35
n = 6
a+(n-1)d = 7+( 6-1 ) 7
= 7+ (5)7
= 42
the five terms are 7,14,21,28,35,48.
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4x-3y=3
- 8x+6y=-6
solve for x and y
The system of equation 4x - 3y = 3and -8x + 6y = -6 has no solution as they are parallel lines.
What is system of equation?When two or more linear equations are there we call them a system of equations.
Given a system of equations 4x - 3y = 3...(i) and -8x + 6y = -6...(ii) this is solvable as the number of variables is not more than the number of equations.
Now to solve for x or y first we have to eliminate one of the varibales by any arithmetic operation.
By observing we conclude that if we multiply equation(i) by 2 and then add both of them the x variable will cancel out and we can solve for y which is
8x - 6y = 6
(+) -8x + 6y = -6
----------------------
As we can see here that both x and y are getting canceled therefore these two equations have no solution and hence they are parallel to each other(lines).
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Can someone please help with my question?
The required line representing the rise and the run of the line is created.
And the slope of the line in its simplest form is 9/-18.
Given a line is represented on the graph.
we need to create lines representing the rise and run of the line.
To find the slope of the line we need to determine the rise and run of the line.
The slope of a line is defined as the rise divided by the run, or the ratio of the rise to the run. It gives information about a line's slope in the coordinate plane. Finding the slope between two separate places is comparable to calculating the slope of a line.
The coordinates of the points are:
(9,0) = (x₁ , y₁)
(₋9 , 9) = (x₂ , y₂)
we know that slope (m) = rise/ run
rise = y₂ ₋ y₁
= 9 ₋ 0
= 9
run = x₂ ₋ x₁
= ₋9 ₋ 9
= ₋18
hence the slope is 9/₋18
The required slope of the line is 9/-18.
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What are the alternate exterior angle pairs in the picture below?
A. ∠1 and ∠7, ∠2 and ∠8
B. ∠1 and ∠8, ∠2 and ∠7
C. ∠1 and ∠2, ∠7 and ∠8
D. ∠1 and ∠3, ∠5 and ∠7
A. 1 and 7 and
2 and 8 alternate exteriora
Answer:
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
Alternate exterior angles are on the exterior of the lines and on opposite sides of the transversal.
A statue is 6 feet tall and weighs about 145 pounds. A second model statue is 4 feet tall.
Assume that the two statues have similar shape.
a) What is the linear scale factor for going from first to second statue?
b) How much does the second statue weigh?
The linear scale factor for going from first to second statue will be 2/3 and the weight of the second statue will be 96 2/3 pounds.
How to illustrate the information?It should be noted that the statue is 6 feet tall and weighs about 145 pounds and second model statue is 4 feet tall.
Therefore, the linear scale factor for going from first to second statue will be:
= 4/6
= 2/3
Therefore, the weight of the second statue will be:
= 2/3 × 145
= 96 2/3 pounds.
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To prepare one bowl of salad, 3 3/4 pounds of vegetables are required. How many pounds of vegetables are required to prepare one-third bowl of salad?
Applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.
How to Solve Fractions?In solving this problem, we would apply our knowledge of fractions as explained below.
One bowl of salad needs 3¾ pounds of vegetables
Let the number of pounds if vegetables needed for ⅓ bowl be represented as x. Therefore, we would have the following proportion:
1 bowl = 15/4 pounds of vegetables [i.e. 3¾]
⅓ bowl = x
Thus:
1/15/4 = ⅓/x
1/1 × 4/15 = 1/3 × 1/x
4/15 = 1/3x
Cross multiply
4(3x) = 1(15)
12x = 15
Divide both sides by 12
12x/12 = 15/12
x = 15/12
x = 5/4
x = 1¼ pounds
Therefore, applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.
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subtracting linear expressions 30 points
Answer:
1) -2a + 2
2) x + 1
3) -5x + 5
Step-by-step explanation(1):
[tex]\left(7a+4\right)-\left(9a+2\right)\\=7a+4-\left(9a+2\right)\\=7a+4-9a-2\\=7a-9a+4-2\\=-2a+4-2\\=-2a+2[/tex]
Step-by-step explanation(2):
[tex]\left(2x+5\right)-\left(x+4\right)\\=2x+5-\left(x+4\right)\\=2x+5-x-4\\=2x-x+5-4\\=x+5-4\\=x+1[/tex]
Step-by-step explanation(3):
[tex]\left(2x+4\right)-\left(7x-1\right)\\=2x+4-\left(7x-1\right)\\=2x+4-7x+1\\=2x-7x+4+1\\=-5x+4+1\\=-5x+5[/tex]
Hope this helps. Notify me of any concerns.
The following angles are supplementary to each other.
mzA= (3x + 21)° and mzB = (6x - 21)°
Determine x.
A10
B20
C36
D60
Answer: 20
Step-by-step explanation: I can help with am explanation if you dm me:)
Out of 340 racers who started the marathon, 311 completed the race, 25 gave up, and 4 were disqualified. What percentage did not complete the marathon?
Determine whether the following procedure results in a binomial distribution or a distribution that
can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not
binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
In a Pew Research Center survey of 150 subjects, the ages of the respondents are
recorded.
From the given parameters in the survey; It is not binomial because the probability of success does not remain the same in all trials.
How to identify a binomial distribution problem?
The conditions for a distribution to be called binomial distribution are as follows;
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes (either a success or failure).
4. The probability of success (p) is the same for each outcome.
Now, from the given question, we can see that the number of observations is fixed and that each observation is independent. However, we don't know the probability of success for each person and as such we can't call this a binomial distribution.
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Mario was asked by his teacher to express 33% in ratio, fraction, and decimal. Which of the following table do you think is an equivalent value of 33% expressed in a ratio, fraction, and decimal? Compute and solve a problem of Mario
The equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively
Ratio, Fraction and decimal33%
In ratio:
33%
= 33 / 100
= 33 : 100
In fraction:
33%
= 33/100
In decimal:
33%
= 33/100
= 0.33
Therefore, the equivalent value of 33% expressed in a ratio, fraction, and decimal is 33 : 100, 33/100 and 0.33 respectively
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A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 100 of a 2% solution and wishes to add some 10% solution to obtain 8% how much 10% solution should she add
Answer:
300 units
Step-by-step explanation:
Given g(a) = 5x - 3, find g(-2)
Answer:
-13
Step-by-step explanation:
Plug in -2 to x:
5(-2) - 3
Multiply 5x-2:
-10 - 3
Because two negatives make a positive, add -10 and -3:
-13
replace the ? with a number to make it correct 9-5=6-?
Is 4x-6=y linear or nonlinear
What are the steps in order to solve this?
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
What is the inverse of a function?The inverse of a function is a function that can reverse into another function.
If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x
Also, if f is a function f⁻¹ is the inverse of x and ff⁻¹(x) = f⁻¹f(x) = x
How to show that the composite fucntions are inverses?Given the functions m(x) = x³ - 5 and n(x) = ∛(x + 5)
If m(x) and n(x) are inverse, then m(n(x)) = n(m(x)) = x
So, we proceed as follows
m(x) = x³ - 5
m(n(x)) = (∛(x + 5))³ - 5
m(n(x)) = x + 5 - 5
m(n(x)) = x + 0
m(n(x)) = x
Also,
n(x) = ∛(x + 5)
n(m(x)) = ∛(x³ - 5 + 5)
n(m(x)) = ∛(x³ - 0)
n(m(x)) = ∛(x³)
n(m(x)) = x
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
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parallel to 3y – 2x = – 2, passes through (3, –3)
y = 2/3x -6
Conditions for Lines to be parallel
If two straight lines are cut by a transversal, the pair of alternate angles are equal, then two straight lines are parallel to each other. the pair of interior angles on the same side of traversals is supplementary, then the two straight lines are parallel.
Given line
3y – 2x = – 2
passes through (3, –3)
The slope-intercept form is
y =mx+b,
where m is the slope and
b is the y-intercept.
y = mx+b
Divide each term in
3y – 2x = – 2 by -2 and simplify.
-3/2y +x =1
Reorder terms.
y = -(2/3)(x+1)
Using the slope-intercept form, the slope is
2/3.m=2/3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope
2/3 and a given point (3, –3)
to substitute for
x1 and y1
in the point-slope form
y−y1=m(x−x1)
which is derived from the slope equation
m=(y2−y1)x2−x1.
y−(-3)=2/3⋅(x−(3))
Simplify the equation and keep it in point-slope form.
y+4=2/3⋅(x-3)
y = 2/3x -6
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What is the solution set for the following equations:
y = 5x -7 and y = 2x + 5
(3,12)
(4, 13)
(-7,5)
(2,5)
please help!
Answer:
(4,13)
Step-by-step explanation:
Set the 2 equations equal to each other and solve for x.
5x - 7 = 2x + 5 Subtract 2x from both sides
3x - 7 = 5 Add 7 to both sides
3x = 12 Divide both sides by 3
x = 4
Now plug 4 back into either of the original 2 equations to find y.
y = 5x -7
y= 5(4) -7
y = 20 -7
y= 13
40 POINTS!
Simplify 3x * 1/x^-4 * x^-3
3x
3x2
3
3x−2
Answer:
[tex]\sf {3x}^{2} [/tex]
Step-by-step explanation:
[tex] \rightarrow \sf 3x(\frac{1}{{x}^{-4}}) {x}^{-3} [/tex]
[tex] \rightarrow \sf \frac{ {3x}^{5} }{ {x}^{3} } [/tex]
[tex] \rightarrow \sf {3x}^{2} [/tex]
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3,\, 12,\, 48,\, ...
3,12,48,...
This is
sequence and the
is equal to
.
The given sequence is an arithmetic sequence and the common difference is 4.
Given, the sequence is :
3,12,48
we need to determine the common difference.
common ratio = a₂/a₁
a₂/a₁ = 12/3
a₂/a₁ = 4
a₃/a₂ = 48/12
a₃/a₂ = 4
hence the common difference is 4.
Therefore, the common difference indicates arithmetic sequence.
There are two approaches to define an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term."
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If y varies directly with x and y=36 when x=6, find the value of y when x=4.
6
12
24
-18
If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
What is direct variation?
The mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. It is a linear function defined by an equation of the form
y = kx when x is not equal to zero.
Given:
If y varies directly with x and y=36 when x=6
According to given question we have
we can write direct variation equation as
y= k*x
where k is constant
y = 36 when x=6,
36 =k(6)
k=6
So, by putting the value of x=4 we get,
y =kx
y=6*4
y=24
Therefore, If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
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Evaluate 4(b + 1)² if b = 4.
Answer:
68
Step-by-step explanation:
4(4 + 1)²
4(16 + 1)
64 + 4
68
Kaleigh's aunt drives for Wheels Around Town, an app-based ride sharing service, to make extra money for her family. The table below shows the relationship between miles driven and money earned. Is the relationship between miles and money earned proportional
Based on the money earned by Kaleigh's aunt from Wheels Around Town, the relationship between miles and money earned is proportional.
How to find a proportional relationship?In a proportional relationship, the rate of increase or decrease in x should be equivalent to the rate of increase or decrease in y. This rate should be constant through the entire distribution.
The equation of the line should take the form:
y = mx
There should be no y-intercept.
The slope is:
= (48 - 72) / (120 - 180)
= -24 / - 60
= 2/5
Every value of y has to be 2/5 of x.
= 160 x 2/5 = 64
= 200 x 2/5 = 80
The relationship is therefore proportional.
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Analyze the diagram below and answer the question that follows.
Which statement describes the shaded region in the Venn diagram?
The statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S
How to determine which statement describes the shaded region in the Venn diagram?The Venn diagram represents the given figure
On the Venn diagram, we can see that:
All region that contains set P and Q are not shaded
This means that
(P u Q)'
The only region that is shaded in the diagram is the region of set S
This is then represented as
(P u Q)' n S
Hence, the statement that describes the shaded region in the Venn diagram is (a) (P u Q)' n S
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What are the square roots of 8,100?
A+B=C make B the subject
Answer:
C - A = B
Step-by-step explanation:
B is now what we are solving for.
Answer:
Flip the equation so B is the sum and also the subject.
Step-by-step explanation:
[tex]A - C = B[/tex]
chapter 8
2.Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
The volume of the given figure is 267.95 mi³.
What is the volume?The given object is a sphere. A sphere is a three-dimensional object that has all its surface points at equal distances from the center. A sphere is round in shape.
The volume of an object is the amount of space in the three-dimensional object. The radius of a sphere is a straight line from the circumference of the sphere to the center of the sphere.
Volume of a sphere = 4/3 × π × r³
Where:
π = pi = 22/7
r = radius = 4
4/3 x 22/7 x 4³ = 267.94667 mi³
267.95 mi³
To round off to the nearest hundredth, if the thousandth digit is equal to 5 or greater than 5, add 1 to the hundredth digit and change all the digits after the hundredth digit to 0.
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Zeke made $10,200 last year working at a fast food restaurant. How much did Zeke make per month?
Evaluate 3x2+8x+8 when x=3.
Answer:
Step-by-step explanation: since X=3 replace X
3 (3)2 +8 (3)+8
18+24+8 =50