Answer:
Step-by-step explanation:
he whole assignment seems to deal only with one simple concept, a direct variation
Sometimes text or your notes have definitions that are difficult to understand.
Here is the definition that is easy to understand:
A direct variation gives you an equation that contains no constants, and there are no exponents on the two variables.
e.g. y = 8x is a direct variation,
but y = 8x + 4 is NOT, since I see a constant of 4
a direct variation can be written in the form
y = kx , where k is the constant of variation
#1, not a variation, I see a +1 sitting there as a constant
#2, yes it is a direct variation:
-12x = 6y
6y = -12x
y = -2x
so the constant of variation is -2 , if y varies directly with x
or
-12x = 6y
x = -(1/2)x
now the constant of variation is -1/2 , if x varies directly as y
so it depends how you express the equation, either in terms of x or in terms of y
#3,
.7x - 1.4y = 0
.7x = 1.4y
1.4y = .7x
y = (.7/1.4)x = (1/2)x
so , yes it is, and the constant of variation is 1/2
From #4 on, you have to first find the equation.
I will do #4, you try the remaining.
#4, they tell us it is a direct variation, so it must look like
y = kx
They give us x=2 when y = -10
let's plug in those values:
-10 = k(2)
2k = -10
k = -5
aaahhhh, so y = -5x is our equation
#6, same way, just some fractions to deal with
#7, to graph, pick any x, and find the y to get ordered pairs,
e.g. let x = 3, then y = (1/3)(3) = 1, --> point(3,1)
let x = 9, then y = (1/3)(9) = 3 ---> point (9,3)
plot those two points, and join with a straight line
Notice how I picked multiple of 3's for my x's so I could take 1/3 of the x without ending up with fractions?
#8 , same as #7, pick multiples of 2 for your x's
#9 and #10 are the same type
#9
assume it is a direct variation, then its equation must be
y = kx
use the first given data: x = 3, y = 5.4
then 5.4 = k(3)
3k = 4.5
k = 1.5
equation is y = 1.5x
do the other points satisfy our equation?
for (7, 12.6)
is 12.6 = 1.5(7) ?
12.6 = 10.5 ??? NO, so the given data is NOT a direct variation
#10 same way
Answer:1. 2y=5x+1 answer is A Not a direct variation
2. -12x=6y answer is D Direct variation, constant of variation is -2
3. 0.7x-1.4y=0 answer is B Direct variation, constant is 1/2
4. y=-10 when x=2 answer is A y=-5x
5. y=7 1/2 when x=3 answer is C y=5/2 x
6. y=10.4 when x=4 answer is D y=2.6x
7. y=1/3 x answer is A the graph that reads (6, 2) where the green arrow is on the top right portion and on the bottom left is (-6, -2)
8 y=-1/2 x answer is C graph
9. the table x is first 3, 7, 12 y is next 5.4, 12.6, 21.6 answer is B Direct variation, y=1.8x
10. the table x is first -2, 3, 8 y is next 1, 6, 11 answer is A not a direct variation
p.s. this is for the direct variation practice
hope i helped
Step-by-step explanation:
what is 2/9+1/3= i need it for for my homework
Answer:
5/9
Step-by-step explanation:
Answer:
5/9
Step-by-step explanation:
Now we need to make our denominators match.
9 goes into 3 evenly, so we only need to multiply one term to get a common denominator.
Multiply 1 by 3, and get 3, then we multiply 3 by 3 and get 9.
Since our denominators match, we can add the numerators.
2 + 3 = 5
That gives us the sum, which is
5/9
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! Here's the final answer to 2/9 + 1/3
find the value of x to the nearest tenth
Answer:
20.8
Step-by-step explanation:
Using Pythagorean theorem, you can find 1/2 of x.
12²= 6² +1/2x²
From this we find 1/2 x is ≈ 10.4
Then x itself would be 2 times that, resulting in 20.8, that is your answer
A 12 pound turkey takes about 180 minutes to cook. How many hours would it take to cook a 20 pound turkey?
These are ratios, which are technically equal to each other. So, you can set up the problem like this:
12/180=20/x
180*20=3600
3600/12=300
So, it would take 300 minutes.
The required time consumed to cook 20 pounds of turkey is 300 minutes.
Given that,
A 12-pound turkey takes about 180 minutes to cook.
To determine how many hours would it take to cook a 20-pound turkey.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
A 12-pound turkey takes about 180 minutes to cook.
rate of cooking = 180 / 12 = 15 minute per pound of turkey
Time consumed to cook 20 pounds of turkey = 20 * 15 = 300 minutes
Thus, the required time consumed to cook 20 pounds of turkey is 300 minutes.
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in a group of 84 kids 3/7 brought their lunches of those who bought their lunches 9 got a slice of pizza. what fraction of the students who bought their lunches got a slice of pizza?
Answer:
3/16
Step-by-step explanation:
4/7 of 84 = 48 kids
9/48 = 3/16
Answer:
9/36=1/4
Step-by-step explanation:
3/7x84=36
Ans: 9/36=1/4
What is 4 divided by 3/5
4 divided by 3/5
pretend that 4 has a denominator which is 1
4/1 divided by 3/5
when dividing always flip over the second fraction
4/1*5/3
multiply the numerators together
4*5=20
multiply the denominators together
1*3=3
answer:
20/3 or 6 2/3
The ratio of pears to green apples is 1:3 how many pears are there
Answer:
There is 1 pear for every green apple! So in this ratio there would be 1 pear!
Step-by-step explanation:
-viridiancat4, an 8th grader! :)
-2.2-(-4x-2)=-(-x-3.1)
Answer: x=1.1
Step-by-step explanation:
-2.2 - (-4x - 2) = - (-x - 3.1)
-2.2 + 4x + 2 = x + 3.1
-0.2 + 4x = x + 3.1
+0.2 + 0.2
4x = x + 3.3
-x -x
3x = 3.3
/3 /3
x = 1.1
hope this helps!
Barry's house has 4 windows that he is planning to replace to improve energy efficiency. The width of each window is between 3.3 and 3.7 ft, and the length of each window is between 3.7 and 4.1 ft. Barry estimates the area of all 4 windows to be 62 sq ft. Is this a reasonable estimate?
A.
No, the estimate should be lower.
B.
No, the estimate should be higher.
C.
Yes, the estimate given is reasonable.
Answer:
B)No, the estimate should be higher
Answer:
no the estimate should be lower
Differentiate from first principle
1. y= x^2 + 3x
2. y= x^2 + 3x + 8
Answer:
Differentiation of both the term is [tex]2x+3[/tex]
Step-by-step explanation:
As we have to use first principle of derivatives lets recall the formula.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
Solving our eqaution.
[tex]y=x^2+3x[/tex]
We will work with [tex]f(x+h)[/tex] then [tex]-f(x)[/tex] separately then put in the above formula.
1.
[tex]f(x+h)=(x+h)^2+3(x+h)[/tex]
[tex](x^2+h^2+2hx+3x+3h)[/tex]
Now [tex]-f(x)[/tex]
[tex]-f(x)=-x^2-3x[/tex]
Plugging the values of both.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x)- x^2-3x}{h}=\frac{h^2+2hx+3h}{h}[/tex]
Taking [tex]h[/tex] as common.
[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]
Putting [tex]h=0[/tex]
Then
[tex]f(x)=2x+3[/tex] is the final derivative.
This will be same for [tex]y= x^2 + 3x + 8[/tex] as we have to put [tex]8[/tex] only.
2.
[tex]f(x+h)=(x+h)^2+3(x+h)+8[/tex]
[tex](x^2+h^2+2hx+3x+3h)[/tex]
Then [tex]-f(x)=-x^2-3x-8[/tex]
Plugging the values of both.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x+8)- x^2-3x-8}{h}=\frac{h^2+2hx+3h}{h}[/tex]
Taking [tex]h[/tex] as common.
[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]
Putting [tex]h=0[/tex]
Then
[tex]f(x)=2x+3[/tex] is the final derivative.
So both the derivatives are same.
Six friends went out to dinner. Each person ordered the same meal, which was $15.85. The friends left a combine tip of $14. What was the total of the bill and the tip?
Answer:
$77.40
Step-by-step explanation:
Which of the following statement are false?
A) 5/9 can be shown as equivalent to an improper fraction.
B) 8/2 can be simplified as a whole number.
C) 1 1/3 can be shown as equivalent to an improper fraction.
D) 6/7 can be shown as equivalent to a proper fraction.
Answer:
A
Step-by-step explanation:
Because 5/9 is an example of a proper fraction. In order to be an improper fraction, the numerator needs to be larger than the denominator. 8/2 can be simplified as 4 and 4 is a whole number. 11/3=3 2/3 is an example of improper fraction. 6/7, again, this is another example of a proper fraction.
It takes b minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 3 same-size bathtubs?
Write your answer as an expression.
Answer:
3b
Step-by-step explanation:
Since it takes b minutes to fill one bathtub, then it will take 3 times b minutes to fill all three bathtubs.
Answer:
3 times b
Step-by-step explanation:
The sum of two numbers is 89. Three times the smaller
number is 71 more than the larger. Find the numbers.
Answer:
The numbers are 40 and 49
Step-by-step explanation:
Smaller number = x
Larger number = y
Let's write our system of equations:
x + y = 89
3x = y + 71
***************************
x = 89 - y
Substituting x in the 2nd equation and solving for y:
3 (89 - y) = y + 71
267 - 3y = y + 71
-3y - y = 71 - 267 (Like terms)
-4y = - 196
y = -196/-4
y = 49
Solving for x in the 1st equation:
x + y = 89
x + 49 = 89
x = 89 - 49
x = 40
The numbers are 40 and 49
please help me with these, oh sweet jesus
Answer:
77. [tex]\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x[/tex]Proved
78. [tex]\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex] Proved
79. [tex]\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x[/tex] Proved.
80. [tex]\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x[/tex] Proved.
Step-by-step explanation:
77. Left hand side
= [tex]\cot^{6} x[/tex]
= [tex]\cot^{4} x \times \cot^{2} x[/tex]
= [tex]\cot^{4}x [\csc^{2}x - 1][/tex]
{Since we know, [tex]\csc^{2} x - \cot^{2}x = 1[/tex]}
= [tex]\cot^{4} x \csc^{2}x - \cot^{4} x[/tex]
= Right hand side (Proved)
78. Left hand side
= [tex]\sec^{4}x \tan^{2} x[/tex]
= [tex]\sec^{2} x [1 + \tan^{2}x] \tan^{2} x[/tex]
{Since [tex]\sec^{2}x - \tan^{2}x = 1[/tex]}
= [tex]\sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex]
= Right hand side (Proved)
79. Left hand side
= [tex]\cos^{3} x\sin^{2} x[/tex]
= [tex]\cos x[1 - \sin^{2} x] \sin^{2} x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex][\sin^{2}x - \sin^{4}x] \cos x[/tex]
= Right hand side
80. Left hand side
= [tex]\sin^{4}x - \cos^{4}x[/tex]
= [tex][\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex]1 - 2\cos^{2} x[1 - \cos^{2}x ][/tex]
= [tex]1 - 2\cos^{2}x + 2 \cos^{4} x[/tex]
= Right hand side. (Proved)
A golf ball, thrown upwards, rises at a speed of v metres per second.
The ball reaches a maximum height of h metres.
h is proportional to the square of v.
When v = 20, h = 8
Work out the maximum height reached by the golf ball when v = 35
Answer:24.5
Step-by-step explanation:
Formula:
H=KV²
8=K×20²(400)
=8/400
=0.02
H=0.02×35²
=24.5
Answer:
The maximum height reached by the golf ball when v = 35 is 24.5 meters.
Step-by-step explanation:
Given : A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres. h is proportional to the square of v. When v = 20, h = 8.
To find : Work out the maximum height reached by the golf ball when v = 35 ?
Solution :
h is proportional to the square of v i.e. [tex]h\propto v^2[/tex]
[tex]h=kv^2[/tex]
Where, k is the constant of proportionality
When v = 20, h = 8,
[tex]8=k(20)^2[/tex]
[tex]8=400k[/tex]
[tex]k=\frac{8}{400}[/tex]
[tex]k=0.02[/tex]
The equation became [tex]h=0.02v^2[/tex].
Now, when v = 35 the value of h is
[tex]h=0.02(35)^2[/tex]
[tex]h=0.02\times 1225[/tex]
[tex]h=24.5[/tex]
Therefore, the maximum height reached by the golf ball when v = 35 is 24.5 meters.
Four more than twice a number is less than negative twelve. Find all numbers that make this statement true.
Answer:
x<-8
Step-by-step explanation:
four more than twice a number = 4+2X
is less than negative twelve = <-12
4+2X<-12
(4-4)+2X< -12-4
2x<-16
X<-8
To find the numbers that make the statement true, we need to solve the equation 2x + 4 < -12 for x. Any number less than -8 will make the statement true.
Explanation:To find the numbers that make the statement true, we need to translate the given sentence into a mathematical equation. Let's denote the unknown number as 'x'. The sentence 'Four more than twice a number is less than negative twelve' can be written as 2x + 4 < -12. Now, we can solve this equation for x:
Subtracting 4 from both sides, we get 2x < -16.
Dividing both sides by 2, we have x < -8.
Therefore, any number less than -8 will make the statement true.
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Which of the following digits might composite numbers greater than 10 have in the ones place? Select all that apply.
1
2
3
4
The digits which a composite number greater than 10 might have include; 1, 2 ,3 and 4.
According to the question;
We are required to determine which of the digits a composite number greater than 10 might have in the ones place.The number 10 has two place values namely;
1 is in the tens place0 is in the ones place.In essence, any composite number greater than 10 can have either of 1, 2, 3 and 4 in the ones place.
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Which of the following pairs are alternate interior angles?
A.6 and 7
B.2 and 7
C.5 and 2
D.5 and 4
Which action describes an aspect of technological design?
O building a telescope to look deeper into space
O creating a collection of mosquitoes that cause disease
o observing Doppler radar as a storm approaches
O designing an experiment to measure the heat of a volcano
Answer: A)
Step-by-step explanation: This is correct because a telescope is a piece of technology use to look further into space
A bag contains 10 red, 9 white, 8 yellow and 2 blue marbles. How many marbles must be taken out from the bag so that there will be 4 marbles of the same colour?
Answer:25
Step-by-step explanation:
10 plus 9+4+2 will give you 21 and it will have 4 yellow ones left
A class is going on a trip to a museum. It costs $750 to rent a bus. Each ticket to the museum costs $12 Write an algebraic expression that represents the cost of the trip for people. Then evaluate this expression for 37
people
The total cost of trip for 37 people will be $1194.
Step-by-step explanation:
Given,
Rent of bus = $750
Cost of one ticket = $12
Let,
x be the number of people.
T be the total cost of the trip for people.
According to given statement;
Total cost = Rent of bus + (Cost of one ticket * number of people)
[tex]T=750+12x[/tex]
For 37 people, x=37
[tex]T=750+12(37)\\T=750+444\\T=\$1194[/tex]
The total cost of trip for 37 people will be $1194.
Keywords: linear expression, addition
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a.3/8
b.1/2
c.5/8
d.7/8
Answer:
3/8
Step-by-step explanation:
You'd first want to count all the triangles (possibilities) which is 8 total numbers
Then find the even numbers. There is 2, 2, and 4 which is a total of 3 even numbers
The fraction would be 3/8 and it can't be simplified any further
Answer:
3/8
Step-by-step explanation:
This is because, out of 8 results, only 3 of them are even numbers. That is the biggest chance you have at getting an even number.
A portion of a daycare has been set aside for toddlers under 2. The dimensions are shown. A scale drawing of the room is 1.5 cm tall. How wide is the scale drawing?
Answer:
2.4 cm.
Step-by-step explanation:
See the given diagram of two similar triangles one with actual dimensions and the other drawn on paper with a certain scale.
The ratio of corresponding sides of two similar triangles is always the same.
Now, 1.5 cm on the drawing is equivalent to 2.5 m i.e. 250 cm. in actual dimension.
So, 4 m i.e. 400 cm in actual dimension will be equivalent to [tex]\frac{1.5}{250} \times 400 = 2.4[/tex] cm. in the drawing. (Answer)
Ashots height changed from 150 cm to 165 cm during the last year. By what percent did Ashot become taller?
150 cm ......... 100 %
165 cm ...............x %
x = 165×100/150 = 16500/150 = 110 %
Answer:
10%
Step-by-step explanation:
Subtract 150 from 165, which gives 15.
Then, do 15/150 = 0.1
Convert decimal to percent by moving the decimal point two spaces back. 0.1 becomes 10%.
EFGH is a parallelogram. Find the measure of FG.
Answer:
FG = 47
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent, thus
EH = FG, that is
5z - 18 = 3z + 8 ( subtract 3z from both sides )
2z - 18 = 8 ( add 18 to both sides )
2z = 26 ( divide both sides by 2 )
z = 13
Hence
FG = 3z + 8 = (3 × 13) + 8 = 39 + 8 = 47
Based on the property of a parallelogram, the measure of FG is: 47.
Opposite Sides of a ParallelogramBased on the properties of a parallelogram, the opposite sides of a parallelogram are equal in length.
Therefore:
EH = FG
Substitute5z - 18 = 3z + 8
Combine like terms5z - 3z = 18 + 8
2z = 26
Divide both sides by 2z = 13
FG = 3z + 8
Plug in the value of zFG = 3(13) + 8
FG = 47
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Which of the following are true of linear functions? Select all that apply.
There is exactly one output for each input.
The graph of a linear function is a straight line.
Alinear function can cross the y-axis in two places
Alinear function has a constant rate of change.
Alinear function must cross the x-axis
Answer:
There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function has a constant rate of change.
Step-by-step explanation:
Answer:
A,B,D
Step-by-step explanation:
i took the assignment and quiz on ed2020
Point D (-1,5) is reflected across the x-axis which statements about D are true
Answer:
When a point is reflected across the x axis, it has the same x axis but the y axis is multiplied by -1. Think about the x axis as a mirror and the point is projected across the x axis.
Hence the x coordinate is -1 and the y coordinate is -5.
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
the x coordinate is -1
Jackson has let out 50 meter of kite string when he observes that his kite is directly above a point on the ground 30 meters away from him, how high is the kite?
The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.
(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)
Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]
(positive root since length is a non-negative quantity).
We have |AC| = length of the kite's string = 50 meters
|AB| = distance of the observer from the point directly above which the kite is flying = 30 meters
Thus, we get the height of the kite from the ground as:
[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]
Thus, the height of the kite from the ground is 40 meters approximately.
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the sum of 2fifteens and 10 fifteens
Answer:4/5
Step-by-step explanation:
2/15 + 10/15=12/15=4/5
easy right?
The graph of a function, f(x), is plotted on the coordinate plane. Select the function that would move the graph of the function to the right of the coordinate plane.
a.f(x+6)
b.f(x)+4
c.f(x-3)+1
d.f(x)-3
Correct option:
c.f(x-3)+1
Explanation:From the options we have either vertical or horizontal shift. So, for this type of transformation we have:
For any real positive number [tex]c[/tex], vertical and horizontal shift in the graph [tex]y=f(x)[/tex] are expressed as follows:
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
From these rules, we know that:
[tex]f(x-3)+1[/tex]
would move the graph of the function to the right of the coordinate plane because of [tex]f(x-3)[/tex]. In other words, the transformation is as follows:
[tex]f(x-3)+1[/tex] shifts the graph of [tex]f(x)[/tex] three units to the right and one unit up
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