Given the equation 6y = 2x, y varies directly with x and the constant of variation k has a value of 1/3.
There are two kinds of variations: direct and inverse.
Direct variation is a linear function defined by an equation of the form y = kx where variable y varies directly as x. On the other hand, inverse variation is a nonlinear function defined by an equation in the form y = k/x where variable y varies inversely as x.
Transforming 6y = 2x into a function of y,
y = 2/6 x
y = 1/3 x
where k = 1/3
Notice that it resembles the form y = kx which describes a direct variation between x and y.
Hence, the equation 6y = 2x shows that y varies directly with x and k = 1/3.
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Find the greatest common factor of 24, 40 and 60.
Answer:
GCF of numbers 24, 40, 60 is 4
GCF(24, 40, 60) = 4
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A ₋trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
Given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
In this question,
We have been given a statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle'
Sometimes, trigonometric ratios used to find the measures of acute angles in a right triangle.
To find the measures of acute angles in a right triangle, you need to know the measures of the two sides of the right triangle.
We determine which ratio to use depending on which sides are given. And we also use the inverse trigonometric functions to find the angle.
Trigonometric ratios are: sine, cosine, tangent, cotangent, secant, cosecant.
These ratios are abbreviated as, sin, cos, tan, cot, sec, cosec.
Therefore, given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
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Which set of ordered pairs (x,y)(x,y) could represent a linear function?{A}= A= {(-6, 6),(-3, 2),(0, -1),,\,(3, -5} {(−6,6),(−3,2),(0,−1),(3,−5)} {B}= B={(-9, 5),(-1, 3),(, 2),(7, 1) {(−9,5),(−1,3),(3,2),(7,1)} {C}= C= {(-9, -3),(-3, 0),(2, 3),(8, 6) {(−9,−3),(−3,0),(2,3),(8,6)} {D}= D= {(-4, -5),(0, -2),(5, 1) (9, 4)} {(−4,−5),(0,−2),(5,1),(9,4)}
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
Linear functionsA set of ordered equation represents a linear function if the domain of the coordinates are not repeated.
For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending c
Rewrite 99 + (88 +77) using the Associative Law of Addition.
O (99 +88) + 77
O (88+77) +99
O (99+77) +88
O 99 + (77 +88)
Step-by-step explanation:
The answer is 99+(77+88)
find the value of z.
Answer:
z = 14.4
Step-by-step explanation:
RX is an angle bisector and divide the opposite side that are proportional to the other 2 sides , that is
[tex]\frac{SX}{XT}[/tex] = [tex]\frac{RS}{RT}[/tex] ( substitute values )
[tex]\frac{5}{6}[/tex] = [tex]\frac{12}{z}[/tex] ( cross- multiply )
5z = 72 ( divide both sides by 5 )
z = 14.4
How many solutions does the equation 12(2x+6)=6−x have?
Answer:x=0
Step-by-step explanation:
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Jose has 13 1/4 cups of raspberries. He uses 7/8 cup of raspberries to make a smoothie. Jose uses the
remaining raspberries to make pancakes. If it takes 1 3/8 cups to make one pancake, how many pancakes can he make?
the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
We are given that:
Total raspberries = 13 1/4 cups
Total raspberries = 53 / 4 cups
Now, he used 7 / 8 cups to make a smoothie.
So, Raspberries left = 53 / 4 - 7 / 8
Left = 99 / 8 cups
Now, for making 1 pancake Raspberries required = 1 3/8 sups
= 11 / 8 cups
So, the number of pancakes will be calculated by using division:
Number = 99 / 8 ÷ 11 / 8
Number = 99 / 11
Number = 9 pancakes
Therefore, we get that, the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
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Write a function rule for the direct variation in the table.
The function rule for the direct variation in the table is [tex]y = 24/x[/tex] , indirect variation ; x = 2.4.
What is direct variation?Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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What is an equation of the line that passes through the point (4,1)(4,1) and is perpendicular to the line 2x-y=42x−y=4?
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
What is the equation of a perpendicular line?The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of the line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
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What are the domain and range of this relation? (-3,14),(0,7),(2,0),(9,-18),(23,-99)
The range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
According to the given question.
We have a relation (-3,14),(0,7),(2,0),(9,-18),(23,-99).
As we know that, the set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation.
And, the set which contains all the second elements of all the ordered pairs of relation R is known as the range of the relation.
Therefore, the domain of the given relation is {-3, 0, 2, 9, 23}.
And the range of the given relation is {14, 7, 0, -18, -99}.
Hence, the range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
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Solve and graph 3|2x+2|-2x=x+3
Answer: x= -1
Step-by-step explanation:
[tex]3\left|2x+2\right|-2x=x+3\\[/tex]
Next, we find Positive and Negative Intervals!
[tex]x < -1,\:\:x\ge \:-1[/tex]
Then Last we Solve The inequality for each interval.
No Solution or x= -1
Need help please asap
Step-by-step explanation:
the circle standard form is
(x - h)² + (y - k)² = r²
(h, k) are the coordinates of the center of the circle.
r is the radius of the circle.
I cannot draw here, but I can describe the details.
9.
the center is therefore at (-1, 2). and the radius is 5.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (-1, 2 + 5) = (-1, 7)
down : (-1, 2 - 5) = (-1, -3)
left : (-1 - 5, 2) = (-6, 2)
right : (-1 + 5, 2) = (4, 2)
10.
the center is therefore at (3, 0). and the radius is 4.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (3, 0 + 4) = (3, 4)
down : (3, 0 - 4) = (3, -4)
left : (3 - 4, 0) = (-1, 0)
right : (3 + 4, 0) = (7, 0)
11.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
remember, this is via Pythagoras in a right-angled triangle
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
for the distance between 2 points the direct distance is the Hypotenuse, and the x and y coordinate differences are the legs.
distance² = r² = (7 - 2)² + (-1 - -1)² = 5² + 0² = 5² = 25
so, the equation is
(x - 2)² + (y + 1)² = 25
12.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
distance² = r² = (4 - 1)² + (6 - 2)² = 3² + 4² = 9 + 16 = 25
so, the equation is
(x - 1)² + (y - 2)² = 25
Please help!!
1.The height of a projectile is a function of the time it is in the air. The height in feet for t seconds is given by the function h(t) = -16t2 + 96t . What is the domain of the function? What does the domain mean in the context of the problem?
2.Use the graph at right to answer the following question.
Solve for f(x) = -3
Problem 1
The domain is [tex]0 \le t \le 6[/tex] which in interval notation is [0, 6]
This is the set of t values where h(t) is positive or zero. Any other t values will make h(t) to be negative. So we ignore those t values. A negative height makes no sense.
The domain in the context of the problem means that the projectile is in the air from the time markers of t = 0 and t = 6. In short, the object is in the air for 6 seconds. It takes 6 seconds for it to hit the ground.
Here's how we can determine those t values. We plug in h(t) = 0 and solve for t.
h(t) = -16t^2 + 96t
-16t^2 + 96t = 0
-16t(t - 6) = 0
-16t = 0 or t - 6 = 0
t = 0/(-16) or t = 6
t = 0 or t = 6
======================================================
Problem 2
Draw a horizontal line through -3 on the y axis.
This horizontal line touches the blue graph at the points (-2,-3) and (2,3)
This means the inputs x = -2 and x = 2 lead to the output of y = -3
Therefore f(-2) = -3 and f(2) = -3
Answer: The solutions are x = -2 and x = 2
11) Each of Jeff's family, of four, buys a new phone. The total cost is $25 above or below $1200. Write
an equation that models the cost x, in dollars, of a single phone.
The equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that total cost of phone is $25 above or below $1200.
This is a case of inequality.
Let's assume the cost of one phone is $x.
So cost of 4 phones will be given by 4x.
and this will be equal to total cost which is given as $25 above or below $1200.
So , the inequality is given by ;
1200 - 25 ≤ 4x ≤ 1200 + 25
1175 ≤ 4x ≤ 1225
If we divide by 4 through this inequality then ;
(1175/4) ≤ (4x/ 4) ≤ (1225/ 4)
or
293.75 ≤ x ≤ 306.25
The cost of one phone will lie between $293.75 and $306.25.
Therefore , the equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C=18 in.
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle is 18 inches. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
18 inches = 2 × π × (Radius of the circle)
(Radius of the circle) = 18 in/ (2 × π)
The radius of the circle = 2.8648 inches
Diameter of circle = 2 × (Radius of the circle)
= 2 × 2.8648 inches
= 5.7296 inches
Hence, the radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
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The directly proportional dependence is given by the formula y=3/8x
For the formula y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
We have the following statement -
'The directly proportional dependence is given by the formula y = 3/8x '.
We have to analyze this statement.
What is the meaning of direct proportionality between variables ?Directly proportional means as the value of one variable increases, the value of another variable increases at the same rate.
According to the question, we have -
y = 3/8x
Here - y is directly proportional to x. This means that as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
The graph of this equation is a straight line passing through origin. Therefore - Direct proportionality is represented by a straight line graphically.
Hence, for the equation y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
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Slope
1/5
y-intercept = -2
I need this in slope intercept form. Can someone help?
Answer:
y= 1/5x + (-2)
Step-by-step explanation:
21. A scuba diver dives to a depth of 50 feet,
then rises 15 feet, then rises 20 feet. Write an
addition expression to describe this situation.
Then determine the sum and explain its
meaning.
Answer:
73
Step-by-step explanation:
Based on the given conditions, formulate: 20+50+15-12
Calculate the sum or difference:70+15-12
Calculate the sum or difference:85-12
Calculate the sum or difference:73
get the result:73
Answer:
50 - 15 = 35
35 + 20 = 55
Total amount of feet diven : 55 feet
Fit for Family offers a membership fee of
$450 for the year or the option to pay $41
per
month. How much do you save each month by
choosing the annual membership fee?
We save $3.5 each month and in total $42 by giving the annual membership fees.
What are mathematics operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.
So,
The yearly pay is $450.The monthly payment is $41.Then, Monthly pay for a whole year:
$41 × 12 = $492Now,
$492 - $450 = $42Saving each month by giving the annual fees:
$42 ÷ 12 = $3.5
Therefore, we save $3.5 each month by giving the annual fees.
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Find the number of possible outcomes for following situation.
Perry chooses from 6 colors and 2 seat designs for his new mountain bike.
The number of possible outcomes is 12.
What do we mean by permutation and combination?A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a collection or group of objects in such a way that the order of the objects is irrelevant. For example, we consist of four letters: P, Q, R, and S. Every possible arrangement is a combination. However, the combinations of P, Q, R, and S are permutations.To find the possible outcomes:
Given: 6 colors and 2 seat designs.
Therefore, the number of possible outcomes is 12.
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What is the equation 2n x 2m equal to?
Answer: 2n x 2m
Step-by-step explanation:
Since the variables are different, you cannot do anything.
Given two terms of each arithmetic sequence, find a₁ and d . a₄=-34.5 and a₅=-12.5
The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 34.5, [tex]a_{5}[/tex] =12.5 are d = 47 and a = -106.5.
What is sequence?[tex]a_{4}[/tex] = 34.5
34.5 = a +3d.............1
[tex]a_{5}[/tex] =12.5
-12.5 = a + 4d...........2
equating equation 1 and 2
34.5 = a +3d
-12.5 = a + 4d
d = 47
d = 47 ..............3
from equation 3
a = -106.5
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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The length of a pool is 5 more than the width. The perimeter is 96. Whats is the are of the pool.
Answer:
569,75
Step-by-step explanation:
(4x^2y)(8x^5y^3 find product of monomials
The product of the monomials is 32x^7y4
What is a monomial?A monomial is said to be a product of powers of variables with a non-negative integer exponents, or a product of variables.
Monomials include numbers, variables or multiple numbers or variables multiplied together.
Given the monomials;
(4x²y)(8x^5y³)
Finding the product is simply done by multiplying the two expressions, we have
The product of the numbers = 4 × 8 = 32
The product of the 'x' variables = x^2 + 5 = x^7
The product of the 'y' variables = y^1 + 3 = y^4
32x^7y4
Thus, the product of the monomials is 32x^7y4
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There are 63 books on the bookshelf. There
are 9 books on each shelf. How many
shelves are there?
Answer:
there are 7 shelves. 9 x 7=63
Answer:
the answer is 7 shelves
Step-by-step explanation:
63÷9=7
2 ___ =4
- _.
3. 9????
A bookcase had nine shelves each shelf had exactly 23 books
___= Books
Answer:
207 book
Step-by-step explanation:
9 shelves x 23 books per shelve=207 books
(x+4) {2}+(y-6) {2} = 48 what is the radius
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
What is the radius of the equation of the circle?
In this question we find the equation of a circle in standard form, whose expression is described and explained below:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center of the circle.r - Radius of the circleAccording to the equation given in the statement, we find a circle with a center at (- 4, 6) and a radius of 6.928 units.
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
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-6x+6=4x-24
with work, if that's alr
Answer:
x = 3
Step-by-step explanation:
-6x+6-6=4x-24-6
-6x=4x-30
-6x-4x=4x-30-4x
-10x=-30
-10x/-10=-30/-10
I forgot how to do these, and i don’t remember whether they have two answers or not.
Solve for d.
-7| d - 1 | = -11
Answer:
=18/7
=−4/7
Step-by-step explanation:
Divide both sides by -7
−7|−1|=−11
The negatives are canceled.
Simplify
|−1|=11/7
Split the problem into two cases: one positive and one negative
=18/7
=−4/7
