we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]
In this problem we have
Points [tex](2,14)[/tex] and [tex](4,28)[/tex]
so
Find the value of k
First point
[tex]\frac{14}{2}=k[/tex]
[tex]k=7[/tex]
Second point
[tex]\frac{28}{4}=k[/tex]
[tex]k=7[/tex]
the function is
[tex]y=kx[/tex] --------> substitute the value of k
[tex]y=7x[/tex]
therefore
the answer is
[tex]y=7x[/tex]
In this problem with a single point was sufficient to calculate the equation, since in a direct variation the line passes through the origin, it is not necessary to use the formula of the slope
[ 3+ ( 18 - 4 ) / 7 ] * 8
Solve the following equation exactly on the interval 0 ≤ θ ≤ 2π ? cos 2θ + sin θ = 0
Helene is finding the sum (9 + 10i) + (–8 + 11i). She rewrites the sum as (–8 + 11)i + (9 + 10)i. Which statement explains the property of addition that she made an error in using?
Answer:
answer is d
Step-by-step explanation:
Write the expressions without using log. Can someone please help with this?
(i) log m^2 n =?
(ii) log (m/n^3)=?
What percent of 450 is 60? Round to the nearest hundredth of a percent.
At time t = π /6 , the position x(t) = 6 cos(t) is given by the following. x (π/6) = 6 cos (π /6 )
Solve the polynomial equation. State the multiplicity of each root. x3 + 15x2 + 75x + 125 = 0
Which of the following graphs represent a function? 4072-01-02-01- a. Graph A and Graph C b. Graph A c. Graph D d. Graph B and Graph D
The graph which represent a graph of a function is:
Graph A and Graph C
Step-by-step explanation:We know that a graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to y-axis should intersect the curve exactly once i.e. corresponding to each x-value there is exactly one y-value.
Hence, from the figure attached to the answer we see that the Graph which is a function is:
Graph A and Graph C
Graph A represents a function.
Explanation:A function is a relation in which each input has only one output. In other words, for every x-value, there can only be one y-value. To determine if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. Looking at the given graphs, Graph B and Graph D do not pass the vertical line test, as there are vertical lines that intersect these graphs at multiple points. Therefore, the correct answer is Graph A.
I NEED ANSWER RIGHT NOW!!!!!!!!! (30 POINTS + BRAINIEST ANSWER REWARD!!!!)
The graph below shows the velocity f(t) of a runner during a certain time interval:
graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 8 and 8, 0. Label on the x axis is time in seconds and label on the y axis is velocity in meters per second
Which of the following describes the intercepts on the graph?
A. The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.
B. The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
C. The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
D. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 seconds.
what 3050 divided by 100
Create a factorable polynomial with a GCF of 2. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
What construction does the image below demonstrate?
Answer:
The construction depicts the inscribing of a hexagon in a circle.
Step-by-step explanation:
These are the following steps to inscribe a hexagon in a circle.
1. We mark a point anywhere on the circle. This mark is the first vertex of the hexagon.
2. Now we will set the compass on this vertex and set the width to the center of the circle. This is the radius of the circle.
3. Now we will make an arc across the circle which is the next vertex of the hexagon.
4. Now moving the compass on to the next vertex and drawing another arc, which becomes the third vertex of the hexagon.
5. Repeat step 4 until all vertices are marked.
6. Lastly, we will draw a line between each successive pairs of vertices, for a total of six lines.
Now we can see a hexagon inscribed in a circle.
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width is 10 cm. if he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
The area of the rectangle board, including the wooden border, is 280 cm².
The student's question pertains to finding the new area of the rectangle board after adding a 2 cm wooden border around it. Initially, the board has dimensions of 16 cm in length and 10 cm in width. To account for the new wooden border, we add 2 cm to each side of the board. This means that the new length will be 16 cm + 4 cm (2 cm for each side of the length) and the new width will be 10 cm + 4 cm (2 cm for each side of the width).
The calculation will be as follows:
New Length = 16 cm + 4 cm = 20 cm
New Width = 10 cm + 4 cm = 14 cm
Area = New Length * New Width
Area = 20 cm * 14 cm
Area = 280 cm²
Therefore, the area of the rectangle board with a 2 cm border added around it will be 280 cm².
what is 8/20 of an hour
Which of the following rules describes the function graphed below? a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
Answer:
Option C
output=0.5(input)+1.5
Step-by-step explanation:
Let
y------> the output
x------> the input
we have
[tex]A(-1,1), B(5,4)[/tex]
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{4-1}{5+1}[/tex]
[tex]m=\frac{3}{6}=0.5[/tex]
Find the equation of the line
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=0.5[/tex]
[tex]A(-1,1)[/tex]
substitute
[tex]y-1=0.5(x+1)[/tex]
[tex]y=0.5x+0.5+1[/tex]
[tex]y=0.5x+1.5[/tex]
remember that
y=output
x=input
substitute
output=0.5(imput)+1.5
Find the coordinates of point P
P
along the directed line segment AB
AB
, from A(1, 6)
A(1, 6)
to B(−2,−3)
B(−2,−3)
, so that the ratio of AP
AP
to PB
PB
is 5
5
to 1
1
.
The calculated coordinates of the point P is P (-3/2, -3/2)
How to determine the coordinates of the point PFrom the question, we have the following parameters that can be used in our computation:
A = (1, 6)
Also, we have
B = (-2, -3)
And we have the partition to be
m : n = 5 : 1
The coordinate of the partition is calculated as
P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Substitute the known values in the above equation, so, we have the following representation
P = 1/(5 + 1) * (5 * -2 + 1 * 1, 5 * -3 + 1 * 6)
This gives
P = 1/6 * (-9, -9)
So, we have
P = (-3/2, -3/2)
Hence, the coordinate is P = (-3/2, -3/2)
Read more about line segment ratio at
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To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula and plug in the given values to find the coordinates (-3/2, -3/2).
Explanation:To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula. The section formula states that if a point P divides a line segment AB in the ratio m:n, then the coordinates of P can be found using the formula:
P(x,y) = [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)]
Using this formula, we can plug in the values: m=5, n=1, x1=1, y1=6, x2=-2, y2=-3 to find the coordinates of point P.
P(x,y) = [(5*(-2) + 1*1)/(5+1), (5*(-3) + 1*6)/(5+1)] = [(-10+1)/6, (-15+6)/6] = [-9/6, -9/6] = (-3/2, -3/2)
Learn more about Section Formula here:https://brainly.com/question/30242641
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Find the median: 95, 103, 98, 62, 31, 15, 82
The quotient Of 30 and the sum of -4 and -6
Aurella wants to enlarge a 4-inch by 6 inch photo so that it has a width of 15 inches. Use a ratio table to determine the new length of the photo
Nick bought a pair of glasses for $200. He later saw the same glasses advertised for 20% less than what he originally paid. What price were the glasses being advertised for?
factor 2x^3+3x^3-18x-27
After combining like terms, the polynomial simplifies to 5x^3 - 18x - 27. It cannot be factored using basic techniques due to the lack of common factors and its incompatibility with simple factoring patterns.
Explanation:To factor the polynomial 2x^3 + 3x^3 - 18x - 27, we first combine like terms and then look for common factors or patterns that we can use to factor the polynomial.
Combining Like Terms
Combining the cubic terms, we get 5x^3. Therefore, the polynomial simplifies to 5x^3 - 18x - 27.
Factoring
We look for a greatest common factor (GCF) among the terms. In this case, there are no common factors other than 1.
Since there is no obvious way to factor by grouping, and the polynomial does not fit the patterns for difference of cubes or sum of cubes, we'd have to consider other methods such as Rational Root Theorem or synthetic division to find if the polynomial has rational roots and can be factored further. However, those methods are more complex and require trial and error or a systematic approach that typically isn't covered until more advanced algebra classes or college algebra.
Conclusion
Without additional methods, we conclude that the polynomial 5x^3 - 18x - 27 cannot be factored over the rationals using basic factoring techniques commonly taught in high school algebra.
To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors and factor out those common factors.
Explanation:To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors. The first two terms, 2x^3 and 3x^3, have a common factor of x^3. The last two terms, -18x and -27, have a common factor of -9. Factoring out these common factors, we get:
2x^3 + 3x^3 - 18x - 27 = x^3(2 + 3) - 9(2 + 3) = x^3(5) - 9(5) = 5x^3 - 45
So, the factored form of the expression is 5x^3 - 45.
for halloween, lana received 7 4/8 pounds of candy. after a week her family had eaten 3 6/8 pounds, how many pounds does she have left?
Answer To Questions :
3 3/4
Kaia needs braces, which will cost $2,400. Her insurance deductible is $1500, after which her insurance pays 80% of all costs. How much will Kaia need to pay for her braces?
A.$2,200
B.$1,680
C.$180
D.$480
Kaia will pay a $1,500 deductible and the remaining 20% not covered by insurance after the deductible, totaling to $1,680 for her braces.
To calculate how much Kaia will need to pay for her braces, we need to take into account her insurance deductible and the percentage her insurance will cover after that deductible is paid. Kaia's braces cost $2,400, so let's break it down step-by-step:
Kaia pays her insurance deductible, which is $1,500. So, $2,400 - $1,500 = $900 remains.
Her insurance then covers 80% of the remaining $900. To calculate this, we use 80% of $900: ($900 x 0.80) = $720.
Since the insurance pays $720 of the remaining cost, Kaia is left with 20% of $900 to pay out of her pocket. To calculate this, we take 20% of $900: ($900 x 0.20) = $180.
Therefore, Kaia will need to pay $1,500 (deductible) plus $180, for a total of $1,680.
Allie wants to arrange her flower garden in eight equal rows.
Derek decided to take a trip to France this summer. He had $30 in U.S. dollars to exchange for Euros. For every U.S. dollar, Derek received .76 Euros. How many Euros did Derek receive for his 30 U.S. dollars?
Quinn spends $16.49 for 3 magazines and 4 sheets of stickers. The magazines cost $3.99 each and the sales tax was $1.02. Quinn also used a coupon for $1.50 off her purchase. If each sheet of stickers had the same cost, how much did each sheet of stickers cost?
Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis
ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx
=√14(x4+2+1x4)dx=√122(x2+1x2)2dx
=12(x2+1x2)dx
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? Zach's method is linear because the number of minutes increased by an equal factor every month. Victoria's method is linear because the number of minutes increased by an equal number every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
(NEVER MIND GUYS IM GOING WITH A)
Let f be the function defined by f(x) = x + lnx. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1, 4]?
hich numbers are to solve this problem? A bicycle shop sold 60 road bikes, 50 racing bikes, and 75 mountain bikes each month for 15 months. How many more mountain bikes than road bikes did the shop sell in the 15 months?