Direct variation
The equation is written as y=mx+b
The variation f(x) = 3x is A. Direct variation.
The function f(x) = 3x represents a type of relationship called a direct variation. In mathematics, a direct variation can be expressed in the form y = kx, where k is a constant. Here, k is 3. This means that as x increases or decreases, f(x) = 3x changes proportionally. The correct answer is therefore:
A. Direct variationTo further illustrate, consider two pairs of values for x and f(x):
if x = 2, then f(x) = 3(2) = 6,
And if x = 4, then f(x) = 3(4) = 12.
Notice that the ratio f(x)/x = 3 is constant.
Stella is recording the temperature every day for five days on the first day it was 0 degrees and the second day was 3 degrees higher then the day before
First day temperature is 0 degree.
Second day temperature is 3 degree higher than first day's temperature.
In order to find the higher temperature we need to add increased temperature in previous day's temperature.
First day given temperature is 0 degree .
Three degree higher than 0 would be 0+3.
On adding 0 and 3 we would get 3.
Therefore, second day temperature would be 3 degrees.Juan drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Juan drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Juan live from the mountains?
Answer:Juan live 384 miles from the mountains.
Step-by-step explanation:
Let x be the speed of Juan for trip to the mountains
Time taken by Juan to reach the mountains=8 hours
then distance traveled by Juan for trip to mountain= speed × time=8x..........(1)
Time taken by Juan to reach the home= 6 hours
Speed increased by 16 miles per hour ∴ the resultant speed to reach the home by Juan =x+16
then distance traveled by Juan to reach the home =speed × time
= (x+16)6......................(2)
Now distance is same in both the case (1) and (2),we get
8x= (x+16)6
⇒8x=6x+96..............(by solving brackets)
⇒2x=96..............(subtracting 6x from both sides )
⇒x=48....................(dividing 2 from both sides)
Putting this value in (1) ,we get
Distance traveled by Juan for trip to mountain =8×48=384 miles.
∴ Juan live 384 miles from the mountains.
By using the rate and time of journey, it is determined that Juan lives 384 miles away from the mountains.
Explanation:This question is about calculating the distance based on the rate and time of travel. Let's denote the distance to the mountains as 'D'. According to the question, Juan drove to the mountains and it took 8 hours. On his way home, there was no traffic and he was able to travel at a faster rate, which took 6 hours.
Let's denote the speed to the mountains as 'S', therefore his speed back was 'S + 16' (16 miles per hour faster). From the formula speed = distance/time (D = S*T), we know that the distance to and from the mountains remained the same, so we can set up the following equation to solve for the unknown distance D:
8S = 6(S + 16)
Solving for 'S' we get 48 mph. We can substitute S=48 into the first equation to get D = 8S = 8*48 = 384 miles. So, Juan lives 384 miles away from the mountains.
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Which statement best describes the function h(t) = 210 – 15t?
h(t) is a linear function with a slope of -15.
Answer:
B
Step-by-step explanation:
80 POINTS!!!!!!
Identify the x-axis on the plane shown below:
Question 1 options:
The green line represents the x-axis
The red line represents the x-axis
The black line represents the x-axis
The blue line represents the x-axis
what two numbers have an absolute value of 21.63
The correct answer would be -21.63 and +21.63
What is the length of DE?
Answer:
18
Step-by-step explanation:
a p e x
Triple a number b is greater than or equal to 21
3/4-5/4m=113/24
please show work
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What is the radical form of the expression?
(5x^3y^4)^3/7
The answer is D
hope this helped
(5x^3y^4)^3/7
= 7th root of (5 x^3 y^4)^3
= 7th root of (5^3 x^9 y^12)
= 7th root of (125 x^9 y^12)
Answer is the last option
7th root of (125 x^9 y^12)
BRAINLIEST!!PLEASE HELP
Which of the points satisfy the linear inequality graphed here?
A) (0, 0)
B) (10, 0)
C) (-10, 0)
D) (10, 10)
C . Find a point that lies in the shaded region, or plug the points in and determine which point makes the inequality true.
Last year 660 people attended the outdoor concert in the park. If 25% more tickets were sold this year than last year, how many people will attend the concert this year
What is the degree of the polynomial in the expression below?
x6 + 3 - 2x2 + 4x7 - 4x
A. 7
B. 6
C. 4
D. 5
Answer:
The degree of the polynomial in the expression below is:
A. 7
(hope this helps :3)
Answer: A.) 7
Step-by-step explanation: a p e x
WIll give brainiest answer if you are correct.
What are the three forms of linear equations?
That would be point-slope form, standard form, and slope-intercept form.
The three forms of linear equations are the standard form (Ax + By = C), the slope-intercept form (y = mx + b), and the point-slope form (y - y1 = m(x - x1)).
The three forms of linear equations are:
The standard form, which appears as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.
The slope-intercept form, given by y = mx + b, with m representing the slope and b representing the y-intercept.
The point-slope form, which is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line.
Each form is useful in different contexts: the standard form is often used when both x and y intercepts are integers; the slope-intercept form is useful for quickly identifying the slope and intercept; and the point-slope form is handy when a point on the line and the slope are known.
The annual tuition at a public two-year college last year was $3,200. For the new school year, Elizabeth’s first year in college, the tuition is expected to increase 5%. She saved the same amount monthly to prepare for the cost of her tuition. What is the minimum amount Elizabeth should have saved monthly during the previous year?
$267
$280
$308
$400
Elizabeth had to save $280 each month.
The correct option is (2).
What is Percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
As per the given data:
The annual tuition at a public two-year college last year was $3,200.
Expected growth in the tuition fee = 5%
We have to find the amount Elizabeth should have saved monthly during the previous year to pay her tuition fees.
For finding the increase in tuition fee:
= 5% of 3200
= (5/100) × 3200
= $160
Tuition fees after growth = 3200 + 160 = $3360
Amount Elizabeth had to save each month = Tuition fees after growth/12
= 3360/12
= $280
Elizabeth had to save $280 each month.
Hence, Elizabeth had to save $280 each month.
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What is the next number in the pattern of 12 24 72 288
The next number is 1440.
Here is the pattern:
12*2=24
24*3=72
72*4=288
So, you have to multiply 288 by 5, which will get you the answer 1440.
Please help and show work!! Will mark brainliest!!
Step 1. Use Multiplication Distributive Property
2^2x^2y^2 * -3x^2 * 4y^4
Step 2. Simplify 2^2 to 4
4x^2y^2 * -3x^2 * 4y^4
Step 3. Take out the constants
(4 * -3 * 4)x^2x^2y^2y^4
Step 4. Simplify 4 * -3 * 4 to -48
-48x^2x^2y^2y^4
Step 5. Use product rule: x^a x^b = x^a + b
-48x^2 + 2 y^2 + 4
Step 6. Simplify 2 + 2 to 4
-48x^4y^2 + 4
Step 7. Simplify 2 + 4 to 6
-48x^4y^6
Given: `Delta`ABC
Prove: The sum of the interior angle measures of `Delta`ABC is 180°.
What is the missing step in this proof?
Answer: Statement: `/_1 ~= /_4`, and `/_3 ~= /_5`.
Reason: Alternate Interior Angles Theorem
I just did the test and got 100%
Answer:
Statement 3:[tex]m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5[/tex].
Reason:Alternate Interior Angles Theorem
Step-by-step explanation:
We are given that a triangle ABC.
We have a proof that the sum of interior angle measures pf triangle ABC is [tex]180^{\circ}[/tex].
We have to find the missing steps in the given proof.
Statement 1 :Let points A,B and C form a triangle.
Reason: Given
Statement 2:[tex]$\overleftrightarrow{DE}$[/tex] is a line passing through B and parallel to [tex]\overline{AC}[/tex] with angles as labeled.
Reason: Definition a parallel line and labeling angles.
Statement 3:[tex]m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5[/tex].
Reason:Alternate Interior Angles Theorem
Statement 4:[tex]m\angle 1=m\angle 4 and m\angle 3=m\angle 5[/tex]
Reason: Congruent angles have same measures
Statement 5 [tex] m\angle 2+m\angle 4+m\angle =180^{\circ}[/tex]
Reason: Angle addition and definition of a straight angle
Statement 6: [ytex]m\angle 1+m\angle 2+m\angle 3=180^{\circ}[/tex]
Reason : By substitution
Hence proved.
Kevin makes $78.37 per day. How much does he make in 7 days
Answer:
$ 548.59
Step-by-step explanation:
The complete solution is given in attachment below.
Becca made 3 dozen cookies with 2/3 of a batch of her mother's cookie dough. How many cookies will she make if she uses that entire batch?
A rectangle is four times as long as it is wide. If it has an area of 36 square inches, what are its dimension?.
a. 6 by 6
b. 3 by 12
c. 4 by 9
d. 4 and 8
Answer:
b on edge
Step-by-step explanation:
The dimensions of the rectangle are 3 inches by 12 inches. This conclusion is achieved by using the supplied information that the rectangle is four times as long as it is wide, and the area is 36 square inches.
Explanation:The problem is describing a rectangle whose length is four times its width and has an area of 36 square inches. The formula for the area of a rectangle is length x width. Given the rectangle is four times as long as it is wide, we can represent the width as 'w' and the length as '4w'. Therefore, the calculation would look as follows: 4w * w = 36. Solving this equation we get w^2=9, so w=3. Consequently, the length would be 4*3=12. Therefore, the dimensions of the rectangle are 3 inches by 12 inches.
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Someone help please?
Answer:
43:76
Step-by-step explanation:
Point P is the mid -point of MN and C is mid point of MP. Prove that, using Euclids axiom, MC =1/2PN
Answer:
Given:-Point P is the mid -point of MN and C is mid point of MP.
To prove:-MC =1/2PN
Proof:- As P is the mid -point of MN then P divides MN into two equal halves
such that MP=1/2MN=PN ....................(1).(by Euclid's axiom "things which are equal to the same thing are also equal to one another")
Similarly as C is the mid point of MP then MC=1/2MP=CP ................(2)
Now replacing MP by PN from (1)in (2),we get
MC=1/2(PN)...................hence proved.
A 20 x 32 rectangle is embedded inside a 98 x 108 rectangle. They share a vertex and their sides partially over lap as shown. Find the distance between the centers of the two rectangles.
Answer:
The distance is 55 units.
Step-by-step explanation:
Think of the bottom left corner of the rectangles, the shared vertex, as the origin of a coordinate plane. The positive x-axis is the lower 108-unit long horizontal side, and the positive y-axis is the left vertical 98-unit long side. The bottom left vertex is (0, 0). The center of the small rectangle is at (10, 16). The center of the large rectangle is at (54, 49). Now use the distance formula to find the distance between those two points.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] d = \sqrt{(54 - 10)^2 + (49 - 16)^2} [/tex]
[tex] d = \sqrt{44^2 + 33^2} [/tex]
[tex] d = \sqrt{1936 + 1089} [/tex]
[tex] d = \sqrt{3025} [/tex]
[tex] d = 55 [/tex]
A recipe for 114 dozen cupcakes calls for 123 cups of flour, but rashida has only 1 cup of flour. How many cupcakes can she make?
Answer:
11 cupcakes
Step-by-step explanation:
Given that 114 dozen cupcakes can be prepared from 123 cups of flour.
i.e. if flour is 123 cups no of cupcakes that can be made = 114x 12 = 1368
For 1 cup how many cupcakes?
i.e. when cup reduces no of cupcakes also will decrease.
This relation is directly proportional.
Hence answer = 1x1368/123 =11.1219
Approximately 11 cupcakes Rashida can prepare
The question is about proportion. The recipe states that 1368 cupcakes require 123 cups of flour. Therefore, with 1 cup of flour, Rashida can make approximately 11 cupcakes.
Explanation:The question is asking for the number of cupcakes that can be made with one cup of flour. This is a problem of ratios or proportions, a common subject in Mathematics. The recipe states that 114 dozen cupcakes (which is 1368 cupcakes) need 123 cups of flour, hence the ratio is 1368 cupcakes to 123 cups of flour.
To find out how many cupcakes we can make with 1 cup of flour, we set up a proportion: 1368/123 = x/1. Here, 'x' represents the number of cupcakes we can make with 1 cup of flour. Solving for 'x' gives us the number of cupcakes we can make. By doing this, we get 'x' = 11.12, but since we can't have a fraction of a cupcake, Rashida can make approximately 11 cupcakes with 1 cup of flour.
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1.When you rotate a figure counterclockwise, is that a positive rotation or a negative rotation?
2.Rotating from the x-axis to the y-axis is a rotation of how many degrees?
1. When you rotate a figure counterclockwise, is that a positive rotation or a negative rotation? It is a positive rotation. Positive rotations are counterclockwise or anti-clockwise.
2. Rotating from the x-axis to the y-axis is a rotation of how many degrees? it is generally 180 degrees. To rotate a figure 180 degrees, we apply the rule (x, y) → (-x, -y).
i dont really know about 2. but i think for 1. is it is a negative rotation if you spin it like that.
Chris wants to tip 15 percent to the waiter at a restaurant. If his meal is $19.50, how much should he tip the waiter?
15% is written as 0.15 in decimal format.
Multiply the cost of the meal by 0.15.
19.50 x 0.15 = 2.925, which would round to $2.93
The tip is $2.93
To calculate a 15% tip for a $19.50 meal, convert 15% to decimal form (0.15), multiply by the cost of the meal ($19.50), and round to the nearest cent, resulting in a $2.93 tip.
Chris wishes to tip 15 percent to the waiter for his meal which costs $19.50. To calculate the amount of the tip, we need to convert the percentage to a decimal and then multiply it by the cost of the meal. Here's how you can do it:
Convert the tip percentage to a decimal: 15% ightarrow 0.15.
Multiply the decimal by the total cost of the meal: $19.50 imes 0.15.
The calculation gives us the tip amount: $2.925.
Since it's difficult to leave a fraction of a cent as a tip, we would round this to the nearest cent, giving us $2.93.
Therefore, Chris should tip $2.93 to the waiter.
Suppose that the cost of renting a snowmobile is $37.50 for 5 hours. What would be the cost of renting 2 snowmobiles for 5 hours?
The cost of renting 2 snowmobiles for 5 hours would be $75, as you double the cost for one snowmobile, which is $37.50.
Explanation:The cost for renting one snowmobile for 5 hours is
$37.50
. If you want to rent 2 snowmobiles for the same amount of time, you simply need to double the cost. In mathematics, this is a simple multiplication operation. So,
2 x $37.50 = $75
. Therefore, the cost of renting 2 snowmobiles for 5 hours would be
$75
.
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Algebra 2 help!! Find the value of k
13 By the factor theorem, if the function is divisible by x - 3 then f(3) = 0. So we have:-
2(3)^3 + k(3)^2 + 7(3) - 3 = 0
9k = 3 - 21 - 54 = -72
k = -72/9 = -8 answer
14. Similarly , f(-4) = 0 , so we have:-
(-4)^3 + 9(-4)^2 + k(-4) - 12 = 0
-64 + 144 - 4k - 12 = 0
4k = -64 + 144 - 12 = 68
k = 68/4
k = 17 answer
complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.)
y = -x2 - 4x - 3
There are multiple ways that you could graph this quadratic equation. I would start by finding the vertex. The x-value in the vertex is found with -b/2a. The take you value and input back into the equation to find the y-value of your vertex. Then, you could make a list of points on both sides of the vertex to create a table with which to create the parabola.
Answer:
Step-by-step explanation:
is equal 45