Answer:
y = -x + 30
Step-by-step explanation:
You will want to put the equation in the form y = mx + b where m is the slope and b is the y-intercept (an example is y = 2x - 1).
First, to find the slope you want to find how much x goes up by when y goes up by 1. You know from the table that when y goes up by 5, x goes up by -5 (using the points (10, 20) and (5, 25))
Then, you can divide each value by 5, so it would be when y goes up by 1, x goes up by -1. That means the slope is -1.
So far, the equation is y = -x + b. To find b, you can plug in one of the points you have and solve for b. For example, substitute in x = 10 and y = 20, so:
20 = -10 + b
add 10 to both sides
30 = b
So you know the equation is y = -x + 30
Please let me know if any parts of these explanation are confusing, I definitely think this concept can be confusing at time. Good luck with your work! :)
Answer:
To create an equation, you need to find the slope first. The slope formula is \(\frac{y^2-y^1}{x^2-x^1}\). Let's use two random coordinates: (10,20) and (5,25). Plug in these digits into the formula to get \(\frac{25-20}{5-10}\). Simplify to get \(\frac{5}{-5}\) or -1. The equation would look like y=-x+b. Now we need to find b. Again, let's use a random coordinate: (10,20). Plug in the digits into the variables to get 20=-10+b. Add 10 on both sides to get 30=b. So, the equation would be y=-x+30.
please please please help
The amount of time it would take for Mr. Smith's rocket to return to the ground is 8 seconds.
How to determine the time when the rocket would hit the ground?Based on the information provided, we can logically deduce that the height (h) in meters, of this rocket above the ground is related to time by the following quadratic function:
h(t) = -16t² + 128t
Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:
0 = -16t² + 128t
16t² = 128t
16t = 128
Time, t = 128/16
Time, t = 8 seconds.
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the ages of John and Harry are in the ratio 5:7.four years from now the ratio of their ages will be 3:4.find their present ages
Answer: 20 and 28 years old
Step-by-step explanation:
Tommy had 40 oranges to give to 3 groups of children.
- The first group ate 30% of the total oranges.
- The second group ate 7 of the total oranges.
- The third group ate 1/8 of the total oranges.
How many oranges were left?
Answer:
16
Step-by-step explanation:
1st group = 30% or .3 as a decimal
.3 * 40 = 12
2nd group = ate 7
Third group = 1/8 or .125 as a decimal
.125 * 20 = 5
12 + 7 + 5 = 24
40 -24 = 16
CAN SOMEONE PLEASE HELP ME
Answer:
Step-by-step explanation:
The first two are parallel but the other are not
Let R be the region in the first quadrant bounded by the graph of y = 2 \sqrt x, the horizontal line y = 6, and the y-axis, as shown in the figure.
a) Find the area of R.
b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 7.
c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the y-axis.
a) To find the area of region R, we need to calculate the area between the curves y = 2√x and y = 6 in the first quadrant. The region is bounded by the y-axis and the horizontal line y = 6.
To find the area, we integrate the difference between the upper and lower curves with respect to x:
Area = ∫[0 to a] (6 - 2√x) dx,
where 'a' is the x-coordinate where the curves intersect.
b) To find the volume of the solid generated when region R is rotated about the horizontal line y = 7, we can use the method of cylindrical shells. Each cylindrical shell has a height of 6 - 7 = -1 (as y = 6 is below y = 7) and a radius equal to x.
The volume is given by the integral:
Volume = ∫[0 to a] 2πx(6 - 7) dx,
where 'a' is the x-coordinate where the curves intersect.
c) To find the volume of the solid generated when region R is rotated about the y-axis, we can use the method of disks. Each disk has a radius equal to y and a thickness given by dx.
The volume is given by the integral:
Volume = ∫[0 to b] π(y^2) dx,
where 'b' is the y-coordinate where the curves intersect.
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find the area of the infinite region in the first quadrant between the curve y=e^-x and teh x-axis
Thus, the area of infinite region in the first quadrant between the curve y=e^-x and the x-axis is 1 square unit.
To find the area of the infinite region in the first quadrant between the curve y=e^-x and the x-axis, we need to integrate the function y=e^-x from x=0 to x=∞.
First, let's find the indefinite integral of e^-x:
∫e^-x dx = -e^-x + C
Next, we can use this indefinite integral to find the definite integral from x=0 to x=∞:
∫[0,∞]e^-x dx = lim┬(t→∞)∫[0,t]e^-x dx
= lim┬(t→∞)[-e^-t + e^0]
= lim┬(t→∞)[-e^-t + 1]
= 1
Therefore, the area of the infinite region in the first quadrant between the curve y=e^-x and the x-axis is 1 square unit.
It is important to note that this region is infinite because the curve y=e^-x approaches the x-axis but never actually touches it.
As we integrate from x=0 to x=∞, we are essentially adding up an infinite number of infinitely small rectangles, resulting in an infinitely large area.
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ask the user to input a number between 1 and 1000 ten times and store that number in the array.
In this task, the user is asked to input ten numbers between 1 and 1000. These numbers will be stored in an array.
To complete this task, we prompt the user to provide a number between 1 and 1000. This process is repeated ten times to collect ten numbers. We store these numbers in an array, which is a data structure that allows us to hold multiple values in a single variable. By using an array, we can easily access and manipulate these numbers for further analysis or calculations.
Storing the numbers in an array provides us with a convenient way to organize and manage the data. We can iterate over the array to perform operations on each number individually or perform aggregate calculations on the entire set of numbers. This approach enables us to process the user's input efficiently and effectively.
By gathering the user's numbers and storing them in an array, we create a structured dataset that can be utilized for various purposes. Whether it's calculating statistics, sorting the numbers, or performing mathematical operations, having the numbers stored in an array allows us to work with the data more flexibly and programmatically.
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I need help. What does n equal.
\(5n^{2}=7n-2\)
Answer:
\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)
Step-by-step explanation:
\(\rightarrow 5n^2 = 7n -2\)
\(\rightarrow 5n^2 - 7n +2=0\)
\(\rightarrow 5n^2 - 5n -2n+2=0\)
\(\rightarrow 5n(n - 1) -2(n-1)=0\)
\(\rightarrow (5n-2)(n-1)=0\)
\(\rightarrow 5n-2= 0,\: n-1=0\)
\(\rightarrow 5n= 2,\: n=1\)
\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)
Step-by-step explanation:
\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)
what’s the answer (question to much to type).
12. Higher Order Thinking Kevin's car can go 315 miles on one tank of gas. He used just under 40% of a full tank of gas to get to a sporting event, traveling at an average speed of 60 miles an hour. About how long did it take him to get there? How did you decide?
The given data is:Kevin's car can go 315 miles on one tank of gas. He used just under 40% of a full tank of gas to get to a sporting event, traveling at an average speed of 60 miles an hour.The main aim of the question is to determine the approximate time taken by Kevin to reach the sporting event.
Firstly, we need to find how much of a full tank of gas Kevin used to reach the sporting event. Given, Kevin used just under 40% of a full tank of gas.Thus, we can write: Amount of gas used by Kevin = 0.4 × Full tank of gas = 0.4 × 315 = 126 milesTo determine the time taken by Kevin to reach the sporting event, we need to use the formula: Time = Distance/SpeedNow, distance traveled by Kevin = 126 miles and speed of the car = 60 miles/hourThus, the time taken by Kevin to reach the sporting event is:Time = Distance/Speed= 126/60 hours= 2.1 hoursApproximately, it took 2.1 hours or 2 hours and 6 minutes for Kevin to reach the sporting event.
Given data:Kevin's car can go 315 miles on one tank of gas. He used just under 40% of a full tank of gas to get to a sporting event, traveling at an average speed of 60 miles an hour. We need to determine the approximate time taken by Kevin to reach the sporting event.How did you decide?To solve the question, we first need to find how much of a full tank of gas Kevin used to reach the sporting event. Given, Kevin used just under 40% of a full tank of gas.Thus, we can write:Amount of gas used by Kevin = 0.4 × Full tank of gas = 0.4 × 315 = 126 milesTo determine the time taken by Kevin to reach the sporting event, we need to use the formula: Time = Distance/SpeedNow, distance traveled by Kevin = 126 miles and speed of the car = 60 miles/hourThus, the time taken by Kevin to reach the sporting event is:Time = Distance/Speed= 126/60 hours= 2.1 hoursTherefore, it took approximately 2.1 hours or 2 hours and 6 minutes for Kevin to reach the sporting event.
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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 27 students, she finds 3 who eat cauliflower. Obtain and interpret a 90% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method.
ANSWER- BETWEEN 9.38% and 12.9%
Step-by-step explanation:
Let X be the number of students who eat cauliflower.
Therefore, X=3
Let N be the total number of students surveyed.
Therefore, N=27
Thus, p'=N/X=3/27=1/9=0.1111
Now, for 90% confidence level, Z=1.645
The formula for the interval range of proportion of students is :
p=p'±[Z(√p'(1−p')/N]
Putting the values we get:
p=0.1111+-[1.645√(0.1111(1-0.1111)/27)]
p=0.1111+-[1 645*0.0109]
p=0.1111+-0.01790
Thus, Jane is 90% confident that the population proportion p, for students who eat cauliflower in her campus is between 9.38%and 12.9% (after converting the answer we got to percentage).
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for the following 3 questions: a study obtained data on the amount of time 28 randomly selected high school students and 31 randomly selected college students spend on their cell phones each day. the investigator is interested in determining whether there is evidence that the amount of time students spend on their cell phone is different between high school and college Let H= time spent on phone by high school students; C= Time spent on phone by college students; and d=H−C
The data are not paired because: o All of these are true o Each element in a sample is measured once: time spent on cell phone o The conclusion pertains to the difference of two independent population means o There are two samples
The correct answer is
H₀ : μh - μc = 0
H₀ : μh - μc ≠ 0
Given that,
Regarding the subsequent 3 inquiries: A study collected information on how much time 28 randomly chosen high school students and 31 randomly chosen college students spent each day on their cellphones. The researcher is interested in learning whether there is proof that students use their phones for varying amounts of time in high school and college.
Because the samples of college and high school students are independent, the independent samples t-test should be utilized.
The study's research (Claim) aims to ascertain whether students' cell phone usage patterns alter between high school and college.
For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,
H₀ : μh - μc = 0
H₀ : μh - μc ≠ 0
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The proper null and alternative hypotheses are
\(H_{0}\) : μh = μc
\(H_{A}\) : μh - μc
The study's research wants to ascertain whether difference between the time spent by high school students and college students.
The actual test begins by considering two hypothesis i.e. null hypothesis and alternative hypothesis.
Let, H= time spent on the phone by high school students;
C= Time spent on the phone by college students; and
d=H−C
For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,
\(H_{0} :\) μh = μc (time spent by high school students is equal to college students)
\(H_{A} :\) μh - μc (difference between the time spent by high school students and college students)
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PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
108º
Step-by-step explanation:
subtract outer angle from circle
360º - 252º = 108º
I hope this helps you
find DCG
360-252=108°
angle DBG=1/2(252-108)
angle DBG=72°
the hypotenuse of a right triangle is 10 inches. the length of the two legs are given by two consecutive even integers. find the length of the two legs. the lengths of the two legs are and inches. license points possible: 1
Answer:
6 and 8
Step-by-step explanation:
x = one integer
x+2 = other integer
Pythagorean Theorem:
x^2 + ( x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x -48 = 0 Use factoring ( or Quadratic Formula)
(x+8)(x-6) = 0 shows x = 6 the other integer is 8
What value of m would make parallelogram wxyz a square.
To make parallelogram WXYZ a square, the following conditions must be met:
1. All four sides of the parallelogram must have equal length.
2. The angles between adjacent sides must be 90 degrees.
Since a square is a special type of parallelogram with all sides equal and all angles equal to 90 degrees, we can determine the value of m that would make WXYZ a square by ensuring that these conditions are met. To find the value of m, we need more information about the dimensions or properties of the parallelogram WXYZ. Please provide additional details or measurements related to the parallelogram. The diagonals of a square are equal in length and bisect each other at 90-degree angles. The perimeter of a square is the sum of all four sides, and the area of a square is calculated by squaring the length of one side.In order for parallelogram WXYZ to be a square, it must have congruent sides and right angles at each vertex.
Since opposite sides of a parallelogram are congruent, we can equate the lengths of adjacent sides to find the value of m that would make it a square.
Let's assume that WX and XY are adjacent sides of the parallelogram.
If WX = XY, then the parallelogram would have congruent sides.
Let's say WX = m and XY = m.
To form a square, the angles at each vertex must be right angles. This means that WX and XY must be perpendicular to each other.
In a square, opposite sides are parallel, so the slopes of WX and XY must be negative reciprocals of each other.
The slope of WX can be represented as (change in y) / (change in x). Since it is perpendicular to XY, its slope will be the negative reciprocal of the slope of XY.
Let's assume the slope of XY is denoted as a. Then the slope of WX would be -1/a.
We can now equate the slopes of WX and XY:
-1/a = (change in y) / (change in x)
Simplifying this equation, we get:
a = -1
Therefore, the slope of XY is -1.
Now, we can equate the lengths of WX and XY:
m = m
Since WX = XY and both sides have length m, we can say that m = m.
So, any value of m would make parallelogram WXYZ a square as long as the sides WX and XY are congruent and perpendicular to each other, with a slope of -1.
hence, the value of m = -1.
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(8.41 x 10^-5) - (7.9 x 10^-6)
Answer:
7.62×10^-5
Step-by-step explanation:
Answer: 0.000076
Step-by-step explanation:
8.41(10^-5) - 7.9(10^10-6)
= 8.41 (1/100000) - 7.9(10^-6)
= 0.000084 - 7.9(10^-6)
= 0.000084 - 7.9(1/000000)
= 0.000084 - 0.000008
= 0.000076
20points!!!!!
A rectangle measuring 5 cm by 3 cm
is scaled up to create an image with
side lengths of 7.5 cm and 4.5 cm.
How do the areas of the
two similar figures compare?
a) The area of the image is 1.5 times larger.
b) The area of the image is 2.25 times larger.
c) They have the same area because
they are similar figures.
d) none of the above
Answer:
The answer is b.
Step-by-step explanation:
Take the areas of the two rectangles by multiplying the numbers. Then divide the two numbers, in this case, 33.75 and 15.
Answer: b) The area of the image is 2.25 times larger.
Step-by-step explanation: !.5 larger in each direction results in 1.5×1.5 which is 2.25 enlargment.
4.5 × 7.5 =33.75 3×5= 15
33.75÷15 = 2.25
Solve: 12 Superscript x squared 5 x minus 4 Baseline = 12 Superscript 2 x 6.
For the exponential equation, having variable x as superscript equation has solution as,
\(x=-5,2\)
What is equality for exponential equation property?According to the equality for exponential equation property, when the bases of both side of a equation is same, then the exponents of both the terms must be equal.
The equation given in the problem is,
\(12^{x^2+5x-4}=12^{2x+6}\)
In the given equation, the base of both side is equal. For the equal base, the exponents of them can be equate as,
\({x^2+5x-4}={2x+6}\)
Arrange all the terms one side of the equation as,
\({x^2+5x-4}-{2x-6}=0\)
Solve it further as,
\({x^2+3x-10}=0\)
To solve the above quadratic equation, use the split the middle term method as,
\({x^2-2x+5x-10}=0\\x(x-2)+5(x-2)=0\\(x-2)(x+5)=0\)
Equating both the factor to the zero, we get the value of the x as -5 and 2.
For the exponential equation, having variable x as superscript equation has solution as,
\(x=-5,2\)
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tricia made 56% on her science test. if she got 14 problems correct, how many questions were on the test
Simplify 6.4k + 2.8 – 0.75 + 1.8k.
Answer:
8.2k +2.05
Step-by-step explanation:
A) NO CHANGE
B) factors, such as altitude and weather,
C) factors such as, altitude and weather,
D) factors, such as altitude and weather
The correct choice according to the given passage is to factors, such as altitude and weather. The correct option is B.
Given a passage which is shown in the attached images.
Option B is the best answer. The comma is correctly positioned after the nouns "factors" and "weather," which separate information that may be useful but is not necessary to comprehend the statement.
Options other than B are A, C and D are incorrect. Option A Choice A is incorrect because commas are needed to set off the nonrestrictive phrase. Option C is incorrect because the first comma is misplaced. Option D is incorrect since "weather" needs to be followed by a comma.
Hence, the correct choice from the given passage is to factors, such as altitude and weather.
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how do you (experimentally) find the surface area of a pear?
Answer:
That's like saying "How do you (hypothetically) write a letter?"
Step-by-step explanation:
But you would probably have to measure the length, height, and width of this experimental pear and go from there.
Then plug your length, width, and height into your surface area formula.
It is also important to know where in the pear you are measuring. The top of the pear will have different measurements than the middle.
Solve the 1-dimensional heat equation problem. əzu ди ət u (0,t) u (x,0) 2 Əx2 u (5,t) = 0, for t > 0 f (x) = -4 sin (TX) + 3 sin (27x), for 0 < x < 5
To solve the given 1-dimensional heat equation problem, we can use the method of separation of variables. The problem is defined as follows:
Partial Differential Equation (PDE): ∂u/∂t = α^2 ∂^2u/∂x^2, for t > 0 and 0 < x < 5.
Boundary conditions:
1. u(0, t) = 0
2. u(5, t) = 0
Initial condition: u(x, 0) = f(x) = -4 sin(Tx) + 3 sin(27x), for 0 < x < 5.
To solve this problem, perform the following steps:
1. Assume a solution in the form u(x, t) = X(x)T(t).
2. Substitute this solution into the PDE and separate the variables.
3. Solve the resulting ordinary differential equations (ODEs) for X(x) and T(t) subject to the given boundary conditions.
4. Obtain the general solution by summing the product of the separated solutions X_n(x)T_n(t) with appropriate coefficients.
5. Determine the coefficients by applying the initial condition and using Fourier series representation.
Since the problem is well-posed, a unique solution exists.
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1= 452 = 6x + 153= 2x + 5
Answer:
Your answer is 8x+607
Step-by-step explanation:
Parralel lines cut by a transversal coloring activity. Please give explanation. Will give brainiest.
Step-by-step explanation:
Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.
What is the order of the reaction with respect to A?
From the question, the order of reaction is second order for A
What is the order of reaction?
The rate of a second-order reaction is exactly proportional to the product of the concentrations of the two reactants or to the square of the concentration of a single reactant. Depending on the particular reaction and its stoichiometry, the rate equation for a second-order reaction can take on several shapes.
Studying reaction kinetics, figuring out reaction processes, and planning and optimizing chemical reactions all depend on understanding the order of events.
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What is 576/9 simplified?
Answer:
It is 64. Pls mark me as brainliest.
Step-by-step explanation:
You divide.
576÷9=64
576÷9
9÷9=1
64/1
or
64
There both the same.
Answer:
Reduce 576/9 to lowest terms
The simplest form of
576 /9 is 64/1
Step-by-step explanation:
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 576 and 9 is 9
Divide both the numerator and denominator by the GCD
576 ÷ 9
9 ÷ 9
Reduced fraction:
64 /1
Therefore, 576/9 simplified to lowest terms is 64/1.
Find The Slope of Each Line
Answer: 2/8 first answer, 6/2 second answer, 3/2 last answer
Step-by-step explanation: The slope should be the rise over the run, so the answer to the first question would be 2/8 which is rise/run which equals the slope the second answer would be 6/2=slope and the the answer to the last question is 3/2 you start from one point, rise until you get next to the other point on the graph, then you run until you get on that point, the you count your rise which will be the top number of your fraction and then you count your run which will be the bottom number of your fraction. I hope this helped if you could even make sense of all of this.
Please help!! this is due TODAY!
A. I only
B. II only
C. II and III only
D. I, II, and III
I do appreciate the help!
someone pls help
asap
ty :)
Answer:
56%
Step-by-step explanation:
We know that there are 6 groups of 6 and 4 groups of 5.
6x6 = 36
4x5 = 20
Add them up. 36 + 20 = 56.
Add the percent sign for 56%.
Answer:
56%
Step-by-step explanation: