Answer:
The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 11&5 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$4 \& 1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$$[/tex]
Step 2 of 2
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$$y-y_{1}=m\left(x-x_{1}\right)$$[/tex]
Substitute 2 for [tex]$m, 1$[/tex] for [tex]$x_{1}$[/tex], and 5 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]$$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$$[/tex]
This is the required linear equation.
Justin's rice ball recipe uses 100 grams of rice to make 1 rice ball. Justin has 700grams of rice.
How many rice balls can Justin make with 700 grams of rice?
The number of rice balls Justin can make with 700 grams of rice is 7.
How many rice balls can Justin make?
In order to determine the rice balls he can make, divide the grams of rice he has by the grams needed to make one rice ball. Division is the process of grouping a number into equal parts using another number.
Rice balls he can make = 700 grams / 100 grams = 7
To learn more about division, please check: https://brainly.com/question/13281206
#SPJ1
Answer:
7 rice balls
Step-by-step explanation:
Which expression can be used to find the difference of the polynomials? (4m – 5) – (6m – 7 2n) (4m – 5) (6m 7 2n) (4m – 5) (–6m 7 2n) (4m – 5) (–6m – 7 – 2n) (4m – 5) (–6m 7 – 2n)
Every weekend me and my brother and my cousin go outside to play basketball and when i was the one who will shoot the ball to the ring i used the things i learned in math so I use SOH-CAH-TOA in measuring it. I want to measure the distance between me and the basketball ring. Supposed the height of the ring is 8ft from the ground and the distance between me and the basketball ring horizontally is 11.5 ft, and the angle of elevation from the ground is 50 degrees, now what is the distance of me and the ring?
Let x be the distance between me and the ring
need urgent answers with equation
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
1) Since we know two of the sides of that right-angled triangle, we can use the Pythagorean Theorem to find x. His theorem is: [tex]c^2 = a^2 + b^2[/tex].
Substitute the values into the formula above.
Let x = c
[tex]c^2 = 8^2 + 11.5^2\\c^2 = 196.25\\c= \sqrt{196.25}\\c=14[/tex]
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Here is the completed table:
Hours Weeks
168 1
1008 6
840 5
How to complete the table?The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.
1008 hours to weeks = 1008 / 168 = 6 weeks
5 weeks to hours = 5 x 168 = 840 hours
To learn more about division, please check: https://brainly.com/question/194007
#SPJ1
A student received test grades of 83, 90, and 88. What was her grade on a fourth test if the average for the four tests is 84
Her grade on a fourth test is 75.
The average of e for the four tests is 84.
By substituting the given data in the equation, we get
Let the fourth test marks be x
83 + 90 + 88 + x / 4 = 84
261 + x / 4 = 84
261 + x = 336
x = 336 - 261
x = 75
An average may be described as the sum of all numbers divided by means of the whole quantity of values.
A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.
Learn more about mean here: https://brainly.com/question/20118982
#SPJ4
what would be the right answer to 71,526 + 262
Answer:
71,788
Step-by-step explanation:
7 1 5 2 6
+ 2 6 2
____________
7 1 7 8 8
Which function has an average rate of change of -4 over the interval [-2,2]?
Only p(x) has an average rate of change of -4 over [-2, 2].
Find the average rate of change of each given function over the interval [-2, 2]]:
The average rate of change of m(x) over [-2, 2]:
What is the average rate?The average rate of change = [tex]\frac{m(b)-m(a)}{b-a}[/tex]
Where, a = -2, m(a) = -12
b = 2, m(b) = 4
Plug the values into the equation
The average rate of change
[tex]=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}[/tex]
The average rate of change = 4
The average rate of change of n(x) over [-2, 2]:
The average rate of change = [tex]\frac{n(b)-n(a)}{b-a}[/tex]
Where, a = -2, n(a) = -6
b = 2, n(b) = 6
Plug the values into the equation
The average rate of change
[tex]=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}[/tex]
The average rate of change = 3
The average rate of change of q(x) over [-2, 2]:
The average rate of change = [tex]\frac{q(b)-q(a)}{b-a}[/tex]
Where, a = -2, q(a) = -4
b = 2, q(b) = -12
Plug the values into the
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
= [tex]\frac{-16}{4}[/tex]
The average rate of change = -2
The average rate of change of p(x) over [-2, 2]:
The average rate of change = [tex]\frac{p(b)-p(a)}{b-a}[/tex]
Where, a = -2, p(a) = 12
b = 2, p(b) = -4
Plug the values into the equation
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
[tex]=\frac{-16}{4}[/tex]
The average rate of change = -4
The answer is D.
Only p(x) has an average rate of change of -4 over [-2, 2].
To learn more about the average rate of visit:
https://brainly.com/question/8728504
#SPJ1
if k = √(49 - 12√5), then find the value of k +2
Step-by-step explanation:
k = √(49 - 12√5)
= √(45 + 4 - 2 √180)
= √45 - √4
= 3 √5 - 2.
So, k + 2 = 3 √5 - 2 + 2 = 3 √5.
Answer:
k + 2 = 3√5
Explanation:
[tex]\sf Given: k = \sqrt{49 - 12\sqrt{5} }[/tex]
[tex]\sf \rightarrow k = \sqrt{49 - 12\sqrt{5} }[/tex]
step 1: breakdown
[tex]\sf \rightarrow k = \sqrt{4 + 45- 2 \times 2 \times 3 \sqrt{5} }[/tex]
step 2: rewrite 45 = (3√5)²
[tex]\sf \rightarrow k = \sqrt{4 + (3\sqrt{5})^2 - 2 \times 2 \times 3 \sqrt{5} }[/tex]
step 3: rearrange as per a² -2ab + b² = (a - b)²
[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5})^2 - 2 \times 3 \sqrt{5} \times 2 +2^2}[/tex]
step 4: comparing, here: a = 3√5, b = 2
[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5} -2)^2}[/tex]
step 5: simplify √a² = a
[tex]\sf \rightarrow k = 3\sqrt{5} -2[/tex]
Then find k + 2
[tex]\rightarrow \sf k = 3\sqrt{5} -2 + 2[/tex]
[tex]\rightarrow \sf k = 3\sqrt{5}[/tex]
Use the data in the table below and a graphing calculator to describe how a linear model compares to a quadratic model. Analyze the "parameters" (as they are called in Desmos) a, b, c for the quadratic model and m & b for the linear model. Write a sentence or two that explains why both graphs look the same, even if you zoom out very far.
PLEASE HELP ME
The quadratic model and the linear model of the table of values are the same
The linear model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 0Sum of Y = 113Mean X = 0Mean Y = 22.6Sum of squares (SSX) = 10Sum of products (SP) = 28The regression equation is
y = mx + b
Where
m = SP/SSX = 28/10 = 2.8
b = MY - bMX = 22.6 - (2.8*0) = 22.6
So, we have:
y = 2.8x + 22.6
See attachment for graph (1)
The quadratic model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
a = 0b = 2.8c = 22.60 X^2 +2.8 X +22.6
The regression equation is
y = ax^2 + bx + c
So, we have:
y = 0x^2 + 2.8x + 22.6
See attachment for graph (1)
Why both graphs look the sameThe graphs look the same because when the quadratic model is simplified, it gives the linear model.
This in other words mean that:
The quadratic model and the linear model of the table of values are the same
Read more about regression at:
https://brainly.com/question/7656407
#SPJ1
In triangle ABC, < a =25
The measures of the remaining side lengths of the triangle, AC and BC is 72 units and 31 units respectively.
Angle B of the triangleB = 180 - (25 + 55)
B = 100⁰
Length of side ACsin (B)/AC = sin (C)/AB
sin (100)/AC = sin (55)/60
sin (100)/AC = 0.01365
AC = sin (100) / (0.01365)
AC = 72 units
Length side BCsin (A)/BC = sin (C)/AB
sin (25)/BC = sin (55)/60
sin (25)/BC = 0.01365
BC = sin (25) / (0.01365)
BC = 31 units
Thus, the measures of the remaining side lengths of the triangle, AC and BC is 72 units and 31 units respectively.
The complete question is below:
In triangle ABC angle A= 25, angle C= 55 and length AB = 60 . What are the approximate measures of the remaining side lengths of the triangle?
Learn more about length of triangles here: https://brainly.com/question/2217700
#SPJ1
Answer: A
Step-by-step explanation: edge2023
Help me please in this question
Answer:Answer
Step-by-step explanation:
For the first part, divide 46.54 by 5.2
46.54/5.2=8.95
$8.95 per pound
For the second part if he buys half as much, its half of 5.2 plus 5.2. Now use similar steps that I used in the first part to solve for your problem.
I got $97.50, but i am not 100% sure if it is correct, so try give it a try.
why is it important to learn valid proportions
Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. B. C. D.
The approximate solution to the given system of equations, considering the graph, is given as follows:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex].
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Answer:
d
Step-by-step explanation:
I am studying geometry this summer but can’t solve this question what would be the correct answer
Answer: F
Step-by-step explanation:
Bisectors of an angle split the angle in half which you can visually see from the image. So, the answer is F.
Which phrases describe the graph of f(x) = |x| ? Check all that apply
The phrases which describe the graph are;
The domain of the graph is the set of all real numbers.The range of the graph is the set of all real numbers greater or equal to zero.The graph in the task content is increasing over the interval (0, ∞).The graph in the task content is decreasing over the interval (-∞, 0).What is the graph of the absolute function?The absolute function in the task conten is;
f(x) = |x|, Hence, the domain and range of the graph are as described above.
Read more on absolute function;
https://brainly.com/question/2473412
#SPJ1
is the number there three? if you answer to me i will give you twenty Points.
Answer:
2
Step-by-step explanation:
3 x 2 = 6
1 x 2 = 2
hope it helps
sorry if I'm wrong
The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is
The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is 116.
Given margin of error of 2,probability of 0.95 and standard deviation is 11.
We have to calculate the sample size needed to provide a margin of error of 2 or less with a 0.95 probability when the population standard deviation of 11.
We know that the margin of error is the difference between the calculated values and actual values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is z value ,σ is standard deviation ,n is the sample size.
First we have to calculate the z value for the corresponding p value which is given of 0.95. We assume that the test is two tailed. z value is 1.96.
Now put the value of z , σ, n and margin of error in the formula of margin of error to get the value of n which is sample size.
2>=1.96*11/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]>=(1.96*11)/2
[tex]\sqrt{n}[/tex]>=10.78
By squaring both sides we get,
n>=116.2064
Hence the sample size which is needed to provide a margin of error of 2 or less with a 0.95 probability when the population standard deviation equals 116.
Learn more about margin of error at https://brainly.com/question/10218601
#SPJ4
A 2-column table with 5 rows. Column 1 is labeled Number of chores, x with entries 2, 4, 6, 8, 10. Column 2 is labeled Days, y with entries 1, 2, 3, 4, 5. The table shows the number of days required to perform a given number of chores. The number of days varies directly with the number of chores. What is the constant of variation? 2 3 One-half One-third\
The constant of variation based on the information is one half.
How to illustrate the information?From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.
This will be illustrated as:
y = kx
when y = 1, x = 2.
1 = 2k
Divide both side by 2.
k = 1/2
Therefore, the constant of variation is 1/2.
Learn more about constant of variation on:
brainly.com/question/25215474
#SPJ1
A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18)? a It has the same slope and the same y-intercept. b It has the same slope and a different y-intercept. c It has the same y-intercept and a different slope. d It has a different slope and a different y-intercept.
The way that this linear function compares to y+11 is that It has the same slope and the same y-intercept.
What is a linear function?This is the type of function that would produce a line when it is graphed out.
When we write out the equations in 1 and 2 we would see that they are basically the same type of equation. A linear equation is made up of the slope and the intercept.
Read more on linear equation here:
https://brainly.com/question/14323743
#SPJ1
Answer:
A) It has the same slope and the same y-intercept.
Step-by-step explanation:
I really hope this helps.
PLEASE help answer all 5 questions
[tex]p(r) = \frac{2}{9} [/tex]
2)We have 3 blue marbles and 9 marbles in total, so the probability of drawing a blue marble, is the number of blue marbles over the total number of marbles.[tex]p(b) = \frac{3}{9} = \frac{1}{3} [/tex]
3)Since we put the marbles back, the sample space stays 9 balls,so we have to multiply the probability of drawing a red marble then a blue one. Since order matters (red before blue) we do not account for permutations.4)Putting the marbles back in the bag makes this these events independent, as the sample space does not change.5)[tex]p(r \: then \: b) = \frac{2}{9} \times \frac{1}{3} = \frac{2}{27} [/tex]Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.
Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ
would rlly appreciate ur help
From the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.
What are congruent angles?Congruent angles are defined as angles with equal measure. According to the question,
m ∠LOM = m ∠JKI (given congruent angles) _____(1)
m ∠MON = m ∠IKH (given congruent angles) _______(2)
Add both the side angle m ∠MON in (1) we get m ∠LOM + m ∠MON = m ∠JKI + m ∠MON
Replace angle m ∠MON = m ∠IKH from (2) on right-hand side we get,
m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH ____(3)
m ∠LOM + m ∠MON = m ∠LON ( M is the interior point of ∠LON) ___(4)
m ∠JKI + m ∠IKH = m ∠HKJ ( I is the interior point of ∠HKJ) ___(5)
Form (3), (4), and (5) we get, m ∠LON = m ∠HKJ (Congruent angles)
Hence, from the given condition it is proved that m ∠LON = m ∠HKJ, are congruent angles.
Learn more about congruent angles on:
brainly.com/question/24887947
#SPJ1
Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
34 feet
23 feet
Answer: [tex]42.6^{\circ}[/tex]
Step-by-step explanation:
Let the angle of depression be x.
[tex]\sin x=\frac{23}{34}\\\\x=\sin^{-1} \left(\frac{23}{34} \right) \approx 42.6^{\circ}[/tex]
A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s. How many possible sequences of rolls could there have been
The possible sequences of rolls could there have been Sequence = 120
Given
6 rolls of a die;
Required
Determine the possible sequence of rolls
From the question, we understand that there were three possible outcomes when the die was rolled;
The outcomes are either of the following faces: 1, 2 and 3
Total Number of rolls = 6
Possible number of outcomes = 3
The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;
Sequence = \frac{6!}{3!}
Sequence = \frac{6 * 5 * 4* 3!}{3!}
Sequence = 6 * 5 * 4
Sequence = 120
Hence, there are 120 possible sequence.
Learn more about Sequences:
https://brainly.com/question/12246947
#SPJ4
Two of them are drawn simultaneously from a deck of 48 cards.
Calculate the probability that:
a) both are cups
b) At least one cup
c) One is a cup and the other is a sword
The required probability is
a) both are cups is 0.05
b) At least one cup is 0.19
c) One is a cup and the other is a sword is 0.06
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
a) for both are cups
P= 12*11/48*47
p = 0.05
b) for At least one cup
p = 12*36/48*47
p = 0.19
c) for One is a cup and the other is a sword
p = 12*12/48*47
p = 0.06
Thus, the required probability is 0.05, 0.19, 0.06
Learn more about probability here:
brainly.com/question/14290572
#SPJ1PLEASE HELP ME ASAP. I REALLY NEED THIS DONE
Answer:
x = 65
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
x² = 25 × 169 = 4225 ( take square root of both sides )
x = [tex]\sqrt{4225}[/tex] = 65
The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 36 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 98% confidence interval for the mean gas mileage for this car model.
The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.
The confidence interval of statistical data is computed using the formula:
[tex](\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})[/tex]
where [tex]\overline{x}[/tex] is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.
In the question, the sample size (n) = 36, the mean of the sample ([tex]\overline{x}[/tex]) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.
The confidence interval given to us is 98%.
Z-score corresponding to this (Z) = 2.33.
Thus, the confidence interval can be calculated as:
(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})
= (28.4 - 2.33,28.4 + 2.33)
= (26.07,30.73).
Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Learn more about constructing confidence intervals at
https://brainly.com/question/17030704
#SPJ4
Which equation is equivalent to log3 (x+5) = 2 ?
Answer:
the anwer is x= -3
Step-by-step explanation:
(3+5)=2
Which graph has the same end behavior as the graph of f(x)=x⁴+x³-x²-x
Using limits, a graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].
What is the end behavior of a function?It is given by it's limits as x goes to negative and positive infinity.
In this problem, the function is:
[tex]f(x) = x^4 + x^3 - x^2 - x[/tex]
The limits are:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow -\infty} x^4 = (-\infty)^4 = \infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow \infty} x^4 = (\infty)^4 = \infty[/tex].A graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].
More can be learned about limits and end behavior at https://brainly.com/question/27830331
#SPJ1
the sum of seven odd consecutive is 217. Find the middle number
Answer:
x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 =217
7x+21=217
7x=196
x=28
Middle Number will be:
x+3
28+3
=31
Therefore, the middle number is 31.
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
Let's put this into equation form.
n + (n + 1) + (n+2) + (n+3) + (n+4) + (n + 5) + (n+6) = 217
Each number is increasingly getting farther away from n (the first number) by 1.
If we simplify, by adding all of the numbers and the n's. We get:
7n + 21 = 217
Let's subtract 21 from both sides to start the process of isolating x.
7n = 196
Now we can divide both sides by 7, to isolate x.
n = 28.
That looks like the answer, but it is not. Remember n is the first number, we want the middle, which out of 7 is the 4th number.
The 4th number is equal to (n+3) or (28 + 3)
The 4th number is 31.
Let's check if this is correct.
28 + 29 + 30 + 31 + 32 + 33 + 34 = 217.
The problem is complete.
Geometry help please
7
Answer:
you should download AIR MATH