How can you write the equation for a linear function if you know only two ordered pairs for the function?
Use the two ordered pairs to find the slope, m. Then substitute m and one set of ordered pairs into y=mx+b, solve for b.
Find the y-intercept. Then use an ordered pair and the y-intercept to find the slope
Find the x-intercept, Then use an ordered pair and the x-intercept to find the slope.
Answers
Finding the x-intercept is not necessary to write the equation for a linear function, as the x-intercept corresponds to the value of x when y is equal to zero.
To write the equation for a linear function using two ordered pairs, you can follow the method of finding the slope (m) and substituting it, along with one set of ordered pairs, into the equation y = mx + b to solve for the y-intercept (b).
Find the slope (m):
Calculate the slope using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two ordered pairs given.
Substitute slope and one set of ordered pairs into the equation:
Using one of the ordered pairs (let's say (x₁, y₁)), substitute the values into the equation y = mx + b:
y₁ = m * x₁ + b
Solve for the y-intercept (b):
Rearrange the equation to solve for b:
b = y₁ - m * x₁
By following these steps, you can find the equation for the linear function in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Finding the x-intercept is not necessary to write the equation for a linear function, as the x-intercept corresponds to the value of x when y is equal to zero. It is more common to find the y-intercept and use it along with the slope and an ordered pair to write the equation.
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Related Questions
How many terms are in this expression?
6q + 7r
Answers
Answer:
3 terms
Step-by-step explanation:
A block is released from rest and slides down a frictionless ramp inclined at 30 degrees from the horizontal. When the block reaches the bottom, the Earth-block system has mechanical energy E0. The experiment is repeated, but now horizontal and vertical forces of magnitude F are exerted on the block as is slides, as shown above. When the block reaches the bottom, the mechanical energy of the Earth-block system...
A) greater than E0
B) equal to E0
C) less than E0
D) cannot be determined without knowing F
Answers
When horizontal and vertical forces of magnitude F are exerted on the block as it slides down the frictionless ramp, the mechanical energy of the Earth-block system at the bottom will be less than E0.
The mechanical energy of a system is the sum of its kinetic energy and potential energy. In this case, as the block slides down the ramp, its potential energy decreases and is converted into kinetic energy. The presence of the horizontal and vertical forces implies that work is done on the block, adding additional energy to the system. This extra energy increases the block's kinetic energy, resulting in a higher speed at the bottom of the ramp. Since kinetic energy is directly proportional to the square of the velocity, a higher speed means a greater kinetic energy.
Therefore, with the additional forces applied, the mechanical energy of the Earth-block system at the bottom will be greater than the mechanical energy E0, making option A) "greater than E0" the correct choice.
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solve the triangle give the measure of angle G
Answers
Answer:
G = 46 degrees
Step-by-step explanation:
Here, we want to find the measure of angle G
Mathematically, as we can see, what we have is a right triangle
For a right triangle , the sum of angles is 90 degrees
Thus, if we add the two internal angles, we get 90 degrees
Hence;
44 + G = 90
G = 90-44
G = 46 degrees
Suppose we have a loaded die that gives the outcomes 1 through 6 according to the following probability distribution. Pips Showing 1 2 3 4 5 6 Probability 0.1 0.2 0.3 0.2 ? 0.1 Find the probability of rolling a 5.
Answers
The probability of rolling a 5 is 0.1.
To find the missing probability for rolling a 5, we can use the fact that the sum of all probabilities for all possible outcomes must equal 1.
Let's calculate the missing probability:
1. Sum the probabilities of the given outcomes: 0.1 + 0.2 + 0.3 + 0.2 + 0.1 = 0.9.
2. Subtract the sum from 1 to find the missing probability: 1 - 0.9 = 0.1.
Therefore, the missing probability for rolling a 5 is 0.1 or 10%.
Here are the steps summarized:
1. Calculate the sum of the given probabilities: 0.1 + 0.2 + 0.3 + 0.2 + 0.1 = 0.9.
2. Subtract the sum from 1 to find the missing probability: 1 - 0.9 = 0.1.
This approach ensures that the probabilities for all possible outcomes in the probability distribution add up to 1, as required. In this case, the sum of all probabilities is 0.9, so the missing probability for rolling a 5 is the remaining 0.1 or 10% needed to reach a total probability of 1.
Hence, the probability of rolling a 5 is 0.1 or 10%.
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Find three consecutive positive integers such that the product of the second integer and the third integer is 20.
Answers
The product of the second integer 4, and the third integer 5, is equal to 20.
The questions asks for three consecutive positive integers. Therefore the first integer of the sequence is 3.
HELP ME PLEASEE Select all of the following that could be classified as a Perfect Square Trinomial.
Answers
Son el B el C y el E
F your f-obtained = 12.98, with dfb =2, dfw=20, alpha = 0.05, you would conclude that (check all that apply, only those that apply):
Answers
The correct answer is on the provided information (F-obtained = 12.98, dfb = 2, dfw = 20, alpha = 0.05)critical F-value.
To provide a conclusion based on the given information, we need to compare the obtained F-value with the critical F-value for the given degrees of freedom (dfb = 2, dfw = 20) and the significance level (alpha = 0.05). Without the critical F-value, it is not possible to determine the conclusion. Please provide the critical F-value, or any additional information, to proceed with the analysis and draw a conclusion.
In order to draw a conclusion based on the given information, we need to conduct an analysis using the F-test. Here are the steps to interpret the results:
The obtained F-value (F-obtained) is given as 12.98.
The degrees of freedom between groups (dfb) is 2, and the degrees of freedom within groups (dfw) is 20.
The significance level (alpha) is 0.05.
To draw a conclusion, we compare the obtained F-value with the critical F-value at the given significance level. The critical F-value is determined by the degrees of freedom and the significance level.
If the obtained F-value is greater than the critical F-value, we reject the null hypothesis and conclude that there is a significant difference between the groups. If the obtained F-value is less than the critical F-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the groups.
However, without the critical F-value, it is not possible to determine the specific conclusion based on the provided information. Please provide the critical F-value, or any additional information, so that I can assist you further in interpreting the results.
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PLease help me ,really need help with explanation
Answers
a)
Check the picture below.
b)
volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.
Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.
Now, what's the ratio of the tiny pyramid to the truncated bottom?
\(\stackrel{\textit{\Large Volumes}}{\cfrac{\textit{small pyramid}}{\textit{frustum}}\implies \cfrac{~~\frac{1}{8}whole ~~}{\frac{7}{8}whole}}\implies \cfrac{~~\frac{1}{8} ~~}{\frac{7}{8}}\implies \cfrac{1}{8}\cdot \cfrac{8}{7}\implies \cfrac{1}{7}\)
Please help 8th grade math
Answers
Answer:
1500 calories
Step-by-step explanation:
2400 is 100% of in this case, 8/8
So then we know that 1/8 of 2400 is 300 because we just divide it by 8. Sarah eats 5/8 that much so we multiply 300 by 5 which gives us 1500
Answer:
2400 x 5/8 = 1500
Step-by-step explanation:
Just multiply the fraction they gave u
What is the answer to this question?
Answers
Answer:
≈ 3.9 miles
Step-by-step explanation:
The third angle in the triangle is
180° - (53 + 78)° = 180° - 131° = 49°
Using the Sine rule in the triangle with distance from 2 being x, then
\(\frac{3}{sin49}\) = \(\frac{x}{sin78}\) ( cross- multiply )
x × sin49° = 3 × sin78° ( divide both sides by sin49° )
x = \(\frac{3sin78}{sin49}\) ≈ 3.9 ( to the nearest tenth )
Jessica ran on the track team at her school. She finished a 200-meter race in 54 seconds.
• What was Jessica’s average speed, in meters per second, for the 200-meter race? Show your work and round your answer to the nearest tenth of a meter.
Answers
Answer:
3.7 meters per second
Step-by-step explanation:
200m/54 secs
you want to find the meters per second so you divide by the number of seconds so 200/54 = 3.7037037 or 3.7 meters per second
EVERYTHING IS IN THE PICTURE!
Answers
Answer:
The answer is B From my calculations
what’s the answer to the question
Answers
The given sequence's nth-term rule is 2 + 7n.
The first term in this series is nine, and the following term is sixteen. 16 - 9 = 7 is the difference between these two terms.
The common difference (d) is thus 7.
Now, we may apply the nth term of an arithmetic formula.
sequence:
\(a_n = a_1 + (n-1)d\)
where:
\(a_n\) = the nth term
\(a_1\) = the first term
d = the common difference
n = the number of the term we want to find
Substituting the values we have:
\(a_n\) = 9 + (n-1)7
Simplifying:
\(a_n\) = 9 + 7n - 7
\(a_n\) = 2 + 7n
The nth-term rule for this arithmetic sequence is as follows:
\(a_n\) = 2 + 7n
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Shanti packs 4689 jelly beans equally into 15 bags and there are some jelly beans left. How many jelly beans are there left?
Answers
Answer:
hi !!
Step-by-step explanation:
you have to do an Euclidean division :
4689/15 = 312
the quotient is 312 so there will be 312 jelly beans per bags . The rest is 9 so there are 9 jelly beans left
Every quadrilateral that has exactly one pair of parallel sides
Answers
Answer:
False. This may be true with a trapezoid but not with a square or rectangle, seeing they have 2.
Step-by-step explanation:
Hope it helps! =D
If the scale factor of volumes of 2 similar shapes is 15.625
what will be the scale factors of lengths?
Answers
Answer:
If the scale factor is one, it means that corresponding sides are equal in length. In this case the shapes would be congruent (ie identical) rather than similar. They have the same shape, the same angles and the same size.
Step-by-step explanation:
Lines T U and R S intersect lines M N and P Q. Where line T U intersects with lines M N and P Q, right angles are formed. Lines M N and P Q are straight lines that are next to each other and they will never intersect. Lines T U and R S are next to each other and could intersect. Which two statements are both true?
Answers
c. Tu | MN and MN || PQ I am done with the interview
As an estimation we are told £3 is €4.
Convert £7.50 to euros.
Answers
Answer:
€5000
Step-by-step explanation:
Create an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six.
1.3 squared over 1.5 cubed
1.3 to the twenty-fourth power over 1.5 to the eighteenth power
1.5 cubed over 1.3 squared
1.5 to the eighteenth power over 1.3 to the twenty-fourth power
Answers
The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.
How to explain the expressionHere are the steps to simplify the expression:
Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.
Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.
Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.
Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.
Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.
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Find m/G.
F
150°
H
G
Answers
The measure of angle G is 121 degrees and this can be determined by using the sum of interior angle properties.
What is sum of interior angles?
Sum of interior angles is calculated using the formula (n 2) 180, where is the total number of sides. In a regular polygon, each inside angle is the same. Interior angle of a polygon is equal to the sum of interior angles divided by the number of sides, according to the following formula. One of the first things we all learned about triangles was that the sum of the internal angles is 180 degrees.
Given :
Triangle FHG
Angle F = (x - 5) degreesAngle G = (3x + 25) degreesAngle H = (x) degreesApplying the sum of interior angles property on the triangle FHG. According to the sum of interior angles property:
\($$\angle \mathrm{F}+\angle \mathrm{H}+\angle \mathrm{G}=180^{\circ}$$\)
Now, substitute the values of the known terms in the above equation.
\($$(x-5)+(x)+(3 x+25)=180$$\)
Simplify the above equation In order to determine the value of ' $x$ '.
\(& 5 x+20=180 \\\)
\(& 5 x=160 \\\)
\(& \mathbf{x}=\mathbf{3 2} \text { degrees }\)
So the angle\($\mathbf{G}$\) is given by:
\(& \angle \mathrm{G}=3(32)+25 \\\)
\(& \angle \mathrm{G}=121^{\circ}\)
The complete question is,
What is m∠G ?
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What is the value of a, if the graphs of 3y + x = 0 and 4y + ax + 3 = 0 are to meet at a right angle?
Answers
Answer:
a = -12
Step-by-step explanation:
For two lines to meet at a right angle, they are perpendicular to each other. Therefore the product of the slopes of the two lines is -1.
The slope of 3y + x = 0 will be -1/3 (rearrange the terms, 3y = -x and therefore y = -1/3 x).
The slope of 4y + ax + 3 = 0 will be -a/4. (4y = -ax - 3, therefore y = -a/4 x - 3/4)
Since the product of the slopes is -1, we can set up an equation now.
-1/3 * -a/4 = -1
a/12 = -1
a = -12
Is it correct in adding subtracting?? Answer is in the picture please give me answer soon
Answers
Answer:
8/24 is correct. However, I would simplify 8/24 down to 1/3, since most teachers want you to do that.
a hospital management system records the wait times for patients checking into the emergency room. based on the records of the management system, the hospital administrator would like to test the claim that the average wait times for patients checking into the emergency room is different than 45 minutes. if the z− test statistic was calculated as z
Answers
To test the claim that the average wait times for patients checking into the emergency room is different than 45 minutes, a z-test statistic can be calculated.
The z-test is used when the population standard deviation is known. To calculate the z-test statistic, you would need the sample mean, sample size, population mean, and population standard deviation. From the given information, the z-test statistic is represented as z. To determine whether the average wait times are significantly different from 45 minutes, you would compare the calculated z-test statistic to the critical value from the standard normal distribution. If the calculated z-test statistic falls outside the critical value range, it indicates that the average wait times are significantly different from 45 minutes. In conclusion, the hospital administrator can use the z-test statistic to test the claim that the average wait times for patients checking into the emergency room is different than 45 minutes. By comparing the calculated z-test statistic to the critical value, they can determine whether the claim is statistically significant or not.
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4 pont possible Submit fast In a nudom sample of ten cell phones, the meantimetal price was, and the word deviation $100 A the per te dwie to trade mayo del 99% condencenter for the population in Interpret this Identity then How to reduce place as wed) Construct 90% confidence were the Pourd to come and Interpret the che conect choice and in the wood (Type an order and O Alicante de pation of cultures in the O Wincide casamento non condence and that these process that OD of random strom the others with OCW Vom OT po This question de possible Subs In a random sample of ten cellphones, the mean til retail pro W550600 and the started deviation was 51780 Armand few a confidence for the population means in the Identity the manner (Round to ane decimal place as treeded) Construct a 90% confidence oval for the population man 00 Round to be decimal placeased) Interpret the results Select the correct ce bw and the box com your cho Type an integrera decimal Deporound) O Garbe sad that the population of culle have fundet OB with confidence to sad that the phone ince of collebo OC with curice, cand that most collphones in the love cenderaan of all random samples of people from the population will be 0
Answers
In a random sample of ten cellphones, the mean till retail price was $550.60 and the standard deviation was $517.80. Following is the solution for the given problem: Confidence Interval Formula is given as follows: \(CI = X ± Z * σ/√n\) Where, CI is the Confidence Interval X is the Sample Mean
Z is the Confidence Levelσ is the Standard Deviation n is the Sample Size(a) To construct a 90% Confidence Interval for the population mean, we need to find the value of Z such that the Confidence Level is \(90%:90% = 0.9\) The area in the middle is 0.9, which leaves \(0.1/2 = 0.05\) probability in each tail.
The Confidence Interval is (216.12, 885.08). This means that we are 90% confident that the true population mean lies between $216.12 and $885.08. That is, if we take all possible random samples of size 10 from the population and construct a confidence interval for each.
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2.859 + 7.31
I have to line up the decimals
Answers
Answer: 10.169
Step-by-step explanation: To add decimals like this we have to line up them in order.
2.859
+
7.31 =
10.169
Above I have to line them up in order.
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
Find the volume of the rectangular prism
Answers
Answer:
V = 882 ft^3
Step-by-step explanation:
To find the volume of the rectangular prism, multiply the area of the base by the height.
V = Bh where B is the area of the base and h is the height.
V = 63*14
V = 882 ft^3
find the value of z?
Answers
What is the simplest form of ^4sqrt324x^6y^8
Answers
\(\rm{\green{Answer \: is:-}}\)
\(3xy \sqrt[24]{ {4x}^{2} } \)(3xy^2 4 sqrt 4x^2)
Step-by-step explanation:
Hope it's helpful to youLet's see
\(\\ \rm\Rrightarrow \sqrt[4]{324x^6y^8}\)
\(\\ \rm\Rrightarrow \sqrt{4}{18^2x^6y^8}\)
m√a^n=a^n/m\(\\ \rm\Rrightarrow 18^{2/4}x^{6/4}y^{8/4}\)
\(\\ \rm\Rrightarrow \sqrt{18}x^{3/2}y^2\)
\(\\ \rm\Rrightarrow \sqrt{18}\sqrt[2]{x^3}y^2\)
15x²y³z÷3xy² simplify
Answers
Answer:
\(5xyz\)
Step-by-step explanation:
\(\frac{15x^2y^3z}{3xy^2}\)
Step 1: Divide the numbers
\(\frac{15}{3}=5\\\\=\frac{5x^2y^3z}{xy^2}\)
Step 2: Simplify
\(\frac{x^2}{x}\\\\= x\\\\=\frac{5xy^3z}{y^2}\)
Step 3: Simplify
\(\frac{y^3}{y^2} = y\\\\=5xyz\)
Therefore, the simplified answer is \(=5xyz\)
Answer:
5x^3 y^5 z
Step-by-step explanation:
See the steps below:)
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given trapezoid ABCD, find the length of THE EF:
possible answers:
EF=11
EF=20
EF=16
EF=22
Answers
The length of EF in the trapezoid ABCD is 22.In a trapezoid, the sides parallel to each other are called bases.
In a trapezoid, the sides parallel to each other are called bases. Let's assume that AB is the longer base and CD is the shorter base. EF is one of the legs of the trapezoid, perpendicular to the bases.To find the length of EF, we can use the properties of a trapezoid. Since EF is perpendicular to the bases, it is also parallel to the other leg of the trapezoid. Therefore, EF is equal in length to the side parallel to it.Among the given options, EF = 22 is the only answer that matches this property. Therefore, the length of EF in the trapezoid ABCD is 22.
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