The solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
Let d = [tex](2a^{2} +29a + 65, a+ 13)[/tex]
Now, we can split [tex]2a^{2} + 29a + 65[/tex] in the following way, so that it becomes easier to factorise.
[tex]2a^{2} + 29a + 65 = (2a^{2} + 29a + 39) + 26[/tex]
From this, we can quantify and notice that -13 is one root of this equation, while the other root is -3/2.
Therefore, [tex]2a^{2} + 29a + 39 = (a+13)(2a+3)+26[/tex]
Thus, [tex]d = ((a+13)(2a+3)+26, a+ 13)[/tex]
The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF).
Now, we can use Euclid's Algorithm.
[tex]= gcd (2a^{2} + 29a + 65, a + 13)\\= gcd (2a^{2} + 29a + 65 - 2a(a+13), a+13)\\= gcd (3a + 65, a + 13)\\= gcd (3a + 65 - 3a(a+13), a+13)\\= gcd (26, a + 13)[/tex]
This is necessarily 1, 2, 13, or 26, which we can see by just looking at the first term. By factoring 1183 and considering that [tex]a[/tex] is an odd multiple, then we should be able to conclude the answer.
Hence, the conclusion is that the solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
A number line from -5 to 10.
1. Using only addition, write an expression that represents Rebecca's score after these three turns. (Remember that she starts at an energy level of 4.). (2 points)
2. What is Rebecca's energy level after Turn 1? (2 points)
3. What is Rebecca's energy level after Turn 2? (3 points)
4. What is Rebecca's energy level after Turn 3? Will she earn bonus points after Turn 3? Explain why or why not. (3 points)
In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is
= 4 + (-6) + (8) + (-1)
Rebecca's energy level after Turn 1 = -2
Rebecca's energy level after Turn 2 = 6
Rebecca's energy level after Turn 3 = 7
she will not earn bonusHow to find the expression that represents Rebecca's scoreFollowing the rule of the video game the expression is written in steps below
Rebecca is currently at energy level 4
= 4
Turn 1: 6 trees cut
= 4 + (-6)
= 4 - 6
= -2
Turn 2: 8 trees planted
= 4 + (-6) + (8)
= -2 + 8
= 6
Turn 3: 1 tree cut
= 4 + (-6) + (8) + (-1)
= 6 - 1
= 7
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which expression can you use to find the number of ways to choose 5 cards from a 52-card deck? how many ways can you choose the 5 cards?
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52!/(47! * 5!).
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.
The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.
Order is irrelevant, therefore we utilize a combination (instead of a permutation)
We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)
so we obtain:
n C r = r!*(n-r)!/(n!)
52 C 5 = (52!)/(5!*(52-5)!)
52 C 5 = (52!)/((52-5)!*5!)
The complete question is:-
Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?
a) (52-5)! / 52!5!
b) 52! / (52-5)!
c) 52! / (52-5)!5!
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A town has three roads that form an obtuse triangle. James wants to set up a refreshment stand so that the shortest distance from his stand to each road is the same for all three roads. Where should he set up the refreshment stand?
A. on the centroid
B. on the circimcenter
C. on the incenter
D. on the median
James should set up the refreshment stand on the incentre of the obtuse triangle.
The incentre of a triangle is defined as the intersection between the angle bisectors of a triangle. The inradius is the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal.
The inradius is defined as the radius of an inscribed circle in the triangle. Therefore, the required shortest equal distance from his stand to each road so that the stand is at the same distance for all three roads is on the incentre.
Hence, the correct option is C.
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You are baking cookies. Each batch makes 24 cookies. You make x batches of cookies. but eat 5 cookies as you are bkaing. Write an expression for the number of cookies you have
My answer from brainly for part a : 24x-5
Is your answer to part a the same if you eat 5 cookies from each batch as you are baking? explain.
You make 3 batches of cookies to make bags for a sale. You put 5 cookies in each bag. Given 14(5)+2=3(24), what do the terms represent?
Answer: The answer to part a is the same if you eat 5 cookies from each batch as you are baking because the number of cookies you have is the product of the number of batches times the number of cookies per batch minus the number of cookies you eat.
In the expression 14(5) + 2 = 3(24)
14(5) represents the total number of cookies you put in 14 bags. (14 x 5) = 70
2 represents the number of cookies left after you have put 5 cookies in each of the 14 bags.
3(24) represents the total number of cookies you made from the 3 batches of cookies. (3 x 24) = 72
So the equation can be read as:
The total number of cookies you put in bags (70) plus the number of cookies left (2) is equal to the total number of cookies made from the 3 batches (72).
Step-by-step explanation:
toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help
The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:
3.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:
N = 3 x 2 x 1
N = 6.
(the first chosen has 3 possible options, the second has two and the third has one).
The six possible outcomes are given as follows, considering the order Red - Green - Blue:
Red - Green - Blue. (all end with theirs).Red - Blue - Green (one, the red, end with theirs).Green - Red - Blue (one, the blue, end with theirs).Blue - Red - Green (none end with theirs).Green - Blue - Red. (none end with theirs).Blue - Green - Red. (one, the green, end with theirs).Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.
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If you work 45 minutes a day for 90 days in row and add an additional 20 hours how many hours do you have?
seniors at a certain high school took a survey regarding future plans. all plan to attend college some time; however, 77% plan to go to college immediately following high school. of those who plan to attend college immediately following high school, 17% plan to major in math. of those who do not plan to attend college immediately following high school, 11% plan to major in math. what is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in math.
The probability that a randomly chosen senior does not plan to attend college right away and majors in math is 12.5%.
Step 1: Calculate the probability of not attending college immediately after high school:
100% - 77%
= 23%
Step 2: Calculate the probability of majoring in math among those who do not attend college right away: 11%
Step 3: Calculate the probability of not attending college right away and majoring in math:
11% / 23%
= 0.125
The probability of a randomly chosen senior not attending college immediately following high school and majoring in math can be calculated by first determining the probability of not attending college right away. This can be done by subtracting the percentage of seniors who plan to attend college immediately from 100%. This yields 23%. Then, the probability of majoring in math among those who do not attend college right away can be determined by taking the percentage of those who plan to major in math among this group, which is 11%. Lastly, the overall probability of not attending college right away and majoring in math can be calculated by taking the probability of majoring in math among those who do not attend college right away and dividing it by the probability of not attending college right away. This yields 11% / 23%, or 0.125.
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Simple and compound interest
1.mr. henry received his back pay from a work abroad and wanted to quit as an ofw. he received p150 000.00. he plans to invest it for 5 years. an abc bank offers him with 2% simple interest rate per year while the union bank offers him 2% compounded annually.
1. make an illustration of simple and compound interest
2.if you were mr. henry which offer will you choose and why?
Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.
1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.
Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.
Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:
Year 1: Interest earned is P3,000 (P150,000 x 2%).
Year 2: Interest earned is P3,000 ($150,000 x 2%).
Year 3: Interest earned is P3,000 ($150,000 x 2%).
Year 4: Interest earned is P3,000 ($150,000 x 2%).
Year 5: Interest earned is P3,000 ($150,000 x 2%).
Interest earned overall: P15,000
After five years, the total will be P150,000 plus P15,000, or P165,000.
Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:
Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.
Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.
Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.
Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.
Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.
Interest earned in whole was P15,612.12096.
2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.
Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .
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he length of a rectangle is 11/5 cm and its breadth is 13/5 cm. What, in sq. cm, is the area of the rectangle?
Answer:
Step-by-step explanation:
The area of a rectangle can be found by multiplying its length and breadth. In this case, the length is 11/5 cm and the breadth is 13/5 cm. Therefore, the area of the rectangle is (11/5 cm)*(13/5 cm) = 143/25 sq. cm = 5.72 sq. cm.
Dianelys has xx dimes and yy nickels. She has a maximum of 18 coins worth at least $1.20 combined. Solve this system of inequalities graphically and determine one possible solution.
One possible solution of the inequality x + y ≤ 18 and 0.1x + 0.05y ≥ 1.20 is 12 dimes and 4 nickels
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Let y represent the nickels and x represent the dimes
1 nickel = $0.05, 1 dime = $0.1
She has a maximum of 18 coins worth at least $1.20 combined. Hence:
x + y ≤ 18 (1)
Also;
0.1x + 0.05y ≥ 1.20 (2)
One possible solution is 12 dimes and 4 nickels
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This table shows some of the values of x and y that satisfy the equation y=acos0+b, find the value of y when x = 45
Answer: [tex]4\sqrt{2}+1[/tex]
Step-by-step explanation:
[tex]x=0 \implies y=a+b \implies a+b=9\\\\x=30 \implies \frac{\sqrt{3}}{2}a+b=1+4\sqrt{3}\\\\\implies \frac{\sqrt{3}}{2}a-a=4\sqrt{3}-8\\\\a=\frac{4\sqrt{3}-8}{\frac{\sqrt{3}}{2}-1}=\frac{8\sqrt{3}-16}{\sqrt{3}-2}=8\\\\\implies b=9-8=1\\\\\therefore y=8\cos x^{\circ}+1\\\\x=45 \implies y=8\left(\frac{\sqrt{2}}{2} \right)+1=4\sqrt{2}+1[/tex]
Five friends are standing in a line. Cliff is standing directly behind Danny, and there are two people between Cliff and Mark. Mark is standing somewhere behind Eric, but somewhere in front of Tom. Which of the five friends is fourth in line
Among the five friends Eric, Mark, Tom, Danny, and Cliff the fourth in line is Danny.
Given the information, we can make the following deductions:
Cliff is standing directly behind Danny.There are two people Cliff and Mark.Mark is standing somewhere behind Eric, but somewhere in front of Tom.From these deductions, we can conclude that Mark is fourth in line.Eric is the first one in line.
Cliff is standing directly behind Danny, so he is the fifth one in line.
Mark is somewhere behind Eric and Tom, but there are two people between Cliff and Mark, so it's Tom is the third one in line.
As we know that Mark is somewhere behind Eric and somewhere in front of Tom, Mark is the second one in line.
The five friends standing sequence will be - Eric, Mark, Tom, Danny, and Cliff.
Hence, the Fourth one in line is Danny.
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Which of the following represents 18 = 3 × 6?
A.
18 is 3 times as many as 6
B.
18 is 2 times as many as 9
C.
3 is 6 times as many as 18
D.
6 is 3 times as many as 18
Answer:
A) 18 is 3 times as many as 6----------------------------
Translate each wording to mathematical expression and compare with the given 18 = 3 × 6.
A) 18 is 3 times as many as 6:
18 = 3 × 6, yes same as givenB) 18 is 2 times as many as 9:
18 = 2 × 9, different from the givenC) 3 is 6 times as many as 18:
3 = 6 × 18, wrongD) 6 is 3 times as many as 18:
6 = 3 × 18, wrongUse quadratic regression to find a
function that fits the following points.
(-1, 21) (3, 45) (4, 81)
The function that fits the points (-1, 21) (3, 45) (4, 81) is 6x²-6x+9.
Quadratic Regression is a method according to which we can make an equation of a quadratic curve from given no. of x and y data points
Quadratic Regression Equation(y) = a + b x + c x^2
The formula for its coefficients is,
c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }
Where,
Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]
Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]
Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]
Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]
Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]
x and y are the Variables.
a, b, and c is the Coefficients of the Quadratic Equation
n = Number of Values or Elements
Σ x= Sum of First Scores
Σ y = Sum of Second Scores
Σ x2 = Sum of the square of the First Scores
Σ x 3 = Sum of Cube of First Scores
Σ x 4 = Sum of Power Four of First Scores
Σ xy= Sum of the Product of First and Second Scores
Σ x2y = Sum of Square of First Scores and Second Scores
when we input the points (-1,21),(3,45),(4,81)
we get the equation 6x²-6x+9
which looks like this (The image has been attached),
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Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Answer: It is not possible to determine whether rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin just by looking at the statement provided.
A dilation is a transformation that changes the size of a shape but not its shape or orientation. In a dilation, the center of dilation is a fixed point and all other points move away from or towards it by a scale factor.
The statement provided does not include any information about the scale factor, the coordinates or measurements of the rectangle's vertices or any other information that would allow to determine if EFGH is the result of a dilation of ABCD. The statement only indicates that the center of dilation is at the origin.
In order to determine if rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin, we would need additional information such as the scale factor, the coordinates or measurements of the rectangle's vertices, and the direction of dilation (enlargement or reduction)
It's worth noting that a dilation with center of dilation at origin can be performed only if the shape is symmetric.
Step-by-step explanation:
Solve for X, Leave in simplest radical
The value of adjacent side x in radical form is obtained as 7/√2.
What is radical form?
Instead of employing exponents to describe the same item, a radical form of an expression uses radical signs like the square root, cube root, etc.
The given triangle is a right-angled triangle with other two angles measuring 45° as given in the diagram.
The value of hypotenuse is 7.
The adjacent side is taken to be x.
Apply the cosine formula -
cos θ = adjacent / hypotenuse
cos 45° = x/7
1/√2 = x/7
x = 7/√2
Therefore, the value of x in radical form is 7/√2.
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A line passes through the point (2, 1) and has a slope of 3. Write the equation of the line in standard form.
Answer:
y-1=3(x-2)
Step-by-step explanation:
This is the equation you have to fill in y-y1=m(x-x1) to fill in this you have to lable the points (2,1)
x,y
A plane is heading in a direction of 045° and changes course in a clockwise direction to 135°. The angle through which the plane turns is A) 45° B) 90° C) 135° D) 180°
The angle through which the plane turns is B; 90 degrees clockwise
How to determine the angle of turn?When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).
We are given that plane is heading in a direction of 045° and changes course in a clockwise direction to 135°.
To Subtract the angles to get the answer
135 - 45 = 90
In terms of compass, 45 degrees is directly pointed at northeast while 135 degrees is pointed directly at southeast. We have zero degrees pointed straight north.
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1. the very first step in verifying a statement about a product is represented by the c in claim. what does the letter c stand for?
Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.
What do the other letters stand for?L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.
A - Attribution: Identifying the source of the assertion and assessing its reliability.
I - Investigation: Research and evidence collecting to support or reject the allegation.
M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.
Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.
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Digital genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes. the analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00 each, the demand would be 16 thousand pads. based on the assumption that a linear relationship exists between price and demand, the price-demand equation is given by where x is the number of thousands of pads in demand. at what price point should they sell the pads to have a demand of 14 thousand pads?
At $63 price point should they sell the pads to have a demand of 14 thousand pads.
p(x) = -5x + 133
Substitute x with 14,
p(14) = -5(14) + 133
= -70 + 133
= 63.
The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. [1] This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.
The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.
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Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ), y = sec(θ), (1,√2)
The equation of the tangent to the curve x=tan(θ) and y=sec(θ) at the point (1,√2) can be found by both eliminating the parameter and without eliminating the parameter.
Find an equation of the tangent to the curve?Eliminating the parameter: y = x + √2Without eliminating the parameter: dy/dθ = sec(θ) + tan(θ) × csc(θ); y = sec(θ) + tan(θ) × (x - tan(θ)).Without eliminating the parameter:The equation of the tangent line at (1,√2) is given by y = (sec(θ)cos(θ))x - (sec^2(θ)) + √2, where θ is the parameter.This is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point, or sec(θ)cos(θ).By eliminating the parameter:The equation of the tangent line at (1,√2) is y = x + (1/√2). This equation is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point.Since the derivative of x = tan(θ) and y = sec(θ) is sec(θ)cos(θ), by setting θ = π/4, we get sec(π/4)cos(π/4) = 1/√2. Therefore, the equation of the tangent line is y = x + (1/√2).To learn more about tangent line approximation refer to:
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find an expression for t1, the tension in cable 1, that does not depend on t2.
The expression for the t1 with the tension in cable 1 that does not depend on t2 is T1sinθ1 + T2sinθ2 = mg
While we looking into the given diagram we have identified that the angle made by strings 1 and 2 are 01 and 02 respectively.
Here we also know that the tension made by strings 1 and 2 are T1 and T2 respectively.
Here let us considering that the diagram shown is the following tension components are available
And the weight of the block mg acting on the body directing the force downwards then the components are written as,
Here the Vertical component of T1 is T1 sinθ1 which acts upwards and the horizontal component of T1 is T1cosθ1 which acts to the left
Where as the another vertical component of T2 is T2sinθ2 which acts upwards then the horizontal component of T2 is T2cosθ2 acting towards right
Here we have to maintain a state of equilibrium, then the upward forces and downwards forces must be equal even as the forces on the right and left hand side must balance
According to this details the balancing the vertical components we obtain
=> T1sinθ1 + T2sinθ2 = mg
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Using your equation from Question 2*, predict the average pulse rate in beats per minute of an animal that weighs 640 kilograms. You can also estimate the weight of the animal using the graph and the line of best fit (extend the line and x-axis farther).
The estimate of the average pulse rate in beats per minute of an animal that weighs 640 kilograms is given as follows:
29.6 beats per minute.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
(this is because there are multiple types of regression, such as logistic, exponential and quadratic regression).
The points for this problem are given as follows:
(3, 130), (28,75), (56, 75), (192, 95), (362,48), (465, 66), (521, 34).
Inserting these points into a calculator, the regression equation is given as follows:
y = -0.11x + 100.
Hence, for a weight of x = 640 kg, the estimate of the average heart rate is given as follows:
y = -0.11(640) + 100
y = 29.6 beats per minute.
Missing InformationThe table is given by the image presented at the end of the answer.
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2) Three trucks can carry 240 bags of cement. How many bags of cement can seven trucks carry?
Answer: 560
Step-by-step explanation:
240 / 3 = 80 x 7 = 560
onex expects to have an ebit of $240,000 with a standard deviation of $90,000. the distribution of operating income is approximately normal. what is the probability that onex will have an ebit below $0
The probability that Onex will have an EBIT that is below $0 is 0.38%. The correct answer is C.
The first step in solving this problem is to calculate the z-score, which is a measure of how many standard deviations a value is from the mean. In this case, the mean EBIT is $240,000, and the standard deviation is $90,000.
To find the z-score for an EBIT of $0, we subtract the mean from the value and divide by the standard deviation as follows:
z = ($0 - $240,000)/$90,000 z = -2.67This gives us a z-score of -2.67. Next, we use Table V, which is a table of standard normal distribution values, to find the probability that a value with a z-score of -2.67 will fall below 0. The probability is 0.38%, which means there is a very low chance that Onex's EBIT will be below $0.
This question should be provided with answer choices, which are:
A.0.47%B.2.67%C.0.38%D.2.25%The correct answer is C.
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Nicole measured a line to be 10.9 inches long. If the actual length of the line is 10.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer: 6.9%
Step-by-step explanation:
Substituting into the percent error formula,
[tex]\frac{|10.9-10.2|}{10.2} \times 100 \approx 6.9\%[/tex]
(WILL GIVE BRAINLIEST!!) Which of the following lengths are Pythagorean Triples? Justify your answers.
10, 24, 26 are the Pythagorean triples. Therefore, option (i), (iii) and (iv) are the correct answers.
What are Pythagorean triples?Pythagorean triples are a²+b² =c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
i) 10, 24, 26
Here, 26²=10²+24²
676=100+576
676=676
So, the given set of numbers are Pythagorean triples
ii) 2, 3, 5
Here, 5²=2²+3²
25≠13
So, the given set of numbers are not Pythagorean triples
iii) 3a, 4a, 5a; where a is any whole number
Here, (5a)²=(3a)²+(4a)²
25a²=9a²+16a²
25a²=25a²
So, the given set of numbers are Pythagorean triples
iv) 7, 24, 25
Here, 25²=24²+7²
625=576+49
625=625
So, the given set of numbers are Pythagorean triples
v) 12, 13, 15
Here, 15²=12²+13²
225=144+169
225≠313
So, the given set of numbers are not Pythagorean triples
Therefore, option (i), (iii) and (iv) are the correct answers.
Learn more about the Pythagorean triple here:
https://brainly.com/question/15190643.
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Write an equation for the line that passes through (8, 2) and is parallel to the graph of y = 3/4x + 2.
Answer: do it youself
Step-by-step explanation:
on a football field, the 20-foot-tall goal post casts a 60-foot shadow. at the same time, another post casts a shadow that is 24 feet long when standing perpendicular to the ground. what is the height, in feet, of the second post?
The second post is 30 feet tall because the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall.
1. ratio of shadows is 2:1, so for every 2 feet of shadow, the post is 1 foot tall
2. 60 feet of shadow divided by 2 is 30 feet tall
3. 24 feet of shadow divided by 2 is 12 feet tall
4. 30 feet tall is the second post
The goal post that casts a 60-foot shadow is 20 feet tall, and the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall. To find the height of the second post, we divide the length of the shadow by 2. The second post casts a 24-foot shadow, so when we divide it by 2, the post is 12 feet tall. Therefore, the second post is 30 feet tall. This is because for every 2 feet of shadow, the post is 1 foot tall, so for the 60-foot shadow, the post was 20 feet tall, and for the 24-foot shadow, the post is 12 feet tall. Therefore, the second post is 30 feet tall.
Learn more about ratio here
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F(x) = 2x² +1
g(x) = 3x - 5
f-g
Answer: The answer is. 2x² - 3x + 6. Step-by-step explanation: f(x) = 2x² + 1. g(x) = 3x - 5. To find f - g(x) subtract g(x) from f(x).
I hope this helps! Have a Wonderful day! <3
