No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1
8² + 15² = 64 + 225 = 289
17² = 289
Therefore, 8, 15, and 17 are not the sides of a right triangle.
The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.
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plsss help
For the given polynomial, determine which of the binomials listed are factors. Pick two.
f(x) = 2x3 + 9x2 + 13x + 6
A.x + 1
B.x – 1
C.x + 2
D.x – 2
E.x + 3
F.x – 3
The factors for the Polynomial are (x+1) and (x+2).
What is Factor Theorem?According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
Given:
f(x) = 2x³ + 9x² + 13x + 6
Now, first (x+1) =0
x= -1
put x= -1 in f(x) as
f(-1) = 2(-1) + 9(1) + 13(-1) + 6
= -2 + 9 - 13 + 6
= 0
So, (x+1) is factor of f(x).
Now, second (x-1)= 0
x= 1
put x= 1 in f(x) as
f(1) = 2(1) + 9(1) + 13(1) + 6
= 2 + 9 + 13 + 6
= 31
So, (x-1) is not a factor of f(x).
Now, second (x+2)= 0
x= -2
put x= -2 in f(x) as
f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6
= -16 + 36 - 26 + 6
= 0
So, (x+2) is factor of f(x).
Now, second (x-2)= 0
x= 2
put x= 2 in f(x) as
f(1) = 2(2)³ + 9(2)² + 13(2) + 6
= 16 + 36 + 26 + 6
= 84
So, (x-2) is not a factor of f(x).
Now, second (x+3)= 0
x= -3
put x= -3 in f(x) as
f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6
= -54 + 81 - 39 + 6
= -6
So, (x+3) is not a factor of f(x).
Now, second (x-3)= 0
x= 3
put x= 3 in f(x) as
f(1) = 2(3)³ + 9(3)² + 13(3) + 6
= 54 + 81 + 39 + 6
= 180
So, (x-3) is not a factor of f(x).
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Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?
Answer:
1) 39
2) 13
3) 2
Step-by-step explanation:
1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.
2) 143/11 = 13
3) 6-4 = 2
A gallon of gas cost $3.50 at the beginning of the month. At the e of the month it cost $3.75. What was the percent change in the price of a gallon of gas?
ty:-;
Answer:
7.14%
Step-by-step explanation:
Any comparison with the increase or decrease in price has to be compared to the ORIGINAL price. (at the beginning of the month.)
The price increased from $3.50 to $3.75, an increase of $0.25
To find what percent it is use:[tex]\frac{change}{original}[/tex]×100%
[tex]\frac{0.25}{3.50}[/tex]×100%
Answer:
7.1428571% increase
7 1/7 % increase
Step-by-step explanation:
To find the percent increase ( we know this is an increase since the amount went up), take the new amount and subtract the original amount
3.75 - 3.50 = .25
Divide by the original amount
.25 / 3.50
.071428571
Multiply by 100 %
7.1428571%
7 1/7 %
Please help!!!! I'LL GIVE 5 STAR RATING AND A THANKS
Answer:
9.1
Step-by-step explanation:
For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!
Using the numbers 4. 3, -1. 07, and -2. 971,write an expression containing both addition and subtraction that simplifies to a negative number
Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.
Define expression.An expression is made up of a number, a variable, or a combination of both, along with certain operation symbols. Two expressions that make up an equation are separated by an equal sign. Example of a Word 8, 3, and the result is 11.
Here,
Given : the numbers 4. 3, -1. 07, and -2. 971
Using the above given numbers we can construct
an expression which contain both
addition and subtract
thus ,
In order to form we use + sign and - sign
We get,
-1.07+(-2.917)-4.3=-8.287
Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.
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What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
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Solve by factorising:
x^2+10x+21=0
Answer:
[tex]x = -7\\x = -3[/tex]
Step-by-step explanation:
The steps are in the image attached to this response.
What is (f + g)(x)?
f(x) = -3x² + 3
g(x) = −3x
Answer:
Step-by-step explanation:
(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]
Sophia buys 11 bottles of pineapple juice at the corner store for a total cost of $9.90. Assume each bottle of juice is the same price. If c represents the total cost in dollars and cents of the juice for any number, j, of bottles of juice, write a proportional equation for c in terms of j that matches the context. How do I do that
The proportion equation for c in terms of j is written as c = 0.9j
How to write the equationIn order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.
This would tell us the price that one of the bottles of juice is been sold for.
Hence we would have
9.90 / 11
= 0.9
Hence the equation would be: c = 0.9j
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n 2010, the population of a small town in Alabama was 8,250 people. By 2015, the population had decreased by 10%. From 2015, to 2020, the population then increased by 15%. What was the population of the town in 2020
The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.
What is population?A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex] people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]
From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]
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slope intercept form of y + 6 = (x - 4)
the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792
Brady tosses a coin three times. Each toss could be heads or tails. Which
outcome would be included in the compound event "at least two tails"?
The outcome for the event "at least two tails" is HTT. Option B
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
HHH → All heads
HHT → Two heads + one tail
HTH → Two heads + one tail
HTT → Two tails + one head
THH → One tail + two heads
THT → Two tails + one head
TTH → Two tails + one head
TTT → All tails
Therefore, At least two tails means → Sample space outcome with two tails Or all tails
Therefore, from the given options HTT is having two tails. Option B is the correct option.
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Which linear graph represents a proportional relationship?
A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.
Answer: The answer is C
Step-by-step explanation: i took the test and got it right
Rewrite 21/3 as a whole number
Answer:
7
Step-by-step explanation:
As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
21/3 = 7
look at picture please
The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ
What are trigonometric identities?Trigonometric identities are equations which contain the trigonometric ratios.
How to show the equivalent identity of cot²θ + 1?Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.
So, we proceed as follows
Since cot²θ + 1 = 1/tan²θ + 1 (since cot²θ = 1/tan²θ)
Now taking the L.C.M, we have that
1/tan²θ + 1 = (1 + tan²θ)/tan²θ
We know that the trigonometric identity 1 + tan²θ = sec²θ
So, substituting this into the equation, we have that
(1 + tan²θ)/tan²θ = sec²θ/tan²θ
Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that
sec²θ/tan²θ = cot²θsec²θ
So, cot²θ + 1 = cot²θsec²θ
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Suppose that X ∼ Geom(p) and Y ∼ Geom(r) are independent. Find the probability P (X < Y )
The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent
What is probability ?
Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.
Given ,
X ∼ Geom(p) and Y ∼ Geom(r) are independent.
P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})
=∑1≤k<n,n∈NP(X=k,Y=n)
=∑n=1∞∑k=1n−1P(X=k)P(Y=n)
=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1
=pq∑n=1∞(1−q)n−11−(1−p)n−1p
=q∑n=1∞(1−q)n−1(1−(1−p)n−1)
=1−q / ∑n=1∞[(1−q)(1−p)]n−1
=1−q / 1−(1−p)(1−q)
=1−(1−p)(1−q)−q / 1−(1−p)(1−q)
=p(1−q) / p+q−pq.
Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent.
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Given: AAED ≈ ABEC and
AC BD.
Prove: AABD≈ ABAC.
Note: quadrilateral properties are not permitted in this
proof.
The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.
What are the four traits of triangles that are similar?The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.
According to given information:Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.
Given that ΔAED ≈ΔBEC & AC = BD.
as ΔAED ≈ΔBEC, AD = BC .................(1)
Now in ΔABD and ΔBAC,
AD = BC
(corresponding sides of similar triangles) [from (1)]
AB = AB
(common side)
AC = BD
(given)
∴ ΔABD ≈ΔBAC (By SSS criteria)
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explain what the slope and intercept mean in each situation the amount of money y in a cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y intercept is 8
Answer:
The (1/4) slope is the prive per ticket. The y intercept is the money in the cash box before any tickets were sold.
Step-by-step explanation:
Let y be the money and x the numbers of tickets sold, as requested. We are told that the equation for this situation is:
y = (1/4)x + 8
Let's assume the money is in units of dollars. The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents. The y-intercept is the value of y when x=0, which means zero tickets have been sold. That means that the cash box had $8 before any sales were made. [perhaps to use for making change].
What are the 13 types of angles?
There are several types of angles, including: acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pair, vertically opposite angles, alternate interior angles, alternate exterior angles, and corresponding angles.
Acute angles: angles measuring less than 90 degrees.
Right angles: angles measuring exactly 90 degrees.
Obtuse angles: angles measuring greater than 90 degrees but less than 180 degrees.
Straight angles: angles measuring exactly 180 degrees.
Reflex angles: angles measuring greater than 180 degrees but less than 360 degrees.
Complementary angles: two angles that add up to 90 degrees.
Supplementary angles: two angles that add up to 180 degrees.
Adjacent angles: two angles that share a common vertex and a common side but no common interior points.
Linear pair: two angles that add up to 180 degrees and share a common side.
Vertically opposite angles: two angles formed by two intersecting lines that are opposite to each other.
Alternate interior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and inside the parallel lines.
Alternate exterior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and outside the parallel lines.
Corresponding angles: two angles formed by two intersecting lines that are in the same relative position.
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graphing piece wise functions
Answer:
thats by step overr.ic. yttt. .
how would you read absolute value -5
Answer:
-5 = |5|
Step-by-step explanation:
Absolute value is the number of distance from zero. Therefore, it doesn't matter if the number is positive or negative in absolute value it is always positive.
How do I find parameter?
Answer:
Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.
Answer:
The perimeter is the distance around a figure.
Step-by-step explanation:
For example, if I have a square where each side is 5 inches. The perimeter would be 20 inches. 5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.
Find value of y
[tex] {y}^{2} - 58 = 25 \times 4 + 11[/tex]
Hello there!
Answer:
y = ± 13
Step-by-step explanation:
[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]
54 is 72% of what number?
Stella took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $1. 20 plus $1. 50 per mile. The total fare was $29. 70, not including the tip. How
many miles was the taxi ride?
09
Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.
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Its pre-algebra. I need it fast
Answer:
Obtuse and isosceles
Step-by-step explanation:
obtuse because an angle is more than 90* and isosceles because two sides are equal.
Hope this helps!
fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.
The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3, 1/5 is a fraction.
We have,
Let the fraction be a/b.
2/5 < a/b < 2/3
Now,
a/b
= (2/3 + 2/5) / 2
= (10 + 6) / 30
= 16/30
= 8/15
= 0.533
Thus,
The fraction is 8/15.
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Graph the line that passes through the points (-3, -1) and (1, -1) and
determine the equation of the line.
Answer:
y = -1
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)
The slope here is 0, and the y-intercept is located at (0,-1), so the equation is
y = -1
Answer:
y = -1
Step-by-step explanation:
A performance score on the normally distributed WAIS Test that is higher than all but 2 percent of all scores earns an intelligence score of:
Scores earns an intelligence score of 130
What percentage of WAIS scores fall into this range?According to the 68-95-99.7 rule, 68% of persons have WAIS scores ranging from 100-15 to 100+15. WAIS scores between 85 and 115 are obtained by 99.7% of the population. As a result, 32% of adults have WAIS scores of 85 or above. Factor Analysis is a statistical process used to discover clusters of similar questions (called factors) on a test; it is used to identify multiple levels of performance that underpin one’s overall score.
The WAIS categories are shown below and are based on a mean of 100: Scores of 130 and higher are deemed talented. Scores between 120 and 129 are regarded extremely intelligent. Normal intellect is defined as a score between 110 and 119.
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Complete question is: A performance score on the WAIS that is higher than all but 2 percent of all scores earns an intelligence score of:
115.120.130.145.