The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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Use the unique factorization theorem to write the following integers in standard factored form. (a) 756 2^2.3^3.7. (b) 819 3^2.7.11 (c) 9,075 3^2.5^2.7
The factorizations of these integers above represent their factorizations into their respective prime numbers.
(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.
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Q4 NEED HELP PLEASE HELP
Answer:
D. The electrician charges $23 per hour.
Step-by-step explanation:
C(h)= 23h+30 is in the form y=mx +b
$30 is the initial fee (b)
$23 is the amount charged per hour (h)
Imagine that 3 committee members arrive late. The other 5 memebers have already shaken hands. How many handshakes will there be when the 3 late members arrive?
There will be a total of 28 handshakes when the 3 late members arrive.
What is sum of n positive integers?The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.
The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.
Given that, 3 members arrive late, and 5 members are already present.
The total members are 5 + 3 = 8.
Now, using the sum of positive integer formula:
n(n-1)/2
We can determine the number of handshakes.
8(8-1)/2 = 28
Hence, there will be a total of 28 handshakes when the 3 late members arrive.
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why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Answer:
Step-by-step explanation:
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Answer:
s= 6
Step-by-step explanation:
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Please help it is due tomorrow
Answer: 30
Step-by-step explanation: So what you do is,
1) Add the 25 to the 8
2) Find the sum
3) Subtract 3 from the sum
4) Done!
I hope this helps!
Best,
Abigail H
8th Grade
what is 2 1/2 + x = 3 1/2. Please answer it quick
Answer:
x=1
Step-by-step explanation:
2.5+x=3.5
3.5-2.5=x
1=x
x=1
Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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What is the y-intercept of the line
with the equation y = - 4x - 12
Answer:
-12 is the y intercept while your slope is -4
Step-by-step explanation:
Find The surface area of the composite figure
Answer: It should be 470 cm^2
Step-by-step explanation:
The average mass of six people is 58kg. The lightest person has a body mass of 43kg. What is the average mass of the other 5 people.
Answer: 61 kg
Step-by-step explanation:
To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:
Find the total mass of all six people:
To find the total mass of all six people, we can multiply the average mass by 6:
Total mass of all six people = 58 kg/person x 6 people = 348 kg
Subtract the mass of the lightest person:
We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:
Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person
Total mass of the other 5 people = 348 kg - 43 kg = 305 kg
Find the average mass of the other 5 people:
Finally, we divide the total mass of the other 5 people by 5 to find the average mass:
Average mass of the other 5 people = Total mass of the other 5 people / 5
Average mass of the other 5 people = 305 kg / 5 = 61 kg
Therefore, the average mass of the other 5 people is 61 kg.
2.3. Ntando can either walk to school at 5 km/h or ride his bicycle at 15 km/h. If he rides his bicycle, it takes him 10 minutes to get to school. 2.3.1. How long will it take him if he walks to school?
Answer:
30 minutes
Step-by-step explanation:
Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.
10 minutes * 3 = 30 minutes
James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).
Answer:
3m
Step-by-step explanation:
red wire = 27
black wire= 12
so, we take HCF (highest common factor)
which would be 3 so all the wires would be cut into 3m long.
I hope it helps.
Answer:2m
Step-by-step explanation:
as the factors of 12 are:1, 2, 3, 4, 6 and 12
and the factors of 26 are:1, 2, 13 and 26
so if you are talking meters 2 would be the longest
i hope you get this right x
solve for x and graph the solution on the number line below
We can graph this solution on the number line by placing a point at 7.6.
What is graph ?Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.
80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x
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We can graph this solution on the number line by placing a point at 7.6.
What is graph ?Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.
80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x
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Can 3 feet, 3 feet and 7 feet create a triangle explain why or why not
The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.
To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:
The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.
The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.
Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.
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A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
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ratings services measure television audiences. the measurement of the percentage of all households with televisions that are tuned into the same show at the same time is called
Therefore , the solution of the given problem of percentage comes out to be were tuned in to a specific program or show at a given moment.
What is percentage?A number or figure stated as a fraction of 100 is referred to as "a%" in statistics. The versions that begin with "pct," "pct," and "pc" are also uncommon. The common way to indicate it is with the numeral "%," though. Furthermore, there are no indicators and a flat ratio of every single thing to the total number. Percentages are basically integers because they frequently add up to 100.
Here,
The TV ratings, also known as the TV audience share, are a measurement of the proportion of all television-owning households that are watching the same program at the same moment.
Networks and marketers use it as a gauge of a TV show's popularity to decide how successful a program will be and how much to charge for advertising during it.
Companies like Nielsen, which use a sample of homes with televisions to estimate the audience size for a given program or show, are usually in charge of gathering the TV ratings.
TV ratings are expressed as a proportion of all households with televisions that were tuned in to a specific program or show at a given moment.
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a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
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Solve the inequality 12≥ 73x + 2
10/73 is the value of x in inequality.
What does the word "inequality" mean?
In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.
However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.
the inequality 12≥ 73x + 2
= 12 - 2 ≥ 73x
= 10 ≥ 73x
= 10/73 ≥ x
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4)) FH and IK are parallel lines. J K F G E Which angles are alternate exterior angles?
Answer: I couldn't honestly help with that I would if I could
Step-by-step explanation:
What is the scale factor of the following pair of similar polygons ?
The scale factor of the following pair of similar polygons after the dilation is 0.7
Calculating the scale factor of the similar polygonsGiven
The pair of similar polygons
From the pair of similar polygons, we have the following corresponding side lengths
Pre-image of the polygon = 30
Image of the polygon = 21
The scale factor of the similar polygons is then calculated as
Scale factor = 21/30
Evaluate the quotient
Scale factor = 0.7
Hence, the scale factor is 0.7
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let x1 and x2 be two independent random variables both with mean 10 and variance 5. let y 2x1 x2 3 2. find the mean and the variance of y.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
what is variable ?A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.
given
To get the mean and variance of y, we can apply the characteristics of expected value and variance:
We can start by determining the expected value of y:
E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]
By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.
Next, we may determine y's variance:
Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4
Var(x1)
Var(x2) + 9
Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
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Find the value of x.
22
39
X
The value of x in the right triangle when calculated is approximately 13.8 units
Calculating the value of x in the triangleGiven the right-angled triangle
The side length x can be calculated using the following sine ratio
So, we have
sin(39) = x/22
To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.
First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.
Then, we can set up the equation:
0.6293 = x/22
To solve for x, we can multiply both sides by 22:
0.6293 * 22 = x
13.8446 = x
Rewrite as
x = 13.8446
Approximate the value of x
x = 13.8
Therefore, x is approximately 13.8 in the triangle
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if a traingle with all sides of equal legnth has a perimeter of 15x 27 , what is an expression for the legnth of one of the sides
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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Binomial Problem:A jury has 12 jurors. A vote of at least 10 out of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?
The probability that the jury makes the correct decision is approximately 0.7063.
To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.
We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.
We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:
P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]
where:
P(X ≥ k) is the probability of at least k successes
n is the total number of trials (in this case, 12 jurors)
p is the probability of success in a single trial (in this case, 0.80)
k is the number of successes we want to find the probability of (in this case, 10)
Plugging in the values, we get:
P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]
Using a calculator or software, we can calculate this to be approximately 0.7063.
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Un número tiene 8 divisores. Además, cada uno de la mitad y la tercera parte de él tienen cuatro divisores. Si la suma de todos los divisores del número es 216, obtén tal número
The number we are looking for is N = 2 × 2^3 × 3^2 = 72.
Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say
n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k
then the number of divisors of n is given by
d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).
Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form
N = p_1^2 × p_2^2, or N = p_1^7,
where p_1 and p_2 are distinct prime numbers.
Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that
N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,
and
N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,
where q_1, q_2, r_1, and r_2 are distinct prime numbers.
To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by
p_1 = q_1^a × q_2^b,
p_2 = r_1^c × r_2^d,
N/2 = q_1^e × q_2^f,
N/3 = r_1^g × r_2^h.
Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:
a + 1 × (b + 1) = e + 1 × (f + 1) = 4,
c + 1 × (d + 1) = g + 1 × (h + 1) = 4,
2a × 2b = ef,
2c × 2d = gh.
We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get
(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.
We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.
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Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
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HELPPPP HURRY PLSS………………..
Answer:
C is your answer
Step-by-step explanation:
in my opinion, i think it would be the mode.
using the net below find the area of the triangular prism
10 cm
7 cm
6 cm
4 cm
4 cm
10 cm
6 cm
4 cm
Answer:51
Step-by-step explanation:
please help with question 6
Answer:
a = -13b = 6f(x) = (2x -1)(x -2)(x +3)Step-by-step explanation:
Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).
RemainderIf (x -2) is a factor, then the value of f(2) is zero:
f(2) = 2·2³ +2² +2a +b = 0
2a +b = -20 . . . . . . . subtract 20
If the remainder from division by (x +1) is 18, then f(-1) is 18:
f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18
-a +b = 19 . . . . . . . . . . add 1
Solve for a, bSubtracting the second equation from the first gives ...
(2a +b) -(-a +b) = (-20) -(19)
3a = -39
a = -13
b = 19 +a = 6
The values of 'a' and 'b' are -13 and 6, respectively.
Factored formWe can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...
[tex]\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}[/tex]
The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).
To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...
2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)
The factored form of f(x) is ...
f(x) = (2x -1)(x -2)(x +3)
