Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Line a passes through (2, 10) and (4, 13). So, the slope of this line is
[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]
Line b passes through (4, 9) and (6, 12). So, the slope of this line is
[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]
Line c passes through (2, 10) and (4,9). So, the slope of this line is
[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]
The product of slopes of perpendicular lines is -1.
and if the slope of 2 lines is equal then those lines are parallel
so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
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Y+2=1/4 x in standard form
Answer:
-[tex]\frac{1}{4}x[/tex] + y = -2
Step-by-step explanation:
Standard form: Ax + By = C
y + 2 = [tex]\frac{1}{4} x[/tex]
Rearrange terms:
1. Subtract 2 from both sides
y = [tex]\frac{1}{4} x[/tex] - 2
2. Subtract [tex]\frac{1}{4} x[/tex] from both sides
-[tex]\frac{1}{4}x[/tex] + y = -2
a square matrix is nilpotent if for some positive integer . let be the vector space of all matrices with real entries. let be the set of all nilpotent matrices with real entries. is a subspace of the vector space ?
An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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A jar contains only pennies, nickels, dimes, and quarters. There are 26 pennies, 12 dimes, and 19 quarters. The rest of the coins are nickels. There are 70 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n? of the coins are not nickels.
Answer:
57 coins are not nickels.
Equation: n + 57 = 70
Step-by-step explanation:
To find how many coins are not nickels, just add up the pennies, dimes, and quarters all together:
26 + 12 + 19 = 57 coins are not nickels.
The equation you could use to find n (nickels) would be:
n + 57 = 70
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What is the constant of variation, k of the direct variation, y=kx,through (5,8)
Constant of variation, k of the direct variation is 8/5.
Equation -> y = kx
Point (x,y) = (5,8)
Putting the value in the equation,
8 = 5k
k = 8/5
Hence, k = 8/5.
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The pages of a book are numbered consecutively from 1 to 100. What is the sum of all the digits used in numbering the pages of the entire book?
5050
Step-by-step explanation:
1+2+3+.....+100 add all the numbers and u get that
Expand and simplify (3x + 4)(2x + 3)
Answer:
6x^2+17x+12
Step-by-step explanation:
(3x+4) * (2x+3)
3x * 2x = 6x^2
3x * 3 = 9x
+4 * 2x = +8x
+4 * +3 = +12
6x^2+ 9x+8x +12
Simplify:
6x^2+17x+12
connie has a number of gold bars, all of different weights. she gives the 2424 lightest bars, which weigh 45\e% of the total weight, to brennan. she gives the 1313 heaviest bars, which weigh 26\&% of the total weight, to maya. she gives the rest of the bars to blair. how many bars did blair receive?
Blair received 15 bars as the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients.
What is average weight?The weighted average is calculated by adding up all the variables, multiplying by their weight, and dividing by the sum of the weights. Instead of treating each item equally, a weighted average or mean multiplies each item being averaged by a number based on its relative importance. The weights or weightings correspond to including that many comparable items of the same value in the average.
Here,
The average weight of the bars given to Brennan (light), Blair, and Maya was higher than the average weight of the bars given to the other two recipients (heavy).
Let X represent the combined weight of all the bars.
The weight of the bars Brennan was given was equal to 45% of X, or 0.45X.
Maya was given bars that weighed 26% of X, or 0.26X.
The weight of the bars Claire was given was the rest, or 29% of X, or 0.29X.
Brennan received bars with an average weight of 0.45 x/ 24.
The weight of the Maya-received bars, on average, is 0.26X/13.
Similar to the previous example, if Blair receives B bars, then their average weight is 0.29X/B.
Similarly, the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients. So blair received 15 bars.
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Find the measure of the exterior angle.
The measure of the exterior angle as shown in the triangle is 140°.
What is exterior angle?
Exterior angle is the angle between a side of a polygon and an extended adjacent side.
Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
From the diagram below, applying the theorem above,
k = 64+76k = 140°Hence, the exterior angle is 140°.
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Complete the table and answer the questions that follow. (If a root occurs twice, count it twice; if
thrice, count it three times, and so on. The first one is done
Polynomial Equation
1. (x+1)² (x-5) = 0
2. X-9 0
3. (x+8) (x-8)= 0
4. x² + 3x +2=0
(x+1)(x+2) = 0
5. (x² - 4x + 4)(x-3)²
(x-2)(x-2)(x-3)(x-3) = 0
6. 2
7. (x-3)(x + 1)(x - 1) = 0
8. (x²-4)(x-3)³ = 0
(x+2)(x-2)(x-3)(x-3)(x-3)=0
9. x(x-4)(x + 5)(x - 1) = 0
10. (x + 1)5 (x - 1)² =0
Degree
3
Real Roots of the
Equation
-1 (2times); and 5
Number of Real Roots
3
An equation of the form P=0 is referred to as a polynomial equation. P is a polynomial with coefficients in some field, typically the field of the rational numbers. A polynomial equation, on the other hand, can include a number of variables. The phrase polynomial equation is typically preferred over algebraic equation when discussing situations with multiple variables.
What is Polynomial Equation ?One or more variables, coefficients, and non-negative integer exponents of variables make up a polynomial, which is an expression. A mathematical statement that has a "equal to" symbol between two algebraic expressions with equal values is called an equation.
Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
4x² + 6x + 21=0 where 4x²+6x+21 is considered as a polynomial expression which is written on the left side and has been fixed to make the polynomial expression equal to zero to form a complete polynomial equation.
1 Already answered
2 Degree:1 Real Roots of an equation:8 Number of Real Roots:1
3 Degree:2 Real Roots of an equation:2,-2 Number of Real Roots:2
4 Degree:5 Real Roots of an equation:-1,1-3,-3,-3 Number of Real Roots:5
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Samuel has a collection of toy cars. His favorites are the 27 red ones, which make up 60%, percent of his collection.
How many toy cars does Samuel have?
Answer:
45
Step-by-step explanation:
The 27 red cars make up 60% of the total collection, here is the equation
to be solved:
27 = 60% of C C is the total cars in the collection
27 = .60 C
27 / .60 = C
45 = C
Hope this helps! :)
The temperature on a summer afternoon is 85°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit.
The expression that can be used to find the temperature after it changes is 85°F + C
How to find a change in temperature?Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.
The instrument used to measure temperature is a thermometer.
Temperature on a summer afternoon = 85°FDecrease in temperature = -11°Flet
C = change in temperatureThe change in temperature = 85°F + C
= 85°F + (-11°F)
= 85 - 11
= 74°F
Therefore, the new temperature after a decrease in 11°F is 74°F
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To train for a triathlon, Mr Greg swims, bikes, and runs everyday. Each day he bikes 10 times the distance he swims, and run 1. 5 miles more than half the distance he bikes. If Mr. Greg covers a total of 25. 5 miles on each day of training, how many miles does he swim? Bike? Run?
He covers 15 miles on the bike, 9 miles by running and 1.5 miles while swimming which sum up to 25.5 miles which is his total training distance.
What is distance?Distance is defined as an object's entire movement without regard for direction. Distance may be defined as how much ground an item has traversed regardless of its starting or finishing place. Distance is a scalar number that indicates "how much ground an item has covered" while moving. Displacement is a vector variable that describes "how far out of place an item is"; it represents the total change in position of the object. Distance is the length along a line or line segment between two locations on the line or line segment.
Here,
He rides 15 miles, which is ten times as far as he swims.
He runs 9 miles, which is half the distance he rides (15/2=7.5). Plus the additional 1.5 miles, totaling 9.
He swims.10 of what he bikes, for a total of 15x.10 = 1.5. As a result, he swims 1.5 miles.
15 miles = bike
9 miles= run
1.5 mile =swim
Add them all together and you get 25.5 miles.
He rides his bike for 15 miles, runs for 9 miles, and swims for 1.5 miles, for a total training distance of 25.5 miles.
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3-107. Find common denominators and calculate each of the following sums.
b. +3
What is the least common multiple of 8 and 4? Of 5 and 3?
T
d. Explain how finding the least common multiple of two numbers can help
you add fractions.
Answer:
LCM(8,4)=8.LCM(5,3)=15. LCM can be used to create equivilant fractions, meaning you can add fractions with much more efficiency.
Step-by-step explanation:
How much money does he earn when he sells 35 wooden toys? Emilio builds and sells homemade wooden toys for $12 each. The festival he is attending charges $50 to set up his booth. How much money does he earn when sells 35 wooden toys?
After selling 35 wooden toys and after cutting the expense of setting up his booth, Emilio earns $370.
What is BODMAS?
BODMAS, often known as the order of operations, is a method for carrying out operations in an arithmetic expression. Math is all about logic and some established principles that facilitate our computations. BODMAS is one of those commonly used rules for consolidating expressions with multiple operators.
Solution Explained:
A/Q, The price of one toy is $12
The cost of setting up the shop is $50
Therefore, the amount Emilio earns after selling 35 toys is:
(12 X 35) - 50
= 420 - 50
= 370
Hence, Emilio earns $370
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which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling
In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.
Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.
An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.
Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.
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Can anyone write the equation of the graph?
Which rational number is equivalent to 0 . ¯¯¯¯¯¯ 36 ?
The rational number is equivalent to 0.36 is 9/25
How to determine the equivalent rational number?From the question, we have the following decimal number that can be used in our computation:
Decimal number = 0.36
To start with, we need to express the decimal number as a fraction
This is represented as follows:
So, we have the following representation
Decimal number = 36/100
Change the label of the above representation to rational number
Rational number = 36/100
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 18/50
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 9/25
Hence, the equivalent rational number is 9/25
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Which of the following would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years? Question content area bottom Part 1 Select all that apply. A. $80 at 75% for 18 months B. $200 at 5% for 8 years C. $225 at 10% for 4 years D. $300 at 2% for 2 years E. $250 at 10% for 2 years
The option that would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years include:
A. $80 at 75% for 18 months
C. $225 at 10% for 4 years
How to calculate the interest?It's important to note that the simple interest can be calculated thus:
= Principal × Rate × Time
Therefore, the amount of interest as a $600 principal with 2.5% interest for 6 years will be:
= PRT
= (600 × 0.025 × 6)
= $90
The interest on $80 at 75% for 18 months will be:
= $80 × 0.75 × 1.5
= $90
The interest on $225 at 10% for 4 years will be:
= $225 × 0.1 × 4
= $90
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nine out of ten student prefer math class over lunch. how many student do not prefer math if 200student were asked
Answer:
Step-by-step explanation:
20? lol
ASAP!! Brainliest to first answer
3x - 2/3x = 14
Answer:
x = 6
Step-by-step explanation:
Given equation,
→ 3x - (2/3)x = 14
Now the value of x will be,
→ 3x - (2/3)x = 14
→ (9/3)x - (2/3)x = 14
→ ((9 - 2)/3)x = 14
→ (7/3)x = 14
→ 7x = 14 × 3
→ x = 42/7
→ [ x = 6 ]
Hence, the value of x is 6.
What number should go in the empty boxes to complete the calculation for finding the product of
To do the multiplication, we multiply 0.63 by each of the digits & decimal places of 0.24 (and align the products that we get) then add them together.
0.63 x 4 = 2.52, therefore the first missing spot is a 2.
0.63 x 2 = 1.26, therefore the second missing spot is a 2 (the 0 is so that the decimal point can be aligned for the result.)
Answer: Box 1: 2 Box 2: 2
Step-by-step explanation:
So, for box one it would be 2 because 3 x 4 = 12, put the 2 on the bottom and the 1 on the 6, then 6 x 4 + 1 = 25, then put the 5 on the bottom and the 2 on the top, then 4 x 0 + 2 = 2, so the answer would be 2.
For box 2, 252 + 1?60 = 0.1512, so we have to find the missing number. So, 2 + 0 = 2, so put the two on the bottom, then 5 + 6 = 11, so put the 1 on the bottom and the other 1 on the 2 from the first box, so 2 + 1 = 3, plus 2 more would equal 5, so the second box would be 2.
Hope this helps!
Order the following from least to greatest -0.2, 4.22,2.02,-3/10, 4 1/8
The correct order is -3/10, -0.2, 2.02, 4.22, 4 1/8 .
Firstly we will convert the fractions into decimal units i.e
-3/10 = -0.3
41/8 = 5.125
We know that the higher the number in negative number line lower will the value of it so the -0.3 < -0.2
Now we can easily arrange these numbers according to the number line i.e;
Negatives will be first to come on number line and the correct order will be as follow :
-0.3 , -0.2, 2.02, 4.22, 4 1/8
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What is the range of the following function
The range of the given function is y ≥ 0 which is option B.
From the graph:
Some points (-1,1),(-2,2),(0,0),(1,1),(2,2)
Range is defined as the set of y values or outputs.
range = 0,1,2,3 ......
Means range starts from zero to infinite(0 to all positive values.
so range = y ≥ 0
Therefore range of the given function is y ≥ 0 which is option B.
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the faa now figures the average checked bag to weigh 30 pounds. this is up from a previous figure of 26 pounds. find the amount of increase and the percent of increase, to the nearest whole percent.
The amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %. The result is obtained by calculating the change of two numbers.
How to find the percent of change?A number can increase or decrease to another number. This change can be counted by subtracting the first number from the second number. If the result is positive, it is an increase. If the result is negative, it is a decrease.
The percent of change would be the ratio of the amount of change to first number times 100.
Given the first figure of bag is 26 pounds and the last figure is 30 pounds.
What is the amount of increase?What is the percent of increase?The amount of increase is subtracting 26 from 30.
30 - 26 = 4 pounds.
The percent of increase is
[tex]= \frac{4}{30} \times 100[/tex] %
[tex]= 0.1333 \times 100[/tex] %
[tex]= 13.33[/tex] %
Hence, the amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %.
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help is needed please and thank you
The required value of h(0) = 5 in the given function is represented in the shown graph.
What is a graph?A graph can be defined as a visual representation or a diagram that represents data or values.
The function is given in the represented graph of g(x)
We have to determine the value of h(0) of the given function in the graph
According to the given graph, we can see that when the value of variable x is 0 and the value of variable y is 5, the domain of the provided function h(x) is 5. This implies that h(0) = 5.
Therefore, the required value of h(0) = 5 in the given function is represented in the shown graph.
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Gabriella is going back to school shopping.each notebook she buys costs $3 and each pack of markers costs $3.she buys 4 packs of markers and n notebooks.she writes the follwing expression represent how much shr spend
Answer:
$24
Step-by-step explanation:
3(4) + 3(4) = x (the total cost)
12 + 12 = x
x = $24
What is the length of the hypotenuse in 2 decimal places
a telephone call arrived at a switchboard at random within a one-minute interval. the switch board was fully busy for 15 seconds into this one-minute period. what is the probability that the call arrived when the switchboard was not fully busy?
The chance that the call arrived when the switchboard was not completely busy is 0.75.
Probability is a branch of mathematics that studies the likelihood of a random event occurring.
It is given that the switchboard is fully busy for the first 15 seconds, that means it is not busy for the next 15 seconds to 60 seconds
Therefore the probability that calls arrived when the switchboard was not fully busy is
P(15< x < 60) = ∫_15^60▒f(x)dx
= ∫_15^60▒〖1/60 dx〗
=1/60 ∫_15^60▒〖1.dx〗
= 1/60 [ x ]6015
= (60 – 15)/60
= 45/60
= ¾
= 0.75
Therefore the probability that the call arrived when the switchboard was not fully busy is 0.75
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What is the value of k? 20+ 7k = 8k+ 16
The solution for k in the equation given as 20+ 7k = 8k+ 16 is 4
How to determine the solution to the variable k in the expression?From the question, the algebraic expression is given as
20+ 7k = 8k+ 16
There is no constant to multiply or divide in the expression
So, the equation remains the same
20+ 7k = 8k+ 16
Collect the like term in the above equation
This gives
8k - 7k = 20 - 16
Evaluate the like term in the above equation
So, we have the following representation
k = 4
The above equation cannot be solved further
Hence, the solution is k = 4
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I really need help with this parallel lines and transversal equations find each angle measure 1-8
Answer:
1 = 88
2 = 92
3 = 88
4 = 92
5 = 92
6 = 88
7 = 92
8 = 88
Step-by-step explanation:
10x + 2 = 14x - 50
52 = 4x
18 = x