What is a slope in math?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
To find the correct answer, we need to look at the formula for a straight line: y=mx+b where m= the slope of the line and b= the y intercept. We know from the problem that the slope must be equal to -4, leaving us with y= -4x +b. From here you can substitute the given point in the equation and solve for b.
-3= -4(4) +b
-3= -16+b
+16 +16
13= b
This tells us that b=13, now we simply substitute that into the formula.
The solution to your question is y=-4x+13
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Triangle DEF is formed by connecting the midpoints of the side of triangle ABC. The lengths of the sides of triangle ABC are shown. Find the perimeter of triangle DEF. Figures not necessarily drawn to scale.
Step-by-step explanation:
as per the midsegment theorem
the lines connecting the half-points are half as long as the corresponding parallel side lines of the main triangle, ABC.
EF is half as long as AB = 4/2 = 2
DE is half as long as AC = 6/2 = 3
DF is half as long as BC = 4/2 = 2
so, the perimeter of DEF is
2 + 3 + 2 = 7
Find an equation of the circle whose diameter has endpoints (-2,-6) and (6,-4)
write 36 as a product of its prime factors, write the factors in order from smallest to biggest
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
From smallest to biggest, the necessary variables are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By expressing 36 as the product of the components, we may get the factors.
how do I solve for x in this equation: 8(x-3)+7=2x(4-7)
Answer:
x = 17/14 = 1 3/14
Step-by-step explanation:
You want the value of x in 8(x-3)+7=2x(4-7).
SolutionIt often works well to simplify the equation first.
8x -24 +7 = 2x(-3) . . . . . use the distributive property
14x -17 = 0 . . . . . . . . add 6x
x -17/14 = 0 . . . . . . divide by 14
x = 17/14 = 1 3/14
What is 1 squares in square Metres?
Answer:
Squares are the most common unit of measurement referenced when it comes to overall house size, and one square is equivalent to 9.290304 square metres (confusing, huh
Which sentence from the article would be MOST important to include in a summary of the article?
What is the slope of the points 1 1 and 2 2?
The slope of the points passes through the two points [tex](1,1)[/tex] and [tex](2,2)[/tex] is [tex]1[/tex].
When the equation of the line passes through the two points [tex](1,1)[/tex] and [tex](2,2)[/tex]
Then we can find the slope m is
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{2-1}{2-1} \\m=1[/tex]
The value of the slope is [tex]1[/tex].
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A farmer has 63 cows and 81 sheep. Write the ratio of cows to sheep in its lowest terms.
Answer:
7:9
Step-by-step explanation:
The basic ratio is 63:81 but to simplify this ratio you can simplify each number as a multiplication of its factors.
63=3*3*7
81=3*3*3*3
Now find the factors they have in common and get rid of them.
63=3*3*7
81=3*3*3*3
The numbers in bold are all the factors that they have in common.
You can cancel these numbers out.
Now the remaining numbers you can put into a ratio in the same order
7:3*3
7:9
express the given function in terms of the unit step function and find the laplace transform. f ( t )
The Laplace transformation is:
[tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]
Rewriting the f in terms of the unit step function:
[tex]\left \{ {{y=5} for 0\leq t\leq 7 \atop {x=-3}for t\geq 7} \right.[/tex]
⇒ f(t) = 5[u(t) - u (t-7)] - 3u(t -7 )
= 5u(t) - 8u (t-7)
Unit Step Function:
The unit step function, also known as the Heaviside function, is known in engineering applications as a function that can describe the switching process mathematically. We often encounter functions whose values change rapidly over a certain time unit t.
where,
u(t) = [tex]\left \{ {{y=1 for t\geq 0} \atop {x=0 for t < 0}} \right.[/tex]
Recall the time-shifting property of the Laplace transform:
L{u(t - c) f( t - c)}
= [tex]e^{-es} L{f(t)}[/tex]
Laplace Transformation:
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that transforms a function of real variables (usually t in the time domain) into a function is. Complex variable (complex frequency domain, also called s-domain or s-plane). As transformations are tools for solving differential equations, they have many applications in science and engineering. In particular, it converts ordinary differential equations to algebraic equations and converts convolutions to multiplications.
and the Laplace transform of a constant function,
L[k] = k/s
So we have
L[f(t)] = L[5u(t) - 8u (t-7)]
= [tex]5[L_{1} ] - 8e^{-7s} L[1][/tex]
Therefore,
[tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]
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Quadrilateral LMNP has diagonals LN and MP. The two diagonals intersect at Point D. If D is the midpoint of LN and MP, which of the following relationships must
be true?
The correct relationship is Δ PDN ≅ Δ MDL
What is a quadrilateral?The quadrilateral is a type of 2D geometrical shape with four sides, the sum of its interior angles is 360°.
Given that, Quadrilateral LMNP has diagonals LN and MP. The two diagonals intersect at Point D. If D is the midpoint of LN and MP.
Considering the triangles, Δ PDN and Δ MDL
According to definition of midpoints,
LO ≅ ON
MO ≅ OP
∠ MDL ≅ ∠ PDN (vertically opposite angles)
Therefore, Δ PDN ≅ Δ MDL by SAS rule.
Hence, option a) Δ PDN ≅ Δ MDL, is correct.
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a basic assumption for a chi-square hypothesis test is . a. the population distribution(s) must be normal b. the scores must come from an interval or ratio scale c. the observations must be independent d. none of the other choices are assumptions for chi-square
option c is correct
c. the observations must be independent
What is a Chi-square test?A Chi-square test is a hypothesis testing method. Two common Chi-square tests involve checking if observed frequencies in one or more categories match expected frequencies.
Types of Chi-square tests
You use a Chi-square test for hypothesis tests about whether your data is as expected. The basic idea behind the test is to compare the observed values in your data to the expected values that you would see if the null hypothesis is true.
There are two commonly used Chi-square tests: the Chi-square goodness of fit test and the Chi-square test of independence. Both tests involve variables that divide your data into categories. As a result, people can be confused about which test to use. The table below compares the two tests.
given that
a basic assumption for a chi-square hypothesis test is
given options are
a. the population distribution(s) must be normal
b. the scores must come from an interval or ratio scale
c. the observations must be independent
d. none of the other
from the above options
the population distribution is need not to be normal
there is no need to come from an interval or ratio scale
but the observation need to be independent
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jason is trying to remember the five digit combination to his safe. he knows that he only used digits $1$ through $5$ (possibly repeated), that every even digit was followed by an odd digit, and every odd digit was followed by an even digit. how many possible combinations does jason need to try?
180 possible combinations does jason need to try
What is Permutation?
In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order. In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered.
What is a Combination?
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.
If the combination begins with an odd digit
We have 3 * 2 * 3 * 2 * 3 = 108 possible combinations
If the combination starts with an even digit
We have 2 * 3 * 2 * 3 * 2 = 72 possible combinations
So 108 + 72 = 180 possible combinations
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Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be good. Assume you have purchased a single-family home that you intend to rent for $850 per month. You will have the following expenses:
The annual return of the investment is 31.1%.
Given that, person has purchased a single-family home that you intend to rent for $850 per month.
What is the return?A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.
First find the amount earned per year:
= 850 x 12
= $10,200
The yearly expenses would be:
= (390 x 12) + (60 x 12) + (340 x 2) + 500 + (100 x 12)
= 4,680 + 720 + 680 + 500 + 1,200
= $7,780
The annual ROI is:
= (10,200 - 7,780) / 10,200 x 100%
= 31.1%
Therefore, the annual return of the investment is 31.1%.
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"Your question is incomplete, probably the complete question/missing part is:"
Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be good. Assume you have purchased a single-
family home that you intend to rent for $850 per month. You will have the following expenses:
Monthly mortgage $390
Monthly insurance $60
Semiannual property taxes $340
Repairs (yearly estimate) $500
Monthly lawn care or snow removal $100
The return on investment for the property is
% (Round to one decimal place.)
A runner i elected at random find the probability that the ditance covered by the runner i a prime number
Probability that the distance covered by the runner is a prime number is 1/5.
How do you calculate probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
What are the 3 types of probability?Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all distinct outcomes that could occur).
Subjective Probability. Definition of Relative Frequency.
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Four times a number is 45 less than the square of that number. Find the negative solution
Answer: x<-9
Step-by-step explanation:
4x-45<[tex]x^{2}[/tex]
x^2+4x-45<0
factor
(x+9)(x-5)<0
x<-9,x<5
the negative solution is x<-9
The midpoint of is M(1, 5). One endpoint is P(–4, 9). Which equations can be used to find the coordinate of endpoint Q(x2, y2)?
If the midpoint is M(1, 5). and One endpoint is P(–4, 9) the other point is solved to be
point Q = (6, 19)How to find the other pointThe formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
solving for Q (x₂, y₂)
1 = (x₂ + -4)/2
2 = x₂ + -4
x₂ = 6
5 = (y₂ + 9)/2
10 = y₂ + 9
y₂ = 19
point Q = (6, 19)
the other point is solved to be Q (6, 19)
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Answer: the answer is C
-4+x2/2 = 1, 9+y2/2 =5
Step-by-step explanation:
154 is the same as the product of 158 and n, decreased by 132
Answer:
Equation: 154 = 158n - 132 n = 11/6
Step-by-step explanation:
Let's start by converting this into an equation. Some keywords to look for are "is" which means an equal sign (=), "product" which is multiplication (*), and "decreased" which means a minus sign (-):
So this is our equation: 154 = 158n - 132
Now we have to solve for n:
First, we add 132 to both sides to isolate the n more:
286 = 158n
Then to completely isolate the n, we divide both sides by 158
286
------ = n
156
n = 11/6, final answer.
Which point is the solution set of the given system of inequalities?
After solving, the solution set of the give inequality is (-1, 3)
In the given question, we have to find the solution set of the given system of inequalities.
The given inequalities are
x+y≥2...................(1)
4x+y≥-1.................(2)
To solve the given inequality we use the elimination method.
Multiply equation 1 by 4 on both side, we get;
4x+4y≥8...................(3)
Subtract equation 3 and 2, we get;
3y≥9
Divide by 3 on both side we get;
y≥3
Put the value of y in equation 1
x+3≥2
Subtract 3 on both side, we get;
x≥-1
Hence, the solution set of the give inequality is (-1, 3).
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The write question is;
Which point is the solution set of the given system of inequalities?
x+y≥2
4x+y≥-1
An electrician account earn $1680 his account had a simple interest rate of 7.5% for the past four years what amount did he deposit four years ago
Thus, the amount he deposited four years ago is 5600.
A simple interest is what exactly?Simple interest is used to determine the amount of interest that will be charged on a sum of money at a specific rate and for a specific amount of time. The principal amount in simple interest does not change, in contrast to compound interest, which adds the interest from the principal of preceding years to determine the interest of the following year.
Here,
Given:
The amount of electrician account earned is 1680
thus total amount is = 1680 + x
where x is the principal amount
Interest rate = 7.5%
and total years = 4 years
Using formula
[tex]\frac{P*R*T}{100}[/tex]= Simple interest
=> 1680 = x*7.5*4/100
=>1680 =x * 30/100
=>1680* 100 /30 = x
=>5600
Thus, the amount he deposited four years ago is 5600.
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Determine the effective tax rate for a taxable income of $75,400. round the final answer to the nearest hundredth.
A. 10.05%
B. 16.27%
C. 22.00%
D. 24.90%
The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate. The effective tax rate is 10.15%. Here option A is the correct answer.
The term effective tax rate refers to the average tax rate that an individual pays on both earned and unearned income, such as stock dividends. According to the progressive tax model, when income rises, the tax rate also rises, putting persons in a higher tax bracket.
Here, the presented data shows that the marginal tax rate is 22% for taxable income in the $40,526 to $86,375 income range.
Effective tax rate = total taxes owed/taxable income × 100.
Effective tax rate = $6,847.50/$67,400 × 100.
The tax rate in effect = 10.15%
Complete question:
Having a total tax liability of $6,847.50, a taxable income of $67,400, and a marginal tax rate of 22%. Determine the effective tax rate for a taxable income of $75,400. round the final answer to the nearest hundredth.
A. 10.15%
B. 18.27%
C. 42.00%
D. 64.90%
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How do you write an area?
To write an area, you need to know the shape and the measurements of the sides.
For example, if you have a square, you can calculate its area with the formula A = s², where A is the area and s is the length of a side.
If the side is 10 cm, then the area would be written as A = 10² = 100 cm².
1. Identify the shape of the area you are trying to calculate.
2. Calculate the measurements of the sides.
3. Use the appropriate formula to calculate the area. For example, for a square, use the formula A = s², where A is the area and s is the length of a side.
4. Plug in the measurements and calculate the area.
5. Write the area using the correct unit of measurement. For example, if the side was 10 cm, the area would be written as A = 10² = 100 cm².
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A hat contains the names of seven boys and three girls. If one name is drawn from the hat at random, what is the probability it is the name of a boy? enter your answer as a reduced fraction.
The probability of one name drawn from the hat is 0.7 if a hat contains the names of seven boys and three girls.
We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.
In hat number of names of boys are =7 and
number of names of girls are =3
So, total number of names are =number of boys names + number of girls names
=>total number of names are =7+3
=>total number of names are=10
Now, number of boys are =7
So, count of favorable outcomes is =7 and total number of outcome is 10
=>Probability of choosing a boy name is =number of favorable outcome/total number of outcome
=>P(E) = 7/10
=>P(E)=0.7
Hence, required probability is 0.7
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130 increases to 182, what percentage increase is this?
Answer:38.4615384615% (increase)
Step-by-step explanation:Percent change = 180 - 130 |130| × 100% = 50 130 × 100 = 38.4615384615% (increase). Where: 130 is the old value and 180 is the new value.
Find the dimensions of a rectangle (in m) with perimeter 92 m whose area is as large as possible.
The dimension of a rectangle is 23m and 23m.
Here we have to find the area of a rectangle as large as possible.
Data given:
Perimeter = 92m
The formula for the perimeter of the rectangle:
perimeter = 2(length + breadth)
92 = 2( l + b)
l + b = 46
We have to find the largest area, so when we will take the length and breadth same then we get the largest area.
So length = breadth
2 length = 46
length = 23m
length = breadth = 23m
Therefore the dimensions are 23m and 23m.
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Im stuck and i need help. Will give brainliest to answer!!!!!
Write an equation of the line with a slope of 3 that passes through the points (1,5) and (-3,-7)
Answer:
y = 3x + 2
Step-by-step explanation:
y = 3x + c
substitute x and y with one of the points (ex: (1,5)):
5 = 3(1) + c
5 - 3 = c
2 = c
so
y = 3x + 2
To make sure this is correct, substitute x and y with the other point (ex: (-3,-7)):
-7 = 3(-3) +2
-7 = -9 + 2
-7 = -7
that means the equation is true and as it passes through both points.
A company manufactures and sells cell phone cases. The revenue obtained by selling a cases is given by the
formula
R = 2.8x -0.01x²
Solve the equation below to find the number of cell phone cases they must sell to receive $192 in revenue.
192 = 2.8x 0.01x²
They need to sell__ or __ cases to make $192 in revenue.
Answer:
Step-by-step explanation:
hi yall funny
Jenna has
131
131131 dog biscuits. She wants to give them as gifts to each of her
4
44 poodles.
How many biscuits does each poodle get?
By using division, it can be calculated that
Each poodle will get 32.75 biscuits
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division
Number of dog biscuits Jenna has = 131
Number of poodles Jenna has = 4
Number of biscuits each poodle will get = 131 [tex]\div[/tex] 4 = 32.75
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Complete Question
Jenna has 131 dog biscuits. She wants to give them as gifts to each of her 4 poodles. How many biscuits does each poodle get?
someone that knows about centers of triangles
Answer:It was not until the eighteenth century that mathematician Leonard Euler (1707-1783) discovered a relationship between the three classical triangle centers.
Step-by-step explanation:
How would you describe the graph for the equation |x|=2?
Answer:
Below
Step-by-step explanation:
It will be just two vertical lines one at x = -2 the other at x = 2
( There are no 'circles' ) ....here is a graph:
Which one of the following is NOT equivalent to 3/4
a 16/24
b 15/20
c 6/8
d 24/32
Which of the following is NOT equivalent to 3/4?
Simplest form:
a. [tex]\dfrac{16}{24}[/tex]
[tex]\dfrac{16\div8}{24\div8} =\dfrac{2}{3}[/tex]
Option A is not equivalent to 3/4
b. [tex]\dfrac{15}{20}[/tex]
[tex]\dfrac{15\div5}{20\div5} =\dfrac{3}{4}[/tex]
Option B is equivalent to 3/4
c. [tex]\dfrac{6}{8}[/tex]
[tex]\dfrac{6\div2}{8\div2} =\dfrac{3}{4}[/tex]
Option C is equivalent to 3/4
d. [tex]\dfrac{24}{32}[/tex]
[tex]\dfrac{24\div8}{32\div8} =\dfrac{3}{4}[/tex]
Option D is equivalent to 3/4.
Option A would be your answer since it is the only option that isn't equivalent to 3/4.