- 5/4 is the slope of line .
What is slope simple explanation?
Slope, usually referred to as rise over run, is a line's perceived steepness.
Slope is calculated by dividing the difference between two points' changes in y values by changes in x values. For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
Slope = y₂ - y₁/x₂ - x₁
the points (6, −3) and (−2, 7)
= 7 - (-3)/-2 - 6
= 7 + 3/-8
= - 10/8
= - 5/4
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What is the actual length of the school?
? ft
Answer:
48 ft
Step-by-step explanation:
The height i the scale drawing is 4 in and the length is 8 in which is twice the height
The actual school has a height of 24 ft so the length is twice the height here = 24 x 2 = 48 ft
Kiran is visiting the Statue of Liberty. He wants to test the mirror method of indirect measurement for calculating heights. He is 5.8 feet tall and knows that the Statue of Liberty is 305 feet tall. The diagram is not to scale but shows where a mirror could be placed to use similar triangles to verify the height of the Statue of Liberty. Drag the measurements to label the heights and distances.
The mirror needs to be at location C.
What is congruency of triangles?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables. Congruent triangles have equal comparable sides and angles.
It is given, height of Kiran is 5.8ft and that of Statue of Liberty is 305 ft.
Let the position of the mirror be at C.
Height of Kiran is AB, which is 5.8ft.
Height of Statue of Liberty is ED, which is 305 ft.
Thus, the triangles EDC and ABC are congruent.
The distance from Kiran to the mirror is BC and the distance between mirror to Statue of Liberty is CD.
Attached below is an image for reference.
Hence the mirror needs to be at location C.
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The better your time management skills are, the more work you are able to do is an example of a Continuous correlation Biserial correlation O Positive correlation O Negative correlation
The time management skill and amount of work done is an example of positive correlation.
Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.
The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.
The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.
It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.
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Microsoft Excel was used to obtain the following quadratic trend equation: Sales = 100 - 10X + 15X2. The data used was from 2004 through 2013 coded 0 to 9. What is the forecast for 2012?
The forecast for 2012 was 980.
Step-by-step explanation:1. Calculate.
From 2004 to 2013 there are 10 years, if we include the initial year. Hence, 2013 must be year 9. Therefore, 2012 must be year 8 (check the attached image to get a better understanding of this logic, in case it's needed). With this information, take the value of 8, substitute it by x in the formula and calculate:
[tex]Sales(8) = 100 - 10x + 15x^{2} \\ \\Sales(8) = 100 - 10(8) + 15(8)^{2}\\ \\Sales(8) =980[/tex]
2. Conclude.The forecast for 2012 was 980.
If a researcher wants to predict the value of a dependent variable based upon known independent variables for a specific case, they would use
A: standardized partial slopes
B: correlations
C: unstandardized partial slopes
D: none of these choices are correct
If a researcher wants to predict the value of a dependent variable based upon known independent variables for a specific case, they would use unstandardized partial slopes
Here the researchers wants to predict the value of a dependent variable based upon known independent variables for a specific case.
The dependent variable is variable that affected by other variables and the independent variable is the variables that does not affected by other variables.
The unstandardized partial slopes is defined as the average changes in the y units change in x units, at the same time all other predictor variable held constant
Therefore, they would use unstandardized partial slopes
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in a circle of 4 meters, what is the measure of the central angle (in degrees) subtended by an arc of length 5 meters
The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees
The radius of the circle = 4 meters
The circumference of the circle = 2πr
Where r is the radius of the circle
The value of π = 3.14
The circumference of the circle = 2π × 4
= 8π
The arc length = 5 meters
Consider the x as the central angle
The proportion of central angle and circumference will be
5/8π = x radiance / 2π
Cross multiply the terms
x × 8π = 5 × 2π
x = 10π / 8π
x = 5/4 radiance
Convert radiance to degrees
We know
1 radiance = 180/π degrees
5/4 radiance = 5/4 × 180/π degrees
= 71.61 degrees
Therefore, the central angle is 71.61 degrees
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Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
In a line When the line is parallel to the x-axis, the slope is zero. The first set of coordinates' slope will be 0.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,where (x₂,y₂) and (x₁,y₁) are the coordinates of any point on the line of slope.
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
1. For the first slope, the given coordinates are;
(-3,2), (-1,2), (1,2) and (3,2).
Now, if we take the first and the last point to calculate the slope of the line, we will get,
m = (y₂- y₁) / (x₂ - x₁)
m = (2-2) / (3+3) = 0
Thus, the slope of the line is 0.
2. For the second slope, the given coordinates are;
(-3,3), (-1,1), (1,-1) and (3,-3).
Now, if we take the first and the last point to calculate the slope of the line, we will get,
m = (y₂- y₁) / (x₂ - x₁)
m = (-3-3) / (3+3) = -1
Thus, the slope of the line is -1.
3. For the third slope, the given coordinates are
(-5,-5), (0,0) and (5,5).
Now, if we take the first and the last point to calculate the slope of the line, we will get,
m = (y₂- y₁) / (x₂ - x₁)
m = (5+5) / (5+5) = 1
Thus, the slope of the line is 1.
4. For the fourth slope, the given coordinates are
(-2,5), (-2,0) and (-2,5)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
m = (y₂- y₁) / (x₂ - x₁)
m = (-2+2) / (5-5) = ∞
Thus, the slope of the line is undefined.
Therefore, the slope of the first pair of coordinates will have no slope or zero slopes.
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What is the range of f(x) = |x| − 5?
−∞ < y ≤ −5
−5 ≤ y < ∞
0 ≤ y < ∞
5 ≤ y < ∞
Answer:
-5 ≤ y < ∞.
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = |x| − 5, we can first consider what happens when x is positive. In this case, the absolute value of x is just x, so the function becomes f(x) = x − 5. For example, if x = 6, then f(x) = 6 - 5 = 1. We can do this for any positive value of x to find the y-values that the function produces when x is positive.
Next, we can consider what happens when x is negative. In this case, the absolute value of x is -x, so the function becomes f(x) = -x - 5. For example, if x = -6, then f(x) = -6 - 5 = -11. We can do this for any negative value of x to find the y-values that the function produces when x is negative.
We can then combine the y-values that the function produces when x is positive and negative to find the range of the function. Since the function produces all y-values greater than or equal to -5 when x is positive and all y-values less than or equal to -5 when x is negative, the range of the function is -5 ≤ y ≤ ∞.
Therefore, the correct answer is -5 ≤ y < ∞.
A truck going at a rate of 20 miles an hour will reach a town 40 miles away in how many hours ?
Answer:
2 hrs
Step-by-step explanation:
d / r = time
40 mi / 20 m/hr = 2 hrs
the number of violent crimes committed in a city on a given day in a random sample of 90 days is a random variable.
The number of violent crimes committed in a city on a given day in a random sample of 90 days is a discrete random variable.
A random variable refers to a numerical quantity that is obtained by a random experiment. A random variable is known as discrete if it has either a finite or a countable number of possible values while it is called continuous if its possible values contain a whole interval of numbers. Hence, a discrete random variable refers to a variable that can take any whole number values as outcomes of a random experiment. It is a variable whose value is obtained by counting. Probability distributions are used to illustrate the values of discrete random variables. A discrete random variable is also known as a stochastic variable. Examples of a discrete random variable are a binomial random variable and a Poisson random variable. As the number of crimes committed in a city can only take discrete values such as 40 crimes, 50 crimes and cannot be 40.5 crimes, it is a discrete random variable.
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Solve x2 + 4x = 1 for x by completing the square.
x = −3
x = −1
x equals plus or minus square root of 5 minus 2
x equals plus or minus square root of 5 plus 2
Using the completing square method, the value of (C) x = ±√5 - 2.
What is completing the square method?A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.
In other words, the quadratic expression is completed by inserting a perfect square trinomial.
So, we have:
x² + 4x = 1
The x-coefficient terms must be divided by two:
4/2 = 2
Square:
2² = 4
Add 4 on both sides as follows:
x² + 4x + 4 = 1 + 4
x² + 4x + 4 = 5
Transform into perfect squares:
(x + 2)² = 5
Both sides of the square root:
x + 2 = ±√5
x = ±√5 - 2
Therefore, using the completing the square method, the value of (C) x=±√5-2.
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Complete question:
Solve x2 + 4x = 1 for x by completing the square.
a. x = −3
b. x = −1
c. x equals plus or minus the square root of 5 minus 2
d. x equals plus or minus square root of 5 plus 2
Answer:
is c correct?
Step-by-step explanation:
URGENT!!!!
Find z such that 7% of the area under the standard normal curve lies to the right of z.
The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4
How to find z such that 7% of the area under the standard normal curve lies to the right of z?
To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.
This value of z is known as the 43rd percentile of the standard normal curve.
We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.
According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4
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Integers Plot -2 1/2 on a number line.
A number line is plotted below:
What is meant by number line?A number line, used to represent the real numbers visually in early mathematics, is a drawing of a graduated straight line. It is presumptively true that each real number and each point on a number line relate to one another. A line with carefully marked, equally spaced-out points on it is frequently used to represent integers. Despite the fact that the image only displays the integers from -3 to 3, the line contains all real numbers, going on forever in both directions, as well as numbers that fall in between the integers. Especially when negative numbers are involved, it is frequently used as a teaching tool for basic addition and subtraction.
The number line is properly known as the real number line in advanced mathematics and can also be referred to as a real line.
A number line is plotted below:
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Screen time Administrators ata small school with 200 students want to estimate the average amount of time students spend looking ata screen (phone, computer; television, and s0 on) per day: The adminis- trators select a random sample of 50 students from the school to ask: (a) Show that the 10% condition is not met in this case_ (b) What effect does violating the 10% condition have on the standard deviation of the sampling distribution ofx?
10% condition is not met in this case because here sample size if 10% of the population is taken = 20.
Standard deviation decreases if 10% condition is violated.
What is 10% condition?10% condition states that the sample size we are working with must not exceed the population size. It is mostly useful when we are working with samples which are not independent.
If we use the 10% condition even with samples which are not actually independent, this condition will make it seem independent.
(a) Here population size = 200
Sample size = 50
If the 10% condition is met, sample size = 10% of population size
= 0.10 × 200
= 20
Sample size has exceeded the 10% condition.
(b) Standard deviation measures how much the set of values differ from it's mean value.
Violating 10% condition increases the sample size which in turn decreases the standard deviation.
Hence the 10% condition has not met in this case as the sample size is larger. Standard deviation decreases if 10% condition is violated.
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At your college, there is a school-sponsored website that matches people looking for roommates. The school claims that 36% of students will find a match their first time using the site. You are a writer for the school newspaper and are suspicious of the claim. To test it, you decide to perform a hypothesis test. To do so, you choose a random sample of 160 students who visited the site looking for a roommate. Of the students surveyed, 48 said they found a match their first time using the site. You confirm that it is appropriate to perform a Z-test. Why is a Z-test appropriate? Find z, the value of the test statistic for your Z-test. Round your answer to three or more decimal places. ZE = 0 5 ?
A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution and he value of the test statistic for your Z-test is 3.1111
Given :
You are a writer for the school newspaper and are suspicious of the claim. To test it, you decide to perform a hypothesis test. To do so, you choose a random sample of 160 students who visited the site looking for a roommate. Of the students surveyed, 48 said they found a match their first time using the site.
we know that ,
z = x - μ / σ
= 160 - 48 / 36
= 112 / 36
= 3.1111
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A survey shows that the probability that an employee gets placed in a suitable job is 0.65. A psychometric test consultant claims that he could help place any employee in a suitable job based on the result of a psychometric test. The test has an accuracy rate of 70%. An employee working in a particular company takes the test. The probability that the employee is in the right job and the test predicts that he is in the wrong job is . The probability that the employee is in the wrong job and the test predicts that he is in the right job is
The probability that someone is in the right job and the test is then wrong is 0.195.
The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In
The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3. Thus, the probability that someone is in the right job and the test is then wrong is:
= 0.65*0.3
= 0.195
The probability that someone is in the wrong job and the test is right is:
= 0.35 × 0.3
= 0.105.
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Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $332 for a total
account balance of $750. The next morning, his wife wrote a check for $1,183.15 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?
Answer: -433.15
Step-by-step explanation:
he's id debt and has to pay off the 433.15 later on.
Answer:
The McQuires' account is currently overdrawn by $483.15.
Step-by-step explanation:
If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.
I need help with this please help me
Answer:
A and B
Step-by-step explanation:
It is transformed fro a to a' by shift left of 7 and down 3 T(-7,-3)
Write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral. r = cos(2θ)
The area of the shaded region - [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi }{4}[/tex] [tex]cos^{2}[/tex] 2θ dθ
Determine α, β and f(θ).
To determine α and β, imagine a clock dial that turns counter-clockwise around the origin. The shaded area must be passed over by the dial. Place the dial in its starting position, and find the angle it makes with the horizontal axis, this angle is α. Do the same for the dial's end position, this angle [tex]\beta[/tex] .
To find f(θ), this equals r.
α= [tex]\frac{3\pi }{4}[/tex]
β= [tex]\frac{5\pi }{4}[/tex]
f(θ)=r=cos2θ
we know the integration formula,
A = [tex]\int\limits^\alpha _\beta[/tex] f (θ )² dθ
Hence, the area of the shaded region:
A = [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi} {4} \,[/tex] [tex]cos^{2}[/tex] 2θ dθ
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What is 0.6 divided by 10
Answer: 0.06
Step-by-step explanation:
Find the slope of the line graphed below.
The slope of the line determined by the points (-3,2) and (2,-2) is -0.8. The slope of a line is a measure of the steepness of the line.
What is slope of line ?It is defined as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line. The slope of a line is a measure of the steepness of the line. It is defined as the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) between two points on the line.The slope is often represented by the letter "m" in the slope-intercept form of a line's equation: y = mx + b. In this form, "m" is the slope and "b" is the y-intercept (the point where the line crosses the y-axis).To find the slope of a line given two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points given, we get:
slope = (-2 - 2) / (2 - (-3))
= -4 / 5
= -0.8
So, the slope of the line determined by the points (-3,2) and (2,-2) is -0.8.
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A cylindrical drinks bottle has a
paper label wrapped around the
outside. The label has a height of
7cm and the bottle has a radius
of 3cm. The label also has a
1.5cm overlap so that it can be
stuck together and held into
place. Calculate the area of the
label.
A soup can is in the shape of a cylinder. A soup can is in the shape of a cylinder. The can has a volume of 342 cm and a diameter of 6 cm.
Why are drink cans cylindrical?A cylindrical can combines the best qualities of a sphere and a cube. When packed in a box, cylinders take up about 90 percent of the available space, and their round shape is able to withstand a good amount of pressurization.Cans are filled before the top is crimped on by seamers. To speed up the production process filling and sealing operations need to be extremely precise. The filling head centers the can using gas pressure, purges the air, and lets the drink flow down the sides of the can.While there are benefits to the ridged design, an increasingly competitive marketplace in the 1980s led most can manufacturers to reduce the amount of aluminum they used, which changed the shape of soda cans. These manufacturers made can lids smaller by altering the shape of the neck and the size of the can opening.Also, a cylindrical container without corners is resistant to pressure from the outside, and it was suitable for containers packing carbonated drinks and food.
first find the area of the circle on top
A= pie*r^2
A= 3.14*5^2
A= 3.14*25
A= 78.5
Then multiply by the height of 14 centimeter and your answer will be 1,099
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Problems 14 and 15 pertain to the following situation: a woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%.
14. The probability that in any one month at least three of the tickets that the woman buys are winning tickets is about?
15. The average number of winning tickets that the woman buys each month is about?
The required probability is P(X≥3) =0.3234
The average number of winning tickets that the woman buys each month is 2.
The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.
The probability mass function of the binomial distribution is defined as:
[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]
Given that,
n = 20
p = 0.10
The required probability is P(X≥3)
P(X≥3) = 1-P(X<3)
P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)
P(X≥3)= 1- 0.1216- 0.270- 0.285
P(X≥3) = 0.3234
The mean of the distribution is defined as μ=n*p= 20*0.10= 2
The average number of winning tickets that the woman buys each month is 2.
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Say that we have three voters deciding among seven candidates, a, b, c, d, e, f, g. Their preference orderings are as follows.
1 2 3
(Best) c f g
a b b
e c c
g g d
b a e
d d f
(W orst) f e a
a. Find the top cycle.
b. For each candidate in the top cycle, write down an agenda (a sequence of majority rule
votes) that makes that candidate win (you can write the agenda as a tree).
c. Say that the voters use the Borda count system (each voter gives 6 points to their first
choice, 5 points to their second choice, and so on) to decide among the candidates. Which
candidate wins?
d. Is the Borda count winner also the Condorcet winner?
e. Which candidate does the worst in the Borda count?
f. Say that the person who does worst in the Borda count (your answer in part e. above) is
embarrassed about their poor performance, and tries to convince another candidate to drop
out so that they are no longer the worst person. If a candidate drops out, there would be
six candidates, and hence in the Borda count system, each voter gives 5 points to their first
choice, 4 to their second choice, and so forth. If a candidate drops out, is it possible for the
person who was originally the worst to no longer be the worst? If so, which candidate should
drop out? If not, please explain why not.
A. The top cycle in this case is a -> b -> c -> a.
B. The agenda that wins the candidate is:
First vote:
a vs b -> a wins
Second voice:
versus. c -> a wins
The agenda that Candidate B wins is:
First vote:
b vs c -> b wins
Second Voice:
b vs a -> b wins
The agenda that Candidate C wins is:
First vote:
c vs a -> c wins
Second Voice:
c vs b -> c wins
C. Using the Borda count system, the candidates' scores are as follows:
a:
18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)
b:
18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)
c:
18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)
d:
12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)
e:
12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)
f:
12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)
g:
6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)
Therefore, candidates a, b, and c tie for first place with 18 points each.
D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.
E. The candidate with the worst score in the Borda count is g of 6 points.
F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:
a:
15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)
b:
15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)
c:
15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)
Day:
10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)
e:
10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)
f:
10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)
In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.
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1. Which property justifies the second line in the following solution?
(1) Multiplicative Property of Equality
(3) Distributive
(2) Associative
(4) Additive Property of Equality
3x+2=8
3x+2-2=8-2
Additive Property of Equality justifies the second line in the 3x + 2 = 8
3x+ 2 - 2 = 8 - 2 solution.
What is Multiplicative Property of Equality?
When we multiply on both sides of an equation then the equation is remain same.
Distributive property: a(b + c) = ab + ac in other words the product of a number with sum of two numbers is equal to the sum of product first two numbers and "first and third" numbers.
Associative property: (a + b) + c = a + (b + c): If we shift the parenthesis then the result will remain the same.
Given equation is
3x+2=8
The second step is 3x + 2 - 2 = 8 - 2.
The additive inverse of 2 is -2.
-2 is added in second step. Thus Additive Property of Equality is used.
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Divide negative 5 and 1 over 7 ÷ negative 7 and 3 over 4.
The value of the fraction, negative 5 and 1 over 7 ÷ negative 7 and 3 over 4 is 144/217
What is a fraction?A fraction can be described as the part of a whole element or value.
The different types of fractions are;
Mixed fractionsImproper fractionsProper fractionsComplex fractionsSimple fractionsExamples of proper fractions; 2/4, 5/6, 7/9
Examples of improper fractions; 4/2, 3/2, 6/5
Examples of mixed fractions; 2 1/4, 4 6/7, 8 1/2
Examples of simple fractions; 1/ 3, 3/4, 1/2
Now, from the information given, we have;
negative 5 and 1 over 7 = -5 1/7negative 7 and 3 over 4 = -7 3/4Convert into improper fractions
-36/7 ÷ -31/4
take inverse of the divisor and multiply
-36/ 7 × 4/-31
-144/-217
144/217
Hence, the value is 144/217
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When graphed, the two linear equations intersect at the point 4x−2y=−2
12x−3y=9
Answer:
Step-by-step explanation:
When graphed they intersect at (2, 5)
Bag A contains 2 black marbles and 3 white marbles. Bag B contains 5 black marbles and 8 white marbles. Sarah adds some marbles to bag B, the probability of picking a black marble at random from either bag is now the same. Work out the smallest number of black marbles and white marbles he adds to bag B
Answer:
add one black and one white marble
Step-by-step explanation:
you have to make bag b equivalent to a 2:3 ratio.
add 1 to 5 to make it divisible by 2
divide 6 by 2
=3
multiply 3 by 3 to get a 2:3 ratio
=9
subtract initial marbles
9-8=1
making several trays of her famous lasagna. She finds the mozzarella cheese on sale for $4.89 per pound at her local grocery store. How much will she pay for four pounds of cheese?
Answer:
$19.56
Step-by-step explanation:
$4.89 per pound times the number of pounds to be purchased (4).
so 4(4.89)=19.56
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = - 0.4x -6
Step-by-step explanation:
The slope-intercept form of a line equation is
y = mx + b
where m is the slope and b the y-intercept where the line crosses the y axis.
From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6
To compute the slope, find another convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope
We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)
So two points to consider are (0, -6) and (10, -10)
Change in y values = rise = -10 - (-6) = 1- + 6 = -4
Change in x values = run = 10 - 0 = 10
So slope m = -4/10 = -0.4
Equation of line is y = -0.4x -6
