Therefore , the solution of the given problem of linear equation comes out to be y= (3/2)x + 5 .
Define linear equation.The equation y=mx+b is the basis of a linear regression model. B is the slope, and m is the y-intercept. The aforementioned sentence is repeatedly alluded to as a "math problem with two variables," despite the fact that y and y are distinct parts. In bivariate linear equations, there are only two variables. The application regions for linear equations have no definitive solutions.
Here,
We must first determine the slope of the line before using the point-slope form of the equation of a line to determine the equation of the line that goes through two points.
The angle of the line that connects the coordinates (2, 8) and (8, 7) is:
=> slope = (−7 − 8) / (−8 − 2)
=> slope = −15 / −10
=> slope = 3/2
When we express the equation of a line in the point-slope format, where (x1, y1) is one of the line's points and m is its slope, we get the following result:
=> y − y1 = m(x − x1)
By selecting the line's origin (2, 8) and substituting the slope m = 3/2, we obtain:
=> y − 8 = (3/2)(x − 2)
The equation y = mx + b is transformed into the slope-intercept form by condensing and reordering the variables.
=> y = (3/2)x + 5
Consequently, y = (3/2)x + 5 represents the equation of the line going through the points (2, 8) and (8, 7) respectively.
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Write each amount as rate
500 words in one minute
Answer:
500 words per minute.
Step-by-step explanation:
Find the slope of the line shown below?
100 POINTS!!!! ILL GIVE BRAINLEIST. What is true when two proper fractions are multiplied together?
The product will be larger than both factors.
The product will be larger than the smaller factor but smaller than the larger factor.
The product will be smaller than both factors.
The product will be an improper fraction.
Answer:
When two proper fractions are multiplied together, the product will be smaller than both factors.
Step-by-step explanation:
To understand why this is true, we can consider the concept of fractions as parts of a whole. When we multiply two proper fractions, we are essentially taking a part of a part, which results in a smaller portion overall.For example, if we multiply 1/2 by 2/3, we are taking half of something and then taking two-thirds of that half. The result is 1/3, which is smaller than both 1/2 and 2/3.Therefore, the correct answer is: The product will be smaller than both factors.
Answer:The product will be smaller than both factors.
When two proper fractions are multiplied together The product will be smaller than both factors.Take a look at the equation below.
¾ * ⅔= 3 times 2 is 6 and 4 times 3 is 12. So the equation is 6/12 .
6/12 is simplified to 1/2. 1/2 is less than both 2/3 and 3/4. Which means the product is smaller. Hence, the correct answer is the product will be smaller than both factors.
I hope this helped & Good Luck <3!!!!
f(a) = 3a +5
g(a)=a²-4
Find f(-7) - g(-7)
The composite function when evaluated is -61
How to evaluate the composite functionFrom the question, we have the following functions that can be used in our computation:
f(a) = 3a +5
g(a)=a²-4
Using the above as a guide, we have the following equations
f(-7) = 3(-7) +5 = -16
g(-7) = (-7)²- 4 = 45
So, we have
f(-7) - g(-7) = -16 - 45
Evaluate
f(-7) - g(-7) = - 61
Hence, the solution is -61
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2. Is AP'Q'R' a 180° rotation about the origin of APQR?
Explain.
4
t
2
20
2
d
P
R
2 4
4.
R
à x*
8
It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.
How to explain the rotationIt should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.
One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:
(x', y') = (-x, -y)
Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.
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Please help me I would appreciate it.
use the Remainder Theorem and synthetic division please
Answer:
f (3) = 142
Step-by-step explanation:
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Number 5 I need help with only C
The probability of F P(F) = 0.33 and the conditional probability of F given G P(F|G) = 0.24. F and G is associated since they are not independent.
What is conditional probabilityConditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. The conditional probability P(A|B) occur only in the case of dependent events. It gives the conditional probability of A given that B has occurred.
P(F|G) = P(F∩G) / P(G)
P(F∩G) = Probability of happening of both F and G
P(F) = 199/600 = 0.3317
P(F∩G) = 79/600 = 0.1317
P(G) = 330/600 = 0.55
P(F|G) = 0.1317/0.55
P(F|G) = 0.2394.
Two events say A and B are independent if the probability of occurrence of one of them is not affected by the occurrence of the other, mathematical expressed as P(A ∩ B) = P(A) × P(B)
P(F) × P(G) = 0.3317 × 0.55
P(F) × P(G) = 0.1824
P(F∩G) is not equal to P(F) × P(G) from the data given.
Therefore, the probability of F P(F) = 0.33 and the conditional probability of F given G P(F|G) = 0.24. F and G is associated since they are not independent.
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Find the area of the figure.
Answer:
16yd
Step-by-step explanation:
I am from Michigan thank me this is really easy you nerd
This is funny helping you big people as a kid.
You decide that the all-white rectangular wall in your living room needs some color. You plan to paint a diagonal stripe to break up the white paint. If the wall measures 9 feet tall by 12 feet wide, what length of diagonal stripe will you paint?
Answer:
15 ft
Step-by-step explanation:
Use the Pythagorean theorem.
9² + 12² = c²
c² = 225
c = √225 = 15
Answer: 15 ft
Answer:
15 feet
Step-by-step explanation:
So, to start we have to find the area of the wall.
9(12)=108
Now, we need to find half of the walls area
108/2=54
We have our length and height, but we need to find the hypotenuse using Pythagoreans theorem.
9 is our A and 12 is our B
a^2+b^2=c^2
81+144=c^2
c^2=225
The square root of 225 is 15.
C=15
Therefore, the stripe will be 15 feet.
Find the last digit of the product of 2001 * 2003 * 2005 * 2007 * 2009... * 2017 * 2019?
The last digit of the product is 5.
How did we get the value?To find the last digit of the product of these numbers, we only need to focus on the last digit of each number, since the other digits do not affect the last digit of the product. We can observe that every odd number has a last digit of 1, 3, 5, 7, or 9. Therefore, we only need to consider the last digit of every fifth odd number in the given sequence.
The last digit of 2001 is 1.
The last digit of 2003 is 3.
The last digit of 2005 is 5.
The last digit of 2007 is 7.
The last digit of 2009 is 9.
The last digit of 2011 is 1.
The last digit of 2013 is 3.
The last digit of 2015 is 5.
The last digit of 2017 is 7.
The last digit of 2019 is 9.
To find the last digit of the product of these numbers, we need to multiply all of these last digits together. We can group the digits into pairs that multiply to 1, and there is one 5 remaining. Multiplying all of these digits together gives:
1 * 3 * 5 * 7 * 9 * 1 * 3 * 5 * 7 * 9 * 5 = 5
Therefore, the last digit of the product is 5.
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What is the value of cos^-1 (-square root 3/2)
Answer:
Step-by-step explanation:
The value of cos^-1(-sqrt(3)/2) is -π/6 or -30 degrees.
We know that cos^-1(x) gives the angle whose cosine is x, in the range [0, π]. In this case, we are looking for the angle whose cosine is -sqrt(3)/2.
Recall that the cosine function is negative in the second and third quadrants of the unit circle. In the second quadrant, the reference angle whose cosine is sqrt(3)/2 is π/6 or 30 degrees, but the cosine function is negative in this quadrant. Therefore, the angle whose cosine is -sqrt(3)/2 is -π/6 or -30 degrees, which is in the fourth quadrant.
So, cos^-1(-sqrt(3)/2) = -π/6 or -30 degrees.
Brainliest for correct answer
The shape below is a rhombus.
a) Which side is parallel to PQ?
b) Which angle is the same size as angle
QRS?
P
S
R
RS is Parallel to PQ and ∠ P has the same size as ∠ QRS. We find the answer by knowing the definition of Rhombus.
What is a rhombus?Rhombus is a special case of a parallelogram having four equal sides and opposite equal acute and obtuse angles . The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths i.e. Rhombus.
In mathematics, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides.
a. RS is Parallel to PQ
b. ∠ P has the same size as ∠ QRS
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is a function 4x + y = 2x -8
The equation defines y as a function of x, where the function has a slope of -2 and a y-intercept of -8.
If there is only one unique value of y for each value of x, then the equation 4x + y = 2x - 8 does not define y as a function of x.
The equation can be rewritten as y = mx + b, where m denotes the slope and b the y-intercept.
4x + y = 2x - 8
Taking 2x away from both sides:
2x + y = -8
When we take away 2x from both sides, we obtain:
y = -2x - 8
As a result, the equation establishes y as a function of x, with a y-intercept of -8 and a slope of -2.
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PLEASE HELP!! THIS IS DUE TONIGHT
The scale factor is 2/3 and the value of x and y are 9 and 10 respectively
What are similar shapes?Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.
scale factor = length of new shape/ length of original
= 8/12 = 2/3
x = 6 ÷ 2/3
x = 6 × 3/2
x = 9
y = 15 × 2/3
y = 10
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Select the graph that represents the solution of the compound inequality –6 ≤ 4x + 6 < 14
By answering the above question, we may state that The range of -3 x 2 inequality is the answer to the compound inequality.
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.
We must first remove 6 from each of the three elements of the compound inequality -6 4x + 6 14 in order to arrive at the following result:
-6 - 6 ≤ 4x < 14 - 6
If we simplify, we get:
-12 ≤ 4x < 8
Then, we divide each of the three inequality components by 4, keeping in mind that we don't need to reverse the inequality's signs because 4 is positive, to arrive at:
-3 ≤ x < 2
The range of -3 x 2 is the answer to the compound inequality.
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It took Matt 25 minutes to read a science article. It took him 13 times as long to read the assigned chapters in a history book. How long did it take Matt to read the history chapters?
The number of hours it would take to read the history chapters is 5 hours 25 minutes.
How long would it take to read the history chapters?In order to determine how long it would take to read the assigned chapters in the history book, multiply the time it take to read the science article by 13.
Multiplication is the mathematical operation that is used to determine the product of two or more values. The sign that is used to represent multiplication is x.
Time it would take to read the history chapters = 25 x 13 = 325 minutes
325 / 60 = 5 hours 25 minutes
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What's the value of X and Y?
(Need answers SUPER fast, please and ty!)
Answer:
x = 9/4 y = 15/4
Step-by-step explanation:
What is the meaning of "cannot always be added or multiplied"?
In addition to being novel, arbitrary matrices with complicated elements are viewed as having potential. It is based on I. Schur's theorem, which states that any complex matrix is valid.
What arbitrary mean in linear algebra?Any number of entries may be present in an arbitrary matrix. [a,b] [c,d] would be a random 2x2 matrix. Where all of the elements of some set (a, b, c, and d) (usually the real numbers.)
The definition of "arbitrary" is "undetermined; not assigned a specific value." As an illustration, the statement x+x=2x is true for any value of xR, whereas the statement x+x=2 is true only for the value x=1.
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Assume a class has 20 members. In how many ways can a committee of three be chosen?
As a result, there are 1140 different methods to select a committee of three from a group of 20 people.
what is probability ?The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to gauge how likely something is to happen. Probability is expressed as a number between 0 and 1, with 0 denoting that the occurrence won't happen and 1 denoting that it will definitely happen. By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. Numerous disciplines, including statistics, finance, engineering, and science, use probability extensively to forecast the chance of an event happening and base decisions on that forecast.
given
The following combination formula determines how many options there are to select a committee of three from a class of 20 members:
C(20, 3) = 20! / (3! * (20-3)!) = 20 * 19 * 18 / (3 * 2 * 1) = 1140
As a result, there are 1140 different methods to select a committee of three from a group of 20 people.
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The question is in the photo
The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.
How to find the value of y ?Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.
This means that 5 y + 8 is equal to 58 degrees.
The value of y is therefore :
5 y + 8 = 58
5 y = 50 - 8
y = ( 50 - 8 ) / 5
y = 50 / 5
y = 10
In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.
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Find the values of x and y.
The value of x and y in the triangle are 0 and 4 respectively.
How to find the side of a triangle?The mid segment of a triangle is a line connecting the midpoints between two sides of a triangle. The mid segment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side .
Therefore,
x + 2 = 3 / 2 x + 2
x - 3 / 2 x = 2 - 2
-0.5x = 0
x = 0
Let's find y
2y - 1 = 3y - 5
2y - 3y = -5 + 1
-y = -4
y = 4
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What is the least possible probability in any experiment
Answer:
0
Step-by-step explanation:
I remember learning this in math class. The smallest possible probability is zero meaning that event can't happen to be true.
The Clarke's son suggests that they rent a car that costs $250 for the week plus $0.22c/km. Their daughter does not want to drive far, so she suggests a car that is only $96 for the week but $0.50/km.
a) Write an equation to represent the cost of the car suggested by the son
b) Write an equation to represent the cost of the car suggest by the daughter
c) When will the two cars cost the same? Used the method of elimination to solve.
d) If the Clarke's plan to drive 500km, which option is less expensive?
Answer: a) The equation to represent the cost of the car suggested by the son is:
C1 = 250 + 0.22k
where C1 represents the total cost of renting the car, and k represents the number of kilometers driven.
b) The equation to represent the cost of the car suggested by the daughter is:
C2 = 96 + 0.5k
where C2 represents the total cost of renting the car, and k represents the number of kilometers driven.
c) To find when the two cars cost the same, we need to solve the equation:
C1 = C2
Substituting the expressions for C1 and C2 from parts a and b, we get:
250 + 0.22k = 96 + 0.5k
Simplifying this equation, we get:
0.28k = 154
Dividing both sides by 0.28, we get:
k = 550
Therefore, the two cars cost the same when the number of kilometers driven is 550.
d) If the Clarke's plan to drive 500km, we can calculate the total cost for each car by substituting k=500 into the equations from parts a and b:
C1 = 250 + 0.22(500) = 360
C2 = 96 + 0.5(500) = 346
Therefore, the car suggested by the daughter is less expensive for a 500km trip, as it would cost $346 compared to $360 for the car suggested by the son.
Step-by-step explanation:
6+2*6+20/4 can someone please answer this
The order of operations (also known as BODMAS) should be used to evaluate this expression:
6 + 2*6 + 20/4 = 6 + 12 + 5 = 23
So the answer is 23.
50 POINTS. if needed rotate in top right corner
The length of the side of the square would be 12 inches.
What is a Square?A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90° angles. The characteristics of a rectangle and a square are somewhat similar, although a rectangle only has its opposite sides equal. As a result, a rectangle is only referred to as a square if its four sides are of the same length.
Given : side of the triangle = 16 inches
So, the perimeter of the triangle = 16+16+16
= 48 inches
Now, the wire is unbent and shaped into a square.
So, the length of the wire would be same.
Hence, we can say that:
Perimeter of triangle = perimeter of square
48 = 4 × side
So, side = 12 inches.
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What is the equation of the line in slope-intercept form? (0,3) (-5,0)
In slope-intercept form, the line's equation is y = (3/5)x + 3.
What sort of equation would that be?The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What does a basic equation mean?A formula that describes how two expressions on either side of a sign are connected. It typically has an equal sign and one variable. similar to this: 2x − 4 Equals 2.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Where (x1, y1) = (0, 3) and (x2, y2) = (-5, 0)
m = (0 - 3) / (-5 - 0) = 3/5
To estimate the y-intercept, we just found the intersection of two endpoints just on line (0, 3):
[tex]y=mx+b[/tex]
[tex]3=(\frac{3}{5} )(0)+b[/tex]
[tex]b=3[/tex]
So the equation of the line in slope-intercept form is: [tex]y=(\frac{3}{5}x )+3[/tex]
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Given: AD ~/= BC and AD || BC. Prove: ABCD is a parallelogram.
Answer:
Its a parallelogram because it has two sets of equal sides.
(let me know if I have to explain it more)
Solve for x. Leave as an improper fraction. 5 = 3x + 9
Answer:
x = -4/3
Step-by-step explanation:
hope this helps^^
In 6th grade you likely solved which one is a better buy problems?
Consider: $68/10 tickets or $15/2 tickets
Which one is a better buy? How do you know?
$68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.
Explain about the unit value?The appraisal of a single item or part within one group is known as unit value.
The unit value is typically the result of dividing the price or worth of a set of things by the total number of items.The unit price is the cost of a single object or measuring unit, which can be a pound, a kilogramme, or a pint, and it's utilized to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.So,
$68/10 tickets = 68/10
$68/10 tickets = $6.8 for each ticket.
Now,
$15/2 tickets = 15/2
$15/2 tickets = $7.5 for each ticket.
Thus, $68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.
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