The general form of a linear equation is y - y1 = m(x - x1) then the point-slope form exists y - 5 = 3(x - 9)
What is point-slope form?The general structure of a linear equation exists y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that exists not the y-intercept).
Given: (x1, y1) = (9, 5) and (x2, y2) = (8, 2)
The point-slope form exists given by,
y - y1 = m(x - x1)
m = (y2 - y1)/(x2 - x1)
substitute the values in the above equation, we get
m = (2 - 5)/(8 - 9)
m = 3
The value of m = 3.
y - 5 = 3(x - 9)
Therefore, the point-slope form exists y - 5 = 3(x - 9).
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. If a and b are negative, then a + b is also negative.\
Answer:
The conditional statement is true.
Step-by-step explanation:
If a and b are negative, it doesn't matter what numbers they are; the sum will always be negative.
Simplify
(Show work)
−6(x−2)+5
Answer:
-6x+17Step-by-step explanation:
[tex]−6(x−2)+50\\\\-6x+12+5\\\\\sf{-6x+17}[/tex]
we are done!! ~~
Answer:
-6x + 17
Step-by-step explanation:
We can use algebraic expansion and order of operations to solve for this expression.
[tex] - 6(x - 2) + 5 \\ = - 6x + 12 + 5 \\ = - 6x + 17[/tex]
Can someone help pls fast
Answer:
b(x) = 4x + 1
Step-by-step explanation:
If x starts from 1, we can give the equation as follows:
b(x) = 4x + 1
Let's check it, for the first one
x = 1, b(x) = 5
for the second, x = 2, b(x) = 4(2)+1 =9
The section of a window consists of a rectangle surmounted by and equilateral triangle. If the perimeters be given as 10ft, find the dimensions of the window in order that the maximum amount of light may be admitted.
100 POINTS PLEASE
Answer:
Solution
verified
Verified by Toppr
Correct option is C)
Perimeter of window P=2y+3x=16
⇒y=
2
16−3x
....(1)
Area A=xy+
4
3
x
2
=
4
3
x
2
+x(
2
16−3x
)
A=8x+(
4
3
−
2
3
)x
2
dx
dA
=8+(
4
3
−
2
3
)2x
For maxima or minima,
dx
dA
=0
⇒4−
4
(6−
3
)
x=0.
∴x=
6−
(3)
16
=
36−3
16(6+
3
)
=
33
16(6+1.73)
=
33
16(7.73)
=
33
123.68
⇒x=3.75 nearly.
Now,
dx
2
d
2
A
=2(
4
3
−
2
3
)<0
Hence A is maximum.
By (1),
y=2.375
Step-by-step explanation:
Give the domain and range of the quadratic function whose graph is described.
The vertex is (-5, -8) and the parabola opens up.
The domain of f is ?
The domain of f is [-5, ∞) because the vertex is the global minimum of a parabola that opens up.
The domain of any polynomial, including quadratics, is (–∞, ∞).
The domain of a parabola is always all real numbers (sometimes written (−∞,∞). The domain is all real numbers because every single number on the x− axis results in a valid output for the function (a quadratic).
When x=−b2a, y=c−b24a. Therefore the maximum or minimum value of the quadratic is c−b24a. Whether it is the maximum or minimum can be determined by examining the sign of a. If a is positive, then the range is y≥c−b24a
Hence, The range here is [-5, ∞), because the vertex is the global minimum of a parabola that opens up, and the global minimum is the lowest value.
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CA=√(d-e²)=d-e
7. (√1+d²)² + (√²+1)'. =?
(1 + ²) + (e²+1)
8.
9.-1 MABMBC
=
2
2+d²+e² =
2 =
-1 = de
OA. -2de
OB. (A + B)2
OC. A²+ B²
OD. (d-e)2
d²2de + e²
d²2de + e²
-2de
Which expression is missing from step 7?
Pythagorean theorem
simplify
substitution property of equality
Answer: [tex]A^{2} + B^{2}[/tex] correct answer.
Step-by-step explanation:
What is Pythagorean Theorem?
Image result for Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.
[tex]A^{2} + B^{2} + C^{2}[/tex]
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
So, We can write,
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
[tex]Hypotenuse^{2}[/tex] = [tex]Perpendicular^{2}[/tex] + [tex]Base^{2}[/tex]
[tex]C^{2} = A^{2} + B^{2}[/tex]
Hence,
[tex]A^{2} + B^{2}[/tex] correct answer.
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A school is studying Math for Data and Financial Literacy standardized test scores. Which of the following displays could be used to represent the data, and why?
Bar chart, because test scores are numerical
Box plot, because test scores are categorical
Circle graph, because test scores are categorical
Stem-and-leaf-plot, because test scores are numerical
its stem and leaf just took the test
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
What is the Stem and leaf plot?In order to help visualize the shape of a distribution, a stem-and-leaf presentation or stem-and-leaf plot is a tool for displaying quantitative data in a graphical manner, comparable to a histogram. They are helpful tools for exploratory data analysis and developed from Arthur Bowley's work in the early 1900s.
This is simply accomplished by creating a draft of the unsorted leaves before arranging them in the final stem-leaf display. On the Undergraduate and graduate levels, you may find a number of examples that have been solved and even obtain expert assistance to learn the subject of stem and leaf plots.
A school is studying Math for Data and Financial Literacy standardized test scores.
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
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891.8 ÷ 5.2 = pls with the work out to
The answer to your question would be, 171.5
solve the equation for the indicated variable
A = 1/2(pi)(r)^2 solve for pi
Answer:
(2A)/(r^2)=pi
Step-by-step explanation:
The goal is to get pi by itself, so you have to move all the other elements over
2A=pir^2
(2A)/(r^2)=pi
what is 36 divided by 7.2
Answer:
36÷7.2=5
So this is the answer
Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple formula or rule.
Answer:
3 5,7,9,11,13,16,17 19,21,23,25,27,29
(3g) ^ 4 i need an expression of what it’s equal to
Answer:
[tex] 81g^4 [/tex]
Step-by-step explanation:
When you raise a product to a power, raise each factor of the product to the power.
Rule:
[tex] (ab)^n = a^nb^n [/tex]
Our problem:
[tex] (3g)^4 = 3^4g^4 = 81g^4 [/tex]
two non-zero real numbers, a and b, satisfy ab=a-b. Find a possible value of [tex]a/b +b/a -ab[/tex]
100 points
Answer:
2
Step-by-step explanation:
Given equations:
[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]
Rewrite the second equation as a rational expression:
[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]
Substitute the first equation [tex]ab=a-b[/tex] into the rational expression:
[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]
Therefore, the possible value of the given expression is 2.
Sketch the region bounded by the curves x=y3,x=1, and y=0 then find the volume of the solid generated by revolving this region about the y-axis.
According to the question, the region is bounded by the curve with the given data as [tex]x = y^{3} , x=1, y=0.[/tex]
To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx[/tex]
As per question, when x = 1 then the value of y is: y = 1
Now, substituting calculated values in the expression:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx[/tex]
Substitute the value of the variable 'x':
Therefore, the expression can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448[/tex]
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Find the distance between each pair of parallel lines with the given equations.
y=4 x
y=4 x-17
The distance between the given parallel lines is
In the given statement is :
The equations of the pair of each parallel lines is:
y = 4x and y = 4x - 17
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2} -c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y - 4x = 0
y - 4x + 17 = 0
Here,
a = -4 , b = 1, c1 = 0, c2 = 17
Therefore, putting the values
d = [tex]\frac{17 -0}{\sqrt{-4^{2}+1^{2} } }[/tex]
d = [tex]\frac{17}{\sqrt{17} }[/tex]
d = root 17
d = 4.12 units
Hence, The distance between the given parallel lines is 4.12 units
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The cost of tennis lessons varies directly with
the number of lessons given. Gustavo spends
$260 on four lessons. What would be the cost
for nine tennis lessons?
Answer:
solve this
Step-by-step explanation:
260*9/4
Simplify the given expression’s
( )
And
( )
Answer:
1. p^10
2. p^24
Step-by-step explanation:
p^6 x p^4=p^(6+4)=p^10
(p^6)^4=p^(6x4)=p^24
Which of the following numbers is between -3/4 and 5/8
-1
-1/2
7/8
0.9
Answer:
7/8 if you divide you will get your answer
Look at this bag of marbles. If you reached into this bag of marble and drew out one marble, find the probability that the marble that you drew was either
blue or green. State your answer as a decimal or a percent.
P (blue or green) there are 4 blue ,3 green , 1 yellow and 2 red
The probability that the marble that you drew was either blue or green is 0.7.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
There are 4 blue ,3 green , 1 yellow and 2 red
In total there are 10 balls.
probability of getting blue or green ball is = 7/10
P (blue or green) = 0.7
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The mean of a distribution of test scores is 80. The standard deviation of the scores is 10. If every
score is doubled and 15 is added to each score, what would the new mean and standard deviation be?
The new mean of a distribution of tests would be 175 and the new standard deviation of a distribution of tests would be 10 which is unchanged.
We have been given that in the question:
Mean of data = 80
Standard deviation = 10.
Then, every score is doubled and 15 is added to each score.
What is the mean of a distribution?The mean of a distribution is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
a) Mean of new data
The mean of the data rises by the same amount when a constant value is applied to each observation.
Mean of new score =
μ' = 2μ + 15 = 2(80) + 15 = 175
b) Standard deviation of new data
Every observation has a constant value added to it, therefore the standard deviation stays constant.
The standard deviation of the new score =
σ' = σ = 10
Therefore, the new mean and standard deviation would be 175 and 10 respectively.
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Determine whether each sequence is geometric. If so, find the common ratio. -1,1,-1,1, . . . . .
The given sequence is geometric, with common ratio = -1.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, Given: -1, 1, -1, 1, ...
Here, a₁ = -1, r = [tex]\frac{1}{-1}=\frac{-1}{1} = \frac{1}{-1} = -1[/tex]
Hence, it is a geometric sequence, with common ratio = -1.
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from
3. Error Analysis A student claims the
sequence 0,1,3, 6, ... is an arithmetic
sequence, and the next number is 10. What
error did the student make?
The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
What is an arithmetic sequence?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
here the given sequence is 0,1,3,6,10,......is an arithmetic sequence
then the common difference between the consecutive terms is constant
lets check take two consecutive terms as 0 and 1 then the difference is 1
take 1 and 3 then common difference is 3-1 =2
take 3 and 6 then common difference is 6-3 =3
take 6 and 10 then common difference is 10-6=4
.............in the same way we check for other terms also
and found that the common difference is not same
Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
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SAT/ACT Mitsu travels a certain distance at 30 miles per hour and returns the same route at 65 miles per hour. What is his average speed in miles per hour for the round trip?
A 32.5
B 35.0
C 41.0
D 47.5
E 55.3
The average speed in miles per hour for the round trip is (D) 47.5.
What do we mean by average?In layman's terms, an average is a single number chosen to represent a set of numbers, typically the sum of the numbers divided by the number of numbers in the set (the arithmetic mean). The average of the numbers 2, 3, 4, 7, and 9 (summed to 25) is 5, for example. An average could be another statistic, such as the median or mode, depending on the context. For example, the average personal income is frequently given as the median—the number below which 50% of personal incomes fall and above which 50% of personal incomes fall—because the mean would be misleadingly high if a few billionaires' personal incomes were included.To find the average speed:
30 miles + 65 miles = 95Formula: Sum of terms/Number of terms
95/2 = 47.5Therefore, the average speed in miles per hour for the round trip is (D) 47.5.
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Question 1 of 5
Drag each equation to the correct location on the table.
Solve the equations for the given variable. Then place the equations in the table under the correct solution.
=9
4 = 1
-6+z=-9
x=3
X 3
25= -2 -² + z = ²
Submit
-14z = -42
Reset
The correct location on the table is:
For x=3: x-5= -2, -3/5+x= 12/5, -14x=-42For x≠3: x/3=9, -6+x= -9, x/4= 6/5Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .
b= the constant term that represents the y-intercept.
For the given example: a=7 and b=2.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
x/3=9, thusx= 9*3
x=27
Therefore, x≠3
-6+x=-9, thusx=-9+6
x= -3
Therefore, x≠3
x-5=-2, thusx= 5 -2
x= 3
Therefore, x=3
-3/5+x= 12/5, thusx= 12/5 + 3/5
x= 15/5
x=3
Therefore, x=3
-14x=-42, thus14x=42
x=3
Therefore, x=3
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The sale price of a item is $300 after a 25%
Answer:
the answer is 225
Step-by-step explanation:
[tex] \frac{300 \times 25}{100} = 75[/tex]
this is the amount of discount
so remove it from the original price
300 - 75 = 225
which is the price after the 25% discount
hope this helps
Please help with this question. It’s over similar triangles, what do I do and what is the answer?
In the similar triangles given, the sum of AB and BD is: B. 4⅓.
How to Find the Side Lengths of Similar Triangles?The corresponding side lengths of two triangles that are similar to each other have equal ratio, that is, they are proportional in size.
Find AC:
AB/CD = AE/(8 - AC) [proportional sides of similar triangles]
AB = 3
CD = 2
AE = 8
Substitute
3/2 = 8/(8 - AC)
3(8 - AC) = 2(8)
24 - 3AC = 16
24 - 16 = 3AC
8 = 3AC
8/3 = AC
AC = 2⅔
Find BD:
AB/CD = BE/(5 - BD) [proportional sides of similar triangles]
BE = 5
AB = 3
CD = 2
Substitute
3/2 = 5/(5 - BD)
3(5 - BD) = 2(5)
15 - 3BD = 10
15 - 10 = 3BD
5 = 3BD
5/3 = BD
BD = 1⅔
AB + BD = 8/3 + 5/3
AB + BD = (8 + 5)/3
AB + BD = 13/3
AB + BD = 4⅓
Thus, in the similar triangles given, the sum of AB and BD is: B. 4⅓.
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The perimeter, P, of a rectangle is found using the formula P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle.
Solution:
The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.
As you stated the formula of a rectangle is P (perimeter) = 2W (the two widths added together) + 2L (the two lengths added together).
To solve this algebraically you need to define your variable, or unknown, which in this case is the width or "W".
Now set this same equation with any symbol you wish, "x" is often used, and solve for x. You could keep W instead of X also if it makes it easier to work on the problem.
P= 2x + 2L
isolate the 2x by subtracting 2L from both sides.
P-2L=2x
Now isolate the x by dividing both sides by 2 and you have
P-2L/2=x
x will be W. Just put in the numbers P and L and you will have solved for W.
One More Solution :
The perimeter of a rectangle is given by the following formula:
P = 2W + 2L
To solve this formula for W, the goal is to isolate this variable to one side of the equation such that the width of the rectangle (W) can be solved when given its perimeter (P) and length (L).
P = 2W + 2L
subtract 2L from both sides of the equation
P - 2L = 2W + 2L - 2L
P - 2L = 2W
divide both sides of the equation by 2
(P - 2L)/2 = (2W)/2
(P - 2L)/2 = (2/2)W
(P - 2L)/2 = (1)W
(P - 2L)/2 = W
Thus, given that the perimeter (P) of a rectangle is defined by P = 2W + 2L ,
then its width (W) is given by W = (P - 2L)/2
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8th grade mathematics| 50 POINTS
The equation y + 6 = 1/3 (x - 9) is written in point-slope form. What is the equation written in slope-intercept form?
A. y = 1/3 x -3
B. y = 1/3 x + 9
C. y = 1/3 x - 9
D. y = 1/3 x + 3
I appreciate all of your answers, even if they are wrong, if answers are taken up but you still would like to answer, please put in the comments. Have an awesome day!!! :)
C. y = 1/3 x - 9
Step-by-step explanation:The slope-intercept form is one way to represent a linear function that is set equal to y.
Simplifying and Solving
To find slope-intercept form from point-slope you should simplify the equation and then solve for y.
y + 6 = 1/3 (x - 9)Firstly, distribute the 1/3.
[tex]y+6=\frac{1}{3}x-3[/tex]Then, subtract the 6 from both sides.
[tex]y = \frac{1}{3} x - 9[/tex]This means that the slope-intercept form is y = 1/3 x - 9.
What Slope-Intercept Form Shows
We use slope-intercept form for 2 main reasons; it shows the slope and the y-intercept of a line (hence the name). The formula of slope-intercept is y = mx + b. In this formula, m is the slope and b is the y-intercept.
So, the slope of the line above is 1/3. The y-intercept of the line is -9.
Solve each system by elimination.
20x + 5y = 120 , 10x + 7.5y = 80
By elimination, the solution of the system of equations, 20x + 5y = 120 and 10x + 7.5y = 80, is (5 , 4).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Multiply first equation 2 by 2.
10x + 7.5y = 80 (equation 2)
20x + 15y = 160
Subtracting the two equations will eliminate the variable x.
20x + 15y = 160 (equation 2)
20x + 5y = 120 (equation 1)
0x + 10y = 40
y = 4
Substitute the value of y to any of the two equations and solve for x.
20x + 5y = 120 (equation 1)
20x + 5(4) = 120
20x = 120 - 20
20x = 100
x = 5
Hence, the solution of the system of equations is (5 , 4).
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A scientist measures 4.62 ml of a chemical into a beaker. \with a pipette, he carefully takes out 0.67 of the chemical. finally, he adds 1.25 ml of water into the beaker. how much liquid is in the beaker now?
Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.
Basic mathematical operations include addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.
4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml
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