Answering the Question
There are a couple ways we can get the equation of a line, depending on what we're given.
The Equation FormMost linear equations are organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of a line can be calculated algebraically when we know two points that fall on the line:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the two pointsY-interceptThe y-intercept is the value of y when the line crosses the y-axis, or when x = 0. When given a graph, you can sometimes read the y-intercept directly from the graph.
For instance, if the line passes through the point (0,5), then the y-intercept is 5.
You can also find the y-intercept algebraically if you know the slope and one point that falls on the line. You plug in that point as (x,y) and isolate b.
Summary
For most cases, you can use the following method to find the equation of a line:
Find the slope of the line (using the slope equation) and plug it into y=mx+bFind the y-intercept of the line algebraically and plug it into y=mx+b
Identify a pattern and find the next three terms in the pattern.
8,9,10,11, . . .
Patterns of the given terms 8,9,10,11,.... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
As given in the question,
Given pattern is 8,9,10,11,...
First term a₁ = 8
Second term a₂ = 9
Third term a₃ = 10
Fourth term a₄ =11
d =aₙ - aₙ₋₁
=a₂ -a₁
=9 -8
=1
8,9,10,11,... represents arithmetic progression
aₙ=8 + (n-1)d
a₅ =8+ 4(1)
=2
a₆ =8 + 5(1)
=13
a₇ =8 + 6(1)
=14
Therefore, patterns of the given terms 8,9,10,11,... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
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Apparently a math question.
Answer:
Since Ian has $75 dollars, it would be enough to buy at least one DVD box set. However, there's not that much information in the statement.
Hope this helps with your question :)
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)? HALP
-439 is the value which is equivalent to (s circle t) (negative 7).
Given,
s(x) = 2 - x²
t(x) = 3x
We have to find the value which is equivalent to (s circle t) (negative 7)
That is,
(s circle t) (negative 7) : This is a notation for compound function.
A function that takes another function as an argument is referred to as a compound function.
s(t(-7)) is the alternative notation for this compound function, which means that the value obtained from the function t(-7) will be used in the function s. (x).
Now, let's calculate the value of t(-7):
That is,
t(x) = 3x
t(-7) = 3 × (-7) = -21
Next, apply the value of t(-7) for s(x)
That is,
s(x) = 2 - x²
s(t(-7)) = s(-21) = 2 - (-21)^2 = 2 - 441 = -439
That is, -439 is the value which is equivalent to (s circle t) (negative 7).
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Evaluate each expression 7^2
Answer:
PLEASE READ! Is that 7 to the second power? if so, here is your answer: 49
Step-by-step explanation:
Question 7 of 10
Given NELR, solve for x.
R
(7x+33)
N
OA. 8
B. 7
O C. 6
O D. 5
(11x+21)
E
For the parallelogram NELR, we get the value of x as 7°.
We are given a parallelogram NELR.
We know that , the adjacent angles of a parallelogram are supplementary.
So, we get that:
∠ N + ∠ E = 180°
Substituting the values, we get that:
7 x + 33 + 11 x + 21 = 180
18 x + 54 = 180
18 x = 180 - 54
18 x = 126
x = 126 / 18
x = 7°
Therefore, for the parallelogram NELR, we get the value of x as 7°.
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Hence, or otherwise, express 0.372 as a fraction.
Answer:
93/250
3/8
0,375 has three numbers after a decimal so we will multiply and divide 0,375 by 1000
What is the equation of the line that passes through the point (-2,-1)(−2,−1) and has a slope of 5/2
The equation of line having slope of 5/2 is given as 2y -5x = 8.
What is termed as the equation of line in point-slope form?A line's equation written in point slope form is (y - y₁) = m(x – x₁).When the line passing through the origin the equation of a line with slope m is: y - 0 = m(x = 0), i.e. y = mx.where m is the slope and (x₁, y₁) are the coordinates passing point on the line .As, per the given question;
The slope of the line is given as; m = 5/2
The coordinates of the passing points (-2, -1).
Thus, (x₁, y₂) = (-2, -1).
The equation of the becomes.
(y - y₁) = m (x – x₁)
Put the values;
y - (-1) = (5/2)(x - (-2))
Simplifying
y + 1 = (5/2)(x + 2)
2y + 2 = 5x + 10
2y -5x = 8
The equation of line is calculated as 2y - 5x = 8.
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Given two functions
F(x) = 2x+1 and G(X) = x^2-40
Find f(-4) + g(-7)
Answer:
f(-4) = -7
g(-7) = 9
Step-by-step explanation:
f(x) = 2x + 1
f(-4) = 2(-4) + 1 = -8 + 1 = -7
g(x) = x^2 - 40
g(-7) = (-7)^2 - 40 = 49 - 40 = 9
Describe the transformation of the parent function f(x) . h(x)=0.25 f(x)
The transformation applied to the parent function is vertical compression by a factor of 0.25.
In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value.
Vertical compression helps shrink features vertically. Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
It is vertically compressed by a factor of 0.25.
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Statement about translated figures
If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.
True False
What is the difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a hexagon?.
The difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a hexagon is 360°.
Interior angle refers to the angle inside a polygon that is formed by two of its adjacent sides. The sum of the measures of the interior angles of a polygon is given by the equation:
180°(n - 2)
where n is the number of sides
An octagon is a polygon that has 8 vertices and 8 sides. The sum of the measures of the interior angles of an octagon is:
180°(8 - 2) = 180°(6) = 1080°
On the other hand, a hexagon is a polygon that has 6 vertices and 6 sides. The sum of the measures of the interior angles of an octagon is:
180°(6 - 2) = 180°(4) = 720°
Subtracting the sum of the interior angles of the two polygons,
1080° - 720° = 360°
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Three divers kept track of the number of crabs they've seen this year.
Diver Crabs observed Dives
Scuba Sam 33 11
Wet Suit Willy 81 18
Deep Diving Dan 104 26
Which diver saw the most crabs per dive?
Choose 1 answer:
The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
What is an average?An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.
Data and Calculations:Diver Crabs observed Dives Average Crab per dive
Scuba Sam 33 11 3
Wet Suit Willy 81 18 4.5
Deep Diving Dan 104 26 4
Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
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Write an equation in slope-intercept form for the line.
(-7,2) and (5,8)
The equation in slope-intercept form for the line that passes from the points (-7,2) and (5,8) is y = (1/2)x -3/2.
We know that, the slope intercept form is given by:-
y = mx + b
Where,
(x,y) is the ordered pair of every point on the line
m is the slope of the line
b is the y-intercept of the line
We know that, slope = (8-2)/(5-(-7)) = 6/12 = 1/2
Putting (-7,2) in (x,y) and m = 1/2 in the slope intercept form, we get,
2 = (1/2)(-7) + b
2 = -7/2 + b
b = -3/2
Hence, the slope intercept form of the line is y = (1/2)x -3/2.
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Find the value of x.
Answer:
43
Step-by-step explanation:
the plane is 180 degrees
subtract 2x4
172
divide by 4
43
BOOM
Eileen is 3y years old now. Her mother is 4 times as old as her. Find their total age in 7 years' time. Give your answer in terms of y.
Answer:
15y+14
Step-by-step explanation
Answer: 14 + 15y
Step-by-step explanation:
E = Eileen’s age = 3y
M = Mum’s age
Total Age = 14 + 3y + 4(3y)
= 14 + 15y
Total age in 7 years time is their current ages plus 7 years for each (14 years)
Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.
Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!
So, the answer is 14 + 15y.
A triangle has base 8 cm and perpendicular height 5.2 cm work out the area of the triangle
The area of the triangle is mathematically given as
A=20.8cm
This is further explained below.
What is the area of the triangle?The region that is surrounded by the perimeter of the triangle, also known as the three sides of the triangle, is referred to as the area of the triangle.
The space that is encompassed by all three of a triangle's sides is referred to as the triangle's area.
It is computed with the assistance of a variety of formulae that differ according to the kind of triangle, and the results are represented in square units such as centimeters squared, inches squared, and so on.
Generally, the equation for Area the is mathematically given as
A = 1/2 * base * height
Therefore
A= 1/2 * 8 * 5.2
A=20.8cm
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For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
a person's age and the number of cassette tapes he or she owns
For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.
Correlation is a relationship between the values of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.
Causality means that one event causes another. Causality can only be determined by well-designed experiments. In such experiments, similar groups receive different treatments, and the results of each group are examined.
From the above information, we concluded that a person's age and the number of cassette tapes he/she owns are correlated more he lives the more he buys the cassette tapes. So we can make relation from this,
Person's Age ∝ Number of Cassette
This clearly states that by increasing/changing one quantity we will increase/change the other quantity as well.
Similarly, now that they have a direct relation if we decrease the Age of the person, the number of Cassette's will also decrease. A positive correlation we can call it.
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The low temperature in degrees celsius for some cities on the same days in march are recorded in the dot plots. Decide if each statement is true or false
Answer:
the statement is true.
Step-by-step explanation:
Piecewise defined functions
Part a
[tex]\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}[/tex]
Part b
[tex]\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}[/tex]
Part c
[tex]\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}[/tex]
use the figure below to answer the following. What is congruent. Given MN=6x-1 and MP=3x+8
The value of x if the sides are congruent is 3
How to determine the congruent sides?The given parameters are
MN=6x-1 and MP=3x+8
For the sides to be congruent, then the following equation must be true
MN = MP
This gives
6x - 1 = 3x + 8
Collect the like terms
6x - 3x = 1 + 8
Evaluate the like terms
3x = 9
Divide by 3
x = 3
Hence, the value of x if the sides are congruent is 3
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Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A) .
The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).
What is said to be dependent events?When the outcome from one event influences the outcome of the other, two events are referred to as dependent.
Dependent events in probability are generally real-life events that depend on another event to occur. Sam, for example, did well on his math test because he prepared; the gym class used to have a football session even though Adam brought a football from home. When you look at these examples, you will realize that one occurrence is dependent on the other.Derivation of conditional probability from two dependent events P(A and B) is-
The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).
This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.
Step 1: Write the multiplication rule down:
P(A and B) = P(A)*P(B|A)
Step 2: P(A) divides both sides of the equation:
P(A and B) / P(A) = P(A)*P(B|A) / / P(A)
Step 3: On the right side of the equation, cancel P(A):
P(A and B) / P(A) = P(B|A)
Step 4: Rewrite the equation as follows:
P(B|A) = P(A and B) / P(A)
Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).
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Triangle ABC has coordinates A(2, 0), B(−1, 5), and C(4, 3). Determine the coordinates of the vertices of the image after a reflection in the x-axis.
Answer:
Co ordinate of A' = (1, -4)
Co ordinate of B' = (3, 2)
Co ordinate of C' = (4, -2)
Explanation:
The figure of the triangle is shown below.
If we are finding image of the triangle about X-axis all the x -co-ordinates will remain same, but y co-ordinate will change it's sign.
So, co ordinate of A' = (1, -4)
Co ordinate of B' = (3, 2)
Co ordinate of C' = (4, -2)
Solve for x. It's telling me right but all have to ask is to just please answer quick
Answer: (7y+237) / 8 = x
Step-by-step explanation:
So your equation is:
(2y+50) + (7x-248) + (5y-17) + (x+44)
First thing to do is combine all the like terms. Lets start with y. So that would be 2y + 5y= 7y and 50 + -17 is 33. The new equation is:
(7y + 33) + (7x-248) + (x+44)
Now we will combine the x. We will do -248+44= -204
and 7x+x= 8x.
Now our new equation is:
(7y + 33) + (8x+-204)
Now we can subtract 33 from -204. That is 237.
Now we have 7y+237 = 8x
To isolate x we need to divide by 8. That will give us this:
(7y+237) / 8 = x
(-8) x (-2/3) =
1/3a = -5
URGENTTT
Answer: -8
Step-by-step explanation:
= 12 * (-2/3)
= -24/3
= -8
(−8) ⋅ (−2/3) = 1/3a = −5
The formula weights=mass of 1 mole of (−8) ⋅ (−2/3) = 1/3a = −5 = 0g
Determine the probability of following event, spinning a spinner numbered 1-8 and not landing on 5
According to the question, to calculate the probability of the event which states that the spinning a spinner whose number is from one-eight and it is not landing on the number 5.
Therefore, the numbers which are greater than five are (6,7,8).
And the spinner numbers are (1,2,3,4,5,6,7,8).
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
Probability of spinning a number greater than 5 is:
P(E) = 3/8
And the probability of tossing a tail on a coin is: 1/2
Now, the total probability is: 3/8 [tex]\times[/tex] 1/2 = 3/16
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PLs solveg g g g g g g g g g g g
Answer:
4°=1
g g g g g g g g g g
Step-by-step explanation:
Lee is laying out a design for the tiles of a section of his bathroom floor. he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design. how many of each type of tile will lee use?
If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.
The number of white and black tiles Lee will use can be determined by using an algebraic expression.
As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,
x + 6x = 28
By solving the value of x, the number of each type of tile that Lee will use can be calculated,
x + 6x = 28
7x = 28
x = 28 ÷ 7
x = 4
As there is one white tile for every six black tiles,
White tiles = 1(x) = 1(4) = 4
Black tiles = 6(x) = 6(4) = 24
Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.
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Solve x+8 = -6.
A. x = 14
OB. x=2
C. x = -2
OD. x= -14
Answer:
-14
Step-by-step explanation:
if you add negative fourteen by 8 you would get 6 and you keep the sign of the greater number
A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters. A larger and similar can of tuna has a radius of 5.2 centimeters.
a. What is the scale factor of the cylinders?
The scale factor of the two similar cylindrical cans of tuna is 13/10.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:
height of A / height of B = radius of A / radius of B
Scale factor refers to the ratio of the corresponding dimensions of similar solids.
If the smaller cylindrical can of tuna has a radius of 4 centimeters and the larger and similar can of tuna has a radius of 5.2 centimeters, then the scale factor is:
scale factor = radius of larger can/ radius of smaller can
scale factor = 5.2 cm / 4 cm
scale factor = 13/10
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find the value of x
2x+5=6x-3
Answer:
Step-by-step explanation:
2x+5=6x-3
subtract 6x
2x-6x+5=6x-6x-3
-4x+5=-3
subrtract-5
-4x+5-5= -3-5
-4x=-8
divide-4
-4x÷-4=-8÷-4
x=2
