Explanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
−
3
y
=
12
into this form
subtract 2x from both sides
⇒
−
3
y
=
−
2
x
+
12
divide all terms by
−
3
⇒
y
=
2
3
x
−
4
←
in standard form
with
m
=
2
3
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
2
3
=
−
3
2
⇒
y
=
−
3
2
x
+
b
←
is the partial equation
to find b substitute
(
2
,
6
)
into the partial equation
6
=
−
3
+
b
⇒
b
=
6
+
3
=
9
⇒
y
=
−
3
2
x
+
9
←
equation of perpendicular line
f(x) = 2x + 10
Find f(20)
The function F(20) is 50
What is function ?The most common symbols for a function are the letters f, g, and h. A function's value at an element of its domain x is denoted by the notation f(x), and the numerical value obtained from the function evaluation at a specific input value is denoted by substituting that value for x. For instance, the value of f at x = 4 is denoted by the notation f(x) (4). When a function isn't given a name and is instead represented by the expression E, the value of the function at, say, x = 4 may be shown by the notation E|x=4.
Given that :f(x) = 2x + 10
f(x) = 2x + 10
F(20)= 2(20) + 10
F(20)= 40 + 10
F(20)= 50
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HELP PLEASE!!!
Which equation matches the graph of the greatest integer function given below?
Answer:
the answer you are looking for is D
Find the equation of the line shown.
Answer:
y = mx + b
y = 1/4x + 2
Step-by-step explanation:
m(slope) = rise/run = 1/4
b(y intercept) = 2
Here is the set of numbers: 4, 5, 11, 12, 5, 38, 44
Based on your results of Mean and Median, is the Mean or Median larger in value?
Please answer with complete sentence(s), which explains why and how you made your choice.
Based on the results of Mean and Median, we can say that Mean is larger than median in value .
Mean of n observations can be calculated using the formula
Mean = (sum of all observations)/(number of observations) .
After arranging the data in ascending or descending order , the middle value can be called as Median .
In the question ,
the set of numbers is given as 4, 5, 11, 12, 5, 38, 44
rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44 .
the sum of all the number = 4+5+5+11+12+38+44
= 119
number of observations = 7
hence the mean = 119/7 = 17
So, mean = 17
from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that
the middle value of the set of numbers is 11 .
So , median = 11 .
On comparing the mean = 17 and the median = 11 ,
we can say that the mean is greater than median.
Therefore , based on the results of Mean and Median, we can say that
Mean is larger than median in value .
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What is the equation in point-slope form of the line that passes through the point (3, −2) and has a slope of 23?
Drag and drop the appropriate number, symbol, or variable to each box.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The linear equation in point-slope form of a line with a slope of 23 and point (3,-2) is y = 23x - 71.
How to determine the equation of a line from a point and slope?The slope intercept formula is expressed as;
y = mx + b
Where m is the slope and b is the y-intercept.
Given the data in the question;
Slope m = 23Point: (3,-2)
x = 3y = -2Equation of line = ?First, use the the formula for the equation of line to determine the y-intercept 'b'.
y = mx + b
Plug in slope m = 23 and point (3,-2)
-2 = (23)3 + b
-2 = 69 + b
b = -2 - 69
b = -71
Now that we have both the slope m ( 23 ) and y-intercept b ( -71 ), plug these values into y = mx + b to find the linear equation.
y = mx + b
y = 23x + (-71)
y = 23x - 71
Therefore, the equation of the line is y = 23x - 71.
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if 2x+y=7 and y=2x-5 what is the value of x. solve using substitution or elimination
The value of x is found as 3 using the method of substitution.
What is the method of substitution?The substitution method is a straightforward method for algebraically solving a system of linear equations and determining variable solutions. It entails determining the value of x-variable in aspects of y-variable using the first equation and afterwards substituting or fixing the value of x-variable with in second equation, as the name implies.For the given expression, use substitution method to solve.
2x + y = 7 ........eq 1
y = 2x - 5 ........eq 2
Substitute the value of y from eq 2 in eq 1.
2x + 2x - 5 = 7
Solving;
4x = 7 + 5
4x = 12
x = 3
Thus, the value of x is found as 3.
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Simplify the following 4 + (-125)
Answer:
4 + (-125)
= 4 - 125
= -121
Approximately 3 out of every 25 Amerloans live in California. About 3 out of every 50
Americane live in New York and about 2 out of every 25 Americans live in Texas.
Which state has the largest population?
10. Which state hos the smallest population?
11. About what percentage of Americans do nar live in Colifornia, New York, or Texas?
California is the most populated state, New York is the least populated, and 26% of Americans live in California, New York, and Texas.
Convert all statistics to percentages:
CA: 3 25 = 0.12 or 12%, 0.12 100 to calculate percentages.
NY: 3 50 = 0.06, or 6%, and 0.06 100 to get the percentage.
TX: 2 25 = 0.08 = 8%, 0.08 100 = percent
(A) California has the largest population of the three states.
(B) New York has the smallest population of the three states.
(C) USA = 100%, CA + NY + TX = 26%, so 74% of Americans do not live in these three states.
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56 out of 79 as a percentage
Find a point-slope form for the line that satisfies the stated conditions
Slope 4, passing through (- 2,1)
The equation of the line in point-slope form is ……
Answer:
y=4x+9
Step-by-step explanation:
y-Y1= m× x-X1
Y-1 = 4×X+2
y-1 = 4x+8
y=4x+9
Which expression has a value of 24?
PLS HELP ASAP
A –6 • 2 – (–7)–6 • 2 – (–7)
B 9 • 4 ÷ 2 + (–3)9 • 4 ÷ 2 + (–3)
C –9 + 3 – 6 • (–5)–9 + 3 – 6 • (–5)
D 9 ÷ 3 • 10 – (–1) + 3
Answer:
a) the answer it 10 so no
b) the answer is −39 so nah
c) the answer is 48, nope
d) the answer is 34, did you mean to write 34 instead of 24?
Step-by-step explanation:
help pls and thanks
Answer:
43°
Step-by-step explanation:
Alternate interior angle are congruent.
is x+y^2 linear?
sos this math hw is killing me rn
Answer:
Not linear
Step-by-step explanation:
Can be written into the form of [tex]y=mx+b\\[/tex].
Africa is 8.2 times 10 to the 3rd power Brazil is 4.4x10 to the third power , what’s the difference
Please Help
Deanna completed 60% of the levels in a recently released video game. If there are 75 levels in
the video game, how many levels did Deanna complete
Answer:
45 levels
Step-by-step explanation:
60% of 75 is 45 i think
write an equation of a parabola in the vertex form if a = -3 and the vertex is (-3,5)
8+ 3x =1 + 7.9x can someone help me out?
[tex]8 + 3x = 1 + 7.9x \\ \\ \implies 3x - 7.9x = 1 - 8 \\ \\ \implies - 4.9x = - 7 \\ \\ \implies \: x = \frac { \cancel{- 7}}{ \cancel{ - 4.9} } \\ \\ \implies \: x = 1.43[/tex]
hope this helpschoti bachi hô kya itne simp question ka answer kon puchta hai xD
Which is the surface area of the cube?
Answer:
54 cm
Step-by-step explanation:
A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.
a = edge
Area = 6a to the power of 2
Given f ( x ) = 1 x + 12 , find the average rate of change of f ( x ) on the interval [ 9 , 9 + h ] . your answer will be an expression involving h
Given,
f(x) = 1x + 12
expression to be in form of h
To find on the interval: [9, 9 + h]
∵ Average rate of change of f(x) on interval (a,b) is
A = f(b) - f(a) / b - a
⇒ f(9) = 1 x 9 + 12 = 21
⇒ f(9 + h) = 9 +h + 12 = 21 + h
⇒ f(b) - f(a) = 21 + h - 21 = h
⇒ (b-a) = 9 + h - 9 = h
∴ Average rate of change = h / h
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Define centroid. If (X₁,Y₁), (X2,Y2) and (x3.3) are the vertices of a triangle, find the co- ordinates of the centroid of that triangle. (Note: Show derivation)
The coordinates of a centroid of a triangle with vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].
Centroid of a triangle
For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.
Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.
Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”
As D is the midpoint of the side LM, we can write,
D = ((x2+x3)/2, (y2+y3)/2)
Now, we know that, G intersects AD in the ratio 2:1 , we get
Hence, using section formula we can write,
The x-coordinates of G will be:-
x = (2(x2+x3)/2 + 1.x1 )/ (2+1) = (x2+x3+x1)/3 = (x1+x2+x3)/3
The y-coordinates of G will be :-
y =(2(y2+y3)/2 + 1.y1 )/ (2+1) = (y2+y3+y1)/3 = (y1+y2+y3)/3
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the lifespans of lizards in a particular zoo are normally distributed. the average lizard lives 3.13.13, point, 1 years; the standard deviation is 0.60.60, point, 6 years. use the empirical rule (68-95-99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lizard living between 2.52.52, point, 5 and 4.34.34, point, 3 years.
The probability of a lizard living for more than 2.5 years is 16%.
What is defined as the normally distributed?The proper term for just a probability bell curve is the normal distribution.The mean of a normal distribution is zero, and the standard deviation is one. It has a skew of 0 and a kurtosis of 3.Although all symmetrical distributions are normal, not all normal distributions are symmetrical.The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.
Average lizard u = 3.1,
standard deviation σ = 0.6
To calculate the likelihood of a lizard living for more than 2.5 years;
p(X<2.5)
μ + aσ = 2.5
3.1 + a(0.6) = 2.5
a(0.6) = −0.6
a = −1
To calculate the probability, apply the empirical rule.
The total area = 100% (since total probability always is 1)
Area from μ to ∞ = p(X > μ) = 50%
Area between (μ−σ) and (μ+σ) = 68%
Area between (μ−σ) and μ is p((μ−σ) < X < μ) =34%
Thus,
p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))
= 1 − (0.34 + 0.5)
p(X< (μ−σ)) = 0.16
Therefore, the probability that a lizard will live longer than 2.5 years 16%.
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Please hep me solve picture below thank uou
Answer:
x= -1, -13
Step-by-step explanation:
Answer: x=-13 x=-1
Step-by-step explanation:
[tex]x^2+14x=-13\\x^2+2(x)(7)+7^2-7^2=-13\\(x^2+2(x)(7)+7^2)-49=-13\\(x+7)^2-49=-13\\(x+7)^2-49+49=-13+49\\(x+7)^2=36[/tex]
[tex](x+7)^2-36=36-36\\(x+7)^2-36=0\\(x+7)^2-6^2=0\\(x+7+6)(x+7-6)=0\\(x+13)(x+1)=0\\x+13=0\\x+13-13=0-13\\x=-13\\x+1=0\\x+1-1=0+(-1)\\x=-1[/tex]
Find the slope of the line that passes through the following points: (4,-2) and (-4,-4)
The value of of slope of is 1/4.
How to calculate the value of the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.
Any two distinct places along the line can be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the "vertical change" to the "horizontal change" in each case. The difference between the line's y and x coordinate changes is known as the slope of the line. Net changes in the y and x coordinates are as follows: y = y and x = x.
m = [tex]y_{2} - y_{1} /x_{2} x_{1}[/tex]
m = 1/4
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Please help me... 5 points
Answer:
Step-by-step explanation:
8(2+3)
If the lower legs of the ironing board are equal in length, what is the measure of n?
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 ≤x≤ 8.
Hence the average rate of change, in simplest form is -10 .
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change. A method that computes the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.Examples of average rates of change include: 80 km/h is the average speed of a bus. In a lake, fish population growth occurs at a pace of 100 per week.Using the coordinate points from the table ( 4,53) ( 8, 13 )
Substitute the coordinate into the expression
Average rate of change = y₂ - y₁/x₂ - x₁
= 13 - 53/8 - 4
= - 4 0/4 ⇒ -10
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geometry, is this answer correct?
Answer: yes, the value of x is 4 and angle HEB is 36 degrees
Step-by-step explanation:
1a. Find the value of angle CEB
Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees
2a.set up an equation
After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2
3a. Solve the equation
13x+9x+2=90
22x+2=90 | combine like terms
22x=88 | subtract 2 from both sides
x=4 | divide by 22 on both sides
1b. Set up equation
Knowing x=4 and that angle HEB is 9x the equation is 9(4)
2b. Solve the equation
9(4)
36
Sonya wants to sew ribbon along each side of a square pillow. The expression 4 ⋅ 144−−−√ gives the exact amount of ribbon she will need for a pillow with an area of 144 square inches. How much ribbon, in inches, must Sonya buy to have the exact amount?
She buy 48 inches of ribbon to have the exact amount that she needs.
Given,
Area of the ribbon = 144 sq. inches
and, We know the formula for side of square is =[tex]\sqrt{Area of a square }[/tex]
Plug the value of area of square in above formula
Side of a Square = [tex]\sqrt{144}[/tex] = 12 inches
Now, we get the side of a square i.e., 12 inches
According to the question:
Sonya wants to sew ribbon along each side of a square pillow.
So, we need to find the perimeter of the square pillow.
and, Perimeter of a square is = 4 x side
=> Perimeter = 4 x 12 = 48 inches.
Therefore, She buy 48 inches of ribbon to have the exact amount that she needs.
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( Please help + Will mark brainliest )
Answer the question in photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
From Devon's total he decided to pay back his brother $17.50 and his best friend the $49 for
concert tickets. How much does Devon now have?
Answer:
Subtract 66.5 from Devon's total to find how much he has left