Answers
The given point is (12,6) and the given line equation is y=1/4 x-12.
It is required to find the equation of the line parallel to the line whose equation is given and passes through the given point.
Recall that the Equation of a Line in point-slope form is given as:
\(y-y_1=m(x-x_1)\)Where m is the slope of the line and (x₁,y₁) is the point the line passes through.
Recall also that the slopes of parallel lines are equal.
The slope-intercept form of the equation of a line with slope m and y-intercept b is:
\(y=mx+b\)Compare with the equation of the given line, it follows that m=1/4.
Hence, the slope of the given line is 1/4.
Since the required line whose equation is to be found is parallel to the given line, it must have the same slope.
Substitute m=1/4 and the point (x₁,y₁)=(12,6) into the point-slope form of the equation of a line:
\(\begin{gathered} y-6=\frac{1}{4}(x-12) \\ \Rightarrow y-6=\frac{1}{4}x-\frac{1}{4}(12) \\ \Rightarrow y-6=\frac{1}{4}x-3 \\ \Rightarrow y=\frac{1}{4}x-3+6 \\ \Rightarrow y=\frac{1}{4}x+3 \end{gathered}\)The required equation is shown above.
Related Questions
(18,‐7)and(18,2) what's the slope
Answers
Answer:
only these 2 terms are given
The slope of the line that passes through (18, ‐7) and (18, 2) will be ∞.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
(18, ‐7) and (18, 2)
The slope of the line is given as,
m = (2 + 7) / (18 - 18)
m = 9 / 0
m = ∞
The slope of the line that passes through (18, ‐7) and (18, 2) will be ∞.
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Accountants often use the median when studying salaries for various businesses. What is the median of the following salary list: $32,019; $21,971; $27,596; $43,715, $38,850, $25,963?
Answers
Answer
40.5
Step-by-step explanation
don't have to answer all just at least 1 pls and write yes if the statement is a proportion or no if it is not a proportion.
2:3 = 9:4
3/8 = 12/32
10/12 = 20/25
4/9 = 17/38
Answers
Answer:
3/8 = 12/32 is a proportion
Step-by-step explanation:
2:3 and 9:4 is not a proportion, 10/12 and 20/25 is not a proportion, 4/9 and 17/38 is not a proportion
graph the function y less than or equal to x^2-3x-1
Answers
Answer: y <= x^(2) - 3x - 1
How to: Graph the inequality by finding the boundary line, then shading the appropriate area.
Have a great day and stay safe !
Pls help
Me i have alot and this is due tomorrow
Answers
8,8,8,8, 9 ,10,12,12,14
Please Help!
The areas of two rectangles can be represented by the functions shown.
Which function represents the difference in the areas, h(x) = f(x) – g(x)?
h(x) = 4x2 – 4x – 11
h(x) = 4x2 – 4x + 11
h(x) = –4x2 + 4x + 11
h(x) = 4x2 – 4x – 9
Answers
Answer:
B. h(x) = 4x² - 4x + 11
Step-by-step explanation:
Given:
f(x) = 5x² - 2x + 1
g(x) = x² + 2x - 10
Required:
h(x) = f(x) - g(x)
Solution:
h(x) = (5x² - 2x + 1) - (x² + 2x - 10)
= 5x² - 2x + 1 - x² - 2x + 10 (distributive property)
Collect like terms
= 5x² - x² - 2x - 2x + 1 + 10
h(x) = 4x² - 4x + 11
The figure shows the graph of f(x)=4+x/x+3, along with it's tangent line at the point (0,4). What is f'(0)?
Answers
Since we know the tangen line:
\(y=\frac{1}{3}x+4\)then f ^prime evaluated at zero is the same as evaluate this last equation at x=0, that is,
\(f\text{´}(0)=\frac{1}{3}(0)+4\)which gives
\(f^{\prime}(0)=4\)then, the answer is 4.
Lets compute the derivative of our given function:
then, f^prime at zero is equal to
then, the answer is 1/3. Then, the given line doesnt correspond with the derivative at x=0
Somebody please help pleaseeeee I’ll make brainlest please help anybody .
Answers
Answer:
C Is The Correct Answer
3 people share a sum of money in a ration of 3:5:7 If one recieves 10 more than the other, what is the amount shared
Answers
Answer:
We have the ration:
3:5:7
This means that, if they receive $15, then:
Person A will get $3
Person B will get $5
Person C will get $10
Let's then define the amount of money shared as:
Amount = K*$15
where we want to find the number K.
In this scenario, each they will get:
Person A : $3*K
Person B: $5*K
Person C: $7*K
Now, we know that one of them gets "10 more than the other"
(The problem here is that we do not know exactly who receives more than who, i will suppose that person B receives $10 more than person A)
then we can have:
$5*K = $10 + $3*K
solving this for K, we have:
$5*K - $3*K = $10
$2*K = $10
K = $10/$2 = 5
Then the amount shared, in this situation, is:
Amount = K*$15 = 5*$15 = $75.
Subtract 4x + 6 from 7 + 2x?
Answers
Answer:
1-2x
Step-by-step explanation:
\((7+2x)-(4x+6)=7+2x-4x-6=1-2x\)
a/56= -1/7, proportions lol, please help
Answers
In given proportion , value of a = -8
A proportion can be defined as an equation in which two ratios are set to be equal to each other. For example, if there is 1 man and 3 women you could write the ratio as: 1 : 3 (for every one man there are 5 women).
And the other way to predict is :
1 : 3 (for every one man there are 3 women)1 / 4 are man and 3 / 4 are women0.25 are man ( dividing 1 by 4)25% are man (0.25 as a percentage of it)Generally, the proportion is written as x:y ,
where x and y are two different values of the ratio.
In the given question,
proportion is a/56 = -1/7
solving equation we get a = -1/ 7 . 56
=> a= -8
hence, In the given proportion , value of a = -8
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too dice are tossed simultaneously, what is the
probability that
the sum of their squares is more than 7
Answers
Answer: 5/13
Step-by-step explanation:
36 possible outcomes
the highest the sum can be is 12
so 8, 9, 10, 11, and 12 are all options
2+6, 4+4, 3+5, 5+3, 6+2 - for 8
3+6, 4+5, 5+4, 6+3 - for 9
4+6, 5+5, 6+4 - for 10
5+6, 6+5 - for 11
6+6 - for 12
total - 15/36 or 5/13
For a given input value a, the function h outputs a value b to satisfy the following equation3a - 5 = -4b + 1Write a formula for h(a) in terms of a.
Answers
We know that function h outputs the value of b when we input a value of a, that means:
\(b=h(a)\)To find the expression for h we just need to solve the equation given for b, let's do that:
\(\begin{gathered} 3a-5=-4b+1 \\ -4b=3a-5-1 \\ -4b=3a-6 \\ b=\frac{3a-6}{-4} \\ b=-\frac{3}{4}a+\frac{6}{4} \\ b=-\frac{3}{4}a+\frac{3}{2} \end{gathered}\)Therefore, we have that:
\(h(a)=-\frac{3}{4}a+\frac{3}{2}\)Given f(x) = -x - 5 find f (0)
Answers
Answer: f(0)=-5
Step-by-step explanation:
f(0) means that x = 0
sub in 0 into the equation
f(0)=-0-5
f(0)=-5
Answer:
f(0) = -5
Step-by-step explanation:
Given f(x) = -x - 5
In order to find f(0), you need to replace x with 0
so f(0) = -(0) - 5
f(0) = -5
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)), then the range of G is
(7, -1),(2, -8),(0, 0),(6, 6)}
(-8,-1, 0,6)
(0, 2, 6, 7)
Answers
9514 1404 393
Answer:
(0, 2, 6, 7)
Step-by-step explanation:
The range is the list of 2nd numbers in the ordered pairs:
(0, 2, 6, 7)
please help me thank you so much
Answers
Answer:
1)
7+9-15 = add 7 and 9, then subtract 15
2)
15-(7+9) = The sum of 7 and 9 subtracted from 15
3)
15-(7+9) = subtract 7 from 15, then add 9
Step-by-step explanation:
Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient
Find the value of x
Answers
Answer: The value of x is 49.
Step-by-step explanation:
To find the value of x, you will first need to cross multiply the fractional variables together.
5x - 80 = 3x + 18
Then, move the numerical term 80 to the right side of this equation and add it to 18.
5x - 80 = 3x + 98
Move 3x to the left side of the equation and subtract it this time to the variable 5x.
2x = 98
Finally, you divide both of the equation's sides by 2 and you will get 49.
x = 49
When you actually add x to this problem, you would get 33/55.
49 - 16/49 +6 = 33/55
You can then simplify 33/55 and get the same answer 3/5.
3/5
Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!
-From 5th Grader Honors Student
PLS HELP MY GRADE DEPENDS ON IT
Image is attached below
Answers
Answer: the first one
Step-by-step explanation: head math
\(f(x) = - 5x - 4\)
which function is the inverse of
Answers
Answer:
5 x - 4
Step-by-step explanation:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .
The area of a rhombus is 32 units? . What would
the product of the diagonals have to be for the
area to be 32 units??
A 87
B 73
C 52
D 64
Answers
Answer:
D. 64 units.
Step-by-step explanation:
The area is 1/2 the product of its diagonals, so
1/2 * P = 32
P = 32 * 2
P = 64.
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answers
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
Answers
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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The diagram below is divided into equal parts. Which shows the ratio of unshaded section to shaded sections
Answers
Answer:
its D
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
there is 5 unshaded and one shaded
Find the length of the loan in months, if $600 is borrowed with an annual simple interest rate of 9% and with $681 repaid at the end of the loan.
Length of the loan =__________ months
Answers
The length of the loan in months is 151. 33 months
How to determine the length of timeThe formula for determining simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal amountR is the simple interest rateT is the time in yearsFrom the information given, we have that;
Principal interest = $600
Simple interest = $681
Rate = 9%
Substitute the values into the formula
$681 = $600 × 9 × T/100
Multiply the numerators
$681 = 5400T/100
cross multiply
68100 = 5400T
Divide both sides by 5400
T = 68100/5400
T = 12. 61 years
Convert the years to months
T = 12.61(12)
T = 151. 33 months
Hence, the value is 151. 33 months
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6 dived by 48 what is the answer
Answers
Answer:
1/8 or 0.125
Step-by-step explanation:
6/48
SOLVING BY ELIMINATION
-10x + y = 0 and 5x 3y = -7
Please help
Answers
I think that the answer would be (-7/150,-7/15)
Step-by-step explanation:
-10x + y = 0
+10x +10x
y = 10x
Put the 10x into 5x3y =-7
5x3(10x) =-7
5x•30x = -7
150x = -7
150x/150 = -7/150
x = -7/150
Put the x value into the first equation to find the y value
-10x + y = 0
-10(-7/150) + y = 0
7/15 + y = 0
-7/15 -7/15
y = -7/15
This gives us (-7/150, -7/15)
*I might be wrong
What is the length of each leg of the triangle below?
Answers
Answer:
C
Step-by-step explanation:
32/sqrt(2) = 32sqrt(2)/2 = 16sqrt2
Answer:
C.
Step-by-step explanation:
It is a right triangle with hypotenuse c = 12, also for having two equal angles is an isosceles triangle, the missing sides (catethus) are equal (a and b)
a = b = the legs
Apply the Pythagorean theorem
\(c^{2}=a^{2} +b^{2} \\c^{2} =2a^{2}\)
\(a^{2} =\frac{c^{2} }{2}=\frac{(32)^{2} }{2} =512\)
\(a=\sqrt{512} =\sqrt{256(2)} =16\sqrt{2}\)
Hope this helps
Find the length of the third side. If necessary, round to the nearest tenth. 8 12
Answers
The length of the third side is 14.4 units.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We find the third side of a triangle by using Pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
8²+12²=x²
64+144=x²
208=x²
Take square root on both sides
x=14.4
Hence, the length of the third side is 14.4 units.
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The table gives the temperature (in °F) in five cities at 6 a.m. on the same day. Use the table to answer the questions.
City Temperature
(°F)
Chicago −6
Toronto −28
Louisville 47
Los Angeles 64
Phoenix 83
(a) How much higher was the 6 a.m. temperature in Los Angeles than in Toronto?
°Fhigher
(b) By noon, the temperature in Toronto had risen by 16°F.
What was the temperature there at noon?
°F
Answers
Answer:
A: 92F
B: -12F
Step-by-step explanation:
A)
LA: 64F, Toronto: -28F.
To find the difference means to subtract.
64 - (-28) = 92F
The difference is 92F
B)
ΔT = Tfinal-Tinitial
16 = Tfinal-(-28)
-28 + 16 = Tfinal
Tfianl = -12F