how do i find the equation of the line
Answers
Answer: look at explanation <3
Step-by-step explanation:
Steps to find the equation of a line from two points:
Find the slope using the slope formula
Use the slope and one of the points to solve for the y-intercept (b).
One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Related Questions
5/6 of what number
= 35
Answers
Answer:
42
Step-by-step explanation:
In order to find the answer to this question, I had to multiply 35 times 6/5.
35x6/5=42
You can check to make sure your answer is right by doing: 42x5/6=35.
You just have to multiply the number that we are using by the reciprocal of the fraction.
For instance: 2/3 of what number is 32
32x3/2= 48
48x2/3=32
The requried number is 42, where 5/6 of 42 is 35.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
Let the number be x,
According to the question,
5 / 6 x = 35
x = 35 × 6 / 5
x = 7 × 6
x = 42
Thus, the requried number is 42, where 5/6 of 42 is 35.
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let f be the function given by . what are all values of c that satisfy the conclusion of the mean value theorem of differential calculus on the closed interval [0,3]?
Answers
The only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b], then there exists some c in the interval such that
f'(c) = (f(b) - f(a)) / (b - a).
In the case of f(x) = x(x-3) , on the closed interval [0,3], we can solve for c using the equation above.
We begin by calculating f'(c), which is equal to 2c - 3. Then, we set the equation equal to (f(3) - f(0)) / (3 - 0), which is equal to -3 / 3.
Substituting this into our equation for f'(c), we get 2c - 3 = -1, which simplifies to c = 2.
Therefore, the only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
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What are the first five terms, a1, a2, a3, a4, a5, of the sequence defined by a subscript n = startfraction n squared minus 9 over n cubed 3 endfraction, and how can the sequence be described?
Answers
The first five terms of the given sequence are:
a1 = -2
a2 = -5/11
a3 = 0
a4 = 7/67
a5 = 1/8
Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.
For given question,
We have been given a sequence \(a_n=\frac{n^2-9}{n^3+3}\)
We need to find the first five terms, a1, a2, a3, a4, a5, of the sequence.
For n = 1,
\(a_1=\frac{1^2-9}{1^3+3} \\\\a_1=\frac{-8}{4} \\\\a_1=-2\)
For n = 2,
\(a_2=\frac{2^2-9}{2^3+3}\\\\ a_2=\frac{-5}{11}\)
For n = 3,
\(a_3=\frac{3^2-9}{3^3+3} \\\\a_3=\frac{0}{30}\\\\ a_3=0\)
For n = 4,
\(a_4=\frac{4^2-9}{4^3+3} \\\\a_4=\frac{7}{67}\)
For n = 5,
\(a_5=\frac{5^2-9}{5^3+3} \\\\a_5=\frac{16}{128}\\\\ a_5=\frac{1}{8}\)
Given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.
Therefore, the first five terms of the given sequence are:
a1 = -2
a2 = -5/11
a3 = 0
a4 = 7/67
a5 = 1/8
Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.
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Rewrite the function to complete the square f(x) = x^2 + 4x + 41
Answers
Answer:
f(x)=(x+2)^2+37
Step-by-step explanation:
Got it right on Khan :)
The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function is given below.
f(x) = x² + 4x + 41.
The quadratic function is converted into square form by adding and subtracting the square of the half of the coefficient of x.
f(x) = x² + 4x + 41
Transform into square form. Then the quadratic function will be
f(x) = (x² + 4x + 4) + 41 – 4
f(x) = (x + 2)² + 37
The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.
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Question 2
Mike deposited $3,000 in the first year of a retirement account, and then increased the deposits by $300 each year. The account earned 8.35%. What was the account value after forty years?
Answers
The account value after forty years is approximately $489,074,140.57.
What is formula for the future value of an annuity?To calculate the account value after forty years, we need to use the formula for the future value of an annuity:
\(FV = P * [(1 + r)^n - 1] / r\)
where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we have:
P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on
r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)
n = 40 years
To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:
S = n/2 * [2a + (n-1)d]
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = $3,000
d = $300
n = 40
Plugging these values into the formula, we get:
S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000
Thus, the aggregate sum of installments more than 40 years is $2,340,000.
We can now enter these figures into the formula for annuity future value:
\(FV = P * [(1 + r)^n - 1] / r\)
\(FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835\)
FV = $2,340,000 * 209.251
FV = $489,074,140.57
Consequently, after forty years, the account's value is approximately $489,074,140.57.
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(Q1) The circumcenter of a(n) _____ triangle will be on the hypotenuse of the triangle.
Answers
The circumcenter of a right triangle will lie on the hypotenuse of the triangle.
The circumcenter is the point at which the perpendicular bisectors of the sides of a triangle intersect. In a right triangle, the perpendicular bisectors of the legs intersect at the midpoint of the hypotenuse. This point is equidistant from all three vertices of the right triangle and is the circumcenter of the triangle.
Since the midpoint of the hypotenuse lies on the hypotenuse itself, the circumcenter of a right triangle must also lie on the hypotenuse. In fact, the circumcenter of a right triangle coincides with the midpoint of the hypotenuse. This is a unique feature of right triangles, and it can be used to find the circumcenter and other important properties of these triangles.
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Select the domain and range of F.
F={(x, y) Ix+y=10].
1. Set F is not a function and does not contain a domain or range
2. Domain: [10] Range: (10)
3. Domain: All Real Numbers Range: All Real Numbers
Answers
The domain and range of F is F={(x, y) Ix+y=10] is: 3. Domain: All Real Numbers Range: All Real Numbers
The given set F={(x, y) | x+y=10} represents a linear equation where the sum of x and y is always equal to 10.
To determine the domain and range of F, we need to consider the
possible values of x and y that satisfy the equation.
Domain: The domain represents the set of all possible values for the independent variable, which in this case is x. Since there are no restrictions on the value of x, the domain is All Real Numbers.
Range: The range represents the set of all possible values for the dependent variable, which in this case is y. By rearranging the equation x+y=10, we can solve for y to get y=10-x. Since x can take any real value, y can also take any real value. Therefore, the range is also All Real Numbers.
The correct answer is: 3. Domain: All Real Numbers Range: All Real Numbers
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a ladder 26 feet long is leaning against the wall of a house (see the figure below). the base of the ladder is pulled away from the wall at a rate of 3 feet per second. how fast is the top of the ladder moving down the wall when its base is 10 feet from the wall?
Answers
The rate at which the top of the ladder is moving down the wall = 9 feet/second.
This is a problem of right triangle similarity.
We can use the Pythagorean theorem to find the height of the ladder, which is the hypotenuse of a right triangle.
We can use the relationship between similar triangles to find the rate at which the top of the ladder is moving down the wall.
Let x be the distance of the base of the ladder from the wall.
We know that the ladder is 26 feet long, so the height of the ladder is the square root of (26^2 - x^2).
We know that the base of the ladder is moving away from the wall at a rate of 3 feet per second.
So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (height of ladder / x)
When x = 10 feet, the height of the ladder is the square root of (26^2 - 10^2) = the square root of (676) = 26 feet.
So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (26 feet / 10 feet) = 9 feet/second.
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is -4 < -5 1/2 a true statement?
Answers
Answer:
It is not true
Step-by-step explanation:
-4 is closer to 0 than -5 1/2
The closer the negative number to 0 the bigger it is
How do you do right triangle trigonometry?
Answers
Right triangle trigonometry involves using the relationships between the angles and sides of a right triangle, as defined by the trigonometric functions sine, cosine, and tangent, to solve for missing angles or sides.
To do right triangle trigonometry, you first need to identify which angles and sides are known and which are unknown. You can then use the definitions of sine, cosine, and tangent, as well as the Pythagorean theorem, to set up and solve equations that relate the known and unknown values.
For example, if you know the lengths of two sides of a right triangle, you can use the Pythagorean theorem to find the length of the third side. Alternatively, if you know the measure of one angle and the length of one side, you can use trigonometric functions to find the length of another side or the measure of another angle.
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A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. What are the speed and magnitude of the acceleration of a bug clinging to the rim of the disk?
1) 10 m/s and 10 m/s^2
2) 1 m/s and 0 m/^2 (Disk spins at constant speed)
3) 0.1 m/s and 1 m/s^2
4) 1 m/s and 10 m/s^2
Answers
A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. The speed of the bug is equal to the tangential speed of a point on the rim of the disk, which can be given by: v = rωWhere:r = 0.1 m (the radius of the disk)ω = 10 rad/sec (the angular speed of the disk)Therefore, the speed of the bug is: v = rω= 0.1 m x 10 rad/sec= 1 m/s
The acceleration of the bug can be given by: a = rαWhere:α = α (angular acceleration)The angular acceleration is zero because the disk is spinning at a constant angular speed. Hence, the acceleration of the bug is zero or a = 0 m/s². Therefore, the correct option is option 2) 1 m/s and 0 m/s² (Disk spins at a constant speed).
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E is the encoding matrix.Use E to decode the coded message matrix.
Answers
To decode a message, we take the string of coded numbers and multiply it by the inverse of the matrix to get the original string of numbers. Finally, by associating the numbers with their corresponding letters, we obtain the original message.
The encoding matrix is given to be:
\(E=\begin{bmatrix}{4} & {3} \\ {5} & {4}\end{bmatrix}\)The inverse of the matrix is calculated to be:
\(E^{-1}=\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\)Next, we break the encoded matrix into single rows of 2 x 1 matrices and multiply each one with the inverse of the encoding matrix:
Row 1
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{59} \\ {76}\end{bmatrix}=\begin{bmatrix}{8} \\ {9}\end{bmatrix}\)Row 2
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{13} \\ {17}\end{bmatrix}=\begin{bmatrix}{1} \\ {3}\end{bmatrix}\)Row 3
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{103} \\ {130}\end{bmatrix}=\begin{bmatrix}{22} \\ {5}\end{bmatrix}\)Row 4
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{20} \\ {25}\end{bmatrix}=\begin{bmatrix}{5} \\ {0}\end{bmatrix}\)Row 5
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{12} \\ {16}\end{bmatrix}=\begin{bmatrix}{0} \\ {4}\end{bmatrix}\)Row 6
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{7} \\ {9}\end{bmatrix}=\begin{bmatrix}{1} \\ {1}\end{bmatrix}\)Row 7
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{75} \\ {100}\end{bmatrix}=\begin{bmatrix}{0} \\ {25}\end{bmatrix}\)Row 8
\(\Rightarrow\begin{bmatrix}{4} & {-3} \\ {-5} & {4}\end{bmatrix}\begin{bmatrix}{56} \\ {70}\end{bmatrix}=\begin{bmatrix}{14} \\ {0}\end{bmatrix}\)Therefore, the combined multiplied matrix is:
\(\Rightarrow\begin{bmatrix}{8} \\ {9}\end{bmatrix}\begin{bmatrix}{1} \\ {3}\end{bmatrix}\begin{bmatrix}{22} \\ {5}\end{bmatrix}\begin{bmatrix}{5} \\ {0}\end{bmatrix}\begin{bmatrix}{0} \\ {4}\end{bmatrix}\begin{bmatrix}{1} \\ {1}\end{bmatrix}\begin{bmatrix}{0} \\ {25}\end{bmatrix}\begin{bmatrix}{14} \\ {0}\end{bmatrix}\)Comparing these with the letter codes shown below:
We have the code to be:
\(\Rightarrow\begin{bmatrix}{H} \\ {I}\end{bmatrix}\begin{bmatrix}{A} \\ {C}\end{bmatrix}\begin{bmatrix}{V} \\ {E}\end{bmatrix}\begin{bmatrix}{E} \\ {-}\end{bmatrix}\begin{bmatrix}{-} \\ {D}\end{bmatrix}\begin{bmatrix}{A} \\ {A}\end{bmatrix}\begin{bmatrix}{-} \\ {Y}\end{bmatrix}\begin{bmatrix}{N} \\ {-}\end{bmatrix}\)The code is "HAVE A NICE DAY".
The THIRD OPTION is correct.
Can some plsss actually help me I have been getting bad luck! I need to submit soon. Plssss
Answers
Answer:
SCB
Step-by-step explanation:
Help with my home work
Answers
A regular polygon has angles that all measure 162 degrees. How many sides does the polygon have?
Answers
A regular polygon with angles that all measure 162 degrees has 20 sides.
Let's first consider a formula to find the measure of an interior angle of a regular polygon. We can use the formula:
Interior angle = (n-2) x 180 / n,
where n is the number of sides of the polygon.
If all angles of the polygon measure 162 degrees, then we can set up an equation:
(n-2) x 180 / n = 162
Multiplying both sides by n, we get:
(n-2) x 180 = 162n
Expanding the left side, we get:
180n - 360 = 162n
Subtracting 162n from both sides, we get:
18n - 360 = 0
Adding 360 to both sides, we get:
18n = 360
Dividing both sides by 18, we get:
n = 20
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What is the answer to 15. -2b=-14
Answers
Answer:
b=7
Step-by-step explanation:
You just divide -2 by -14
Answer:
I think its b=7
Step-by-step explanation:
when you divide both sides by -2 you get positive 7
them to check
-2(7)= -14
that equation is correct bc -2 times 7 is -14
-14=-14
the lines whose equations are 7x-3y=1 and 6x+y=8 intersect at one point. What is the x-coordnate at that point
Answers
Answer:
x = 1
Step-by-step explanation:
Using the second equation to substitute for y in the first equation will eliminate the y-variable and give you an equation for the x-coordinate.
y = 8 -6x . . . . second equation solved for y
7x -3(8 -6x) = 1 . . . . substituted into the first equation
7x -24 +18x = 1 . . . . eliminate parentheses
25x = 25 . . . . . . . . add 24
x = 1 . . . . . . . . . . . . divide by the coefficient of x
The x-coordinate of the point of intersection is 1.
__
Additional comment
The y-coordinate can be found using our equation for y:
y = 8 -6(1)
y = 2
A gumball machine has 130 red gumballs. If the red gumballs are 25% of the total number of gumballs, how many gumballs are in the gumball machine?
A. 520
B. 32.5
C. 105
D.155
Answers
Answer:
A
Step-by-step explanation:
100/25=4
130x4=520
Will give brainliest and 25 points!!! Pls help me out!!!
What is the midpoint between (-8, 5) and (2, -2)?
(-5, 1.5)
(-6, 3)
(-3, 1.5)
(-5, 3.5)
Answers
Answer:
(-3, 1.5)
Step-by-step explanation:
-8 +5 = -3
2 + -2 = 1.5
Evaluate the algebraic expression.
z^2+1+y when y=4, and z=3.
Answers
Answer:
your question is
z²+1+y where, y=4,z=3
3²+1+4
9+5
14
is your answer
20 POINTS
Look at the figure. How can you prove AABD and AACD are congruent?
is it
A)
B)
C)
Answers
I beileve the anwser is A
HELP ME PLEASE I NEED A EXPLIANTION
Answers
Answer:
i DONT KNOW THIS BECAUSE I HAVEN'T GONE OVER THIS IN SCHOOL
Step-by-step explanation:
Find a power series representation for the function and determine the radius of convergence.
f(x)=x/(1+6x)2
Answers
After considering the given data we conclude that power series representation is \(\sum_n=0^\infty (n+1)(-6)^n x^{(n+1)}\)and the radius of convergence is 1/6.
To evaluate a power series representation for the function \(f(x) = x/(1+6x)^2\)and describe the radius of convergence, we can use the following steps:
Apply the formula for the geometric series to write \((1+6x)^{(-2)}\) as a power series: \((1+6x)^{(-2)} = \sum_n=0^\infty (n+1)(-6)^n x^n.\)
Applying multiplication both sides by x to get \(x/(1+6x)^2\) = \(\sum_n=0^\infty (n+1)(-6)^n x^{(n+1)} .\)
Hence, the power series representation for f(x) is \(\sum_n=0^\infty (n+1)(-6)^n x^{(n+1)}\)
In order to describe the radius of convergence, we can apply the ratio test: \(\limt_n- > \infty |(n+2)(-6)^{(n+1)} x^{(n+2)} / ((n+1)(-6)^{n} x^{(n+1))} | = 6|x| \limt_n - > \infty (n+2)/(n+1).\)
Therefore, the limit of \((n+2)/(n+1)\) as n approaches infinity is 1, so the radius of convergence is 1/6.
Hence, the power series representation for f(x) is \(\sum_n=0^\infty (n+1)(-6)^n x^{(n+1)}\) and the radius of convergence is 1/6.
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Which of the following best describes a figure in which the bases are squares and the lateral faces are rectangles?
Hint: The lateral faces of an object are the faces that are not bases.
A.
square pyramid
B.
rectangular pyramid
C.
square prism
D.
triangular prism
Answers
The only figure that fits the description of having square bases and rectangular lateral faces is a square prism.
What are lateral faces?In geometry, lateral faces are the faces of a three-dimensional object that are not its base. Lateral faces are usually vertical and connect the edges of the base(s) of the object. The term "lateral" comes from the Latin word "latus", which means "side".
For example, in a rectangular prism, the top and bottom faces are rectangles and the lateral faces are rectangles as well. There are four lateral faces that connect the corresponding edges of the rectangles. In a square pyramid, the base is a square and the lateral faces are triangles that meet at a common vertex above the base. In a cylinder, the base is a circle and the lateral face is a rectangle that wraps around the curved surface of the cylinder.
What is a square prism?A square prism is a three-dimensional object that has two congruent square bases and rectangular lateral faces. It belongs to the family of right prisms, which means that the lateral faces are perpendicular to the base(s) of the prism.
The shape of a square prism can be visualized as a solid shape with two parallel, congruent square bases connected by four rectangular lateral faces. The lateral edges of the prism connect the corresponding edges of the bases and are perpendicular to both the bases and the lateral faces.
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DE D 5х - 12 Е Зх 3х - 4 4 F
Answers
EXPLANATION
We have an equilateral triangle because the 3 angles are congruent as shown in the picture and all legs are congruent:
So, 5x-12 = 3x - 4
Adding +12 to both sides:
5x - 12 + 12 = 3x - 4 + 12
Simplifying:
5x = 3x + 8
Subtracting both sides by -3x:
5x - 3x = 3x - 3x + 8
Simplifying:
2x = 8
Dividing both sides by 2:
x = 8/2
Simplifying:
x=4
Now, replacing in any equation, as 5x - 12:
5*(4) - 12= 8
In conclusion, all the legs are congruent and equal to 8.
Answer: DE= 8
Determine the intercepts of the line.
Do not round your answers.
3x + 2y = 5
Y=0
X=0
Answers
Answer:
Step-by-step explanation:
X axis intercept (y=0)
3x+2(0)=5
3x=5
x=5/3
Y axis intercept (x=0)
3(0)+2y=5
2y=5
y=5/2
so, the interception points are: (5/3,0) and (5/2,0)
The measure of one angle of a right triangle is 28∘ more than the measure of the smallest angle. Find the measure of the smallest angle.
Answers
solve the matrix equation
Answers
Answer:
c
Step-by-step explanation:
A fifth factory (factory E) can make shirts at the same rate as the first four factories. Which table(s) could represent the production rate of factory
E?
Factory
Number of
Days
1
Number of
Shirts
400
E
Factory
Number of
Days
1
Number of
Shirts
300
E
Factory
Number of
Days
Number of
Shirts
1,800
E
6
Factory
Number of
Number of
Days
Shirts
2,400
E
Answers
Answer:
you are right
Step-by-step explanation:
How many solutions does the following equation have?
23y+50+27y=50y+5023y+50+27y=50y+50
Answers
The equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.
How to infer the number of solutions of a linear equation of the form f(y) = 0
In this question we have an equation in implicit form: 23 · y + 50 + 27 · y = 50 · y + 50, we need to transform its expression into explicit form by using algebra properties:
23 · y + 50 + 27 · y = 50 · y + 50 Given
50 · y + 50 = 50 · y + 50 Commutative, associative and distributive properties / Definition of addition
0 = 0 Compatibility with addition / Existence of additive inverse / Modulative property / Result
The equivalence indicates that the equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.
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