Writing Prompt:Explain how to write an equation in Point-Slope Form using the graph below.
Answers
point slope formular is as follows
\(\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ m=\text{slope} \end{gathered}\)The point slope form using the graph can be represented below. let us find the slope first
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{400-175}{8-3} \\ m=\frac{225}{5}=45 \end{gathered}\)using one point on the graph(3, 175) to represent the point slope equation is represented below
\(\begin{gathered} y-175=45(x-3) \\ y-175=45x-135 \\ y=45x-135+175 \\ y=45x+40 \end{gathered}\)Related Questions
the equation is X - 1/2 = 1/6
Answers
Given
\(x-\frac{1}{2}=\frac{1}{6}\)Solve as shown below
\(\begin{gathered} \Rightarrow x-\frac{1}{2}+\frac{1}{2}=\frac{1}{6}+\frac{1}{2} \\ \Rightarrow x=\frac{1}{6}+\frac{1}{2}=\frac{2+6}{6\cdot2}=\frac{8}{12}=\frac{2}{3} \\ \Rightarrow x=\frac{2}{3} \end{gathered}\)Therefore, the answer is x=2/3
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answers
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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A graphing calculator is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in, by 20 in. by cutting out equal squares of side x at eech corner and then folding up the sides (see the figure). 20 in. 12 in. (a) Find a function that models the volume V of the box. (b) Find the values of x for which the volume is greater than 230 in2. (Rgund your answers to three decimal places. Enter your answer using interval notation) (c) Find the largest volume that such a box can have. (Round your answer to three decimal places) in2
Answers
A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.
A function that models the volume V of the box can be found by subtracting four \(x2\)from both the length and the width, and then multiplying the result to get the volume:
V = \((12 - 4x2)(20 - 4x2)\)
To find the values of x for which the volume is greater than 230 in2, we can solve the equation
V = \((12 - 4x2)(20 - 4x2) = 230\) for x.
This gives x values of ±2.636
Thus, the values of x for which the volume is greater than 230 in2 are x = [\(-2.636, 2.636\)].
The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.
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find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}
Answers
The lub is 0.23\(\mathbf{\overline{43}}\), while the glb is 0.2
The given set is presented as follows;
E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}
The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x ≤ B, while there all y ∈ E has a x ∈ E such that t < x
Therefore;
The supremum, lub of the given set is 0.23\(\overline{43}\)
The greatest lower bound, glb, b, also known as the infimum, is defined as follows;
b is the greatest lower bound if for all x ∈ E then x ≥ b
Given that b < t, then where x ∈ E, there exist a x < t
The glb of the given set is 0.2
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Evaluate the surface integral. S xz dS S is the boundary of the region enclosed by the cylinder y2 + z2 = 16 and the planes x = 0 and x + y = 10
Answers
If you project S onto the (x,y)-plane, it casts a "shadow" corresponding to the trapezoidal region
T = {(x,y) : 0 ≤ x ≤ 10 - y and -4 ≤ y ≤ 4}
Let z = f(x, y) = √(16 - y²) and z = g(x, y) = -√(16 - y²), each referring to one half of the cylinder to either side of the plane z = 0.
The surface element for the "positive" half is
dS = √(1 + (∂f/∂x)² + (∂f/dy)²) dx dy
dS = √(1 + 0 + 4y²/(16 - y²)) dx dy
dS = √((16 + 3y²)/(16 - y²)) dx dy
The the surface integral along this half is
\(\displaystyle \iint_T xz \,dS = \int_{-4}^4 \int_0^{10-y} x \sqrt{16-y^2} \sqrt{\frac{16+3y^2}{16-y^2}} \, dx \, dy\)
\(\displaystyle \iint_T xz \,dS = \int_{-4}^4 \int_0^{10-y} x \sqrt{16+3y^2}\, dx \, dy\)
\(\displaystyle \iint_T xz \,dS = \frac12 \int_{-4}^4 (10-y)^2 \sqrt{16+3y^2} \, dy\)
\(\displaystyle \iint_T xz \,dS = 416\pi\)
You'll find that the integral over the "negative" half has the same value, but multiplied by -1. Then the overall surface integral is 0.
A line has a slope of 5 and includes the points (1,t) and (3,2). What is the value of t?
Answers
Hello!
\(\large\boxed{t = -8}\)
We can find the value of t using the slope formula:
\(slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Plug in the given slope and coordinates into the appropriate places:
\(5 = \frac{2-t}{3-1}\)
Simplify:
\(5 = \frac{2-t}{2}\)
Multiply both sides by 2 to begin isolating for t. Simplify and solve for t:
\(5 * 2 = 2 - t\\\\10 = 2 - t\\\\8 = -t\\\\t = 8\)
What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
Answers
The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)
To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:
1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).
2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).
4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).
This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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¿Qué es y cómo se forman un enlace químico?
Answers
subtract 2: 30,28,26,
Answers
The answer here is 24
According to the question
The pattern of the given numbers is that each number is 2 less than the previous number.
So the next number in the sequence is 26 - 2 = 24.
So subtracting 2 from 30, 28 and 26 gives the sequence 28, 26 and 24.
What is a pattern?
A pattern is a repeated sequence of elements that follow a certain rule or formula, which can help us make predictions and solve problems.
What is a sequence?
A sequence is a collection of numbers, shapes, or other objects arranged in a specific order or pattern, which can be finite or infinite and may follow a certain rule or formula.
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The sequence of numbers obtained after subtracting 2 is 28, 26, 24.
What is a sequence?A sequence is a collection of numbers, shapes, or other objects arranged in a specific order or pattern, which can be finite or infinite and may follow a certain rule or formula.
According to given information:In the given sequence of numbers, we are asked to subtract 2 from each of the numbers. To do this, we simply subtract 2 from the first number, which gives us the second number in the sequence. Then we subtract 2 from the second number to get the third number, and so on.
So, starting with the first number 30, we subtract 2 from it to get the second number 28. Then we subtract 2 from 28 to get 26, and finally, we subtract 2 from 26 to get 24.
Therefore, the sequence of numbers obtained after subtracting 2 from each of the given numbers is 28, 26, 24.
Subtracting 2 from each of the given numbers, we get:
30 - 2 = 28
28 - 2 = 26
26 - 2 = 24
Therefore, the sequence of numbers obtained after subtracting 2 is 28, 26, 24.
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does the equation y^2-y^2x = 6 describe y as a function of x
Answers
The equation y² - y²x = 6 can be describe as a function of x as:
y = √(6/(x - x)).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y² - y²x = 6
Taking y² as common.
y²(1 - x) = 6
Divide both sides with (1 - x).
y² = 6/(1 - x)
Square root on both sides.
y = √(6/(x - x))
This is a function of x.
Thus,
y = √(6/(x - x)) is a function of x.
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Nicole took out an 80/20 mortgage to buy a house that cost $205,000. The first (80%) mortgage has an interest rate of 4.65%, and the second (20%) mortgage has an interest rate of 7.525%. Both the first mortgage and the second mortgage are 30 year fixed rate mortgages. What is the amount of Nicole's first morgage?
Answers
The total monthly payment for both mortgages will be the sum of the monthly payments for each mortgage, which is $848.27 + $294.41 = $1,142.68.
how to calculate?Nicole's 80/20 mortgage means that she took out two mortgages to cover the cost of the house: one for 80% of the total cost and another for 20%. We can start by finding the amount of the first mortgage as follows:
80% of $205,000 = 0.8 x $205,000 = $164,000
So the amount of Nicole's first mortgage is $164,000.
To find out what her monthly payments will be, we need to calculate the monthly payments for each mortgage separately using the given interest rates and loan terms. For the first mortgage:
Loan amount: $164,000
Interest rate: 4.65% per year
Loan term: 30 years (or 360 months)
Using a mortgage calculator or formula, we can calculate the monthly payment for the first mortgage:
Monthly Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Loan term in months))
where Monthly interest rate = Annual interest rate / 12
Plugging in the values for the first mortgage, we get:
Monthly interest rate = 4.65% / 12 = 0.003875
Monthly Payment = (164000 x 0.003875) / (1 - (1 + 0.003875)^(-360)) = $848.27
So Nicole's monthly payment for the first mortgage is $848.27.
We can repeat the same calculation for the second mortgage, which has the following details:
Loan amount: $41,000 (20% of $205,000)
Interest rate: 7.525% per year
Loan term: 30 years (or 360 months)
Using the same formula, we get:
Monthly interest rate = 7.525% / 12 = 0.006271
Monthly Payment = (41000 x 0.006271) / (1 - (1 + 0.006271)^(-360)) = $294.41
So Nicole's monthly payment for the second mortgage is $294.41.
Note that the total monthly payment for both mortgages will be the sum of the monthly payments for each mortgage, which is $848.27 + $294.41 = $1,142.68.
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Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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what is da rate to question
Answers
The calculated value of the rate of the graph is 0.8
How to determine the rate of the graphfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
(0, -16) and (20, 0)
The rate of the graph is calculated as
Rate = Change in y/x
using the above as a guide, we have the following:
Rate = (0 + 16)/(20 - 0)
Evaluate
Rate = 0.8
Hence, the rate is 0.8
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Translate the following sentence into an algebraic inequality:
The quotient of a number, n, and ten is no less than twelve.
Question 1 options:
A)
n∕10 ≥ 12
B)
n + 10 ≥ 12
C)
10∕n ≥ 12
D)
10n ≥ 12
Answers
Answer: A). \(\ \dfrac{n}{10}\geq12\)
Step-by-step explanation:
We know that, the quotient of a and b \(=\dfrac{a}{b}\)
Given: The quotient of a number, n, and ten is no less than twelve.
\(i.e. \ \dfrac{n}{10}\geq12\) [no less than means either greater or equal]
The required algebraic inequality:
\(\ \dfrac{n}{10}\geq12\)
Hence, the correct option is A). \(\ \dfrac{n}{10}\geq12\)
The segments shown below could form a triangle.
A. True
B. False
Answers
answer TRUE because they would make a triangle
A biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road. How much more does he need to travel? (distance)
Answers
The biker needs to travel 45 km more to complete his journey.
Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,
Let the total distance of the road be x,
So,
2x/5 - 5 = 3x/8
2x/5 - 3x/8 = 5
Solving for x,
Multiply by 40 to both sides,
16x-15x = 200
x = 200
Therefore, the total distance of the road is 200 km.
Since, he travelled =
200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km
Therefore, he needs to travel 200-155 = 45 km more.
Hence, the biker needs to travel 45 km more to complete his journey.
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Plus help if u can ❤️❤️
Answers
Answer:
0
Step-by-step explanation:
The ratio of boys to girls in a math class is 7:8. Which
statement must be true about this math class?
Answers
You didn't give me answer choices.
There are no statements to pick from. Please write a proper answer.
The graph of a piecewise function is shown.
What is the range of the function?
Answers
Answer:
(c) (-∞, -2] ∪ (-1, ∞)
Step-by-step explanation:
You want the range of the piecewise function shown in the graph.
RangeThe range is the vertical extent of the graph, the set of possible output values of the function.
This graph shows a gap between y = -2 and y = -1. The value y = -2 is included in the range, but the value y = -1 is not. (That's what the open circle means.)
Hence, the range is ...
(-∞, -2] ∪ (-1, ∞)
If the circumference of a circle is known, how can the radius be found?
Answers
Answer:
the equation to find radius from circumference is r = C2pi
B
Step-by-step explanation:
6x = 52 − 2y 5x + 7y = 70 Question 1 What is the first step when solving the given system by the elimination method?
Answers
The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equations are given below.
6x = 52 - 2y
6x + 2y = 52
3x + y = 26 ...1
5x + 7y = 70
(5/7)x + y = 10 ...2
Subtraction equation 2 from equation 1, then we have
3x - (5/7)x = 26 - 10
(16/7)x = 16
x = 7
Then the value of 'y' is given as,
3(7) + y = 26
21 + y = 26
y = 5
The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).
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By applying the elimination method, solve the following pair of simultaneous equations:
− 2 = 4
4 + 2 = 6
Answers
By applying the elimination method the value of x is - 2 and y is 7.
This is a problem from algebraic equations and we have to apply the elimination method. We can solve this problem by following a few steps.
So, the given equation according to the question is,
− 2x = 4 ................ ( equation 1 )
4x + 2y = 6 ............... ( equation 2 )
While applying the elimination method we have to multiply equation (1) with the positive coefficient of x in the second equation and vice versa.
Here the coefficient of x in the first equation is 2 and in the second equation is 4.
Now, we have to multiply equation ( 1 ) with 4 and equation ( 2 ) with 2.
Therefore,
− 2x = 4 ................ ( equation 1 ) × 4
4x + 2y = 6 ............... ( equation 2 ) × 2
Now, we can rewrite the equations as,
− 8x = 16 .................. ( equation 3 )
8x + 4y = 12 .................. ( equation 4 )
Now the coefficient of x in both equations are same but opposite sign. So, we have to add the equations.
Here we get , -8x + 8x + 4y = 16 + 12
Or, 4y = 28
Or, y = 7
Now, we have to put the value of y in any equation.
4x + 2.7 = 6 ( equation 2 )
Or, 4x = 6 - 14 = -8
Or, x = -2
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The correct question :
By applying the elimination method, solve the following pair of simultaneous equations:
− 2x = 4
4x + 2y = 6
10
If a translation of (x, y) - (x + 6, y - 10) is applied to
figure ABCD, what are the coordinates of D'?
O (-5,-2)
O (1, -12)
O (4, -15)
0 (-9, 6)
17
Save and Exit
Next
Submit
Mark this dretum
Answers
Answer:
without seeing the original D coordinates, I can't give an answer.
But if you take the original D coordinates and add 6 to the x value, then subtract 10 from the y value, you'll have the answer
Step-by-step explanation:
A crafter is making a triangular flag. She has two sides of length 22 in and 36 in. What are the length possibilities for the third side?
Answers
Answer:
22 in.
Step-by-step explanation:
IN MY BRAIN
The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 5in. width is 4/5and the height is 1 3/5the cube side is 1/5
Answers
Answer:
Explanation:
The dimensions of the rectangular prism are:
• Length = 5in.
,• Width = 4/5 in.
,• Height =1 3/5 in.
The cube has a side length of 1/5 inches.
The number of cubes to pack the prism is determined using the formula below:
\(\begin{gathered} \text{Number of Cubes=}\frac{\text{Volume of }Rec\tan gular\text{ Prism}}{\text{Volume of one cube}} \\ =\frac{\text{lwh}}{s^3} \\ =\frac{5\times\frac{4}{5}\times1\frac{3}{5}}{(\frac{1}{5})^3} \\ =(5\times\frac{4}{5}\times1\frac{3}{5})\div(\frac{1}{5})^3 \end{gathered}\)The operation is simplified below:
\(\begin{gathered} =\mleft(5\times\frac{4}{5}\times\frac{8}{5}\mright)\div\frac{1}{5^3} \\ =\frac{32}{5}\times5^3 \\ =32\times25 \\ =800\text{ cubes} \end{gathered}\)800 cubes are required to completely pack the prism without any gap or overlap.
Points A and B are 15 m apart on a flat road on opposite sides of a prayer flag. The angle of elevation is 22" from point A and 31° from point B. How far above road level is the top of the prayer flag?
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pls help and explain how you got the answer
Answers
The class of the equation and the cross section equation are;
The equation is a hyperboloid of two sheets
The cross sections are;
Equation at z = 0 is; y²/8 - x²/8 = 1
Equation at y = -4 is; x²/8 + z² = 1
Equation at y = 0 is; x²/8 + z² = -1
Equation at y = 4 is; x²/8 + z² = 1
Equation at x = 0 is; y²/8 - z² = 1
What is an equation ?An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.
The equation can be presented as follows;
y² = x² + 8·z² + 8
y² - x² - 8·z² = 8
y²/8 - x²/8 - z² = 1
The above equation is the equation of an hyperboloid of two sheets, where;
a² = 8, b² = 1, and c² = 8
Please find attached the diagram of the surface, created with an online 3D graphing tool.
The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;
y²/8 - x²/8 - 0 = 1
y²/8 - x²/8 = 1
The above equation is the equation of an hyperbola in the xy plane
The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;
4²/8 - x²/8 - z² = 1
- x²/8 - z² = 1 - 4²/8 = -1
- x²/8 - z² = -1
x²/8 + z² = 1
The above is an equation of an ellipse in the xz plane
The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;
0²/8 - x²/8 - z² = 1
- x²/8 - z² = 1
Therefore; x²/8 + z² = -1
The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;
4²/8 - x²/8 - z² = 1
- x²/8 - z² = 1 - 2 = -1
x²/8 + z² = 1
The above equation is the equation of an ellipse in the xz plane
The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;
y²/8 - 0²/8 - z² = 1
y²/8 - z² = 1
The equation is the equation of an hyperbola in the yz plane
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what is 111% as a decimal
Answers
To find the decimal expression for a percent we divided it by 100. In this case:
\(\frac{111}{100}=1.11\)Therefore, 111% is 1.11 as decimal.
If Clare takes out a mortgage for 22 years at an interest rate of 3% and her monthly repayments are $984, what is the principal loan amount? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
The principal loan amount on the mortgage taken by Clare is $1,490.
Given the following data:
Interest rate = 3 %Simple interest = $984Time = 22 yearsTo determine the principal loan amount on the mortgage taken by Clare:
Mathematically, simple interest is given by the formula:
\(S.I = \frac{PRT}{100}\)
Where:
S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.Making P the subject of formula, we have:
\(P=\frac{100S.I}{RT}\)
Substituting the given parameters into the formula, we have;
\(P=\frac{100 \times 984}{3 \times 22}\\\\P=\frac{98400}{66}\)
P = 1,490.909
To the nearest dollar:
Principal loan amount = $1,490.
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12. (5+4 -2)* (-2) = ?
O A.-22
O B. 14
O C.22
O D.-14
Answers
Answer:
D : -14
Step-by-step explanation:
(5+4-2)(-2) = x
7(-2) = x
-14 = x
x = -14