the slope of a graphed line is -8/7. Write the standard-form equation of the line using the coordinates of the labeled point.
Answers
The standard-form equation of the line using the coordinates of the labeled point is: B. 8x + 7y = 60.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At data point (4, 4) and a slope of -8/7, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -8/7(x - 4)
By multiplying all through by 7, we have:
7(y - 4) = -8(x - 4)
7y - 28 = -8x + 32
7y + 8x = 32 + 28
8x + 7y = 60.
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Related Questions
If P(B)=0.3,P(A∣B)=0.5,P(B ′ )=0.7, and P(A∣B ′ )=0.8, find P(B∣A).
Answers
If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113
To find the value of P(B|A), follow these steps:
The probability of B given A can be given by the product of the probability of A given B and the probability of B, divided by the total probability of B. So, the formula for P(B|A) = P(A|B) * P(B) / [P(A|B)*P(B)+P(A|B')*P(B')]. Substituting the values, we get P(B|A) = (0.5) (0.3) / [(0.5) (0.3) + (0.8) (0.7)] ⇒P(B|A) = 0.15 / [0.15 + 0.56] ⇒P(B|A) = 0.15 / 0.71 ⇒P(B|A) = 0.2113. Therefore, P(B|A) = 0.2113.Learn more about probability:
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in a park, a bike path and a horse riding path are parallel. In one part of the park a hiking trail intersects the two paths. Find the measures of angle one and angle two
Answers
Answer:
angle one
Step-by-step explanation:
Plssss help meeee I need help??
Answers
Answer:
The y-intercept will be moved 11 units downward.
Step-by-step explanation:
AB has endpoints A(4, ‐3) and B(3, 7). Line d is the perpendicular bisector of AB .
Which of the following is NOT an equation of line d?
Answers
Answer:
B
Step-by-step explanation:
We know that AB has endpoints at A(4, -3) and B(3, 7).
To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.
So, let's find the slope of AB using the slope formula:
\(\displaystyle m=\frac{y_2 - y_1}{x_2 - x_1}\)
Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:
\(\displaystyle m=\frac{7-(-3)}{3-4}=\frac{10}{-1}=-10\)
So, the slope of AB is -10.
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.
So, Line D has a slope of 1/10.
Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.
To find the midpoint, we can use the midpoint formula:
\(\displaystyle M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\)
We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:
\(\displaystyle M=\left(\frac{4+3}{2},\frac{-3+7}{2}\right)\)
Evaluate. So, the midpoint is:
\(\displaystyle M=\left(\frac{7}{2},2\right)=(3.5,2)\)
Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:
\(y-y_1=m(x-x_1)\)
Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:
\(\displaystyle y-2=\frac{1}{10}(x-3.5)\)
This is the same as choice C. So, choice C is indeed an equation of Line D.
We can distribute the right to obtain:
\(\displaystyle y-2=\frac{1}{10}x-0.35\)
Add 2 to both sides to acquire:
\(\displaystyle y=\frac{1}{10}x+1.65\)
This is the same as choice D. So, choice D is indeed an equation of Line D.
Moreover, we can put this into standard form by multiply everything by 10, which gives:
\(10y=x+16.5\)
Subtracting x from both sides yields:
\(-x+10y=16.5\)
This is the same as A. So, choice A is also an equation of Line D.
There is no way to acquire choice B. So, B is not an equation of Line D.
Therefore, our answer is B.
And we're done!
Answer:
a, c and d are not equation lines of d
Step-by-step explanation:
your answer is b i wanna type the whole explanation like i did in my
note book but my hand hurts...hope this helped
Select all expressions that are equivalent to 3 x 5 − 6 x 4 y + 3 x 3 y 2 . A. 3 x 3 ( x − y ) 2 B. 3 x 3 ( x 2 − 2 x y + y 2 ) C. 3 x 3 ( x + y ) 2 D. 3 x 3 ( x − y ) ( x + y ) E. 3 x 3 ( x − y ) ( x − y )
Answers
Answer:
B
Step-by-step explanation:
Factorizing 3x^5−6x4y+3x^2y^2
\(= (3x\left(x^4-8y+xy^2\right)\)
=
\(3x^3 ( x^2-2 x y + y^2 )\)
Answer:
B
Step-by-step explanation:
5.22 write the decimal as a fraction or mixed number in simplest form
Answers
Answer:
5 and 11/50
Step-by-step explanation:
5.22 = 261/50 = 5 and 11/50
evaluate x^1-x^-1+x^0 for x=2
Answers
Answer:
5/2
Step-by-step explanation:
\(x^1=x\text{ and }x^{-1}=\frac{1}{x} \text{ and }x^0 = 1\)
These make the expression \(x^1-x^{-1}+x^0=x-\frac{1}{x}+1\) .
Plug in x = 2 to get \(2-\frac{1}{2}+1=\frac{5}{2}\)
Answer:
given equation = x¹-x⁻¹+x⁰
lets subtitute the value of x in this equation = 2-1/2+1
= 3-1/2 =5/2 =2.5 (ans)
Hope it helps
The volume of a cube is 614.125 cubic inches. What is the length of each side of the cube?
Answers
The length of the side of cube is 8.5 inches.
What is volume of a cube?
A cube is a solid object that is three dimensional and has six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, and the only regular hexahedron, is the cube. It consists of 8 vertices, 12 edges, and 6 faces.
The volume of a cube is a^3 cubic inches where a is the length of side of cube.
Give volume of a cube is 614.125 cubic inches.
Let the length of a side of cube is x inches.
Then volume of cube = x^3 cubic inches.
Now,
x^3 = 614.125
Finding cube root and we get
=> x^3 = 8.5 * 8.5 * 8.5
=> x = 8.5 inches
Therefore, the length of the side of cube is 8.5 inches.
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I need help on this and the person who answer this correctly gets a BRANLIST(answer if you know)
Answers
Answer:
A)
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y
if a cylinder has a volume of 99 cubic centimeters , what is the volume of a cone with the same dimensions
Answers
Answer:
900
Step-by-step explanation:
area of a pentagon 16 18 20 15
Answers
The area of the pentagon (assuming it is valid and regular) is approximately 1693.08 square units.
The given sides do not form a valid pentagon as the sum of any three sides of a pentagon must be greater than the fourth side. However, assuming that the sides are valid and the pentagon is regular,
we can use the formula A = (1/4) * n * s^2 * cot(pi/n), where n is the number of sides and s is the length of each side. Since we are given the length of each side (16, 18, 20, 15), we can substitute these values into the formula to find the area of the pentagon.
A = (1/4) * 5 * (16^2) * cot(pi/5) + (1/4) * 5 * (18^2) * cot(pi/5) + (1/4) * 5 * (20^2) * cot(pi/5) + (1/4) * 5 * (15^2) * cot(pi/5) A = 1693.08
Therefore, the area of the pentagon (assuming it is valid and regular) is approximately 1693.08 square units.
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the local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. there are three appetizers, four soups, three main courses, and three desserts. your diet restricts you to choosing between a dessert and an appetizer. (you cannot have both.) given this restriction, how many three-course meals are possible? choices
Answers
The possible combination for three-course meals to be chosen from given the restriction is equal to 16.
The restriction that can only choose either a dessert or an appetizer,
Have two choices for the first course.
For the second course,
Have 4 choices for the soup.
For the third course,
Have 3 choices for the main course,
And since can only choose one of the remaining two categories (dessert or appetizer),
Have 2 choices for the third course.
Using the multiplication principle of counting,
The total combinations of number of three-course meals possible under these conditions by multiplying the number of choices for each course,
= Number of choices for the first course × Number of choices for the second course × Number of choices for the third course
= 2 × 4 × 2
= 16
Therefore, there are 16 possible combination for three-course meals that can be chosen.
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Which of these triangles are translations of Triangle A?
Select all that apply.
А
E
D
B
F
С
please help
Answers
Answer:
B and D
Step-by-step explanation:
A translation of a triangle is moving it up down or side to-side on the axis, not changing the shape flipping it or the orientation,so the translations of a would be B and D!
Hoped this helped, have a good one!
Answer:
B, D
Step-by-step explanation:
Tim would like to use his income tax return to pay off one of his four credit cards. His previous plan was to pay off all four credit cards in the same timeline of 36 months. He wants to eliminate the card that is charging him the most interest on a monthly basis. The chart below outlines Tim's four credit cards, their balances, and their APRs. Which credit card should Tim use his tax return to pay off? Credit Card Balance APR A $1,260. 00 12% B $900. 00 18% C $1,290. 00 9% D $1,200. 00 16% a. A b. B c. C d. D.
Answers
Tim should use his income tax return to pay off credit card B, as it has the highest APR of 18% and eliminating this debt will save him the most in interest on a monthly basis.
By paying off credit card B, Tim will eliminate the debt with the highest interest rate of 18%. This means he will no longer have to pay the 18% interest on the $900 balance, resulting in significant savings. Although credit card D has a slightly higher balance, its APR is lower at 16%, making credit card B the more cost-effective choice to eliminate with the income tax return.
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Thi i a pond in the hape of a prim. It i completely full of water. Colin ue a pump to empty the pond. The level goe down by 20cm in the firt 30min. How many minute until completely empty
Answers
This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.
We have a pond which is completely filled with the water.
Area of the side face ( trapezium shaped)
= 1/2 x (1.4 + 0.6) x 2
= 2 m²
Volume = area x height (here width)
V = 2x1 = 2 m³
The level goes down by 20cm in the first 30 mins
Volume of water that will be taken down =
=0.2 x 1 x 2
=0.4 m³ ( upper water will form cuboid face)
Now,
⇒0.4 m³ water is taken out in 30 minutes
⇒1 m³ water is taken out in 30/0.4 minutes
⇒2 m³ water is taken out in 30/0.4 x 2 minutes
⇒30x2/0.4
⇒150 minutes.
So the pond will be completely empty in 150 min that is 2hrs30mins.
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Which function has a greater initial value.
Answers
Answer:
Function A
Step-by-step explanation:
The Y-Intercept for Function A is 4, the initial value, where the line starts.
For Function B, there's no way to tell the Y-Intercept because there isn't a Y which is 0, but it definitely can't be bigger than 4.
The coffee shop is 5 blocks East of Amber's house. The park is 3 blocks West of Amber's house.
How many blocks is it from the coffee shop to the park?
Answers
If "coffee-shop" is 5 blocks East of Amber's house and park is 3 blocks West of Amber's house, then the distance in blocks between "coffee-shop" to park is 8 blocks.
The distance between the "coffee-shop" and "Amber's house" is 5 blocks to the East, and the distance between the "park" and "Amber's house" is 3 blocks to the West.
To find the distance between the "coffee-shop" and the park, we can add the distances from the coffee shop to Amber's house and from Amber's house to the park:
On adding both the distance ,
We get,
⇒ 5 + 3 = 8,
Therefore, the distance between the coffee shop and the park is 8 blocks.
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This shows a figure. What is the measure of angle MRX?
Answers
The measurement of the angle MRX is 130°.
Given that a figure we need to find the angle MRX,
The lines TP and ZX are perpendicular to each other, and there is a line MQ intersecting at R,
So,
Angles MRT and MRZ are complementary so,
m ∠MRZ + m ∠MRT = 90°
50° + m ∠MRT = 90°
m ∠MRT = 40°
Also,
Angles TRX and TRZ are supplementary so, and equal to right angle, so,
m ∠MRX = m ∠MRT + m ∠TRX
m ∠MRX = 90° + 40°
m ∠MRX = 130°
Hence the measurement of the angle MRX is 130°.
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Find the x value?
Help pls
Answers
Answer:
Step-by-step explanation:
sin(63°) = x/22
x = 22sin(63°) ≅ 19.6 units
A tank holds a 112-liter solution of alcohol and salt. Initially, the solution contains 6 grams of salt. Pure alcohol begins flowing into the tank at the rate of 2 liters per minute and the solution in the tank begins flowing out at a rate of 1 liter per minute.
a) Find an expression for the amount of salt in the tank at any time.
b) How much salt is present after 56 minutes?
Answers
The amount of salt in the tank at any time is given by the expression S(t) = 6(1 - \((\frac{1}{2} )^t\) ), where t is time in minutes. After 56 minutes, there are approximately 5.18 grams of salt present.
To find an expression for the amount of salt in the tank at any time, we need to consider the rate at which the salt concentration is changing. Since pure alcohol is flowing in at 2 liters/min and the solution is flowing out at 1 liter/min, the tank's volume remains constant at 112 liters.
The concentration of salt decreases by half for every doubling of the volume of the solution. Thus, the amount of salt after t minutes is given by:
S(t) = 6(1 - \((\frac{1}{2} )^t\) )
To find the amount of salt present after 56 minutes, plug t = 56 into the equation:
S(56) = 6(1 - (1/2)⁵⁶)
S(56) ≈ 5.18 grams of salt
Therefore, after 56 minutes, there are approximately 5.18 grams of salt in the tank.
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Multiply 9.70×38.5 you can use the estimate to place the decimal in a product
Answers
373.45 is the answer.
31. What is the measure of
a. 30 degrees
b. 45 degrees
c. 60 degrees
d. 90 degrees
Answers
option (a) 30 degrees
Step-by-step explanation:
Sum of all the angles in a triangle equals to 180°
So, 30° is answer
x>-4
except the greater than symbol has a line under. Graph each inequality and write the solution set using both set-builder notation and interval notation.
Answers
The solution set of the inequality x ≥ - 4 using set builder notation and interval notation is {x | x ∈ Z, - 4 ≤ x ≤ ∞ } and [ - 4, ∞ ) respectively.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Interval Notation: A set of real numbers known as an interval contains all real numbers that fall inside any two of the set's numbers.
Consider the inequality,
x ≥ - 4
In the number line, the value of x is equal to and greater than - 4 increasing to infinity.
Therefore,
The solution set using the set builder notation is:
{x | x ∈ Z, - 4 ≤ x ≤ ∞ }
The solution set of the inequality using the interval notation is:
[ - 4, ∞ )
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To plot (5,- 9), in which direction do you move
first?
Answers
Answer: You are gonna want to move right 5 times then down nine times!
Step-by-step explanation:
Answer:
if you are doing a number line then you start at 0 then go to right 5 times go to the left 7 times which would give you -2
Step-by-step explanation:
Suppose you bought five sodas and three hamburgers for a total $10.25. Later that day, you bought
two sodas and four hamburgers for a total of $8.30. What is the price of one hamburger?
Show your work.
Answers
Answer:
1.30$
Step-by-step explanation:
THIS IS EXPONENTIAL FROM TWO POINTS
If f(x) is an exponential function where f(3.5)=21 and f(6.5)=69, then find the value of f(9), to the nearest hundredth.
Answers
Answer:
i think the answer is 144
Step-by-step explanation:
ohhh so first we should try finding the slope here. since we know the points are (3.5 , 21) and (6.5, 69) we can use the formula to look for the slope
the formula is:
y2 - y1 / x2 - x1
lets substitute
69 - 21 / 6.5 - 3.5
48 / 3
16
f(x) = 16x + b
now we just substitute
btw i dont think we need to find b because this inst a linear equation? im not sure but yea i dont think we need to find the y-intercept
so anyways
f(9) = 16(9)
= 144
Does anyone know this correctly?
Answers
Ziyad’s family owns a rectangular piece of land. If the length of the land is represented by 2x - 6 and the width is represented by 3x - 5,
Answers
Answer:7686
Step-by-step explanation
The area of the Ziyad family land has a length of (2x - 6) and a width of (3x - 5). Then the area in the form of a polynomial is 6x² - 28x + 30.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Ziyad’s family owns a rectangular piece of land. If the length of the land is represented by 2x - 6 and the width is represented by 3x - 5.
Then the area of the given rectangle will be
Area = length × width
Area = (2x - 6)(3x - 5)
Area = 6x² - 10x - 18x + 30
Area = 6x² - 28x + 30
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A company claims that their new bottle holds 40% more laundry soap. If their original container held `53` fluid ounces of soap, how much does the new container hold?
Answers
Answer:
I need help to sooo yeah
Step-by-step explanation:
Soryy
compute the volume of a solid obtained by rotating a region below the graph of =(2 16)−1 about the ‑axis for −[infinity]<<[infinity].
Answers
The volume of the solid obtained by rotating a region below the graph of y=(2x+16)−1 about the x-axis is infinite.
A graph is a visual representation of data that displays the relationship between different variables or sets of data. It consists of points, called vertices or nodes, connected by lines or curves, known as edges or arcs. Graphs are commonly used to present complex information in a more organized and intuitive way, enabling easier analysis and understanding
To compute the volume of the solid obtained by rotating a region below the graph of y=(2x+16)−1 about the x-axis, we can use the method of cylindrical shells.
First, we need to find the limits of integration. Since the region extends from negative infinity to positive infinity, we can set up the integral as follows:
V = ∫[from -∞ to ∞] 2πx(f(x))dx
where f(x) = (2x+16)−1.
Next, we need to express x in terms of y so that we can integrate with respect to y.
y = (2x+16)−1
1/y = 2x + 16
x = (1/2y) - 8
Substituting this expression for x in the integral, we get:
V = ∫[from 0 to ∞] 2π((1/2y)-8)(y)dy
Simplifying,
V = ∫[from 0 to ∞] π(4 - y^2/2)dy
Evaluating the integral,
V = π [4y - (y^3/6)] [from 0 to ∞]
V = ∞
Therefore, the volume of the solid is infinite.
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