The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).
What is meant by slope?Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.
The slope-intercept form is y=mx+c
Given points are (2,7) and (-1,-5)
Slope m= (y₂-y₁)/(x₂-x₁)
m=(-5+7)/(-1-2)
m=-2/3
By substituting m value in the above equation we get,
y=(-2/3)x + c
Given that, the above equation is passing through the point (-1,-5)
-5=(-2/3)(-1)+c
c=-5-(2/3)
c=-17/3
y=(-2/3)x-(17/3)
Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)
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can you solve this quickly
Answer:
A
Step-by-step explanation: The lines are only intersecting with each other once
Answer:
A) 1 solution; consistent and independent
Step-by-step explanation:
on the graph the line only intersects once so there is only 1 solution and if 2 graphs have at least 1 solution it is considered consistent and if it has only one solution then it is independent.
Hopes this helps please mark brainliest
Which of the following lines goes through the point -3,4 and is perpendicular to y= 3/2x+6?
The slope of equation [tex]y=\frac{3}{2}x+6[/tex] is [tex]m=\frac{3}{2}[/tex].
The equation of line perpendicular to another line in point slope form:
[tex]y-y_1 = -\frac{1}{m}(x-x_1)[/tex]
Substitute [tex]m=\frac{3}{2}[/tex] and the point [tex](-3,4)[/tex] into the above equation form:
[tex]y-4=-\frac{1}{3/2}(x-(-3))\\y-4=-\frac{2}{3}(x+3)\\-----------\times 3\\3y-12=-2(x+3)\\3y-12=-2x-6\\2x+3y-12+6=0\\2x+3y-6=0[/tex]
Hence the equation of the line is [tex]2x+3y-6=0[/tex].
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A patient is advised by his doctor to reduce his daily soda intake by 25%. Currently, he drinks 4.5oz. cans of soda per day. How many ounces of soda can the patient drink if he reduces his intake by 25%?
Answer: 3.375oz
Explanation
Given
• Reduce his daily soda intake by 25%.
,• Currently, he drinks 4.5oz. cans of soda per day.
,• Ounces of soda can the patient drink if he reduces his intake by 25%?
We have to build a relation, where 4.5 is our 100% and x is 75% (100 - 25 = 75%):
[tex]\frac{x}{75}=\frac{4.5}{100}[/tex][tex]x=\frac{4.5}{100}\cdot75[/tex]Solving for x:
[tex]x=4.5\cdot0.75[/tex][tex]x=3.375[/tex]43 divided by 516
Please help
Answer:
IT IS 12
Step-by-step explanation:
find the Area and Perimeter of the shaded figure Area = x squre unitsPerimeter = x units
Solution
We want to find the area and perimeter of the shaded figure.
The shape below is a rectangle
Therefore, the area of a rectangle is
[tex]\begin{gathered} A=L\times W \\ \text{ Where L is the length and W is the width} \end{gathered}[/tex]while the perimeter of a rectangle is given by
[tex]P=2(L+W)[/tex]Here, L = 2 unit and B = 3 units
[tex]A=2\text{ units}\times3\text{ units}=6\text{ square units}[/tex][tex]P=2(2+3)=2\times5=10\text{ units}[/tex]Hence,
Area = 6 square units
Perimeter = 10 units
joshua likes to make sure he gets enough exercise, so he always moves at least 4 1 /4 miles each day. on days when he doesn't walk, he runs all that distance at the gym. but if he walks 2 blocks, he cuts of 1/12 a mile off his run. today joshua walked 12 1 12 blocks. how far will he run at the gym?
3.75 miles he run at the gym.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given: Joshua likes to make sure he gets enough exercise, so he always moves at least 4 1 /4 miles each day.
On days when he doesn't walk, he runs all that distance at the gym.
But he walks 2 blocks, he cuts of 1/12 a mile off his run.
Today Joshua walked 12 blocks.
As he walked 12 blocks - 6 times 1/12 miles - so that's 0.5 a mile he cut from the exercise.
He will run at the gym for 4.25 - 0.5 = 3.75 miles in total.
4.25 - 6(1/12) = 3.75
Therefore, 3.75 miles he run at the gym.
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Find the number that makes the ratio equivalent to 1:2 5:_
Answer:
10
Step-by-step explanation:
1x5=5
2x5=10
Which ordered pair is the solution to this system of equations?• y=x+4x + y = 21 (1,5)2 (0,2)3 (-1,3)4 (4.0)
Given the system of the equations:
y = x + 4
x + y = 2
By substitution with y from the first equation at the second equation
so,
x + (x+4) = 2
solve to find x
so,
x + x + 4 = 2
2x = 2 - 4
2x = -2
Divide both sides by 2
x = -2/2 = -1
Substitute at the first equation with x to find y
So, y = -1 + 4 = 3
so, x = -1 and y = 3
so, the order pair which a solution is (-1 , 3)
which function is the inverse of f(x)= arccsc x
Let's begin by identifying key information given to us:
[tex]\begin{gathered} f(x)=arccsc(x)_{} \\ f\mleft(x\mright)=y \\ \Rightarrow y=arccsc(x) \\ We\text{ will proceed to i}nterchange\text{ }the\text{ }variables,\text{ we have:} \\ x=arccsc(y) \\ We\text{ will make ''y'' the subject of the formula, we have:} \\ y=\frac{x}{arccsc}\Rightarrow y=csc(x) \\ y=csc(x) \\ y=f^{-1}\mleft(x\mright) \\ \Rightarrow f^{-1}(x)=csc(x) \\ \\ \therefore f^{-1}(x)=csc(x) \end{gathered}[/tex]What are the properties of a translation?Give the coordinates of the.T(3, -1 (AABC) for A(5, 0), B( -1, 2), C(6, -3)
Solution:
Given the coordinates of the image;
[tex]T_{(3,-1)}(\triangle ABC):A(5,0),B(-1,2),C(6,-3)[/tex]The coordinates of the new image is;
[tex]\begin{gathered} A^{\prime}(5+3,0-1),B^{\prime}(-1+3,2-1),C^{\prime}(6+3,-3-1) \\ \\ A^{\prime}(8,-1),B^{\prime}(2,1),C^{\prime}(9,-4) \end{gathered}[/tex]Kayle is playing a game. She starts the game with 500 points. Her first 5 turns and the change in points are shown in the table.
How many points does Kayle have after her 5th turn?
Responses
−550 points
negative 550 points
−150 points
negative 150 points
350 points
350 points
1,150 points
Kayle have 1300 points after her 5th turn as the final score is sum of all score in the 5 rounds that come up to 1300.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The total amount or sum of the two whole numbers is obtained by adding them. Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation. When you add two or more numbers together, you get the sum of the numbers. The sum is the outcome of adding two or more numbers.
Here,
The final score will be the sum of all scores after 5th turn.
initial score=500
first round=−550 points
second round=−150 points
third round=350 points
fourth round=1,150 points
500+-550+-150+350+1150
=500-550-150+350+1150
=1300 points
After her fifth turn, Kayle had 1300 points because the total of her five rounds' scores added up to 1300.
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Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation.
The equation of line in point slope form created is
[tex]y - 3 = 1(x - 2)\\[/tex]
What is equation of line in point slope form?
The most general form of equation of line in point slope form is given by
[tex]y - y_1 = m(x - x_1)[/tex]
Where m is the slope of the line and ([tex]x_1, y_1[/tex]) is the coordinate of the point through which the line passes
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
Here
Let the line passes through ( 2, 3) and (4, 5)
Slope = [tex]\frac{5-3}{4-2}[/tex]
= [tex]\frac{2}{2}[/tex]
= [tex]1[/tex]
Equation of line in point slope form
[tex]y - 3 = 1(x - 2)\\[/tex]
This is equation of line in point slope form.
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For the model y = 150(0.8)^x in the problem, what will be the world population of Iberian lynx in 2020? Year Population2003 1502004 120 A.2B.3C.20D.39
B
1) In this question, y stands for population, and x stands for year.
2) Since the first year is 2003, then 2020 -2003 = 17. Let's plug into x, this value:
[tex]\begin{gathered} y=150(0.8)^{17} \\ y=3.37\text{ } \\ y\approx3 \end{gathered}[/tex]3) Rounding off to the nearest whole number, the population of Iberian lynx will be approximately 3 lynxes.
Someone please help me out I rlly need help
The equation that could be used to solve for x is (3x-1) = 140 and the value of x is 47°.
According to the question,
We have the following information:
We have two lines that are intersecting each other at a point. The angles made on this point are given.
Now, we know that these two angles are vertically opposite angles. And we also know that vertically opposite angles are equal.
So, we will have the following equation:
3x-1 = 140
Now, we can easily find the value of x from this equation:
Adding 1 on both sides of the equation:
3x = 140+1
3x = 141
Dividing by 3 on both sides:
x = 141/3
x = 47°
Hence, the equation that could be used to solve for x is (3x-1) = 140 and the value of x is 47°.
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Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. he is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. he assumes each cookie will have the same number of sprinkles.
Using tha basic multiplication and division, Stan will need 960 sprinkles to make 60 cookies.
What is algebra?In the branch of mathematics known as algebra, a situation is described using mathematical symbols, variables, and arithmetic operations like addition, subtraction, multiplication, and division that produce meaningful mathematical expressions.
The sprinkles needed for 1 cookie are given by
24 cookies need sprinkles = 384
1 cookie will need sprinkles = 384 ÷ 24
= 16 sprinkles
Now, sprinkles needed for 60 cookies are given by
1 cookie needs sprinkles = 16
60 cookies will need sprinkles = 16 × 60
= 960 sprinkles
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The correct question is:
"Stan's cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. He is wondering how many sprinkles (p) he will need to make 60 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 60 cookies?"
Solve y=9/5x +5
Find the slope
Answer:
m=9/5
Step-by-step explanation:
find the slopes of the given points -5,-1 and -5,-10
The slope (m) of the given points is -9.
What do we mean by slopes?A line's steepness can be determined by looking at its slope. In mathematics, the slope is determined by dividing the change in y by the change in x, or "rise over run."Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.So, the slope will be:
Slope formula: m = y₂ - y₁/x₂ - x₁Now, calculate as follows:
m = y₂ - y₁/x₂ - x₁m = -10 - (-1)/-5 - (-5)m = -10+ 1/-5 + 5m = -9/0m = -9Therefore, the slope (m) of the given points is -9.
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find the product of (4x +1)(4x -1)
(4x +1)(4x -1)
Apply the distributive property:
4x (4x ) + 4x (-1) + 1 (4x) + 1 (-1)
16x^2 -4x + 4x -1
Combine like terms:
16x^2-1
Answer:
16x² - 1
Step-by-step explanation:
(4x + 1)(4x - 1)
each term in the second factor is multiplied by each term in the first factor , that is
4x(4x - 1) + 1(4x - 1) ← distribute parenthesis
= 16x² - 4x + 4x - 1 ← collect like terms
= 16x² - 1
Square root of 4n^2+4n^2
PLEASE HELP
Giving brainliest
Answer: 8n^2
Step-by-step explanation:
I did test and got 100
a bag of 13 marbles contains 5 marbles with red on them, 6 with blue on them, 7 with green on them and 5 red and green on them....... I'll take a picture of the rest of the question
We have to calculate the probability that we choose a marble that has either red or green on it.
We have a total of 13 marbles.
We can draw a Venn diagram to look at the green and red marbles:
We can see in the diagram that is expected to all the marbles that have red on it to have also green, because they are not mutually exclusive.
Then, we can calculate the probabilities as:
[tex]\begin{gathered} P(G\cup R)=P(G)+P(R)-P(G\cap R) \\ P(G\cup R)=\frac{7}{13}+\frac{5}{13}-\frac{5}{13}=\frac{7}{13} \end{gathered}[/tex]NOTE: If we write the exact color of each marble we will get:
1) 6 blue marbles
2) 2 only green marbles, as 5 of the 7 marbles that have green are "red and green" marbles.
3) 0 only red marbles: all 5 of the marbles that have red are "red and green"marbles.
4) 5 red and green marbles.
Then, if we add, we get 6 + 2 + 5 = 13 marbles.
The marbles that have red or green are: 2 green and 5 red and green, so there are 7 marbles that have red or green.
Then, the probability is equal to number of successful events / total events = 7/13.
It is the same result as the previous calculation.
Answer: the probability is 7/13.
Review Josh’s steps for solving the equation :
[tex]x^2-6x-7=0\\ \\ x^2-6x=7\\\\x^2-6x+9=7+9\\\\(x-3)^2=16\\\\x-3=6\\x=19\\\\x-3=-16\\x=-13[/tex]
a) State what method he was using to solve the equation.
b) Explain where in his work he had a mistake.
c) Show how to fix his mistake and what the correct answer should be.
The method Josh was using to solve the equation is completing the square method.
Josh made mistake where he was supposed to find the square root of both sides.Josh should fix his mistake by finding the the square root of both sides and the correct answer should be x = 1 or -7How to solve quadratic equation?x² - 6x -7 = 0
a = 1
b = -6
c = -7
x² - 6x = 7
Find the half of b and square it, then add to both sides
x² - 6x + 9 = 7 + 9
factorize the expression on the right
(x - 3)² = 16
Find the square root of both sides(x - 3) = √16
x - 3 = ± 4
x = 4 - 3 or x = -4 - 3
x = 1 or -7
Therefore, the correct answer to the quadratic equation using completing the square method is x = 1 or -7
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Here is a graph representing the relationship in question 3. Interpret the set of coordinates (30, 7).
children's tickets sold
60
55
50
45
40
30
25
20
5
(30, 7)
10 15 20 25 30 35 40
adult tickets sold
O 7 children's tickets and 30 adult tickets were sold
O 30 children's tickets and 7 adult tickets were sold
O When 7 tickets are sold, $30 is collected
O (30, 7) is not a possible solution
The correct option 2 that is 30 children's tickets and 7 adult tickets were sold.
Given : A graph which has adult tickets in the x - axis
and children tickets in the y - axis
The marked point is ( 30, 7 )
this means that the value of x axis 30 and y axis is 7
thus from the above information it is clear that there are 30 children's tickets and 7 adult tickets were sold.
So the correct option is Option 2
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Challenging. A cylinder has a diameter of 12 inches at its base. The height of the cylinder is 1.25 feet. What is the volume of the cylinder in cubic inches? Use 3.14 for 7 and round your answer to the nearest cubic inch.
Diameter of cylinder = 12 inches
radius of cylinder (r) = 1/2 x diameter = 6 inches
Height of cylinder (h) = 1.25 feet
We can convert feet to inches using the relation: 1 foot = 12 inches
So, 1.25 feet = 12 x 1.25 inches
=> 15 inches
The volume of the cylinder is given by:
[tex]V\text{ = }\pi r^2\text{ h}[/tex]Upon substituting the values of r and h
[tex]\begin{gathered} V\text{ = 3.14 x 6 x 6 x 15} \\ \\ V=\text{ }1695.6\text{ cubic inches} \\ V=1696inches^3 \end{gathered}[/tex]
Which expressions are equal to 11 x 10³2 Select all that apply.
Answer:
Option B,A,C is correct
Explanation:
You're missing some info. But I did this question before.
A. 11x100
B. 11,000
C. 11x10x10x10
THESE ARE ALL CORRECT SINCE THEY ALL EQUAL 11000 .
Please help me!
What is the probability distribution table for this bar graph?
A. Pink 0.3 Green 0.2 Yellow 0.05 Blue 0.45
B. Pink 0.6 Green 0.2 Yellow 0.4 Blue 0.9
C. Pink 0.25 Green 0.25 Yellow 0.25 Blue 0.25
D. Pink 6 Green 4 Yellow 1 Blue 9
Answer:
A. Pink 0.3 Green 0.2 Yellow 0.05 Blue 0.45
Step-by-step explanation:
Adding up the total number of values:
[tex]6+4+1+9=20[/tex]
Then, finding the probability of each color:
Pink: [tex]6/20=0.30[/tex]
Green: [tex]4/20 = 0.20[/tex]
Yellow: [tex]1/20=0.05[/tex]
Blue: [tex]9/20=0.45[/tex]
Which of the following is equivalent to 1.92?
A.1.92%
B.19.2%
C.25/23
D.1 23/25
Answer :A i think
Step-by-step explanation:
If a television screen is 20 inches wide
and 15 inches high, what is the size of the
TV?
Diagonal problems
25 is the diagonal of tv with the given dimensions .
What is diagonal ?In geometry, a diagonal is a line segment connecting two vertices of a polygon or polyhedron that are not on the same edge. A diagonal is an informal term for any sloping line.
CalculationThe length of diagonal is the length of the hypotenuse of a right angled triangle for which the lengths of the sides making right angle are 20" and 15", hence is
=
√20^2 + 15^2
=√400 + 225
= √625
= 25
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is y=5^w an exponential function if so state the initial value and the base if not then which type of function is it
By using the property of exponential function, the results obtained are
Base of the function is 5.
Initial value of the function is close to zero.
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2\times 2\times 2\times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a\times a....\times a[/tex] (m times), a is the base and m is the index.
Here,
[tex]y = 5^w[/tex] is an exponential function.
The base of the function is 5.
As [tex]x \rightarrow -\infty[/tex], the function tends to 0
So the initial value of the function is close to zero.
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The volleyball team has a record of 6 wins and 2 losses. What other team has a proportional win-loss record? Basketball: 12 wins, 5 losses Football: 3 wins, 1 loss Wrestling: 12 wins, 6 losses Debate: 3 wins, 4 losses
The number of win and losses of the volleyball team is related by a constant number, 3. This means that they're proportional. To find if the other teams also have proportional win-loss records we need to divide the number of their wins by the number of losses, if the result is an integer number, then they're proportional. We have:
[tex]\begin{gathered} \text{ basketball=}\frac{12}{5}=2.4 \\ \text{ football=}\frac{3}{1}=3 \\ \text{ wrestling=}\frac{12}{6}=2 \\ \text{ debate =}\frac{3}{4}=0.75 \end{gathered}[/tex]Since the football team has a proportional win-loss record with the same proportion as the Volleyball team, then this is the correct answer.
Raj ahs put a soup intot he freezer to cool down. The soups temperature started at 170 °F and decreased at a rate of 30 °F per hour. Let h represent the number of hours the soup stays in the freezer.
Actual question:
Raj wants the soup to cool down so that its temperature, when he takes it out of the freezer, is at most 74 °F. Write an inequality in terms of that represents all times when the soup is cool enough for Raj to take it out of the freezer.
The inequality in terms that represents all times when the soup is cool enough for Raj to take it out of the freezer is:
170 - 30h ≤ 74
Given, Raj has put a soup intot he freezer to cool down.
The soups temperature started at 170 °F and decreased at a rate of 30 °F per hour.
Let h represent the number of hours the soup stays in the freezer.
Raj wants the soup to cool down so that its temperature, when he takes it out of the freezer, is at most 74 °F.
we are asked to determine an inequality in terms of that represents all times when the soup is cool enough for Raj to take it out of the freezer.
⇒ 170 - 30h ≤ 74
⇒ 170 - 74 ≤ 30h
⇒ h ≥ 3.2
Hence we get the required inequality form.
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