Answer:
B
Step-by-step explanation:
The rise is +7, and the run is -6
so, -6, +7
Write an equation of a line that is perpendicular to y = 6x + 3 that passes through (−6, 4).
Answer:
y = - [tex]\frac{1}{6}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x + 3 ← is in slope- intercept form
with slope m = 6
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then
y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 6, 4 ) into the partial equation
4 = 1 + c ⇒ c = 4 - 1 = 3
y = - [tex]\frac{1}{6}[/tex] x + 3 ← equation of perpendicular line
0n Monday the school library started the day with 12,765 books. During the day students checked out 398 books, and a certain number of books were returned. If the library ended the day with 12,479 books, how many books were returned?
Lets start with the basics. 12,765 books are in total. We need to take 398 from that. 12765 - 398 = 12367. That means x people returned the book to reach 12,479. 12,479 - 12367 = x. X = 112.
112
what is the solution for
-x + 3/7 = 2x - 25/7
?
In linear equation, 4/3 is the solution for equation .
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.-x + 3/7 = 2x - 25/7
On solving
- 7x + 3/7 = 14x - 25/7
- 7x + 3 = 14x - 25
14x + 7x = 25 + 3
21x = 28
x = 28/21 = 4/3
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Alejandro buys 4 bottles of pineapple juice at the corner store for a total cost of
$2.64. If each bottle costs the same amount, how much is 15 bottles of juice?
Answer:
$9.9
Step-by-step explanation:
4 = $2.64
15= ?
15 × $2.64 = 39.6
39.6 ÷ 4 = $9.9
From least to greatest
-17,-4, 7
Answer:
+ 10
Step-by-step explanation:
Identify the volume of the composite figure. Round to the nearest tenth.
Answer:
860.7 m³ (nearest tenth).
Step-by-step explanation:
The given composite figure appears to be a rectangular prism with a cylinder omitted.
Volume of a rectangular prism
[tex]V=w\:h\:l[/tex]
where:
w = widthh = heightl = lengthVolume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r = radiush = heightTherefore, the formula for the volume of the composite figure is:
[tex]\large\boxed{V=whl- \pi r^2h}[/tex]
From inspection of the given diagram:
w = 10 ml = 10 mh = 12 mr = 3 mSubstitute these values into the formula to find the volume of the composite figure:
[tex]\begin{aligned}\implies V&=whl - \pi r^2h\\& = 10 \cdot 12 \cdot 10- \pi \cdot 3^2 \cdot 12\\& = 120 \cdot 10- \pi \cdot 9 \cdot 12\\& = 1200- 108 \pi\\& = 1200 - 339.292006...\\& = 860.7\; \sf m^3\;(nearest\:tenth)\end{aligned}[/tex]
Therefore, the volume of the composite figure is 860.7 m³ (nearest tenth).
Daniel decided to take part in a 10-day fitness challenge for his PE class. Each day, Daniel has to do 5 more push-ups than he did the day before. If Daniel did 20 push-ups on the first day of the challenge, how many total push-ups will he have done during the 10-day challenge?
The answer is 495
Step-by-step explanation:
If you need to add 5 more push-ups every day and find the total it would be 20+25+30+35+40+45+50+55+60+65+70=495
Solve by factoring 6x^2-x-13
Answer:
Step-by-step explanation:
6x^2 - x - 13 = 0
6 * -13 = -78.
So, to factor this we need 2 integers whose product is -78 and whose sum is -1.
There are no such integers so we can't solve this by factoring.
These triangles are congruent by the triangle congruence postulate ___
Answer:
6.8Equils5 so the awnser is sas
The endpoints of AB are A (-8, 5) and B (0,7). Find the coordinates of the midpoint M.
The coordinates of the midpoint M are
The coordinates of the midpoint M are (-4,6)
Midpoint is the middle point of line segment. Measuring the distance between the two end points and divide the result by 2 this distance is known as midpoint of that line. Adding two end point of x and y and divide the sum by 2 we get coordinates of midpoint.
We can calculate the coordinates of midpoint by Midpoint formula
[tex]=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex],
Endpoints of AB are A(-8,5) and B(0,7)
[tex](x_1,y_1)=(-8,5) and (y_1,y_2)=(0,7)[/tex]
Put the value of x and y in the above formula we get
[tex]=(\frac{-8+0}{2}),(\frac{5+7}{2}\\ =(\frac{-8}{2}),(\frac{12}{2})\\ =(-4,6)[/tex]
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⚠️ARE YOU A PRO AT ALGEBRA⁉️❓? I NEED HELP. BE SURE TO EXPLAIN WHAT METHOD YOU USED (GRAPHING, ALGEBRAIC, NUMERIC) TO DETERMINE WHETHER THEY ARE INVERSE OR NOT AND EXPLAIN HOW YOU KNOW YOU ARE CORRECT ⚠️
I used the Algebraic Method to solve the questions
The First functions are inverses but the Second set aren't
Construct three different isosceles right triangles. Explain your method. then verify your constructions using measurement and mathematics.
A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle.
What is an Isosceles Right Triangle?A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle. A right triangle that is also isosceles is known as an isosceles triangle. It therefore has two sides that are identical and one right angle.
A right triangle with two equal-length legs is called an isosceles right triangle. The corresponding angles would also be congruent because the lengths of the two legs of the right triangle are equal. As a result, the two acute angles and two legs of an isosceles right triangle are congruent.
How to construct three different triangles?Constructing triangles will consist of the development of various triangles the use of a protractor, a compass and a ruler.
How constructions will use measurement and mathematics?Construction of triangles is straightforward while the measurements are given to us primarily based totally on extraordinary homes which include SSS, SAS and ASA.
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Sandi and Felipe are participating in a Walk for Life to raise money for charity. Sandi will raise $30, plus $2.50 for each mile she walks. Felipe will raise $20, plus $5 for each mile he walks. The total amount that each will raise can be calculated using the following expressions, where n stands for the number of miles walked: Sandi: 30 + 2.5n Felipe: 20 + 5n After how many miles will Sandi and Felipe have raised the same amount of money?
Using linear equations, Sandi and Felipe have raised the same amount of money after 4 miles.
We can calculate using linear equations
Formulate based on the criteria stated: 30 +2.5 x x = 20 + 5 × x
Unknown terms should be moved to the left side of the equation:
2.5x-5x= 20-30
combining similar terms
-2.5x = 20 - 30
Determine the total or difference: 2.5x = -10
Subtract the coefficient of the variable from both sides of the equation: = -10 ÷ (−2.5)
Take the parenthesis out: 10 ÷ 2.5 =
Determine the quotient or product:
x = 4
find the outcome: = 4
Response: x = 4.
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Evaluate each expression for x=0 . (x-4)+12
After evaluating the expression for x=0, the equation (x-4)+12 = 8
⇒ ((0)-4)+12
⇒ -4 + 12
⇒ 8
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Joan drives 333.5 miles before she has to buy gas. Her car gets 29 miles per gallon.
How many gallons of gas did the car start out with?
Answer:
11.5 gallons
Step-by-step explanation:
Let the amount of gas be x gallons.
The product of gallons and MPG gives us the number of miles, show this as equation and solve for x:
miles/gallons * gallons = miles29x = 333.5x = 333.5/29x = 11.5PLEASE HELP! i just need someone to check my answer
3y=84 y=?
does it equal 28?
Answer:
yes, because 3 X 28 is 84
Step-by-step explanation:
Solve.
please and thank you!
Answer:
Step-by-step explanation:
2(x+3)/3 + 3(x-6)/2=1-x
2x+6/3 + 3x-18/2=1-x
2(2x+6)/3 + 3(3x-18)=6-6x
4x+12+9x-54=6-6x
13x-49=6-6x
13x+6x=6+42
19x/19=48/19
x=49/19
Cole is taking a 170-mile trip by car. If he drives for 2 hours with an average speed of 60 miles per hour, how many miles will he still need to drive to complete his trip?
A: 50
B: 110
C: 120
D: 340
Cola need 50 miles to drive to complete his trip.
Option A is true.
What is Distance?
The total movement of an object without any regard to direction is called distance.
Given that;
Cole is taking a 170-mile trip by car.
He drive for 2 hours with an average speed of 60 miles per hour.
Now, Distance cover in 2 hours with speed 60 miles per hour is calculated as;
Since, Distance = Speed x time
Hence, Distance = 60 x 2 = 120 miles.
So, Remaining speed to complete his trip = 170 - 120 = 50 miles.
Hence, Cola need 50 miles to drive to complete his trip.
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The continental U.S is about 200 miles wider than Australia.
What number should replace the question mark on the U.S map?
A sequence is defined by a₁ = 4, an = a(n-1) + 4. What is the 6th term of the
sequence?
Hence , the 6th term of the sequence is 24
Arithmetic Progression (AP) could be a sequence of numbers so as, during which the distinction between any 2 consecutive numbers could be a constant worth. it's conjointly known as Arithmetic Sequence. as an example, the series of natural numbers: one, 2, 3, 4, 5, 6,… is associate degree patterned advance, that includes a common distinction between 2 serial terms (say one and 2) adequate to one (2 -1).
It is given that first term is 4 and nth term is a(n) = a(n-1) + 4 ......(1)
Putting n = 6 in equation (2) , we get sixth term
a(6) = 4(6-1) +4
a(6) = 4(5) + 4
a(6) = 20 + 4
a(6) = 24
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What is the domain and use properties of continuity to support your answer
The domain of the function is x < 2 and it is discontinuous at x = 2
What is the domain of a function?The domain of a function is the range of input values to the function.
How to find the domain of the given function?Given that the above function f(x) = √[(x² + 1)/(2 - x)]
The domain of the function is the range of values of x that make the denominator greater than zero
So, the domain is √(2 - x) ≥ 0
2 - x ≥ 0
2 ≥ x
x ≤ 2
So, the function is valid for x < 2 and discontinuous at x = 2 since at x = 2, √(2 - x) = √(2 - 2) = 0
So, we see that the function is valid for x < 2 and discontinuous at x = 2
So, the domain of the function is x < 2 and it is discontinuous at x = 2
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A school allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £48 each and are on offer for
1/6
off.
A train ticket for the day will cost £15 each.
If 2 teachers and the maximum number of students attend, how many students go on the trip
Answer: 38 pounds
Step-by-step explanation: School allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off
therefore 4/5*35 = 28 for the tickets
:
A train ticket for the day will cost £15 each.
therefore total cost for each: 28 + 15 = 43 pounds each
:
If 2 teachers and the maximum number of students attend, how much money will the school have left over?
:
let s = no. of students
43(s+2) =< 1500
43s + 86 =< 1500
43s =< 1500 - 86
43s =< 1414
s =< 1414/43
s =< 32.88, 32 students max
:
find how much left over. plus 2 teachers = 34 people
1500 - 43(34) =
1500 - 1462 = 38 pounds left over
Solve each system by substitution. Check your answers.
t = 2r + 3 , 5r - 4t = 6
By substitution, the solution of the system of equations, t = 2r + 3 and 5r - 4t = 6, is (r , t) = (-6 , -9).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in r and t,
t = 2r + 3 (equation 1)
5r - 4t = 6 (equation 2)
Since the first equation is already expressed in variable t in terms of r, substitute the value of t to the second equation.
5r - 4t = 6 (equation 2)
5r -4(2r + 3) =6
5r - 8r - 12 = 6
Combining all terms containing the variable r on one side and the constants on the other side of the equality, and solving for r.
5r - 8r - 12 = 6
5r - 8r = 6 + 12
-3r = 18
r = -6
Substitute the value of r in the first equation and solve for t.
t = 2r + 3 (equation 1)
t = 2(-6) + 3
t = -12 + 3
t = -9
Hence, the solution of the given system of equations is (r , t) = (-6 , -9).
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NEED HELP ASAP! will rate 5 stars!!
Answer:
The first one is the answer
Step-by-step explanation:
Write the equation of the line through each point. Use slope-intercept form. (1,-1) ; parallel to y = (2/{5)x - 3
The equation of the line in slope-intercept form passing through the point (1 , -1) and parallel to y = (2/5)x - 3 is y = (2/5)x - 7/5.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is parallel to y = (2/5)x - 3, then their slopes are equal.
y = (2/5)x - 3 : m = 2/5
m = 2/5
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
-1 = 2/5(1) + b
b = -7/5
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (2/5)x - 7/5
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Identify the hypothesis and conclusion of conditional statement.
If you have a driver's license, then you are at least 16 years old.
The hypothesis is the phrase following the word if = " The hypothesis is: You have a driver's license."
The conclusion is the phrase following the word then = " The conclusion is: You are at least 16 years old."
What is hypothesis?A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.
Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).
The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.
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A surveyor standing on a horizontal plain can see a volcano in the distance. The angle of elevation
to the top of the volcano is 23°. If the surveyor moves 750 m closer, the angle of elevation is
now 37°. Determine the height of the volcano above the plain.
Height of the volcano = 729
The elevation angle to the peak of the volcano is 23 degrees.
The surveyor goes 750 feet closer to the volcano, and the angle of elevation now equals 37 degrees.
It forms an ABC triangle.
Point A = the volcano's summit
Point B is the volcano's lowest point.
Point C = height of 23 degrees to the volcano
Point D = going 750 towards the volcano and establishing a 37-degree elevation angle
BD = ?
DC = 750
Tan 23 degrees AB/BC
Tan 23 degrees AB = BC
Tan 37 degrees AB/BD
Tan 37 degrees = AB
23 degrees BC Tan 37 degrees BD Tan
(BD +750)
BD (.7536-.4245) = 318.356
BD = 967.35
Height of the volcano = 729
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Joanna went to the farmers market to buy some apples and oranges. She bought 8 oranges and some apples. The cost per orange was $1.79 and the cost per pound of apples was $1.49. Joanna spent a total of $23.26 on apples and oranges at the farmers market.
Let p represent the number of pounds of apples Joanna bought.
Create the equation that symbolizes this situation, and then answer the question below.
$
p + $
= $
Did Joanna buy a total of 5 pounds of apples at the farmers market?
The number of apples that were bought by Joanna is 6 pounds.
How to calculate the value?Let p = the number of pounds of apples Joanna bought.
Let o = oranges
Therefore, the equation will be:
1.49p + 8o = 23.26
1.49p + 1.79 × 8 = 23.26
1.49p + 14.32 = 23.26
1.49p = 23.26 - 14.32
1.49p = 8.94
p = 8.94/1.49
p = 6
No. Joanna didn't buy a total of 5 pounds of apples at the farmers market.
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Fran's account balance is -$22.91, and Zach's account balance is -$26.45. Which of the following is true?
A.
Fran's account balance = Zach's account balance
B.
Fran's account balance > Zach's account balance
C.
Fran's account balance < Zach's account balance
Answer:
B.
Fran's account balance > Zach's account balance
Step-by-step explanation:
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=-9 x-2 for x=
f (7) = -65 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= -9 x-2
Put x = 7 ⇒ - 9 * 7 - 2
⇒ -63 - 2
⇒ -65
Therefore f (7) = -65
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The complete question is -
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=-9 x-2 for x= 7
