A linear equation or function is always a representation of a straight line in the coordinate plane. The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
The equation of a straight line is given by, y = mx + c
Where m is the slope while c is the y-intercept.
The slope of line passing by two points (x₁, y₁) and (x₂, y₂)
Slope(m) = (y₂ - y₁)/(x₂ - x₁)
The slope of the line that passes through (4, 5) and (−3, −1) will be,
m = (-1 -5)/(-3-4)
m = -6/-7 = 6/7
So equation converts as, y = (6/7)x + c
Substitute, (4,5)
5 = (6/7)4 + c
c = 9/7
So, y = (6/7)x + 9/7 will be the equation.
Hence "The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7".
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Is y=8.5x a proportional relationship? If so, why? If not, why?
Convert 232°F to Celsius.
55°C
95°C
100°C
110°C
Answer:
the answer is 100"C
Step-by-step explanation:
4(5n+7)-3n=3(4n-9) Solve. Its supposed to equal -11
I have no idea how it got to -11 mine is always -6.5...
HELP??
What is the value of r? 35(r−7)=1 Enter your answer in the box.
The undefined terms line and plane are needed to precisely define which mathematical term?
line segment
perpendicular lines
parallel lines
ray
The correct answer is:
parallel lines
Explanation:
Parallel lines are two lines in a plane that never intersect. This means the definition uses the undefined terms "line" and "plane."
The undefined terms line and plane are needed to precisely define which mathematical term will be parallel lines so option (C) will be correct.
What are a line and plane?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
A plane is a surface that is straight in nature a plane has a certain area but in most cases.
We know that parallel line are those lines which not intersect and lies on a plane.
Hence there are two things that are needed first is a line and the second is a plane the plane should be single for both lines not different.
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Karissa plays on a basketball team. each day after school she goes to a basketball practice that last for h hours. on friday karissa practices for and extra half-hour at home.
write an expression for the number of hours karissa practices basketball in a 5-day week of school?
A 64-cm strip is cut into eight equal pieces . What is the length in mm of one piece
PLEASE HELP ME you measured 6 cups of water and 5 cups of lemon juice to make how many in total quarts of lemonade
Total cups of lemonade:
6 cups + 5 cups = 11 cups
Total quarts and cups of lemonade:
11 cups ÷ 4 cups = 2 quarts 3 cups
The rectangular backboard of a basketball court needs to be assembled. Its area is given as 18,900 cm2 and the width as 1.8 m.
What is the backboard’s length in metres?
Answer:
1.05 m
Step-by-step explanation:
The area of the rectangular backboard is A = 18900 cm²
And the width is w = 1.8 m = 1.8 ×100 = 180 cm
The area of the rectangle is given by
[tex]A=l\cdot w[/tex]
Substituting the known values
[tex]18900=l\cdot 180\\\\l=\frac{18900}{180}\\\\l=105\text{ cm}[/tex]
Thus, the length of the backboard's is 105 cm = 1.05 m
A movie made $297.2 million in 22 weeks. How much did the movie make on average each week?
The movie made about $13.5 million per week.
I hope this helps!
30% of what number is 21
Nina received two emails on Monday every day that she received one more than twice as mini as the day before how many emails did she receive on Thursday
Keith buys a bag of dog food. The bag contains 16 1/2 cups of food. If his dog eats 1 3/8 cups a day, how long will the bag last?
The number of days required to feed dog food will be 12.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Keith buys a bag of dog food. The bag contains 16¹/₂ cups of food. If his dog eats 1³/₈ cups a day,
The time will be calculated as:-
T = ( 16¹/₂ ÷ 1³/₈ )
T = ( 16.5 ÷ 1.375 )
T = 12 days
Therefore, the number of days required to feed dog food will be 12.
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Joy ate 1/4 of a pizza. If she divides the rest of the pizza into pieces equal to 1/8 pizza for her family how many pieces will her family get
Answer:
her family will have 6 slices of pizza
Step-by-step explanation:
1/4 is the same as 2/8 so all the slices are worth 1/8 so there are 6 eighths left
What is the part of a line with two endpoints?
WILL MARK BRANNLIEST
The GCF of 14 and a number is 7. Which of the following could be the number?
28
42
49
56
Answer:
Factors of 28 = 1,2,4,7,14,28
Factors of 42= 1, 2, 3, 6, 7, 14, 21, 42
Factors of 49 =1, 7, 49
factors of 56 = 1, 2, 4, 7, 8,14, 28, 56
Factors of 14 = 1,2,7,14
⇒49 is the number
Step-by-step explanation:
What is the algebraic expression for: four less than three times the number of egg orders and six more than two times the number of waffle orders
Show me a place value chart
Use compatible numbers to find two estimates
A ski lift begins at ground level 0.75 miles from the base of a mountain whose face a 50° angle of elevation. The ski lift ascends in a straight line at an angle of 20°. Draw a diagram to illustrate this situation and find the length of the ski lift from the beginning of the ski lift to the top of the mountain, to the nearest hundreth
The length of the ski lift is approximately 1.15 miles.
We can use the formula of sum of all angle of triangles which is equal to 180°.
∠C = 180 - 50
= 130
By using law of sines
[tex]\frac{a}{sin A} = \frac{c}{sin C} \\\frac{0.75}{sin 30} = \frac{c}{sin 130} \\\\\\\frac{0.75 \times 0.766}{0.5}[/tex]
c= 1.149 mile
c = 1.15 mile (nearest hundred)
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which numbers below are even? 6, 12, 15, 24, 30
Veronica is shopping for school clothes. She wants to buy pants and shirts. The cost of her clothes can be found using the expression 30x + 25y where x is the number of pants and y is the number of shirts. She will also have to pay 8% tax. If Veronica buys two pants and eight shirts, what expression could be used to determine the total cost of the bill including 8% tax?
Final answer:
To find the total cost of Veronica's school clothes including 8% tax, first calculate the cost before tax with her specific quantities of pants and shirts, and then add the tax. The final expression shows a total cost of $280.8.
Explanation:
Veronica is shopping for school clothes, and the cost of her clothes can be found using the expression 30x + 25y, where x is the number of pants and y is the number of shirts. She will also have to pay 8% tax. If Veronica buys two pants and eight shirts, the expression to determine the total cost of the bill including 8% tax would be:
First, substitute x = 2 (pants) and y = 8 (shirts) into the expression to find the total before tax: 30(2) + 25(8).Calculate the cost before tax: 60 + 200 = 260.Calculate the total with 8% tax: 260 + (0.08 × 260).The final expression to determine the total bill is: 260 + 20.8 = 280.8.Simplify: Negative two and one-third minus negative ten and one-sixth
a Negative twelve and one-half
b Twelve and one-half
c Seven and five-sixths
d Negative seven and five-sixths
Determine the answer to (−3) + (−5) and explain the steps using a number line. please give example and how you did it
Use absolute value to express the distance between −12 and −15 on the number line.
a |−12 − (−15)| = −27
b |−12 − (−15)| = −3
c |−12 − (−15)| = 3
d |−12 − (−15)| = 27
please help im failing and its stressing
Answer:
[tex]1.\rightarrow -2 \frac{1}{3}-(-10) \frac{1}{6}\\\\\rightarrow \frac{-7}{3} -\frac{-61}{6}\\\\\rightarrow \frac{-14+61}{6}\\\\\rightarrow \frac{47}{6}\\\\\rightarrow 7\frac{5}{6}[/tex]
Option C→Seven and five-sixths
2.
(-3) +(-5)
Mark -3 and -5 on the number line.Move 5 units left of -3 to reach at -8.That is required sum.
3.
Distance between −12 and −15 on the number line is given by
|-12 -(-15}| or |-15 -(-12)|
=|-12+15| or |-15+12|
=|3| or |-3|
=3 units
Option C
|−12 − (−15)| = 3
Answer:
Its A its right
Step-by-step explanation:
not C
Since 43 is a 2 digit odd number is it a composite and why
How do I solve 24 - (7+5) /. 6+8
I suck a writing proofs in geometry.... please someone explain it to me, i cant seem to reconize what's going on. I need major help in properties of congruent proofs.
In earlier mathematics courses, you have learned concepts like the commutative or associative properties. These concepts help you solve many types of mathematics problems. There are a few properties relating to congruence that will help you solve geometry problems as well. These are especially useful in two-column proofs, which you will learn later in this lesson!
The Reflexive Property of Congruence
The reflexive property of congruence states that any shape is congruent to itself. This may seem obvious, but in a geometric proof, you need to identify every possibility to help you solve a problem. If two triangles share a line segment, you can prove congruence by the reflexive property.
The number line below represents which combined inequality?
number line with a closed circle on negative 6 and 5 with shading in between
x greater than or equal to −6 or x less than or equal to 5
x greater than or equal to −6 and x less than or equal to 5
x less than or equal to −6 and x greater than or equal to 5
x less than or equal to −6 or x greater than or equal to 5
we know that
number line with a closed circle on negative [tex]6[/tex] and [tex]5[/tex] with shading in between represent the combined inequality
[tex]x\geq-6\\x\leq5[/tex]
the solution is the closed interval---------->[tex][-6,5][/tex]
therefore
the answer is the option
x greater than or equal to [tex]-6[/tex] and x less than or equal to [tex]5[/tex]
see the attached figure to better understand the problem
Neptunes average distance from the sun is 4.503x10^9 km. Mercurys average distance from the sun is 5.791x10^7 km. About how many times farther from the sun is Neptune than mercury? Write your answer in scientific notation
A store sells grapes for $1.99 per pound. You buy 2.34 lbs. of grapes. How much do you pay? Please help!
What is 12x3 – 9x2 – 4x + 3 in factored form?
The factors of the given polynomial 12x^3-9x^2-4x+3 are
(4x-3) (3x^2-1).
Given: Polynomial 12x^3-9x^2-4x+3
We have factorized the given polynomial.
What is the meaning of factors?The factor means a number that can be multiplied or divided to produce a given number.
Consider the given polynomial 12x^3-9x^2-4x+3.
We will factorize using a grouping of terms,
Taking 3x^2 common from the first two terms and -1 common from the last two terms, we have,
3x^2(4x-3)-1(4x-3)
Now, again taking (4x-3) common, we have,
(4x-3)(3x^2-1)
Thus, The factors of the given polynomial are (4x-3)(3x^2-1).
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The factored form of 12x3 - 9x2 - 4x + 3 is (3x2 - 1)(4x - 3).
Explanation:The expression 12x3 - 9x2 - 4x + 3 can be factored as follows:
First, identify any common factors among the terms. In this case, the greatest common factor (GCF) is 1.
Next, group the terms:
12x3 - 9x2 - 4x + 3 = (12x3 - 9x2) + (-4x + 3)
Factor out the GCF from each group:
12x3 - 9x2 = 3x2(4x - 3)
-4x + 3 = -1(4x - 3)
Combine the factored terms:
(3x2 - 1)(4x - 3)
Therefore, the factored form of 12x3 - 9x2 - 4x + 3 is (3x2 - 1)(4x - 3).