Considering the definition of perpendicular line, the correct option is option C): the line passing through (0,-9) and (5, -8) is perpendicular to the line 10x + 2y = 2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Perpendicular line in this caseIn this case, the line is 10x + 2y=2. Expressed in the form y = mx + b, you get:
2y=2 - 10x
y= (-10x +2)÷ 2
y= -10/2x +2/2
y= -5x +1
The line has a slope of -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:
-5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-5)
slope perpendicular line= 1/5
The line through two points must have a slope equal to 1/5. So you calculate the slope of each line that passes through two points as follows:
(x₁, y₁)= (-2, -7) and (x₂, y₂)= (1, 8): m= (8 - (-7))÷(1 - (-2)) → m= (8+7)÷ (1+3) → m= 15÷4= 15/4(x₁, y₁)= (-5, 5) and (x₂, y₂)= (0, 4): m= (4- 5)÷(0 - (-5)) → m= (-1)÷ (0 + 5) → m= -1÷5= -1/5(x₁, y₁)= (0, -9) and (x₂, y₂)= (5, -8): m= (-8 - (-9))÷(5 - 0) → m= (-8+9)÷ (5) → m= 1÷5= 1/5(x₁, y₁)= (-4, 12) and (x₂, y₂)= (-2, 2): m= (2 - 12)÷(-2 - (-4)) → m= (-10)÷ (-2+4) → m= -10÷2= -5(x₁, y₁)= (-2, 11) and (x₂, y₂)= (1, -4): m= (-4 -11)÷(1 - (-2)) → m= (-15)÷ (1+2) → m= -15÷3= -5Since the perpendicular line must have a slope equal to 1/5, the line passing through (0,-9) and (5, -8) is the correct line.
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Write the equation of the arithmetic sequence “24, 34, 44, 54...” and then Find the 100th term.
show your work.
Answer:
1014
Step-by-step explanation:
Remember this formula to find certain terms in arithmetic sequences:
[tex]t_{n} =t_{1} +(n-1)d[/tex]
n = term number
[tex]t_{1}[/tex] = term #1
d = common difference
Sequence = 24, 34, 44, 54...
We are looking for term #100
So we do
[tex]t_{100} = 24 + (100-1)10\\t_{100} = 24 + 1000 - 10\\t_{100} = 24 + 990\\t_{100} = 1014[/tex]
Please help me! I will mark brainliest if correct! (Question is in the image shown)
2nd one the combining with y one
A jar contains 0.25 liter of apple juice and 0.30 liter of grape juice. Melissa poured 0.75 liter of pineapple juice into the jar. She then drank 0.20 liter of the mixture. Part A: Write an expression to represent the total amount of juice left in the jar. (5 points) Part B: Simplify the expression and identify which property is used in each step. (5 points)
Answer:
Part A: Total amount of juice left = 0.25 + 0.30 + 0.75 - 0.20
A larger kind of bacteria is about 0.00039 in. long. Write this length using
scientific notation
Answer:
3.9X10^-4
Step-by-step explanation:
The value is increasing so your exponent increases
decrease £7720 by 20%
Answer: Percentage decrease = 20% × 7,720
New value = 7,720 - Percentage decreaseNew value =
7,720 - Percentage decrease =
7,720 - (20% × 7,720) =
7,720 - 20% × 7,720 =
(1 - 20%) × 7,720 =
(100% - 20%) × 7,720 =
80% × 7,720 =
80 ÷ 100 × 7,720 =
80 × 7,720 ÷ 100 =
617,600 ÷ 100 =
6,176
New value - 7,720 =
6,176 - 7,720 =
- 1,544
Step-by-step explanation:
For a fundraiser, a school club is selling raffle tickets for $2 each and healthy snacks for $1.50 each. What is the total cost of y raffle tickets and x healthy snacks?
Answer:
1.5x+2y=total cost
Step-by-step explanation:
am i correct ?? for a brainly and pls explain
Answer:
Yes.
Step-by-step explanation:
Because
6*4 =24
and 4*0 = 0,
24+0=24
have a nice day!!!
wus 9 + 10 equal please help wus 9 = 10
Answer:
19
Step-by-step explanation:
it is 19
yes
wait no its 100000000000
I big brain UwU
Answer:
Step-by-step explanation:its 21
Find the value of x that makes lines u and y parallel.
Answer:
x = 7
Step-by-step explanation:
If u // v, then
19x - 3 = 130 {Corresponding angles are congruent}
19x = 130 + 3
19x = 133
x = 133/19
x = 7
How many video games were sold in the year 2001
Answer:
265
Step-by-step explanation:
you only need to do is simplify the expression.
Complete the equation to calculate the cost of the portable speaker, including sales tax.
$53
=
% of $50
Answer: The answer to this math question about completing the equation in order to calculate the cost of the portable speaker, including the sales tax is $94.34.
Step-by-step explanation: I don't have any step-by-step explanation, I'm sorry about that, but anyway, I hope that my given short answer is very helpful to your own math question about completing the equation in order to calculate the cost of the portable speaker, including the sales tax, please mark me as Brainliest, take care, always be safe, and have a great rest of the day! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
independent practice write linear equations lesson 6
Answer:
1)y=2x+7
2) unsure what the question is due to blur
3)y=3/4x-2
4)y=-2x
Answer:
Step-by-step explanation:
1) (1,9) ; slope = 2
Point slope form:
y - y₁ = m(x - x₁)
y - 9 = 2(x - 1)
Slope intercept form:
y - 9 = 2x - 2
y = 2x - 2 + 9
y = 2x + 7
3) (-4 , -5) ; slope = 3/5
Point slope form:
y - y₁ = m(x - x₁)
[tex]y - [-5] = \dfrac{3}{4}(x - [-4])\\\\\\y + 5 = \dfrac{3}{4}(x + 4)[/tex]
Slope intercept form:
[tex]y + 5 = \dfrac{3}{4}x + 4*\dfrac{3}{4}\\\\y + 5 =\dfrac{3}{4}x + 3\\\\y = \dfrac{3}{4}x +3 -5 \\\\\\y = \dfrac{3}{4}x - 2[/tex]
-2z+3-z=□-4z+2
please give me the answer
Step-by-step explanation:
[tex]\displaystyle \rm -2z+3-z=-4z+2 \\\\ -3z+3=-4z+2 \\\\ 4z-3z=-3+2 \\\\ \underline{z=-1 \ \ \ \ } \\\\[/tex]
[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]
Given to solve: -2z+3-z = -4z+2
⇛ -3z + 3 = -4z + 2
⇛ -3z + 4z = 2 - 3
⇛ z = -1
Required value of z is -1. The steps we followed are: We shifted z to a single side and other numbers to other side. Then we equated to get the result.
c.
The family purchased refreshments and spent a total of $18.50. If the total amount of money spent
on tickets and refreshments was $94.50, use an equation to find the cost of one regular admission
ticket.
How would you write the equation?
(94.50 - 18.50) ÷ f = a
f=family members
a=answer
I don't know how many family members there are, but you would just replace f with the amount.
(-9,6) and (-3,2) help pls
(-9,6) and (-3,2) help pls
Answer : -12.8
(Please Help) (50 Points) Write the equation for the transformations of the graph of y = x^2
Use the form: y = a (x-h)^2 +k
Translated 2 units left and 7 units down.
A is the scale or vertical stretch
H is what makes it move right or left.
K is what makes it move up or down.
a = 1
h = -2
k = -7
y = (1) (x-(-2))² + (-7)
y= (x + 2)² -7
(Also, you will learn b in the equation. The equation would be a(b(x-h))² + k. B would be about horizontal compression.)
four spheres of radius 6cm fit into a cylinder with a height of 12cm. calculate the volume inside the cylinder that is empty. leave your answer in terms of pi.
Answer:
V = 432pi cm^3
Step-by-step explanation:
Pi x r^2 x h
Pi x 6^2 x 12 cm = 432 pi cm^3
Determine if the leading coefficient of the following function is positive or negative and whether the function has a minimum or maximum vertex point.
Answer:
The leading coefficient of the function shown is negative and the function shown has a maximum vertex point.
Step-by-step explanation:
The leading coefficient is the term with the highest degree in a polynomial.
For example in 4x² + 3x + 1 the leading coefficient would be 4x² as 4x² is the term with the highest degree.
The leading coefficient tells us whether the equation, when graphed, will rise or fall.
If the leading coefficient is negative then the equation will fall when graphed, in contrast if the leading coefficient is positive the equation will rise when graphed.
Looking at the graph, it appears that the equation is falling, meaning that the leading coefficient must be negative.
If the equation falls then it has a maximum point, if it rises then it has a minimum point.
Because the equation shown falls it will have a maximum point.
PLS HELPPP
FIND X
I will mark braniliest
Answer:
x = 11
Step-by-step explanation:
∠ EAB = ∠ AED = 4x ( alternate angles )
∠ AEB and ∠ GEB are adjacent angles on a straight line and sum to 180° , so
∠ AEB + 125° = 180° ( subtract 125° from both sides )
∠ AEB = 55°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ EBC is an exterior angle of the triangle , then
∠ EBC = ∠ AEB + ∠EAB , that is
9x = 55 + 4x ( subtract 4x from both sides )
5x = 55 ( divide both sides by 5 )
x = 11
50PTS PLZ HELP ME I'M STUCK
Answer:
m∠O = 80°
Step-by-step explanation:
m∠O = 4x - 20
m∠Q = 3x + 5
m∠O and m∠Q are congruent
4x - 20 = 3x + 5
Solve for x = 25
Plug back in
m∠O = 4(25) - 20
m∠O = 100 - 20
m∠O = 80°
a reasonable estimate for 621 times 29 is
Answer:
18,009
Step-by-step explanation:
18000 would be a reasonable estimate
Which equation demonstrates the additive identity property?
0 (7+4i)+(7-4i) = 14
O (7+4i)+ 1 = 7+4i
(7+4)(1) = 7+4)
O (7+4i)+(-7-4i)= 0
Answer:
A
Step-by-step explanation:
The Explication 0 (7+4i)+(7-4i) = 14
The correct equation which demonstrates the additive identity property is,
⇒ (7 + 4i) + 0 = 7 + 4i
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Now, If we add a real number to zero or add zero to a real number, then we get the same real number back.
Hence, The number zero is known as the identity element, or the additive identity.
For example: a + 0 = a
Hence, we can see that;
⇒ (7 + 4i) + 0 = 7 + 4i
Since, 0 is the additive identity here.
Thus, The correct equation which demonstrates the additive identity property is,
⇒ (7 + 4i) + 0 = 7 + 4i
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Round 0.41275 to the nearest thousandth
Answer:
0.41, 2 is lower than 5 so we round down
Answer:
0.41300
Step-by-step explanation:
0.41275.
0.4: tenths place. 0.01: hundredths place. ...
Now look at the next decimal place, which is 0.0007: the ten thousandths place . This number determines whether the thousandths place will be rounded up or down. ...
Therefore, 0.41275 rounded to the nearest thousandth is:
A company has 24 employees. Each employee volunteers to bring 1 item to the local school fundraiser.
One-fourth of the employees bring pencils.
One-third of the employees bring paper.
The rest of the employees bring notebooks.
How many employees bring notebooks?
Answer:
6 employees bring pencils
8 employees brings paper
6+8=14
Company:24 employees- 14 employees who brong paper and pencils.=10 so 10 employees brings notebooks.
Step-by-step explanation:
Answer:
6 employees bring pencils
8 employees bring paper
10 employees bring notebooks
Step-by-step explanation:
1/4= 6
1/3= 8
the rest = 10
Proportions
Rectangular Prism
I'm decreasing the rectangular prism
H= 10
W=13.7
L: 16.6
scale: 1/4
ratios: 2:3
Charise's expenses for the month of July are outlined below.
Car insurance: $120.54
Cell phone bill: $55.99
Groceries: $65.00
Her monthly income is $1,050.00. What percentage of her income are expenses?
Solve by drawing an area model and then use the standard algorithm: 432 x 620
You are recently promoted as the chief traffic management officer of a major city in the country. Based on recent data, you learned that one of the leading causes of road accidents is over speeding.
In your desire to minimize road accidents, you went out to observe how traffic management rules are implemented on the streets. Your attention was caught by a fast - moving car that seemed to be breaking the speed limit of 100 kilometers per hour(km/hr.), and so you followed it along the highway. After a short time, the driver of the car noticed you and started to slow down. Eventually, he stopped on the side of the road.
Supposed the speed of the car had been noted during this time and is modeled by the quadratic equation y = 3x² + 17x - 20, where y represents the speed of the car in km/hr. and x represents the number of minutes after you started following the car. How long did it take for the car to be under surveillance before it could finally stop on the side of the road? Did the driver of the car really break the speed limit of 100 km/hr.? Explain. The result of your observation will be presented to the students in your section and will be graded by your teacher.
Step-by-step explanation:
3(100)2 + 17(100) - 203(10000) + 1700 - 20
30000 + 1700 - 20
31680
The size of an insect population doubles every week. If there are 25 insects initially present, how many insects will there be in eight weeks?
Answer:
tence there will be 6,00 insects abter 8 weeks.
Step-by-step explanation:
The table below represents a linear function. Identify the rate of change of the function.
(0,4) (4,-3) (8,-10) (12,-17)
Step-by-step explanation:
the rate of change is the slope of the line y/x. it is always the factor of x in the equation.
it indicates how many units y changes, when x changes a certain amount of units when going from one point to another.
we only need to look at 2 points.
to go from (0, 4) to (4, -3)
x changes by +4 (from 0 to 4),
y changes by -7 (from 4 to -3).
so the rate of change is -7/3
