Answer:
2,1
Step-by-step explanation:
y=-3x+7
y=-3(2)+7
y=-6+7
y=1
so (2,1)
One week a company filled 546 boxes with widgets each box held 38 widgets how many widgets did the company pack in boxes that week
Answer:
20748
Step-by-step explanation:
546 times 38
When 90 is added to a number it equals 30 less than 3 times the number.
Answer:
90+x=30-3[x]
Step-by-step explanation:
collect like terms
x+3x=30-90
4x=-260
divide both sides by 4
x=-60/4
x=-4*3*5/4
x=-[3*5/1]
x=-[3*5]
x=-15
Answer:
The number is 60.
Step-by-step explanation:
Let x = unknown number.
Now we translate the sentence into an equation, one piece at a time.
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90 = 3x - 30
We now solve the equation for x.
Subtract 3x from both sides.
-2x + 90 = -30
Subtract 90 from both sides.
-2x = -120
Divide both sides by -2.
x = 60
The number is 60.
Check:
When 90 is added to a number it equals 30 less than 3 times the number.
Add 90 to 60:
90 + 60 = 150
We get 150.
When 90 is added to a number it equals 30 less than 3 times the number.
Now multiply 60 by 3 and subtract 30.
3(60) - 30 = 180 - 30 = 150
We also get 150.
That means our answer of 60 is correct.
Answer: 60
Is 9/10 larger than 13/14
Answer:
13/14 is greater
Step-by-step explanation:
Find the lcm for both:
9 x 7 = 63
10 x 7 70
13 x 5 = 65
14 x 5 70
so therefore 13/14 is greater since it has a greater value when finding the lcm
Find the range of 4/3-t
Answer:
4/3 is 1.3333333333,so the range of it is that
Which statements accurately describe the function f(x) = 3(16) Superscript three-fourths x? Select three options.
The initial value is 3.
The domain is x > 0.
The range is y >0.
The simplified base is 12.
The simplified base is 8.
Answer:
The initial value of the function is 3.
The range of the function is y > 0.
The simplified base value of the function is 8.
Step-by-step explanation:
The given function is [tex]f(x) = 3(16)^{\frac{3}{4}x }[/tex]
Therefore, the simplified function will be [tex]f(x) = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}[/tex] ........ (1)
Now, at x = 0, f(x) = 3.
Hence, the initial value of the function is 3. (Answer)
The value of x in the equation (1) can be any real value but for any value of x, the f(x) value will be greater than 0.
Hence, y > 0 that is the range that the function has. (Answer)
Again, from equation (1) we get the simplified base value of the function is 8. (Answer)
Answer:
A, C, E
Step-by-step explanation:
Egde 2020
please help thanks ❗
Answer:
The Two Column Proof is given below.
Step-by-step explanation:
Given:
[tex]\overline{MP} \cong \overline{MN}[/tex]
[tex]\overline{PO} \cong \overline{NO}[/tex]
To Prove:
∠ P ≅ ∠ N
Proof:
In Δ MPO and Δ MNO
STATEMENT REASONS
1. MP ≅ MN 1. Given
2. PO ≅ NO 2. Given
3. MO ≅ MO 3. Reflexive property
4. ΔMPO ≅ ΔMNO 4. Side-Side-Side congruence test}
5. ∠MPO ≅∠MNO 5. Corresponding parts of congruent Triangles
i.e ∠ P ≅ ∠ N ..................Proved
If triangle pqr is and equilateral triangle, pq = 18x+1, qr = 24x-17, and pr = 15x+10, find x and the measure of each side.
Answer:
The value of x is 3 ,
The measure of each side is 55 units .
Step-by-step explanation:
Given as :
The sides of the equilateral Triangle are pq , qr , pr
The measure of side pq = 18 x + 1
The measure of side qr = 24 x - 17
The measure of side pr = 15 x + 10
∵ The triangle is equilateral then all sides are equal
i.e pq = qr = pr
So, 18 x + 1 = 24 x - 17
Or, 24 x - 18 x = 17 + 1
Or, 6 x = 18
∴ x = [tex]\dfrac{18}{6}[/tex]
i.e x = 3
So, Putting the value of x
The measure of side pq = 18 × 3 + 1 = 55 unit
The measure of side qr = 24 × 3 - 17 = 55 unit
The measure of side pr = 15 × 3 + 10 = 55 unit
Hence The value of x is 3 ,
And The measure of each side is 55 units . Answer
Answer:
x = 3.
Measure of each side is 55 units.
Step-by-step explanation:
In an equilateral triangle, the length of all the three sides are equal.
Therefore, Side PQ = QR = PR.
⇒ 18X + 1 = 24X - 17
⇒ 24X - 18X = 18
⇒ 6X = 18
⇒ X = 3
Substituting the value of X, we get:
PQ = 18(3) + 1 = 55 Units.
QR = 24(3) - 17 = 55 units.
PR = 15(3) + 10 = 55 units.
We see the length of all the sides are equal.
factor the polynomial completely x^2-x-20
Answer:
(x − 5) (x + 4)
Step-by-step explanation:
x² − x − 20
Factor using AC method:
1 × -20 = -20
Factors of -20 that add up to -1: -5 and 4
Divide by 1 and reduce: -5/1 and 4/1
(x − 5) (x + 4)
Answer:
[tex]\displaystyle [x + 4][x - 5][/tex]
Step-by-step explanation:
Find two quantities that when differed to −1, they also multiply to −20, and those numbers are 4 and −5.
I am joyous to assist you anytime.
Help please please help!!!!!
Answer:
I have no idea
Step-by-step explanation:
Problem: you must find the horizontal distance between two towers (points a and b) at the same elevation on opposite sides of a wide canyon running east and west. The towers lie directly north and south of each other. You mark off an east/west line CD running perpendicular to AB.
A) From C you measure the angle between the two towers (angle ACB) as 88.60 degrees. Given the distance from C to B is 389 feet, write an equation and solve it to find an expression for the distance AB to the nearest whole foot. (Note: AB is perpendicular to CD)
B) You want to check your work to make sure it’s right. You should be able to both measure and compute the angle at D. Knowing the distance between the two towers from above and the distance BD is 459 feet, what is the angle at D to the nearest hundredth degree?
C) What is angle CAD in radians? Give your answer rounded correctly to 4 decimal places.
The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.
Step-by-step explanation:
Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.
Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length
tan 88.60°=O/A
tan 88.60°=AB/389
AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)
B.
Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.
tan Ф=O/A where Ф=∠D
tan ∠D =15917/459
tan ∠D =34.6772834701
tan⁻(34.6772834701) =88.35°
C.
Finding angle ∠A in radians will be;
Applying the sum of angles in a triangle theorem
∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°
Changing degrees to radians, multiply value of degrees by π/180°
3.05×π/180 =0.05323254 ⇒ 0.0532 rad
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The point (-4,0) is rotated 180 degrees counterclockwise using center (0,0). what are the coordinates of the image?
Answer:
The new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).
i.e. [(-4,0)→(4,0)]
Step-by-step explanation:
The rule for rotation a point 180° counterclockwise about the origin states that when a point (x, y) is rotated 180° counterclockwise about the origin, the new position of the coordinates of point P(x, y) becomes (-x, -y).
Hence,
Rotate (x, y) counterclockwise 180° about the origin: [(x,y)→(-x,-y)]So, when the given point (-4,0) is rotated 180 degrees counterclockwise using center (0,0), the new coordinates of the image will be:
Rotate (-4, 0) counterclockwise 180° about the origin: [(-4,0)→(4,0)]Therefore, the new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).
i.e. [(-4,0)→(4,0)]
Keywords: rotation, origin, image
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Write the value of 17 tens three different ways. Use the largest unit possible. Standard form. Expanded form. Unit form
Final answer:
The value of 17 tens can be written in standard form as 170, in expanded form as (1 × 10²) + (7 × 10¹), and in unit form as '1 hundred 7 tens 0 ones'.
Explanation:
When asked to write the value of 17 tens three different ways, we first recognize that '17 tens' is essentially the number 170, since 17 tens are 17 multiplied by 10.
Standard Form
The standard form is simply writing the number as it is, so in this case, it would be 170.
Expanded Form
The expanded form breaks down the number into its place value components. Since 170 comprises 1 hundred, 7 tens, and 0 ones, it can be written as:
(1 × 10²) + (7 × 10¹) + (0 × 10°)
Unit Form
Last, the unit form expresses each digit's value according to its place value, which for 170 is '1 hundred 7 tens 0 ones'.
A summer camp cookout is planned for the campers and their families. There is room for 525 people. Each adult costs $9, and each camper costs $5. There is a maximum budget of $1,200. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.
A
x + y ≤ 525
5x + 9y ≤ 1,200
B
x + y ≤ 1,200
5x + 9y ≤ 525
C
x + y ≤ 525
9x + 5y ≤ 1,200
C
x + y ≤ 1,200
9x + 5y ≤ 525
Need help ASAP.
x+y≤525 and 9x+5y≤1200 represents the scenario.
Step-by-step explanation:
Given,
Room for people at summer camp = 525 people
Maximum budget = $1200
Cost per adult = $9
Cost per camper = $5
It means that there cannot be spent more than $1200.
x represents the number of adults.
y represents the number of campers.
x+y≤525
9x+5y≤1200
x+y≤525 and 9x+5y≤1200 represents the scenario.
Keywords: inequality, budget
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Answer:
x+y≤525
9x+5y≤1200
Step-by-step explanation:
Need some help boyss
Answer: 0
Step-by-step explanation: The answer would be 0 since if y = -4, the graph of the line would just be a horizontal line through the point (0,-4). This would be like saying that y = 0x-4. Hope this helped!
Answer:
slope = 0
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
y = - 4 ← is therefore a horizontal line
with slope = 0
question 14. Select the correct answer. If f(x)=x^2/x+3, find f(x+h)
In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:
1. Write down the original function:
\( f(x) = \fraction{x²}{x+3} \)
2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
\( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)
3. Now expand the numerator and simplify the expression:
\( (x+h)² = x² + 2xh + h² \)
Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)
That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).
Marcos has $24. Yaneliz has 1/6 of the amount of money Marcos has. Write an expression.
Answer:4
Step-by-step explanation: since he has 24
Yaneliz has 24 X 1/6 = 4
Answer: y = 24 x 1/6
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Marcos: $24
Yaneliz: 1/6 of the amount of money Marcos has
So, to write an expression we have to multiply the amount of money Marcos has (24) by 1/6.
Mathematically speaking
Y = 24 x 1/6
Where "y" is the amount of money Yaneliz has.
Solving:
24 x 1/6 = 4
Yaneliz has $4.
Feel free to ask for more if needed or if you did not understand something.
WILL MARK BRAINLIEST!!! I need the answer. please help!!!!
Answer:
Step-by-step explanation:
Later area of Pyramid = 2 * 1/2 * 9 * 12.3 + 2*1/2*11*11.9
= 9*12.3 + 11*11.9
= 110.7 +130.9
= 241.60 sq.feet
[Answer For Brainliest]
Solve for d.
[tex]0.5(7d+4)=7-1.5d[/tex]
Ming took a cab across town. His fare was
$22 sign, and he leaves an 18% percent tip.
Question:
Ming took a cab across town. His fare was $22 and he leaves an 18%, percent tip. What is the total amount Ming pays the cab driver?
Answer:
Ming pays the $25.96 to cab driver
Step-by-step explanation:
Given:
the fare of the car = $22
Percentage of tip paid by the Ming = 18%
To Find:
Total amount Ming pays the cab driver=?
Solution:
The total amount of the tip paid by the Ming to the cab driver be x
then
x = car fare + 18% of cab fare
substituting the values we get
x = 22 + 18% of 22
x = 22 + [tex]\frac{18}{100} \times 22[/tex]
x = 22 + [tex]\frac{18}{100} \times 22[/tex]
x = 22 + [tex]0.18 \times 22[/tex]
x = 22 + 3.96
x = 25.96
Round each number to the nearest 10 and 1000
What numbers??? You need to either add a picture or just write the numbers
Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.
They equation needs to be in the form y=kx
K=
Equation:
Answer:
[tex]k=\frac{32}{5}[/tex], [tex]y=\frac{32}{5}x[/tex]
[tex]k=6.4[/tex], [tex]y=6.4x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Find the value of the constant of proportionality k
take any ordered pair from the data
For x=25, y=160
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{160}{25}[/tex]
simplify
[tex]k=\frac{32}{5}[/tex]
The linear equation is equal to
[tex]y=\frac{32}{5}x[/tex]
or
[tex]y=6.4x[/tex]
Answe 25 and 26 easy
Answer:
25. rational
26. irrational
Step-by-step explanation:
A rational number is a number that can be written as a fraction. It may have decimals that end or repeating decimals.
An irrational number cannot be written as a fraction. It's decimals continue on and do not repeat.
25.
When you multiply two rational numbers, the product is rational. The square root of 16 is 4, which is rational because it is a whole number. 4/7 is written as a fraction so it is rational.
26.
The square root of 2 is an irrational number because its decimals go on and do not repeat. 7 is a whole number so it is rational. Subtracting a irrational number from a rational number gives an irrational number.
1. A school booster club is selling
T-shirts. The silk-screening company
is selling shirts to the boosters for
$3 each, plus a one-time fee of $150
to cover supply costs. If the boosters
want to make at least $300 in profits
and they sell a shirt for $12, how
many shirts do they need to sell?
Answer:
Step-by-step explanation:
sales - expenses = profit
lets x represent number of shirts sold
12x - (3x + 150) > = 300
12x - 3x - 150 > = 300
9x - 150 > = 300
9x > = 300 + 150
9x > = 450
x > = 450/9
x > = 50 <== they would need to sell at least 50 shirts
how do i find the volume of these similar solids? round to the nearest tenth HELP
Answer:
The volume of the larger solid is [tex]592.6\ mm^3[/tex]
Step-by-step explanation:
The question is
If these solids are similar, find the volume of the larger solid
step 1
Find the scale factor
we know that
If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
x ----> the height of the larger solid in mm
y ----> the height of the smaller solid in mm
z ---> the scale factor
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=4\ mm\\y=3\ mm[/tex]
substitute
[tex]z=\frac{4}{3}[/tex] ---> scale factor
step 2
Find the volume of the larger solid
we know that
If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
x ----> the volume of the larger solid in cubic millimeters
y ----> the volume of the smaller solid in in cubic millimeters
z ---> the scale factor
[tex]z^3=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{3}[/tex]
[tex]y=250\ mm^3[/tex]
substitute the values
[tex](\frac{4}{3})^3=\frac{x}{250}[/tex]
solve for x
[tex](\frac{64}{27})=\frac{x}{250}[/tex]
[tex]x=250(\frac{64}{27})[/tex]
[tex]x=592.6\ mm^3[/tex]
determine the area of the yellow sector
Answer:
Step-by-step explanation:
To find out the area just compare the amount of green space and yellow space then calculate the numbers.
Answer:
The answer is D
Step-by-step explanation:
[tex]sector = \frac{θ}{360} \times π {r}^{2} [/tex]
Given that θ = 75° and r = 3in, so use the formula to find the shaded region :
A = (75/360)×π×3²
= (15/8)π
I’m not good at Algebra please lend a hand
1. Is the actual equation, so this is Given
2. removing the parenthesis is the Distributive Property
3. Combining like terms.
4. They add 6x to both sides, this would be the Addition Property of Equality
5. Subtract 4 from both sides, this is the Subtraction Property of Equality.
6. Divide both sides by 8, this would be the Division Property of Equality.
Answer:
1. Given
2. Distributive property
3. Combining like Terms
4. Addition property of Equality
5. Subtraction property of equality
6. Division Property of Equality
Wanni cycled 6 km from her house to the school at a uniform speed, v km/h. If she increased her speed
by 2 km/h, she would arrive at the school 4 minutes earlier. Form a quadratic equation in term of v.
Final answer:
To form the quadratic equation, we consider the original time to cover 6 km at speed v km/h and the new time at speed (v+2) km/h, then equate the difference in time to 4 minutes. Solving for v using a common denominator and simplifying, we obtain the quadratic equation 15v^2 + 30v - 90 = 0.
Explanation:
To form a quadratic equation from the given scenario, we’ll first define the relationship between distance, speed, and time. The time taken to travel 6 km at the original speed v km/h is distance divided by speed, which is 6/v hours. If Wanni increased her speed by 2 km/h, her new speed would be v + 2 km/h, and the new time taken would be 6/(v+2) hours.
We are told that by increasing her speed, Wanni arrives 4 minutes earlier. Since 1 hour is 60 minutes, 4 minutes is 4/60 or 1/15 hours. We can now set up an equation relating the difference between the two times to 1/15 hours:
6/v - 6/(v+2) = 1/15
To solve for v, we first find a common denominator for the fractions on the left side of the equation, which is v(v+2). Multiplying both sides by the common denominator, we get:
6(v+2) - 6v = v(v+2)/15
Expanding the terms and moving everything to one side of the equation, we get our quadratic equation in terms of v:
15v2 + 30v - 90 = 0
NEED ASAP!!!! BRANELIEST IF ANSWERED CORRECTLY WITH SHOWN WORK.
Carolyn is searching online for tickets to a concert. Two weeks ago, the cost was $30. Now the cost is $39. What is the percent increase? What would be the percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price?
Answer: at new cost increase is 30%
after additional $4.50 fee increase would be 45%
Step-by-step explanation:
use equation
30:100=39:x
30x=3900
x=3900/30
x=130
130-100=30%
39+4.50=43.5
30:100=43.5:x
30x=4350
x=4350/30
x=145
145-100=45%
The increase percent will be 30%
And, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is 45%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The old cost of the tickets = $30
And, New cost of the ticket = $39
Now,
The increase percent is calculate as;
Increase percent = (39 - 30) / 30 x 100
= 9/30 x 100
= 30%
And, When the ticket agent charges an additional $4.50 fee with the new ticket price.
Then, The new cost of the tickets = $39 + $4.50
= $43.50
Thus, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is calculated as;
Increase percent = (43.50 - 30) / 30 x 100
= 13.50/30 x 100
= 45%
Therefore, The increase percent will be 30%.
And, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is 45%.
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Determine whether the equation represents a direct variation. If it does, find the constant of variation:
1. 2y=5x+1
A. Not a direct variation
B. Direct Variation, constant of variation is 5/2
C. Direct Variation, constant of variation is 2/5
D. Direct Variation, constant of variation is 1 -2/5
2. -12x=6y
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2
3. 0.7x-1.4y=0
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2
Answer:
1) A. Not a direct variation 2) D. Direct Variation, constant of variation is -2 C) B. Direct Variation, constant of variation is ½
Step-by-step explanation:
Direct Variation requires that [tex]y=kx[/tex] with k≠0. K its constant of variation and its slope. It is a linear function with b =0
1) Examining 2y =5x + 1. Rewriting it as standard form:
[tex]2y =5x + 1\\\\y=\frac{5}{2}x+\frac{1}{2} \\\\[/tex]
Since this function cannot be written as y=kx as b ≠ 0 (b=1) then we can say that this is not a direct variation.
A. Not a direct variation
2) [tex]2). -12x=6y \Rightarrow y=-2x[/tex]
This linear function has no linear parameter. And its line goes through the origin varying directly. The constant k is equal to -2. So,
D. Direct Variation, constant of variation is -2
3) [tex]0.7x-1.4y=0\\\\-1.4y=-0.7x* (-1)\\y=0.5 \:or\,y=\frac{1}{2}[/tex]
The Constant of Variation is 1/2 and K>0. There is a direct variation between x and y of 1/2. So it's B.
B. Direct Variation, constant of variation is ½
The equation 2y = 5x + 1 represents a direct variation with a constant of variation of 5/2. The equation -12x = 6y represents a direct variation with a constant of variation of -2. The equation 0.7x - 1.4y = 0 represents a direct variation with a constant of variation of 0.5.
Explanation:For the equation 2y = 5x + 1, we need to determine if it represents a direct variation. In a direct variation, y is directly proportional to x, meaning that when x increases, y also increases or when x decreases, y also decreases. To check if it's a direct variation, we can rearrange the equation to y = mx + b form, where m is the constant of variation. In this case, rearranging the equation gives us y = (5/2)x + 1/2, so the constant of variation is 5/2. Therefore, the equation represents a direct variation and the constant of variation is 5/2.
For the equation -12x = 6y, we can rearrange it to y = (-12/6)x = -2x. Since the constant of variation is -2, the equation represents a direct variation.
For the equation 0.7x - 1.4y = 0, we can rearrange it to y = (0.7/1.4)x = 0.5x. Since the constant of variation is 0.5, the equation represents a direct variation.
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Answer 20 points pls
The sum of slopes b and c is 0
This statement is NOT always true
Step-by-step explanation:
(1) According to the graph, line a and b are parallel to each other. This, therefore, means that they have the same slope/gradient.
(2) Line c however, is perpendicular to both lines a and b. The slope of two lines that are perpendicular to each other is always the negative inverse of the slope of the other. This means that the product of their slopes will become -1.
An example is that if the slope of a line is 2, then a line perpendicular to it will have a slop of – ½
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Answer:
The sum of the slopes of line b and line c is 0
Step-by-step explanation:
Verify each statement
case a) The sum of the slopes of line b and line c is 0
we know that
Line b and line c are perpendicular lines
If two lines are perpendicular, then their slopes are opposite reciprocal
If the slope of line c is n
then the slope of line b is -1/n
[tex]-\frac{1}{n}+n=0[/tex]
Solve for n
[tex]n^{2}=1[/tex]
[tex]n=\pm1[/tex]
That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1
therefore
NOT always true
case b) Line a and line b have the same slope
This statement is always true, because the lines are parallel
Remember that
If two lines are parallel, then the lines have the same slope
case c) The product of the slopes of line a and line c is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
case d) The product of the slopes of line c and line b is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)