Answers
Answer:
a = 1
Step-by-step explanation:
The important point here is that both lines are horizontal reflections of each other. If we treat the line x = a as a kind of "mirror" for these lines, every point at the same y value on each line is going to be an equal horizontal distance from that "mirror". If that's confusing, think about how, as you pull your hand away from a mirror, your hand's reflection seems to go deeper into it. As you bring it closer, your reflection gets closer too. And when you're touching the mirror, it seems like your hand and its reflection are touching!
We want to find that "touching" point for the two lines, the intersection, because it'll tell us exactly where our "mirror" - more commonly called the axis of symmetry - is. The point of intersection of any two lines is the point where their equations are exactly equal to each other.
Our equations are y = 3x - 5 and y = 1 - 3x, so setting those two equal to each other and solving for x:
[tex]3x-5=1-3x\\6x=6\\x=1[/tex]
This tells us that the two lines intersect at x = 1, which is exactly our axis of symmetry, so a = 1!
Related Questions
How to calculate slope for a line that goes through
two points.
10.2: Practice
y
Find the slope of the line through these points. Try
making a table.
-3
6
(5.-3) and (-1.6)
Answers
Answer:
The slope is [tex]m=-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope point equation is given by:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here:
The first point is (x1,y1)=(5,-3)
The first point is (x2,y2)=(-1,6)
Then, the slope will be:
[tex]m=\frac{6-(-3)}{-1-5}[/tex]
[tex]m=\frac{9}{-6}[/tex]
[tex]m=-\frac{3}{2}[/tex]
I hope it helps you!
9. The hypotenuse of a 45°-45°-90° triangle is 5 sqrt 6. Find the length of one leg of the right triangle.
Answers
Answer:
5 ✓ 3
Step-by-step explanation:
using Pythagoras Theory
(5 ✓ 6 )2 =, 2 x square side
square leg length= 150/ 2=, 75
length =5 ✓ 3
4. Solve the inequality. 9+8 l 4a - 5 l >113
Answers
Answer:
i need this for a challenge
Step-by-step explanation:
How to find percents of numbers using multiples of 100, 10, and 1%?
I need this for my summary, please help!!
Answers
Answer:
Im not too sure what the question is
Step-by-step explanation:
but when finding the percent of any number, 10% will always move the decimal over to the left once. So 10% of 300 is 30.0 This also works for 1%, you just move the decimal over twice. So 1% of 300 is 3
Solve for X
6(x + 2) = 66
X =
Answers
Answer:
6(x+2)=66
6x+12=66 -12
6x= 54 :6
x=9
Step-by-step explanation:
prove me wrong
ASAP! please help, thanks
Answers
Answer:
d should be correct
Step-by-step explanation:
prove me wrong
Sue makes and sells cupcakes. If she has a cost of $1,500 per year plus a cost of $1 per cupcake, how many cupcakes must she sell in order to make a profit if each cupcake sells for $3?
Answers
Answer:
751 cupcakes must be sold to make a profit
Step-by-step explanation:
From the question we are told that
Annual cost= $1,500 per year plus a cost of $1 per cupcake
Each cup cake sell at $3
Generally the profit off the top of each cupcake is $2
Therefore
[tex]\frac{1500}{2}=750[/tex]
This implies that 750 cupcakes will be sold to cover the annual cost excluding cupcake cost
Generally
751 cupcakes=$1502
Total Annual cost to make a profit
[tex]1(cost\ of\ each\ cupcake)*751+1500=\$2251[/tex]
Total Annual sale
[tex]3(sale of each cupcake)*751=\$2253[/tex]
Mathematically
[tex]2253\$-2251\$=2\$[/tex]
Therefore
751 cupcakes must be sold to make a profit
solve for x each figure is a parallelogram
Answers
Answer:
[tex]18x + 8= (180 - 46) = 134 \\ 18x = 126 \\ \boxed{x = 7}[/tex]
7 is the right answer.A motorboat travels 172 km in 3 hours going upstream and 372 in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answers
Answer:
The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h
Step-by-step explanation:
System of Equations
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
[tex]\displaystyle B-S=\frac{172}{3}[/tex]
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
[tex]\displaystyle B+S=\frac{372}{4}=93[/tex]
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
[tex]S = \frac{107}{6}\approx 17.83\ km/h[/tex]
From [2]:
[tex]B = 93 - \frac{107}{6}[/tex]
[tex]B=\frac{451}{6}\approx 75.17\ km/h[/tex]
What is the simplest form of this expression?
-x(4x2 - 6x + 1)
Answers
Answer:
−4x3+6x2−x
Step-by-step explanation:
(−x)(4x2−6x+1)
=(−x)(4x2+−6x+1)
=(−x)(4x2)+(−x)(−6x)+(−x)(1)
=−4x3+6x2−x
When paying for a restaurant order, a customer spent $18.00 ( for tip and cost) for a $15.00 meal. What percent was the tip? *
Answers
Answer:
16.67%
Step-by-step explanation:
The customer spent a total of $18 on a $15 meal. This means that, if counting tax within the $15 meal, the tip is $3.
Divide 3 with the total cost:
3/18 = ~0.1667
Change to percentage. Simply move the decimal point to the right two place values, and add a percentage sign:
0.1667 to a percent = 16.67%
16.67% is your answer.
~
Answer:
1.6 %
Step-by-step explanation:
15/18= 8.4
CAN SOMEONE PLEASE HELP ME???
Answers
Answer:
f(x)=525+4.75x
HELP PLEASE!!!!!!!
A restaurant sells 10 garden salads. If garden salads represent 20% of their total salad sales, how many salads did they sell?
Answers
20%=10
100=20x5
5x10=50 salads
pls help as soon and as quick as possible I really need help
Answers
Answer:
(1,7)
(0,2)
(-1,-3)
(-2,-8)
put dots on these points and put a line through all of them making on line
Pls help me I’ll give 100 points
Answers
Answer:
Try option B
Step-by-step explanation:
sub to Pen Paper
Hi there!
So what we have to do here is...
turn 2³ - 1 into 2·2·2-1=4·2=8-1=7.
[tex]\frac{35}{7}=5[/tex]
Final Result: 5
In a complete paragraph, explain why it's important to think about the complexity of your speech.
Use your own words please.
Answers
Answer:
I will try it :)
Step-by-step explanation:
thanks for the points.
Krutika, David and Mark share some sweets in the ratio
2:2:1. Krutika gets 48 sweets. How many sweets are there
altogether?
Answers
Answer:
120
Step-by-step explanation:
Krutika:48
David: 48
Mark: 48÷2= 24
Because 2 : 2 : 1
48+48+24=120
Can someone please help me with number 16?
Answers
Answer:
I got 105°
Step-by-step explanation:
Triangle ABC is an isosceles triangle so base angles are equal. <A = 30° (given)
180 - 30 = 150°
150/2 = 75°
the little triangle is also isosceles. the original base angles have been bisected so the base angles are 37.5.
37.5 X 2 = 75°
180-75 = 105°
D = 105°
Class A has 20 pupils and class B has 19 pupils.
Both classes site the same maths test
The mean score for class A is 33.
The mean score for class B is 62
What is the mean score (rounded to 2 DP) in the maths test across
both classes?
Answers
Answer:
47.5
Step-by-step explanation:
33+62=95
95/2=47.5
I= $164.50, P = $940, t = 2.5
Find the annual interest rate
Answers
250.35 that the anwers hope this help a lot
Merideth made a model of a pyramid like the one shown for history class.
What is the height of the model?
I un
15 in
app
The
Great!
e Building on the Essential Question How do you solve
Answers
Answer:
12
Step-by-step explanation:
there is a right angle so you can use Pythagoras therom to get the height it's going to be (15)^2-(9)^2 all under a square root = 12 in.
What should be done to both sides of the equation in order to solve -5 m = -40?
Multiply by -5.
Multiply by -40.
Divide by -5.
Divide by -40.
Answers
Answer:
I know for a fact that it is Devide by nagative 5
Step-by-step explanation:
Yuto and Hila attempted to solve the same inequality. Their work is shown below.
Yuto’s Work
Hila’s Work
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than negative 2. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (Negative StartFraction 2 over 1 EndFraction). x less-than 3.
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than 16. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (StartFraction 16 over 1 EndFraction). x less-than negative 24.
Which statement is true about the work shown above?
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Yuto is incorrect because he should not have reversed the inequality symbol.
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
Hila is incorrect because she should not have reversed the inequality symbol.
Answers
Answer:
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Step-by-step explanation: hi
Answer:
The answer is A
Step-by-step explanation:
In other words, Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Good Mornting hru?
3(7)+4(6)=
Answers
Answer:
45
Step-by-step explanation:
im good, u?
Determine, in general form, the equation of the line that goes through the
point (3,-6) and is perpendicular to the line shown: 5x + 3y + 9 = 0
Answers
Answer:
I got
y=3/5x -39/5
Step-by-step explanation:
Hope this helps
Order from least to greatest.
1.603; 1.036; 1.36; 1.063
Answers
Answer:
1.036, 1.063, 1.36, 1.603
Step-by-step explanation:
Hope this helped, have a great day :)
Work out the surface area of the solid cuboid.
8m
5m
2m
Answers
Answer:
Step-by-step explanation:
T.S.A=2(LXW) + 2(LXH) + 2(WXH)
=2(8mx5m) + 2(8mx2m) + 2(5mx2m)
=(2x40m²) + (2x16m²) + (2x10m²)
=80m² + 32m² + 20m²
=132m²
Hi I need help please
Answers
Answer:
15%
Step-by-step explanation:
Percent Error formula is the difference between the Actual and the guess value divided by the actual.
So it's 198- 172 / 172 x 100
= 15%
The value of a baseball player's rookie card began to increase once the player retired. When he retired in his card was worth $. The value has increased by $ each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in ?
Answers
Answer:
No, x and y are not proportional
The value of card in 2006 = $38.05
Step-by-step explanation:
I got this! I hope this helps!
Lee needs some school supplies. He will buy 3 notebooks for $1.29 each, 2 dozen
pencils at $3.45 a dozen and a box of pens for $14.85.a box. Lee estimates that he
will spend about $25 on these school supplies.
Is Lee's estimation reasonable? How much will he spend exactly?