Answer:
1 litre = 1000 millilitres (ml)
35 litres = 35×1000 => 35000 ml
So your fish tank holds 35000 ml of water
I NEED HELP RN PLEASEEEE ITS AN EMERGENCY!!
Simplify.
The square root of 24 multiplied by the square root of 12
Answer Choices:
A) 2sqroot 12
B) 6
C) 12sqroot 2
D) 288
I need the CORRECT ANSWER ASAP! (worth 10 points)
Answer:
The answer is C) [tex]12\sqrt{2}[/tex].
Step-by-step explanation:
For a real number [tex]a[/tex],
[tex]\sqrt{a} \cdot \sqrt{a} = a[/tex].
In other words, multiplying a square root by itself gets rid of the square root.
How does this rule apply here?
[tex]24 = 2\times 12[/tex].
Similarly,
[tex]\sqrt{24} = \sqrt{2}\times \sqrt{12}[/tex].
That is:
[tex]\begin{aligned}\sqrt{24}\times \sqrt{12} &= (\sqrt{2}\times \sqrt{12}) \times \sqrt{12}\\&=\sqrt{2}\times (\sqrt{12}\times \sqrt{12}) && \begin{array}{l}\text{By the associative property}\\\text{of multiplication}\end{array}\\&=\sqrt{2} \times 12\\ &= 12\sqrt{2}\end{aligned}[/tex].
Answer: The correct answer is: [C]:
______________________________________________
→ " 12sqroot " ; or, write as: " 12√2 " .
______________________________________________
Step-by-step explanation:
______________________________________________
√24 * √12 = ?
Let us start by simplifying: " √24 " ;
24 = 4 * 6 ;
So; √24 = √4 *√6 ;
√4 = 2 ;
So: " √24 = √4 *√6 = 2√6 " .
______________________________________________
Now, let us simplify: " √12 " :
______________________________________________
" √12 = ? "
12 = 4 * 3 ;
So: "√12 = √4 *√3 " ;
√4 * √3 = 2√3 ;
So: "√12 = √4 *√3 = 2√3 " .
______________________________________________
We are asked to solve—"simplify"— "√24 * √12 " .
√24 = 2√6 ; as we simplified above.
√12 = 2√3 ; as we simplified above.
______________________________________________
So: " √24 * √12 " ;
= 2√6 * 2√3 ;
= ? ; Note: "2 * 2 = 4 " ; and: "√6 * √3 = √(6*3) = √18 ;
So; 2√6 * 2√3 ;
= 4√18 ;
Now, we can simplify this value further:
by simplifying: " √18 " ;
18 = 9 * 2 ;
So: " √18 = √9 *√2 = 3 √2 " ;
So: " 4√18 = 4 * (3√2) = 12√2 " .
→ which is our answer: " 12√2 " .
→ which corresponds to:
→ Answer choice: [C]: " 12 * sq root 2 " . {or, write as: " 12√2 ".}.
_____________________________________________
Hope this answer and explanation is of help to you!
Wishing you the best in your academic endeavors
— and within the "Brainly" community!
_____________________________________________
The appropriate translation of the phrase 11 more than 20 percent of a number is 0.2n + 11. Is that true or false?
False.
The statement "11 more than 20 percent of a number" is best expressed as 11 + 0.20n, where n represents the number.
The appropriate translation of the phrase 11 more than 20 percent of a number is 0.2n + 11 is false.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
In order to derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Given; 11 more than 20 percent of a number
The statement:"11 more than 20 percent of a number" is best expressed as 11 + 0.20n.
where n represents the number.
Therefore, The appropriate translation of the phrase 11 more than 20 percent of a number is 0.2n + 11 is false.
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write a verbal expression to represent the given equation BRAINLIEST!!!!
v/12=4(v+3)
Answer:
The quotient of v and twelve is equal to the product of 4 and the sum of v and three.
Step-by-step explanation:
The expression v/12 can be described several ways:
v divided by 12the ratio of v to 12the quotient of v and 12one-twelfth of vv over 12The product 4(v+3) can also be described several ways. The trick is to pick one that is not ambiguous.
the product of 4 and 3 more than v (could mean 4·3 +v)4 times the quantity v plus 3 (could mean 4v +3)the quantity v plus 3 multiplied by 4 (could mean v +3·4)4 times the sum of v and 3The verbal expression written above is among the least ambiguous. (The least ambiguous way to write it is: v/12 = 4(v+3).)
Answer: The Correct Answer is
A number divided by 12 is equal to 4 multiplied by the sum of that number and 3.
Step-by-step explanation:
Need help with this math question
Answer:
83.0 degrees to the nearest tenth.
Step-by-step explanation:
17^2 = 8^2 + 16^2 - 2*8*16 cos X
cos X = (17^2 - 8^2 - 16^2) / - 2*8* 16
cos X = 0.12109
X = 83.04 degrees
Line H is represented by the following equation:
2x + 2y = 8
What is most likely the equation for line K so the set of equations has infinitely many solutions? (4 points)
x + 2y = 2
x + y = 4
2x + y = 6
x – y = 8
Answer:
b. x + y = 4
Step-by-step explanation:
For to lines to have an infinite number of points that intersect, the lines have to have the exact same equation, so that every coordinate of H and K is the exact same.
Simplify the equation for H:
[tex]2x+2y=8\\2y=8-2x\\y=4-x[/tex]
Rearrange the equation:
[tex]x+y=4[/tex]
internal memoriam menino
The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width. L= yards, W=yards
Answer:
L = 90 yardsW = 60 yardsStep-by-step explanation:
The formula for the perimeter of a rectangle is ...
P = 2(L+W)
If the length is 30 yards more than the width, we can use L = W+30 and substitute known values into the above formula:
300 = 2((W+30) +W)
150 = 2W +30 . . . . . divide by 2 and collect terms
120 = 2W . . . . . . . . . subtract 30
60 = W . . . . . . . . . . . divide by 2
60+30 = L = 90
The length is 90 yards; the width is 60 yards.
Last year amusement park received 236,758 visitors it was open every day of the year but 7 Holliday's what was the average number of visitors to the park per day
Answer:
ABOUT 661 visitors per day
Step-by-step explanation:
There are 365 days in a year and they were not open 7 so you do
365-7=358
Now, you know that out of those 358 days the total is 236758 visitors.
So you would divide 236758 by 358
236758/358 = 661.33519553072625698324022346369
I would recommend rounding this number to 661,
the amusement park had a average of ABOUT 661 visitors per day it was open.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation to find the width of the run. Which statements are true of the solution? Check all that apply. The value of w is 10 feet. The value of w can be zero. The value of w cannot be a negative number. Substitution is used to replace the variable l with a value of 20. The subtraction property of equality is used to isolate the term with the variable w.
Answer:
Width of the rectangular Park = 11 feet
Step-by-step explanation:
Given that the total length of the fencing is 62 feet. As has to be fenced around a rectangular park , it would be the perimeter of the rectangular park.
Also Shana wants the length of the run to be 20 feet. Hence the length of the park is 20 feet.
Here we will use the formula for perimeter to find the width of the run
Perimeter = 2(l+w)
62=2(l+w)
l+w = [tex]\frac{62}{2}[/tex]
l+w=31
20+w=31
w=31-20
w=11
Hence the width of the run for her dog in park would be 11 feet.
Answer:
The correct options are C, D and E.
Step-by-step explanation:
Consider the provided information.
Perimeter of a rectangular field is:
[tex]P= 2 (length) + 2( width)\\P= 2 l + 2w[/tex]
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet.
Substitute the L=20 and P=62 in above formula.
[tex]P= 2 l + 2w[/tex]
[tex]62= 2 (20) + 2w[/tex]
[tex]62= 40 + 2w[/tex]
Isolate the variable w by subtraction property of equality.
[tex]62-40= 40-40 + 2w[/tex]
[tex]22=2w[/tex]
[tex]w=11[/tex]
Hence, the length of width is 11.
Now consider the provided options.
Option A) The value of w is 10 feet.
This option is incorrect as the value of w is 11.
Option B) The value of w can be zero.
This option is incorrect as the value of w is 11.
Option C) The value of w cannot be a negative number.
This option is correct as the value of w is a positive number and length cannot be a negative number.
Option D) Substitution is used to replace the variable l with a value of 20.
This option is correct as we substitute L=20 in above calculation.
Option E) The subtraction property of equality is used to isolate the term with the variable w.
This option is correct as we use the subtraction property of equality in above calculation.
Hence, the correct options are C, D and E.
If a seller prepaid the taxes of $4,400 and the closing is set for May 19, using the 12 month/30 day method what will the buyer owe the seller as prorated taxes?
Answer:
$2701.11
Step-by-step explanation:
The buyer owes for taxes for the remainder of the year, 11 days in May and 7 more months: 7 11/30 months out of 12.
(7 11/30)(1/12)(4400) = (221/360)(4400) = 2701 1/9 ≈ 2701.11
The buyer will owe prorated taxes of $2701.11.
The following equation represents the number of fish in a pond, F(x), after x number of weeks. F(x) = 500 (1.2)^x. How many fish are in the zoo at the beginning of the study (week 0)? (4.2)
a. 500
b. 120
c. 20
d. not enough information
Answer:
500
Step-by-step explanation:
They are asking what happens at x=0. Plug it in and you should see you get 500(1.2)^0=500(1)=500.
500 is the initial amount of fish
Johnny wants to sell his car that he paid $7,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Johnny can sell his car for today?
7,000 − 24x
7,000 − 2x
7,000 + 24x
7,000 + 2x
Answer:
Option. 7,000 − 24x
Step-by-step explanation:
Let
y ----> depreciated value of the car
x---> rate of depreciation
t ----> the time in months
we know that
The linear equation that represent this situation is
y=7,000-xt
For
t=2 years
Convert to months
t=2*12=24 months
substitute
y=7,000-x(24)
y=7,000-24x
The segments shown below could form a triangle. 4,3,6 PLZ HELP ASAP
Answer:
Option A. True
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
we have
4,3 and 6
Applying the triangle inequality theorem
case 1) 4+3 > 6 -----> is true
case 2) 3+6 > 4 ----> is true
therefore
The given segments could form a triangle
Is true
Answer: true
Step-by-step explanation:
Please help!!! What is the equation of the graph?
Answer:
y = sec(x) +2
i got you
What equation results from completing the square and then factoring?
Answer:
YOUR ANSWER IS C.(x-6)²=94
Step-by-step explanation:
(x-6)²=94x²+36-12x=94x²-12x=54HENCE PROVED
If each shirt requires 3/8 square yard of cloth, how many shirts can be made from 6 square yards of cloth. please show work.
Answer:
16 shirts
Step-by-step explanation:
To determine the number of shirts that can be made, take the total amount of cloth and divide by the cloth needed per shirt
6 ÷ 3/8
Copy dot flip
6 * 8/3
48/3
16
We can make 16 shirts
HELPPPP WITH MATH QUESTION
Answer:I think its the third answer
ANSWER
The correct answer is B.
EXPLANATION
The cosine rule can be used to find the relation for b.
According to the cosine rule:
[tex] {b}^{2} = {a}^{2} + {c}^{2} - 2ac \cos( B ) [/tex]We have that a=4 and c=5 and B=60°
We plug in these values to get:
[tex]{b}^{2} = {4}^{2} + {5}^{2} - 2(4)(5) \cos( 60 \degree ) [/tex]
[tex]{b}^{2} = 16+ 25 - 40 ( \frac{1}{2} ) [/tex]
[tex]{b}^{2} = 16+ 25 - 20[/tex]
Take positive square root.
[tex]b = \sqrt{25 + 16 - 20} [/tex]
The correct answer is B
NEED HELP NOW! WILL MARK BRAINLIEST
In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 54% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 85% take prescription drugs regularly. For adults age 18 to 64, 45% take prescription drugs regularly. The age 18–64 age group accounts for 84.5% of the adult population (Statistical Abstract of the United States, 2008).
Round your answers to 4 decimal places.
a. What is the probability that a randomly selected adult is 65 or older?
b. Given an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older?
Final answer:
The probability that a randomly selected adult is 65 or older is 15.5% or 0.1550 in decimal form. The conditional probability that an adult is 65 or older, given that they take prescription drugs regularly, is approximately 24.63% or 0.2463 when rounded to four decimal places.
Explanation:
To answer these questions, we can use the information provided about the adult population and their prescription drug use.
Probability an Adult is 65 or Older
To calculate the probability that a randomly selected adult is 65 or older (Part a), we can subtract the percentage of the adult population that is age 18–64 from 100%. The provided statistics state that 84.5% of the adult population are 18 to 64 years old. Therefore, the probability that an adult is 65 or older is:
100% - 84.5% = 15.5%
This gives us a probability of 0.1550 (converted to decimal format).
Probability an Adult is 65 or Older Given They Take Prescription Drugs Regularly
For Part b, we are asked to find the probability that an adult is 65 or older, given that they take prescription drugs regularly. This is a conditional probability problem. We know the following:
54% of all adults take prescription drugs regularly.
85% of adults 65+ take prescription drugs regularly.
15.5% of all adults are 65 or older.
To find the required probability, we apply Bayes' theorem:
Probability (Adult is 65+ | takes prescription drugs) = (Probability (takes prescription drugs | Adult is 65+) * Probability (Adult is 65+)) / Probability (Adult takes prescription drugs)
Inserting our known values:
P(Adult is 65+ | takes prescription drugs) = (0.85 * 0.155) / 0.54 = 0.2463
Janet can do a job in three hours while Gary can do the same job in two hours. If Janet works for an hour before Gary be in helping her how long will it take them to finish the job together?
Janet = 1/3
Gary = 1/2
(1/3) + (1/2) = 5/6
Let x = time they both can do the job together
(1/2) + (5/6)x = 1
Solve for x to find your answer.
Factor the polynomial, if possible. If the polynomial cannot be factored, write prime. 9n^3 + 27n^2 – 25n – 75
Answer:
(x+3)(3x-5)(3x+5)
Step-by-step explanation:
Let's consider the possible rational zeros: factors of -75 over factors of 9
So one such possible 0 is -3
let's try it and see if it works:
-3 | 9 27 -25 -75
| -27 0 75
------------------------------------------
9 0 -25 0
So x+3 is a factor and we have another there which is 9x^2+0x-25 or 9x^2-25
So far we have this as the factored form (x+3)(9x^2-25)
The second factor is a difference of squares so we can factored this more:
(x+3)(3x-5)(3x+5)
--------You could have also done factored by grouping here:
9x^3+27x^2-25x-75
(9x^3+27x^2)+(-25x-75)
9x^2(x+3)+-25(x+3)
(x+3)(9x^2-25)
(x+3)(3x-5)(3x+5)
Answer:
Step-by-step explanation:
9n^3 + 27n^2 – 25n – 75=9n²(n+3)-25(n+3)
= (n+3)(9n²- 25)
but : 9n²- 25 = (3n)² - 5²
by identity : a²-b² =(a-b)(a+b)
now : a =3n and b = 5 you have : 9n²- 25 = (3n)² - 5² = (3n-5)(3n+5)
Factor the polynomial :
9n^3 + 27n^2 – 25n – 75=(n+3)(3n-5)(3n+5)
which of the following best describes the slope of the line below
Answer:
B. Negative
Step-by-step explanation:
A line that has a negative "rise" (vertical change) for a positive "run" (horizontal change) has a negative slope. The slope is calculated from rise/run, so if the signs of rise and run are different, the slope is negative.
Any line that goes downward to the right has negative slope.
_____
Any line that goes upward to the right has positive slope.
Juan construyó una rampa que tiene 5 m de largo y 1 m de altura. ?Cuánto mide la distancia (d) que recorre al subir la rampa
Answer:
[tex]d=\sqrt{26}\ m[/tex] or [tex]d=5.1\ m[/tex]
Step-by-step explanation:
The question in English is
Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?
let
x -----> the length of the ramp
y ----> the height of the ramp
d ----> the distance Juan travels when he climbs the ramp
we know that
Applying the Pythagoras Theorem
[tex]d^{2}=x^{2}+y^{2}[/tex]
we have
[tex]x=5\ m[/tex]
[tex]y=1\ m[/tex]
substitute the given values
[tex]d^{2}=5^{2}+1^{2}[/tex]
[tex]d^{2}=26[/tex]
[tex]d=\sqrt{26}\ m[/tex] -----> exact value
[tex]d=5.1\ m[/tex] ----> approximate value
Sam has 3 types of toys. Teddy bears cost $10, toy cars cost $7, and legos cost $13. The total cost of his 15 toys is $171. There are five times as many legos as there are teddy bears. How many toys of each type are there?
PLS help
Answer:
2 bears, 3 toy cars, and 10 legos
Step-by-step explanation:
We have 2 things going on here: the NUMBER if toys and the COST of the toys. They are not similar so they cannot be combined. We have to have 1 equation represent each.
First, the NUMBER of toys:
We are told that he has 15 toys altogether, and they are bears, cars, and legos. b = bears, c = cars, l = legos, ok? The equation for the number of toys is:
b + c + l = 15. But we are told then that the number of legos is 5 times more than bears, so l = 5b. We make the replacement:
b + c + 5b = 15 and
6b + c = 15
Next we deal with the COST. If each bear costs $10, we represent that as 10b; if each car costs $7, we represent that as 7c; if each set of legos costs $13, we represent that as 13(5b) = 65b. So the equation for the cost is
10b + 7c + 13(5b) = 171 and
75b + 7c = 171
Now we have 2 equations with only 2 unknowns so we solve this system using the method of elimination/addition. We can cancel out the c terms if we multiply the first equation by -7 to give us the new system:
75b + 7c = 171
-42b - 7c = -105
The c's are gone, leaving us with
33b = 66 and b = 2.
Now sub that in to folve for c:
6(2) + c = 15 and
c = 3.
Sub both of those in to find l:
2 + 3 + l = 15 and
l = 10
Mr Solidarios charged Randolf Php 320.00 for parts and Php 150.00 per hour for labor to repair his bicycle.If he spent 3 hours repairing his bicycle,how much does Randolf owe him?
Answer:
Php 770.00
Step-by-step explanation:
The cost of labor is ...
(hours) × (hourly rate)
= (3 h) × (Php 150.00/h) = Php 450.00
The total cost is ...
total cost = cost of labor + cost of parts
= (Php 450.00) + (Php 320.00) = Php 770.00
Randolf owes Mr. Solidarios Php 770.00 for the repair.
You have been asked to select a marble from a bag that contains 3 blue marbles and
4 red marbles and flip a coin for heads or tails.How many possible outcomes are there in this sample space?
14 different outcomes.
3 blue + 4 red = 7 different marbles you could draw total.
since you have heads or tails possible with each of the 7, you multiply by 2(heads & tails)
7x3=14
Follow below steps:
When selecting a marble from a bag and flipping a coin, we are combining two separate actions that result in a compound event. The number of possible outcomes in the sample space can be calculated by multiplying the number of outcomes for each action. Since there are 3 blue marbles and 4 red marbles, there are 3 + 4 = 7 possible outcomes for drawing a marble. For flipping a coin, there are 2 possible outcomes: Heads (H) or Tails (T). To find the total number of possible outcomes for the combined actions, we multiply the outcomes for drawing a marble by the outcomes for flipping a coin: 7 (marble outcomes) times 2 (coin outcomes) = 14 possible outcomes in the sample space.
Solve the equation.
42x – 5 = 64
Answer:
23/14
Step-by-step explanation:
42x - 5 = 64
Add 5 to both sides in order to isolate 42x
42x = 64 + 5
42x = 69
Divide 42 from both sides in order to isolate x
x = 69/42
The answer gives an uneven decimal so it'd be best to leave it as a simplified fraction. The simplified fraction is 23/14.
Answer:
x = 1.64
Step-by-step explanation:
42x – 5 = 64
add 5 to both sides
42x - 5 + 5 = 64 + 5
42x = 69
divide via by 42
x = 69/42
x = 1.64
Hope this helps!
The variable z is inversely proportional to x. When x is 3, z has the value 2.
What is the value of z when x= 13?
Answer:
z = 6/13
Step-by-step explanation:
The new value of x is 13/3 times the old value. Since z is inversely proportional to x, it will be multiplied by the inverse of that, 3/13.
2 × 3/13 = 6/13 . . . . value of z when x=13
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A teacher asked her students how many pets they own. Here are the results:
Answer:
B.
Step-by-step explanation:
Basically, to draw a dot plot, what you do is place one circle above the corresponding value on the number line for each value in the data set, ie. if there is a 0 in the data set, then you would draw one 'dot' above 0 on the number line. If there was another 0, then you would draw another dot above the dot you drew for the first 0, and so on.
The data set given is:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
If we count the number of each value, then we can say that:
a) there are three 0's
b) there are four 1's
c) there are three 2's
d) there are two 3's
e) there are two 4's
f) there is one 8
Now you could draw this up on a dot plot and compare this with the answers, or you could technically also just look at the dot plots in the multiple choice answers and count each of the values to see which one matches up with the values we defined above. So:
A. There are three 0's (correct), four 1's (correct), three 2's (correct), but there are no 3's - therefor this is not the correct dot plot.
B. There are three 0's (correct), four 1's (correct), three 2's (correct), two 3's (correct), two 4's (correct) and one 8 (correct) - therefor this is the correct dot plot.
We could use the same method to check if C and D were correct; then we would see that C only has two 0's and one 3 and is thus incorrect, and D only has one 3 and one 4, and has an extra value of 5, thus it is also incorrect.
Therefor, the answer is B.
Whilst this method may be used, a quick sketch of the dot plot may be a little easier to work with to compare visually with the answers, however everyone has their own way so try both methods and see what works for you.
''Option B'' shows the correct dot plot.
We have to given that,
A teacher asked her students how many pets they own.
Here are the results:
0,0,0,1,1,1,1,2,2,2,3,3,4,4,4,8
Now, From the data set,
0 is repeat 3 times.
1 is repeat 4 times.
2 is repeat 3 times
3 is repeat 2 times.
4 is repeat 3 times
8 is repeat only 1 times.
Hence, Option B shows the correct dot plot.
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The Great Pyramid is a square pyramid with a base area of 571,536 ft2 and a height of 48 stories. Each story is approximately 10 feet. Estimate the volume in cubic yards.
a. 274,337,280 yd3
b. 3,386,880 yd3
c. 91,445,760 yd3
d. 30,481,920 yd3
Answer: c. 91,445,760 yd3
Step-by-step explanation:
571,536 x 48 = 27,433,728
27,433,728 ÷ 3 = 9,144,576
9,144,576 x 10 = 91,445,760
Answer one of them!
1.Write a function that is shifted down 2 units and then reflected over the x-axis. Parent function is y = -5x - 8
2.Write a function that is reflected over the x-axis. Parent function is y = 5x - 8
3.Let g(x) be a vertical shift of f(x)= -x up 3 units followed by a vertical stretch by a factor of 4. Write the rule for g(x) .
4.Which transformation from the graph of a function f(x) describes the graph of 1/3 f(x)?
5.Write a function that is reflected over the x-axis. Parent function is y = -5x - 8
6. Let g(x) be a vertical shift of f(x)= -x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).
Answer:
1. y=-5x+10
Step-by-step explanation:
if it reflect over the x it changes the y if it reflects over y it changes the x
The function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
What is reflection of line? What is the general equation of a straight line? What is triangle? What are parallel lines?A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically : ∠x + ∠y + ∠z = 180°. There are different types of triangles such as : equilateral triangle , scalene triangle , isosceles triangle etc.Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions. These lines have same slope.We have the some sub - questions given in question.
We will solve part [1].
We have -
y = - 5x - 8
Shifting down by 2 units, we get -
y = - 5x - 8 - 2
y = - 5x - 10
Reflection over the [x] axis, would be -
g(x) = - y
g(x) = - (- 5x - 10)
g(x) = 5x + 10
Therefore, the function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
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