Answer:
Writing an equation to model a real-world problem is often easier when you take the information given in the problem and express it in verbal form by using a few key words. This is very similar to translating verbal phrases into variable expressions. The difference is you will be translating a verbal sentence into an equation. Then, you can solve the equation using inverse operations.
Let’s look at an example.
Monica purchased a pair of tennis shoes that had this sticker on the bottom of the shoe.
$99.00$65.99
Use a verbal model to write and solve an equation to determine the amount of money Monica saved by purchasing the shoes on sale.
First, write a verbal model to represent the problem.
Verbal Model:
Sales Price+Amount Saved=Original Price
Next, name the variable.
Let ‘
s
’ represent the amount saved.
Next, solve the equation you have written. Remember an equation is like a balance scale. To keep the scale balanced, what you do to one side of the equation you must also do to the other side. When solving an equation your goal is to isolate the variable on one side of the equation and the numerical terms on the other side. This is done by performing inverse operations.
65.99+s=99.00
First, isolate the variable ‘
s
’ by subtracting 65.99 from both sides of the equation. Subtraction is the inverse of addition.
65.99−65.99+s=99.00−65.99
Next, simplify each side.
s=33.01
The answer is $33.01.
A variable can be any element that we can, in some way, change.
The general form of modeling and solving real life problems that involve one variable is:
Identify what the variable is and define it.Write the equation.Isolate the variable on one side of the equation.So for example, something that we can define with a variable is "How many of one type of item we can buy if we know its price"
For example, if we know that a shirt costs $10, then the price of x of these shirts is:
y = $10*x
Now, if you know how much money you have, you can use this equation to find how many shirts you can buy.
For example, you know that you have $20, then y = $20
$20 = $10*x
To solve this we need to isolate the variable on one side:
$20/$10 = x
2 = x
You can buy two shirts.
Now, the general form of modeling and solving real life problems that involve one variable is:
Identify what the variable is and define it.Write the equation.Isolate the variable on one side of the equation.If you want to learn more, you can read:
https://brainly.com/question/1806181
The measure of the supplement of ∠BAC is (18x+22) degrees. The measure of the complement of ∠BAC is (9x-5) degrees. Determine m∠BAC.
Answer:
∠ABC = 32°
Step-by-step explanation:
We know that the two angles are termed as supplementary when their angle measures add up to 180 degrees.Given that the measure of the supplement of ∠BAC is (18x+22) degrees.
so
∠ABC + (18x + 22)° =180°
∠ABC + 18x =180°-22°
∠ABC + 18x =158°
∠ABC = 158° - 18x ----[Equation A]
We know that the two angles are termed as complementary when their angle measures add up to 90 degrees.Given that the measure of the complement of ∠BAC is (9x-5) degrees.
so
∠ABC + (9x-5)° =90°
∠ABC + 9x =90°+5°
∠ABC + 9x =95°
∠ABC = 95° - 9x ----[Equation B]
Equating [Equation A] and [Equation B]
158° - 18x = 95° - 9x
-18x+9x = 95° - 158°
-9x = -63
divide both sides by -9
x = 7
Now, substituting the value x=7 in the [Equation A]
∠ABC = 158° - 18(7)
= 158° - 126°
= 32°
Thus,
∠ABC = 32°
what are the prime factors of 1,512?
Answer: the Prime Factors of 1512 are: 2, 2, 2, 3, 3, 3, 7.
Step-by-step explanation:
solve for the variable 12=5x+7
Answer:
would the variable be like one or something because 7 plus 5 is just 12 and that variable isn't needed so postive one
Step-by-step explanation:
brainlist plz thx
Answer: it is -1
Step-by-step explanation:
I just finished the test
I need help doing these questions asking for two column proofs.
Answer:
1. SSS
2. ASA
3. SAS
4. SSS
5. AAS
6. ASA
7. SSS
8. SAS
Step-by-step explanation:
How far does a horse travel if it gallops at an average speed of 15 km/h for 2 hours?
Answer:
30 km/h
Step-by-step explanation:
For every hour it goes 15 so for 2 hour 15x2 = 30.
WHICH ANIMAL IS CUTER?????
Answer:
panda
Step-by-step explanation:
Answer:
The pig because it so cute in my opinion
Helpppp Pleaseee....
Answer:
[tex] \frac{4 \sqrt{10} }{5} [/tex]
Step-by-step explanation:
[tex] \frac{8}{ \sqrt{10} } \times \frac{ \sqrt{10} }{ \sqrt{10} }[/tex]
[tex] \frac{8 \sqrt{10} }{ {\sqrt{10}}^{2} } [/tex]
[tex] \frac{8 \sqrt{10} }{10} [/tex]
[tex] \frac{4 \sqrt{10} }{5} [/tex]
Answer:
4√10/5
Step-by-step explanation:
8/√10
=8/√10 ×√10/√10
=8√10/√10√10
=8√10/10
=4√10/5 (ans)
=2.53 (approximately)
Aldo went to the store and purchased 8 notebooks for school. He gave the cashier a $20.00 bill and received$4.08. Each notebook cost the same amount. Describe the process you would use to find the cost of each notebook
Answer:
1.99 per notebook
Step-by-step explanation:
I did have an explanation here but someone *cough* *cough* laurenercsp6fpli deleted all my answers for no reason. But I did the math and I assure you that the answer is correct.
How many solutions does x + y = 1 and 2x + 2y = 2 have?
Answer:
2•(y +1) - 2y = 2 [2] 0 = 0 => Infinitely many solutions
Step-by-step explanation:
please help i begggggggggggggggg
Hi can you help with some ratio and proportion questions
Answer:
1a. 12 : 40
1b. 15 : 21
1c. 24 : 44
1d. 2 : 25
2. 40 boys and 100 girls
3. 96 girls
4. £71.43
5a. 9 : 4
5b. 3 : 1
5c. 3 : 5
6. 210 : 90
7. Sorry, I couldn't figure out how to solve this question :(
Step-by-step explanation:
Since I'll be using a similar method to solve these questions, I won't go into a detailed explanation for how I solved every single question. If you do need extra help, please ask in the comments below my answer.
1. Let's use part (a) as an example. The ratio is 3:10. To new ratio is ?:40. So, 10 becomes 40. What number multiplied by 10 equals 40? The answer is 4. If 10 is multiplied by 4, then 3 must be multiplied by 4 as well. 3*4 = 12, so the ratio is 12:40.
In part b the ratio is multiplied by 3, part c is 4, and part d is 1/2.
2. To solve this, add the values on both sides of the ratio together: 2 + 5 = 7. Now, divide the total number of pupils, 140, by 7: 140/7 = 20. Finally, multiply 20 by both sides of the ratio: 2 * 20:5 * 20 = 40:100. There are 40 boys and 100 girls.
3. To solve this I used the same method as the one I used in question 1.
4. The ratio is 5:140, where 140 becomes 2000. To solve, use the method used in question 1.
5. Simplifying ratios is the same as simplifying fractions. Find the greatest common factor of the values on both sides of the ratio and divide both sides by that factor. For example, in part a the factor for 45:20 is 5. 45/5 = 9 and 20/5 = 4. The ratio becomes 9:4.
For part b the factor is 9 and for part c the factor is 50.
6. Same method as was used in question 2.
Hope this helps :)
“ Triangle A has side lengths 3,4 and 5 . Triangle B has side lengths 6,7 and 8 “
“1. Explain how you know that triangle B is not similar to triangle A”
“2. Give possible side lengths for triangle B so that it is similar to triangle A”
Answer/Step-by-step explanation:
A. Given that ∆A has side lengths 3, 4, and 5, that corresponds to the side lengths 6, 7, and 8 of ∆B, both ∆s can only be similar to each other if the ratios of their corresponding side lengths are equal.
Thus:
[tex] \frac{3}{6} [/tex] ≠ [tex] \frac{4}{7} [/tex] ≠ [tex] \frac{5}{8} [/tex] .
✅The ratio of their corresponding side lengths is not equal, therefore, triangle B is not similar to triangle A.
B. To get the possible side lengths for triangle B to make it similar to triangle A, simply multiply each side length of triangle A by a scale factor.
Let's use a scale factor of 2.
3 × 2 = 6
4 × 2 = 8
5 × 2 = 10.
✅Possible side lengths for triangle B that will make it similar to triangle A are: 6, 8, and 10.
Subtract -2x^2+3x-9
from 8x^2+10x-10
Answer:
-6x^2 - 7x +1
Step-by-step explanation:
2x^2+3x-9 -(8x^2+10x-10)
3x^2+3x-9 -8x^2-10x+10
Combine like terms
-6x^2 - 7x +1
ASAP I need to know how to do these
1. idk
2. x^2+3x-4>0write 3x as a difference
x^2+4x-x-4>0
then factor out x from the expression
X x (x+4)-x-4>0
factor the negative sign
X x (x+4)- (x+4)>0
( x+4)x (x-1)>0
aneswer: (-∞ , -4) ( 1, + ∞)
BRAINLIEST GIVEN FOR CORRECT ANSWER. ANSWER 28, 30, AND 32
Answer:
that gabiella needs to get life like what a brat
Step-by-step explanation:
The height H in feet of a ball suspended from a spring as a function of time T in seconds can be modeled by the equation h=3sin (pi/2 (t+2))+5 which of the following is the graph of this equation
Answer:
From what I see, the answer is graph D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
The dimensions of a rectangular prism is 24 ft 20 feet and 15 feet what is the volume
Answer: 7200
Step-by-step explanation: the formulae is w times l times h. So you just multiply them all together. 24x15x20= 7200
Find the area of a triangle with a base length of 4 units and a height of 5 units. (1 point) 8 square units 9 square units 10 square units 20 square units
Answer:
10 square units
Step-by-step explanation:
Because to get the area of a triangle you cut the base length in half then multiply it by the height, in this case 2.5*4 = 10 square units
Answer:
The correct answer is 10 units.
Step-by-step explanation:
A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip took 7 hours?
Answer:
The fisherman row 14 mph
Step-by-step explanation:
downstream means to subtract so you subtract 6-4 which will gives you 2 then you multiply 2 times 7 which is 14 because it says hours.
Alright last question i need. Please if you can write out the steps on how to do this.
Answer:
y= x* 4
Step-by-step explanation:
x*n= y
0* 4= 0
1* 4= 4
2* 4= 8
3* 4= 12
4* 4= 16
x* 4= y
y= x* 4
Solve for x:
Question 9 options:
x = 10
x = 3
x = 30
x = 7
Joseph makes ornaments to sell at the craft fair. Each ornament requires 0.5 yards of velvet. At the fabric store, felt is sold by the foot. If Joseph wants to make 45 ornaments, how many feet of velvet must be buy? If the felt costs 10 cents ($0.10) per foot, what is the total cost of the velvet in dollars? A manufacture is making 1,000 times as many ornaments as Joseph to sell in stores nationwide. Write an expression using exponents to show how many yards of velvet the manufacture will need. Do not calculate the total.
Answer: See explanation
Step-by-step explanation:
A. Since each ornament requires 0.5 yards of velvet and Joseph wants to make 45 ornaments, the number of yards of velvet she must be buy will be:
= 45 × 0.5
= 22.5 yards
Since 1 yard = 3 feet
22.5 yards = 22.5 × 3 = 67.5 feet
B. If the felt costs 10 cents ($0.10) per foot, what is the total cost of the velvet in dollars.
Total Cost = 67.5 × $0.10 = $6.75
C. A manufacture is making 1,000 times as many ornaments as Joseph to sell in stores nationwide. The amount of yards needed will be:
= 1000(45 × 0.5)
Alex knows 18% of the students surveyed at his school are dropped off by car, while 22% walk or ride bikes, and the rest ride the bus.
Answer:
B
Step-by-step explanation:
How to find the value
Answer:
x = 4°
Step-by-step explanation:
According to exterior angle sum property , sum of two opposite interior angles of the triangle is equal to the exterior angle.
So, using exterior angle sum property :-
mBDC + mBCD = mWBC
=> 8x - 1 + 46° = 18x + 5
=> 18x - 8x = 46 - 1 - 5
=> 10x = 40
=> x = 4°
Is 1+4(3x-10)-12x equivalent to -9?
Answer:
No it is equal to -39
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
1+4(3x+10)-12x
1+12x+40-12x --> distribute
41+0x --> add like terms
1+4(3x+10)-12x = 41 not -9
40% of what number = 18
Answer:
The answer is 45
Step-by-step explanation:
Follow the steps:
set it up:
18/? = 40%/100%
18 x 100= 1800
1800 divided by 40 equals 45
Hope this helps! :)
since there are 5,280 feet in one mile and 3.3 feet in one meter how many meters per second are equivalent to 50 miles per hour
Given:
1 mile = 5280 feet
1 meter = 3.3 feet
convert 60 miles per hour to meters per second
60 miles to meters
60 miles x 5280ft x 1meter = (60*5280m)/3.3 = 316800m/3.3
1 mile 3.3ft
= 96,000 meters
1 hour to seconds
1 hour x 60 minutes x 60 seconds = 1 * 60 * 60sec = 3600 seconds
1 hour 1 minute
unit rate: meters per second
96000 meters ÷ 3600 seconds = 26 2400/3600
simplify 26 2400/3600 ⇒ 26 2/3 meters per second
2400 ÷ 1200 = 2
3600 ÷ 1200 = 3
Write the slope intercept form of the equation of each line plz
Answer: B . y = 5/6x + 7
Step-by-step explanation:
5x - 6y = - 42 To write it in slope intercept form, we need to solve for y.
-5x -5x Subtract 5x from both sides
-6y = -5x - 42 Divide both sides by -6
y = 5/6x + 7
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
5/8
Step-by-step explanation:
Answer:
it was 3/8 inches longer than the shorter bug.
Step-by-step explanation:
3/8 inches longer.
What is the binary number for 19
Answer:
the answer is 10011 hope it helps
Answer:
10011
Step-by-step explanation:
128 64 32 16 8 4 2 1
1 1 1 (fill the rest with zeros, ignore left zero)
16+2+1 = 19