To make expressions in mathematics we must set a variable value that varies according to the conditions of our problem.
Let's define what a mathematical expression is:
Mathematical (algebraic) expressionAlgebraic expressions are expressions composed of numbers and letters, where the letters are called variables and each of them adopts a specific value according to the process in which it is used.
To make an expression in mathematics you must set a variable, since an expression is a numerical solution of a process, and by having a variable we will have the result on it, for example:
I have a business and every day I earn 2 times more than the previous day:
variable = profit = xvariable = number of day = nexpression:
x = 2n
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3. The width of a rectangle is 4 feet less than the length. The area is
12 ft. Find the dimensions of the rectangle.
Answer:
L = 6, w = 2
Step-by-step explanation:
Let w = width of rectangle
Let L = length of rectangle
w = L - 4
Area of rectangle = Lw
L (L - 4) = 12
L^2 - 4L = 12
L^2 - 4L - 12 = 0
(L - 6)(L + 2) = 0
L - 6 = 0
L = 6 (the other option doesn't work because dimensions can't be negative)
w = L - 4
w = 6 - 4
w = 2
Double check
A = Lw
A = 6 x 2
A = 12
It matches so we are right.
A bird flying at an elevation of 110 ft swoops down to grab a mouse on top of a 3 foot tall rock. What is the change in the birds elevation?
Answer:
Bird swoops down by 107 feet to grab a mouse on top of a [tex]3[/tex] foot tall rock
Step-by-step explanation:
Given
The level of mouse from the ground is [tex]3[/tex] foot as it is on the top of a [tex]3[/tex] foot tall rock.
The level of bird at which it is flying from the ground is [tex]110[/tex] feet
Change in elevation when the bird swoops down to grab the mouse
[tex]= 110 -3\\= 107[/tex]feet
Bird swoops down by 107 feet to grab a mouse on top of a [tex]3[/tex] foot tall rock
he line segment is rotated by 270 degrees counterclockwise about the origin to form C′D′. Which statement describes C′D′?
1. C′D′ is 4 units long.
2. C′D′ is 8 units long.
3. C′D′ is parallel to CD.
4. C′D′ is half the length of CD.
Answer:
it is parrell
Step-by-step explanation:
 Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III
Given:
[tex]\sin x=-\dfrac{15}{17}[/tex]
x lies in the III quadrant.
To find:
The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].
Solution:
It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.
We know that,
[tex]\sin^2 x+\cos^2 x=1[/tex]
[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]
[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]
[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]
x lies in the III quadrant. So,
[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]
[tex]\cos x=-\dfrac{8}{17}[/tex]
Now,
[tex]\sin 2x=2\sin x\cos x[/tex]
[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]
[tex]\sin 2x=-\dfrac{240}{289}[/tex]
And,
[tex]\cos 2x=1-2\sin^2x[/tex]
[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]
[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]
[tex]\cos 2x=\dfrac{289-450}{289}[/tex]
[tex]\cos 2x=-\dfrac{161}{289}[/tex]
We know that,
[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]
[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]
[tex]\tan 2x=\dfrac{240}{161}[/tex]
Therefore, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
Write an equation to represent the situation. Cayla was going to sell all of her stamp collection to buy video game after selling half of them she changed her mind she then bought four more. How many did she start with if she now has 26.
Answer:
[tex]y = \frac{1}{2}x + 4\\\\[/tex]
Cayla started with 44 stamps
Step-by-step explanation:
Let x = the number of stamps in Cayla's stamp collection;
[tex]y=\frac{1}{2}x + 4[/tex]
[tex]26 = \frac{1}{2}x + 4\\\\22 = \frac{1}{2}x\\\\44 = x[/tex]
Which is more 35 inches or 3 feet
Answer:
3 feet
Step-by-step explanation:
3 feet is more because 35 inches = 2 feet and 11 inches.
Taylor is producing graphic T-shirts that
will come in three different colors. He
randomly surveys 100 people, asking which
one of the three colors they prefer. Of the
100 people surveyed,55 say that they prefer
the white T-shirt. If Taylor is going to produce
500 graphic T-shirts, about how many should
be white?
If Taylor is producing graphic T-shirts that will come in three different colors then about 275 graphic T-shirts should be white.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Since Taylor randomly surveyed 100 people and 55 of them said they prefer the white T-shirt
we can estimate the proportion of people who prefer the white T-shirt as:
p = 55/100 = 0.55
We can assume that this proportion is a good estimate of the true proportion of people who will prefer the white T-shirt among all potential customers.
To estimate the number of people who will prefer the white T-shirt among 500 potential customers
The formula for the expected value of a binomial random variable is
E(x) = np
Substituting the values, we get:
E(x) = 500 × 0.55 = 275
Therefore, about 275 graphic T-shirts should be white.
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Cindy put equal sized marbles into a bowl. Then, she shook the bowl until 3 marbles fell out. Is this a random sample of the marbles? YESS OR NOO?
ANSWER FAST!!
Answer:
Yes
Step-by-step explanation:
I'm assuming this is right
2 1/5+6 4/5 6 5/12 -2 1/12 11 8/9+4 1/3 7 1/6-5 3/4 11/18+ 6 1/10 15 1/3- 2 5/8 mixed numbers
Answer:
2 1/5+6 4/5 = 9
6 5/12 -2 1/12 = 4 1/3
11 8/9+4 1/3 =16 2/9
7 1/6-5 3/4 = 1 5/12
11/18+ 6 1/10 = 6 64/90
15 1/3- 2 5/8 = 12 17/24
Step-by-step explanation:
Using the technique of mixed numbers to add the fractions
2 1/5+6 4/5
=2+6 + 1/5+4/5 add the whole numbers separately and then the fractions
=8 5/5= 9
6 5/12 -2 1/12
=6-2 + 5-1/12
=4 4/12
= 4 1/3
11 8/9+4 1/3
=11+4 +8/9+1/3 adding the whole numbers separately
=15 + 8+3/9
= 15+11/9 adding the fractions separately
= 15+1+2/9
= 16+2/9
=16 2/9
7 1/6-5 3/4
= 7-5 +1/6 -3/4 subtracting the whole numbers separately
= 2+ 2-9/12 subtracting the fractions separately
= 2-7/12
= 24-7/12
= 17/12
=1 5/12
11/18+ 6 1/10
= 11/18 + 61/10
= 110 +1098/180
= 1208/180
= 6 128/180
= 6 64/90
15 1/3- 2 5/8
=15- 2 + 1/3- 5/8
=13 + 8- 15/24
= 13 + -7/24
= 312-7/24
= 12 17/24
Can someone please help me with this because I don’t get it
Answer:
161
Step-by-step explanation:
the sum of the two interior angles equals that exterior angle
121+40=161
Jose wants to pay off his credit card balances within 18 months. He is trying to decide if he should use his $1,750 in
savings to pay off part of the balances or if he should transfer the balances to a new card with a low introductory
rate. The new credit card has an introductory rate of 8% but charges a balance transfer fee of $60 for each balance
transfer. Jose decides to pay off Credit Card B using his savings and then transfer the balance of Card A to the new
card. Which of the following options shows the amount of Jose's new monthly payment?
Credit Card A: $1,154
Credit Card B $1,469
A. $90.43
B. $68.25
C. $71 80
D. $75.34
Answer:
ANSWER IS C: 71.80
Step-by-step explanation:
hope this helps :D you got this!!
The amount that corresponds to the new monthly payment of Jose is approximately $75.34. Hence, option D is correct.
What is use of credit card ?Credit cards are a widely used financial tool that allow individuals to make purchases on credit. The main use of a credit card is to allow the cardholder to borrow money from the card issuer
If Jose decides to pay off Credit Card B using his savings of $1,750, he will have a remaining balance of $1,154 on Credit Card A.
If he transfers the balance of Credit Card A to the new card with a low introductory rate of 8%, he will incur a balance transfer fee of $60.
The total balance transferred = $1,154 + $60 = $1,214.
To determine his new monthly payment, we need to calculate the monthly interest rate on the new card.
At an annual interest rate of 8%, the monthly interest rate is :
8% / 12 = 0.67%.
Using an online loan calculator or spreadsheet, we can calculate that the monthly payment required to pay off a balance of $1,214 in 18 months at a monthly interest rate of 0.67% is $75.34 (rounded to the nearest cent).
Therefore, the answer is D. $75.34, which represents Jose's new monthly payment.
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what is the answer please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
22/75
Step-by-step explanation:
To find the average add up the values and divide the sum by the number of values.
Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem
=1/2+1/5+1/5+1/10+7/15
The least common denominator (LCD) is: 30.
Rewriting as equivalent fractions with the LCD:
=15/30+6/30+6/30+3/30+14/30
Rewriting numerators over the common denominator,
=15+6+6+3+1430
Totaling the numerator:
=44/30
Reducing the fraction:
=22/15
Dividing by the number of values: 5
22/15÷5=22/15×15=22/75
Average of the fractions is:
Average=22/75
please help me do it
Answer:
D) FJ is a perpendicular bisector
The PS4 cost $650 when it first came out. Two years later it was only worth $250. By what percentage did the price decrease?
Answer:
It decreased by 61.5%
Step-by-step explanation:
With spring break approaching, Travis plans to play more 2k every day. Right nowhe plays about 40 minutes per day. He expects that number will increase by 10 minutes per day
Write an equation that shows the number of minutes of 2k played as a function of the day
You are planning to go to the movies tonight, but you only have 25
dollars to spend. The ticket for the movie that you want to see is 9
dollars plus 4 dollars for each snack. Write an equation that would
represent how many snacks you can buy after purchasing the ticket. Use
x to represent the number of snacks purchased.
Answer:
9+4x=25
Step-by-step explanation:
Bruce drewa scale of a resturaunt the scale he used was 1 milimeter 10 meters the resteraunt kitchen is 3 milimeters long in the drawing how long is the actual kitchen
Answer: 30 meters.
Step-by-step explanation:
Since the scale used by Bruce in the drawing that she made is:
1 milimeter = 10 meters
If the restaurant kitchen is 3 milimeters long in the drawing, the length of the actual kitchen will then be:
1/3 = 10/x
Cross multiply
1 × x = 3 × 10
x = 30
Therefore, the actual length is 30 meters.
[tex]product \: of \: 5x \: 6y \: and7z[/tex]
Answer:
210xyz
Step-by-step explanation:
Given
5x × 6y × 7z
= 5 × x × 6 × y × 7 × z
= 5 × 6 × 7 × x × y × z
= 210xyz
PLEASE HELP ASAP PLEASE
Please hurry!!!! I need answer ASAP!!!!!
David wants to buy a new bicycle
that cost $295 before a 40%
discount. He finds the cost after the
discount, in dollars, by evaluating
295 – 295(0.40). His brother Michael
finds the same cost by evaluating
295(1 – 0.40). What property can be
used to justify that these two
expressions represent the same cost
after the discount?
A. associative property
B. cominutative property
C. distributive property
D. subtraction property of equality
Answer:
subtraction property for sure its that
Need help! Marking brainliest. Need step by step solution
Answer:
400 J
Step-by-step explanation:
Kinetic energy = ½ mv²
mass = 50 kg
velocity = 4 m/s
Kinetic energy = ½×50×(4)²
= ½×50×16
= 50×8
= 400 J
Option Four
[tex]mass(m) = 50kg \\ velocity(v) = 4ms {}^{ - 1} \\ kinetic \: energy = \frac{1}{2} mv {}^{2} \\ = \frac{1}{2} \times 50 \times (4) {}^{2} \\ = 400[/tex]
Which one? Do i chose
Answer:
226 inches cube
Step-by-step explanation:
The volume of the cylinder is the area of the base X height therefore it would be 3^2 * 3.14 * 8 = 72 * 3.14 = 226.08.
Answer:
151 in^3
Step-by-step explanation:
pi x 3^2 x 5.5 (the approximate water level)
= 155
151 is the closest answer
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Answer: 3.6
Step-by-step explanation:
Using pythagorean we can determine that a^2+b^2=c^2
In this case the leg and adjacent make a distance of 2 and 3 we can substitute for a and b so
[tex]2^{2}+3^{2}=c^{2}[/tex]
13=[tex]c^{2}[/tex]
c= 3.605 rounded is 3.6
What is -8w-4 simplified?
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]
[tex] - 4(2w + 1)[/tex]
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]
[tex] - 8w - 4[/tex]
Bind the expression with the common factor -4
[tex] - 8w - 4[/tex]
#❀CARRY ON LEARNING❀#❀KEEP ON LEARNING❀#❀LEARNING IS FUN❀#❀LETS LEARN❀#❀NoToCopyPaste❀❀hope it helps(◕ᴗ◕✿)❀❀Keep safe!❀シ︎Answer: −4(2w+1)
Step-by-step explanation: Hope this help :D
A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water
bottle. Which of the following methods would work to create the larger water bottle with the intended volume?
1. Double the radius of the original water bottle. Keep the height the same.
II. Double the height of the original water bottle. Keep the radius the same.
III. Double the height and double the radius of the original water bottle
IV. Quadruple the height of the original water bottle. Keep the radius the same
o I and IV
O I and 11
O I, II, III, and IV
O III and IV
Answer:
option 3, double the height and with of original bottle
The methods which will create the larger water bottle with the intended volume is 1 and IV.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water bottle.
Volume of a cylindrical shape = π r² h
Let V be the original volume.
If radius is doubled, then the new volume is,
V' = π (2r)² h = 4(π r² h) = 4V
So 1 is an option.
When the height is Quadrupled,
V' = π r² 4h = 4(π r² h) = 4V
Hence the correct options are 1 and IV.
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Andresssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
Anderess?
Step-by-step explanation:
A classmate stated, "A concave polygon be can be regular because it can have all sides congruent." Is this student's claim valid?
Why or why not?
Answer:
No.
Step-by-step explanation:
A regular polygon has all sides and angles congruent. This is not possible with a concave polygon. If the sides are congruent in a concave polygon the angles are not congruent.
HELP ASAP PLS!!! I WILL MARK BRAINLIEST, PROMISE!!!
Select the correct answer.
Which number is a rational number?
this is for PLATO, btw
Answer: 17.156
Step-by-step explanation:
A rational number is any number that has a pattern (in decimals) and can be written as a fraction. 17.156 is a terminating decimal. So its a predicting pattern therefore is a rational number.
Confused on this one help me solve for point B
Answer:
1,-1
Step-by-step explanation:
because section be is for +,-
Answer:
1,-1
Step-by-step explanation:
What is the SLOPE and Y-INTERCEPT of the following equation. y = -x +7