Answer:
Algebra (from Arabic: الجبر al-jabr, meaning "reunion of broken parts"[1] and "bonesetting"[2]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;[3] it is a unifying thread of almost all of mathematics.[4] It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[5] For example, in {\displaystyle x+2=5}x+2=5 the letter {\displaystyle x}x is an unknown, but applying additive inverses can reveal its value: {\displaystyle x=3}x=3. In E = mc2, the letters {\displaystyle E}E and {\displaystyle m}m are variables, and the letter {\displaystyle c}c is a constant, the speed of light in a vacuum. Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words.
The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.
A mathematician who does research in algebra is called an algebraist.
In the triangle below,
y = [ ? ]°. Round to the nearest
tenth.
ly
8 cm
90°
X
10 cm
I
Enter
9514 1404 393
Answer:
51.3°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle.
Here, you're given the side opposite angle y and the side adjacent to it. This suggests that the TOA relationship is most useful:
Tan = Opposite/Adjacent
tan(y) = (10 cm)/(8 cm) = 1.25
Then the angle is found from the inverse tangent function:
y = arctan(1.25)
y ≈ 51.3°
What is the volume of the rectangular prism?
Answer:
15 0/0
Step-by-step explanation:
15 cubes on each side which totals to 30 cubes. To get the volume 15 cm multiply 30 x 1/2 = 15 the amount of volume
Answer:
15[tex]cm^{3}[/tex]
Step-by-step explanation:
ok...each of those boxes are 1/2 cm
What is the easiest thing to do is to count the front of the rectangular prism and there are 15 cubes. Now double it, and you get 30 cubes, now since each cube is 1/2 or 0.5, we get can do 0.5 x 30 and we get 15
Hope this helped!
Have a supercalifragilisticexpialidocious day!
sophie uses 18 beads to make a neckalace , 3/6 of the beads are purple
Answer:
9 beads are purple
Step-by-step explanation:
we know that
To find out how many beads are purple, multiply the total beads by the fraction of the beads that are purple
so
therefore
9 beads are purple
Another way to solve the problem is convert the fraction in percentage
we have
so
If the total are 18 beads
50% is 9 beads
therefore
9 beads are purple
Change 8.94 into a fraction
Answer:
447 / 50
Step-by-step explanation:
447 / 50 Because if you divide it you will get 8.94 same answer
Answer:
inproper fraction would be 447/50 but the proper fraction would be 8 47/50
"What is the difference between a ratio and its related rate and unit rate?"
Answer:
Step-by-step explanation:
The ratio is the relationship of two numbers. ... A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1.
The difference between ratio and unit rate is that both of them are measures of two units and are written in the form of a numerator and a denominator but the unit rate denominator must be one.
What is a ratio?It shows how many times one value is contained in another value.
The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Ratio and unit rate
Ratio and unit rate both are written in the form of a numerator and a denominator.
The ratio is a measure of two units contained in a whole amount.
Example: 3 apples and 3 mangoes are contained in a bag
The ratio of apple and mango is 3:3 = 1:1
The unit rate is also a measure between two units but the denominator should always be one.
Example: A man can run 10 miles in 10 hours
In one hour 1 mile.
The unit ratio is 10miles per hour.
Thus,
The difference between ratio and unit rate is that both of them are measures of two units and are written in the form of a numerator and a denominator but the unit rate denominator must be one.
Learn more about ratios here:
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Andre says that x is 7 because he can move the two 1s with the x to the other side.
Do you agree with Andre?
The image necessary to answer this question is below in the attachment.
Answer: No.
Step-by-step explanation: For this hanger to be in equilibrium, both sides have to equal.
The diagram can be represented as
x + 1 + 1 = 1 + 1 + 1 + 1 + 1
x + 2 = 5
x = 3
So, for this hanger to work, x = 3.
Average of 5 numbers is 7. Four of the numbers are 3, 5, 7 and 9. Find the 5th number is
Triangle Sum Theorem Review The following is a review of an important theorem from first semester. Please complete problems 2-4 and submit. Problem 1 is done for you to model the theorem as a review.
9514 1404 393
Answer:
see the attachment
Step-by-step explanation:
The sum of angles is 180°, so the value of x is found by subtracting the given angles from 180°.
For example, ...
2. x = 180° -23° -68° = 89°
__
When a number of similar calculations are required, I like to enter the formula once and let a spreadsheet do the math. In the attached, the units of x are degrees. The problems are in order 1–4.
A prize was awarded to 24 women and 1010 men.
a. What fraction of the prize winners were women?
b. What fraction were men?
Answer:
[tex]W = \frac{12}{17}[/tex] -- Women
[tex]M = \frac{5}{17}[/tex] --- Men
Step-by-step explanation:
Given
[tex]Men = 10[/tex] --- not 1010
[tex]Women = 24[/tex]
Solving (a) Fraction of Women
This is calculated as:
[tex]W = \frac{Women}{Men + Women}[/tex]
Substitute values for Women and Men
[tex]W = \frac{24}{10+24}[/tex]
[tex]W = \frac{24}{34}[/tex]
Simplify fraction
[tex]W = \frac{12}{17}[/tex]
Solving (b) Fraction of Men
This is calculated as:
[tex]M = \frac{Men}{Men + Women}[/tex]
Substitute values for Women and Men
[tex]M = \frac{10}{10+24}[/tex]
[tex]M = \frac{10}{34}[/tex]
Simplify fraction
[tex]M = \frac{5}{17}[/tex]
What is the minimum depth of the water in the pool?
1 foot
2 feet
3 feet
4 feet
Answer:
1 foot
Step-by-step explanation:
The minimum value is the lowest y-value on the graph. The graph shows that at 6 hours there is only 1 foot of water in the pool. In this case, the y-values never go below 1, this must mean that 1 is the minimum.
Work out the circumference of this circle with radius 7.5cm
Take pi to be 3.142
Answer:
15pi cm or 47.12
Step-by-step explanation:
Radius= 7.5cm
7.5 x 2 = 15
diameter= 15cm
circumference = pi x diameter
circumference= pi x 15
=15pi cm or 47.12
What is the distance between (4, 3) and (9, 15) on the coordinate plane? Select two that apply.
V169 units
V144 units
5 units
13 units
12 units
Answer:
169 units
13 units
The distance between the two points (4, 3) and (9, 15) will be 13 units. Then the correct options are A and D.
What is the distance between two points?Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The coordinate of the points is given below.
(4, 3) and (9, 15)
Then the distance between the two points (4, 3) and (9, 15) will be given as,
D² = (9 - 4)² + (15 - 3)²
D² = 5² + 12²
D² = 25 + 144
D² = 169
D = 13 units
The distance between the two points (4, 3) and (9, 15) will be 13 units. Then the correct options are A and D.
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Would the hypotenuse of a right triangle with a vertical length of 6 and a horizontal length of 10 have the same slope as the hypotenuse of the blue and red
triangles shown in the graph?
The length of each side of parallelogram RSTU is multiplied by three to create parallelogram WXYZ.
What is the ratio of the area of parallelogram RSTU to the area of parallelogram WXYZ?
A.1:3
B.1:6
C.1:9
D.1:27
E.1:81
Answer:
I believe A?
Step-by-step explanation:
The table gives information about the lengths of time, in hours, some children
spent watching TV last week.
Length of time (7) Frequency
0
8
3
3
10
15
15
10
20
11
2
Frequency density
Draw a histogram for
the information in the table.
1
0+
0
10
30
40
20
Length of time (t)
Answer:
Step-by-step explanation:
The histogram of the distribution plotted with the frequency density on the y - axis and the interval for the length of time on the x - axis is attached below.
The first bar denotes the length of time between 0 and 10 having a frequency of 8 The second bar denoted the interval between 10 and 15 with a frequency of 15 The third bar denoted the interval between 15 and 20 with a frequency of 10The fourth bar denoted the interval between 20 and 30 with a frequency of 11Therefore, the histogram of the distribution is attached below.
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If you had a million dollars what would you do with it?????
PLZ don't report...
Answer:
a huge mansion out somehwere in europe or go traveling around the world
Step-by-step explanation:
can you imagine wow
Answer:
I would give some to people who are homeless and need help paying rent and ig get a mansion.
Step-by-step explanation: Ty for free pointz. Have a great day!
You have 4.5 pounds of egg whites. You need 8 oz to make one serving of consomme. How many can you
Question 4 Not Yet Answered Points Out Of 1.00 You Have 4.5 Pounds Of Egg Whites. You Need 8 Oz To Make One Serving Of Consomme. How Many Servings Can You Make? Answer: Swer
swer
Determine the greatest common factor of the given expressions.
75m^4p^6(-m + n)
65m^4 n^5(-m + n)^5
Answer:
75m^4 p^6
Step-by-step explanation:
Solve for w. -2 > W - 12
Answer:
10 > w
Step-by-step explanation:
-2 > w-12
Add 12 to both sides of the equation in order to isolate w
-2+12 > w-12+12This will cancel out 12 on the right side of the inequality as well as give the value of w on the left side of the inequality.
10 > wstate whether the two triangles are similar, and if so, by which theorem? justify your answer
Answer:
it's a congruent triangle and the scale factor is 2
Step-by-step explanation:
i don't know what you mean by theorems if you mean circle theorems well that obviously is not a circle so it's not one.
Find the X and Y intercept of line 2x+3y=-12
X-intercept -
Y- Intercept-
Answer:
Let us rearrange 3y=-2x-12y=-2/3x-4 So y intercept is -4 I also do exams and quizzes if your interested :)Robert mixed 113 liters of blue paint with 123 liters of red paint to make 3 liters of purple paint. To make a new batch of purple paint he used 2 liters of red paint. Using the same ratio, Robert should use Response area liters of blue paint .
Answer:
[tex]Blue =1\frac{3}{5}[/tex]
Step-by-step explanation:
Given
[tex]Blue = 1\frac{1}{3}[/tex]
[tex]Red = 1\frac{2}{3}[/tex]
Required
Determine the amount of blue paint when Red = 2
To do this, we make use of the following equivalent ratios
[tex]Ratio = Blue : Red[/tex]
When [tex]Blue = 1\frac{1}{3}[/tex] and [tex]Red = 1\frac{2}{3}[/tex]
[tex]Ratio = 1\frac{1}{3} : 1\frac{2}{3}[/tex]
When Red = 2
[tex]Ratio = Blue : 2[/tex]
Equate both ratios
[tex]Blue : 2 = 1\frac{1}{3} : 1\frac{2}{3}[/tex]
Convert to division
[tex]\frac{Blue}{2} =1\frac{1}{3} / 1\frac{2}{3}[/tex]
Convert fractions to improper fraction
[tex]\frac{Blue}{2} =\frac{4}{3} / \frac{5}{3}[/tex]
[tex]\frac{Blue}{2} =\frac{4}{3} * \frac{3}{5}[/tex]
[tex]\frac{Blue}{2} =\frac{4}{5}[/tex]
Make Blue the subject
[tex]Blue =\frac{4}{5}*2[/tex]
[tex]Blue =\frac{8}{5}[/tex]
[tex]Blue =1\frac{3}{5}[/tex]
Determine the value of x in the figure
A) x = 8
B) x = -4
C) x = 4
D) x = 4/3
Answer:
Step-by-step explanation:
X=8
A group of people went to a restaurant.
Each person chose one starter and one main course.
starter
main course
soup
lasagne
prawns
curry
the number of people who chose soup: the number of people who chose prawns = 2:3
Of those who chose soup,
the number of people who chose lasagne : the number of people who chose curry = 5:3
Of those who chose prawns,
the number of people who chose lasagne : the number of people who chose curry = 1:5
What fraction of the people chose curry?
Answer:
The fraction of the people who choose curry = [tex]\frac{13}{4}[/tex]
Step-by-step explanation:
As given,
Starter Main course
Soup Lasagna
Prawns Curry
The number of people who choose soup: the number of people who choose prawns = 2 : 3
Of those who chose soup,
The number of people who choose Lasagna : the number of people who chose curry = 5 : 3
Of those who chose prawns,
The number of people who chose Lasagna : the number of people who chose curry = 1 : 5
Let total number of people goes to restaurant = 5x
People who choose soup = [tex]\frac{2}{5}[/tex]×5x = 2x
People who choose prawns = [tex]\frac{3}{5}[/tex]×5x = 3x
Now, given,
Of those who choose soup,
The number of people who choose Lasagna : the number of people who chose curry = 5 : 3
So,
People who choose Lasagna after choosing soup = [tex]\frac{5}{8}[/tex]×2x = [tex]\frac{5}{4}x[/tex]
People who choose Curry after choosing soup = [tex]\frac{3}{8}[/tex]×2x = [tex]\frac{3}{4}x[/tex]
Also, given,
Of those who chose prawns,
The number of people who chose Lasagna : the number of people who chose curry = 1 : 5
So,
People who choose Lasagna after choosing prawns = [tex]\frac{1}{6}[/tex]×3x = [tex]\frac{1}{2}x[/tex]
People who choose Curry after choosing prawns = [tex]\frac{5}{6}[/tex]×3x = [tex]\frac{5}{2}x[/tex]
So,
Total number of people who choose curry = [tex]\frac{3}{4}x[/tex] + [tex]\frac{5}{2}x[/tex] = [tex]x ( \frac{3}{4} + \frac{5}{2} ) = x (\frac{3 + 10}{4} ) = x ( \frac{13}{4} ) = \frac{13}{4}x[/tex]
So ,
The fraction of the people who choose curry = [tex]\frac{Total number of people who choose curry}{Total number of people who go to restaurant} = \frac{\frac{13}{4} x}{x} = \frac{13}{4}[/tex]
A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by
(25t2 + 150t + 100)/(t2 + 6t + 24)
A) Find the rate at which Glen Cove's population is changing with respect to time.
B) What will be the population after 10 years?
C) At what rate will the population be increasing when t = 10?
Answer:
See explanation
Step-by-step explanation:
We have that;
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
a) rate at which Glen Cove's population is changing with respect to time.
dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
b) population after 10 years
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)
P(t) = 4100/184
P(t) = 22283
c) when t = 10
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2
dP/dt = 13000/33856
dP/dt = 0.384
The length of a rectangle is 2ft longer than its width.
If the perimeter of the rectangle is 40ft , find its area.
Select the algebraic expression for the word expression.
24 less than h
24 - h
24 - h
h - 24
h - 24
24 ÷ h
24 ÷ h
h
Step-by-step explanation:
The Answer Is 24 - h
As, 24 Is Less Than "h"
What is an equivalent expression for 3(x-12)? *
O
3x-12
3x+12
O
3x-36
3x+36
Answer:
3x-36 is equivalent to 3(x-12)
Line m is intersected by line t , as shown in the diagram below. Based on the diagram, which of the following equations must be true? A m∠1+m∠2=180°
B m∠1+m∠3=180°
C m∠2+m∠3=90°
D m∠2+m∠4=90°
the answer is quite simple on this one. angles 1 and 3 are equal, and angles 2 and 4 are equal.
if you thi k about moving line t then you can see 2 and 4 will not add to 90°. angles 2 and 3 do not add to 90° because their angles added make a straight line (180°). answer B is almost true but not quite since the angles are not perpendicular to each other (1 and 3).
therefore, answer is A because of said explanation about answer B in previous paragraph. they make a straight line (180°). just basic geometry.
0.12 divided by 5.676
Answer:
47.3
Step-by-step explanation: