The area of circle with radius 42.5 m is 5671.875 m².
What is area?In mathematics, the area is the measure of the size of a surface, usually expressed in square units such as square meters or square feet. It is the extent of a two-dimensional region enclosed within a specified boundary. The formula for finding the area of basic shapes such as rectangles, triangles, and circles may differ, but the concept of area remains the same.
Here,
Given:
C = 85π meters
D = 85 meters
We know that the diameter of a circle is twice its radius, so:
R = D/2 = 85/2 = 42.5 meters
The circumference of a circle is given by the formula:
C = 2πR
Substituting the value of R, we get:
C = 2π(42.5) = 85π meters
The area of a circle is given by the formula:
A = πR²
Substituting the value of R, we get:
A = π(42.5)²
= 5671.875 square meters (rounded to four decimal places)
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Given the grammar G =(V,T,S,P), where V = {a,b,c,A,B,C,S},
T={a,b,c},S is the starting symbol, and the productions are:
S → AB
A → Ca
B → Ba
B → Cb
B → b
C → cb
C → b.
use top-down parsing (i.e., start with the starting symbol) to determine whether each of the following strings belong to the language:
a) baba b) abab
c) cbaba d) bbbcba
Using the top-down parsing technique it is obtained that the given strings belong to the language generated by the grammar.
What is parsing technique?
The process of analyzing a text that contains a sequence of tokens to ascertain its grammatical structure in relation to a particular grammar is known as parsing, also known as syntax analysis.
We can use the top-down parsing technique to determine whether each of the given strings belongs to the language generated by the given grammar.
Starting with the starting symbol S, we have the following steps -
a) baba -
S → AB
→ CBa
→ bBa
→ bbA
→ bba
Therefore, baba belongs to the language.
b) abab -
S → AB
→ CAaB
→ abAB
→ abCB
→ abBb
→ abCb
→ abb
Therefore, abab belongs to the language.
c) cbaba -
S → AB
→ CBa
→ cBa
→ cbA
→ cba
Therefore, cbaba belongs to the language.
d) bbbcba -S → AB
→ CBa
→ bBa
→ bbA
→ bbbC
→ bbbcB
→ bbbcbB
→ bbbcbcA
→ bbbcbca
Therefore, bbbcba belongs to the language.
Therefore, all of the given strings belong to the language generated by the given grammar.
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An asset is purchased on January 1 at a cost of $78,000. It is expected to be used for five years and have a salvage value of $8,000. Calculate the depreciation expense for each year of the asset's useful life under each of the following methods:
a. Straight-line method
b. Double-declining-balance method
c. Sum-of-the-years’-digits method
The depreciation expense for each year of the asset's useful life is $10
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Asset cost=78000
After 5 years=8000
Now,
a. Straight-line method:
Depreciable cost = Cost - Salvage value
Depreciable cost = $78,000 - $8,000
Depreciable cost = $70,000
Depreciation expense per year = Depreciable cost / Useful life
Depreciation expense per year = $70,000 / 5 years
Depreciation expense per year = $14,000
Therefore, the depreciation expense for each year of the asset's useful life under the straight-line method is:
Year 1: $14,000
Year 2: $14,000
Year 3: $14,000
Year 4: $14,000
Year 5: $14,000
b. Double-declining-balance method:
Straight-line rate = 1 / Useful life
Straight-line rate = 1 / 5
Straight-line rate = 0.2 or 20%
Double-declining-balance rate = 2 x Straight-line rate
Double-declining-balance rate = 2 x 0.2
Double-declining-balance rate = 0.4 or 40%
Year 1 depreciation expense = Book value x Double-declining-balance rate
Year 1 depreciation expense = $78,000 x 40%
Year 1 depreciation expense = $31,200
Book value at the end of Year 1 = Cost - Year 1 depreciation expense
Book value at the end of Year 1 = $78,000 - $31,200
Book value at the end of Year 1 = $46,800
Year 2 depreciation expense = Book value x Double-declining-balance rate
Year 2 depreciation expense = $46,800 x 40%
Year 2 depreciation expense = $18,720
Book value at the end of Year 2 = Book value at the end of Year 1 - Year 2 depreciation expense
Book value at the end of Year 2 = $46,800 - $18,720
Book value at the end of Year 2 = $28,080
Year 3 depreciation expense = Book value x Double-declining-balance rate
Year 3 depreciation expense = $28,080 x 40%
Year 3 depreciation expense = $11,232
Book value at the end of Year 3 = Book value at the end of Year 2 - Year 3 depreciation expense
Book value at the end of Year 3 = $28,080 - $11,232
Book value at the end of Year 3 = $16,848
Year 4 depreciation expense = Book value x Double-declining-balance rate
Year 4 depreciation expense = $16,848 x 40%
Year 4 depreciation expense = $6,739.20
Book value at the end of Year 4 = Book value at the end of Year 3 - Year 4 depreciation expense
Book value at the end of Year 4 = $16,848 - $6,739.20
Book value at the end of Year 4 = $10,108.80
Year 5 depreciation expense = Book value x Double-declining-balance rate=$10
Therefore by algebra answer will be $10.
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Find the equation of the straight line passing through the point (0, -1)
which is perpendicular to the line
y=-3/4x-3
Answer:
Step-by-step explanation:
The given equation of the line is y = (-3/4)x - 3.
To find the equation of a line perpendicular to this line, we need to determine its slope first.
The slope of the given line is -3/4.
Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of -3/4, which is 4/3.
So the slope of the line passing through (0, -1) and perpendicular to the given line is 4/3.
Using the point-slope form of the equation of a line, we can write:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting the values we have, we get:
y - (-1) = (4/3)(x - 0)
Simplifying, we get:
y + 1 = (4/3)x
Subtracting 1 from both sides, we get:
y = (4/3)x - 1
Therefore, the equation of the straight line passing through the point (0, -1) and perpendicular to the line y = (-3/4)x - 3 is y = (4/3)x - 1.
Answer:
y = (4/3)x - 1.
Step-by-step explanation:
we have
y=-3/4x-3
comparing it with y=mx+c
where m is the slope and is c the y-intercept.
we get
slope (m) = -3/4.
Any line perpendicular to it will have a slope that is the negative reciprocal of -3/4, which is 4/3.
Let's call the equation of the line we're trying to find y = mx + b, where m is the slope and b is the y-intercept.
We know that the line passes through the point (0, -1), so we can substitute these values into the equation to get:
-1 = (4/3)(0) + b
Simplifying this, we get:
-1 = b
So the y-intercept of our line is -1.
Now we can substitute the slope and y-intercept into the equation to get:
y = (4/3)x - 1
Therefore, the equation of the straight line passing through the point (0, -1) which is perpendicular to the line y=-3/4x-3 is y = (4/3)x - 1.
For any element a in any group G, prove that < a > is a
subgroup of C(a) (the centralizer of a).
To reflect the point A=(7,3) over the x-axis, we need to keep the x-coordinate the same and negate the y-coordinate. So the reflected point A' is:
A' = (7, -3)
Therefore, the reflected point A' over the x-axis is (7, -3).
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20\30 + 1 over 3 =. On a number line grade 8 math
Consequently, the answer is 1. We can note the spot on the line marked "1" to plot this on a number line, and that would be the answer.
What is the equation's solution?Any number of the variable that renders the Left Hand Side (LHS) and or the Right Hand Side (RHS) of a equation equal is considered an answer to the equation. To answer a problem, one must identify its solution or solutions.
20/30 + 1/3 = (20/30) + (10/30) = 30/30 = 1
In other words, 1 is equal to 20/30 + 1/3.
We just place the number 1 where it belongs to plot this on a number line. For instance, we would put 1 in the middle of a number line that goes from 0 to 2.
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PLEASE HELP FAST!! IT IS URGENT!!
The correct interpretation of P ( X ≤ 3 ) would be A. The probability of the number of free throws made out of 8 is at most 3.
How to interpret the probability ?In probability theory, P(X ≤ 3) is the probability that a random variable X takes on a value less than or equal to 3. In this case, X is the number of free throws made out of 8. So, P(X ≤ 3) is the probability that the player makes at most 3 free throws out of 8.
Other possible interpretations of P(X ≤ 3) are the probability of making 3 or fewer free throws out of 8 and the probability of making at most 3 free throws and no more than 3 free throws.
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In order to have P250 000 in 5 years, how much should you invest if the compound interest is 12%?
Pls. Show the complete solution
In order to have 250 000 in 5 years, you should invest 141,856.71.
What is meant by Compound Interest?Compound interest is the interest which is calculated on the principal amount and the amount accumulated over the previous period.
Given,
Final amount = 250,000
Time in years = 5 years
Rate of interest = 12% = 0.12
We have to find the principal amount.
The formula of compound interest is,
A = P( 1 + [tex]\frac{r}{n}[/tex]) ^ (nt)
Here A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest compounded in a year and t is the number of years.
Here n = 1, since the interest is compounded annually
Substituting,
250,000 = P (1 + 0.12)⁵
P = 250,000 / (1 + 0.12)⁵
= 141,856.71
Hence the amount to be invested is 141,856.71.
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Keith is hiring a contractor to do some work on his
house. He asks eight contractors to provide an estimate
of their total time to complete the work and the total
amount of money they will charge. The results are shown
in the graph to the right.
Which equation most closely matches the line of best fit
for Keith's time and cost estimates?
A.y=10x+160
B.y=200
C.y=15x+50
D.y=10x+115
The equation most closely matches the line will be y = 10x + 160. Then the correct option is A.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The table is given below.
Total time Total cost
2 180
8 240
14 300
From the table, the two points are (2, 180) and (14, 300). Then the equation of the line is given as,
(y - 180) = [(300 - 180) / (14 - 2)](x - 2)
y - 180 = 10(x - 2)
y - 180 = 10x - 20
y = 10x - 20 + 180
y = 10x + 160
The equation most closely matches the line will be y = 10x + 160. Then the correct option is A.
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The complete question is given below.
Keith is hiring a contractor to do some work on his house. He asks eight contractors to provide an estimate of their total time to complete the work and the total amount of money they will charge. The results are shown in the graph to the right.
Total time Total cost
2 180
8 240
14 300
Which equation most closely matches the line of best fit for Keith's time and cost estimates?
A.y=10x+160
B.y=200
C.y=15x+50
D.y=10x+115
Complete the point-slope equation of the line through (-8,−8) (-7,9)
Use exact numbers. y-9=
Thus, the complete point- pitch equation of the line passing through (- 8, -8) and (- 7, 9) is y- 9 = 17(x 7).
What's equation?An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of variables, constants, and fine operations, similar as addition, deduction, addition, division, expounders, and roots
Given by question.
To find the equation of the line passing through the given points (-8, -8) and (-7, 9), we need to first find the slope of the line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = ([tex]y_{2}[/tex] - [tex]y_{1}[/tex]) / ([tex]x_{2}[/tex] - [tex]x_{1}[/tex])
Plugging in the given values, we get:
m = (9 - (-8)) / (-7 - (-8)) = 17 / 1 = 17
So, the slope of the line passing through the given points is 17.
Next, we use the point-slope equation of a line to write the equation of the line passing through (-8, -8) with slope 17:
y - [tex]y_{1}[/tex]= m (x - [tex]x_{1}[/tex])
Plugging in the values, we get:
y - (-8) = 17(x - (-8))
Simplifying and solving for y, we get:
y - (-8) = 17x + 136
y = 17x + 128
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identify the intercepts
The intercept of the linear function is equal to - 24.
How to find the intercept of a function described in a table
In this question we find a table representing a set of values from a linear function, since every pair of coordinates report the same slope (m), in meters per second, according to secant line formula:
m = Δy / Δx
Where:
Δx - Change in time, in seconds.Δy - Change in depth, in meters.Then, we find that the table represent an expression of the form:
y = m · x + b
Where:
m - Slopeb - InterceptThe value of the intercept is found by evaluating the linear function at x = 0. By direct inspection, the table say that the intercept is:
- 24 = m · 0 + b
b = - 24
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A long year-end status report for work is 99 pages long. You need to print 15 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.56 each.
Answer:
$10.68
Step-by-step explanation:
Well to start out, you need 15*99 or 1485 pieces of paper.
This is in the 1001-1500 range so you need to buy 3 reams
3*3.56=10.68
Answer: $10.68
Step-by-step explanation:
Evaluate the function over the domain {-2,0,2} . As the values of the domain increase, do the values of the range increase or decrease? y=1.1^x
Therefore, in this instance, the values of a range also rise as the values of a domain do.
What is the mathematics domain?The range of numbers that we are permitted to enter into our function is known as the scope of a function. The x numbers for a function like f make up this collection (x). A function's range is the collection of numbers it can take as input. After we enter an x number, the function outputs this collection of values.
We can evaluate the function y = 1.1ˣ for the given domain of {-2, 0, 2} as follows:
When x = -2, y = 1.1⁻² = 1/1.1² = 0.82645 (rounded to 5 decimal places)
When x = 0, y = 1.1⁰ = 1
When x = 2, y = 1.1² = 1.21
As we can see, the values of the function increase as the values of x increase from -2 to 0 to 2.
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What type of number is
2
π
Answer: Irrational
Step-by-step explanation:
Two pie is the same as saying 2 x π
This means that 2π is an irrational number
The type of number of 2 π is Irrational number.
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
It is an irrational number. A number is rational if it can be expressed as a quotient of 2 integer numbers. Number π 2 cannot be expressed as a quotient of integers, so it is an irrational number.
Hence, The type of number of 2 π is Irrational number.
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Evaluate f(x)=-2x+13 for the sum of f(-4) and f(0)
The value of the functions at f(-4) = 21 and f(0) = 13.
To evaluate f(x)=-2x+13 for f(-4) and f(0), we need to substitute the values into the equation and solve:
f(-4) = -2(-4) + 13 = 8 + 13 = 21
f(0) = -2(0) + 13 = 13
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CAN SOMEONE HELP WITH THIS QUESTION?✨
All the values are,
a) f ' (8) = 3
b) f ⁻¹ (y) = (x - 9) / 3
c) ( f ⁻¹ )' (f (8)) = 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The linear function is,
⇒ y = f (x) = 3x + 9
Now, We can differentiate with respect to x as;
⇒ f = 3x + 9
⇒ df/dx = d/dx (3x + 9)
⇒ df/dx = 3
At x = 8
⇒ f ' (8) = 3
Now, We can find the inverse as;
⇒ y = 3x + 9
Solve for x;
⇒ y - 9 = 3x
⇒ x = (y - 9) / 3
⇒ f ⁻¹ (y) = (x - 9) / 3
Now, We can differentiate with respect to x above equation as;
⇒ f ⁻¹ (x) = (x - 9) / 3
⇒ df ⁻¹ / dx = d/dx (x - 9) / 3
⇒ df ⁻¹ / dx = 1/3
⇒ ( f ⁻¹ )' = 1/3
Hence, We get;
⇒ ( f ⁻¹ )' (f (8)) = 1/3 × 3 = 1
Thus, All the values are,
a) f ' (8) = 3
b) f ⁻¹ (y) = (x - 9) / 3
c) ( f ⁻¹ )' (f (8)) = 1
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In the figure below, AD=5cm, CD=12cm and points C and D are on the perpendicular bisector of segment AB. What is the perimeter of triangle ABC
so we know that CD is a perpendicular bisector to AB, if that's so, that means the triangle is an isosceles triangle, the hell does that mean? well, it means that AC = CB and that AD = DB.
now, we know that DB = AD = 5, and let's use the pythagorean theorem to get AC and CB.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ AC=\sqrt{ 5^2 + 12^2} \implies AC=\sqrt{ 169 }\implies AC=13=CB \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{13~~ + ~~13~~ + ~~5~~ + ~~5}\implies \text{\LARGE 36}[/tex]
'Paraphrasing'
Original: Over four thousand years ago, ancient Egyptians used early beekeeping practices, from keeping beehives to producing honey in sealed pots.
Which one is correct?
A- Several thousand years ago, ancient Egyptians followed early beekeeping practices, from keeping beehives to making honey in sealed pots.
B- Ancient Egyptians, in the past, followed the practice of getting honey from bees, including keeping beehives. They also found honey in pots.
C- A long time ago, early Egyptians followed old beekeeping customs of maintaining beehives and making honey in covered jars.
D- Egyptians have always liked bees and honey. Many years ago, they used early beekeeping practices. They kept beehives and produced honey in sealed pots.
Answer: c
Step-by-step explanation: 100% positive
How many cups of flour should be used with 5 cups of milk in a recipe that calls for 3 parts of milk and 4 parts of flour?
F) 3
G) 4
H) 5
J). 6 2/3
K) 7
EXPLAIN PLEASE
To solve the problem, we need to use proportions. The recipe requires 3 parts of milk and 4 parts of flour. This means that for every 3 cups of milk, we need 4 cups of flour. If we have 5 cups of milk, we can set up a proportion:
3/5 = 4/x
where x is the number of cups of flour needed.
We can solve for x by cross-multiplying:
3x = 20
x = 20/3
x ≈ 6.67
Therefore, we need approximately 6 2/3 cups of flour, which is answer (J).
a) Express 525 as a product of its prime factors in index form. Write the prime factors in ascending order.
b) What is the Highest Common Factor (HCF) of 525 and 70?
We can rewrite:
525 = 3*5*5*7
And the highest common factor of 525 and 70 is 35.
How to find the prime factors?We want to write the number 525 as a product of the prime factors, to do so, just try to divide it by prime numbers (2, 3, 5, etc..) until you find the factors.
We can write:
525 = 5*105 = 5*5*21 = 3*5*5*7
Now we want to find the HCF of 525 and 70, we can rewrite 70 as:
70 = 7*10 = 2*5*7
The greatest common factor between the two is (5*7) = 35
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kindly check if it’s correct and correct those that are wrong. thank you! as well as calculations
The following information is known for the month of December:
1. Purchases of supplies for cash during December were $3,300. Supplies on hand at the end of December equal $2,900.
2. No insurance payments are made in December. Insurance expired in December is $1,400.
3. November salaries payable of $9,800 were paid to employees in December. Additional salaries for December owed at the end of
the year are $14,800.
View transaction list
4. On December 1, Golden Eagle received $2,700 from a customer for rent for the period December through February. By the end of
December, one month of rent has been provided.
Required:
For each item, (a) record any transaction during the month of December, and (b) prepare the related December 31 year-end adjusting
entry. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field.)
no random answers ty!
Correction in point 1: Purchases of supplies for cash during December were $3,300. Supplies on hand at the end of December equal $2,800.
What is Journal Entry?
The act of recording any economic transactions is called a journal entry. An accounting journal lists transactions and displays a company's debit and credit balances. Each recording in the journal entry can be either a debit or a credit, and it can be made up of multiple recordings. The way an accounting transaction is entered into a company's accounting records is through an accounting journal entry.
This question is related to the account and finance subject.
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Suppose a pharmaceutical company has 11 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.)
Given the above conditions, the least-squares equation forecasts a mean number of patents per program of 1.11 for a pharmaceutical company with 11 different research programs.
What is the rationale for the above response?We can use the least-squares regression equation to forecast the mean number of patents per program for a pharmaceutical company with 11 different research programs. The least-squares regression equation is:
y = a + bx
Note that full answer is attached due to Profanity Word Issues. See the attachments for Full question and Full answer.
The least-squares equation forecasts a mean number of patents per program of 1.11 for a pharmaceutical company with 11 different research programs.
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Full Question:
See the attached image.
Determain the value of y, if x is -11.
Y=x^2-2
Answer:
y=119
Step-by-step explanation:
11^2-2 =119
-11^2 goes into -11×-11
then do 11x11= 121
y=x^2-2
121-2=119
Given:
Y = x²-2
To find:
The value of y
Solution:
As given, x = -11.
First of all, we have to apply the values. Value of x = -11X² = -11 x (-11)= 121
Y = 121-2Y = 119Therefore, the value of y is 119.
Over which interval is the graph of the parent absolute value function f(x)= |x| decreasing?
The parent absolute value function f(x) = |x| is not decreasing over any interval. It is a V-shaped graph with its vertex at the origin, and it increases on the interval (-∞, 0) and increases on the interval (0, ∞). Therefore, it is not possible for it to be decreasing over any interval.
I need Help please asap
The simplification of the division of the fraction is found to be -49/ 24.
Explain about the fractions?The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction. The 1 can be written on top of the 2 only with slash here between two numbers, or you could write the number with a slanted slice like we have. The denominator is 2, and the numerator is 1.The given division of the fraction is-
= 7/8 / 1 - 10/7
Taking LCM at the denominator.
= 7/8 / 7 - 10/7
= 7/8 / -3/7
Further simplifying:
= - 7*7 / 3*8
= -49/ 24
Thus, the simplification of the division of the fraction is found to be -49/ 24.
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Select all simplified expressions of 3^4 ÷ 3^9.
The simplified form of the expression 3⁴ ÷ 3⁹ is 1/3⁵ or 1/243.
What is the simplified form of the expression?Given the expression in the question;
3⁴ ÷ 3⁹
To simplify the expression, we use the rule of exponents which states that;
When you divide two powers with the same base, you can subtract their exponents.
Now, using this rule, we can rewrite the expression as:
3⁴ ÷ 3⁹ = 3^( 4 - 9 )
Since 4-9 is equals -5, we can simplify the expression to:
3^(4-9) = 3^(-5)
Now, we have a negative exponent which means we can flip the base to get a positive exponent. That is:
3^(-5) = 1/3⁵
Therefore, the simplified form of the expression 3⁴ ÷ 3⁹ is 1/3⁵ or 1/243.
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Please help needed!!
A point= zero-dimensional object designates a particular place on a plane. Moreover, a little dot is used to symbolize it.
What is a geometric figure?A geometric figure is a collection of lines, planes, or points that together form the shapes of various three-dimensional things.
A geometric figure is referred to in geometry using the terms and definitions below:
A point, or zero-dimensional object, designates a particular place on a plane. Moreover, a little dot is used to symbolize it. ⇒Image 4.A line is a one-dimensional shape that stretches in two (2) directions without having an end. (Image 5)Line segments are the discrete portions of a line that connect any two (2) points on the line. (Image 1.)A ray is a half-line that begins at one place and extends in one direction indefinitely (forever) (Image 3).A plane is a two-dimensional surface that never ends( Image 2.).To know more about Geometry visit:
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Read the clues about the current ages of some of the members of the Ruiz family.
Write an equation that relates Juan's age, j, to Maria's age, m.
Amara is 18 years old. Use the equation from question 1 to write an equation that relates Amara's age to Maria's age m. How old is Maria?
1. Write an equation that relates Juan's age j to Maria's age m.
2. Write an equation that relates Amara's age to Maria's age m.
How old is Maria?
Maria is __ year(s) old.
An equation that relates Juan's age j to Maria's age m can be expressed as j = m + x, where x is the age difference between Juan and Maria.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
Given:
Amara is 18 years old.
Let's assume that Amara is y years younger than Maria, then we can write an equation relating their ages as:
Amara's age = Maria's age - y
Substituting Amara's age as 18 in the above equation, we get:
18 = m - y
Rearranging the equation, we get:
m = 18 + y
Therefore, an equation that relates Amara's age to Maria's age m is
m = 18 + y.
Therefore, we don't have enough information to determine Maria's age as we don't know the value of y.
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What is the measure of 23, in degrees, in the figure shown? 30° 137° 3
Answer:
73°
Step-by-step explanation:
This equation uses two supplementary angles. Supplementary angles are two angles that add up to 180 degrees.
The triangle has two angles implied, 30 degrees and (180-137) degrees.
(180 - 137) = 43 degrees
Now that we have two angles inside the triangle, we subtract them from 180 to find the last angle.
180 - 43 - 30 = 107
The angle with a measure of 107 degrees and angle 3 are supplementary
180 - 107 = 73 degrees
Answer:73.4° Fahrenheit.
Step-by-step explanation:
Which multiplication expression is represented by the shaded part of the model?
Responses
A 17
× 31 7 × 3
B 27
× 32 7 × 3
C 23
× 72 3 × 7
D 13
× 71 3 × 7
Therefore, the options do not include the right expression response. None of the examples fit the result of multiplying 9 by 2.
Explain expression.Multiplying, dividing, adding, but also deleting are essential arithmetic operations. If they were put together, the sentence that would emerge would be: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and operations like additions, subtractions, multiplications, and divisions. It is possible to analyse and rank words and phrases.
Here,
Each shaded rectangle in the model corresponds to a portion of 1/21 of its overall area because it is divided into 7 equal parts laterally and 3 equal sections vertically.
The amount of sets being multiplied together can be determined by counting the number of shaded squares in the model.
Consequently, the model's darkened portion represents the following multiplication expression:
=> 9 × 2 = 18
Therefore, the options do not include the right response. None of the examples fit the result of multiplying 9 by 2.
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What is the area of a rectangle with a length of Four and two-fourths meters and a width of Seven and five-sixths meters?
Answer:
the area of the rectangle is 35.25 square meters.
Step-by-step explanation:
To find the area of a rectangle, we multiply the length by the width.
First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:
4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4
7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6
Now we can multiply the length and width:
Area = (18/4) * (47/6)
Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)
Area = (9 * 47) / (2 * 6)
Area = 423/12
Area = 35.25
Therefore, the area of the rectangle is 35.25 square meters.
