The equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively
Perimeter of rectangleLength of the rectangle, l = 1 + 2wWidth of the rectangle = wPerimeter = 104 cmPerimeter of rectangle = 2(L + W)
104 = 2{(1 + 2w) + w}
104 = 2(1 + 2w + w)
104 = 2(1 + 3w)
104 = 2 + 6w
104 - 2 = 6w
102 = 6w
w = 102 / 6
w = 17 cm
Recall,
Length of the rectangle, l = 1 + 2w
= 1 + 2(17)
= 1 + 34
= 35 cm
Therefore, the equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively
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PLEASE HELP ME!!! DUE TODAY, I WILL GIVE 20 POINTS!!!! NO EXPLAINATION NEEDED!!!! FIRST PERSON TO ANSWER GETS BRAINLIEST AWARD!!!!
Answer:
The weight of gold in the alloy is 32 g.
Answer:
The weight is 32 grams
Step-by-step explanation:
A farmer looks over a field and sees 34 heads and 94 feet. Some are goats, some are geese. How many of each animal are there?
Answer: 13 goats and 21 geese
Step-by-step explanation:
Since we know some are goats, which have four feet, and some are geese, which have two feet, we will set up an equation.
Let x be goats and y be geese.
4x + 2y = 94
Next, we know both animals [usually] only have one head.
x + y = 34
Lastly, we will solve this as a system of equations.
➜ I graphed the equations, see attached, but you can also solve by substitution or other methods.
➜ When graphing, the point of intersection is the solution. This means there are 13 goats and 21 geese.
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How is the product of 3 and -2 shown using integer tiles?
Answer:
C) 3 sets of -2 tiles
Step-by-step explanation:
Its -2 three times, making it -6
If you multiply a positive and negative it is always negative
3 1/3 (y plus 1 1/8) = 6 11/12
HELp
The value of y in the given equation is 19/20
Solving linear equationsFrom the question, we are to determine the value of y in the given equation
The given equation is
3 1/3(y + 1 1/8) = 6 11/12
First, convert the the fractions into improper fractions
10/3(y + 9/8) = 83/12
Multiply both sides of the equation by 3/10
3/10× 10/3(y + 9/8) = 3/10× 83/12
y + 9/8 = 3/10× 83/12
y + 9/8 = 83/40
y = 83/40 - 9/8
y = (83 - 45)/40
y = 38/40
y = 19/20
Hence, the value of y in the given equation is 19/20
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Solve for g.
9g - 8g - 1 = 16
g=
9g-8g-1=16
g-1=16
g=17
A child’s pool is filled to the top. On Day 1, the level of the water in the pool decreases by 1
1
3
inches. On Day 2, the level of the water decreases by
3
8
inch. What number represents the water level after 2 days?
Answer:
this makes no sense but I think the answer is 38 inches
Step-by-step explanation:
you deposit $4800 in an account that earns simple interest . After 2 years, the account ears $537.60 in interest. What is the annual interest rate to the nearest tenth of a percent? use the formula i=prt
Annual interest rate on $4800 for 2 years is 5.6%.
What is Interest rate?An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.
Given,
The principal amount = $4800
Time period = 2 years
Interest rate = $537.60
I = P × R × T / 100
where P = principal amount,
R = rate of interest,
T = Time period
537.60 = 4800 × R ×2 / 100
⇒ R = 537.60 ×100 / 4800 × 2
⇒ R = 5.6%
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Which numbers are 4 units from −2 on this number line?
Drag and drop all the numbers that are 4 units from −2 to their correct position on the number line
Pls Show A Picture With The Number Line And Numbers
The numbers are 4 units from -2 on this number lines are -6, 2 and 6.
A number line is a horizontal line that has equally spread number increments.
The numbers included on the line will determine how the number on the line can be marked.
According to the question,
Firstly, we will add the two numbers.
4 + (-2) = 4 - 2 = 2
Then, we will subtract the two numbers.
4 - (-2) = 4 + 2 = 6
-2 - 4 = -6
The numbers 2, 6 and -6 are represented on the number line.
Therefore, the numbers are 4 units from -2 on this number lines are -6, 2 and 6.
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You play a board game with your little brother. You pick a card that sends you back five spaces. On your next turn, you must move back three more spaces. On your third turn, you get to move forward three spaces. Which expression best shows how you could find your new spot on the game board? CLEAR CHECK -5 + (-3) + (-3) -5 + 3 + 3 -5 + (-3) + 3 5 + (-3) + (-3)
Expression best shows above condition is -5-3+3
What is an expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Here, it is given that while playing board game we pick a card that sends us back five spaces. On our next turn, we must move back three more spaces. On our third turn, we get to move forward three spaces.
and, expression best shows how we could find our new spot on the game board will be :
for first move, five spaces back means = -5
for second move, three spaces back means = -3
and for third move, three spaces move forward = +3
combining all the three terms we get : -5-3+3
Therefore, expression best shows above condition is -5-3+3
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To find the average of a student's test scores, add the scores and divide by the number of tests. Suppose George scored 83, 91, 82, and 95 on four
tests. Write a numerical expression to describe Chase's average test score.
Please use the test scores in order of the question to earn full credit.
Answer: (83 + 91 + 82 + 95) / 4
Step-by-step explanation:
The information given tells us how to complete the question. We will be finding the average.
Add all the scores together, and divide by the number of tests.
(83 + 91 + 82 + 95) / 4
Since this question asks for an expression, we will end here. If it asked us to solve, we would do the following;
(83 + 91 + 82 + 95) / 4
(351) / 4
87.75
Margaret uses 1 3/4 teaspoons of key lime zest to make 12 like cupcakes. She wants to make 30 cupcakes. How much key lime zest will margaret use?
The number of teaspoons of key lime zest to make 30 cupcakes is
35/8 or 4 3/8
Given,
Margaret uses 1 3/4 teaspoon of key lime zest to make 12 cupcakes.
She wants to make 30 cupcakes.
We need to find how much key lime zest will Margaret use.
How to compare given two units?Example:
1 bag = N mango
Then to find the number of mangoes in 5 bags we need to multiply 5 on both sides.
5 bags = 5 x N mangoes.
We have,
1 3/4 teaspoons of key lime zest = 12 cupcakes
7/4 teaspoons of key lime zest = 12 cupcakes
7/4 = 12 cupcakes
Multiply 30 on both sides.
7/4 x 30 = 30 x 12 cupcakes
Divide both sides by 12.
7/4 x 30/12 = 30 cupcakes
35 / 8 = 30 cupcakes
or
4 3/8 = 30 cupcakes
This means,
35/8 or 4 3/8 teaspoons of key lime zest to make 30 cupcakes.
Thus the number of teaspoons of key lime zest to make 30 cupcakes is
35/8 or 4 3/8.
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Yolanda opened a retirement account earning 5.5% interest per year, compounded monthly. She deposited $100 each month. Assume that no other deposits or withdrawals were made. Answer the following, writing your answers to the nearest dollar.
The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29
What is the future value of an ordinary?
An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:
FV=PMT*(1+r)^N-1/r
FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown
PMT=monthly deposit=$100
r=monthly interest rate=5.5%/12=0.00458333333333333
N=number of monthly deposits in 4 years=4*12=48
FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333
FV=$5,355.29
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Missing question:
What was the balance in dollars and cents in Yolanda's account at the end of 4 years?
Halp me
Vtxtvdcvdtcgdtgcgdtcgcvfg
Answer: 5578
Step-by-step explanation:
1058 + 4520 = 5578
Solve w(2v + 9) = 3w(v - 1) given that w(v) = 3v + 2.
Enter the exact answer.
V=
After solving the given equation the two values of V are (v = 12) and
(v = -2/3).
What exactly are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, substitute 'w = 3v + 2' in w(2v + 9) = 3w(v - 1):
w(2v + 9) = 3w(v - 1)3v + 2(2v + 9) = 3(3v + 2)(v - 1)3v(2v + 9) + 2(2v + 9) = 3[3v(v - 1) + 2(v - 1)]6v² + 27v + 4v + 18 = 3(3v² - 3v + 2v - 2)6v² + 31v + 18 = 3(3v² -1v - 2)6v² + 31v + 18 = 9v² -3v -69v² - 6v² -3v - 31v - 6 - 18 = 03v² - 34v - 24 = 03v² - v ( 36 - 2 ) - 243v² - 36v + 2v - 243v (v - 12) + 2 (v - 12)(v - 12) and (3v + 2)Values: (v = 12) and (v = -2/3)Therefore, two values of v are (v = 12) and (v = -2/3)
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Find the quadratic function (0,7)(2,15)(3,10)
The quadratic equation that contains (0, 7), (2, 15) and (3, 10) is y = - 3 · x² + 10 · x + 7.
What is the quadratic equation associated with a given set of points?
Quadratic functions are polynomials of the form y = a · x² + b · x + c, where a, b, c are real coefficients. To determine the coefficients, we need at least three distinct points on Cartesian plane. A solution that is algebraic exact only need three points, then we must resolve this system of linear equations:
c = 7 (1)
4 · a + 2 · b + c = 15 (2)
9 · a + 3 · b + c = 10 (3)
The solution to this system of linear equations is (a, b, c) = (- 3, 10, 7).
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1. Airline A and Airline B both have earnings before interest and taxes (EBIT) of $100 million. Airline B has no debt, while Airline A has interest expenses of $20 million. Assume a tax rate of 35% applies to both airlines.
How many dollars will Airline A pay in taxes? Type your answer into the textbox.
2. Discuss in a the importance of understanding taxes and what financial choices will have an impact on taxable income. Would Airline A have been willing to take on a debt that would cost $20 million in interest if they had not considered the tax break it would afford
Airline A will pay $28 million in taxes based on the EBIT of $100 million
The increase in interest expenses by $20 million means that the income tax expense decreases by $7 million.
What is the taxable earnings for company A?
The fact that company A has debt and would pay interest expenses of $20 million means that its taxable income is the earnings before interest and tax minus the interest expense
taxable income=$100 million-$20 million
taxable income=$80 million
taxes=taxable income*tax rate
tax rate=35%
company A's taxes=$80 million*35%
company A's taxes=$28 million
It should be noted that the higher the increase in interest expenses, the higher the tax savings that Airline A would achieve, hence, adding an additional borrowing which costs an extra $20 million in interest means that the company's taxes can be computed as shown below:
taxable income=$100 million-$20 million-$20 million
taxable income=$60 million
taxes=taxable income*tax rate
tax rate=35%
company A's taxes=$60 million*35%
company A's taxes=$21 million
In other words, Airline A would achieve a $7 million savings in taxes since the increase in interest expenses means that taxes decrease from $28 million to $21 million
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Teresa borrowed $8,000 at a rate of 15.5% , compounded semiannually. Assuming she makes no payments, how much will she owe after 3 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.
What is compound interest?The interest you earn on interest is known as compound interest. This can be demonstrated with simple math: if you have $100 and it earns 5% interest per year, you will have $105 at the end of the first year. You'll have $110.25 at the end of the second year. Compound interest accelerates the growth of your money because interest is calculated on both the accumulated interest over time and the original principal. Compounding can cause a snowball effect, in which the initial investments and the income earned from those investments grow in tandem.So, Teresa borrowed $8,000 at a rate of 15.5%:
(Refer to the table given below)
Owe in 3 years: $12.519.69Rounding off: 12.520Teresa will owe $12.520 in 3 years.Therefore, Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.
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Andy has 20 coins made up of quarters and half dollars, and their total value is $9.25. How many quarters does he have?
Using simple linear equations, we can calculate that Andy has 3 quarters.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Let the number of quarters Andy has = x
number of dollars Andy has = 20 - x
value of quarter = 0.25x
value of dollars = 0.5(20 - x)
Total value = $9.25
⇒ 0.25x + 0.5(20 - x) = 9.25
⇒ 0.25x + 10 - 0.5x = 9.25
⇒ - 0.25x = 9.25 - 10
⇒ - 0.25x = - 0.75
⇒ x = 3
Andy has quarter = 3
He has dollars = 20 - 3 = 17
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At Acme Supermarket there are 12 full-time employees; 10 of them earn $12 per hour each, and the assistant manager and manager make $18 and $20 per hour respectively. What is the average rate of pay for the 12 employees? What is the median rate of pay? Which do you think is the better summary model to represent the pay rate of Acme’s employees?
Answer:
Average salary 13.16 120 + 18 + 20/12
1. What is the sum of three thousand two hundred and forty seven hundredths, and thirteen and seven
hundred ninety-nine thousandths?
A. 3,247
B. 13,790
C. 213.790
D. 3,214.269
Answer: i think it is d but im not sure
Step-by-step explanation:
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $20. For one performance, there were 45 tickets sold in all, and the total amount paid for them was $1125. How many tickets of each type were sold?
By solving a system of equations, we conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.
How many tickets of each type were sold?Let's define the variables that we will be using:
x = number of advance tickets sold.y = number of same-day tickets sold.We can write the system of equations:
x + y = 45
x*35 + y*20 = 1125
Isolating x on the first equation we get:
x = 45 - y
Repacing that in the other equation we get:
(45 - y)*35 + y*20 = 1125
1,575 - y*15 = 1125
1,575 - 1125 = y*15
(1,575 - 1125)/15 = y = 30
Then:
x = 45 - y = 45 - 30 = 15
We conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.
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The diameter of Mars is 6.794 × 106 m.
The diameter of Earth is 1.2756 × 107 m.
Jo says, ‘Earth is more than ten times the diameter of Mars.’ Is Jo right? You must show how you get your answer.
Mars is half as big as Earth and that they each have an equal amount of dry land surface to determine by how much the circumference of the Earth is larger than that of Mars.
we need D(Earth) / D(Mars).
D(Earth) / D(Mars) = 1.2763 x 10⁴km/6.8 x 10³ km ≈ 1.9
D(Earth) / D(Mars) ≈ 1.9
The fifth-largest planet in our solar system by radius, the Earth has a circumference of 3,959 miles.
The other seven planets are joined by Earth and Mars. These two planets in our solar system share some geological characteristics, such as the fact that Mars, the seventh-largest planet in our solar system, has a radius of 2,106 miles. There are a few distinctions between Mars and Earth, though.
Hence, these planets differ in terms of their sizes, atmospheres, and temperatures.
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Misses Ali owns a business. She assigns two of her employees their shifts. She assigns the first employee 6 hour shift and the second employee 15 hours shift. If both workers recieved same number of hours what is the mininum number of hours each employee will be assigned.
Based on the fact that both workers received the same number of hours, the minimum number of hours that each employee will be assigned is 60 hours.
What is the minimum assigned hours?One worker gets 15 hours shifts and the other gets 6 hour shifts.
If they will have the same number of working hours, the minimum number of hours for these workers will be the lowest common multiple of 6 and 15.
Multiples of 15:
15, 30, 45, 60, 75Multiples of 6:
6, 18, 30, 42, 60, 72The minimum number of hours is therefore 60 hours.
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Answer: 60
Step-by-step explanation:
LCM of 6 & 15
15
-------------
15
30
45
60
75
90
105
6
---------
6
12
18
24
30
36
42
48
54
60
LCM of 6 & 15 is 60
Write an inequality that represents the statement “x is greater than -2 and less than 8.”
The inequality which represents the statement given in the task content; x is greater than -2 and less than 8 is; -2 < x < 8.
Which inequality correctly represents the statement as given in the task content?It follows from the task content that the inequality which represents the statement given in the task content is to be determined.
First each section of the statement must be highlighted as follows;
x is greater than -2 can be written as;
x > -2 or -2 < x
x is less than 8 can be written as:
x < 8.
Therefore, the compound inequality which represents the word phrase is; -2 < x < 8.
Ultimately, The inequality which represents the statement given in the task content; x is greater than -2 and less than 8 is; -2 < x < 8.
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Emily has a spool of yarn that is. 12 1/8 yards in length Emily uses 2 2/3 from the spool there helppppp
Answer:
What do I solve for? If it's the length of spool not used, then the answer is
9 11/24 yards of spool.
Step-by-step explanation:
12 1/8 - 2 2/3=
12 - 2 + 1/8 - 2/3=
10 + (1/8 - 2/3)*24/24 = ==> multiply by 24 to get rid of denominator
10 + (24*1/8 - 24*2/3)/24 =
10 + (24/8 - 48/3)/24 =
10 + (3 - 16)/24 =
10*24/24+ (-13)/24 =
240/24 - 13/24=
(240-13)/24=
227/24=
(216+11)/24=
216/24 + 11/24=
9 + 11/24=9 11/24 yards of spool
Henry bought a bag of 5 onions for a total cost of $4.75. At that rate, how
much would Henry pay for 12 onions?
A. $ 9.75
B. $11.40
C. $11.75
D. $16.75
can someone help me with this question? :)
Thank you so much for the help
For the given function, we have that:
The domain is [-4,4].The function has no zeros.The function is positive for x ≤ 0.The function is negative for x > 0.What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.
Hence, the domain is [-4,4] for the given function.
What are the zeros of a function?The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.
For this problem, the function does not cross the x-axis, hence it has no zeros.
When a function is negative and when it is positive?Looking at the graph of the function, we have that:
It is positive if it is above the x-axis.It is negative if it is below the x-axis.Hence, for the function in the given graph:
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HELP ME OUT PLEASE!!!!
Answer:
b
Step-by-step explanation:
Which type of compound inequality is 3|y+7|-16>5
-union
-hole
-disjunction
-intersection
The type of the compound inequality 3|y+7| - 16 > 5 is an intersection
How to determine the type of the compound inequality?The compound inequality is given as
3|y+7| - 16 > 5
Add 16 to both sides of the inequality
So, we have
3|y+7| > 21
Divides both sides by 3
So, we have
|y+7| > 3
When the above inequality is solved, the region between the boundaries are shaded
This represents an intersection
Hence, the type of the compound inequality 3|y+7| - 16 > 5 is an intersection
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Answer:The answer is disjunction !!
Step-by-step explanation:
I took the test and got this correct.
At the end of a snow storm, Emily saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 15 inches of snow on the lawn when the storm ended and after 4 hours, the depth of snow was down to 12 inches. Write an equation for S,S, in terms of t,t, representing the depth of snow on Emily's lawn, in inches, tt hours after the snow stopped falling.
The equation that represents the depth of snow on Emily's lawn t hours after the snow stopped falling is
S = 15 - 0.75t
Writing an equationFrom the question, we are to write an equation for S, in terms of t, that represents the depth of the snow on Emily's lawn, t hours after the snow stopped falling
From the given information,
"There was a depth of 15 inches of snow on the lawn when the storm ended"
and
"after 4 hours, the depth of snow was down to 12 inches"
That is,
The snow has reduced by 15 - 12 inches after 4 hours
15 - 12 = 3
Thus,
The snow has reduced by 3 inches after 4 hours
Now,
If the snow reduced by 3 inches after 4 hours,
Then,
The snow will reduce by x inches after 1 hour
x = (3×1)/4
x = 3/4 inches
x = 0.75 inches
This means the snow reduces by 0.75 inches every hour.
Now,
After t hours, the snow would have reduced by 0.75t
Thus, the depth of the snow, S, after t hours will be
S = 15 - 0.75t
Hence, the equation that represents the depth of snow on Emily's lawn t hours after the snow stopped falling is
S = 15 - 0.75t
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