Step-by-step explanation:
Let x be the width of the uniform strip floor around the rug.
Then the width of the rug is (21 - 2x) and the length of the rug is (29 - 2x).
(21 - 2x)(29 - 2x) = 345
609 - 100x + 4x^2 = 345
4x^2 - 100x + 264 = 0
x^2 - 25x + 66 = 0
(x - 22)(x - 3) = 0
x = 3 or x = 22 (rejected as x must be less that the width of the room)
Hence the width of the rug is 21 - 2(3) = 15 feet and the length of the rug is 29 - 2(3) = 23 feet.
What is 13.7 billion years in scientific notation
Answer:
1.37 * 10^10 years.
Step-by-step explanation:
Billion = 9 zeroes
13.7 billion = 13.7 * 10^9 = 1.37 * 10^10.
Find the value of 2x+y when x=4 and y=3
Find the value of a^2 + b when a= -2 and b=5
Answer:
2x + y = 11
a² + b = 9
Step-by-step explanation:
I solved these by using order of operations and subsitution.
Turn the Mix Number into a Improper Fraction a) 5 5 4 b) 3 8 3
Answer:
A: 25/4 B: 17/3
:)))))))))))))))))
Use the number line below, where RS = 5y +3, ST = 3y + 4, and RT = 10y - 3.
a. What is the value of y?
b. Find RS, ST, and RT.
Answer:
(a). y = 5
(b). RS = 28
ST = 19
RT = 47
Step-by-step explanation:
(a). There are three points R, S and T on a number line.
Therefore, RT = RS + ST -------(1)
Since, RT = 10y - 3
RS = 5y + 3
ST = 3y + 4
By substituting these values in the equation (1)
10y - 3 = (5y + 3) + (3y + 4)
10y - 3 = 8y + 7
10y - 8y = 7 + 3
2y = 10
y = 5
(b). RS = 5y + 3
= 25 + 3
= 28
ST = 3y + 4
= 15 + 4
= 19
RT = 10y - 3
= 50 -3
= 47
Carla needs to rent storage space for some of her belongings. She paid a one-time original storage fee of $25.00, and now pays $36.00 each month (m). Which answer choice shows an expression that represents the total amount Carla has paid after a certain number of months (m)?
Answer:
TC = 36t + 25
Step-by-step explanation:
The amount paid by Carla as a storage fee or fixed cost = $25
Monthly rent or variable cost = $36
Let the number of months = t
Now we have to find the expression that represents the total cost. Below is the formula to find the expression.
Total cost = Variable cost + Fixed cost
Total cost = 36t + 25
TC = 36t + 25
A product at the grocery store is priced $12.84 for 6 ounces. What is the cost per ounce?
Answer:
Step-by-step explanation:
$12.84/6 = $2.14 per ounce
The volume of a box is 400 in.³ if the height is 10 inches and the length is 8 inches what is the width of the box
Answer:
5
Step-by-step explanation:
Step 1:
10 × 8 × x = 400
Step 2:
80 × x = 400
Step 3:
x = 400 ÷ 80
Answer:
x = 5
Hope This Helps :)
YR 8 MATHS PLS HELP!!!!!!
Answer:
6.54
Step-by-step explanation:
you have to add up all of the numbers then divide by how many numbers there are to get the mean
Answer:
6.54
Step-by-step explanation:
Add up all thee numbers:
11+11+5+6+6+11+04+8+2+5+7+9=85
Divide by how many numbers there are:
85/13=6.538
6.54
which statement best describes the realationship between the numbers divisable by 6, 2 and 3
Thank yousunshinemadison101
17-||-9|+3|
Can anyone help me out?
Answer:
Step-by-step explanation:
Step 1:
17 - 9 + 3
Step 2:
8 + 3
Answer:
11
Absolute Value turns everything positive.
Hope This Helps :)
What is the answer? 1/2 + 1/7 =?
Answer:
9/14
Step-by-step explanation:
Just Multiply the numerator and denominator of both fraction with the opposite denominator for the denominators to become the same. Since they have aa common denominator, you can just add the numerators to get 9/14.
Two integers have a sum of -11 and a difference of 5. What are the two
integers?
(23 points!!)
Answer:
x = -3
y = -6
Step-by-step explanation:
x+y = -11
x-y = 5
x+y+x-y= -6
2x= -6
x = -3
y = -6
A rectangle has a length represented by the function )
and a width represented by g )
Which statement accurately describes the combined
functions, P(x) and A(x)?
Answer: P(x) has a constant rate of change, but A(x) does not
Step-by-step explanation:
Can 7,11, and 3 make a triangle?
Answer:
No
Step-by-step explanation:
to form a triangle:a=7 , b=11, c=3
a+b>c a+c>b b+c>a
7+11>3 7+3<11 3+11>7
one condition is not applied, so no
Write the polynomial in standard form, then give the leading coefficient.
Answer:
-3y^8+18y^5+10y is the standard form of the equation. The leading coeficients are -3, 18 and 10
Step-by-step explanation:
The highest power awlays goes at the beginning of the equation. In this situation the highest power is 8, followed by 5 and then by 1. Usually the 1 as a power is not written. The leading coeficients are the numbers infront each term. If there is -4xy, the leading coeficient is -4.
solve for x
3(2-x)=5(2x-7)+2
Answer: X = 3
Step-by-step explanation:
3(2-x)=5(2x-7)+ 2
First, distribute
6-3x = 10x -35 + 2
Now subtract and add
6+35-2= 10x-(-3x)
Which gives
39= 13x
X=3
Hope this helps!
A cake mix calls for these ingredients. 2 cups of sugar 7 cups of flour 3 cups of milk 1 cup of oil Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios? StartFraction 3 Over 7 EndFraction greater-than StartFraction 2 Over 1 EndFraction StartFraction 2 Over 7 EndFraction less-than StartFraction 3 Over 1 EndFraction StartFraction 7 Over 1 EndFraction less-than two-thirds
Answer:
milk to oil - correctly shows ratio 3:1
Answer:
B 2/7 <3/1
Step-by-step explanation:
Which parent function is f(x) = |x|?
A. The quadratic parent function
B. The absolute value parent function
C. The linear parent function
D. An exponential parent function
Answer:
B. The absolute value parent function
Step-by-step explanation:
[tex]f(x)=|x|[/tex]
Referred to as absolute value, the value inside the bars is measured in terms of its distance from 0. Therefore:
[tex]|0|=0\\|3|=3\\|-3|=3[/tex]
In essence, a negative value within the bars becomes positive, while a positive value remains positive.
Estimate the annual wages for Hourly rate $7.15
Lets assume someone works 10 hours a day for 5 days a week.
Weekly total:
10 * 7.15 = $71.50 per day
71.5 * 5 = $357.50 per week
There are 52 weeks in a year so we can multiply.
357.50 * 52 = $18,590 per year
This is how you can solve this problem if you are given these details.
Best of Luck!
João emprestou R$ 1000,00 a seu amigo José. Para que José conseguisse o empréstimo com o amigo, foram definidas as seguintes condições de pagamento: prazo de 6 meses e taxa de juros simples de 10% ao trimestre. Sendo assim, passados os seis meses do empréstimo, quanto o amigo José terá de pagar ao amigo João? a) R$ 100,00 b) R$ 1.100,00 c) R$ 200,00 d) R$ 1.200,00 e) R$ 1.400,00
Answer:
La opción correcta es;
d) R $ 1.200,00
Step-by-step explanation:
El monto que Joao prestó a José = R $ 1.000,00
La duración del préstamo = 6 meses
El plazo de interés del préstamo = interés simple del 10% por trimestre
La cantidad que José tiene que pagarle a Joao después de 6 meses viene dada por la siguiente fórmula de interés simple;
A = P · (1 + r · t)
A = La cantidad que José tiene que pagarle a Joao después de 6 meses
P = La cantidad que Joao prestó a José = R $ 1.000,00
r = La tasa de interés = 10% / trimestre = 10% / (3 meses) = 0.1 / (3 meses)
t = La duración del préstamo = 6 meses
Por lo tanto, al sustituir los valores anteriores en la fórmula de interés simple, tenemos;
A = R $ 1.000,00 × (1 + 0,1 / (3 meses) × 6 meses) = R $ 1.000,00 + R $ 200,00 = $$ 1.200,00
El monto que José debe pagar a Joao después de 6 meses = R $ 1.200,00
Identify the hypothesis of the statement. If a number is negative, then the number is less than zero. A) a number is negative B) a number is positive C) the number is less than zero D) the number is greater than zero
Answer: A) a number is negative
Step-by-step explanation:
A conditional statement is written as:
If P, then Q.
Where P is the hypothesis and Q the conclusion.
In this case, we have:
If a number is negative, then the number is less than zero.
then we have:
P = a number is negative.
Q = the number is less than zero.
Then the hypothesis will be "a number is negative"
The correct option is A.
Answer:
number is negative
Step-by-step explanation:
Which two ratios represent quantities that are proportional?
A 22/33 and 14/21
B 48/60 and 35/42
C 25/28 and 5/7
D 16/13 and 13/16
Please help
The two ratios represent proportional quantities is A: 22/3 and 14/21 = 1/3
When do two ratios form a proportion?Two ratios form a proportion if the simplified form of both ratios comes out as the same ratio. Suppose that we've got two quantities with measurements as 'a' and 'b' Then, their ratio(ratio of a to b) a:b
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.
A.) 22/33 and 14/21
Here. the two ratios represent quantities that are proportional to 1/3.
B.) 48/60 and 35/42
Here. the two ratios represent quantities that are not proportional.
C.) 25/28 and 5/7
Here. the two ratios represent quantities that are not proportional.
D.) 16/13 and 13/16
Here. the two ratios represent quantities that are not proportional.
Hence, The two ratios represent proportional quantities is A: 22/3 and 14/21 = 1/3
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The Five Fives Challenge
In this mathematical challenge, you must use only five fives and mathematical operations/ symbols to achieve the number 0-30. Mathematical operations/symbols include addition, subtraction, multiplication, division, grouping symbols, decimal points, exponents, square roots, and factorials.
There are many solutions for each number. Be creative and try and find different solutions.
5) A tortoise's fastest rate of travel is 225 feet in 15 minutes. Write
this rate as a Unit Rate.
Answer:
900 feet per hour
Step-by-step explanation:
225×4 = 900
15×4=60
the tortoise's rate of speed is 900 feet per hour
hope that helps.
please help me with this i don’t understand at all!
Answer:
2x+8=3x-2
8=x-2
x=10'
the answer is 10
Step-by-step explanation:
sorry i didnt put an answer at the start
i was in a rush
What percent is represented by the diagram below?
A 13%
B
65%
C 130%
D
650%
Answer:
Step-by-step explits its C.130%anation:
A vine called the mile-a-minute were is known for growing at a very fast rate it can grow up 2ft per day how fast in inches per hour can the mile-a-minute weed grow up to?
Answer:
1 inch/hr
Step-by-step explanation:
Rate of growing of weed mile-a-minute = 2 ft per day
To find:
Rate of growth of weed in inches per hour ?
Solution:
First of all, let us have a look at the following units conversion:
1 ft contains 12 inches
and 1 day is equal to 24 hours.
Rate of growth of weed is Length divided by number of days.
2 ft per day means Length of 2ft divided by 1 day.
i.e.
[tex]\dfrac{2\ ft}{1\ day}[/tex]
Let us put the units for conversion as discussed above:
[tex]\dfrac{2\times 12\ inches}{24\ hours}\\\Rightarrow \dfrac{24\ inch}{24\ hours}\\\Rightarrow \bold{1\ inches/hr}[/tex]
So, the answer is: 1 inch/hour
Solve for x.
[tex]4x+6=10-4[/tex]
Steps to solve:
4x + 6 = 10 - 4
~Simplify
4x + 6 = 6
~Subtract 6 to both sides
4x = 0
~Divide 4 to both sides
x = 0
Best of Luck!
Answer:
[tex]\large\boxed{x = 0}[/tex]
Step-by-step explanation:
4x + 6 = 10 - 4
Subtract 10 - 4
4x + 6 = 6
Subtract 6 from both sides of the equation
4x = 0
Divide both sides of the equation by 4
[tex]\large\boxed{x = 0}[/tex]
Hope this helps :)
On a baseball field the pitcher's mound is 60.5 ft away from home plate. Second base is 127.28 ft from home plate. Is the pitcher's mound the midpoint of home plate and second base? Explain your reasoning
Answer and Step-by-step explanation: Midpoint is the middle point in a segment line, i.e., it is at the center of a segment line.
On a baseball field, distance between home plate and second base is 127.28ft. The midpoint will be:
midpoint = [tex]\frac{127.28}{2}[/tex]
midpoint = 63.64ft
To be the midpoint, pitcher's mount must be 63.64ft away from the home plate. Since it's less than that, pitcher's mount is not the midpoint between home plate and second base.
Write an equation that would model the tile pattern above where x represents the figure number and y represents the number of tiles
The equation that would model the tile pattern above where x represents the figure number and y represents the number of tiles is y = 2x + 5.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The three figures are shown in the picture.
After analysis:
2(3) + 1 = 7
2(4) + 1 = 9
2(5) + 1 = 11
The standard form:
y = 2(x+2) + 1
y = 2x + 4 + 1
y = 2x + 5
Thus, the equation that would model the tile pattern above where x represents the figure number and y represents the number of tiles is y = 2x + 5.
Learn more about the linear equation here:
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