Answer:
The width of the door is 36 inches
Step-by-step explanation:
The given parameters are;
The given area of the door = 3024 in.²
The length of the door = 48 + The width of the door
Let W represent the width of the door
Therefore, we have;
The length of the door = 48 + W
The area of the door = The length of the door × The width of the door
∴ By substitution, the area of the door = 3024 = W × (48 + W)
3024 = W × (48 + W) = 48·W + W²
48·W + W² = 3024
∴ 48·W + W² - 3024 = 0
Rearranging, we get;
W² + 48·W - 3024 = 0
By trial and error, we have;
(W + 84)×(W - 36) = 0
Therefore, given that the width of the door is a natural number, we have;
The width of the door, W = 36 inches
the sum of twice a number and three is 21
Answer:
9
Step-by-step explanation:
9+9+18
18+3=21
determine whether the triangles are similar by angle-angle similarity. if yes, write a similarity statement.
Step-by-step explanation:
angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
Topic: congruence and similarity
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What is the fraction 24/4 simplified?
Answer:
6
Step-by-step explanation:
The fraction 24/4 simplified is 6.
To simplify the fraction 24/4, we find the greatest common divisor (GCD) of the numerator (24) and the denominator (4), and then divide both the numerator and denominator by the GCD to obtain the simplified form.
Step 1: Find the GCD of 24 and 4.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 4 are 1 and 4.
The GCD of 24 and 4 is 4, as it is the largest number that divides both 24 and 4.
Step 2: Divide both the numerator and denominator by the GCD.
24 ÷ 4 = 6
4 ÷ 4 = 1
So, the simplified form of 24/4 is 6/1. However, any fraction divided by 1 remains the same, so the simplified fraction is 6.
Therefore, 24/4 simplified is 6.
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Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Column EndMatrix x plus 2 y equals 8 nbsp 2 x plus 6 y equals 9 What is the inverse matrix?
Answer:
[tex]\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right][/tex]
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
[tex]\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right][/tex]
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
[tex]A^{-1}[/tex] = (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A = [tex]\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right][/tex]
[tex]A^{-1}[/tex]= [tex]\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right][/tex]
In right triangle ABC, angle C is a righ angle, AB=13, and BC=5 .what is the length of AC?
Answer:
12
Step-by-step explanation:
Since this is a right triangle you can you pythagorean theorem.
a^2+b^2=c^2
A= shortest side.
B=middle side.
C=longest/slanted side or hypotenuse.
So AB is the hypotenuse.
BC is the short side.
this means that AC is the middle side. Plug your numbers in.
25 + b^2 =169
b^2=144
b=12
AC=12
help plss me ndfkfhfiklfjkfbufjriowxrkoek
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Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
We can use the rise over run method to do this question.
Let's start at the coordinates (1,1)
If we go down 2 from that point and to the right 3 times then we see another point on the line (3, -1).
We would express this as 2 over 3 or [tex]\frac{2}{3}[/tex].
We aren't done yet however.
The line is sloping downwards and this means that the slope is negative.
So, the final answer is [tex]-\frac{2}{3}[/tex]
I hope this helps!!
- Kay
50+30x=250+10x Help!!!!!
Answer:
x = 10
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
Step 1: Define equation
50 + 30x = 250 + 10x
Step 2: Solve for x
Subtract 10x on both sides: 50 + 20x = 250Subtract 50 on both sides: 20x = 200Divide both sides by 20: x = 10Step 3: Check
Plug in x to verify it's a solution.
Substitute: 50 + 30(10) = 250 + 10(10)Multiply: 50 + 300 = 250 + 100Add: 350 = 350solve the equation:
(p + 3)(1 - p)
Answer:
p²-2p+3
Step-by-step explanation:
(p + 3)(1 - p)
p-p²+3-3p
=p²-2p+3
Hope this helps :)
If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball costs $28 to make, plus $15,000 per month in overhead costs (mostly Gabe's extravagant salary) find: a. The average cost c(x) of producing each soccer ball b. Algebraically find the number of soccer balls Gabe's company must produce per month in order to break even (Profit = 0). Profit = Total Revenue – Total Cost c. Algebraically find the number of soccer balls Gabe's company must make to earn a profit of $10,000 per month. d. If Gabe took a pay cut to reduce the overhead costs to $8,000 per month, how many fewer balls would the company have to sell to break even. (There are multiple ways to get this result).
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Selling price= $60
Unitary variable cost= $28
Fixed costs= $15,000
First, we need to calculate the average total cost:
Average cost= total cost / number of units
For example, for 1 unit and 10,000 units:
1 unit:
Average cost= 15,028/1 = 15,028
10,000 units:
Average cost= (15,000 + 28*10,000) / 10,000
Average cost= $29.5
Now, we can calculate the break-even point in units:
0= (60*x) - (28*x) - 15,000
x= number of units to break-even
0= 32x - 15,000
15,000/32= x
468.75=x
break-even point in units= 469
For the desired profit of $10,000:
10,000 = (60*x) - (28*x) - 15,000
25,000= 32x
781.25= x
Break-even point= 782 units
Finally, fixed costs dropped by $8,000:
0= 32x - 7,000
x= 7,000/32
x= 218.75
Break-even point= 219
Difference= 250 units
Given ABC, m A= 60 degrees, m c=45 degrees, AB=8 Find the perimeter of ABC
Answer:113
Step-by-step explanation:
What is 7505 divided by 11?
Answer:
7505÷11 = 682.27272727
Step-by-step explanation:
or you can just put a line over the 27
Answer:
682.27Step-by-step explanation:
7505÷11= 682.272727
deandreh can work three math problems in five minutes . How long will it take him to work fifteen problem ? Plz show ur working out and thank u so much
Answer:
25 minutes
Step-by-step explanation:
Because 3 × 5 is 15 problems so multiple he 5 minutes by 5 and you get 25 minutes.
are my answers correct
Answer:
yesn't
Step-by-step explanation:
Answer:
yes last Friday i did this and i do it the same i got it correct.
Step-by-step explanation:
A person who weighs 105 pounds on Earth weighs 175 pound on the moon How much does a pound person weigh on the moon?
Answer:
1.67 pounds
Step-by-step explanation:
The problem above can be solved by using "direct proportion." This proportion shows that as one quantity increases, the other quantity increases and vice-versa.
Step 1: Represent the weight of the person on the moon by n.
Step 2: Set up a proportion.
[tex]\frac{105}{175}[/tex] = [tex]\frac{1}{n}[/tex]
Step 3: Cross multiply.
105 x n = 175 x 1
105n = 175
Step 4: Find n by dividing both sides by 105.
n = [tex]\frac{175}{105}[/tex]
n = 1.666 or 1.67 pounds (lowest term)
A pound of person on Earth will weigh 1.67 pounds on the moon.
What is the equation of the line through the points (3, 2), (8, 5), (13, 8) and (18, 11)?
A. y= 5/3x- 1/3
B. y= 3/5x- 1/5
C. y= 5/3x+ 1/3
D. y= 3/5x+ 1/5
Answer:
Option D.) y = 3/5 + 1/5
Step-by-step explanation:
First, we find the Slope using the formula: m = y2 - y1/x2 - x1
You may choose any two points but I will use these two for no reason at all.)
Points: (3,2) and (8,5)
m = y2 - y1/x2 - x1
m = 5 - 2/8 - 3
m = 3/5
Now that we have the slope, we can now find the Slope Intercept Form by using the Slope Form Formula. (need at least one point and slope.)
Formula: y - y1 = m(x - x1)
Point: (3,2) (you may choose any point but I will choose this for no reason at all xD)
y - y1 = m(x - x1)
y - 2 = 3/5(x - 3)
y - 2 = 3/5x - 9/5
y - 2 = 3/5x - 9/5
y = 3/5x - 9/5 + 10/5 (2 can be is any fraction that consists of the numerator multiplied twice by the denominator, such as 2/1, 4/2, 8/4, etc.)
y = 3/5 + 1/5
The final equation of the line can be written as -
y = (3/5)x + 1/5
What is the general equation of a straight line?
The general equation of a straight line is given by -
y = mx + c
Given is a line that passes through the points (3, 2), (8, 5), (13, 8) and (18, 11).
The line passes through the points (3, 2) and (8, 5). Therefore, the slope of the line will be -
m = (5 - 2)/(8 - 3) = 3/5
Now, consider the line : y = mx + c. For a point (3, 2) -
2 = (3/5) x 3 + c
2 = 9/5 + c
c = 2 - 1.8
c = 0.2
c = 1/5
Therefore, the final equation of the line can be written as -
y = (3/5)x + 1/5
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a candle is burning at a linear rate. The candle measures five inches two minutes after it was lit. It measures three inches eight minutes after it was lit. What was the original length of the candle?
Answer:
5 2/3 inches.
Step-by-step explanation:
8-2=6 minutes and 5-3=2 inches so it lost 2 inches in 6 minutes. This means it loses an inch every three minutes. Since we have to go back by 2 minutes we will have to figure out how much length we have to add to the candle to figure out how long it was originally by multiplying by 2/3 as 2 inches is 2/3 the required to remove an inch, so 1 inch * 2/3 = 2/3 of an inch. Add that to the length at two minutes and we have 5 2/3 inches as its original size.
Question in picture solve
Answer:
36
Step-by-step explanation:
You substitute 9 in for x so it would look like this 5(9)-9 then you solve and you get the solution of 36.
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Jyoti collects stamps. The table shows the number of stamps she collected over a 12-week period.
Find the rate of change for each time period to the nearest hundredth. Identify the time period
during which the number of stamps increased at the fastest rate.
to find the square root of a number do you divide by 2
Two towns on a map are 2 1/4inches apart. The actual distance between the towns is 45 miles. Which of the following could be the scale on the map?
a. 1/2 inch : 10 miles b. 1 inch: 5 miles c. 1 inch : 20 miles
Answer:
A. 1/2 inch:10 miles
Step-by-step explanation:
1/2*4.5=2 1/4
10*4.5=45
2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4. How many votes did she get?
Answer:
473 or 472, depends on how you round
Step-by-step explanation:
378/4 = 94.5
94.5 x 5 = 472.5
The number of votes she gets will be 473.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4.
Then the number of votes she gets that will be
→ 378 x 5 / 4
→ 378 x 1.25
→ 472.5 ≅ 473
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80 points!
A store had 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.
Which recursive function best represents the number of bottles of water in the store, given that f(0) = 250?
A. f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0
B. f(n) = 250 − f(n − 1) ⋅ 0.4 + 48, n > 0
C. f(n) = f(n − 1) ⋅ 0.4 + 48, n > 0
D. f(n) = 250 − f(n − 1) ⋅ 0.6 + 48, n > 0
pls give reason
Answer:
A
Step-by-step explanation:
Given:
Initial number of bottles = 250
Every week = 40% is sold and 48 bottles arrive.
Week 1 = 250 - (250 x 0.40) + 48 = 250 - 100 + 48 = 198
Week 2 = 198 - (198 x 0.40) + 48 = 198 - 79 + 48 = 167
Answer is: A. f(n ) = f(n - 1) • 0.6 + 48, n > 0.
Miguel used the graph below to represent a system of equations. On a coordinate plane, 2 lines will intersect at one point. Which statement is the best conclusion for Miguel’s system?
Answer b,since the lines will intersect at one point, this system has one solution:
Step-by-step explanation:
Took the test
Answer:
B
Step-by-step explanation:
The sum of a number, n, and a number 5 larger than it is 41. Which of the following equations could be used
to solve for the number?
(1) +5n41
(3) 5(n+1) = 41
(2) +n+ 5-41
(4) 5n+n+1-41
In the diagram below, AB≅AD, m∠A=48° and m∠BCD=40°. Which statement is true?
Answer:
3
Step-by-step explanation:
I’m failing all my classes please help
Answer:
b
Step-by-step explanation:
Joseph is reading a 32 page book he read 6 pages in 15 minutes if he continues to read at the same rate how long will it take him to read the entire book
Answer:
80 minutesssssss
Answer:
(edit) your answer is 80 min
Step-by-step explanation:
first we can set this up as a proportion.
so it would be 15 over 6 and your other side would be x over 32
so when u cross multiple your equation would be 6x = 480
then you divide both sides by 6 and when you divide 480 by 6 u will get 80
Find the simple past tense of these verbs in the passage.
is
go
begin
do
make
grow
sell
get
ring
Answer:
was
went
began
did
made
grow
sell
get
rang
I don't know if it's right though?
Answer:
was
went
began
did
made
grew
sold
got
rang
Find x no need for explanation I just need answer thanks
Answer:
x = 12 m
Step-by-step explanation:
Length = x m
Width = 3⅔ = 11/3
Area = 44 m²
Area of rectangle = length × width
Plug in the values into the equation
[tex] 44 = x \times \frac{11}{3} [/tex]
[tex] 44 = \frac{11x}{3} [/tex]
Multiply both sides by 3
[tex] 44 \times 3 = \frac{11x}{3} \times 3 [/tex]
[tex] 132 = 11x [/tex]
Divide both sides by 11
[tex] 12 = x [/tex]
x = 12
A coach brought 12,000 milliliters of water to a tournament. How many liters of water did the coach bring?
Answer:
0.012
Step-by-step explanation:
Answer:
12 liters
Step-by-step explanation:
on google