Let x be the length of the shorter wall of the rectangular room and y be the length of the longer wall of the rectangular room. Since the longer wall is 7 ft longer than the shorter wall, we can write the equation y = x + 7. We can also express the diagonal of the rectangular room using the Pythagorean theorem as x^2 + y^2 = 13^2. We can solve for x and y by substituting the equation y = x + 7 into the equation x^2 + y^2 = 13^2 and then solving for x. Doing this, we get x^2 + (x + 7)^2 = 13^2. Expanding the square on the right side of the equation and then rearranging the terms, we get x^2 + 2x^2 + 14x + 49 = 169. Combining like terms, we get 3x^2 + 14x - 120 = 0. This quadratic equation can be factored as (x - 8)(3x + 15) = 0. Since the length of a side of a rectangle must be positive, we can ignore the solution x = -15/3. So, the length of the shorter wall of the rectangular room is x = 8 ft. The length of the longer wall can be found by substituting this value into the equation y = x + 7, giving us y = 8 + 7 = 15 ft. Therefore, the dimensions of the rectangular room are 8 ft by 15 ft.
The perimeter of a rectangular plot of land for a new housing development is 270 m.
The width of the site is 60 m.
Calculate the length of the building site.
The length of the building site is 75 meters.
To calculate the length of the rectangular plot of land, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (Length + Width)
In this case, the width is given as 60 m, and the perimeter is given as 270 m. We can substitute these values into the equation and solve for the length.
270 = 2 * (Length + 60)
Dividing both sides of the equation by 2 gives:
135 = Length + 60
Subtracting 60 from both sides of the equation gives:
Length = 135 - 60
Length = 75
It's important to note that the length of the building site is specific to this particular rectangular plot of land with a given width and perimeter. If the width or perimeter were to change, the length would also change accordingly. Additionally, this calculation assumes that the shape of the plot is a rectangle and that the perimeter only includes the sides of the plot, not any internal structures or obstacles.
For more such questions on length
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3. Find the missing side lengths. Leave your answers as radicals in simplest form. Show your work to support
your answer.
Answer: b=2(square root of 2) and a=4
Step-by-step explanation:
Since this is a 45-45-90 triangle we know that side b is equal to [tex]b=2\sqrt{2}[/tex].
In a 45-45-90 triangle, the hypotenuse is equal to [tex]x\sqrt{2}[/tex] this means in order to find missing side length a, we have to multiply [tex](2\sqrt{2})(\sqrt{2})[/tex] this will give us 4
so the missing side lengths are, [tex]b=2\sqrt{2}[/tex] and [tex]a=4[/tex]
Answer: B = 2 (Square root of 2) A = 4
Explanation: This is an isosceles triangle so the legs will be the same. To get the hypotenuse I simply just multiplied one leg by the square root of 2 and two square roots of the same number multiply the whole number by whatever number is in the square root (so in this case it's multiplying 2 by 2)
what is the missing reason in the proof shown ?
a. symmetric property
b. reflexive property
c. transitive property
d. commutative property
Answer:
A symmetric property
Step-by-step explanation:
Answer:
Reflexive property
Step-by-step explanation:
m(x) = -3x + -2
Find m(-4)
Answer:
3x +2 =5
and m(x) was x=5 ,= m= -4
please help me with this asap
Answer:
76
Step-by-step explanation:
I rewrote the question so I wouldn't have to keep going back to the picture.
A poll asked 1000 adults who own smartphones where they put their smartphone while sleeping. The following two-way table of relative frequencies shows the data collected on age and smartphone habits. Of the adults polled, 200 were 65 or older.
How many of the adults polled that were 65 or older sleep with their smartphone within reach?
---------------------------------------------------------------------------------
I bet if I called this a two- way table of "percentages, written as decimals", it would make more sense.
Total number of adults 65 and older = 200. The 0.38 of them that sleep with their phone in reach = 38% of them. Multiply 200 x 0.38 = 76
To check the math, 200 x 0.62 = 124, and 124 + 76 = 200.
As always, please let me know if you have questions. I've answered each of your open questions as of now (11am CDT, USA)
Solve the right triangle.
Round your answers to the nearest tenth.
Answer:
A = 48°
b = 13.5
c = 20.2
Step-by-step explanation:
✔️A = 180° - (90° + 42°) (sum of triangle)
A = 48°
✔️To find b and c, apply trigonometric function.
Reference angle = 42°
Opposite = b
Hypotenuse = c
Adjacent = 15
✅Apply TOA to find b:
Tan 42 = Opp/Adj
Tan 42 = b/15
15 × Tan 42 = b
13.5060607 = b
b = 13.5 (nearest tenth)
✅Apply CAH to find c:
Cos 42 = Adj/Hyp
Cos 42 = 15/c
c × Cos 42 = 15
c = 15/Cos 42
c = 20.1844909
c = 20.2 (nearest tenth)
6 cm
6 cm
1
6 cm
9 cm
-6 cm
-15 cm
Answer:
180 cm^2
Step-by-step explanation:
Remark
If you put the slices that have been removed back into the figure, and figure out the resulting rectangle and subtract the slices, you get an answer that is easily calculated.
Note
The square on the upper right is 6 cm high. That makes the width of the rectangle 9 + 6 = 15. The length is already known as 15. So this square is 15 by 15 = 225
The lower right triangle is a little harder to handle. The total width is 15. The height of the triangle is 6 + 6. The first 6 comes from the square that was removed. The total with is 15. So the height of the lower right triangle is 15 - 12 = 3
Answer
The answer to the square on the upper left that was removed = 6*6 = 36
The answer to the triangle on the lower right is 1/2 * 6 * 3 = 9
The total of the removed figues is 36 + 9 = 45
The area of the figure with both figures removed is 225 - 45 = 180 cm^2
3. You have a yard that has a width of 5 yd 1 ft and a
length of 30 ft. Find the simplified ratio of the width
to the length:
Answer:
5:47
Step-by-step explanation:
Consider the following statement. ∀a ∈ Z, (a − 1) a is not an integer. (a) Select the correct negation for this statement. For every integer a, a − 1 a is an integer. There is an integer a such that a − 1 a is not an integer. For every integer a, a − 1 a is not an integer. There is an integer a such that a − 1 a is an integer. (b) Is the given statement true or false? If the statement is true, enter TRUE; if the statement is false, enter a value of a that could be used as part of a counterexample that justifies its falseness.
Answer:
a) There is an integer a such that [tex]\frac{a-1}{a}[/tex] is an integer
b) False
Step-by-step explanation:
Statement : ∀a ∈ Z, (a − 1) a is not an integer
A) The correct negation will be :
There is an integer a such that [tex]\frac{a-1}{a}[/tex] is an integer
B) The Given statement is FALSE because
when we assume the value of a = 1
( a - 1 ) / a = (1 - 1 ) / 1 = 0 ; which is an integer
I have a standard deck of playing cards in one pile, and a deck of 10 distinct Pokémon cards in another
pile. If I randomly choose 3 playing cards and 4 Pokémon cards (and I don't care about the order I draw
them), how many different choices could I make?
Answer:
You could make 4,641,000 different choices.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different choices could I make?
3 cards from a set of 52(number of cards on a standard deck).
4 Pokemon cards from a set of 10. So
[tex]T = C_{52,3}*C_{10,4} = \frac{52!}{3!49!}*\frac{10!}{4!6!} = 22100*210 = 4641000[/tex]
You could make 4,641,000 different choices.
Answer choices
4 feet
5feet
6feet
8feet
Please help if you send a link I will report
Answer:
d
Step-by-step explanation:
only reasonable answer
Please answer the questions below.
Answer:
i can't see the question
!!ASAP!! Please help marking brainliest w/ points!!
—————-
Select yes or no for each expression to determine whether it is or can be written as a monomial!
Answer:
1. yes
2. no
3. yes
4. yes
5. no
Step-by-step explanation:
You are considering a project in Bolivia that would generate 3 million dollars in cash flows per year going forever. The cost of the project is 10 million dollars. The discount rate for the project is 15%. You believe that there is some probability of expropriation prior to the 3rd year (after the 2nd cash flow). Which of the following statements is most correct?
a. This is a good project if the probability of expropriation is larger than.33.
b. This is a good project if the probability of expropriation is smaller than.33.
c. This is a good project if the probability of expropriation is smaller than .
d. This is a good project if the probability of expropriation is smaller than .66.
Answer:
b. This is a good project if the probability of expropriation is smaller than .33.
Step-by-step explanation:
a) Data and Calculations:
Cash inflows per year going forever = $3 million
Cost of project = $10 million
Discount rate for the project = 15%
The present of a perpetuity = Cash inflow/Discount rate
= $3/0.15 million
= $20 million
NPV = $10 million ($20 - $10 million)
b) The probability of expropriation indicates that the government of Bolivia may likely take over the project after the initial investment had been made. This will cause the investor to lose her investments. If the probability of the expropriation taking place is equal to 0.33, the investor may recover the cost of investment without making any profit in three years' time. But if the probability of expropriation happening is less than 0.33, the investor could recover enough to cover the investment cost.
9+99999+99999-9999999999+9999999
Answer:
-9989799993
Step-by-step explanation:
Put it in a calculator
Ty for points
Answer:
Step-by-step explanation:
-989,799,993
PLEASE HELP !!
ILL GIVE 40 POINTS !
PLUS BRAINLIEST!!
NO LINKS OR FILES.
Answer: answer is C my fellow hooman
Step-by-step explanation:
Answer:
It is B
Step-by-step explanation:
squares rectangles and rhombl are types of trapezoids true or false
Answer:
false
Step-by-step explanation:
if the value of 12.5% equals 4,000, what is the value of 87.5%?
Answer:
12.5%*7=87.5%
4000*7=28000
28000
Answer:
28,000
Step-by-step explanation:
Since 4,000 is 12.5%, you can divide 87.5/12.5 to see how many times 12.5 goes into 87.5, which is 7 times. so then since you need to find the value of how much 87.5% is, then you can multiply 4,000 by 7 since 7 is 87.5 percent, leaving us with 28000
Guys I don't need you to answer the question I just want to know what the math is called
Answer:
that's the quadratic formula:)
Step-by-step explanation:
P = 3. Q = -2. Solve 4PQ
Answer:
-24
Step-by-step explanation:
4(3)(-2) = -24
What is the area, in square units, of the parallelogram shown below? A parallelogram ABCD is shown with height 8 units and base 6 units. 24 square units 48 square units 52 square units 64 square units
Answer:
Step-by-step explanation:
Area of parallelogram = base * height
= 6 * 8
= 48 square units
Answer:
Solution :-Area = Base × Height
Area = 6 × 8
Area = 48 units²
[tex] \\ [/tex]
please help me and fast
Simplify: (3^5)^2 / 3^-2
A) 3^10
B) 3^9
C) 3^12
D) 3^8
Answer:
C
Step-by-step explanation:
(3^5)^2= 59049 divided
(3)^-2 = 0.11111111
531441 = 3^12
An exercise machine with an original price of $626 is on sale at 20% off
a. What is the discount amount?
b. What is the exercise machine's sale price?
Answer:
$125.2-discount
$500.8-sale price
Step-by-step explanation:
hope it helps
LOOK AT THE PHOTO AND HELP GIVE ME EXPLANATION
exterior angle
60 + 2x = 180 - 602x = 120 - 60x = 30then
x + y + 60 = 18030 + 60 + y = 180y = 180 - 90y = 90°Answer:
90 degrees
Step-by-step explanation:
The angle is a right angle, because its straight up. A right angle is always 90 degrees.
What is the value of the expression shown?
24 − 62
A.-6
B.-12
C.12
Answer:
None
Step-by-step explanation:
what is 91,360 in expanded form
Answer:
Expanded Notation Form:
91,360 =
90,000
+ 1,000
+ 300
+ 60
+ 0
Expanded Factors Form:
91,360 =
9 × 10,000
+ 1 × 1,000
+ 3 × 100
+ 6 × 10
+ 0 × 1
Expanded Exponential Form:
91,360 =
9 × 104
+ 1 × 103
+ 3 × 102
+ 6 × 101
+ 0 × 100
Word Form:
91,360 =
ninety-one thousand three hundred sixty
Hope this helps! mark me as brainliest if possible, you dont have too!
Step-by-step explanation:
Consider the division problem. 68)472 Which would be the best replacement for 68 to get a quick, but close, estimate of this quotient O A. 50 ОВ. 65 OC. 69 D. 70 E. 100
Answer:
Step-by-step explanation:
.........................................
Answer:
yes
Step-by-step explanation:
Answer:
.......
Step-by-step explanation:
What is the answer please help if you put a link I will report
Answer:
A .27 miles
Step-by-step explanation:
brainliest pls