Answer:
3 meters
Step-by-step explanation:
We assume the storage room is a rectangle, like most rooms, no indication it is otherwise.
We know it's a rectangle and not a square because it is longer than wide.
We have the perimeter measurement (16 meters).
So, we can make the following equation:
2x + 2y = 16
x being the width of the room, y being it's length. A perimeter is the sum of all sides.
We also know the room is 2 meters longer than wide... so:
y = x + 2
If we replace y in the first equation by its value relative to x, we get:
2x + 2(x + 2) = 16 which becomes
2x + 2x + 4 = 16
4x =12
thus x = 3
Width: 3 meters
Length: 5 meters.
Confirms the 16 meters perimeter.
Answer:
Width = 3 meters
Step-by-step explanation:
We are given that for an equipment storage room, it is 2 meters longer than its width and the perimeter of this room is 16 meters.
Given the above information, we are to find the width of the room.
Perimeter = [tex]2l+2w[/tex]
Supposing [tex]x[/tex] to be the width and [tex]x+2[/tex] to the length, we can write it as:
[tex]16=2(x)+2(x+2)[/tex]
[tex]16=2x+2x+4[/tex]
[tex]12=4x[/tex]
[tex]x=\frac{12}{4}[/tex]
x = 3
Therefore, the width = 3 meters.
What is the length of a rectangle whose perimeter is P, if the width is 6?
Answer:
(P-12)/2 = L
Step-by-step explanation:
1. Start off with an equation in terms of perimeter
P = (2)(6) + (2)(L)
2. Multiply the two and the six
P = 12+ (2)(L)
3. Move the terms around so only "L" is on one side
(P-12)/2 = L
hope this helped :)
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Step-by-step explanation:
Answer:
And for people struggling with simpler answers, here!
Step-by-step explanation:
P-12
———-
2
or
P-12/2
Justin walked his dog 2 blocks west,6 blocks north,2 blocks east,and 6 blocks south.Then he walked he walked his other dog the same route.How many blocks did Justin walk in all?
Answer:
32
Step-by-step explanation:
Thankyouuuuuuuuuuuuuuuuuu
Is √1/√49 rational ???
The number √1/√49 is a rational number.
Given a number √1/√49.
Here the numerator and the denominator includes the square root.
We can see that both the numbers inside the square root is a perfect square.
So the number can actually be written in the integer form.
So,
√1/√49 = 1/7, since 7² = 49
Now rational numbers are numbers which can be written in the form of p/q where p and q are integers with q not equal to 0.
Here the number can be written as 1/7, where 1 and 7 are integers.
Hence it is rational.
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7x^2−5x=9x^2+7x
SOLVE THE EQUATION
PLZZZ SOLVE QUICKLY
Answer:
x=0 x = -6
Step-by-step explanation:
7x^2−5x=9x^2+7x
subtract 7x^2 from each side
7x^2-7x^2−5x=9x^2-7x^2+7x
-5x = 2x^2 +7x
Add 5x from each side
-5x+5x = 2x^2 +7x+5x
0 = 2x^2 +12x
Factor out a 2x
0 = 2x(x+6)
Using the zero product property
2x =0 x+6 = 0
x=0 x = -6
Chen completed the division problem below.
Answer:
B. He multiplied the dividend by 100 instead of 10.
Step-by-step explanation:
Chen had to divide [tex]1.926[/tex] by [tex]0.9[/tex]. To make it easier to divide, he thought of multiplying both the dividend and the divisor by 10.
Chen multiplied the divisor by 10 but mistakenly multiplied the dividend by 100 instead of 10.
So his whole division problem was changed.
Therefore, the correct answer option is B. He multiplied the dividend by 100 instead of 10.
Answer:
option B
He multiply the dividend by 100 instead of 10
Step-by-step explanation:
Given that,
divisor = 0.9
dividend = 1.926
Chen decided to multiply each by 10 to get
divisor = 0.9 x 10 = 9
dividend = 1.926 x 10 = 19.26
but unfortunately he multiply the dividend by 100
As,
1.926 x 100 = 192.6
So,
Chen's error was that he multiply the dividend by 100 instead of 10.
PLEASE HELP WITH THIS QUESTION
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x------> the length of rectangle
y----> the width of rectangle
we know that
The area of the constructed figure is equal to
[tex]A=xy+2x^{2} +2y^{2}\\A=120\ cm^{2}[/tex]
so
[tex]120=xy+2x^{2} +2y^{2}[/tex] -----> equation A
[tex]x=y+5[/tex] -----> equation B
substitute equation B in equation A
[tex]120=y(y+5)+2(y+5)^{2} +2y^{2}\\120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\5y^{2}+25y+50-120=0\\5y^{2}+25y-70=0[/tex]
using a graphing calculator to resolve the quadratic equation
the solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
The perimeter of rectangle is equal to
[tex]P=2(x+y)\\P=2(7+2)=18\ cm[/tex]
Carol’s last credit card statement said that she had an account balance of -$130. Which of the following accounts balances represents a debt greater than Carol’s?
A debt greater than Carol's would bear a value that is numerically larger but still under the negative sign. In simpler terms, any debt greater than -$130 is indeed a greater debt.
Explanation:The question asks, 'Which of the following account balances represents a debt greater than Carol's?' When working with debts in math, it's important to remember that the larger the number, the greater the debt. So any number larger than -$130 represents a debt greater than Carol's.
For example, a balance of -$150 would be a larger debt than Carol's -$130. Why? Because when you owe $150, it's more than owing $130, despite the negative sign. Conversely, a balance of -$100 would be less of a debt than Carol's, because owing $100 is less than owing $130.
It's a somewhat counterintuitive part of working with negative numbers, but once you understand that the negative sign represents a debt, it starts to make sense. The concept of debt here is similar to examples provided where people often have a tendency to hold onto a savings account while carrying a credit card debt.
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An account balance which represents a greater value than Carol's account balance is -$165
Using the parameters given for our Calculation;
Carol's account balance = -$130Values which represents a greater debt than Carol's are values which falls farther to the left of 130 on a number line.
From.the values given, only -165 falls further to the left of -130 on a number line.
Hence, the correct answer is -$165.
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which value of b makes the trinomial a perfect square
Answer:
12
Step-by-step explanation:
Given trinomial is [tex]x^2-bx+36[/tex].
Now we need to find the value of b that will make the trinomial [tex]x^2-bx+36[/tex] a perfect square.
[tex]x^2-bx+36[/tex]
[tex]=x^2-bx+36[/tex]
[tex]=x^2-bx+6^2[/tex]
compar with [tex]=a^2-2ab+b^2=(a-b)^2[/tex]. we get:
a=x and b=6
then middle term -2ab=-2(x)(6)=-12x
compare -12x with -bx, we get b=12
Hence choice C. 12 is correct.
Answer:
The correct answer is option C. 12
Step-by-step explanation:
It is given a quadratic expression
x² - bx + 36
To find the value of b
From the above expression we can see that 36 is a perfect square,
6² = 36
We can write this expression as ( x - 6)² if b = 12
(x - 6)² = x² - 12x + 36
Therefore the correct answer is option C. b = 12
joshua,steve,antonioare baking pie.joshua has 1/2 cups of flour, steve has 1 3/4 cups of flour ,and Antonio has 1 4/6 cups of flour . how may cups of flour do they have all together ?
Answer:
They all have 3 cups together.
Step-by-step explanation:
I added 1/2 plus 1 3/4 plus 1 4/6 on a calculator and got 3.91666666667
Basically 3.
I was supposed to determine the length of the winding path through the circle.
my answer is
[tex]12.56 \: in {}^{2} [/tex]
Is this correct?
Check the picture below.
the idea being, the winding path is made out of semi-circles, each semi-circle has a diameter of 3, as you see there in the picture.
now, if we could just take two semi-circles, we'd have a full circle, with a diameter of 3, so from all 4 semi-circles we can actually get two full circles, as you see there, and the circumference of those two full circles, is the length of the winding path.
[tex]\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=3 \end{cases}\implies C=3\pi \qquad \stackrel{\textit{two circles added together}}{3\pi +3\pi \implies 6\pi ~~\approx~~18.85}[/tex]
3/5 divided by 3/10 equals what
Answer:
2
Step-by-step explanation:
If sinv=-5/13, pi
1. cos(u+v)=
2. sin(u-v)=
the answer is number 2 sin (u-v)÷
Dawn has 1.20 in nickels, dimes and quarters. For each nickel she has one dime and for each dime she has one quarter. How many total coins does she have?
Answer:
9
Step-by-step explanation:
"For each nickel, she has one dime"
That means she has the same number of nickels and dimes.
"for each dime she has one quarter"
That means she has the same number of quarters and dimes.
She has the same number of each coin.
Let's say she has x coins of each type.
The nickels are worth 0.05x; the dimes are worth 0.10x. The quarters are worth 0.25x. Altogether, the coins are worth
0.05x + 0.10x + 0.25x
We are told her coins are worth $1.20, so we set those two amounts equal and solve for x.
0.05x + 0.10x + 0.25x = 1.20
0.40x = 1.20
x = 1.20/0.40
x = 3
She has 3 coins of each type. Since there are 3 types of coins, she has 9 coins.
Dawn has a total of 9 coins, which include 3 nickels, 3 dimes, and 3 quarters.
Explanation:The subject of this question is a math problem involving counting coins. In this scenario, dawn has a total of $1.20 in nickels, dimes, and quarters. And the number of nickels, dimes and quarters are equal since for every nickel Dawn has, she also has a dime and a quarter.
Now, the value of a nickel is $0.05, a dime is $0.10 and a quarter is $0.25. So, the total value of a nickel, a dime and a quarter is $0.40. Therefore, since the total amount of money she has is $1.20, we divide that amount by the total value of each group of coins: $1.20 / $0.40 gives us 3.
So Dawn has 3 nickels, 3 dimes, and 3 quarters, for a total of 9 coins.
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Given a=-3,b=4 and c=-5, evaluate a-b-c
A.-12
B.-6
C-2
Answer:
C
Step-by-step explanation:
a-b-c
-3-4-(-5)
-3-4+5 [as - - = +]
-2
in a game the player wins if he rolls a 6 on a number cube .if the number cube is rolled 18 times then what is the reasonable
prediction for the number of unsuccessful rolls
Prediction for the number of unsuccessful rolls is 15.
Step-by-step explanation:There is [tex]\frac{1}{6}[/tex] chance of rolling number 6 on the cube. If we want to find out what is the prediction for rolling number 6 in 18 rolls, we need to multiply [tex]6*\frac{1}{6}[/tex] which is 3. So if we roll a cube 18 times, we will probably got number 6 three times. When we subtract 3 from 18 (18-3), we get 15. That is the answer to your question.
I hope I helped you. I will be really happy, If you mark my answer as the brainliest.Your David
Find the arc length of the partial circle..
Answer:
The arc length of the partial circle is [tex]6\pi\ units[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
In this problem we have a 3/4 of a circle
so
the circumference is equal to
[tex]C=(\frac{3}{4})2\pi r[/tex]
[tex]C=\frac{3}{2}\pi r[/tex]
we have
[tex]r=4\ units[/tex]
substitute
[tex]C=\frac{3}{2}\pi (4)[/tex]
[tex]C=6\pi\ units[/tex]
Carli made a photo book.she put 9 pictures on each page. She filled 6 pages with pictures of her trip to Fort Lauderdale and 4 pages with pictures of her trip to Las Vegas. How many pictures are in her photo book?
Answer:
90
Step-by-step explanation:
If you take 9 pictures on each page that is gonna be its own number so you than add 6 and 4 and get ten than multiply it by 9 and boom you get 90
Carli has a total of 90 pictures in her photo book, with 54 pictures from her trip to Fort Lauderdale and 36 pictures from her trip to Las Vegas.
Explanation:In order to find the total number of pictures in Carli's photo book, we need to calculate the number of pictures on each page for both trips and then sum them up. Carli put 9 pictures on each page. She filled 6 pages with pictures of her trip to Fort Lauderdale, so the number of pictures for this trip is 6 pages x 9 pictures per page = 54 pictures. Carli also filled 4 pages with pictures of her trip to Las Vegas, so the number of pictures for this trip is 4 pages x 9 pictures per page = 36 pictures. The total number of pictures in her photo book is 54 pictures + 36 pictures = 90 pictures.
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he front of an A-frame house is in the shape of a triangle.The height of the house is 20 feet.The area of the A-frame is 600 square feet.Write and solve an equation to find the base of the A-frame house.
Answer:
Equation: [tex]600=\frac{20b)}{2}[/tex]
Base: 60 feet.
Step-by-step explanation:
The formula for calculate the area of a triangle is:
[tex]A=\frac{bh}{2}[/tex]
Where:
A: is the area of the triangle.
b: is the base of the triangle.
h: is the heigth of the triangle.
Knowing the area of the triangle and its height, you can write the equation:
[tex]600=\frac{20b}{2}[/tex]
Where b is the base in feet of the A-frame house.
To solve it:
Multiply both sides of the equation by 2.
Divide both sides of the equation by 20.
Then:
[tex](2)(600)=(\frac{20b}{2})(2)\\\\1200=20b\\\\\frac{1200}{20}=\frac{20b}{20}\\\\60=b[/tex]
The base of the A-frame house is 60 feet.
A rectangular flowerbed is 22 inches long by 8 inches wide. The flowerbed is filled to a depth of 6 inches with dirt. What is the volume, in cubic inches, of the dirt in the flowerbed?
176
180
712
1056
Answer:
The volume of the dirt in the flowerbed is [tex]1,056\ in^{3}[/tex]
Step-by-step explanation:
we know that
To find the volume of the dirt in the flowerbed, multiply the long by the width by the depth
so
[tex]V=(22)(8)(6)=1,056\ in^{3}[/tex]
Final answer:
To calculate the volume of dirt in a rectangular flowerbed with dimensions of 22 inches by 8 inches by 6 inches, use the formula Volume = length × width × height, resulting in 1056 cubic inches.
Explanation:
The question asks for the volume of dirt a rectangular flowerbed can hold. To find the volume, we use the formula Volume = length × width × height. Given the dimensions are 22 inches (length) by 8 inches (width) by 6 inches (height), we calculate the volume as:
Volume = 22 in. × 8 in. × 6 in. = 1056 cubic inches. Therefore, the volume of the dirt in the flowerbed is 1056 cubic inches.
caitlin had some money. after her shopping spree at redmond town center she had $5 left. she bought a new pair of shoes for $48, 2 pais of jeans at $19 each, and 2 t-shirts at $13 each. how much money did she have at the beginning
Answer:
$117
Step-by-step explanation:
Add 48 + 19 + 19 + 13 + 13 + 5 = 117
URGENT!!! Write the product as a sum or difference.
18cos(29x)cos(17x)
Select the correct answer below:
9sin(46x)+9sin(12x)
9sin(46x)−9sin(12x)
9cos(46x)+9cos(12x)
9cos(46x)−9cos(12x)
9cos(46x)+9sin(12x)
9sin(46x)−9cos(12x)
Answer:
9cos(46x) + 9cos(12x)
Step-by-step explanation:
18cos(29x)cos(17x)
According to Product-Sum identities
cos(α)cos(β)= (1/2)[cos(α+β)+cos(α-β)]
Putting α=29x and β=17x in Product-Sum identity we get
= 18×(1/2)[cos(29x+17x)+cos(29x-1`7x)]
Dividing 18 by 2 we get 9
= 9[cos(46x)+cos(12x)]
Multiplying 9 with both the terms we get
= 9cos(46x)+9cos(12x)
Which number is 4 units from-1
A farmer has 1600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?
Answer:
A = (800 yd - x)x, [0, 800]
Step-by-step explanation:
The farmer fences in this rectangular garden using 1600 yds of fencing. Using the formula for the perimeter of a rectangle,
P = 2x + 2L, where x is the width and L is the length. Here P = 1600 yd.
Solving for L: 1600 yd = 2x + 2(L) → 800 yd = x + L → L = 800 yd - x.
The area of the rectangle is A = L·x. Subbing (800 yd - x) for L, we get:
A = (800 yd - x)x. This is the desired formula for the area of the rectangle as a function of x alone. Neither length nor width can be negative, so the domain of this function A is x ≤ 800 yd.
Let the length of the rectangular garden = l yards
And the width of the garden = w yards
Farmer has the fence in length = 1600 yards to cover all the sides of the garden
Therefore, Perimeter of the rectangular garden = 1600 yards
Since, perimeter of the rectangular garden is given by the expression,
Perimeter = 2(l + w)
By substituting the values in the expression,
1600 = 2(l + x)
l + x = 800
l = 800 - x -------(1)
Since, area of the rectangle = Length × Width
= l × w
= lx
Therefore, by substituting the value of 'l' in terms of 'x' in from equation (1),
Area of the rectangular garden = (800 - x)x
If the area of the garden is represented by by the function A(x),
A(x) = (800 - x)x
A(x) = 800x - x²
Since, Area can not be negative or zero,
Domain of the function will be 0 < x < 800
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243 is 60% of what amount
Answer:
60% of 243 = 145.80
Hope this helps,
Davinia.
60% × 243 =
(60 ÷ 100) × 243 =
(60 × 243) ÷ 100 =
14,580 ÷ 100 =
145.8
how to make sure it is right we do the reverse of what we did
145.8 ÷ 243 =
0.6 =
0.6 × 100/100 =
0.6 × 100% =
(0.6 × 100)% =
60%
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What is the slope of the line through the points (–2, –1) and (8, –3)?
-3 + 1 = -2
8 + 2 = 10
-2/10 = -1/5
Answer = -1/5
The slope of the line through the points (2, 1) and (8, 3) is calculated using the slope formula and is -1/5.
To find the slope of a line passing through two points, you will need to use the slope formula, which is:
(change in y) / (change in x)or (y2 - y1) / (x2 - x1).
For the points given (–2, –1) and (8, –3), you would calculate the slope as follows:
Slope (m) = (-3 - (-1)) / (8 - (-2)) = (-3 + 1) / (8 + 2) = (-2) / (10) = -1/5.
So, the slope of the line through the points (–2, –1) and (8, –3) is -1/5.
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has no oil and the test predicts it has oil?
Answer:
Don't take my word for it but I think it would be 55% chance. I'm Probably wrong.
Step-by-step explanation:
Answer:
9% or 0.09
Step-by-step explanation:
Given, chance of land having oil is 45%. Which is 0.45
So, chance of land NOT having oil is percent. Which is 0.55
Given, kit's accuracy rate of finding oil as 80%. Which is 0.80
So, kit's accuracy rate of NOT finding oil is percent. Which is 0.20
These 2 events are INDEPENDENT, which means that the probability of one event occurring does not affect the probability of another event occuring.
The formula, if we let the two evens be A and B, is:
P(A and B)=P(A) * P(B)
Now, "the probability that the land has oil (event A)AND the test predicts that there is no oil (event B)" will be:
P(A and B) = P(A) * P(B)
Hence, the probability is 0.09 or 9%
The reduced row-echelon form of the augmented matirx of a system of equations is given. Find the solution of the system.
Answer:
option C)
(19,2,5)
Step-by-step explanation:
| 4 | x
| 12 | y
| 5 | z
After reducing the matrix in row-echelon form we are left with three equation as following
Equation 1
0x + 0y + 1z = 5
Equation 2
0x + y1 + 2z = 12
Equation 3
1x + 0y -3z = 4
SolutionAs in first equation
0 + 0 + z = 5
z = 5
Put this value of z in equation 2 and 3
y + 2(5) = 12
y + 10 =12
y = 12 - 10
y = 2
x + 0 -3(5) = 4
x - 15 = 4
x = 4 + 15
x = 19
So the solution of the system is (x,y,z) = (19,2,5)
Find the exact circumference of a circle with diameter equal to 8 ft. 8 ft. 16 ft. 64 ft.
Answer:
[tex]8\pi\ ft[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]D=8\ ft[/tex]
substitute
[tex]C=\pi (8)=8\pi\ ft[/tex]
Answer: [tex]8\pi\ \text{ft.}[/tex]
Step-by-step explanation:
We know that formula to calculate the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.
Given: The diameter of the circle : [tex]d=\ 8\ ft.[/tex]
Then , the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi (8)=8\pi\ \text{ft.}[/tex]
Hence, the exact circumference of a circle with diameter equal to 8 ft = [tex]8\pi\ \text{ft.}[/tex]
Use the drawing tool(s) to form the correct answer on the provided number line.
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.
Answer:
n < 18
Step-by-step explanation:
The condition you are looking for is that
94 + 4.50n < 175
Subtract 94 from each side 4.50n < 81
Divide each side by 4.50 n < 18
The number of devices must be fewer than 18 for the new plan to cost less than the current plan.
The diagram is a graph of the inequality 94 + 4.50n < 175. Any value of n less than 18 (that is, in the pink zone and not on the vertical dashed line) will satisfy the inequality.