Answer:
l = 26, w = 10
Step-by-step explanation:
These types of word problems always want you to use variables to find the answer. Variables are always going to represent the numbers you don't know.
This question wants you to find the length and width of the wall of the barn, so let's just use l for length (let l = length of barn wall) and w for width (let w = width of barn wall); this is called defining your variables, so that you--or anyone who looks at your work--know what the letter variable represents.
Now we use the other information we have to find what values the variables actually equal.
We know that the length is 6 feet longer than twice the width. To express this in terms of numbers and variables: l = 6 + 2w. This makes sense, right?
length = 6 + (2 * width)
If the total area of the wall is 260 square feet and we need to find the length and width, we can use the A = lw formula, which you can use for any rectangle. Since 260 is the area (A), we can put that into the formula so that we have 260 = lw.
Next, use the expression we came up with earlier (l = 6 + 2w) to help find the answer.
We have two equations now (l = 6 + 2w and 260 = lw) and we just need to put them together.
This part is the same as solving any other linear equation.
The approach I'll use is substitution:
l = 6 + 2w
260 = lw
Substitute 6 + 2w in for l:
260 = (6 + 2w) w
Distribute:
260 = 6w + 2w²
Solve:
w² + 3w - 130 = 0
w = -13, w = 10
(The width of a rectangle cannot be negative, so it has to be 10 ft.)
We're almost there. The last thing to do is to find the length. Just plug in 10 for w in the l = 6 + 2w formula:
l = 6 + 2(10) = 6 + 20 = 26
To check your work, we can double the width and add 6 to get 26, and 26 * 10 is 260.
So, the length of the wall of the barn is 26 and the width of the wall of the barn is 10.
If $4x=3y$, what is the value of $\frac{2x+y}{3x-2y}$?
Answer:
10
Step-by-step explanation:
Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\
&=
\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\
&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}
Answer:
10
Step-by-step explanation:
Substitution and simplification
expansion of (−1−2√3)^2
(- 1 - 2√3)²
applicating (a - b)² = a² + b² - 2ab
a = - 1
b = 2√3
so:
(- 1 - 2√3)² =
(- 1)² + (2√3)² - 2(- 1)(2√3) =
1 + (2² * √3²) + 2(2√3) =
1 + (4 * 3) + 4√3
ps. √x² = x1 + 12 + 4√3 = 13 + 4√3
Rosa's golf score was -3. The next game, her score went down by 2. What was her new
score?
Answer:
-5
Step-by-step explanation:
-3 - 2 = -5
Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t) (in cm) as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a cos(b. t) + d. , At t = 0, when she starts jumping, her rope is 0 cm off the ground, which is the minimum. After [tex]\frac{\pi }{12}[/tex] seconds it reaches a height of 60 cm from the ground, which is half of its maximum height. Find R(t). t should be in radians.
Answer:
R (t) = 60 - 60 cos (6t)
Step-by-step explanation:
Given that:
R(t) = acos (bt) + d
at t= 0
R(0) = 0
0 = acos (0) + d
a + d = 0 ----- (1)
After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.
i.e
[tex]R ( \dfrac{\pi}{12}) = 60[/tex]
[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]
Recall from the question that:
At t = 0, R(0) = 0 which is the minimum
as such it is only when a is negative can acos (bt ) + d can get to minimum at t= 0
Similarly; 60 × 2 = maximum
R'(t) = -ab sin (bt) =0
bt = k π
here;
k is the integer
making t the subject of the formula, we have:
[tex]t = \dfrac{k \pi}{b}[/tex]
replacing the derived equation of k into R(t) = acos (bt) + d
[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]
Since we known a < 0 (negative)
then d-a will be maximum
d-a = 60 × 2
d-a = 120 ----- (3)
Relating to equation (1) and (3)
a = -60 and d = 60
∴ R(t) = 60 - 60 cos (bt)
Similarly;
For [tex]R ( \dfrac{\pi}{12})[/tex]
[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]
where ;
[tex]cos (\dfrac{\pi b}{12}) =0[/tex]
Then b = 6
∴
R (t) = 60 - 60 cos (6t)
A bag has 13 red candies 7 pink candy 12 orange candies what is the possibility that you will choose an orange candy at random
Answer:
12/32, 3/8, or 37.5%
Step-by-step explanation:
Add the candies in the bag together
13+7+12=32
12 out of the thirty-two are orange
12/32
After dividing by 4 to simplify, you get
3/8
3÷8 will give us the decimal which we can then turn into a percentage
37.5%
12/32, 3/8, or 37.5%
Hope this helps :-)
FOR THE FUNCTION F(X) =6x - 8 what is f(3)?
Replace x in the equation with 3
6(3) -8 = 18 -8 = 10
The answer is 10
Answer:
10
Step-by-step explanation:
To find f(3), substitute 3 in the function
f(3) = 6*3 - 8
= 10
Hi guys, can anyone help me with this, Thanks a lot:)
Answer:
k = 1/9
Step-by-step explanation:
In order for the function to be continuous at x=9, the values of the two expressions must be the same at x=9.
The first expression evaluates to ...
[tex]\dfrac{\sqrt{9}-3}{-9}=-\dfrac{3-3}{9}=0[/tex]
The second expression needs to have the same value:
[tex]1 -k(9) = 0\\\\1 = 9k\\\\\boxed{k=\dfrac{1}{9}}[/tex]
Answer:
[tex]k=1/9[/tex]
Step-by-step explanation:
A function is continuous at a point if and only if:
[tex]\lim_{x \to n} f(x)=f(n)[/tex]
So, we have the piecewise function:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-kx & \quad x\geq 9 \end{array} \right.$$[/tex]
And we want to find the value of k such that the function is continuous.
First, find the left hand limit of f(x):
[tex]\lim_{x\to9^-} f(x)[/tex]
Since we're coming from the left, we'll use the first equation. Thus:
[tex]=\lim_{x\to9^-} \frac{\sqrt{x}-3}{-9}[/tex]
Direct substitution:
[tex]=\frac{\sqrt{9}-3}{-9}[/tex]
Simplify:
[tex]=\frac{3-3}{-9}[/tex]
Subtract and divide:
[tex]=\frac{0}{-9}=0[/tex]
So, what this tells us is that for the function to be continuous, the right hand limit as f(x) approaches 9 from the right must also be equal to 0.
Therefore:
[tex]\lim_{n \to 9^+} 1-kx=0[/tex]
Direct substitution:
[tex]1-9k=0[/tex]
Subtract 1 from both sides:
[tex]-9k=-1[/tex]
Divide both sides by -9:
[tex]k=1/9[/tex]
Therefore, the value of k is 1/9.
So, our equation in the end is:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-\frac{1}{9}x & \quad x\geq 9 \end{array} \right.$$[/tex]
If each chip has a length of 35 nanometers (nm), how many would you need to circle the Earth. Which has a radius of 6,371 km? (Show all your workings. Final answer MUST be in scientific notation.)
Answer:
1144.18 e-12 chips
Step-by-step explanation:
Conversation rate of nanometers
1 nanometers =1* 10^-12 km
35 nanometers= 35 *10^-12
Radius of earth= 6371 km
Circumference of earth = 2πr
Circumference= 2*22/7*6371
Circumference=40046.29 km
The number of chips to be used to circle the earth
= 40046.29/35 *10^-12
=1144.18 *10^-12
= 1144.18 e-12 chips
the product of a number and 8
Answer:
[tex]8n[/tex]
Step-by-step explanation:
The answer would be [tex]8n[/tex] because [tex]8*n[/tex] = [tex]8n[/tex]
Estimate the value of √2π/√5
Answer: 1.12099824328 or estimated is 1
An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners and 23 city owners. The mean number of hours per week that city owners spend walking their dogs is 10.0. The standard deviation of hours spent walking the dog by city owners is 3.0. The mean number of hours country owners spent walking theirs dogs per week was 15.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city?
Answer:
Yes dog owners in the country spend more time walking their dogs than do dog owners in the city
Step-by-step explanation:
From the question we are told that
The sample size from country is [tex]n_1 = 21[/tex]
The sample size from city is [tex]n_2 = 23[/tex]
The sample mean for country is [tex]\= x_1 = 15 [/tex]
The Sample mean for city is [tex]\= x_2 = 10[/tex]
The standard deviation for country is [tex]\sigma _1 = 4[/tex]
The standard deviation for city is [tex]\sigma _2 = 3[/tex]
Let the level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 > \mu_2[/tex]
The pooled standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{s_1 ^2 * (n_1 - 1 ) + s_2 ^2 * (n_2 - 1 )}{ df} }[/tex]
Here df is the degree of freedom which is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 21 + 23 -2 [/tex]
[tex]df = 42[/tex]
So
[tex]s = \sqrt{ \frac{4 ^2 * (15.0 - 1 ) + 3 ^2 * (10 - 1 )}{ 42} }[/tex]
[tex]s = 3.5[/tex]
Generally the test statistics is mathematically represented
[tex]t = \frac{\= x_1 - \= x_2 }{ s * \sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex]
[tex]t = \frac{ 15 -10 }{ 3.5 * \sqrt{\frac{1}{ 21 } + \frac{1}{23} } }[/tex]
[tex]t = 4.733[/tex]
Generally the p-value is obtained from the student t-distribution table table , the value is
[tex]P(T > 4.733)= t_{4.733, 42 } = 0.000013 [/tex]
From the calculation we see that
[tex]p-value < \alpha[/tex]
So we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city
Please help!!!! 40 POINTS 1. By the square root property, if k is a real number and x^2=k, then what is x equal to? (See picture) 4. Solve x^2=64. What property did you use? (See picture)
Answer:
x = ± sqrt(k)
x = ± 8 by the square root property
Step-by-step explanation:
x^2 = k
K is a real number
Take the square root of each side
sqrt(x^2) = ± sqrt(k)
x = ± sqrt(k)
Letting k = 64
x = ± sqrt(64)
x = ± 8 by the square root property
Answer:
x = ± √k
x = ± √8 by the square root property
Step-by-step explanation:
x² = k
where k is a real number
square root of each side
√x² = ± √k
x = ± √k
let k = 64
x = ± √64
therefore
x = ± 8 by the square root property
can someone please help me with this :) i only have one more try to get it right and if not i get 0/10
Answer: [tex]\sqrt[5]{27}[/tex], fifthroot(27) [according to your picture, I think there will be no space between fifth and root]
Step-by-step explanation:
concept to know: any exponent that is performed in fraction, the numerator will be the real exponent for the base, while the denominator will be the root
-------------------------------------
[tex]27^{\frac{1}{5}[/tex]
This has 1 as the numerator and 5 as the denominator.
1 can be ignored because any number to the 1 power is equal to itself.
5 is the root for 27
[tex]\sqrt[5]{27}[/tex]
Hope this helps!! :)
Please let me know if you have any question
Simplify: 5x+2(3−2x)+7
Answer:
x + 13
Step-by-step explanation:
5x + 2(3 - 2x) +7
Distribute the 2 into (3 - 2x)
5x + 6 - 4x + 7
Combine like terms
x + 13
PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
What is PEMDAS?PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.
The given expression 5x+2(3−2x)+7 can be simplified as shown below.
5x + 2(3−2x) + 7
Open the parenthesis,
= 5x + 6 − 4x + 7
Bring the like terms together,
= 5x − 4x + 7 + 6
Add the like terms,
= x + 13
Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
Learn more about PEMDAS here:
https://brainly.com/question/36185
#SPJ2
The gasoline consumption of a small car is advertised as 16.3 km/L (1L=1liter). How many miles per gallon is this? One mile is 1.609 km and one gallon is 3.788 L.
Answer:
38.38 miles per gallon
Step-by-step explanation:
16.3 km/L to miles per gallon
1 mile = 1.609 km
16.3 km = 16.3/1.609 = 10.13 miles
1 gallon = 3.788 L
1 L = 1/3.788 = 0.2639 gallon
therefore,
16.3 km/L = 10.13/0.2639 = 38.38 miles per gallon
2. Solve the equation below and find the variation constant, k. Find y when x= 18, if y varies directly as x, and y=37 when x=5
*Round your answer to the nearest thousandth, if necessary.
Answer:
k = 7.4y = 133.2Step-by-step explanation:
To find the value of y when x= 18 we must first find the relationship between them
The statement
y varies directly as x is written as
[tex]y \: \: \alpha \: \: kx[/tex]
where k is the constant of proportionality
when y = 37
x = 5
Substitute the values into the above formula and solve for k
That's
37 = 5k
Divide both sides by 5
k = 7.4So the formula for the variation is
y = 7.4xWhen x = 18
y = 7.4(18)
We have the answer as
y = 133.2Hope this helps you
(Please help fast!) ..........
Answer:
the sum would be located 2 notches to the right from 0.
Step-by-step explanation:
since the notches are already split up into 5, you just count 2 notches to the left (since its negative) and then count 4 notches to the right and then you land on your sum :) btw I like your profile picture
Solve for x using
cross multiplication.
Find the volume of the solid in the first octant bounded by the cylinders r = 2 r = 5 z = 8-x-y g
Answer:
[tex]42\pi -78[/tex]
Step-by-step explanation:
Attached below is the detailed solution of the volume of the solid in the first octant bounded by the cylinders r = 2 r = 5 z = 8-x-y
The volume of the solid in the first octant bounded by the cylinders r = 2 r = 5, z = 8-x-y : [tex]42\pi -78[/tex]
What is the measure of angle AOB?
Answer:
let angle AOB and angle COD be x
the it would be
x+x+110=180
2x+110=180
2x=180-110
2x=70
x=70/2
x=35 degree.
hope it will help you.
What is 3.59×6.2
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
What is standard form for 400,000+60,000+5,000+100
Answer:
[tex]\boxed{\bold 4.651 \times {10}^{5}}}[/tex]
Step-by-step explanation:
[tex]400000 + 60000 + 5000 + 100 \\ = 465100[/tex]
Now write it in standard form.
[tex]465100 \\ = 4.651 \times {10}^{5} [/tex]
hope this helps you.
will give the brainliest!
follow~Hi1315~
A parent died and left in the state to four children one inherited 1/9 of the estate the second inherited 5/81 of the estate and the third inherited 17/27 of the estate how much did the fourth inherit?
Answer:
I think it's (16/81)
Step-by-step explanation:
Will give brainliest if you complete all of them
Answer:
14 is 4
15 is check your self
in Google
70- -72 can someone give me the answer to this please.
Answer:
142
Step-by-step explanation:
Step-by-step explanation:
70 - -72
= 70+ 72
= 142
I think this should be the answer
When do lunar eclipses occur?
Step-by-step explanation:
Lunar eclipses can only happen when the Moon is opposite the Sun in the sky, a monthly occurrence we know as a full Moon.
— 6— (—12) help me plz
Answer:
Hey there!
-6-(-12)
-6+12
6
Hope this helps :)
Answer:
[tex]6[/tex]
Step-by-step explanation:
[tex]-6-(-12)[/tex]
[tex]-6+12[/tex]
Since 12 - 6 is equal to 6, -6 + 12 would be 6.
[tex]=6[/tex]
Now you have your answer!
Hope this helps!
A rectangular piece of metal is 20 in longer than it is wide Squares with sides 4 in long are cut from the four comers and the flaps are folded upward to form an open
box. If the volume of the box is 1354 in what were the original dimensions of the piece of metal?
What is the original width? in
Answer:
14 [tex]\frac{5}{48}[/tex]
Step-by-step explanation:
rectangular volume = length * height * width
1354 = (20+4) * 4 * width
1354 = 24 * 4 *w
1354 = 96w
14.1 = w
What are the coordinates for the origin of the coordinate plane? (0.1) (1,0) (1,1) 0 (0.0)
Step-by-step explanation:
Remember: the origin is at the very center of the graph: (0,0). Not (0,1), (1,0), or 0. The first two options are not at the center. (0,1) takes us one unit above the middle, and (1,0) takes us one unite to the right of the origin. The number 0 is not used to find a point. So, our final answer is: (0,0).
I need help finding the domain and range, I already know is not a function
Answer:
Domain: [-4, 4]
Range: [-3, 5]
Function? No
Step-by-step explanation:
Domain is all x-values that can be inputted in the graph that returns an output.
Range is all y-values that are outputted when x is inputted.
A function has to pass the Vertical Line Test.