Answers
Answer:
The value of x is 12 feet
Step-by-step explanation:
The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.
To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.
Area of rectangle = length X breadth
Area of triangle = 1/2 base X height.
However, to calculate the area of the triangle, we need to find its height first.
The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.
Height of triangle = 16 ft - 10 ft = 6 ft
recall area = 156 square feet.
We now have most of our missing dimensions
We can now set up an equation as follows:
[tex](10 \times x) +0.5 \times x \times 6 = 156[/tex]
[tex]10x +3x=156\\13x=156\\x=12 feet[/tex]
Therefore the value of x is 12 feet
Related Questions
How do you make a decimal into a fraction?
Answers
Answer:
Step 1: Write down the decimal divided by 1, like this: decimal 1.
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify (or reduce) the fraction.
list down all the prime numbers which are factors of 30
Answers
Hey!!
Here's your answer:
prime numbers which are factors of 30 are:
1,2,3 and 5
Hope it helps
Answer:
1, 2, 3, 5
sorry for the confusion i didn't read it correctly
what is 8 - 3x > -25 because i have been wondering all day
Answers
Answer:
[tex]8 - 3x > -25 : \left[\begin{array}{ccc}solution: x < 11\\Interval Notation:(-\infty,11)\end{array}\right][/tex]
Step-by-step explanation:
[tex]8-3x>-25[/tex]
Subtract [tex]8[/tex] from both sides:
[tex]8-3x-8>-25-8[/tex]
Simplify:
[tex]-3x>-33[/tex]
Multiply both sides by [tex]-1[/tex] (reverse the inequality):
[tex]\left(-3x\right)\left(-1\right)<\left(-33\right)\left(-1\right)[/tex]
Simplify:
[tex]3x<33[/tex]
Divide both sides by [tex]3[/tex] :
[tex]\frac{3x}{3}<\frac{33}{3}[/tex]
Simplify:
[tex]x < 11[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you, have a good day! =)
Kim's business earns $10,000 per month. Kim's non-employee expenses are $3,000 per month. If Kim wants $2,000 in profit per month, how many employees can Kim have if each employee costs $1,000 per month?
Answers
Answer:
Kim's business earns $10,000 per month.
Kim's non-employee expenses are $3,000 per month.
If Kim wants $2,000 in profit per month, then the maximum amount Kim can spend for employee:
10000 - 3000 - 2000 =5000
If each employee costs $1,000 per month, Kim can recruit 5000/1000 = 5 as the maximum number of employees.
Hope this helps
:)
Answer:
5
Step-by-step explanation:
Revenue - profit = expense
10000 - 2000 = 8000
8000 = 3000 + 1000n
1000n = 5000
n = 5
Calculate CDEFtrapezium
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
You need to find the length of A F and BC first
Lets call BC --> 'x'
Lets form an equation
9 + 9 + x + x = 28
18 + 2x = 28
- 18
2x = 10
/ 2
x = 5
So now we have the length BC
We can subtract this length from the 11cm to find the vertical height of the trapezium
11 - 5 = 6
Now we have all we need to work it out.
area = (a + b) / 2 x h
area = (5 + 9) / 2 x 6
area = 42 cm^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
42 cm²
Step-by-step explanation:
We can see this shape is made of 2 shapes that we are familiar with which are a rectangle and a trapezium.
⇒ The first step in working out the area of the trapezium is working out the length of CB and then working out the height of trapezium. We are given that the perimeter of the rectangle is 28 cm and we know that opposite sides of a rectangle are equal so we will call the length we want to work out x
→ x + x + 9 + 9 = 28
⇒ Simplify
→ 2x + 18 = 28
⇒ Minus 18 from both sides to isolate 2x
→ 2x = 10
⇒ Divide both sides by 5 to isolate x
→ x = 5
5 cm is the length of CB, we will need to minus that from 11 to find the height of the trapezium so,
11 - 5 = 6. The height of the trapezium is 6
Now we have the height of the trapezium (6), we have the base (9) and we have the top length (5). All we do now is substitute these numbers into the trapezium formula which is
→ 0.5 × ( a + b ) × h
Where 'a' and 'b' are the parallel sides and 'h' is the height
Now we begin to substitute in the values,
→ 0.5 × ( a + b ) × h
⇒ Substitute in the values
→ 0.5 × ( 5 + 9 ) × 6
⇒ Simplify
→ 0.5 × ( 14 ) × 6
⇒ Simplify further
→ 42
The area of the trapezium is 42 cm²
16x^4-25 Which pattern can we use to factor the expression?
Answers
Step-by-step explanation:
Hope this helps you... Lemme know if you don't understand
PLEASE HELP ME with an explanation. Thanks in advance
Answers
Answer:
3) 0.30
The probability a randomly selected student plays a sport given they work part time = 0.30
Step-by-step explanation:
Step(i):-
Given 'A' plays a sport
B work part time
Given P(A) = 0.48
P(B) = 0.40
P(A∩B) =0.12
P(A∪B)¹ =0.24
Step(ii):-
By using conditional probability
[tex]P(B/A) = \frac{P(BnA}{P(A)}[/tex]
and similarly [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
The probability a randomly selected student plays a sport given they work part time
Now [tex]P(A/B) = \frac{P(AnB}{P(B)}[/tex]
[tex]P(A/B) = \frac{0.12}{0.40}= 0.30[/tex]
Final answer:-
The probability a randomly selected student plays a sport given they work part time = 0.30
A football team scored fewer than 16 points in Saturday’s game. Than wants to write an inequality for the number of points. He uses the variable s in his inequality. What does s represent? A - the number of fans of the team
B - the number of games played by the team
C - the number of points scored by the team
D - the number of players on the team
Answers
Since it says that they scored less than 16 points on Saturday, the variable has to be the number of points that are scored by the team.
Enter the solution (x, y) to the system of equations shown. y=2x+1 3y=4x+7
Answers
Answer:
Step-by-step explanation:
3(2x + 1) = 4x + 7
6x + 3 = 4x + 7
2x = 4
x = 2
y = 2(2) + 1
y = 4 + 1
y = 5
(2,5)
Answer:
2,5
Step-by-step explanation:
Consider a vat that at time t contains a volume V (t) of salt solution containing an amount Q(t) of salt, evenly distributed throughout the vat with a concentration c(t), where c(t) = Q(t) / V(t). Assume that water containing a concentration k of salt enters the vat at a rate rin, and that water is drained from the vat at a rate rout > rin.
(a) If V (0) = V0, find an expression for the amount of solution in the vat at time t. At what time T will the vat become empty? Find an initial value problem that describes the amount of salt in the vat at time t <= T. You may assume that Q(0) = Q0.
(b) Solve the initial value problem in part (a). What is the amount of salt in the vat at time t? What is the concentration of the last drop that leaves the vat at time t = T
Answers
Answer:
a.i [tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii. time at which vat will be empty
[tex]T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex] when dQ/dt = 0
b. i Amount of salt at time t
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
ii. Concentration at t = T
c(T) = [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Step-by-step explanation:
a.
i. We determine the differential equation for the solution in the vat at time,t.
Let Q be the quantity of salt in the vat at any time,t.
So, dQ/dt = rate of change of quantity of salt in the vat. = rate of change of quantity of salt into the vat - rate of change of quantity of salt out of the vat.
Now, since a concentration of salt, k enter the vat at a rate of rin, rate of change of quantity of salt into the vat = krin.
Let V(0) = V₀ be the volume of water int the vat at time t = 0. Now, the volume of water in the vat increases at a rate of (rin - rout). The increase in volume after a time t is (rin - rout)t. So the volume after a time, t is V(t) = V₀ + (rin - rout)t. The concentration of this liquid is thus Q(t)/V(t) = Q(t)/V₀ + (rin - rout)t. Now, the rate of change of quantity of salt out of the vat is thus [Q(t)/V₀ + (rin - rout)t]rin = Q(t)rout/[V₀ + (rin - rout)t].
So, dQ(t)/dt = krin - Q(t)rout/[V₀ + (rin - rout)t].
[tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii Time T at which vat will be empty
At time T, when the vat is empty, dQ(T)/dt = 0.
So
[tex]\\\frac{dQ(T)}{dt} + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\0 + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex]
b. i
i. We solve the differential equation to find the amount of salt at time,t
The integrating factor is ex
[tex]exp(\int\limits {\frac{r_{out} }{V_{0} + (r_{in} - r_{out})t} } \, dt ) = exp(\frac{r_{out}}{(r_{in} - r_{out})} \int\limits {\frac{ (r_{in} - r_{out})}{V_{0} + (r_{in} - r_{out})t} } \, dt )\\= exp(\frac{r_{out}}{(r_{in} - r_{out})} ln [V_{0} + (r_{in} - r_{out})t} ]) \\\= [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]
Multiplying both side of the equation by the integrating factor, we have
[tex][V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{dQ(t)}{dt} + [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt = krin[V(0) + (rin - rout)texp(rout/(rin - rout))]
Integrating both sides we have
∫(dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt)dt = ∫(krin[V(0) + (rin - rout)texp(rout/(rin - rout))])dt
Let exp(rout/(rin - rout) = A
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + C
At t = 0, Q(t) = Q(0),
So,
Q(0)[V(0) + A(rin - rout)×0] = AkrinV(0)t + A(rin - rout)×0²/2 + C
C = Q(0)V(0)
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + Q(0)V(0)
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
The above is the amount of salt at time ,t.
ii. The concentration of the last drop of salt at time, t = T
To find the concentration of the last drop of salt at time t = T, we insert T into Q(t) to find its quantity and insert t = T into V(t) = V₀ + (rin - rout)t.
So
Q(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]
Q(T) = [[exp(rout/(rin - rout)]krin[V(0)T + [exp(rout/(rin - rout)](rin - rout)T²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)T]
the volume at t = T is
V(T) = V₀ + (rin - rout)T.
The concentration at t = T is c(T) = Q(T)/V(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]/V₀ + (rin - rout)T.
= [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/([V(0) + A(rin - rout)T][V₀ + (rin - rout)T])
= [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 5x^6=30
Answers
Answer:
The real solutions are
[tex]x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]
Step-by-step explanation:
The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.
To find the real solutions of the equation [tex]5x^6=30[/tex]:
[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x^6}{5}=\frac{30}{5}\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]
Use substitution to solve each system of equations:
x=y+6
x+y=10
Answers
= 2y + 6 = 10
= 2y = 4
Y= 2
I need help!!! And fast!!!!
Answers
6p=36
Divide both sides by six to get the value of p
36/6 is 6
p is equal to six
Which are the center and radius of the circle with equation (x + 5)2 + (y − 4)2 = 9?
A. (−5, −4); r = 3
B. (5, −4); r = 9
C. (−5, 4); r = 3
D. (5, 4); r = 9
Answers
Answer:
C)
Step-by-step explanation:
*Look at the picture*
3y + 6 = 18y
- What does the ( y ) variable stand for and how exactly do you find it?
Answers
Answer:
y=2/5 or 0.4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
3y + 6 = 18y -->
subtract 3y from both sides to get rid of it.
6 = 15y -->
isolate the variable by dividing it by 15.
6/15 = 15y/15 -->
simplify.
2/5 = y
Of the 34 cars in the parking lot, 12 are blue, 8 are red, 4are white, and 10 are silver. In simplest form, what are the odds in favor that the next car that leaves the lot will be red or white
Answers
Answer:
0.3529411765
Step-by-step explanation:
add red and white and divide it by the total
Instructions : integrate the following
Answers
You can simplify the integrand:
[tex]\dfrac{3x^2+4x+1}{2x}=\dfrac{3x}2+2+\dfrac1{2x}[/tex]
Then integrate term-by-term:
[tex]\displaystyle\int\frac{3x^2+4x+1}{2x}\,\mathrm dx=\frac32\int x\,\mathrm dx+2\int\mathrm dx+\frac12\int\frac{\mathrm dx}x[/tex]
[tex]=\dfrac{3x^2}4+2x+\dfrac12\ln|x|+C[/tex]
Which are equations? CHECK all that apply.
X+3=12
Z/7+1
25-q
6g=18
2/3m
P/3.5=2.25
9=100-f
K divided by 5.8
Answers
Answer:
X + 3 = 12
6g = 18
P/3.5 = 2.25
9 = 100 - f
Step-by-step explanation:
Equations have equal signs.
Expressions do not.
Therefore, any expression with an equal sign is an equation, making it one of the correct answers.
Answer:
X + 3 = 12
6g = 18
P/3.5 = 2.25
9 = 100 - f
Step-by-step explanation:
Just did it!
helpp me nowwwwwww dew Help Marshmello i wasn't born yesterday. xd
Answers
Answer: A) DE = 24 yd and EF = 10 yd
Step-by-step explanation:
Shape EFD is just a dilate of 2, meaning BCA x 2.
13 x 2 = 26
12 x 2 = 24
5 x 2 = 10
Therefore, DE = 24 yd and EF = 10 yd
I hope this helps!
Answer:
DE = 24, EF = 10
Step-by-step explanation:
We can use ratios to solve
13 ft 12 ft
---------- = -----------
26 ft x ft
Using cross products
13x = 12*26
Divide each side by 13
13x/13 = 12*26/13
x = 24
13 ft 5 ft
---------- = -----------
26 ft y ft
Using cross products
13y = 5*26
Divide each side by 13
13y/13 = 5*26/13
y = 10
solve each of the equations below and classify them based on their solution.
1.) -8x - 3x= -11x
2.) 6x = -6y - 12
3.) -3z = 8 -z
4.) -5n = 3 - 5n
No Solution, Unique Solution, Infinitely many Solution
Answers
Answer:
Answers are below
Step-by-step explanation:
1.) No solution
2.) Unique solution
3.) Unique solution
4.) No solution
I graphed the equation that had a unique solution on the graph below.
If these answers are correct, please make me Brainliest!
graph y=-2/3x-3 i need help quick
Answers
Answer: just get gud at math lol
Step-by-step explanation: no
Which statement is true regarding the graphed functions? On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2). f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)
Answers
Answer:
none of the above
Step-by-step explanation:
The attached graph shows that none of f(-2), f(2), or f(4) matches any of g(-2) or g(4).
None of the offered statements is true.
___
Please report this problem to your teacher.
Answer:
The answer is not C
Step-by-step explanation:
I think the answer is D sooooo Pray it will be
UPDATE IT IS D
HOPE THIS HELP STAY SAFE
the circumference of a circle is 107.81 yards. Find the diameter of the circle to the nearest tenth
Answers
Answer:
68
Step-by-step explanation:
Divide the circumference by pi, approximately 3.14, to calculate the diameter of the circle. For example, if the circumference equals 56.52 inches, divide 56.52 by 3.14 to get a diameter of 18 inches. Multiply the radius by 2 to find the diameter.
Answer:
the answer is attached to the picture
Which expression is equivalent to (3b + 2r)+(4b + r)
Answers
Answer:
7 b + 3 r
Step-by-step explanation:
(60 POINTS) The figure is transformed as shown in the diagram. Describe the transformation.
A) dilation, then reflection
B) reflection, then rotation
C) rotation, then translation
D) translation, then reflection
Answers
Answer:
The solution is rotation, then translation. The figure has been rotated about the origin by 90° and then translated 6 units to the right.
Juan spins two different fair spinners. One spinner has numbers 1 through 8. The other has letters A through F. What is the probaility that one spinner will land on 3 and the other will land on C?
Answers
Answer:
...
Step-by-step explanation:
plzzzzzzzz i need help
Michael is cutting a 100-yard ribbon into pieces 3.4 yards long. He says that an inequality that represents his project is 3.4x < 100. Explain what this statement means, in words, and what each part of the inequality represents.
Answers
Answer:
Okay well the 3.4 yard pieces are the constant in which Michael will be cuttings that number stays the same an will not change. The (X) represents the unknown number of how many times the ribbon will be cut. As the whole inequality states the unknown number of pieces that are 3.4 yards long are less than 100 yards.
Answer:
The variable, x, is the number of pieces of ribbon Michael cuts. Since each piece is 3.4 yards long, 3.4x is the total length of all the pieces together. This total length cannot be more than the 100 yards of ribbon he has, so 3.4x must be less than or equal to 100.
division concepts
how many times can 9 go into .7632 ?
Answers
Answer:
None! .7632 is smaller than 9.
Step-by-step explanation:
What’s the correct answer for this?
Answers
Answer:
D = 23.4 units
Step-by-step explanation:
In the attached file
Which geometric series converges?
CO
Σ(-3) 2-1
Η =1
O
Σ5-1) 2-1
CO
Ο Σ4(-02 - 1
H=1
CO
Σ06(-2) 2-1
h=1
Answers
Answer:
its C
Step-by-step explanation:
i just did it on edge and plus its really not cool to post answers when you dont actually know the answer bc people that actually want to help cant bc there only two answers allowed per question. so please dont answer if your not trying to help.
The geometric series [tex]\sum_{n=1}^{\infty} 5(-1)^{n-1}[/tex] converges to zero.
What is convergent and divergent geometric series?A mathematical term denoting an endless series of the form
a + ar + ar² + ar³ + ⋯, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward example.
A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit.
In contrast, a divergent series is one whose partial sums do not reach a limit. The Divergent series usually approaches infinity.
From the given options let us try with [tex]\sum_{n=1}^{\infty} 5(-1)^{n-1}[/tex].
[tex]= 5\sum_{n=1}^{\infty} (-1)^{n-1}.[/tex]
[tex]= 5\sum_{n=1}^{\infty} (-1)^{n}.\frac{1}{-1}[/tex].
[tex]= -5\sum_{n=1}^{\infty} (-1)^{n}.[/tex]
= - 5[- 1 + 1 - 1 + 1 ...+ 1].
= - 5[0].
= 0.
learn more about geometric sequences here :
https://brainly.com/question/19235539
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