Using the proportional relationship, it is found that the radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
[tex]y = kx[/tex]
In which k is the constant of proportionality.
If they are inverse proportional, the relationship is:
[tex]y = \frac{k}{x}[/tex]
In this problem, the amount of time is inversely proportional to the square of the radius of the pipe, hence:
[tex]t = \frac{k}{r^2}[/tex]
A pipe of radius 1 cm can empty a sink in 22 seconds, hence k = 22.
The radius for 14 seconds is:
[tex]t = \frac{k}{r^2}[/tex]
[tex]14 = \frac{22}{r^2}[/tex]
[tex]r^2 = \frac{22}{14}[/tex]
[tex]r = \sqrt{\frac{22}{14}}[/tex]
[tex]r = 1.25[/tex]
The radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.
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find the area of a triangle 4cm height 6cm base
Answer:
12cm²
Step-by-step explanation:
Area of triangle =1/2×h×b
1/2×4×6
2×6
12cm²
hope dis helps!!!!!
Victor is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a red fabric.
How much fabric does Victor need in order to cover 12 of these blocks?
156 cm²
24 cm²
13 cm²
2 cm²
Answer:
(a) 156 cm²
Step-by-step explanation:
The total surface area of the 12 blocks can be computed by first finding the surface area of one block. That result can then be multiplied by 12. The area of one rectangular prism is given by the formula ...
A = 2(LW +H(L +W))
A = 2(4·1 +1/2(4+1)) = 2(4 +5/2) = 13 . . . cm²
The area of 12 such prisms will be ...
12 × (13 cm²) = 156 cm²
Victor needs 156 cm² of fabric to cover 12 blocks.
_____
Additional comment
This problem offers an opportunity to exercise your number sense. The area of the largest surface of one block is (4 cm)×(1 cm) = 4 cm². 12 of these surfaces will have an area of 48 cm². This is only part of the total area, so the only reasonable choice among those offered is 156 cm².
Answer:
156 cm² for K12
help!
Fill in the empty spaces with monomials that make each equality
into an
indentity.
(3x - ...)? = 9x2 - 6x +1
Answer:
1
Step-by-step explanation:
The square of the value in the empty space is the constant in the expanded expression. That is ...
[ ]² = 1
The value in the space is ...
[ ] = √1 = 1
The filled-in equation is ...
(3x -1)² = 9x² -6x +1
_____
The expansion of the square of a binomial is ...
(ax -b)² = a²x² -2abx +b²
Above, we used the constant term to find 'b', but we could also have used the linear term:
-6x = -2(3)bx . . . . . a=3 in this problem
1 = b . . . . . . . divide by -6x
Is 206 – 3x) + x equivalent to 2(3x) + x + 12?
Answer:
Step-by-step explanation:(206-3x)+x
2(3x)+x+12
ok as i think one no is statsfy this equation .
Find the value of X for these twi
Answer:
11: x=60 12:x=27
Step-by-step explanation:
For the first one, we know that all triangle angles add up to 180, so we take 180 and divide by 3 to get each of the angles and we get 60. For the second one, like I said earlier, all triangles add up to 180 so you add all the angles together and make them equal 180. You simplify and you get x=27
(also i changed my answer because I double checked it and it was wrong
which features of a figuer JKLM remain the same after any rigid transformation i-ready
The rigid transformation of figure JKLM would not change the side length and angle measure
The features of the figure JKLM that would remain the same are its side lengths and angles
How to determine the features?A rigid transformation is any of the following
TranslationRotationReflectionAll of the above transformation do not change the side length and the angle measure of the shape they transform
Hence, the features of the figure JKLM that would remain the same are its side lengths and angles
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Solve the initial value problem d y d x = 2 x 1 , y ( 0 ) = 2
Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is given by:
[tex]\frac{dy}{dx} = 2x[/tex]
Then, applying separation of variables:
[tex]dy = 2x dx[/tex]
[tex]\int dy = \int 2x dx[/tex]
[tex]y = x^2 + K[/tex]
Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:
y(x) = x² + 2.
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The differential equation is y(x) = x² + 2.
What is the differential equation?Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.
The given equation is;
[tex]\rm \dfrac{dy}{dx}=2x[/tex]
Applying the variable separation method;
[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]
The value of c when y( 0 ) = 2 is c =2.
Hence, the required differential equation is y(x) = x² + 2.
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Write an equation for the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form.
(-5.--3) and (1. -8)
(a) The equation of the line in slope-intercept form is
(Use integers or fractions for any numbers in the equation)
The equation of the line in slope-intercept form and standard form that passes through the line are y = -5 / 6x - 43 / 6 and 5x + 6y = -43 respectively.
Slope intercept equationThe Slope intercept equation is use to represent a linear table or graph. Therefore, the formula is represented as follows
y = mx + b
where
m = slope
b = y-intercept
Hence,
(-5, -3)(1, -8)
m = -8 + 3 / 1 + 5 = - 5 / 6
Using (1, -8) let's find b
-8 = -5 / 6 (1) + b
-8 + 5 / 6 = b
-48 + 5/6 = b
b = -43 / 6
Therefore, the slope intercept equation is y = -5 / 6x - 43 / 6
The equation in standard form is represented as Ax + By = C. Therefore,
y + 5 / 6 x = - 43/6
5x + 6y = -43
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The area and the perimeter of a square are equal. Find the side
length of the square.
please help me
Answer:
side length = 4
Step-by-step explanation:
Let x = the side length
Area is x•x, which is x^2.
Perimeter is x+x+x+x, which is 4x.
x^2 = 4x
x^2 - 4x = 0
Factor.
x(x-4) = 0
x = 0 or x = 4
Discard 0 as an answer as it is not useful.
x = 4.
Area = 4^2 = 16
Perimeter = 4(4)= 16
The side length is 4.
Given the function h of x equals 8 times the cube root of x minus 6 end root plus 16, what is the x-intercept of the function?
–6
–2
2
16
The x-intercept of the function h(x) is when the function h(x) = 0
The x-intercept of the function is -2
How to determine the x-intercept?From the question, the function is given as:
[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]
Set the function h(x) to 0, to calculate the x-intercept
[tex]8 * \sqrt[3]{x - 6} + 16= 0[/tex]
Subtract 16 from both sides of the equation
[tex]8 * \sqrt[3]{x - 6} +=-16[/tex]
Divide through by 8
[tex]\sqrt[3]{x - 6} =-2[/tex]
Take the cube of both sides
[tex]x - 6 =-8[/tex]
Add 6 to both sides
[tex]x =-2[/tex]
Hence, the x-intercept of the function is -2
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Answer:
-2
Step-by-step explanation:
The person above me explained it perfectly! Also, I got this answer correct on my test.
What percentage of Africa is savanna?
less than ten percent
approximately twenty-five percent
almost fifty percent
close to seventy percent
Answer:
C, Almost fifty percent
Step-by-step explanation: I just got it right.
Which point is not on the graph of the function y = x + 2?
(3, 5)
(6, 8)
(7, 9)
(2, 0)
Answer:
(2,0) is not a point on the graph of the function y=x+2
Step-by-step explanation:
Go to the TI-84 plus calculator and go to the y= button and then type in x+2 and then press the 2nd button and then the graph button and then you should get your answer.
help worth a lot of pounts
You want to buy a new computer that costs $2250. You check your savings-account balance and realize that to buy the computer, you will need $125 more than what you have in your savings account. How much money do you have in your savings account?
Equation:
Define the Variable:
How much money in your savings account?
Answer:
See below.
Step-by-step explanation:
Let x = amount of money you have in your account.
The money in your account plus the $125 extra that you need equals the total cost of the computer.
The equation is:
x + 125 = 2250
Now we solve the equation by subtracting 125 from both sides.
x = 2125
Answer: You have now $2125 in your account
Answer:
$2125Step-by-step explanation:
A husband and wife are building a tiny house for a vacation getaway, and they want to measure the height of the roof of the house to see if they will be able to have a bedroom on the second floor. One side of the house is 18 ft long and the slant height of the roof along this side is 13 ft. The point on the roof's peak is above the center of the house. What is the height of the roof of the house? Round your answer to the nearest hundredth. Question 4 options: 9.38 ft 11.28 ft 15.21 ft 9.4
By using a right triangle as a model, we will see that height of the roof is 9.38 ft.
What is the height of the roof of the house?The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft
We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:
X^2 + (9ft)^2 = (13 ft)^2
X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft
So the height of the roof is 9.38 ft.
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Find the area of triangle
Answer:
Step-by-step explanation:
A = 1/2 bh = 1/2 (12)(17) = 204 square inches
Please help me with my home work
2.334567890 x 3.04576879 =
What is 7/15+13/19+5/12 expressed as a fraction in lower terms
why is a parallelogram not always a rectangle
Answer:
A parallelogram by definition has 2 pairs of parallel sides.
A parallelogram could be:
____________
| |
|___________|
A rectangle in euclidean geometry has 4 right angles.
For example:
________________
| |
|_______________|
However, a parallelogram may have 2 pairs parallel sides but not 4 right angles.
For example:
______________
\ \
\______________\
Therefore, A parallelogram is not always a rectangle.
Hope this helps!!!
Please mark me as brainliest!!!
Solve for x: 2(x 3)2 − 4 = 0 Round your answer to the nearest hundredth. X = 4. 41, 1. 59 x = 1. 34, 5. 24 x = −1. 34, −5. 24 x = −4. 41, −1. 59.
The two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here, (a,b,c) are the real numbers and x is the variable.
To find the value of x, the following formula is used,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The given equation is,
[tex]2(x+ 3)^2 - 4 = 0[/tex]
To solve this equation, we need to apply some mathematical operations over it. Let's start with opening the brackets.
[tex]2(x+ 3)^2 - 4 = 0\\2(x^2+6x+9)-4=0\\2x^2+12x+14-4\\2x^2+12x+12=0\\x^2+6x+7=0[/tex]
On comparing with standard equation we get,
[tex]a=1, b=6, c=7[/tex]
Put this values in the above formula,
[tex]x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=-4.41,-1.59[/tex]
Hence, the two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
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six hundred kilograms of tea were packed in 500 g packets. how many packets of tea were there?
Answer:
1200 packets of tea
Step-by-step explanation:
Its because theres 1000 grams in 1kg so it would be 600000 grams and you would divided 600000 over 500 and get 1200
Can you mark brainlyist?
Answer:
1,200 packets of tea
Step-by-step explanation:
1. First, convert 600 kilograms into grams.
1 kilogram = 1,000 grams
So,
600 kilograms = 600,000 grams.
Now divide the previous value by 500.
[tex]\frac{600,000 g}{500 g} = 1,200[/tex]
Therefore, there are 1,200 packets of tea.
In the figure diameter DE is drawn with the midpoint of the circle at C(-3; 2).
EA is a tangent to the circle at E (1,3).
Answer:
4
Step-by-step explanation:
[tex]gradient = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]y2 = - 3 \\ y1 = 3 \\ x2 = 2 \\ x1 = 3[/tex]
[tex] \frac{ - 3 - 1}{2 - 3} = \frac{ - 4}{ - 1} = 4[/tex]
An account with $300 gains 0. 5% annual interest compounded continuously. How
many years would it take to reach $600? Round to the nearest whole year and type
your answer into the box.
Formula: A=
Pert
Answer:
139
Step-by-step explanation:
A = Pe^rt
A = 600$
P = 300$
R = 0.005
T = ?
600 = 300e^(0.005)(t)
t = 138.63
16 more than craigs score is 62
Step-by-step explanation:
what is the question ?
to find Craig's score ?
if that is the case :
Craig's score = 62 - 16 = 46
Multiply. What is the product (3 x 10^9) * (2 * 10^17) in scientific
notation?
?
(3 * 10^9) * (2 x 10^17 = ? * 10^?
DONE
Answer:
[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]
Step-by-step explanation:
[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]
If x represents the molar solubility of b a 3 ( p o 4 ) 2 , what is the correct equation for the k s p ?
The molar solubility of Ba₃(PO₄)₂ is its concentration of pure substance
The correct equation for the ksp is Ksp = 6x⁵
How to determine the equation of ksp?Start by writing the reaction for the solution of Barium phosphate
Ba₃(PO₄)₂ ⇌3Ba²⁺ +2PO₄³⁻
Next, we make an ICE chart
Let "x" be the molar solubility of Barium phosphate
Ba₃(PO₄)₂(s) ⇌3Ba²⁺ +2PO₄³⁻
I 0 0
C +3x +2x
E 3x³ 2x²
Lastly, we write the expression for the solubility product constant (Ksp)
This is represented as:
Ksp = [3Ba²⁺] × [2PO₄³⁻]²
Ksp = 3x³ × 2x²
Evaluate the product
Ksp = 6x⁵
Hence, the correct equation for the ksp is Ksp = 6x⁵
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The molar solubility of Ba₃(PO₄)₂ is its concentration of a pure substance.
The correct equation for the ksp is Ksp = 6x⁵.
How to determine the equation of ksp?The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is denoted by the symbol Ksp.
Start by writing the reaction for the solution of Barium phosphate.
Ba₃(PO₄)₂ ⇌3Ba²⁺ +2PO₄³⁻
Let "x" be the molar solubility of Barium phosphate
Ba₃(PO₄)₂(s) ⇌3Ba²⁺ +2PO₄³⁻
I 0 0
C +3x +2x
E 3x³ 2x²
Lastly, we write the expression for the solubility product constant (Ksp),
This is represented as:
Ksp = [3Ba²⁺] × [2PO₄³⁻]²
Ksp = 3x³ × 2x²
Evaluate the product
Ksp = 6x⁵
Hence, the correct equation for the ksp is Ksp = 6x⁵
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Help me !!!! Emergency .
50 points + Brainliest
No spammers please
Leaders please answer this question
No. 8. a
Answer:
[tex] \frac{1}{ \sqrt{2} } [/tex]
Step-by-step explanation:
Given
[tex]theta = 22 \frac{1}{2} = \frac{45}{2} [/tex]
[tex]2 \times theta = \frac{45}{2} \times 2 = 45[/tex]
Sin2theta=sin45⁰=1/√2
[tex] \frac{1}{ \sqrt{2} } [/tex]
is your answer
Answer:
[tex]\sf \dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
[tex]\sf If\:\theta=\left(22\dfrac12\right)^{\circ}[/tex]
[tex]\sf \implies2\theta=2\cdot\left(22\dfrac12\right)^{\circ}=45^{\circ}[/tex]
[tex]\sf Therefore\:\sin2\theta=\sin(45)^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
Proof
If a right triangle has an interior angle of 45°, then the third interior angle will also be 45° (since the sum of the interior angles of a triangle is 180°).
This means that the two legs of the right triangle are equal in length.
Using Pythagoras' Theorem, we can state that the hypotenuse of a right triangle with two legs of equal length will be √2 times the length of a leg.
Let a = b = 1
⇒ 1² + 1² = c²
⇒ c = √2
The sine trig ratio is:
[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse[tex]\implies \sf \sin(45^{\circ})=\dfrac{1}{\sqrt{2} }[/tex]
[tex]\implies \sf \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies \sf \sin(45^{\circ})=\dfrac{\sqrt{2}}{2}[/tex]
Hello people ~
Factorise: x^2 + 7x + 12
Step-by-step explanation:
x^2 + (4+3)X + 12
x^2 + 4x + 3X + 12
X (X + 4) + 3 ( X + 4)
( X + 3) (X +4)
Solving steps:
[tex]\sf \rightarrow x^2\:+\:7x\:+\:12[/tex]
breakdown the following
[tex]\sf \rightarrow x^2\:+\:3x + 4x\:+\:12[/tex]
break the expressions into groups
[tex]\sf \rightarrow \left(x^2+3x\right)+\left(4x+12\right)[/tex]
factor the following
[tex]\rightarrow \sf x\left(x+3\right)+4\left(x+3\right)[/tex]
factor the common term: (x+3)
[tex]\rightarrow \sf \left(x+3\right)\left(x+4\right)[/tex]
yeah help me okay thanks
Answer:
4
3
Step-by-step explanation:
1. Jennifer can mow the lawn in 20 min. Kristen can mow the lawn in 30 min. If they work together, how long will it take them to mow the lawn
Answer:
Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.
So he does 1/20 of the job per minute.
.
Rob can do the job in 30 min. His rate is 1/30 of the job per minute.
.
Working together how does it take?
.
1/20*x + 1/30*x = 1 job done
, where x = minutes.
.
Step-by-step explanation:
¿Cuáles son los términos algebraicos que representan a una función cuadrática incompleta
con solamente término cuadrático?
Una ecuación cuadratica que solo tiene el termino cuadratico se escribe como:
y = a*x^2
¿Como escribir esta ecuación cuadratica?
La ecuación cuadratica general se escribe como:
y = a*x^2 + b*x + c
Donde el termino cuadratico es el primero, el segundo es el lineal y el tercero es el constante.
Entonces, si queremos una ecuación cuadratica que solo tenga el termino cuadratico, la ecuación sera:
y = a*x^2
Sí quieres aprender más sobre cuadraticas, puedes leer:
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