please explain how you got your answer because i cant grasp this :/

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.

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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Answer:

first would be a translation of (2,-3) second one is another 90 degree rotation counter clockwise.

Answer:

okay so think of the polygon as like a rectangle in a way now use the method of finding a area with a triangle  

Step-by-step explanation:

A= bxh divide by 2 then A= bxh x 2

it worked for me

Answer: (2,1)

Step-by-step explanation:

The two equations given are:

           y = 3 -x

           y = x - 1

The question is asking to determine the point of intersection for two linear functions aka two lines.

Step #1: Both functions must be in slope intercept form which is y = mx+b. In this case, this step can be skipped because both functions are in slope form. At an intersection, x and y must have the same value for each equation. This means that the equations are equal to each other. Therefore, we can set both equations equal to each other to solve for x.

Step #2: We found the x-coordinate, but we need to find the y-coordinate. We know that the x-coordinate is 2, so substitute the number 2 into any of the given equations. So, either into y = 3 - x or y = x - 1.

The point of intersection is (2,1).

Hope this helps ^_^

Answer:

The price for each pound of tuna is not always the same.

Step-by-step explanation:

What we do is divide the price by the amount of tuna to find the price for each amount of tuna

For the 1st one, we have $8 for 2 tuna so we do 8/2

8/2 = 4

For the 2nd we have $16 for 4 so we do 16/4

16/4 = 4

For the 3rd, we have $27 for 9 so we do 27/9

27/9 = 3

Answer: Division of Equality

Step-by-step explanation: In this equation, using division, we can find what y is by dividing 5 on both sides. Y equals to 15.

The length of one of the legs  of an isosceles right triangle and has a hypotenuse length of seven times the square root of two is 7 units.

Isosceles triangles are triangles that has two of it sides equal to each other. The base angles of an isosceles triangle are equal.

The  isosceles triangle is also a right angle triangle. The hypotenuse is the longest side of a right angle triangle.

Therefore,

hypotenuse = 7(√2)

let the length of the other legs = x

Therefore, using Pythagoras theorem

c² = a² + b²

(7(√2))² = x² + x²

49 × 2 = 2x²

98 = 2x²

x² = 98 / 2

x = √49

x = 7 units

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Answer:

  AA similarity postulate

Step-by-step explanation:

Triangles are similar if corresponding angles are congruent or if corresponding sides are proportional.

Here, the missing reason in the proof follows a step in which two angles are shown congruent. That means you can claim similarity by the AA similarity postulate.

__

Additional comment

The similarity postulates include ...

  AA -- two corresponding angles (the third angle is determined by these two)

  SSS -- three proportional corresponding sides

  AAS -- two congruent angles and a proportional corresponding side

  ASA -- a variation of AAS

  SAS -- proportional corresponding sides flanking a congruent angle

With the exception of AA, these are the same postulates as used to prove triangle congruence when the corresponding sides are congruent, rather than proportional.

The 100th term of the sequence is -273

Arithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference

first term a = 222

common difference, d = -5

nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d

T100 = a + ( 100 - 1 ) d

T100 = 222 + 99 * -5

T100 = -273

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Answer:

9/7

Step-by-step explanation:

2+2+1+3+4+6+8+1/10+4+3+4

Hope this helps!!!

Total Amount on principal 7000dollars  at the rate of interest 3%  for time period 7years is equals to $8470.

" Simple interest is a method of calculating interest on the amount of money deposited for fixed period on fixed rate of interest."

Formula used

[tex]Amount = P ( 1+ rt) \\P= Principal\\r= Rate of interest\\t= time period[/tex]

According to the question,

Given,

Principal 'P' = $7000

Rate of interest 'r'= 3%

Time period 't' = 7years

Substitute the value in the formula to get total amount with interest,

[tex]Amount = 7000 [ 1+ (\frac{3}{100} )(7)][/tex]

             [tex]=7000[ 1+ (0.03)(7)]\\=7000(1.21)\\=8470 dollars[/tex]

Hence, the total Amount on principal 7000dollars  at the rate of interest 3%  for time period 7years is equals to $8470.

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well, we know that he makes $60 weekly, that'd be the 100%, we also know that he saves 30% of that and the rest, well, 100% - 30% = 70%, so 70% he spends it on food.

if we take 60 to be the 100%, what is 70% of it?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 60 & 100\\ x& 70 \end{array} \implies \cfrac{60}{x}=\cfrac{100}{70}\implies \cfrac{60}{x}=\cfrac{10}{7} \\\\\\ 420=10x\implies \cfrac{420}{10}=x\implies 42=x[/tex]

Answer: look at the image

Step-by-step explanation:

Answer:

x=-8

Step-by-step explanation:

5x-3x=-2-14

2x=-16

x=-8

Answer:

y = -1/2x + 1

Step-by-step explanation:

We find slope using rise-over-run and by counting I got 1/2 but the slope is also negative. The y-intercept is 1 because the points are counting by 1/2 and the line goes through where half of 2 is on the y-axis. Hope this helps!

Answer:

B. y = 5x-1

Step-by-step explanation:

B. y = 5x-1 is not an exponential function.

Answer:

68 degrees

Step-by-step explanation:

EHD and CHF are vertical angles, meaning their angle measures are the same.

Answer:

m<CHF = 68°

Step-by-step explanation:

Angles EHD and CHF are vertical angles, so their measures are equal.

m<CHF = m<EHD = 68°

Answer:

{- 1, 0, 4 }

Step-by-step explanation:

the range is the y- coordinates of the plotted points

the coordinates of the points are

(- 4, - 1 ) , (1, 0 ) , (1, 4 ) with y- coordinates - 1, 0, 4

then range is { - 1, 0, 4 }

Answer:

make the n in side and join together

Hello !

_______

[tex]\huge {\boxed {\underline{Explanation :}}}[/tex]

[tex]\sf{5 \: x \: \frac{3}{4}[/tex]

_______

[tex]\sf{Apply \: the \: fraction \: rule :} \: a \: ^. \: \frac{b}{c} = \frac{a \: ^. \: b}{c}[/tex]

[tex]\sf{\frac{5x \: ^. \: 3}{4}[/tex]

_______

[tex]\sf{Multiply \: the \: numbers:} \: 5 \: ^. \: 3 = 15[/tex]

[tex]\sf{= \frac{15x}{x}[/tex]

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Dollixna ~

Answer:

Step-by-step explanation:

Assuming you can use any digit from 0-9

You can do 5% of 260 = 13 . All of which are different digits and not the same

This is true because 260 x .05 = 13

Answer:

b) one quarter hour

Step-by-step explanation:

every section is worth 5 minutes, there are three sections, which equals 15 minutes, 15 minutes is a one-quarter hour. hope this helps :)

Answer:

B

Step-by-step explanation:

it Is one quarter of an hour because they are exactly 15 minutes

Answer:

3217.00

Step-by-step explanation:

V=πr^2h=π·8^2·16≈3216.99088

Answer:

804.2 or 803.8

Step-by-step explanation:

volume = π · r2 · h

π · [tex]4^{2}[/tex] · 16 = 804.2

3.14 · [tex]4^{2}[/tex] · 16 = 803.8

Answer:

A

Step-by-step explanation:

tanΘ = [tex]\frac{\sqrt{3} }{3}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{3}[/tex] ) = [tex]\frac{\pi }{6}[/tex]

since tanΘ > 0 then Θ is in first / third quadrants

Θ = π + [tex]\frac{\pi }{6}[/tex] = [tex]\frac{7\pi }{6}[/tex]

solution is { [tex]\frac{\pi }{6}[/tex] , [tex]\frac{7\pi }{6}[/tex] } in the interval 0 < Θ < 2π

Answer:

X= 5/18

Step-by-step explanation:

Answer/Step-by-step explanation:

 All of the solutions to the equation 3x^2 - 12 = 0 are x = 12 and x = -2

Answer: False

Explanation:

[tex]3x^2-12+12=0+12[/tex]

[tex]3x^2=12[/tex]

[tex]\frac{3x^2}{3}=\frac{12}{3}[/tex]

[tex]x^2=4[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{4},\:x=-\sqrt{4}[/tex]

[tex]x=2,\:x=-2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are two unique solutions to the equations (x-3)^2 = 16

Note: Each variable in the matrix can have only one possible value, and this is how you know that this matrix has one unique solution.

Answer: True

Explanation:

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=7,\:x=-1[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Ths solutions for the equation 2(x-3)^3 - 18 = 0 are x = 6 and x = 0

Answer: False

Explanation:

[tex]2\left(x-3\right)^3-18+18=0+18[/tex]

[tex]2\left(x-3\right)^3=18[/tex]

[tex]\frac{2\left(x-3\right)^3}{2}=\frac{18}{2}[/tex]

[tex]\left(x-3\right)^3=9[/tex]

[tex]\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}[/tex]

[tex]=\sqrt[3]{9}+3,\:x=\frac{6-\sqrt[3]{9}}{2}+i\frac{\sqrt[3]{9}\sqrt{3}}{2},\:x=\frac{6-\sqrt[3]{9}}{2}-i\frac{\sqrt[3]{9}\sqrt{3}}{2}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7

Answer: False

Explanation:

[tex]2\left(x-5\right)^2-8+8=0+8[/tex]

[tex]2\left(x-5\right)^2=8[/tex]

[tex]\frac{2\left(x-5\right)^2}{2}=\frac{8}{2}[/tex]

[tex]\left(x-5\right)^2=4[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=7,\:x=3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation (x + 3)^2-25 = -8 are x = 2 and x = -8

Answer: False

Explanation:

[tex]\left(x+3\right)^2-25+25=-8+25[/tex]

[tex]\left(x+3\right)^2=17[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{17}-3,\:x=-\sqrt{17}-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4

Answer: False

Explanation:

[tex]\frac{2\left(2x-1\right)^2}{2}=\frac{18}{2}[/tex]

[tex]\left(2x-1\right)^2=9[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=2,x=-1[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The only solution for equation (2x-1)^2-49=0 is x = 4

Answer: False
Explanation:

[tex]\left(2x-1\right)^2-49+49=0+49[/tex]

[tex]\left(2x-1\right)^2=49[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=4,\:x=-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 3(x+2)^2 - 3 = 0 are x = -3 and x = -1

Answer: True
Explanation:

[tex]3\left(x+2\right)^2-3+3=0+3[/tex]

[tex]3\left(x+2\right)^2=3[/tex]

[tex]\frac{3\left(x+2\right)^2}{3}=\frac{3}{3}[/tex]

[tex]\left(x+2\right)^2=1[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=-1,\:x=-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 5x^2 - 180 = 0 are x = 6 and x  = -6

Answer: True

Explanation:

[tex]5x^2-180+180=0+180[/tex]

[tex]5x^2=180[/tex]

[tex]\frac{5x^2}{5}=\frac{180}{5}[/tex]

[tex]x^2=36[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{36},\:x=-\sqrt{36}[/tex]

[tex]x=6,\:x=-6[/tex]

~Lenvy~

Answer:

Option C :- 7.5x + 8.1

Step-by-step explanation:

Let's simplify step-by-step.

4.5x+3.1−(−3x−5)

Distribute the Negative Sign:

=4.5x+3.1+−1(−3x−5)

=4.5x+3.1+−1(−3x)+(−1)(−5)

=4.5x+3.1+3x+5

Combine Like Terms:

=4.5x+3.1+3x+5

=(4.5x+3x)+(3.1+5)

=7.5x+8.1

Answer:

=7.5x+8.1

Answer:

Area of shaded rectangle = 42 cm²

55%

Step-by-step explanation:

The length of the shaded area is equal to the length of the white rectangle.

Therefore, length of shaded rectangle = 7 cm

The width of the shaded rectangle is equal to the length of the white rectangle minus two widths of the white rectangle.

Therefore, width = 7 - (2 x 0.5) = 6 cm

Area of shaded rectangle = width x length

                                          = 6 x 7

                                          = 42 cm²

----------------------------------------------------------------------------------------------

Perimeter of a square = 4 × side length

If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm

Area of a square = side length x side length

⇒ area of this square = 10 x 10 = 100 cm²

To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.

Area of a triangle = 1/2 x base x height

⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²

⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²

Therefore, shaded area = 100 - 15 - 30 = 55 cm²

To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:

(55 ÷ 100) × 100% = 55%

Answer:

0.92 cm

Step-by-step explanation:

Do not pick 0.920 as it is the same as 0.92 but 0.92 is always the preferable option

The accurate measurement for the length of the green box is indeed 0.92 cm.

To measure the length of the green box accurately, we must carefully analyze the given image. By comparing the green box to the provided scale, we can deduce the correct measurement.

Upon examination, the green box appears to span almost the entirety of the "0.1 cm" scale division and extends slightly beyond it. Given that the box reaches around 9 divisions on the scale, it is reasonable to deduce that its length is 0.92 cm. This is because it's covering 9 divisions of 0.1 cm each, and considering the small extension.

Hence, the accurate measurement for the length of the green box is indeed 0.92 cm. This value takes into account its coverage of 0.9 cm (9 divisions) and a slight extension, aligning with the provided options.

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