The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate how much water was in the pool initially

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

The side y is across from the angle Y which is 68 degrees. Angle Y is next to both the hypotenuse (14 units) and adjacent to the side XY (5 units). If we are finding side y, we need to use one of the trig ratios that relates the angle Y to the side across from it. That would be either the sin of Y which is the side opposite y) over the hypotenuse (14) or the tan of Y which is the side opposite over the side adjacent. Either one will get you the side lengths within a tenth or hundredth of each other. Let's do both, just because. First the sine:

[tex]sin(68)=\frac{y}{14}[/tex] and

14sin(68) = y so

y = 12.98 and rounded to the nearest tenth is 13.0

Now the tangent:

[tex]tan(68)=\frac{y}{5}[/tex] and

5tan(68) = y so

y = 12.37 and rounded to the nearest tenth is 12.4.

As an integer, your answer would be 13; as a decimal it would be the 12.4

Apparently, either is fine.

Answer:

49 cupboards

Step-by-step explanation:

See the steps below, it is self-explanatory:

As 14*14/4= 49, the answer is 49 cupboards

Answer:

  [tex]\dfrac{8m^7n^6}{3}[/tex]

Step-by-step explanation:

  [tex]\dfrac{(2mn)^4}{6m^{-3}n^{-2}}=\dfrac{2^4}{6}m^{4-(-3)}n^{4-(-2)}=\boxed{\dfrac{8m^7n^6}{3}}[/tex]

__

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  1/a^b = a^-b

  (a^b)(a^c) = a^(b+c)

Answer:

A

Step-by-step explanation:

Answer:

Most likely the answer is

3x^2+4x-6

Answer:

3x^2+4x-6 is correct

Answer:

Lines a and c.

Step-by-step explanation:

m∠1=42° and m∠3=138°. 42 + 138 = 180, so the two angles form a 180° angle. That means that lines a and c are parallel.

Hope this helps!

Answer:A is parallel to C

Step-by-step explanation:

Statement            |    Reason

42*+138*=180*     |Corresponding angles

There fore A||C aka a parallel to c

42*+140*=180*   | Same side int. angles

Therefore A no || B aka A is not parallel to B

138*=140*            | Same side int. Angles

Therefore B And C are not parallel and A,B. and C are not parallel

The answer is A||C or A is parallel to C

Answer:

Check below

Step-by-step explanation:

Hi there let's graph.

[tex]y>-4x-1\\ y<\frac{3}{2} x-1[/tex]

(Check below)

A) Looking at the pair of inequalities, the solutions is the interval that have the common points that satisfy both inequalities. Look at the graph for the point (6,4) this point satisfy both inequalities.

Plugging in those values (6,4)

[tex]4>-4(6)-1\\4>-25 \\\\[/tex]

Similarly for the second inequality

[tex]4 < 3/2(6)-1\\4<8[/tex]

Since the signal is lesser (<) and greater than (>) the lines are dashed.

B) No. (-1,-1) does not belong to any of those intervals. Check below. By the same procedure above. Check it out algebraically:

-1>4-1

-1>3  False!

And

-1<-3/2-1

-1<-1 False

Answer:

y = - 4x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4 , thus

y = - 4x + c ← is the partial equation

To find c substitute (- 4, 6) into the partial equation

6 = 16 + c ⇒ c = 6 - 16 = - 10

y = - 4x - 10 ← equation of line

Answer:

y = -4x+10

Step-by-step explanation:

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = -4x +b

Substituting the point in

6 = -4(-4) + b

6 = 16+b

Subtract 16 from each side

-10 =b

The equation is

y = -4x+10

Answer:

x = 6.375

Step-by-step explanation:

Step 1:

4.2+0.8 = 5

(1.6x+1.8)÷2.4 = 5

Step 2:

5 · 2.4 = 12

1.6x + 1.8 = 12

Step 3:

12 - 1.8 = 10.2

1.6x = 10.2

Step 4:

10.2 ÷ 1.6 = 6.375

x = 6.375

Answer:

C

Step-by-step explanation:

This is because it has a constant rate of change.

5 x 1.5 = 7.5

6 x 1.5 = 9

7 x 1.5 = 10.5

You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.

Answer:

x= 20      x =-5

Step-by-step explanation:

x^2 – 15x – 100 = 0.

What two numbers multiply to -100 and add to -15

-20 * 5 = -100

-20 +5 = -15

(x-20) (x+5) =0

Using the zero product property

x-20 =0     x+5 = 0

x= 20      x =-5

x = 20 and x = -5

Step-by-step explanation:

x² – 15x – 100 = 0

First, find factors that multiply to get -100 and add to -15.

These factors are -20 and 5.

So we have (x - 20)(x + 5) = 0.

Now use the zero product property to get x - 20 = 0 or x + 5 = 0.

Solving from here, we get x = 20 or x = -5.

Answer:

448

Step-by-step explanation:

Formula

tn = a + (n - 1)d

Givens

a = - 11

n = 52

d = 9

Solution

t52 = -11 + (51)*9

t52 = - 11 + 459

t52 = 448

Answer:

The answer is 21.25cm

Step-by-step explanation:

Hope i am marked as brainliest

Answer:

The distance between two cities is 60 miles.

Step-by-step explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = u mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed = [tex](u+5)\ mph[/tex]

While moving against the current, speed = [tex](u-5)\ mph[/tex]

Formula for Distance = Speed [tex]\times[/tex] Time

Distance traveled in each case is same i.e. D.

So,

[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]

Now,

[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]

So, the distance between two cities is 60 miles.

Answer:

I believe that the answer is 60 miles

Step-by-step explanation:

Answer: Option C, 1 unit bellow.

Step-by-step explanation:

The residual of a data point is equal to the vertical distance between the point and the regression line

If the data point is above the line, the residual is positive

if the data point is below the line, the residual is negative.

So here we have a negative residual equal to -1

This would mean that our point is 1 unit below the regression line.

Then the correct option is C.

Answer:

The answer is 1 unit below.

Step-by-step explanation:

This is because the residual is the difference between the actual value of a dependent variable & the value predicted by a regression equation. So if the data point has a residual of -1, that means that the data point lies 1 unit below the regression line.

Answer: The missing side is 5 units.

Step-by-step explanation:

Pythagorean Theorem states that a^2+b^2=c^2.  Let the hypotenuse be x.

[tex]4^2+3^2=x^2\\16+9=x^2\\25=x^2\\\sqrt{25}=\sqrt{x^2}\\\left[\begin{array}{c}x=5\end{array}\right][/tex]

Hope it helps <3

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

Step-by-step explanation:

The inequality is [tex]\frac{x}{-3}[/tex] >2

x is less than -6  and -6 is excluded so it will be represented by an empty circle and a line going toward negative values

so it's D

Answer:

Graph 4

Step-by-step explanation:

The graph of f(x) = x^3 includes point (0, 0) since f(0) = 0^3 = 0.

The exponent of x is 3. This is not a linear function.

Negative values of x cubed are negative, and positive values of x cubed are positive.

For x < 0, f(x) < 0, and for x > 0, f(x) > 0.

Answer: Graph 4.

Step-by-step explanation:

Y varies directly as cube root of x is written as

y = k³√x

where k is the constant of proportionality

when y = 3

x = 27

We have

[tex]3 = k \sqrt[3]{27} [/tex]

But ³√27 = 3

That's

3 = 3k

Divide both sides by 3

k = 1

The value of the relationship is

When x = 8

We have

Hope this helps you

Answer: the answer is 151

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

1) 4a + 8

2) 12a² - 8a

3) 2a² + 8a

4) 4 - 6a

Step-by-step explanation:

The GCF of two numbers is the greatest common number each of the original two numbers can be divided by to get a whole number.

Hope it helps <3

Answer:

4     4a+8

4a   [tex]12a^{2}[/tex]+8a

2a   [tex]2a^{2} +8a[/tex]

2     4-6a

Step-by-step explanation:

Okay basicly you wand to find the biggest number that can go into both numbers

like the greatest common fact for 4a+8 would be 4 since only one of the numbers have an a you would just leave that out

Since you can take a 4 and an a out of [tex]12a^{2} \\[/tex] and out of 8a the greatest common factor would be 4a

Since you are able to take a 2 and an a out of [tex]2a^{2} +8a[/tex] your greatest common factor would be a

Since the largest number that can go into 4 and 6 is 2 your answer would be 2

Hope this helps you understand!

Answer:

(1/2)x + (1/4)y <= 200

Step-by-step explanation:

If

x = # of lbs of House blend he makes/sells a day

y = # of lbs of Exotic blend he makes/sells a day

then constraints are

(1/2)x + (1/4)y <= 200  ....................(1)

x+y <= 530  .....................................(2)

The exact answer choices are not very clear from the question, but either (or both) (1) or (2) must be one of them.  If not, please edit question or add a comment to show the answer choices.

Answer:

Options (1), (2), (4) and (5) are correct.

Step-by-step explanation:

Characteristics of the given hyperbola,

1). Vertex of the given hyperbola are at (-3, 6) and (-3, 4).

2). Since center of a hyperbola is the center of a line joining vertices of the hyperbola,

Center of the given parabola will be,

[tex](\frac{-3-3}{2},\frac{6+4}{2})[/tex] ⇒ (-3, 5)

3). Vertical line joining the foci of the hyperbola is the transverse axis.

4). A line perpendicular to the transverse axis and passing through the center will be the conjugate axis.

5). Directrices of a horizontal hyperbola are the horizontal lines.

Therefore, Options (1), (2), (4) and (5) are correct.

Answer:

check photo. <3

Step-by-step explanation:

Answer:

[tex]\boxed{\sqrt{37} }[/tex]

Step-by-step explanation:

Use Pythagorean theorem.

Create a right triangle, with legs of length 6 and 1 units. Find the length of hypotenuse.

[tex]6^2+1^2 =c^2 \\36+1=c^2 \\37=c^2 \\c=\sqrt{37}[/tex]

Answer:

When you use Pythagorean theorem, the answer is √37.

Step-by-step explanation:

Answer:

Sum of two rational numbers-

-10 = -5+-5

0= -5+5

15= 10+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

[tex]\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\ \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o[/tex]

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = [tex]\frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2[/tex]

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = [tex]\frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm[/tex]

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

C). (3, 29) would be your answer.

Explanation?:

Rewrite the equation in vertex form.

y = -3(x - 3)^2 + 29

use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 3

k = 29

The vertex = (h, k)/(3, 29)

Hope this helps!

Answer:

It would be c

Step-by-step explanation: