Follow the process of completing the square to solve x = 4x +3.
x -
Which of the following equations is used in this process?
(2x - 42.19
(2x4,2= 12
(2x 42-28

Answer:

[tex]x ^{m - 3} \div x^{m - 4} \\ \frac{ {x}^{m - 3} }{ {x}^{m - 4} } \\ \frac{ {x}^{m - 3 - m + 4} }{x} \\ \frac{ {x}^{1} }{x} \\ x \: and \: x \: will \: cancel \: each \: other \: hence \: answer \: will \: be \: 1[/tex]

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2m

3m

4m

5m

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Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1[/tex]

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

[tex]\displaystyle y - y_1 = m( x - x_1)[/tex]

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

[tex]\displaystyle y - (4.8) = 0.1(x - 10)[/tex]

Simplify:

[tex]\displaystyle y = 0.1(x-10) + 4.8[/tex]

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

The initial volume is when t = 0. Evaluate:

[tex]\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8[/tex]

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

[tex]60 = 0.1(t - 10) + 4.8[/tex]

Subtract:

[tex]55.2 = 0.1(t - 10)[/tex]

Divide:

[tex]552 = t - 10[/tex]

Add. Therefore:

[tex]t = 562\text{ minutes}[/tex]

It will take 562 minutes for the tank to be completely filled.

If L(t) = ⟨5 + t, 1 + 5t⟩, then the tangent vector to L(t) is

dL/dt = ⟨1, 5⟩

Any line parallel to L(t) will have the same tangent vector, up to some scalar factor (that is, if the tangent vector is a multiple of ⟨1, 5⟩).

Any line r(t) with tangent vector T(t) = dr/dt that is perpendicular to L(t) will satisfy

T(t) • ⟨1, 5⟩ = 0

• r(t) = ⟨-5, -2t, 1 - 10t⟩ is parallel to L(t) because its tangent vector is

T(t) = ⟨-2, -10⟩ = -2 ⟨1, 5⟩

• r(t) = ⟨1 + 1.5t, 3 + 7.5t⟩ is parallel to L(t) because

T(t) = ⟨1.5, 7.5⟩ = 1.5 ⟨1, 5⟩

• r(t) = ⟨-2 - t, 2 - 2t⟩ is neither parallel nor perpendicular to L(t) because

T(t) = ⟨-1, -2⟩ ≠ k ⟨1, 5⟩

for any real k (in other words, there is no k such that -1 = k and -2 = 5k), and

⟨-1, -2⟩ • ⟨1, 5⟩ = -1 - 10 = -11 ≠ 0

• r(t) = ⟨3 + 15t, -3t⟩ is perpendicular to L(t) because

T(t) = ⟨15, -3⟩

and

⟨15, -3⟩ • ⟨1, 5⟩ = 15 - 15 = 0

Answer:

3m = -3

Step-by-step explanation:

2m−6=8m

Subtract 2m from each side

2m−6-2m=8m-2m

-6 = 6m

Divide by 6

-6/6 = 6m/6

-1 = m

3m = 3(-1) = -3

2m - 6 = 8m

2m - 8m = 6

-6m = 6

m = -6/6

m = -1

the answer will be 0.092 as a decimal

This requires finding the number of small sweaters the company made last week

Number of small sweaters the company produced last week is 372

Total sweaters made = 1,612

Let

Small sweaters = 3x

Medium sweaters = x

Large sweaters = 3(3x) = 9x

Total = small + medium + large

1,612 = 3x + x + 9x

1612 = 13x

Divide by 13

x = 1612/13

Medium sweaters = x = 124

Small sweaters = 3x

= 3(124)

= 372

Read more:

https://brainly.com/question/24326559

Answer:

B: 30 and 60

Step-by-step explanation:

First, let's set up an equation. Since the two angles are complementary, we can write the equation like this:

2p + p = 90

Now, let's solve it!

2p + p = 90

Combine like terms:

3p = 90

Divide each side by 3 to isolate p:

3p/3 = 90/3

p = 30

Now that we know how many degrees one of our angles is, we can subtract that from 90 to get both of the complementary angles.

90 - 30 = 60

Therefore, the two angles that are complementary in this case are 30 and 60 degrees.

Answer:

this will give you the answer: for cylinder

V = 3×2^2×7 = 84cm

this will give you the answer for cone:

V = 3× 2^2 × 6/3 = 24cm

then we just add

84 + 24 = 108cm^3

Step-by-step explanation:

hope it helps!

Answer:

proper fraction

Step-by-step explanation:

a proper fraction has smaller numerator than its denominatot.

Answer: Proper Fraction

Step-by-step explanation:

The denominator is equal or bigger than the numerator.

Must click thanks and mark brainliest

Answer:

∠ ABC = 125°

Step-by-step explanation:

∠ ABC = ∠ ABD + ∠DBC that is

∠ ABC = 65° + 60° = 125°

Answer:

[tex]x=5[/tex]

[tex]h=\sqrt{(5)^{2}+x^{2} } =\sqrt{(5)^{2}+(5)^{2} }[/tex]

[tex]h=\sqrt{25+25} =\sqrt{50}[/tex]

[tex]h=5\sqrt{2}[/tex]

OAmalOHopeO

The required function of h i.e f(h) is expressed as

[tex]f(h) = \dfrac{1}{h^2-3}[/tex]

Substitution of a function means replacing a variable with another variable without changing the structure of such function. According to the function given, we can see that we are simply meant to replace x with h as shown below:

Given the expression

[tex]f(x) = \frac{1}{x^2-3}[/tex]

To get f(h), we will substitute f in place of x that is x -> h as shown

[tex]f(h) = \frac{1}{h^2-3}[/tex]

Hence the required function of h i.e f(h) is expressed as

[tex]f(h) = \dfrac{1}{h^2-3}[/tex]

Learn more: https://brainly.com/question/4357143

Answer:

the second option #2

one fourth x (26-10) x 3

Step-by-step explanation:

Two of the options (#1 and #4) can be ruled out immediately since they don't involve the difference of 26 and 10.

#3 can be ruled out because the difference needs to be multiplied by one fourth, but this option gives the wrong answer since the multiplication is done before subtraction (BODMAS)

Answer:

c

Step-by-step explanation:

I got it correct on a quiz

After storing 5/9 in the large silo there was 4/9 left ( 1-5/9 = 4/9)

A. Multiply 4/9 by 3/4:

4/9 x 3/4 = 12/36 = 1/3

1/3 of the corn was in the small silo.

B. 1-5/9 -1/3 = 4/9-1/3 = 4/9-3/9 = 1/9

1/9 of the corn went to market:

18 x 1/9 = 18/9 = 2

2 ton went to market.

Answer:

9√2 units

Explanation:

Coordinates of point 1 = (0,10)

Coordinates of point 2 = (-9,1)

distance

=√[(x2-x1)²+(y2-y1)]²

= √[(-9-0)²+(1-10)]²

=> √[(-9)²+(-9)]²

=> √(81+81)

=> √162

=> 9√2

So, the distance between these points is 9√2 units.

Answer:

a) The rocket travels 200 meters horizontally.

b) The height of the rocket mid-flight is of 1000 meters.

Step-by-step explanation:

Height of the rocket:

The height of the rocket, in meters, after an horizontal distance of x, is given by:

[tex]y = 0.1x(200 - x)[/tex]

a) How far does the rocket travel horizontally?

This is x when [tex]y = 0[/tex]. So

[tex]0.1x(200 - x) = 0[/tex]

Then

[tex]0.1x = 0[/tex]

[tex]x = 0[/tex]

And

[tex]200 - x = 0[/tex]

[tex]x = 200[/tex]

So

The rocket travels 200 meters horizontally.

b How high does the rocket reach mid-flight?

This it the height y when x = 0, so:

[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]

The height of the rocket mid-flight is of 1000 meters.

Answer: Distance = √145

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Given information

(x₁, y₁) = (4, -9)

(x₂, y₂) = (5, 3)

Given formula

[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the formula

[tex]Distance = \sqrt{(5-4)^2+(3+9)^2}[/tex]

Simplify values in the parentheses

[tex]Distance = \sqrt{(1)^2+(12)^2}[/tex]

Simplify exponents

[tex]Distance = \sqrt{1+144}[/tex]

Simplify by addition

[tex]Distance = \sqrt{145}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\boxed {\boxed {\sf \sqrt {145} \ or \ 12.04}}[/tex]

Step-by-step explanation:

The distance between 2 points is calculated using the following formula.

[tex]d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2)[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

We know the two points are (4, -9) and (5,3). If we match the values of the points and the coordinating variable, we see that:

Substitute the values into the formula.

[tex]d= \sqrt { ( 5 -4)^2 + ( 3 --9)^2[/tex]

Solve inside the parentheses.

[tex]d= \sqrt {(1)^2 + (12)^2}[/tex]

Solve the exponents.

[tex]d= \sqrt{ 1+144}[/tex]

Add.

[tex]d= \sqrt{145[/tex]

Take the square root.

[tex]d=12.04159458[/tex]

Let's round to the nearest hundredth. The 1 in the thousandth place tells us to leave the 4 in the hundredth place.

[tex]d \approx 12.04[/tex]

The distance between the 2 points is √145 or approximately 12.04.

Answer:

Step-by-step explanation:

Each number increases by 3. Therefore, n+3.

Answer:

It's a decimal, so it's around 6.771cm

Step-by-step explanation:

First, divide 144cm² by pi, or 3.14. Then find the square root of the answer, giving you the radius. The formula for the area of a circle is pi x radius squared, so to find out the radius you just use this formula in reverse.

If I messed up or didn't make my explanation clear, please comment.

Answer:

radius is [tex]\frac{12}{\sqrt{\pi } }[/tex] = 6.77 cm

Step-by-step explanation:

we know,

[tex]\pi[/tex] × r² = Area

⇒ [tex]\pi[/tex] × r² = 144

⇒ r² =[tex]\frac{144}{\pi}[/tex]

⇒ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

∴ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

pls mark this as the braniliest

Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

50 is the multiple of 10 that is closest to 47.

Step-by-step explanation:

yo

so sorry I can't

really answer it

Answer:

[tex]i)14 + 4 \sqrt{6} [/tex]

[tex]ii) \sqrt{10} + 28[/tex]

[tex]iii) 243[/tex]

Step-by-step explanation:

[tex]i)(2 \sqrt{3} + \sqrt{2} {)}^{2} [/tex]

➡️ [tex]12 + 4 \sqrt{6} + 2[/tex]

➡️ [tex]14 + 4 \sqrt{6} [/tex] ✅

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

[tex]ii)(3 \sqrt{5} - \sqrt{2} ) \times ( \sqrt{2} + 2 \sqrt{5} )[/tex]

➡️ [tex]3 \sqrt{10} + 30 - 2 - 2 \sqrt{10} [/tex]

➡️ [tex] \sqrt{10} + 28[/tex] ✅

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

[tex]iii)3 \sqrt{81} \times 3 \sqrt{9} [/tex]

➡️ [tex]3 \times 9 \times 3 \times 3[/tex]

➡️ [tex]243[/tex] ✅

the models aren't given..

Answer: no models given

Step-by-step explanation:

Answer:

There are four ways to represent an inequality: Equation notation, set notation, interval notation, and solution graph.

Answer:5

Step-by-step explanation:

On the first day he ate 5. Second day he ate 7. Then 9, 11, and finally 13. That all equals to 45. I don't know for sure though...

Answer:

Hence the correct option is option c has a Binomial distribution with n=21 and p=50%.

Step-by-step explanation:

1)  

A coin is tossed 19 times,  

P(Head)=0.5  

P(Tail)=0.5  

We have to find the probability of a total number of heads in all the coin tosses equals 9.  

This can be solved using the binomial distribution. For binomial distribution,  

P(X=x)=C(n,x)px(1-p)n-x  

where n is the number of trials, x is the number of successes, p is the probability of success, C(n,x) is a number of ways of choosing x from n.  

P(X=9)=C(19,9)(0.5)9(0.5)10  

P(X=9)=0.1762  

2)  

A fair die is rolled twice.  

Total number of outcomes=36  

Possibilities of getting sum as 9  

S9={(3,6),(4,5)(5,4),(6,3)}  

The total number of spots showing in all the die rolls equals 9 =4/36=0.1111  

3)  

The event of getting a good number of spots on a die roll is actually no different from the event of heads on a coin toss since the probability of a good number of spots is 3/6 = 1/2, which is additionally the probability of heads. the entire number of heads altogether the tosses of the coin plus the entire number of times the die lands with a good number of spots has an equivalent distribution because the total number of heads in 19+2= 21 tosses of the coin. The distribution is binomial with n=21 and p=50%.

Answer:

Domain { -6,3,4,6,10}

The range is the output values, listed from smallest to largest with no repeats

Range { -13,-9,2,14,19}

Step-by-step explanation:

The domain is the input values, listed from smallest to largest with no repeats

Domain { -6,3,4,6,10}

The range is the output values, listed from smallest to largest with no repeats

Range { -13,-9,2,14,19}

Answer:

Range: 14, 19, -9, 2, -13

Domain: -6, 10, 4, 3, 6

Step-by-step explanation:

I don't know but this is it I think .