through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?

The gallons of milk were in each container originally is 2.4 and 4.8 gallons respectively.

Let us say that:

V₁ = initial gallons in the first container

V₂ = initial gallons in the second container.

From the problem statement, we can create the expression:

V₁ = 2 V₂

V₁ – 3 = 45 (V₂ – 2)

Combining the two expressions:

2 V₂ – 3 = 45 (V₂ – 2)

2 V₂ – 3 = 45 V₂ – 9

2.5 V₂ = 6

Divide

V₂ = 6 / 2.5

V₂ = 2.4 gallons

V₁ = 2 V₂:

= 2 × 2.4

= 4.8 gallons

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Complete question

The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 4.5 times as much milk as the second, How many gallons of milk were in each container originally?

Answer:

Step-by-step explanation:

-4(x - 1) + 6x =34

-4x + 4 + 6x = 34

-4x + 6x + 4 = 34

2x + 4 = 34

2x + (4-4) = (34-4)

2x = 30

2x/2 = 30/2

x = 15

The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

Given,

Number of social networking sites being surveyed = 6

Sample mean = 9.05 million visitors per month

Standard deviation = 5 million

We have to find the 98% confidence interval of the true mean;

Here,

Sample mean, x = 9.05 million

Standard deviation, σ = 5 million

Sample size, n = 6

z score of 98% is 2.326

Now,

9.05 million - 2.326 × (5 million / √6) < true mean < 9.05 million + 2.326 × (5 million / √6)

43.02 million < true mean < 13.80

Therefore,

The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

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Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]

[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex

Apply completing the square method to find vertex

[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]

Lets take half of coefficient of x is -6

divide by 2 that is -3

square it [tex](-3)^{2}[/tex] that is 9

Add and subtract 9

[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]

Take out -9 and multiply by -2

[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]

Now factor the parenthesis part

[tex]f(x) = -2(x-3)^{2} +23[/tex]

The value of h=3  and k=23

So vertex is (3,23)

The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum

Hence the answer is the vertex is maximum at (3,23)

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The joint relative frequency of students who use a computer in a traditional class is of:

37%.

The relative frequency of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, we want the joint relative frequency of students who use a computer in a traditional class, hence the total and desired outcomes are given as follows:

Hence the joint relative frequency of students who use a computer in a traditional class is calculated as follows:

28/74 = 37%. (rounded down).

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Answer:

14%



Step-by-step explanation:

1. I took the test

2.Likes running and swimming=28

Total=200

28/200=.14

.14 in percent form is 14%

PLS GIVE BRAINLIST MEAN THE WORLD

Answer:

Step-by-step explanation:

an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:

4x - 8 = 22 + x

4x -x = 22 + 8      

3x = 30

x = 10          

Answer:

[tex] \sf \: \frac{7}{12} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

[tex] \sf \rightarrow \: \frac{(1) \times 3}{(4) \times 3} + \frac{(1) \times 4}{(3) \times 4} [/tex]

[tex] \sf \rightarrow \: \frac{3}{12} + \frac{4}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(3 + 4)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{7}{12} [/tex]

Hence, the answer is 7/12.

The rectangle with the sides 4 and 3 is the required rectangle.

The correct option is third shape.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 6 x 4

= 12 square millimeters.

And rectangle has the same area as the triangle.

The rectangle with the sides 4 and 3 is the required.

Therefore, the rectangle with the sides 4 and 3 is the required rectangle.

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The critical value is 2.65

Given,

The confidence interval = 99%

Sample size, n = 12

We have to find the critical value;-

Critical value;-

A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.

Here,

The sample size n = 12,

Then, the degrees of freedom is n - 1 = 12 - 1 = 11

The critical value= t₀.₀₀₁/2 = t₀.₀₀₅

Using the t-table and selecting df =12  and  since it’s a 2 tail the corresponding t-score is 2.65

Therefore, the critical value is 2.65

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The solution to the system is x = 0, y =2, z = 5

Given the following system:

x+ 2y+z=9      -------- (1)

x- y+3z = 13    -------- (2)

2z = 10            -------- (3)

From (3):

2z = 10

z = 10/2 = 5

Put z = 5 into (1) and (2):

x+ 2y+z=9

x+ 2y+5 = 9

x +2y = 9-5

x +2y = 4     -------- (4)

x- y+3z = 13

x -y + 3(5) = 13

x-y + 15 = 13

x-y = 13 -15

x-y = -2     --------   (5)

Using elimination method on (4) and (5):

Subtracting (5) from (4):

x +2y = 4

x-y =   -2

3y = 6

y = 6/3 = 2

Put y = 2 into (4):    

x +2y = 4

x + 2(2) = 4

x + 4 = 4

x = 4-4 = 0

Therefore, the solution is x = 0, y =2, z = 5. The 3rd option is the answer.

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A quadratic equation in one unknown;

has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.

If we apply discriminant for the above equation, we obtain the following expression;

If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.

Now let's remember our formula for finding the roots and solve the problem using the discriminant value.

Therefore;

Other root is;

The best solution for the given equation is x=4

What are logarithmic functions?

The inverse function to exponentiation in mathematics is called the logarithm. Accordingly, the exponent to which b must be raised in order to obtain a number x is determined by its logarithm to the base b.

Use Property:

logb(xy)=logbx+logby and logby = x ⇔ x^b = y

log2(x(x−2))=3
2^3 =x^2 −2x
8=x^2−2x
0=x^2−2x−8
0=(x−4)(x+2)
x−4=0
or
x+2=0
x=4
or
x=−2
Hence, x=4

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Answer: X=16

Step-by-step explanation:

trust,, also good luck to plato 2b algebra people

Answer:

$28

Step-by-step explanation:

5.5%=0.055

1.54/0.055=28

Step-by-step explanation:

are you sure there is no other given info? do you have to solve in terms of m and D?

Answer:

[tex]f( x) = x2 - 7 x[/tex]

you need to plug the coordinates into the slope formula, which is m=(y2-y1)/(x2-x1).

m=(9-6)/(5-4)

m=(3)/(1)

m=3

The given expression rewritten in simplified exponential form is [tex]5x^{\frac{3}{2}}[/tex]

From the question, we are to rewrite the given expression is simplified exponential form.

The given expression is

[tex]\sqrt{\sqrt{25^{2} x^{6} } }[/tex]

First, we will evaluate the inner square root

[tex]\sqrt{25^{\frac{2}{2} } x^{\frac{6}{2} } }[/tex]

[tex]\sqrt{25 x^{3 } }[/tex]

Simplifying further

[tex]\sqrt{25 } \times \sqrt{x^{3}}[/tex]

[tex]5\times x^{\frac{3}{2}}[/tex]

= [tex]5x^{\frac{3}{2}}[/tex]

Hence, the expression in simplified form is [tex]5 x^{\frac{3}{2}}[/tex]

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If the steps follow an arithmetic series, the concrete required for the first 12 steps is 140.4.

Given, the first term of the arithmetic series, a=1.8 and the sum of first five terms that is s5=27, we have to find the sum of first 12 steps.

The formula to calculate the sum of the terms in AP is

Sn = n/2 {2a + (n - 1) d}

S5=5/2(2(1.8) +(5-1)d)

27=2.5(3.6+ 4d)

27=9+10d

27-9=10d

18=10d

d=18/10

d=1.8

The common difference d is 1.8.

Now we have to find S12,

S12=12/2(2(1.8) +(12-1)1.8)

= 6(3.6+19.8)

=6(23.4)

=140.4

S12=140.4

Therefore, the concrete required for the first 12 steps is 140.4.

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Answer:

#0.85

Step by step:

13.60/16 = #0.85

pls give me brainliest

pls:(

Answer:

  1 1/2

Step-by-step explanation:

You want the other number when one of the two numbers that have a product of 7 is 4 2/3.

Let x represent the unknown factor. Then we have ...

  (4 2/3)x = 7

  (14/3)x = 7 . . . . . . write as improper fraction

  x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x

  x = 3/2 = 1 1/2

The other number is 1 1/2.

Answer:

x = 139°

Step-by-step explanation:

The sum of the internal angles of a triangles is 180°

a + 59 + 80 = 180

a = 180 - 139

a = 41°

a and x are supplementary angles. Supplementary angles sum 180°.

Then:

a + x = 180

41 + x = 180

x = 180 - 41

x = 139°

The sequence of transformations that we should apply is the one that appears on the top left option:

Reflection across the y-axis followed by a rotation of 90° counterclockwise.

We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.

First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.

Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.

Concluding, the sequence of transformations is:

Notice that this is equivalent to:

Then the correct option is the one in the top left corner.

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The equation of the parallel line is 4x + 5y - 12 = 0

The equation is given as

4x + 5y + 2 = 0

The x-intercept is also given as

x-intercept = 3

We have

4x + 5y + 2 = 0

Make y the subject

5y = -4x - 2

Divide through by 5

y = -4x/5 - 2/5

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -4/5

This means that the slope of 4x + 5y + 2 = 0 is =4/5

The slopes of parallel lines are equal

This means that the slope of the other line is -4/5

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4/5

(x₁, y₁) = (3, 0) i.e. the x-intercept

So, we have

y = -4/5(x - 3) + 0

Multiply through by 5

5y = -4(x - 3)

Open the brackets and evaluate

5y = -4x + 12

This gives

4x + 5y - 12 = 0

Hence, the parallel line has an equation of 4x + 5y - 12 = 0

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Answer: r = 19.35 ft

Step-by-step explanation:

[tex]Volume = V = \pi r^{2} \frac{h}{3} \\235.5 = \pi r^{2} 15/3\\r^{2} = \frac{235.5}{\pi} 5\\r = \sqrt{374.8} = 19.35[/tex]

Answer: miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:

18.75 miles in 1/4 hour.

that is the ratio 18.75 / 1/4

but we want the miles in an hour.

so, how many 1/4 are in a whole ?

well, 4.

so we need to multiply the ratio by 4/4 (so that on one hand we multiply the denominator by 4 to make it a whole, and on the other hand we are not changing the value of the ratio) :

18.75 × 4 / (1/4 × 4) = 75 miles / 1 hour = 75 mph.

Answer:

1.38461538462

Step-by-step explanation:

Answer: 5:1

Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1

The rectangular coordinates are

a. (1,0,0) ⇒ (x,y,z) = (0,0,1)

b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)

Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then

x   =   r.sinΘ.cos∅      →   1

y   =   r.sinΘ.sin∅       →   2

z   =   r.cosΘ               →   3

According to the given problem,

a.)   ( 1, 0, 0 )  =   ( r, Θ, ∅ )

Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅          

           =   1.sin0.cos0

           =   1.0.1

      x   =   0

2 ⇒ y   =   r.sinΘ.sin∅

            =   1.sin0.sin0

            =   1.0.0

      y   =   0

3 ⇒ z   =   r.cosΘ

            =   1.cos0

            =   1.1

       z   =   1

∴   ( x, y, z )   =   ( 0, 0, 1 )

b.)   ( 18, π/3, π/4 )   =   ( r, Θ, ∅ )

Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅

           =   18.sinπ/3.cosπ/4

           =   18.√3/2.1/√2

      x   =   11.022

2 ⇒ y  =   r.sinΘ.sin∅

           =   18.sinπ/3.sinπ/4

           =   18.√3/2.1/√2

       y  =   11.022

3 ⇒ z   =   r.cosΘ

            =   18.cosπ/3

            =   18.1/2

       z   =   9

∴   ( x, y, z )   =   ( 11.022, 11.022, 9 )

Therefore the rectangular coordinates for the spherical coordinates of

a. ( 1, 0, 0 )   is   ( 0, 0, 1 )

b. ( 18, 1/3, 1/4 )   is   ( 11.022, 11.022, 9 )

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