HELP: Write whether the ratio demonstrates a proportional relationship

Sandra swam 8 laps in 16 minutes. George swam 18 laps in 38 minutes.

The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 5/6 and (x1 , y1) = (22 , 12)

(y - 12) = 5/6(x - 22)

In slope-intercept form, the equation of the line is:

(y - 12) = 5/6(x - 22)

y - 12 = 5/6 x - 110/6

y = 5/6 x - 19/3

In standard form, the equation of the line is:

y = 5/6 x - 19/3

5/6 x - y = 19/3

Multiplying both sides by 6,

5x - 6y = 38

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The value of x will be 1099.8 when rounded it to the nearest decimals.

㏑(x-4)=7

Taking the exponential (e) both side, we get

[tex]e^{ln(x-4)} = e^{7}[/tex]

since 'e' and 'ln' cancels each other,

therefore

[tex]x-4 = e^{7}[/tex]

[tex]x = e^{7} + 4[/tex]                                                                                                  ..eq 1

Exponential 'e' is the Euler's number, which is a constant having the value of around 2.718281828459045235360.

so putting the value of 'e' in eq 1

[tex]x = (2.718)^{7} + 4[/tex]

x = 1095.838 + 4

x = 1099.838

therefore when ㏑(x-4)=7 is solved the value of x will be 1099.8.

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Answer:

So C

Step-by-step explanation:

Average = all values added up/ how many numbers there are

(400.5+560.35+628.29)/3=Average

Average = 529.71

Answer:

The point of intersection is the number of gigabytes and the total cost when the two plans cost the same.

Step-by-step explanation:

Company A doesn't charge a fee "per gigabyte", there's just a flat fee and it is $100. Company B only charges a flat fee of $20, BUT there IS a "per gigabyte" charge. These two plans actually cost exactly the same when the customer uses 16 gigabytes.

answer

3 Laps

Step-by-step explanation:

Using the Fundamental Counting Theorem, it is found that the website would have 30,891,577,600 passwords.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the first six spaces of the password are letters, and each can assume 26 values, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 26[/tex]

The last two spaces are composed by digits, and each can assume 10 values, hence the parameters are:

[tex]n_7 = n_8 = 10[/tex]

Hence the number of possible passwords is given by:

N = 26^6 x 10² = 30,891,577,600.

The website would have 30,891,577,600 passwords.

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The domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}

The given relation is {(-3,2), (-1,3), (0,0), (-2,-1)}. Here, the relation is given as a set of ordered pairs. Domain in mathematics is defined as the all the inputs that are possible to be part of functions. Range refers to the values assumed by function and these are the output values.

The domain of the function is the set of x- coordinates.

∴ The domain is {0, -1, -2, -3}

The Range of the function is the set of y- coordinates.

∴The Range is {0, -1, 2, 3}

Hence, the domain is {0, -1, -2, -3} and the range is {0, -1, 2, 3}.

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Answer:

x= 42°

Step-by-step explanation:

The missing angle can be found by using the property '∠ sum of Δ'. The sum of the interior angles in a triangle is 180°.

The square symbol in the triangle represents a right angle, i.e. 90°.

Form an equation:

x +90° +48°= 180° (∠ sum of Δ)

x +138°= 180°

x= 42°

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Answer:  x=55 over 6

Step-by-step explanation:

Using linear functions, the costs are given as follows:

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

A linear function is modeled by:

y = mx + b

In which:

For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:

A(x) = 16x + b.

When x = 2, A(x) = 33, hence we use it to find b as follows:

33 = 16(2) + b

b = 1.

Hence:

A(x) = 16x + 1.

Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:

For 4 hours, the costs are given as follows:

The difference is:

72 - 57 = 15.

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

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Answer:

42 feet

Step-by-step explanation:

1 1/2 * 28 = 42

The numeric values for the functions are given as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For the first problem, we have that:

For the second problem, we have that:

For the third problem, we have that:

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Ф2 = E2 L² is  the electric flux through the cube face in the plane z = 0.

What exactly are electric flux and unit?

given ,

          edge length = L

 Area of each surface = L²

Ф = E . A

    = E . A Cos θ

Φ1 = E1  A Cosθ

Φ1 = E1 L²

Similarly we get

Ф2 = E2 L²

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By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given three equations in x, y, and z,

x - 2y + z = -4     (equation 1)

-4x + y -2z = 1     (equation 2)

2x + 2y - z = 10     (equation 3)

Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.

x - 2y + z = -4     (equation 1)

x = 2y - z - 4     (equation 4)

Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.

-4x + y -2z = 1     (equation 2)

-4(2y - z - 4) + y -2z = 1

-8y + 4z + 16 + y -2z = 1

-8y + y = 2z - 4z + 1 - 16

-7y = -2z - 15

y = -(2z + 15)/-7

y = (2z + 15)/7     (equation 5)

2x + 2y - z = 10     (equation 3)

2(2y - z - 4) + 2y - z = 10

4y - 2z - 8 + 2y - z = 10

4y + 2y = 2z + z + 10 + 8

6y = 3z + 18

y = (1/2)z + 3     (equation 6)

Substitute the value of y from equation 5 to equation 6 and solve for z.

y = (1/2)z + 3     (equation 6)

(2z + 15)/7 = (1/2)z + 3

2z + 15 = 7[(1/2)z + 3]

2z + 15 = (7/2)z + 21

2z - (7/2)z = 21 - 15

(-3/2)z = 6

z = -4

Substitute the value of z in either equation 5 or 6.

y = (1/2)z + 3     (equation 6)

y = (1/2)(-4) + 3

y = -2 + 3

y = 1

Finally, substitute the value of y and z to equation 4 and solve for x.

x = 2y - z - 4     (equation 4)

x = 2(1) - (-4) - 4

x = 2 + 4 -4

x = 2

Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).

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Answer: Yes

Step-by-step explanation:

If these lengths were to form a right triangle, then 51 and 68 would be the legs and 85 would be the hypotenuse.

[tex]51^2 +68^2 =7225\\\\85^2 =7225\\\\\therefore 51^2 +68^2 =85^2[/tex]

So, the side lengths form a right triangle.

Answer: x = 3/4

Step-by-step explanation:

The first step to solve this equation would be to simplify both sides of the equation by multiplying

1/4*12 - 1/4*8x = 2/3*6x

3 - 2x = 2x

3= 2x+2x

3=4x

x=3/4

Answer:

Step-by-step explanation:

AS THERE ARE 2 fractions 1/4 and 2/3, one way would be to first get rid of these by multiplying through by the LCM  12, giving:

12*1/4(12 – 8x) = 12*2/3(6x)

3(12 - 8x) = 8(6x)

36 - 24x = 48x

36 = 72x

x = 1/2.

The coordinates are (100, 173.2) after 5 seconds.

What are examples of coordination?

Let x represent the angle of rotation in 5 seconds.

[tex]\frac{Irotation }{time} = \frac{current position}{time}[/tex]

360° / 30 = x°/ 5

30x = 1800

x = 60°

To find the coordinates, use sine and cosine ratios.

Sin60 = opposite/ hypotenuse

sin60 = y / 200

 y = 200sin60

y ≈ 173.2

cos60 = adjancent/ hypotenuse

cos60 = x / 200

x = 200cos60

x = 100

The coordinates are (100, 173.2).

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Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

Answer:

1 dollar and 6 cents

Step-by-step explanation:

What error did your classmate make? This series is divergent so does not have a sum.

How is the divergence of the series proved?

Given:

[tex]a(\text{ the first term })=1\\\\r(\text{ the common difference })=1.1[/tex]

Since, [tex]\vert r \vert > 1[/tex] the infinite series diverges.

What is an infinite geometric series?

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Answer:

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

To solve by factoring, we will split up the equation using our factoring rules.

In this particular instance, we will factor out common variables.

We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.

[tex]x^2 + 4x + 3 = 0[/tex]

[tex](x+3)(x+1)=0[/tex]

Set each factor equal to zero and solve.

Root 1

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Root 2

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

As requested in the question, we must now check with the quadratic formula.

To solve this quadratic equation, we will utilize the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].

We will define our variables:

Now, we will plug these into the equation and solve the equation.

[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]

[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]

Root 1

[tex]\displaystyle x=\frac{-4+2}{2}[/tex]

[tex]\displaystyle x=\frac{-2}{2}[/tex]

[tex]\boxed{x=-1}[/tex]

Root 2

[tex]\displaystyle x=\frac{-4-2}{2}[/tex]

[tex]\displaystyle x=\frac{-6}{2}[/tex]

[tex]\boxed{x=-3}[/tex]

The final answer is [tex]\boxed{x = -1, -3}[/tex].

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Given the equation, we can start by rewriting:

x^2 + 4x + 3 = 0

Now, let’s write in factored form:

(x + 1) (x + 3) = 0

since x is the only variable and there are 2 numbers, we can make 2 equations:

x + 1 = 0

x + 3 = 0

This forms:

(X + 1) (x + 3) = 0

Now, we can solve:

? + 1 = 0

? + 3 = 0

-1 + 1 = 0 and -3 + 3 = 0

x = -1 AND -3

The ratio of the surface area of the large sphere to the surface area of the small sphere of radius 20π meters and 6π meters, respectively, is B. 100/9.

Surface area refers to the total area covering the outside of a three dimensional shape. The surface area of a sphere is given by the formula:

A = 4πr^2

Solving for the surface area of each sphere:
1. larger sphere, r = 20π meters

A = 4πr^2

A = 4π(20π meters)^2

A = 4π(400π^2 square meters)

A = 1600π^3 square meters

2. smaller sphere, r = 6π meters

A = 4πr^2

A = 4π(6π meters)^2

A = 4π(36π^2 square meters)

A = 144π^3 square meters

Getting the ratio of the surface area of the large sphere to the surface area of the small sphere:

1600π^3 square meters / 144π^3 square meters = 100/9

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Answer:

Step-by-step explanation:

the answer is -26 but it is not in the choices

-32+(-4+7)*(2)=

-32+3*2=

-32+6=

-26

Applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

All interior angles of a triangle have a total sum of 180 degrees when added together, according to the triangle sum theorem.

Given:

Measure of angle C = 90 degrees

In △CAD, we have the following angle measures:

m∠A = 65° (given)

m∠ADC = 90° [right angle]

m∠ACD = 180 - 90 - 65 [triangle sum theorem]

m∠ACD = 25°

In △CBD, we have the following angle measures:

m∠CDB = 90° [right angle]

m∠BCD = 90 - m<ACD [complementary angle]

m∠BCD = 90 - 25

m∠BCD = 65°

m∠CBD = 180 - m∠BCD - m∠CDB [triangle sum theorem]

m∠CBD = 180 - 65 - 90

m∠CBD = 25°

In summary, applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°

In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°

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The value of b (real number) can be anything greater than zero so we cannot be determined with the given information so option (C) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the absolute equation,

|x| = b for b >0

b is a set of all positive real numbers and we know that real number goes 0 to infinite means,

b could be 1,2,3... anything.

It means the corresponding solution will also be 1,2,3... anything.

Therefore we cannot determine the solution.

Hence "We cannot predict the number of solutions of the given mode function  |x| = b, such that b>0 without more information".

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Answer:

The sun of 10 is 2 times much 4.

Answer:

x=3

Step-by-step explanation:

➡️ Let x be the number;

4(x+2)=20

x+2=5

x=3

The number is 3.

Answer: -41.5

Hope that helped.

The equation of the circle with radius 4.5 and center at (2 , 3) is (x - 2)^2 + (y - 3)^2 = 20.25.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 3)

r = 4.5

(x - 2)^2 + (y - 3)^2 = 4.5^2

(x - 2)^2 + (y - 3)^2 = 20.25

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