y varies as t. If y = 6 when t =4, calculate:
a) the value of y, when t = 6
b) the value of t, when y = 4

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 0.25 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 0.25}(x-\stackrel{x_1}{5}) \implies y +2= 0.25 (x -5)[/tex]

By rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.

For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The crucial figures are preserved when numbers are rounded off.

Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up.

So, Mike calculated 79 as 79.44 and 7 as 6.7, so he calculated the difference as follows:

79 - 7 = 72

Actual figures that differ are:

79.44 - 6.7 = 72.74

Therefore, by rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

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Correct question:

Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be . The actual difference is .

Answer:

4.89

Step-by-step explanation:

6×4 and the root of that is 4.8989794

Between the time interval 0 to 1 hour, the greatest average rate of change is 700. Therefore, the option (1) is the correct answer.

The slope or rate of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here,

1) 0 to 1 hour

Consider the coordinate points (0, 0) and (1, 700)

Now, rate = (700-0)/(1-0)

= 700

2) 1 hour to 1.5 hours

Consider the coordinate points (1, 700) and (1.5, 900)

Now, rate = (900-700)/(1.5-1)

= 200/0.5

= 400

3) 2.5 hours to 5 hours

Consider the coordinate points (2.5, 1000) and (5, 1640)

Now, rate = (1640-1000)/(5-2.5)

= 640/2.5

= 256

4) 5 hours to 8 hours

Consider the coordinate points (5, 1640) and (8, 1800)

Now, rate = (1800-1640)/(8-5)

= 160/3

= 53.33

Therefore, the option (1) is the correct answer.

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Answer: Their car got an average of 23.6 miles per gallon.

BTW I just searched it up so I'm sorry if it is wrong.

The statement "F(x) > 0 over the interval (-∞, -4)" is true.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. The addition, subtraction, multiplication, and division of functions are discussed in function algebra. We just perform the same operation for individual functions at the same input for every arithmetic operation of two functions at an input.

Here,

For any value of x less than -4, substituting it into the expression f(x) = x² + 4 will result in a positive value since x² is always positive. For example, if x = -5, then f(x) = (-5)² + 4 = 9 + 4 = 13, which is positive.

So, for all values of x that are less than -4, the function f(x) will have a positive value, making the statement "F(x) > 0 over the interval (-∞, -4)" true.

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Answer:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

Step-by-step explanation:

The surface area of the sphere has formula of [tex]\displaystyle{4\pi r^2}[/tex] where r is radius. Therefore, set the equation:

[tex]\displaystyle{4\pi r^2=156}[/tex]

Divide both sides by 156:

[tex]\displaystyle{\dfrac{4\pir^2}{4}=\dfrac{156}{4}}\\\\\displaystyle{\pi r^2=39}[/tex]

Then divide both sides by [tex]\displaystyle{\pi}[/tex]:

[tex]\displaystyle{\dfrac{\pi r^2}{\pi} = \dfrac{39}{\pi}}\\\\\displaystyle{r^2=\dfrac{39}{\pi}[/tex]

Square root both sides:

[tex]\displaystyle{\sqrt{r^2}=\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{r=\pm\sqrt{\dfrac{39}{\pi}}}[/tex]

However, radius can only be positive. Therefore:

[tex]\displaystyle{r=\sqrt{\dfrac{39}{\pi}}}[/tex]

To find the volume, we have to know that the sphere's volume is:

[tex]\displaystyle{\dfrac{4}{3}\pi r^3}[/tex]

Thus, substitute the value of r in:

[tex]\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \left(\sqrt{\dfrac{39}{\pi}}\right)^3}\\\\\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \dfrac{39}{\pi}\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{\text{V} = 52 \sqrt { \dfrac{39}{\pi}}}[/tex]

Therefore, the volume of sphere is:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

If the Car drive 15, 000 miles then gas used is 315 galloons.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

In 16.8 galloons of gas the Car can travel 400 miles.

So, if they dive about 15,000 miles then the gas in galloons used

= 16.8/400 x 15000

= 2.1 x 150

= 315 galloons.

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Answer:

see below

Step-by-step explanation:

90 x, y, z

x pennies =1/2y

y nickels

z quarters = 3 1/2 y

so 1/2y+y+3 1/2 y =90

total 5y =90

y =18

x=9

z = 63

The dimension of the rectangular prism will be x, x + 2, and x + 1.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

The volume of the rectangular prism is given as,

V = x³ + 3x² + 2x

Factorize the equation, then we have

V = x³ + 3x² + 2x

V = x(x² + 3x + 2)

V = x(x² + 2x + x + 2)

V = x[x(x + 2) + 1(x + 2)]

V = x(x + 2)(x + 1)

The dimension of the rectangular prism will be x, x + 2, and x + 1.

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F(x) = 4x & g(x) = 3x are the two functions which the (f o g)(x) was equal to "12x".

Legislation, a regulation, or a declaration that demonstrates the relationships between the independent and relationship between the factors (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The functions f(x) & g(x) are given, and the task is to determine (f o g) (x).

For the following two functions, (f o g)(x) was identical to "12x":

f(x) = 4x and g(x) = 3x.

Proof :

g(x) = 3x

(f o g)(x) = f(x = 3x) = 4(3x) = 12x

(f o g)(x) = 12x

Hence, f(x) = 4x or g(x) = 3x are the 2 type which the (f o g)(x) was equal to 12x.

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Jayden is folding a paper strip of 66 cm into a 6 sided honeycomb. So the length of each side will be 11cm.

Jayden has a paper strip of length 66 cm. He had to make a honeycomb with it. It will have six equal sides. To calculate the length we have to formulate the equation.

Total length = number of sides × length of one side

 66 = 6 × x

Dividing by 6 on both sides,

66÷6 = 6x ÷ 6

11 = x

So the length of the side of honeycomb will be of 11 cm.

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The complete question is as below

Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?

The inequality used to determine v, the minimum number of visits Taylor needs to earn her first free movie ticket is 75 + 6.5v ≥ 100.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given,

Points for signing up = 75 points

Points for each visit to the movie theater = 6.5 points

Let v be the minimum number of visits Taylor needs to earn her first free movie ticket.

Points earned for v visits = 6.5v

She needs at least 100 points for a free movie ticket.

75 + 6.5v will be the points she earn for a free movie ticket.

This expression must be greater than 100, which is the required points for a free movie.

75 + 6.5v ≥ 100

Hence the inequality representing the situation is 75 + 6.5v ≥ 100.

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The constant of proportionality is 12, and the  equation to represent the direct proportion is y = 12x

A proportion is a comparison of two numbers that each represent the parts of a whole.

Given that, Karl hikes 3 km in 36 minutes, his distance is directly proportional to the time he walks,

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

Put y = 36 and x = 3, to find the constant of proportionality,

k = 36/3

y = 12

Therefore, the constant of proportionality is 12,

The equation to represent the direct proportion =

y = 12x

Hence, the constant of proportionality is 12, and the  equation to represent the direct proportion is y = 12x

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The average rate of change of the temperature from 0 to 2 minutes is given as follows:

-6ºC per minute.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The temperatures for this problem are given as follows:

Hence the change in the output is given as follows:

62 - 74 = -12ºC.

The change in the input is of:

2 - 0 = 2 minutes.

Hence the rate is given as follows:

-12/2 = -6ºC per minute.

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The values of p and q are p = 35 and q = 12

From the question, we have the following parameters that can be used in our computation:

Intersecting chords in a circle

To solve this question, we make use of the intersecting chords theorem

This is represented as

q/12 = 35/p

Cross multiply

So, we have the following representation

pq = 35 * 12

From the circle, we have

p > q

So, we can rewrite the equation as

p = 35 and q =12

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The sketch of cylinder is shown in the figure.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Volume=36pi

Diameter=6cm

Now,

Radius=6/2=3cm

Volume= 36pi

pi*R^2*h=36pi

3^2*h=36

h=36/6

h=6cm

Therefore, by the given volume the radius and height will be 3cm and 6cm.

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Answer:

850 miles on 25 gallons

Step-by-step explanation:

Answer: 850 miles on 25 gallons is more efficient, meaning it covers a greater distance per gallon of fuel.

Step-by-step explanation:

Using the Pythagorean theorem, if AL is perpendicular to BD and CM is perpendicular to BD, then quadrilateral ABCD is a parallelogram.

In a parallelogram, the opposite sides are equal in length, i.e. AL = CD and BM = AD.

By the Pythagorean theorem, we know that the length of the diagonal BD can be found as the square root of the sum of the squares of AL and CM:

BD = √(AL^2 + CM^2)

Since AL = CD, the area of quadrilateral ABCD can be found as:

ar (quad.ABCD) = AL × BD

Substituting BD = √(AL^2 + CM^2) and combining the two equal length sides, we get:

ar (quad.ABCD) = (AL + CM) × √(AL^2 + CM^2) / 2

Finally, dividing both sides by √(AL^2 + CM^2) and using the fact that BD = √(AL^2 + CM^2), we get:

ar (quad.ABCD) = 1/2 × BD × (AL + CM)

Thus, we have proved that the area of quadrilateral ABCD is equal to 1/2 × BD × (AL + CM).

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Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3600\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A = 3600\left(1+\frac{0.02}{12}\right)^{12\cdot 18}\implies A=3600(\frac{601}{600})^{216} \implies A \approx 5158.44[/tex]

The equation of the line parallel to y = 3x - 4 is y + 5 = 3(x+1)

The equation of a line expressed in point slope form is expressed as:

y-y0 = m(x-x0)

where

m is the slope

(x0, y0) is any point on the line

Given the following parameters

(x0, y0) = (-1, -5)

slope of the given line is 3

Substitute

y - (-5) = 3(x-(-1))
y + 5 = 3(x+1)

Hence the required equation of the line is y + 5 = 3(x+1)

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Answer:

y = -x +8

Step-by-step explanation:

The line crosses the x axis at 8. So we know when y = 0 then x = 8

The line cross the y axis at 8. so we know when x = 0 then y = 8

the equation of a line we know to take the form y = mx + c

When x = 0 and y = 8, and y = mx+ c then then c =8

when y = 0 x = 8. y = mx + c, 0 = m(8) +8. for this to be true m must be equal to -1

so the equation of the line, the inequality is y = -x +8

Answer:

[tex]\frac{597}{283750}+3*10^8[/tex]

Step-by-step explanation:

[tex]((2848*838449)/(294949*3848483))+300,000,000\\or\\\frac{2848*838449}{294949*3848483}+300,000,000\\\\\frac{2.388*10^9}{1.135*10^{12} } +3x10^8\\\\\\\frac{597}{283750}+3*10^8[/tex]

Answer: 31457261583.3

Step-by-step explanation:

Answer:

13/24

Step-by-step explanation:

First we create a common denominator by multiplying the denominators of 8 and 3 to get 24. Now we convert the two given fractions

[tex] \frac{1}{8} = \frac{3}{24} [/tex]

[tex] \frac{1}{3} = \frac{8}{24} [/tex]

A full circle is 24/24. Now all we do is subtract

[tex] \frac{24}{24} - \frac{8}{24} - \frac{3}{24} = \frac{13}{24} [/tex]

Answer:

13/24

Step-by-step explanation:

1-11/24

=

13/24

Answer:

To find 47% of 900, you can multiply 900 by 0.47, which represents 47% as a decimal:

47% = 47/100 = 0.47

So, 47% of 900 is:

0.47 x 900 = 423

Therefore, 47% of 900 is 423.

Convert 47% to a decimal

= 47% = 47/100 = 0.47

47%= 0.47 × 900

=423

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 5 ) and (x₂, y₂ ) = (7, - 5 )

m = [tex]\frac{-5-(-5)}{7-2}[/tex] = [tex]\frac{-5+5}{5}[/tex] = [tex]\frac{0}{5}[/tex] = 0

Answer:

a= 17* √2

Step-by-step explanation:

a=17*cosec45