What is an equation of the line that passes through the points (6, -1) and (1, 4)?

Answer:

In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.

Conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip.

Answer:

Approximately 1.86 times smaller

Step-by-step explanation:

5×10-7 = (5×10=50) = 50-7 = 43

8.5×10-4 = (8.5×10=84) = 84- 4 = 80

80/43 = approximately 1.86

43×1.86 = approximately 80

80/1.86 = approximately 43

If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex].

We are required to calculate an equivalent simplified form of the above mentioned expression.

To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:

[tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}[/tex]

Hence, If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].

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The required cost is $ 101.22.

This problem can be solved by unitary method.

Given that monthly cost of customer if he uses 410 minutes is $71.

So, cost per minute = [tex]\frac{71}{410}[/tex]

                               =$ 0.17

And if the customer uses 720 minutes then the cost is $118.

So, cost per minute is = [tex]\frac{118}{720}[/tex]

                                   =0.16

Now if he uses 687 minutes then for 410 minutes cost incurred will be

= 410 × 0.17

= $ 69.7

And for next 197 minutes cost incurred will be = 197 × 0.16

                                                                         = $ 31.52

Total cost for 687 minutes = $(69.7 + 31.52)

                                         = $ 101.22

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Step-by-step explanation:

80.3÷9.4

80/3÷9/4

80/3×4/9

26.6×4/9

=17.733

This means that Kenna will get 18 pieces from one lenght of pipe

The probability that both of the boxes one would select had the decoder ring is 9.9%.

Given, the store manger gives the surety that 19 out of 59 boxes on the shelf have the secret decoder ring.

The boxes on the shelf which have a different gift inside is = 40 boxes.

If one randomly selects two boxes from the shelf to purchase, the probability that both of them have the secret decoder ring = ?

You can imagine that someone used invisible link to label each box with a number, and knows that boxes number 1 through 19 have decoder rings, while boxes number 20 through 59 have other gifts.

There are 59×58/2

= 3422/2

= 1711 possible sets of two boxes that one could select, but there are only 19 × 19/2

= 342/2

= 171 possible sets of two boxes with decoder rings.

The fraction of possible pairs of boxes where both boxes have the secret decoder ring is:

= 171/1711

= 0.099 = 9.9%

Hence there is 9.9% probability that both of the boxes one might select had a decoder ring.

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There is a difference between the expressions -x/y and -x/-y

The expressions are given as:

-x/y and -x/-y

When the expression -x/-y is evaluated, we have:

-x/-y = x/y

This means that

-x/y = -x/y

-x/-y = x/y

When the above expressions are compared, we can see that both expressions are not equal

Hence, there is a difference between the expressions -x/y and -x/-y

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Answer:

Only one equation fits all the information on the table which is:

y = 1/6x

Answer:

y = 1/6x

Step-by-step explanation:

To find the equation, let's see if each option works by plugging in x into each equation.

y = –1/4x

Plug -6 into x

y = –1/4(-6)

y = 1.5

y = –1/4x doesn't work because we didn't get -1.

y = 6x

Plug -6 into x

y = 6(-6)

y = -36

y = 6x doesn't work because we didn't get -1.

y = 1/6x

Plug 1/6x into x

y = 1/6(-6)

y = -1

Let's see if the other x values work.

Plug 0 into x

y = 1/6(0)

y = 0

Plug 12 into x

y = 1/6(12)

y = 2

y = 1/6x works.

y = –2x

Plug -6 into x

y = –2(-6)

y = 12

y = -2x doesn't work because we didn't get -1.

y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.

Hope that helped and have a lovely rest of your day!

In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3

In the graph, we can see a parabola.

We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.

Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:

y = a*(x - h)^2 + k

In the image we can see that the vertex is (2, -3), then:

y = a*(x - 2)^2 - 3

And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:

1 = a*(0 - 2)^2 - 3

1 = a*4 - 3

1 + 3 = a*4

4/4 = a = 1

Then the quadratic equation is y = (x - 2)^2 - 3

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Answer:

-5 ≤ y ≤ 5

Step-by-step explanation:

Hello!

The range is the set of y-values that the graph passes through.

Since the endpoints of the graph are filled in, meaning they include the values they end on, we use the ≥ or ≤ symbols to write the inequality for the range.

The minimum y-value is -5, and the maximum y-value is 5.

The inequality for the range would be -5 ≤ y ≤ 5.

the correct option is the first one (counting from the top).

The true statement is:

"The leading coefficients of f(x) and g(x) are opposites"

We know that f(x) and g(x) are quadratic functions, and the sum of these two functions is shown in the graph.

We can see that the sum gives a linear graph, so the terms with the exponents of 2 are cancelled by the sum.

This only can happen if f(x) and g(x) have opposite (same absolute value but different sign) leading coefficients, so the quadratic terms are cancelled when we add the functions.

For example in f(x) = 2*x^2 + 3x + 4

                         g(x) = -2x + x + 13

If we add these two functions, we would end with a line.

With that in mind we can conclude that the correct option is the first one (counting from the top).

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Answer:

B. 5/9

Step-by-step explanation:

You can just divide 5 and 9 and you get the repeating decimal

The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4. Option E

This is further explained below.

Generally,   the equations equivalence is  mathematically given as

-2m - 5m - 8 = 3 + (-7) + m

Therefore

-7m - 8 = 3 + (-7) + m

When we write the equation such that the variable appears on the right-hand side first, we get the following:

-7m - 8 = m - 4

In conclusion, The equation  equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4.

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Answer:

1/12

Step-by-step explanation:

All you need to do is subtract 3/4 by 2/3, the difference of those two numbers is 1/12.

The total amount of each ingredient are as follows;

Pears = 1/2 pound

Grapes = 3/8 pounds

Pineapple = 3/4 pounds

Oranges = 3/8 pounds

We are given the amounts of fruits as;

4 pounds of pears

3 pounds of grapes

6 pounds of pineapple

3 pounds of oranges

Now, total pounds of fruits = 4 + 3 + 6 + 3 = 16 fruits

Ratio of pears = 4/16 = 1/4

Ratio of grapes = 3/16

Ratio of pineapple = 6/16 = 3/8

Ratio of oranges = 3/16

Thus. amount of each ingredient required are;

Pears = 1/4 * 2 = 1/2 pound

Grapes = 3/16 * 2 = 3/8 pounds

Pineapple = 3/8 * 2 = 3/4 pounds

Oranges = 3/16 * 2 = 3/8 pounds

Thus, the total amount of each ingredient are as follows;

Pears = 1/4 * 2 = 1/2 pound

Grapes = 3/16 * 2 = 3/8 pounds

Pineapple = 3/8 * 2 = 3/4 pounds

Oranges = 3/16 * 2 = 3/8 pounds

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(a) The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.

What is velocity?

(a) For Alicia,

m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4

f(t)=0.4t+4

for Damon,

m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9

g(t)=0.9t

The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) Value and meaning of the slope is

m for Alicia =0.4

Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².

m for Damon=0.9

Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Value and meaning of the average rate of change on the interval:

the average rate of change of Δ on the interval [4,8] =

[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]

=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²

So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Let both are walking with the same velocity at t sec.

So, Let's equate their velocities

0.4t+4=0.9t

t=4/0.5 = 8 sec

The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec

The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec

So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.

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APY for Kevin's account = 1.67%

The interest on a loan or deposit that is computed based on both the original principle and the accumulated interest from prior periods is known as compound interest (also known as compounding interest). Compared to simple interest, which is computed just on the principal amount, it will cause a sum to increase more quickly.

The frequency of compounding determines the pace at which compound interest accumulates. The compound interest increases with the number of compounding periods.

APY = [tex](1 + \frac{r}{n})^{n} - 1[/tex]  =   [tex](1 + \frac{1.667}{365})^{365} - 1[/tex]  =  1.0167 - 1 = 0.0167

APY = 1.67%

Therefore, APY for Kevin's account = 1.67%

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Answer:

r = [tex]\frac{k}{pt}[/tex]

Step-by-step explanation:

I think that you mean

K = PRT  Divide both sides by pr

[tex]\frac{k}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex]  On the right sides the pr's on the top and bottom cancel each other out and you are left with

r = [tex]\frac{k}{pr}[/tex]

Answer:

i think is 7/12

because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.

hope that helps

Answer:

(6x) + 9 = 4

Step-by-step explanation:

Times means 'The answer when you multiply' So we are working in multiplication. ( x )

6x is the multiplication.

It says 'more than' which means adding to our answer. So we add 9. So far our equation is: (6x) + 9 (Brackets are needed as we are multiplying 6 by x and not multiplying 6 by x+9)

Lastly, it says the answer must be 4 so we add that at the end. So the answer is:

(6x) + 9 = 4

Answer:

$2,400,000

Step-by-step explanation:

Just multiply them together