2. What is the equation of a line that passes through the points (-0.92, 2.49) and (-5.62, 9.76)? Write your answer in point-slope form.​

Answer:

The answer is 35

Step-by-step explanation:

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EXPLANATION :

The cost of a 12 nights camp accommodation is 6720.

We need to divide the cost by 12 to get the cost per day.

Now, we are asked to find the cost of 7 nights and 4 nights.

We just need to multiply the daily rate by the number of nights.

a. 7 nights :

7 x 560 = 3920

b. 4 nights :

4 x 560 = 2240

ANSWER :

a. 3920

b. 2240

The required equation of line would be 2y = 5x - 8 which is shown in the given graph.

The slope of a line is defined as the angle of the line.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, -4).

The value of the x-coordinate is 2 when y-coordinate is 1.

Here the line passes through the points (0, -4) and (2, 1).

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = -4

x₂ = 2, y₂ = 1

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 1 = (1 - (-4))/(2 - 0 )[x -2]

⇒ y - 1 = 5/2[x -2]

⇒ 2y - 2 = 5[x -2]

⇒ 2y = 5x - 10 + 2

⇒ 2y = 5x - 8

Therefore, the required equation of line would be 2y = 5x - 8 which is shown in the given graph.

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Answer:

1/24

Step-by-step explanation:

.........................

Answer:

I'll assume that "2 (1/2)^3" means 2*(1/2)^3.

Step-by-step explanation:

(1/3)/(2*(1/2)^3)

(1/3)/(1)^3

= (1/3)

===========================

If "2(1/2)^3" means (2+1/2)^2:

((5/2)^2 = (25/4)

--

(1/3)/(25/4)

(1/3)*(4/25) = 4/75 or 0.05333

Answer:

A' = (0, 0)

B' = (-5, -2)

C' = (2, 4)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x - 2, y + 3)

This notation tells you that the x-coordinate is translated 2 units to the left, and the y-coordinate is translated 3 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 - 2, -3 + 3) = (0, 0)

⇒ B' = (-3 - 2, -5 + 3) = (-5, -2)

⇒ C' = (4 - 2, 1 + 3) = (2, 4)

Remember that

1 m3=1,000 lt

2 m3=2,000 lt

The volume of the tank is equal to

V=L*W*H

we have

V=2 m3

L=4 m

W=1.5 m

H=?

substitute given values

2=4*1.5*H

solve for H

2=6H

H=2/6

A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

What is a heart rate?

The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.

Here,

We let his normal heart rate = h

and given in the question,

20% of h = 10

20/100 * h = 10

h = 10*5

= 50 beats/min

Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

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here's your answer hope it helps

Using ratios, we can conclude that Chris gets 12 sweets.

So, a number of sweets Chris receive:

Now, 7:3 = x+20:x, solve as follows:

Therefore, using ratios, we can conclude that Chris gets 12 sweets.

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The correct question is given below:
Alex and Chris share sweets in the ratio Alex: Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives.

The fraction of the poster does Dwayne use for his friends from school is 5/12.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number that is above the line and the denominator is the number below the line. An example of a fraction is 5/12.

In this question, the numerator is the number of parts he gives his friends from school. The denominator is the total number of parts he divides the poster.

Fraction = parts he gave his friend from school / total number of parts

5 / 12.

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Aaron has to pay $ 115 when the usage gets over by 3 GBs and
$ (40 + 25x) when the usage gets over by x GBs.

How can one calculate the cost for a multiple of the same entity?
To calculate the cost of a multiple entities when the cost of a single one is given, we linearly multiply a fixed proportion to it to calculate the same.

Given, monthly fixed cost of the smart phone data plan = $ 40
Also, amount charged by the firm for each extra GB used = $ 25
Now, amount charged for three extra GBs = 25*3 = 75
Thus, net total that Aaron has to pay for 9 GBs = 40 + 75 = $ 115
Following similar arguments, amount charged for extra 'x' GBs = 25x
Thus, net total that Aaron has to pay for x GBs = 40 + 25x = $ (40 + 25x)
Therefore, Aaron has to pay $ 115 when the usage gets over by 3 GBs and $ (40 + 25x) when the usage gets over by x GBs.

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Answer:

912

Step-by-step explanation:

the assumption is that this is an arithmetic progression

the nth term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

use this to find which term 120 is in the sequence

with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then

32 + 8(n - 1) = 120 ( subtract 32 from both sides )

8(n - 1) = 88 ( divide both sides by 8 )

n - 1 = 11 ( add 1 to both sides )

n = 12

given the first and last terms in the sequence then sum is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)

S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912

1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:

So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.

2) For the Volume of the Pyramid, we can write out the formula below:

Since the scale factor is 1.5 Then we can state that

the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.

3) Hence, the answers are:

1.k=1.5

2. 32 m³

Answer:

Slope is 1 and y-intercept is 9

Step-by-step explanation:

y=mx+b

The slope is the coefficient of x in this case it would be 1

The y-intercept is whatever b is and it is +9 so it is 9

Answer:

Step-by-step explanation:

First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)

Answer:

f(x)= -x^2-6x+7

Step-by-step explanation:

Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.

Now use the remaining possible equations and solve for the vertex.

Using  x= -b/2a to solve for the x value of the vertex plug in the values to solve.

a= -1 b= -6  c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.

Then plug in -3 into the equation to get the y-value.

- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.

Hope this helped! :)

The greatest possible value of n is -5

From the question, the given parameters are:

The second highlight above can be represented as

n < -3.25

Since n is an integer, then the possible values of n are

n = -4, -5, -6, -7, -8....

Remove the even integers from the above list of numbers because n is an odd integer

So, we have

n = -5, -7, -9....

The greatest value above is n

This means that n can have the highest value of -5

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Answer:

Explanation:

Given the function f(x)

A translation of 2 units up = f(x)+2

Next, a translation of 2 units right = f(x-2)+2

When we reflect the result above in the x-axis, we have:

A rule for g is therefore:

Answer:

18*19 BECAUSE 19 is a prime number and g has to be 1 since if g was anything else like 2 it wouldn't be the same for gh

Answer:

The answer is d) 22.4

Step-by-step explanation:

I attached a file below if you want to see the process!

We will have the following:

We can see that the shape of the head can be subdivided in smaller shapes, that is:

Now, we calculate the 5 areas, that is:

Now, the total area is:

So, the total area is 108 mm^2-

Answer:

2 pizzas

Step-by-step explanation:

5 7/8 - 4 1/16=

5 14/16 - 4 1/16 ==> make the denominators equal to each other so they can be easily subtracted in the next step

5 + 14/16 - (4 + 1/16)=

5 + 14/16 - 4 - 1/16 =

5 - 4 + 14/16 - 1/16 =

1 + 13/16 = 1 13/16 which is approximately 2 pizzas

(a) Complex zeros of a polynomial come in pairs.

If a + bi is a zero of a polynomial then its conjugate a - bi is also a zero of the polynomial.

The given complex zeros of R(x) are 1 + 3i and -2i.

1 - 3i is the conjugate of 1 + 3i.

Hence, another zero of R(x) is 1 - 3i

b)

Since the polynomial R(x) is of order 13 then R(x) must have 13 zeros.

The given complex zeros of R(x) are 1 + 3i and -2i. We also know that the conjugates of 1 + 3i and -2i are zeros of R(x). Hence, R(x) has at least 4 complex roots

Hence, the maximum number of real zeros of R(x) is (13 -4).

The maximum number of real zeros of R(x) is 9

c) Let the maximum number of nonreal zeros (complex roots) be n

Complex roots come in pairs. Therefore, n must be even.

Hence, n ≤ 13 - 1 = 12

n ≤ 10

We have been given a real zero of R(x), 3 ( With the multiplicity of 4).

12 - 4 = 8

Therefore,

n ≤ 8.

Hence the maximum number of nonreal zeros of R(x) is 8

An exponential function has the form

Therefore, to find an exponential function that satisfies our condition, we need to find a and b.

From f(-2) = 1, we have

and from f(7) = 63, we have

Solving for a in equation (1) gives

substituting this value of a into equation (2) gives

With the value of b in hand, we now find the value of a:

Hence, the exponential function is

Evaluating the above function at x = 1 gives

which is our answer!

Option C, 59° is correct answer, The angle JIL is equal to 59 degree.

What is angle?

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.

Given information in the question,

∠HIL = (6x-7)°

∠JIL = (5x+4)°

The ray IL bisects the ∠HIJ

Since, IL bisects angle HIJ then, angle HIL = angle JIL

So,

6x - 7 =  5x + 4

x = 11

Putting the value of x in given value of JIL to get the angle JIL

∠JIL = (6x-7)°

∠JIL = (6(11)-7)°

∠JIL = 59°

Therefore angle JIL is equal to 59 degrees.

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The total number of files after 16 days using the function P(t) = 3t² + 5t + 8 is 856.

A relationship between a group of inputs having different outputs is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.

The function P(t) represents the population of a collection of fruit flies at a particular time in days.

P(t) is the number of flies and t is the time in days.

Now, consider the function:

P(t) = 3t² + 5t + 8

Therefore, the number of flies after 16 days will be:

When t = 16,

P(t) = 3t² + 5t + 8

P(16) = 3(16)² + 5(16) + 8

P(16) = 3 × 16 × 16 + 5 × 16 + 8

P(16) = 768 + 80 + 8

P(16) = 856

Hence, the number of flies after 16 days will be 856 flies using the function P(t).

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Let's find the unit price of each store

Store A : $8.16 /4 = $2.04 per pound

store B: $6.51 / 3 = $2.17 per pound

store c: $2.66 / 2 = $1.33 per pound

store D : $11.40 / 4 = $ 2.85 per pound

Therefore, store A, store B, store C and store D sells at a lower unit price than Corner grocery store.

Answer:

2.5

Step-by-step explanation:

$12.50 ÷ 5 bags = $2.5 per bag

Answer:

2.50

Expination:

devide 12.50 by the total amount of dog food purchased (5 bags)

12.50/5 = 2.50

the price per bag is $2.50