You travel 5 hours and 50 minutes. If you drove at an average of 41 mph, how much distance you traveled?

Determine the value of x.

So there are 45 markers originally in each box.

The scatter plot shows a linear association.

The scatter plot shows a positive association.

we have, the equation is of the form

then, first calculate the radius of the circle

so, (h,k) is the center and the equation is

1) Gathering the data

3 ¼ cups of sugar------------------ 2 ⅓ cups of flour

x 4

2) Let's set a proportion, and then cross multiply those ratios but before that

let's convert those mixed numbers:

So rewriting it above, we have. 39/7 as 39/7 is >1 then we can rewrite it into a Mixed Number:

3) Hence, I'll need 5 4/7 cups of sugar

Solution

Step-by-step explanation:

Here we are given the volume of rectangular pyramid as 90 cubic feet as we are required to find the volume of rectangular prism.

For that we need to use the theorem which says that

the volume prism is always one third of the volume of the pyramid . Whether it is rectangular of triangular base. Hence in this case also the volume of the rectangular prism will be one third of the volume of the rectangular pyramid.

Volume of Rectangular prism = 1/3 x Volume of rectangular pyramid

Therefore the volume of the rectangular pyramid = 30 cubic feet

The given system of equations is expressed as

-10x - 10y = 10

-2x - 5y = -19

The first step is to make the coefficients of one of the variables in each equation equal. To make the coefficient of x equal, we would multiply the first equation by 2 and the second equation by 10. It becomes

- 20x - 20y = 20 equation 3

- 20x - 50y = - 190 equation 4

We would eliminate x by subtracting equation 4 from equation 3. It becomes

- 20x - - 20x - 20y - - 50y = 20 - - 190

- 20x + 20x - 20y + 50y = 210

30y = 210

y = 210/30

y = 7

Substituting y = 7 into the second equation, it becomes

- 2x - 5 * 7 = - 19

- 2x - 35 = - 19

- 2x = - 19 + 35 = 16

x = 16/- 2

x = - 8

The solution is

(- 8, - 7)



Answer:

1077.19 ft

Explanation:

Using the depression angle, we get that one of the angles of the formed triangle is also 18° because they are alternate interior angles, so we get:

Now, we can relate the distance x, the angle of 18°, and the height of the tower using the trigonometric function tangent, so:

Now, solving for x, we get:

Using the calculator, we get that tan(18) = 0.325, so x is equal to:

Therefore, the forest ranger is at 1077.19 ft from the fire.

Answer:

• (0,0) and (3, 2)

• (1,5) and (4,7)

• (-2,-2) and (4,2)

Explanation:

Points (0,0) and (3, 2)

Points (1,5) and (4,7)

Points (-2,-2) and (4,2)

Points (0,0) and (2,3)

Points (20, 30) and (-20, -30)

The first three options are correct.

Let 'y' be the weight of the airplane corresponding to when the amount of fuel is 'x'.

Given that the airplane weighs 2104 when fuel is 16 gallons, this can be represented as the ordered pair,

Also, given that the airplane weighs 2312 when fuel is 48 gallons.The corresponding ordered pair will be,

It is mentioned that there is a linear relationship between the amount of fuel (x), and the weight of airplane (y).

Consider that the equation of a straight line passing through two given points is given by,

As per the given problem,

Substitute the values,

At the instant when the fuel is 66 gallons,

The corresponding weight of airplane is calculated as,

Thus, the airplane weighs 2429 if it is carrying 66 gallons of fuel.

8 x 8 x8 x8 x8 x8 can be written as;

The correct option is A)  [tex]8^6[/tex] . In the expression 8x8x8x8x8x8 can be written  in the exponentiation as [tex]8^6[/tex].

.

To write the expression 8x8x8x8x8x8 as a power, we can use exponentiation to represent the repeated multiplication.

Step by step, we can simplify the expression as follows:

Start with the given expression: 8x8x8x8x8x8.

Since all the factors are the same (8), we can rewrite the expression using the base (8) and the exponent representing the number of times it is multiplied (6 times).

Therefore, we can write 8x8x8x8x8x8 as  [tex]8^6[/tex].

Hence, the expression 8x8x8x8x8x8 can be written  in the exponentiation as [tex]8^6[/tex]. The correct option is A)  [tex]8^6[/tex]

.

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The expanded quadratic equation with real coefficients is y = x² + 14 · x + 45.

In this problem we need to determine the expanded quadratic equation with real coefficients such that one of its roots is - 7 + i 2. According with the quadratic formula, quadratic equations can have two conjugated complex roots, that is:

r₁ = α + β, r₂ = α - β

Then, the complete set of roots of the quadratic equation are r₁ = - 7 + i 2 and r₂ = - 7 - i 2. Then, the factor form of the polynomial is:

y = (x + 7 - i 2) · (x + 7 + i 2)

y = x · (x + 7 + i 2) + (7 - i 2) · (x + 7 + i 2)

y = x² + 7 · x + i 2 · x + (7 - i 2) · x + 7 · (7 - i 2) + i 2 · (7 - i 2)

y = x² + 7 · x + i 2 · x + 7 · x - i 2 · x + 49 - i 14 + i 14 - i² 4

y = x² + 14 · x + 45

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Explanation

let's remember this property of the exponent number

Step 1

solve by applying the property. ( let the same base and add the exponents)

hence, the answer is

I hope this helps you

Answer:  The correct answer is y = 10x – 45

Step-by-step explanation:

When graphing a line with a slope of 10 from point (5,5), we find that the y-intercept (where the line crosses the y-axis) is -45

Use the slope-intercept form (y=mx+b), where m=slope (10) and b=the y-intercept (-45)

y = 10x - 45

See explanation and graph below

For x less than or equal to zero, we would apply the function f(x) = (1/2)^x

For x greater than zero, we would apply the function f(x) = 2^x

when x = - 2 (less than 0)

This falls in the 1st function

when x = -1 (less than 0)

This falls in the 1st function

when x = 0 (equal to 0)

This falls in the 1st function

when x = 1 (greater than 0)

This falls in the 2nd function

when x = 2 (greater than 0)

THis falls in the 2nd function

Plotting the graph:

The end with the shaded dot reresent the function with equal to sign attached to the inequality [f(x) = (1/2)^x].

The end with the open dot represent the function without the equal to sign [f(x) = 2^x)

Probability is the chance that an event will occur and it's measured by the ratio of the favorable cases to the total number of cases possible.

The ratio for probability is given by:

The given number in scientific notation is:

In order to write it in standard notation, first take a look at the power: -6.

As it is a negative number, it means we need to move the dot to the left 6 units.

Therefore, we need to fill the blank places with zeros:

Answer:

3(3x - 7)

Step-by-step explanation:

9x - 21

GCF of 9 and 21 is 3

3(3x - 7)

I hope this helps!

Given the function:

As x goes to infinity, the term (2^-x) will go to zero

And the overall value of the function will be -5

So, the end behavior of f(x) as x goes to infinity = -5

The straight line that best represents something probable but not certain is option D.

It shows a probability of approximately 80%.

We can solve for the value of x using pythagorean theorem

where c is the hypotenuse ( in this case is 15) and a, b are the other legs of the triangle ( in this case is 8 and x).

Let's substitute the given values to the formula

Now please follow this solution to solve for x in:

We must find the zeros of the following function:

1) First, we plot a graph of the function:

From the graph, we see that the function crosses the x-axis at x = 3, so x = 3 is one of the zeros of the function.

2) Because x = 3 is a zero of the function, we can factorize the function in the following way:

To find the coefficients b and c, we compute the product of the parenthesis and then we compare the different terms:

To have the same expressions at both sides of the equality we must have:

So we have the following factorization for the function f(x):

3) To find the remaining zeros, we compute the zeros of:

The zeros of this 2nd order polynomial are given by:

where a, b and c are the coefficients of the polynomial. In this case we have a = 1, b = 2 and c = -5. Replacing these values in the formula above, we get:

s

Hello!

We know that the robot can complete 10 tasks in 3/4 hour.

To solve this exercise, we can use the rule of three, look:

So, we have:

Let's write it as a mixed number:

Answer:

We'll solve it in a similar way, look:

Answer:

To calculate the ampount of money in the account after 5 years, we will use the formula:

where A is the final amount

P is the initial amount or principal

r is the rate

n is the number of times the interest is applied

t is the time in years

From the question,

P = $6000 r = 2.12/100 = 0.0212 t= 5 n=365

substitute the values ibto the formula and evaluate

The amount is $6670.91

b)

To find the annual percentage yield (APY) on this account, we will use the formula:

All the answers to the given parts are mentioned below -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

Now, from the given information, we can write -

2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

So -

k = 2/0.5

k = 2/(1/2)

k = 2 x 2 = 4

Equations that represents the relationship can be written as -

y = 4x + c

Now, 2 scoops need 0.5 gallon of water.

2 = 4 x 1/2 + c

2 = 2 + c

c = 0

So, the equation will be y = 4x.

Graph of y = 4x is attached at the end.

For 10 scoops of water -

10 = 4x

x = 2.5 gallons of water is needed.

Therefore, all the answers to the given parts are mentioned above.

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The radius of the circle is half of the diameter. Therefore, if the diameter is 2 units, then the radius is 1 unit. If the diameter is 6 units, the radius will be 3 units. The graph that represents the relationship between radius and diameter is Graph B.

The circumference of the circle can be solved by multiplying the diameter and the value of pi. Therefore, this is a linear function. If the diameter is 4 units, the circumference is approximately 12.57 units. If the diameter is 6 units, the circumference is approximately 18.85 units. The graph that best represents the relationship between diameter and circumference is Graph C.

Lastly, the area of the circle with respect to the diameter is a quadratic function due to the nature of the formula that is A = πr². The graph of a quadratic function is parabolic in nature. Therefore, the graph that best represents the relationship between diameter and area is Graph A.

To summarize, the vertical axis for each graph is:

Graph A → Area

Graph B → Radius

Graph C → Circumference

The given expression is:

This can also be written as:

The result = 2.71

Since 7 is greater than 5, it will become 0 and add 1 to 2 to become 3

Therefore, the closest approximation is 3

Answer:

The distance from campsite A to campsite B is;

Explanation:

Given that The two campsites A and B form a right triangle with Sam's position, S.

The distance from campsite B to Sam's position is 1,300 yards, and campsite A is 1,700 yards from his position;

Applying pythagorean theorem, to solve for the third side AB;

Substituting the given values;

Therefore, the distance from campsite A to campsite B is;

We have to use the compound interest formula to solve this problem.

The compound interest formula:

Where

F is the future value [what we are solving for]

P is the principal, or initial, amount [It is $1000]

r is the rate of interest per period [It is given 8% annual interest, so 8/12 = 0.66% per month, in decimal that is r = 0.0066]

n is the time period [monthly compounding for 9 years is n = 12 * 9 = 108]

Now, we can substitute all the known information and solve for F:

After 9 years, the balance is: