Mentally solve 93 - 27 in as many ways as you can

Mrs. Duggin walked every day for seven days. If she walked 9/10 of a mile each day for seven days, how many total miles did she

Molodets [167]

Answer:

Mrs. Duggin walked a total of $\frac{63}{10} \ miles.$ .

Step-by-step explanation:

Given:

Number of miles walked on each day = $\frac{9}{10} \ mile$

Number of days she walked = 7

We need to find the Total miles she walked using repeated addition method.

Solution:

Now we know that Repeated Addition means adding each group together and it is also known as Multiplication.

So we can Find Total miles she walked by adding Number of miles walked on each day with number of day times.

OR

we can Find Total miles she walked by Multiplying Number of miles walked on each day with number of days.

framing in equation form we get;

Total miles she walked = $\frac{9}{10}+\frac{9}{10}+\frac{9}{10}+\frac{9}{10}+\frac{9}{10}+\frac{9}{10}+\frac{9}{10}= \frac{9+9+9+9+9+9+9}{10} = \frac{63}{10}\ miles$

OR

Total miles she walked = $\frac{9}{10}\times7= \frac{63}{10} \ miles.$

Hence Mrs. Duggin walked a total of $\frac{63}{10} \ miles.$ .

4 0

4 years ago

The function f(x)=x^3+6x^2+8x

dem82 [27]

The function increases in the interval (-∞, -3) and the function also increases in the interval (-1,∞) .

The given function is of the form

f(x) = x³ + 6x² + 8x

Now we take the first differentiation of the function

f'(x) = 2x² + 12x + 8

f'(x) = 2 (x² + 6x + 9) -10

f'(x) = 2(x+3)² - 10

Therefore at x = -3 , f'(x) = -10.

Hence the function is increasing in the interval of (-∞, -3)

Again f'(x) = 2x² + 12x + 8 , so after first differentiation we get :

That the function is also increasing in the interval (-1,∞)

Now for the interval (-4,-2), we can say that the graph of the function is positive as the y value increases and then decreases but all y values are positive as illustrated in the graph.

In the interval (0,∞) the function is strictly increasing and has positive values only.

To learn more bout function visit:

brainly.com/question/21753201

#SPJ1

6 0

1 year ago

Kendra dives off of a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation

il63 [147K]

Answer:

1) How high is the diving board?:  6 feet above the water surface

2) How deep does the diver dive into the water?: 6.5feet into the water

3) At what horizontal distance from the board does the diver enter the water? 1 feet from the board

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive? 6 feet from the board

Explanation:

The dive is modeled by the equation h(x) = x² - 7x + 6.

Two important features that you must notice quickly are:

That is a quadratic function, which is a parabola.

Since the leading term, x², is positive, the parabola open upwards, and the vertex is a minimum.

As for the questions:

1) How high is the diving board?

The diving board is the place from which Kendra dives off. At this point, the horizontal distance, x, from the diving board is 0.

Then, the height will be given by h(x) with x = 0. Substitute into the equation and compute:

h(0) = 0² - 7(0) + 6

h(0) = 0 - 0 + 6

h(0) = 6

Therefore, the diving board is 6 feet above the water surface.

2) How deep does the diver dive into the water?

This is the minimum heigth given by the function h(x).

As explained above, this is the vertex of the parabola.

You can find the x-coordinate of the vertex with the equation:

x-coordinate of the vertex = -b/(2a)

Where b and a are the coefficients of the linear term and the quadratic terms in the equation for h(x), respetively:

a = 1
b = -7

x-coordinate = - (-7) / (2 × 1) = 7/2 = 3.5

Now you can find h(x) for x = 3.5

h(3.5) = (3.5)² - 7(3.5) + 6 = 12.25 - 24.5 + 6 = - 6.25

That is 6.25 feet below the water surface.

3) At what horizontal distance from the board does the diver enter the water?

That is the x-intercept of the function. This is, the value of x when h(x) = 0.

Thus, solve the equation 0 = x² - 7x + 6.

You can factor the equation:

Find two numbers that add up -7 and their product is +6. Those are - 6 and -1:

0 = (x - 1) (x - 6)

Using the zero product property:

(x - 1) = 0 or (x - 6) = 0

x = 1 or x = 6

Thus, you have two solutions, which are the two x-intercepts of the funtion.

x = 1 represents the horizontal distance from the board where the diver enters the water.

The other solution is the answer to the next question.

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?

As explained above, the equation has two x-intercepts. They both are the points where the parabola crosses the x-axis, which is when the height, h(x) is 0. That height is the surface of the water level.

The first x-intercept is the point (horizontal distant from the board) where the diver enters the water, such as asserted above.

The other x-intercept is where the diver comes to the surface of water after the dive and after being submerged in the water: the diver enters the water, dives 6.5feet into the water, and returns to the surface.

Thus, this is the solution x = 6 for h(x) = 0.

Hence, Kendra comes to the surface of water at 6 feet from the board.

7 0

3 years ago

Read 2 more answers

The Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they travel

Otrada [13]

Answer:

5/12

Step-by-step explanation:

Total distance travelled = 30% + 1/4

To add these numbers, convert 30% to fraction

30% = 1/3

1/3 + 1/4 = 7/12

Remaining distance = 1 - 7/12 = 5/12

7 0

3 years ago

Simplify 3(2x+4y-y) Someone please explain the steps to solve this equation in DETAIL.

il63 [147K]

3 (2x + 4y - y) Combine like terms (4y and -y)
3 (2x + 3y) Use the Distributive Property [(3 · 2x) + (3 · 3y)]
6x + 9y

7 0

4 years ago

Read 2 more answers