Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?

The product of matrices[tex]\(B\) and \(A\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

To find the product (BA), we multiply each row of (B) by each column of (A) and sum the products.

Let's calculate the elements of the resulting matrix (BA):

  a. First row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. First row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. First row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. First row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the first row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Similarly, for the second row of (BA):

  a. Second row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. Second row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. Second row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. Second row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the second row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Hence, the product [tex]\(BA\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

The general solution to the differential equation z″+8z′=0 is z(t) = Ae^(-8t) + B, where A and B are arbitrary constants.

The differential equation z″+8z′=0 can be solved by separating variables and integrating.

Let v = z′ be the derivative of z.

Then the equation becomes v′+8v=0.

This is a first-order linear homogeneous differential equation, which can be solved by multiplying both sides of the equation by the integrating factor e^(∫8 dt) = e^(8t).

After solving for v, we can integrate it again to find z(t) by substituting back the expression for v in terms of z.

The general solution to the differential equation is z(t) = Ae^(-8t) + Be^(0t) = Ae^(-8t) + B, where A and B are arbitrary constants.

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The Distributive Property allows you to multiply the terms within (z−5)(z+3) to obtain z² + 3z - 5z - 15. After combining like terms, the final result is z² - 2z - 15.

To use the Distributive Property to find the product of (z−5)(z+3), you multiply each term in the first parenthesis by each term in the second parenthesis. Here are the steps:

Multiply z by z, which is z².

Multiply z by +3, which gives you +3z.

Multiply -5 by z, which results in -5z.

Finally, multiply -5 by +3, which is -15.

After multiplication, you combine like terms:

z² + 3z - 5z - 15

Combine +3z and -5z to get -2z

So, the final result is z² - 2z - 15.

Answer:

256

Step-by-step explanation:

Answer:

wht the girl ontop said

Step-by-step explanation:

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Answer with explanation:

Number of cups of peanut that Dana has =10 cups

Number of cups of flour that Dana has =12 cups

Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Constraints

⇒x>0, y>0

⇒3 x+y ≤10

⇒2 x+4 y ≤ 12

Maximize(Objective Function):

Z=6 x +7 y

⇒⇒ The most reasonable definition for the variables x and y as Dana wants to maximize her income from selling the dog treats

Option D: Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Answer:d

Step-by-step explanation:

The average human heart beats approximately 108,000 times in one day, 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. In a lifetime, your heart will beat an estimated 2.925 x 10^9 times.

The average human heart beats approximately 108,000 times in one day, 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. To estimate the number of times your heart will beat in your lifetime, we can multiply the number of heartbeats in one year by the average life span:

39 million heartbeats/year x 75 years = 2.925 billion heartbeats in a lifetime

In scientific notation, this can be expressed as 2.925 x 10^9 heartbeats.

The average heart beats approximately 3 billion times during a 75-year lifespan.

The average heart beats approximately 108,000 times in one day, more than 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. To estimate the number of times your heart will beat in your lifetime, you multiply the average heartbeats per year by the number of years in your lifespan.

For example, if we assume an average lifespan of 75 years, we can estimate the number of heartbeats in a lifetime:

39,000,000 heartbeats/year x 75 years = 2,925,000,000 heartbeats in a lifetime (2.9 x 10^9)

Answer:

Cost of each pillow is $120.

Step-by-step explanation:

Let P denotes cost of each pillow and M denotes cost of mattress.

Then, given cost of mattress is $769

also, Ally gave the cashier $1300 and received $51 change.

Total amount Ally paid = total amount she gave - total amount she receives back.

                                     = $( 1300 - 51 )

                                     = $1249

Since, Ally brought one mattress and 4 pillow . Thus, Total cost is given as,

⇒ M + 4 P = 1249

⇒ 769 + 4 P = 1249

⇒ 4 P = 1249 - 769

⇒ 4 P = 480

⇒ P = 120

Thus, cost of each pillow is $120.

Answer:

6ft 6 in

Step-by-step explanation:

Write a proportion that uses the scale factor 1/16. The numerator corresponds to the dollhouse, and the denominator corresponds to the actual house. So 4 7/8 goes in the numerator, and the variable goes in the denominator.

1/16=478xx=16⋅478x=78

There are 12 in. in a foot, so 78 in. equals 6 ft 6 in.

Answer:

4, -32

2, -15

Step-by-step explanation:

Trust me bro.

Answer:

3.19495491 rounded to the nearest hundredth is 3.19

Step-by-step explanation:

The distance from the skydiving center did Alexa land will be 3.19 km. The formula of trigonometry is used in the given problem.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

[tex]\rm Cos A = \frac{AC}{AB} \\\\ COS 20^0 = \frac{AC}{3.4} \\\\ AC= 0.9694 \times 3.4 \\\\ AC = 3.19 \ km[/tex]

Hence the distance from the skydiving center did Alexa land will be 3.19 km.

To learn more about the trigonometry refer to the link;

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Answer:  Our factorized term will be

2xy(2x+5)(2x-3)

Explanation:

Since we have given that

[tex]8x^3y-8x^2y-30xy[/tex]

All we need to do is to factorise this expression.

Here are the steps given below:

[tex]2xy(4x^2-4x-15)[/tex]

By manipulating the terms, we get:

[tex]2xy[(2x)^2-4x+1-16]\\\\2xy[(2x-1)^2-16]\\\\2xy[(2x-1)^2-(4)^2]\\\\2xy[(2x-1-4)(2x-1+4)]\\\\2xy[(2x-5)(2x+3)][/tex]

Alternatively,

By using splitting the middle terms,

[tex]2xy(4x^2-4x-15)\\\\2xy(4x^2-10x+6x-15)\\\\2xy[2x(2x-5)+3(2x-5)]\\\\2xy(2x-3)(2x+5)[/tex]

Hence, our factorized term will be

2xy(2x+5)(2x-3)

Answer:

C

Step-by-step explanation:

Right in edge2020