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3 years ago

8

At the dog park, there are several dogs with their owners. Counting heads, there are 20; counting legs, there are 62. How many d

ogs and owners are there?

1 answer:

Nataly_w [17]3 years ago

6 0

There are 9 owners and 11 dogs
9×2=18
11×4=44
44+18=62

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Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)

svetoff [14.1K]

Answer:

The rate of change of the function at x = 0.6 is approximately -0.72

Step-by-step explanation:

The given information from the graph are;

Points (0, 0) and (1, -0.5)

We have that the graph is that of a cubic function, therefore;

f(x) = ax³ + bx² + cx + d

At f'(x) at (0, 0) and (1, -0.5) = 0 gives;

3ax² + 2bx + c = 0

∴ c = 0

Also

ax³ + bx² + cx + d = 0

d = 0

We have

3a(1)² + 2b(1) + 0 = 0

3·a + 2·b = 0..............(1)

a(1)³ + b(1)² + c(1) + d = -0.5

a + b + 0×(1) + 0 = -0.5

a + b = -0.5..........(2)

Multiplying equation (2) by 2 and subtracting it from equation (1) gives;

2 × (a + b = -0.5) = 2·a + 2·b = -1

3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1

a = 1

From

a + b = -0.5, we have;

1 + b = -0.5 = 0

b = -0.5 - 1 = -1.5

The equation becomes

f(x) = x³ - 1.5·x²

The rate of change of the function at x = 0.6 is therefore given as follows;

f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x

At x = 0.6, we have;

f'(0.6) = 3·(0.6)² - 3·(0.6)

f'(0.6) = 3×0.6² - 3×0.6 = -0.72

The rate of change of the function at x = 0.6 ≈ -0.72

4 0

3 years ago

What is 25% of 400 5% of 20

stiks02 [169]

Hello there!

What is 25% of 400?

$\frac{25*400}{100}$

= $\frac{10,000}{100}$

= 100

Thus,

25% of 400 is 100

What is 5% of 20?

Well, we just need to follow the previous steps.

$\frac{5*20}{100}$

= $\frac{100}{100} = 1$

Thus,

5% of 20 is 1

I hope this answer helps. Let me know if you have additional questions about the answer. As always, it is my pleasure helping student like you.

5 0

3 years ago

What is the best approximation of the area of a circle with a diameter of 17 meters? Use 3.14 to approximate pi. 53.4 m² 106.8 m

Arte-miy333 [17]

R = 17/2 =8.5 m
A = 3.14 x (8.5)^2
A = 3.14 x 72.25
A = 226.865

answer <span>226.9 m² (third choice)</span>

8 0

3 years ago

A negative value of r means that:

tatuchka [14]

Answer:

(d.) Those who score high on one variable tend to score low on the other.

Step-by-step explanation:

A negative value of correlation coefficient (r) shows a relationship between two variables such that as one variable increases, the other decreases. It shows the inverse relationship between two variables with the dependence determined by the value of the correlation coefficient (r).

It can be observed that for graphs with negative slope, the correlation coefficient (r) is similarly negative. This speaks about its relationship too.

The correlation coefficient being negative doesn't mean the relationship between the two variables in question is bad, it just means that the correlation relationship is inverse (still dependent). A perfectly negative correlation is -1.

6 0

3 years ago

What is the product of the polynomials shown below?

Sindrei [870]

Answer:

B. 14x^3+39x^2+18x+20

Step-by-step explanation:

Given polynomials are:

$(7x^2+2x+4)(2x+5)\\For\ product\\(2x+5)(7x^2+2x+4)\\= 2x(7x^2+2x+4)+5(7x^2+2x+4)\\= 14x^3+4x^2+8x+35x^2+10x+20\\Combining\ alike\ terms\\= 14x^3+4x^2+35x^2+8x+10x+20\\=14x^3+39x^2+18x+20$

The product of given polynomials is:

14x^3+39x^2+18x+20

Hence, Option B is correct ..

8 0

3 years ago

Read 2 more answers