Corey is out on the roads doing a long run, and also doing some mental calculations at the same time. corey's pace is 3 strides per second, and each stride covers 5 feet. (a) how much time does it take corey to cover a mile? (b) if corey's stride increased to 5.5 feet per step, how much time would be needed to cover a mile? (c) at five feet per step, how many steps would corey need to run the marathon distance, which is 26 miles and 385 yards?

Answer:  D. g(x)

Step-by-step explanation: since,f(x)=-x^4-2

x^4>=0 for all x so,-x^4<=0 for all x

⇒ -x^4-2<=-2 for all x

⇒ f(x)<=-2 for all x so, maximum possible value of f(x)=-2

whereas g(x)= -3x^3+2 can take values from (-∞,∞)

so, g(x) has the maximum y value

Answer:

1.a

2.d

3.c

4.a

5.b

Step-by-step explanation:

The equation [tex] p= 1.7t^{2}+18.75t+175 [/tex] approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.

We have to calculate the best estimate for the price of the house in year 2020.

So, we have to calculate the best price of the house after 10 years.

So, putting the value t=10 in the given equation.

[tex] p= 1.7t^{2}+18.75t+175 [/tex]

[tex] p= (1.7 \times 100)+(18.75 \times 10)+175 [/tex]

p = 532.5= 533 (Rounded)

Since it approximates the average sale price p of a house (in thousands of dollars).

Therefore p=$533,000

Therefore, the best estimate for the price of the house in year 2020 is $533,000.

the correct answer is C. x = (T - 2y) / 2.

To find the value of x in terms of T (the perimeter) and y for an isosceles triangle with two sides of length x and one side of length y, we use the fact that the perimeter is the sum of all three sides. The equation representing the perimeter of the triangle is T = x + x + y, which simplifies to T = 2x + y. To solve for x, we rearrange the equation to x = (T - y) / 2. Therefore, the correct answer is C. x = (T - 2y) / 2.

Final answer:

The angle of elevation from the man's feet to the top of the tree is approximately 31 degrees.

Explanation:

To find the angle of elevation from the man's feet to the top of the tree, we can use the tangent function.

The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (24 ft) and the adjacent side is the horizontal distance between the two trees (40 ft).

Therefore, tan(angle) = opposite/adjacent = 24/40 = 0.6.

Taking the inverse tangent, we get angle = arctan(0.6).

Rounding to the nearest degree, the angle is approximately 31 degrees.

The question requires the application of combination formulas to calculate the number of possible subcommittees with specific party member composition requirements.

The question deals with combinations in mathematics, specifically combinatorial calculation to determine the number of ways a subcommittee can be formed given certain restrictions on a party composition.

Part 1:

To find out how many subcommittees can be formed containing exactly 3 Republicans and 4 Democrats, we use the combination formula which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. There are 6 Republicans, so we can choose 3 of them in C(6, 3) ways and there are 8 Democrats from which we can choose 4 in C(8, 4) ways. The total number of such subcommittees is the product of these two combinations.

Part 2:

For the second part, we consider subcommittees with at least 1 and no more than 3 Republicans. This means we must calculate the sum of subcommittees for when there are exactly 1, 2, or 3 Republicans, combined with the appropriate number of Democrats to make a total of 7 members. We use the combination formula again for each scenario and add the results together.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]-18\dfrac{1}{4}\div 2\dfrac{2}{3}[/tex]

We need to find the best estimation:

First we change the mixed fraction into improper fraction:

[tex]-18\dfrac{1}{4}\approx -18[/tex]

and

[tex]2\dfrac{2}{3}=\dfrac{8}{3}=2.6666....\approx 3[/tex]

So, it becomes,

[tex]-18\div3\\\\=\dfrac{-18}{3}[/tex]

Hence, Second option is correct.

The x-intercept of the function f(x) = x^ 2-25 is -5. The correct option is A.

A rational function's intercept is the location on its graph where it crosses either the x- or y-axis. When the independent variable is 0, use the intercept function to find the value of the dependent variable (zero).

For instance, if your data points were collected at room temperature and above, you can use the intercept function to forecast a metal's electrical resistance at 0°C.

The x-intercept of a function is when the y-value is 0.

Replace y with 0 in the equation. You get the following.

[tex]x^2 - 25 = 0[/tex]

Add 25 to both sides

[tex]x^2 = 25[/tex]

Take the square root.

[tex]x = - \sqrt{25}[/tex]

[tex]x = -5[/tex]

Therefore, the correct option is A. -5.

To learn more about the intercept function, refer to the link:

https://brainly.com/question/11872755

#SPJ2

Answer:

GF=26.4

Step-by-step explanation:

21^2+16^2=C^2

441+256=c^2

697=c^2

GF=26.4

I hope this helps

The value of [tex]$a + b$[/tex] is 9.

To solve this problem

We can use the fact that the roots of the equation are given as[tex]$2 - 3i$ and $2 + 3i$.[/tex]

Quadratic equation roots occur in pairs of complex conjugates. Since[tex]$2 - 3i$[/tex] is the first root in this instance,[tex]$2 + 3i$[/tex] is the other root.

We now understand that the coefficient of the [tex]$z$[/tex] term is equal to the opposite of the sum of the roots of a quadratic equation. Stated otherwise, the total of the roots equals [tex]a[/tex] Thus, the two roots can be added together:

[tex]$(2 - 3i) + (2 + 3i) = 4$[/tex]

Therefore[tex], $-a = 4$, or $a = -4$.[/tex]

Next, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the [tex]$z^2$[/tex]term.

[tex]$(2 - 3i)(2 + 3i) = 4 - 6i + 6i - 9i^2 = 4 + 9 = 13$[/tex]

So, [tex]$b = 13$.[/tex]

Finally, we can find the sum[tex]$a + b$:[/tex]

[tex]$a + b = -4 + 13 = 9$[/tex]

Therefore,  the value of [tex]$a + b$[/tex] is 9.

Answer:

37

Step-by-step explanation:

bc its 37

Final answer:

The equation equivalent to (x^2+6)^2-21=4x^2+24 in terms of p is A. p² - 4p - 21 = 0.

Explanation:

To find which equation is equivalent to (x²+6)²-21=4x²+24 in terms of p, we follow a series of algebraic steps, substituting p with x²+6. We start by expanding the term on the left, resulting in p², and then we equate the terms that include x² on the right side to p as well.

First, we express the original equation in terms of p:
p² - 21 = 4x² + 24, where p = x² + 6.

Next, we substitute p in place of x² + 6:
p² - 21 = 4(p - 6) + 24

Now, we simplify the right side of the equation:
p² - 21 = 4p - 24 + 24

Which simplifies further to:
p² - 21 = 4p

Finally, we rearrange the equation to get all terms on one side:
p² - 4p -21 = 0

Therefore, the correct answer is A. p² - 4p - 21 = 0.