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3 years ago

Five times the smallest of three consecutive odd integers is seven more than twice the largest. Find the largest

Mathematics

1 answer:

Dmitrij [34]3 years ago

8 0

Answer: 9

Step-by-step explanation:

Let the consecutive odd numbers be y, y+2 and y+4.

Five times the smallest of three consecutive odd integers is seven more than twice the largest. Find the largest integer can be expressed as:

5y = 2(y+4) + 7

5y = 2y + 8 + 7

5y = 2y + 15

5y - 2y = 15

y = 3

The smallest odd number is 5

The largest integer will be:

= y + 4

= 5+4

= 9

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The function f(x) = x is translated using the rule (x, y) - (x - 6, y + 9) to create A(x).

anyanavicka [17]

It seems the correct function you need to mention is f(x) = sqrt x

so, I am assuming $f(x) = \sqrt{x}$ and will solve the question based on it.

Answer:

Check the explanation

Step-by-step explanation:

Given the function

$f(x) = \sqrt{x}$

As the function is translated according to the rule

(x, y) → (x - 6, y + 9)

Translation of the function $f(x) = \sqrt{x}$ 6 units to the left will bring the function

$g(x) = \sqrt{x+6}$

Translation of the function $g(x) = \sqrt{x+6}$ 9 units up will bring the function

$A\left(x\right)=\sqrt{x+6}+9$

Determining the range of $A\left(x\right)=\sqrt{x+6}+9$

As we know that the range is the set of dependent values for which the function is defined.

$\mathrm{The\:range\:of\:an\:radical\:function\:of\:the\:form}\:c\sqrt{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k$

$k=9$

$f\left(x\right)\ge \:9$

$\mathrm{Range\:of\:}\sqrt{x+6}+9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:9\:\\ \:\mathrm{Interval\:Notation:}&\:[9,\:\infty \:)\end{bmatrix}$

Therefore, the expression describes the range of A(x) will be:

$f\left(x\right)\ge \:\:9\:or\:y\:\ge \:\:\:9$

3 0

3 years ago

(09.05 MC) Derek kicks a soccer ball off the ground and in the air, with an initial velocity of 31 feet per second. Using the fo

ivann1987 [24]

In order to find the maximum of the function, we have to find the roots of the first derivative.
$H(t)=-16t^2+vt+s\\ H'(t)=-32t+v=0\\ v=32t\\ t=\frac{v}{32}=\frac{31}{32}=0.97s$
This gives us the time at which the ball reaches its maximum height.
We don't know s. We can find it because we know that at t=0 the ball is on the ground and its height has to be zero.
$H(0)=0=-16(0)^2+v(0)+s\\ s=0$
Finally, we can find the maximum height:
$H(0.97)=-16(0.97)^2+31\cdot 0.97=15.0156 \simeq15$ft$
The answer is C.

4 0

4 years ago

Read 2 more answers

The perimeter of the triangle below is 75 m. Determine the measure of each side of the triangle

vaieri [72.5K]

Step-by-step explanation:

The perimeter is the sum of all sides.

AB+AC+CB=75

(2x-9) + (2x+3) + (3x+4) = 75

Combine like terms:

(2x+2x+3x) + (-9+3+4) = 75

7x - 2 = 75

7x = 77

x=11

Replace 'x' with '11' in the above equations to find that:

AB = 2(11) - 9 = 22 - 9 = 13 m

AC = 2(11) + 3 = 22 + 3 = 25 m

CB = 3(11) + 4 = 33 + 4 = 37 m

13 + 25 + 37 = 75 m

8 0

3 years ago

Given the functions below, find (h+g) (10). g(x) = 3x + 3 h(x) = - 4x + 1

alexandr402 [8]

Answer:

-6

Step-by-step explanation:

Find the sum of these two functions when x equals 10.

h(10) + g(10)

- 4(10) + 1 + 3(10) + 3

-40 + 1 + 30 + 3

Add the numbers.

-39 + 30 + 3

-6

The value of the function (h+g)(10) is -6.

6 0

3 years ago

Identify an expression that is equivalent to 0.3(12y)

lutik1710 [3]

3.6y is the answer. If you multiply the 0.3 times the 12 it equales 3.6 and add the y because it’s a variable.

3 0

4 years ago