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2 years ago

What is the domain of y = log Subscript 4 Baseline (x + 3)?

Mathematics

2 answers:

quester [9]2 years ago

5 0

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

Virty [35]2 years ago

5 0

Answer:

(B) all real numbers greater than –3

Step-by-step explanation:

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the total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m +5. After a p

Luba_88 [7]

Answer:

The slope becomes 0.5625 and y intercept becomes 12.5.

$65.9375

Step-by-step explanation:

Given that

the total reimbursement function in terms of $m$ miles:

$f(x) = 0.45m +5$

After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.

To find:

How to transform the graph of f.

Total reimbursement for a trip of 95 miles?

Solution:

$f(x) = 0.45m +5$ can also be written as:

$y = 0.45m +5$

It is nothing but slope intercept form, comparing with $Y = M X+ C$

M is the slope and C is the y intercept.

Slope of the graph is 0.45.

Y intercept is 5.

After change in the function, first of all add $5.

$0.45m + 5+5 = 0.45m+10$

Now, multiply with 1.25

Resulting function becomes:

$f(x) =1.25\times (0.45m+10)\\\Rightarrow f(x) =0.5625m+12.5$

Kindly refer to the attached image for the graph of the two functions.

Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.

To find the reimbursement for a trip of 95 miles:

Put m = 95

$f(95) =0.5625\times 95+12.5 = \bold{\$65.9375 }$

8 0

2 years ago

Find the values of x and y that make these triangles congruent by the HL Theorem

Misha Larkins [42]

<span>The correct answer is A. X=5, Y=6. Both triangles are right triangles. Each triangle has corresponding sides that are congruent which makes the triangles congruent. The answer A has the values that make each side of both triangles equal to the other triangle.</span>

7 0

2 years ago

Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a

Artyom0805 [142]

Answer:

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Step-by-step explanation:

Given

Represent radius with r and height with h

$h = 12ft$

$r = 10ft$

$Rate = \frac{8ft^3}{min}$ when $h = 10ft$

Express radius in terms of height

$\frac{r}{h} = \frac{10}{12}$

$\frac{r}{h} = \frac{5}{6}$

$r = \frac{5}{6}h$

First, we need to determine the volume of the cone in terms of height.

$Volume = \frac{1}{3}\pi r^2h$

Substitute $r = \frac{5}{6}h$

$V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^3$

$V = \frac{25}{108} \pi h^3$

Differentiate both sides w.r.t time (t)

$\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}$

$\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}$

Solve for $\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}$

At this point, $h = 10$ and $\frac{dv}{dt} = \frac{8ft^3}{min}$

So, we have:

$\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{864}{7500\pi}$

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Hence:

The rate is $\frac{216}{1875\pi} ft/min$

6 0

2 years ago

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from th

jeyben [28]

Weight = k/(distance)². Let's find the value of k when distance = earth radius:

180 = k/(3900)² → k = 180 x 3900² → k = 2,737,800,000

If he is at 325 miles ABOVE the earth, the distance becomes: 3,900+325=4,225 miles and his weight becomes:

Weight = k/(distance)² → Weight = 2,737,800,000/(4225)² = 153.37

Weight = 153.37 lb

8 0

2 years ago

The expression 10a+6c gives the cost (in dollars) for a adults and c children to eat at a buffet restaurant.

katrin [286]

Answer:

Answer: The total cost is assuming the cost for 1 adult is and the cost for 1 child is

Step-by-step explanation:

5 0

2 years ago