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2 years ago

If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4).

Mathematics

1 answer:

Naya [18.7K]2 years ago

4 0

Answer:

Step-by-step explanation:

We are given two functions: f(x) = x^2 + 1 and g(x) = 3x + 1.

To find 2f(1), firstly find f(1) by substituting 1 in place of x and then multiply the result by 2 to get:

f(1) = (1)^2 + 1 = 1 + 1 = 2

2f(1) = 2(2) = 4

To find 3g(4), find g(4) and then multiply the result by 3 to get:

g(4) = 3(4) + 1 = 12 + 1 = 13

3g(4) = 3(13) = 39

Now add the values for 2f(1) and 3g(4):

2f(1) + 3g(4) = 4 + 39 = 43

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an ellipse has a center at the origin, a vertex along the major axis at (13, 0), and a focus at (12, 0). What is the equation of

yan [13]

Hi, as the elipce has a center at the origion and tha major distance is the axis

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

But,

c = 12 Distance of focus

a = 13 -> Major distance

b = ? ->

But,

$\\ b^2 + c^2 = a^2
 \\ 
 \\ b^2 + 12^2 = 13^2
 \\ 
 \\ b^2 + 144 = 169
 \\ 
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 \\ 
 \\ b^2 = 25
 \\ 
 \\ b = \sqrt{5} 
 \\ 
 \\ b = 5

$

Then,

$\\ \frac{x^2}{(13)^2} + \frac{y^2}{(5)^2} = 1
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5 0

2 years ago

Read 2 more answers

The probability of a train arriving on time and leaving on time is 0.8. The probability that the train arrives on time and leave

kkurt [141]

Answer:

0.9524

Step-by-step explanation:

Note enough information is given in this problem. I will do a similar problem like this. The problem is:

The Probability of a train arriving on time and leaving on time is 0.8.The probability of the same train arriving on time is 0.84. The probability of the same train leaving on time is 0.86.Given the train arrived on time, what is the probability it will leave on time?

Solution:

This is conditional probability.

Given:

Probability train arrive on time and leave on time = 0.8
Probability train arrive on time = 0.84
Probability train leave on time = 0.86

Now, according to conditional probability formula, we can write:

$P(Leave \ on \ time | arrive \ on \ time)$ = P(arrive ∩ leave) / P(arrive)

Arrive ∩ leave means probability of arriving AND leaving on time, that is given as "0.8"

and

P(arrive) means probability arriving on time given as 0.84, so:

0.8/0.84 = 0.9524

This is the answer.

5 0

2 years ago

A druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of

vladimir1956 [14]

Let x=amount of 10% and y=amount of 40%. Since we are making 10oz total, y=10-x so we can say:

(.1x+.4(10-x))/10=.25

(.1x+4-.4x)/10=.25

4-.3x=2.5

-.3x=-1.5

x=5, and since y=10-x, y=5

So 5oz of 10% is mixed with 5oz of 40% to make 10oz of 25% solution.

check

(.1(5)+.4(5))/10=.25

(.5+2)/10=.25

2.5/10=.25

.25=.25

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2 years ago

-Rounded to the nearest ten, the number is 61 460.

cricket20 [7]

Answer:

61464

Step-by-step explanation:

61464 ~ 61460 to the nearest ten

61464 ÷ 4 = 15366

61464 is an even number

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2 years ago

A new golf bag has a compartment that is roughly a rectangular prism that has dimensions of 6 inches by 8 inches by 9 inches. Ho

Ivahew [28]

Answer:

The dimensions of the rectangular prism is 5 inches by 7 inches by 8 inches. Volume of the rectangular prism is expressed as

Length of the base × width of the base × height of the prism.

Volume = 5×7×8 = 280 inches ^2

Each golf ball has the shape of a sphere. The volume of a sphere is expressed as

Volume of sphere = 4/3πr^3

The golf ball has a diameter of 1.7 inches. It means that the radius of the golf ball is 1.7/2 = 0.85

Volume of each golf ball = 4/3 × 3.14×0.85^3

= 2.57 inches^3

The number of golf balls that will fit into the compartment would be

Volume if compartment/ volume of each golf ball. It becomes

280/2.57 = 109 golf balls

Step-by-step explanation:

6 0

2 years ago