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3 years ago

Given f(x)=2x+3 find f(x)=27

Mathematics

2 answers:

RSB [31]3 years ago

6 0

F(27) = 2(27) + 3

f(27) = 54 + 3

57

scoundrel [369]3 years ago

6 0

Use the substitution method

f(x)=2x+3

f(27)=2(27)+3

Multiply first and then add

=54+3

=57

Answer: f(27)=57

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Suppose you have a bag containing 2 black marbles and 3 red marbles. You reach into the bag, select a marble, see what color it

TiliK225 [7]

Answer:

$\dfrac{9}{25}$

Step-by-step explanation:

Given that the bag contains black and red marbles.

Number of black marbles in the bag = 2

Number of red marbles in the bag = 3

Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5

Let us have a look at the formula for probability of an event E, which can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(\text{First red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5 }$

Now, the marble chosen at first is replaced.

Therefore, the count remains the same.

$P(\text{Second red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5}$

Now, the required probability can be found as:

$P(\text{First red marble})\times P(\text{Second red marble}) = \dfrac{3}{5}\times \dfrac{3}{5} = \bold{\dfrac{9}{25} }$

3 0

2 years ago

Please answer each one. Disclaimer: don't do it for points

Gre4nikov [31]

Answer:

for question 1 the answer is 1.5 cm

for question 2 the answer is 0.75 cm

for question 3 the answer is 2.3 inches

for question 4 the answer is 3.3 inches

for question 5 the answer is 4 cm

for question 6 the answer is 0.75 inches

7 0

3 years ago

Two ships leave the same port at the same time. Two hours later ship A has traveled 12 miles and ship B has traveled 8 miles.

sashaice [31]

Answer:

the angle between their paths is 100.8°

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the Cosine Rule which is:

c² = b² + a² - 2 b c cos(θ)

where

c = 16 miles
b = 8 miles
a = 12 miles

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

θ = 100.8°

Therefore, the angle between their paths is 100.8°

4 0

3 years ago

En un polinomio P(x,y), homogéneo y completo en "x" e "y", la suma de los grados absolutos de todos sus términos es 420. ¿Cuál e

Mandarinka [93]

Answer:

the degree of homogeneity is 20.

Step-by-step explanation:

In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?

A homogeneous polynomial is one in which all monomials have the same degree.

This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):

x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.

As you can see, the sum of the exponents of the variables x, y in each monomial is 4.

And the number of terms is 5, that is, it is the degree of homogeneity plus 1.

In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.

In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)

Calling n, the degree of our polynomial, it must be fulfilled:

n (n + 1) = 420

=> n ^ 2 + n = 420

=> n ^ 2 + n - 420 = 0

Factoring:

(n + 21) (n - 20) = 0

=> n = -21 and n = 20.

Only the positive value makes sense, therefore n = 20.

In other words, the polynomial is of the form (excluding the coefficients):

x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20

That polynomial has 21 terms.

So the sum of the degrees will be 20 * 21 = 420, as required in the statement.

Therefore, the degree of homogeneity is 20.

8 0

3 years ago

Plot two points to graph the equation. y=−1/3x+1

Viktor [21]

Answer:

(3,0) & (-6,3)

Step-by-step explanation:

-1/3(3)+1= -1+1=0

-1/3(-6)+1= 2+1= 3

8 0

2 years ago