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1 year ago

The sum of three consecutive even integers is 114. What are the integers?

Mathematics

2 answers:

AnnZ [28]1 year ago

7 0

Answer:

Hence, the four consecutive integers whose sum is 114 are 27, 28, 29 and 30.

Step-by-step explanation: hope this helps

Gwar [14]1 year ago

6 0

Answer:

Step-by-step explanation:

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Solve 4 cos2x-3 = 0 for all real values of x.

vichka [17]

4 cos² x - 3 = 0

4 cos² x = 3

cos² x = 3/4

cos x = ±(√3)/2

Fixing the squared cosine doesn't discriminate among quadrants. There's one in every quadrant

cos x = ± cos(π/6)

Let's do plus first. In general, cos x = cos a has solutions x = ±a + 2πk integer k

cos x = cos(π/6)

x = ±π/6 + 2πk

Minus next.

cos x = -cos(π/6)

cos x = cos(π - π/6)

cos x = cos(5π/6)

x = ±5π/6 + 2πk

We'll write all our solutions as

x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k

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3 years ago

Please help!!!!! It's urgent

Evgesh-ka [11]

2b 2a
----------------- + -----------------
(b+a)^2 (b^2 - a^2)

2b 2a
= ----------------- + -------------------
(b+a)(b+a) (b+a)(b-a)

2b(b - a) + 2a(b + a)
= ------------------------------------
   (b+a)(b+a)(b-a)

2b^2 - 2ab + 2ab + 2a^2
= ---------------------------------------
     (b+a)(b+a)(b-a)

2b^2 + 2a^2
= ------------------------
   (b+a)(b+a)(b-a)

2(b^2 + a^2)
= ------------------------
   (b+a)^2 (b-a)

Answer:

Numerator: 2(b^2 + a^2)
Denominator: (b+a)^2 (b-a)

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4 years ago

How do you find the slope equation of x+4y=16

tankabanditka [31]

x+4y=16

4y= -x +16

y = -1/4x + 4

so slope = -1/4

5 0

4 years ago

Find the missing exponent.

vlada-n [284]

The missing exponent is 21 :)

Explanation: when dividing exponents, subtract them so in this case, it’s 25-19 to get 6 as the answer

6 0

3 years ago

Two part-time instructors are hired by the Department of Statistics and each is assigned at random to teach a single course in p

scZoUnD [109]

Answer:

The probability that they will teach different courses is $\frac{2}{3}$ .

Step-by-step explanation:

Sample space is a set of all possible outcomes of an experiment.

In this case we will write the sample space in the form (x, y).

Here x represents the course taught by the first part-time instructor and y represents the course taught by the second part-time instructor.

Denote every course by their first letter.

The sample space is as follows:

S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}

The outcomes where the the instructors will teach different courses are:

s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}

The probability of an events E is the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

Compute the probability that they will teach different courses as follows:

$P(\text{Different courses})=\frac{n(s)}{n(S)}=\frac{6}{9}=\frac{2}{3}$

Thus, the probability that they will teach different courses is $\frac{2}{3}$ .

3 0

3 years ago