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3 years ago

B=? Angle A=? Angle B=?

Mathematics

1 answer:

babunello [35]3 years ago

6 0

1.) Solve for length b.

The simpler method is to use the Pythagorean theorem. If $a^2 - b^2 = c^2$ , then this means that $c^2 - a^2 = b^2$ .

Plug in the values:

$11^2 - 7^2 = b^2$

--> $121 - 49 = 72$

So this means that b is the square root of 72, which is 8.49

2.) Solve for ∠A.

Let's refer to the law of sines. If $\frac{a}{sin(A)} = \frac{c}{sin(C)}$ , then this means we can cross multiply. Since A is the value we are solving for, the equation should be written out like this:

$A = sin^-1(\frac{sin(C) * a}{c})$

--> $A = sin^-1(\frac{sin(90) * 7}{11})$

A is 39.52°

3.) Solve for ∠B.

This is the easiest one. The sum of all three angle measures in a triangle add up to 180°. We already know that one of the angles is a right angle and the other 39.52°.

39.52 + 90 = 129.52

180 - 129.52 = 50.48

∠B is 50.48°.

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7

taurus [48]

Answer:

$12942$ is the sum of positive integers between $1$ (inclusive) and $199$ (inclusive) that are not multiples of $4$ and not multiples $7$ .

Step-by-step explanation:

For an arithmetic series with:

$a_1$ as the first term,
$a_n$ as the last term, and
$d$ as the common difference,

there would be $\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)$ terms, where as the sum would be $\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)$ .

Positive integers between $1$ (inclusive) and $199$ (inclusive) include:

$1,\, 2,\, \dots,\, 199$ .

The common difference of this arithmetic series is $1$ . There would be $(199 - 1) + 1 = 199$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}$ .

Similarly, positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $4$ include:

$4,\, 8,\, \dots,\, 196$ .

The common difference of this arithmetic series is $4$ . There would be $(196 - 4) / 4 + 1 = 49$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $7$ include:

$7,\, 14,\, \dots,\, 196$ .

The common difference of this arithmetic series is $7$ . There would be $(196 - 7) / 7 + 1 = 28$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $28$ (integers that are both multiples of $4$ and multiples of $7$ ) include:

$28,\, 56,\, \dots,\, 196$ .

The common difference of this arithmetic series is $28$ . There would be $(196 - 28) / 28 + 1 = 7$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}$ .

The requested sum will be equal to:

the sum of all integers from $1$ to $199$ ,
minus the sum of all integer multiples of $4$ between $1\!$ and $199\!$ , and the sum integer multiples of $7$ between $1$ and $199$ ,
plus the sum of all integer multiples of $28$ between $1$ and $199$ - these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

$19900 - 4900 - 2842 + 784 = 12942$ .

8 0

3 years ago

Are these correct? Im having trouble

Gennadij [26K]

Answer:

yes

Step-by-step explanation:

it is correct

3 0

3 years ago

Read 2 more answers

Which of the following equations have no solution? Select all that apply.

lana [24]

The answer should be B and A

3 0

3 years ago

Read 2 more answers

A dairy sells $3 and $5 ice creams. In one day they sell 50 ice creams earning a total of $180. How many of each type of ice cre

murzikaleks [220]

We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream

Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50

3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + <u>75
</u> $180

8 0

3 years ago

Find the solution of the inequality<br> of b > 11.3

Tems11 [23]

The solution is the interval b is in ]11.3, infinity[

4 0

4 years ago