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3 years ago

What is the value of b? A right triangle with an angle measure of fifty-one degrees and an unknown angle measure, b degrees.

2 answers:

8 0

A triangle will have a total of 180 degrees.

Since it is a right triangle, we know that one angle is 90 degrees. We also know that one of the other angles is 51.

90 + 51 + x = 180
141 + x = 180

Subtract 141 on both sides.

x = 180 - 41
x = 39

The value of b is 39 degrees.

lozanna [386]3 years ago

3 0

90 + 51 = ?

90 + 51 = 141

180 - 141 = 39

Answer: B = 39 degrees

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

The sum of 5 consecutive odd numbers is 135 what is the second number in this sequence

hoa [83]

Step-by-step explanation:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

5·x + 20 = 135

5·x = 115

x = 23

So the sequence is

23, 25, 27, 29, 31

The second number is 25.

Do you agree?

6 0

3 years ago

Find m∠DEC (the picture is not drawn to scale).

pochemuha

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

(x - 45) + (x - 12) = x

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x Remove parenthesis

2x - 57 = x Combine like terms

2x = x + 57 Add 57 to both sides

x = 57 Subtract x from both sides

Finding m∠D:

x - 45 = ?

57 - 45 = 12º

Finding m∠C:

x - 12 = ?

57 - 12 = 45º

** (Checking x: 12 + 45 = 57) **

Finding m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

❤A.W.E.S.W.A.N.❤

8 0

3 years ago

The cost of a bagel and a cup of coffee is $2.35. The cost of 2 bagels and a cup of coffee is $4.20. What is the cost of one cup

Gnesinka [82]

Hey!

--------------------------------------------

Solution and Answer:

4.20 - 2.35 - $1.85 per bagel.

1.85 x 2 = $3.70 for 2 bagels.

4.20 - 3.70 = $0.50 per coffee.

--------------------------------------------

Hope This Helped ;)

7 0

2 years ago

What is 2/5-1/3 fractions

patriot [66]

You have to make the denominators (bottom numbers) the same via multiplication, it's best to do it to the first number they meet at. that would be fifteen (15)
5×3=15
3×5=15
you then have to multiply the numerators by the respective numbers.
2×3=6
1×5=5
you then subtract the numerators normally
6-5=1
slap back on the denominator
1/15
there's your answer.
(the number you multiply them by isn't the other denominator, it just happens to be the denominators for this equation)

8 0

3 years ago