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3 years ago

hhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllppppppppppppppppppppp plz im almost done

Mathematics

2 answers:

posledela3 years ago

8 0

Answer:

a = 76

Step-by-step explanation:

a - 40 + a + 180 - (a + 36) = 180

a - 40 + a + 180 - a - 36 = 180

a + 104 = 180

a = 180 - 104

a = 76

kykrilka [37]3 years ago

7 0

Answer:

a = 76

Step-by-step explanation:

The remote angles theorem states that when one extends one side of a triangle, the sum of the two non-adjacent angles will equal the measure of the angle formed between the side of the triangle and the extension.

One can apply this theorem here by stating the following,

(a - 40) + (a) = (a + 36)

Simplify,

a - 40 + a = a + 36

2a - 40 = a + 36

Inverse operations,

2a - 40 = a + 36

-a -a

a - 40 = 36

+40 +40

a = 76

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What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

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3 years ago

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Answer:

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6 0

3 years ago

The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.

solong [7]

Answer:

$20$ .

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are $a$ , $b$ , and $c$ :

$a + b > c$ ,

$a + c > b$ , and

$b + c > a$ .

In this question, the length of the sides are $10$ , $24$ , and $x$ . The length of these sides should satisfty the following inequalities:

$10 + 24 > x$ ,

$10 + x > 24$ , and

$24 + x > 10$ .

Since $x > 0$ , the inequality $24 + x > 10$ is guarenteed to be satisfied.

Simplify $10 + 24 > x$ to obtain the inequality $x < 35$ .

Similarly, simplify $10 + x > 24$ to obtain the inequality $x > 14$ .

Since $x$ needs to be a whole number, the greatest $x$ that satisfies $x < 35$ would be $34$ . Similarly, the least $x\!$ that satisfies $x > 14$ would be $15$ . Thus, $x\!\!$ could be any whole number between $15\!$ and $34\!$ (inclusive.)

There are a total of $34 - 15 + 1 = 20$ distinct whole numbers between $15$ and $34$ (inclusive.) Thus, the number of possible whole number values for $x$ would be $20$ .

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3 years ago

A circle has a center at 3,5 the point 3,8 is On the circle. What is the circumference of the circle to the nearest tenth of a u

Blizzard [7]

28.3 units
thats answer for your question

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3 years ago

At 5:00 p.m., the outside temperature was –9.2°C. By 10:00 p.m., the outside temperature had dropped 4.5°C. What was the outside

s344n2d4d5 [400]

It dropped by 4.5 means that we have to subtract 4.5 from 9.2

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