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3 years ago

7

Find the value of W please help me

1 answer:

Aleonysh [2.5K]3 years ago

5 0

Answer:

w=58 degrees

Step-by-step explanation:

The sum of all angles in a triangle should add up to 180 [ its a fact]

and the square-like shape inside the triangle represents the fact that that angle is 90 degrees.

So, we can make an equation

32+90+w=180

122+w=180 [if u add 32+90, u'll get 122]

w=180-122 [subtract 122 from both sides to isolate "w"]

w=58

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The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible length

Mademuasel [1]

Answer:

10.2 inches

Step-by-step explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

$a=12\ in, b=15\ in$

Applying the Pythagoras Theorem

Find the length of the hypotenuse

$c^{2}=a^{2} +b^{2}$

substitute

$c^{2}=12^{2} +15^{2}$

$c^{2}=369$

$c=19.2\ in$

Second case

The given lengths are one leg and the hypotenuse

so

$a=12\ in, c=15\ in$

Applying the Pythagoras Theorem

Find the length of the other leg

$b^{2}=c^{2} - a^{2}$

substitute

$b^{2}=15^{2} - 12^{2}$

$b^{2}=81$

$b=9\ in$

Find the difference between the two possible lengths of the third side of the triangle

so

$19.2-9=10.2\ in$

3 0

4 years ago

Read 2 more answers

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

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3 years ago

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Flura [38]

0.11 * 320 +43 =78.2
So B is right.

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4 years ago

Read 2 more answers

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dangina [55]

Answer:

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Step-by-step explanation:

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4 years ago

F(4) if f(x) = 3x - 1

pashok25 [27]

Answer:

f(4) = 11

Step-by-step explanation:

To evaluate f(4) substitute x = 4 into f(x)

f(4) = 3(4) - 1 = 12 - 1 = 11

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3 years ago