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3 years ago

Circle O is shown below. The diagram is not drawn to scale. What is the measure of angle BAC?

Mathematics

2 answers:

mafiozo [28]3 years ago

5 0

56.5, since its (180 - 67)/2

allsm [11]3 years ago

4 0

Answer:

angle BAC = 56.5 degree

Step-by-step explanation:

In the given circle O, AO and BO are the radius of the circle

AO and BO are same

So the angle opposite of AO and BO are also same

Angle BAC = angle ABO

WE know the sum of angles in a triangle is 180 degree

Angle BAC + ABO + O = 180 degree

Angle O = 67 degree

angle ABO = angle BAC

BAC + BAC + 67 = 180

2BAC + 67= 180

Subtract 67 on both sides

2BAC = 113

Divide by 2 on both sides

BAC = 56.5

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Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard

Bumek [7]

Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

<em><u>The question is</u></em>

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

$V=LWH$

we have

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

5 0

3 years ago

10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x

ddd [48]

Rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

$\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}$

$\bf \cfrac{4\sqrt{28350x}}{189x}\qquad 
\begin{cases}
28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\
\qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\
\qquad 2\cdot (45)^2\cdot 7\\
\qquad 14\cdot 45^2
\end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x}
\\\\\\
\cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}$

4 0

4 years ago

If the quadrilateral below is a kite, find m

Debora [2.8K]

Answer:

49°

Step-by-step explanation:

7.5x-15+90=180

7.5x+75 =180

7.5x=105

x =14

so NPQ = ( 4×14 -7 ) = 49° this the answer

6 0

3 years ago

Read 2 more answers

Como calcular el 15% de 300

ArbitrLikvidat [17]

300 x .15 y te dará la respuesta

4 0

3 years ago

Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?

Serga [27]

Answer:

No, They are not equivalent

Step-by-step explanation:

The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.

The variable in this question is x.

To prove this, we equate both expressions:

$10x + 6 = 5x + 11$

$10x - 5x = 11 - 6\\\\\\5x = 5\\\\\\x = 1$

This shows that they have the same value ONLY when x is 1.

This is why Andre says that they are equivalent, but they are not.

8 0

3 years ago