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2 years ago

8

Find the measure of the missing angles.

2 answers:

Alekssandra [29.7K]2 years ago

8 0

Answer: B= 20 degrees
C= 160 degrees

Why? B is the angle across from 20 and that means they are equal. To find C you do 180-20 to get your answer

Hope this helps :D

Masteriza [31]2 years ago

6 0

Answer:

b = 20, c = 160

Step-by-step explanation:

b and 20 degrees are vertical angles, so they are equal.

b (20 degrees) and c are on a line together, so they add up to 180. 180 - 20 = 160 degrees

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What is the range of possible values for x?

Talja [164]

The minimum value for 2x is 0
<span>the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC </span>
<span>base AB = 52 and vertical angle 2x + 34° </span>

<span>For the sine law </span>
<span>(sin 2x)/22 = (sin ADB)/AB </span>
<span>(sin 34°)/30 = (sin BDC)/BC </span>

<span>is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from </span>
<span>(sin ADC)/AB = (sin BDC)/BC </span>

<span>it follows </span>
<span>(sin 2x)/22 = (sin 34°)/30 </span>

<span>sin 2x = 22 (sin 34°)/30 </span>

<span>2x = asin(22 (sin 34°)/30) ≈ 24.2° </span>

<span>x = 0.5 asin(22 (sin 34°)/30) ≈ 12.1° </span>

<span>0 < x < 12.1°</span>

7 0

3 years ago

Let a= x2 +4 rewrite the following equation in terms of a and set it equal to zero. (X2 + 4)2 + 32 = 12x2 + 48 in the resulting

Alex73 [517]

$Answer: \\ {( {x}^{2} + 4) }^{2} + 32 = 12 {x}^{2} + 48 \\ \Leftrightarrow {a}^{2} + 32 = 12( {x}^{2} + 4) \\ \Leftrightarrow {a}^{2} + 32 = 12a \\ \Leftrightarrow {a}^{2} - 12a + 32 = 0 \\ \Rightarrow Coefficients:1, \: -12. \: Constant:a$

5 0

3 years ago

Cristina uses a ruler to measure the length of her math textbook.she says that the book is 4/10 meter long.Ise her measurement i

NNADVOKAT [17]

The simplest form iz 2/5

3 0

3 years ago

Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.

Setler79 [48]

Answer:

Therefore values of a and b are

$a=3\ and\ b = 2$

Step-by-step explanation:

Rewrite $x^{2}-6x+7=0$ in the form

$(x-a)^{2}=b$

where a and b are integers,

To Find:

a = ?

b = ?

Solution:

$x^{2}-6x+7=0$ ..............Given

Which can be written as

$x^{2}-6x=-7$

$(\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9$

Adding half coefficient of X square on both the side we get

$x^{2}-6x+9=-7+9=2$ ...................( 1 )

By identity we have (A - B)² =A² - 2AB + B²

Therefore,

$x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}$

Substituting in equation 1 we get

$(x-3)^{2}=2$

Which is in the form of

$(x-a)^{2}=b$

On comparing we get

a = 3 and b = 2

Therefore values of a and b are

$a=3\ and\ b = 2$

4 0

3 years ago

A brand of grape juice that's is 25% grape juice is mixed with another brand that is 75% grape juice. The result is 7 gallons of

garri49 [273]

Answer:

5.6 gallons.

Step-by-step explanation:

If we take x gallons of 25% grape juice then it will contain $\frac{x}{4}$ gallons of pure grape juice.

Again, if we take y gallons of 75% grape juice then it will contain $\frac{3y}{4}$ gallons of pure grape juice.

If we mix them then the total volume will become x + y = 7 gallons ...... (1)

Again the mixture will become 35% juice.

So, $\frac{\frac{x}{4} +\frac{3y}{4} }{x+y} =\frac{35}{100}$

⇒ 0.25x + 0.75y = 0.35x + 0.35y

⇒0.1x = 0.4y

⇒x = 4y........ (2)

Now, solving equations (1) and (2) we get, 5y = 7, ⇒ y = 1.4 gallons

Hence, x = 4y = 5.6 gallons

Therefore, the 25% grape juice was mixed by 5.6 gallons. (Answer)

4 0

2 years ago