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3 years ago

Given the following diagram, enter the required information.

Mathematics

2 answers:

devlian [24]3 years ago

8 0

CXB = 40 degrees

I am not positive but from what I have looked up this is the answer.

vitfil [10]3 years ago

3 0

we have

m∠DXB= $70\°\ 15'\ 12''$

m∠DXC= $30\°\ 30'\ 20''$

we know that

m∠DXB=m∠DXC+m∠CXB

m∠CXB=m∠DXB-m∠DXC

remember that

$1\°=60'$

$1'=60''$

m∠DXB= $70\°\ 15'\ 12''$

convert one grade to minutes

m∠DXB= $69\°\ 75'\ 12''$

convert one minute to seconds

m∠DXB= $69\°\ 74'\ 72''$

Find the value of m∠CXB

m∠CXB= $(69\°\ 74'\ 72'')-(30\°\ 30'\ 20'')=39\°\ 44'\ 52''$

therefore

the answer is

the measure of angle CXB is equal to $39\°\ 44'\ 52''$

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HELP PLEASE ! find the area of the shape below

White raven [17]

Answer:

area = 202.5 yd²

Step-by-step explanation:

area = (15 x 12 ) + (3)(15)(0.5)

area = 180 + 22.5 = 202.5 yd²

8 0

3 years ago

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1. The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Enter

Elodia [21]

Answers:
1. 8 m
2. 17 m
3. 7 cm
4. 2 s

Explanations:

1. Let x = length of the base
x + 6 = height of the base

Then, the area of the triangle is given by

(Area) = (1/2)(base)(height)
56 = (1/2)(x)(x + 6)
56 = (1/2)(x²  + 6x)

Using the symmetric property of equations, we can interchange both sides of equations so that

(1/2)(x²  + 6x) = 56

Multiplying both sides by 2, we have

x² + 6x = 112

The right side should be 0. So, by subtracting both sides by 112, we have

x² + 6x - 112 = 112 - 112
x² + 6x - 112 = 0

By factoring, x² + 6x - 112 = (x - 8)(x + 14). So, the previous equation becomes

(x - 8)(x +14) = 0

So, either

x - 8 = 0 or x + 14 = 0

Thus, x = 8 or x = -14. However, since x represents the length of the base and the length is always positive, it cannot be negative. Hence, x = 8. Therefore, the length of the base is 8 cm.

2. Let x = length of increase in both length and width of the rectangular garden

Then,

14 + x = length of the new rectangular garden
12 + x = width of the new rectangular garden

So,

(Area of the new garden) = (length of the new garden)(width of the new garden)

255 = (14 + x)(12 + x) (1)

Note that

(14 + x)(12 + x) = (x + 14)(x + 12)
= x(x + 14) + 12(x + 14)
= x² + 14x + 12x + 168
= x² + 26x + 168

So, the equation (1) becomes

255 = x² + 26x + 168

By symmetric property of equations, we can interchange the side of the previous equation so that

x² + 26x + 168 = 255

To make the right side becomes 0, we subtract both sides by 255:

x² + 26x + 168 - 255 = 255 - 255
x² + 26x - 87 = 0

To solve the preceding equation, we use the quadratic formula.

First, we let

a = numerical coefficient of x² = 1

Note: if the numerical coefficient is hidden, it is automatically = 1.

b = numerical coefficient of x = 26
c = constant term = - 87

Then, using the quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-26 \pm \sqrt{26^2 - 4(1)(-87)} }{2(1)} 
\newline x = \frac{-26 \pm \sqrt{1,024} }{2}
\newline
\newline x = \frac{-26 \pm 32 }{2}$

So,

$x = \frac{-26 + 32 }{2} \text{ or } x = \frac{-26 - 32 }{2}
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\newline \boxed{ x = 3 \text{ or } x = -29}$

Since x represents the amount of increase, x should be positive.

Hence x = 3.

Therefore, the length of the new garden is given by

14 + x = 14 + 3 = 17 m.

3. The area of the shaded region is given by

(Area of shaded region) = π(outer radius)² - π(inner radius)²
= π(2x)² - π6²
= π(4x² - 36)

Since the area of the shaded region is 160π square centimeters,

π(4x² - 36) = 160π

Dividing both sides by π, we have

4x² - 36 = 160

Note that this equation involves only x² and constants. In these types of equation we get rid of the constant term so that one side of the equation involves only x² so that we can solve the equation by getting the square root of both sides of the equation.

Adding both sides of the equation by 36, we have

4x² - 36 + 36 = 160 + 36
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x² = 49

Taking the square root of both sides, we have

$x = \pm 7$

Note: If we take the square root of both sides, we need to add the plus minus sign $(\pm)$ because equations involving x² always have 2 solutions.

So, x = 7 or x = -7.

But, x cannot be -7 because 2x represents the length of the outer radius and so x should be positive.

Hence x = 7 cm

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h(t) = 0 (1)

Moreover, since $v_0 = 27$ and $h_0 = 10$ ,

h(t) = -16t² + 27t + 10 (2)

Since the right side of the equations (1) and (2) are both equal to h(t), we can have

-16t² + 27t + 10 = 0

To solve this equation, we'll use the quadratic formula.

Note: If the right side of a quadratic equation is hard to factor into binomials, it is practical to solve the equation by quadratic formula.

First, we let

a = numerical coefficient of t² = -16
b = numerical coefficient of t = 27
c = constant term = 10

Then, using the quadratic formula

$t = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-27 \pm \sqrt{27^2 - 4(-16)(10)} }{2(-16)} \newline t = \frac{-27 \pm \sqrt{1,369} }{-32} \newline \newline t = \frac{-27 \pm 37 }{32}$

So,

$t = \frac{-27 + 37 }{-32} \text{ or } t = \frac{-27 - 37 }{-32} \newline t = \frac{-10}{32} \text{ or } t = \frac{-64 }{-32} \newline \boxed{ t = -0.3125 \text{ or } t = 2}$

Since t represents the amount of time, t should be positive.

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3 years ago

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Sergio039 [100]

Answer:

E=x

or 110= x ( opposite angles of parallelogram are congurent)

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110+D =180

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fiasKO [112]

The reaction is missing and it's ;

N2H4 + H2 ---> 2NH3

It asks for the total pressure too.

Answer:

A) Rate of change for NH3 = 152 torr/h

B) The total pressure in the vessel will remain the same.

Step-by-step explanation:

N2H4 + H2 ---> 2NH3

1 mole of N2H4 yields 2 moles of NH3.

From the question, the rate given for N2H4 is 76 torr/h.

Thus, The rate of change for NH3 will be = 2 x 76 = 152 torr/h

Now, on the reaction side, 1 mole of N2H4 reacts with 1 mole of H2. So we have 2 moles on the left hand side.

While on the product side, 2 moles of NH3 are produced.

So the total pressure will remain the same because for every 2 moles on the reaction side, 2 moles are gotten on the product side.

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Jose earned 50 points in a video game. He lost 40 points, earned 87 points, then lost 30 more pints. Write and evaluate an expre

Aneli [31]

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hope i helped

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3 years ago