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1 year ago

Are the angle measurements in this triangle correct?

Mathematics

2 answers:

german1 year ago

8 0

OD

In a triangle there is 180 degrees

Mars2501 [29]1 year ago

5 0

Answer:

D

Step-by-step explanation:

The Angle Sum Property of a Triangle states that the internal angles of a triangle add up to 180°
Here, the sum is : 130 + 30 + 30 = 190°
Therefore, the angle measurements are not correct
The total angle measure of triangle should decrease by 10°
By making the top angle 120°, the sum becomes 180°
Hence, D is the correct option

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How do I solve this?

diamong [38]

$\bf 8m + 95 < -87m+5\implies 95m+95$

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2 years ago

A town's public works department has ordered sand to spread on roadways during the upcoming winter snows. The delivered sand for

ira [324]

Answer:

1256 cubic yards of sand.

Step-by-step explanation:

In this question we have to find the volume of cone formed by sand.

Height of the cone is = 36 feet

Radius of the cone = 60/2 =30 feet.

Now we know the formula of volume of cone v = π r² (h/3)

By putting the values of r and h we can get the volume of sand to spread.

Volume = π×(30)²×(36/3) = 3.14×900×12 feet³

= 33912 feet³

Now we will convert feet³ to cubic yards

Since 1 cubic feet = .037037 cubic yards

therefore 33912 cubic feet = 33912×.037 = 1256 cubic yards.

So the answer is 1256 cubic yards of sand has the department received.

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2 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(t) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

2 years ago

In the rhombus, m angle 1 = 18x, m angle 2 = x+y and m angle 3 = 30z. Find the value of x+y+z. The diagram is not drawn to scale

Ratling [72]

The value of x+y+z = 93

Explanation:

angle 1 = 18x

angle 2 = x+y

angle 3 = 30z

In rhombus, the diagonals intersect at 90°

Therefore,

angle 1 : 18x = 90

x = 90/18 = 5

angle 2: x+y = 90

5+y = 90

y = 85

angle 3: 30z = 90

z = 90/30 = 3

Value of x+y+z = 5+85+3 = 93

Thus, the value of x+y+z = 93

5 0

3 years ago

Number of College Faculty The number of faculty listed for a variety of private colleges that offer only bachelor’s degrees is l

lesya692 [45]

Answer: Number of College Faculty The number of faculty listed for a variety of private colleges which offer only bachelor’s degrees is listed below. Use these data to construct a frequency distribution with 7 classes, a histogram, a frequency polygon, and an ogive. Discuss the shape of this distribution. What proportion of schools have 180 or more faculty? 165 221 218 206 138 135 224 204 70 210 207 154 155 82 120 116 176 162 225 214 93 389 77 135 221 161 128 310 Source

8 0

2 years ago