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2 years ago

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After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets

and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x?
A. y + 300 = 2.5 (x + 100)
B. y - 300 = 4 (x - 100)
C. y - 300 = 2.5 (x - 100)
D. y + 300 = 4 (x + 100)

1 answer:

ZanzabumX [31]2 years ago

4 0

Answer:

B. y-300=4(x-100)

Step-by-step explanation:

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A triangle has interior angles measuring 36° and 112°. Which triangles are similar to this triangle? Select True or False for ea

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Hi there!

Since the interior measures of triangles added up always equals 180 degrees, the other interior angle of the triangle must be 32 degrees.

180 - 112 - 36 = 32

So, any triangle with interior measures that measure any angles of 36, 112, and 32 degrees are similar.

<span>triangle with interior angles measuring 36° and 32° - true
triangle with interior angles measuring 36° and 148° - false
triangle with interior angles measuring 32° and 112° - true
triangle with interior angles measuring 112° and 148 - </span>false

Hope this helps!

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A man is in a boat that is floating 175 feet from the base of a 200 foot cliff. What is the angle of depression between the clif

LUCKY_DIMON [66]

Answer:

The of depression between the cliff and the boat is 48.74 degrees.

Step-by-step explanation:

We have,

Height of the cliff is 200 foot

Distance of boat from the cliff is 175 feet

It is required to find the angle of depression between the cliff and the boat.

Here, 200 foot is perpendicular distance and 175 is base.

Using trigonometry :

$\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{200}{175}\\\\\theta=\tan^{-1}(1.14)\\\\\theta=48.74^{\circ}$

So, the of depression between the cliff and the boat is 48.74 degrees.

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Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at

Westkost [7]

Answer:

$\large\boxed{\large\boxed{3\times 10^8meters}}$

Explanation:

One of the applications of scientific notation is to make estimations rounding the whole part of the numbers, i.e. the digits before the decimal point, to the nearest integer, and adding the exponents of the powers of base 10.

Here, you must estimate this product of two numbers written is scientific notation:

$(3.21\times 10^3)(1.13\times 10^5)$

Then, for an estimation you round 3.21 to 3 and 1.13 to 1, then multiply 3 × 1 = 3. That will be the coefficient of your new power of 10.

The power or exponent will be the sum of the powers of the numbers that are being multiplied, i.e. 3 + 5 = 8.

And the result is $3\times 10^8$

The unit is meters, so you write your answer as: $3\times 10^8meters$

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2 years ago

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Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (-2,1), (-2,-3), (1,-1) , (

Greeley [361]

The given points are the vertices of the quadrilateral

$Q=\left\{(x,y)\mid-2\le x\le1,\dfrac{2x-5}3\le y\le\dfrac{4x+11}3\right\}$

By Green's theorem, the line integral is

$\displaystyle\int_C2xy\,\mathrm dx+xy^2\,\mathrm dy=\iint_Q\frac{\partial(xy^2)}{\partial x}-\frac{\partial(2xy)}{\partial y}\,\mathrm dA$

$=\displaystyle\int_{-2}^1\int_{(2x-5)/3}^{(4x+11)/3}y^2-2x\,\mathrm dy\,\mathrm dx=\boxed{61}$

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2 years ago

For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.

luda_lava [24]

Answer:

In the figure ∠ABO and ∠BCO have measures equal to 35°.

Step-by-step explanation:

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

For circle O, m CD=125° and m∠ABC = 55°

In the figure<____, (AOB, ABO, BOA) and <_____ (BCO, OBC,BOC) have measures equal to 35°

The picture in the attached figure

step 1

Find the measure of angle COB

we know that

$m\angle COB=arc\ CD$ ----> by central angle

we have

$arc\ CD=125^o$

therefore

$m\angle COB=125^o$

step 2

we know that

AB is a tangent to the circle O at point A

so

ABC and ABO are right triangles

In the right triangle ABC

Find the measure of angle BCA

Remember that

$m\angle BCA+m\angle\ ABC=90^o$ ---> by complementary angles in a right triangle

we have

$m\angle ABC=55^o$

substitute

$m\angle BCA+55^o=90^o$

$m\angle BCA=90^o-55^o=35^o\\$

step 3

In the triangle BCO

Find the measure of angle CBO

we know that

$m\angle CBO+m\angle COB+m\angle BCO=180^o$ ---> the sum of the interior angles in any triangle must be equal to 180 degrees

we have

$m\angle COB=125^o$

$m\angle BCO=m\angle BCA=35^o$ -----> have measure equal to 35 degrees

substitute

$m\angle CBO+125^o+35^o=180^o$

$m\angle CBO=180^o-160^o=20^o$

step 4

Find the measure of angle ABO

In the right triangle ABO

we know that

$m\angle ABC=m\angle CBO+m\angle ABO$ ----> by angle addition postulate

we have

$m\angle ABC=55^o$

$m\angle CBO=20^o$

substitute

$55^o=20^o+m\angle ABO$

$m\angle ABO=55^o-20^o=35^o$ ----> have measure equal to 35 degrees

therefore

In the figure ∠ABO and ∠BCO have measures equal to 35°.

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