Basic geometric shapes unit test part 2
Explain why m angle 4 is equal to the sun of the measure of the two nonadjancent interior angels

The simplification of the equation (5x²+x-3)-(-2x³+4) will be 2x³ + 5x² + x - 7.

Simplification refers to the technique of lowering an expression, equation, or mathematical problem to a less difficult or extra concise form.

It includes applying mathematical rules and operations to remove unnecessary phrases, combine like phrases, and decrease complexity.

To simplify the expression (5x² + x - 3) - (-2x³ + four), we will distribute the bad sign inside the parentheses:

(5x² + x - 3) - (-2x³ + 4) = 5x² + x - 3 + 2x³ - 4

5x² + x - 3 + 2x³ - 4 = 2x³ + 5x² + x - 7

Therefore, the simplified form of the expression is 2x³ + 5x² + x - 7.

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Answer: D, C, 18

Step-by-step explanation:

The first one is trigonometry. It takes a long time to calculate, but sin20 degrees=0.342, and 15/43.8 is about 0.342

From that, we get the answer as D.

The second one is a bit of guesswork and logic

Notice that the angle on the left is 24

The angle on the right is 45

24 is about one-half of 45

51/3=17

So the triangle on the left has sides x, 24, and approx. 17.

17^2=289 and 24^2=576

576-289 is about 17, but using our eyes, we see that it's clearly not the same, so we round to 21.9 or C (risky, but don't know how to solve, sorry)

Last one:

Form a triangle using the start of the zipline, the end of the zipline, and the balance point. This forms a right triangle with angles 72, 90, and (2)

The triangles angle add up to 180, and 180-90=90 and 90-72=18 so (2)=18.

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

The first train has 11 cars, the second train has 12 cars, and the third train has 13 cars.

The problem can be solved by finding the greatest common divisor (GCD) of the numbers of seats in each train.

Find the GCD of 418, 456, and 494. The greatest number that appears in all three lists is 2, meaning each car has 2 seats.

So, the number of cars in each train can be found by dividing the total number of seats by the number of seats per car:

First train:

= 418 seats / 38 seats per car

= 11 cars

Second train:

= 456 seats / 38 seats per car

= 12 cars

Third train:

= 494 seats / 38 seats per car

= 13 cars

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We can answer the questions having in mind the concepts of speed and distance, and using that knowledge to make the necessary calculations, as below.

A truck moving at a constant speed of 90 km/h will:

Let's briefly explain the concepts of speed and distance and how they were used in the answers provided. Speed is a measure of how quickly an object moves. It is defined as the distance traveled per unit of time. In the given context, speed is typically expressed in kilometers per hour (km/h) or meters per second (m/s).

Distance is the length of the path traveled by an object. It represents the total amount of ground covered by an object in its motion. In the given context, distance is typically expressed in kilometers (km) or meters (m).

For example, the first question involves calculating the distance traveled by a truck at a constant speed of 90 km/h. By multiplying the speed by the time, the distance covered can be determined. For example, in 2 hours, the truck covers a distance of 180 km.

In the second question, the task is to find the required speed of a race car to cover a specific distance in a given time. By dividing the distance by the time, the speed can be calculated. For instance, to cover 50 km in a quarter of an hour (15 minutes), the race car needs to travel at a speed of 200 km/h.

The third question asks for the distance covered by a bicycle traveling at a given speed for a specific duration. By multiplying the speed by the time, the distance can be determined. For example, a bicycle traveling at 15 km/h for 45 minutes covers a distance of 11.25 kilometers.

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16 cubic meters of cement is needed to build the monument.

The figure has a cuboid and two triangular prisms.

Volume of cuboid is length times width times height.

Volume = 4×4×0.5

=8 cubic meters.

Volume of prism =Bh

B is area of base.

Base edge is pf 2m.

Area of base is 2×2=4 m

Now Volume =4×1 where 1 is height of the prism.

Volume =4 cubic meters.

As there are two prisms , the volume is 2×8 cubic meters.

Total volume =8+8=16 cubic meters.

Hence, 16 cubic meters of cement is needed to build the monument.

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Answer:

Here's a table showing the possible numbers of positive real, negative real, and complex zeros of the given polynomial function:

Number of Positive Real Zeros Number of Negative Real Zeros Number of Complex Zeros

0 3 2

In this case, the polynomial function f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3 has no positive real zeros, three negative real zeros, and two complex zeros.

Step-by-step explanation:

GIVE ME BRAINLIEST PLS

Answer:

Thank you for saying I'm awesome I appreciate it :)

Step-by-step explanation:

The missing symbol in the equation 9x ____ = 3/2 + 3/2 + 3/2 is the equal sign =. The equation can be simplified to 9x = 9/2, which means that x = 1/2.

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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Answer:

Step-by-step explanation:

In 30, 60, and 90 triangles, it includes sides with ratios 1, 2x, and xsqrt3 with 2x reflective of 90, xsqrt3 of 60, and 1 of 30.
So if 2x = 6, then x = 3 so 3sqrt3 = 5.19. Using the Pythagorean theorem we find that the last length is 3.
If xsqrt3 = 3, then x = sqrt3, angle reflective of 90 is 2sqrt3.

Answer:

4 sides

It is a Quadrilateral

The percentage of the seats that is filled is 39%.

A fraction or share of a whole is expressed as a percentage by dividing it by 100. It is a fundamental idea in arithmetic, finance, statistics, and daily life.

100% is a percentage that denotes the completeness or whole of something. A value is effectively represented as a piece or fraction of the entire when it is expressed as a percentage. "%" is the symbol for percentage.

We can see that the number of the filled seats would be;

1700 -  1037

= 663 seats

Percentage of the filled seats = 663/1700 * 100/1

= 39%

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Missing parts;

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

The present value of the tax benefits from depreciation is approximately $14,550.43.

Under straight-line depreciation, the asset will depreciate evenly over its useful life. In this case, the depreciation expense for each year can be calculated as:

(Initial cost - Salvage value) / Useful life

= ($100,000 - $5,000) / 10

= $9,500 per year

This annual depreciation will provide a tax shield, as it reduces the firm's taxable income. The value of this tax shield each year is:

Depreciation expense * Tax rate

= $9,500 * 21%

= $1,995

This tax shield is received each year for the next 10 years. To calculate the present value of this stream of tax shields, we use the formula for the present value of an annuity:

PV = C * (1 - (1 + r)^-n) / r

where:

C = annual cash flow (our tax shield),

r = discount rate (the firm's cost of capital), and

n = number of periods (the depreciable life of the asset).

Substituting the values into the formula:

PV = $1,995 * (1 - (1 + 14%)^-10) / 14%

= $1,995 * (1 - 0.2706) / 14%

= $1,995 * 0.7294 / 14%

= $14,550.43

So the present value of the tax benefits from depreciation is approximately $14,550.43.

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Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Stephanie has the longer room.

Here, we have,

given that,

Stephanie and Amanda measure the lengths of their room.

Stephanie's room is 4.4 m long

and Amanda's is 4410 mm long.

now, we need to find that who has the longer room.

we have,

we know that,

1000mm = 1m

so, as 1 m = 1000mm

then, 4.4m = 4400mm

now, we get

Stephanie's room is 4400mm long

and Amanda's is 4410 mm long

so, we get,

that, 4400> 4100

so, Stephanie has the longer room.

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The measure of the two line segments are 36 and 27.

We have,

The secant and tangent rule on a circle.

DC is the tangent and ABC is the secant.

Then,

DC² = (AB + BC) x BC

Now,

Substituting.

(4x + 11)² = (27 + 5x - 11) x (5x - 11)

To solve the given equation (4x + 11)² = (27 + 5x - 11) x (5x - 11) for x, we will expand both sides of the equation and then simplify:

Expanding the left side:

(4x + 11)² = (4x + 11)(4x + 11) = 16x² + 44x + 44x + 121 = 16x² + 88x + 121

Expanding the right side:

(27 + 5x - 11) x (5x - 11) = (16 + 5x)(5x - 11) = 80x² - 176x + 75x - 165 = 80x² - 101x - 165

Setting the left and right sides equal to each other:

16x² + 88x + 121 = 80x² - 101x - 165

Rearranging the equation:

0 = 80x² - 16x² - 101x - 88x - 165 - 121

0 = 64x² - 189x - 286

Now, we have a quadratic equation.

We can solve it by factoring, completing the square, or using the quadratic formula.

Let's use the quadratic formula to find the solutions for x:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 64, b = -189, and c = -286.

Substituting these values into the quadratic formula:

x = (-(-189) ± √((-189)² - 4(64)(-286))) / (2(64))

x = (189 ± √(35721 + 73216)) / 128

x = (189 ± √108937) / 128

Since the discriminant (b² - 4ac) is positive, we have two distinct real solutions. Evaluating the square root:

x = (189 ± 329) / 128

We have two possible solutions for x:

x₁ = (189 + 329) / 128 = 518 / 128 = 4.047 = 4

x₂ = (189 - 329) / 128 = -140 / 128 = -1.094 (rejected)

Now,

The line segments are:

AC = 27 + 5x - 11 = 27 + 5 x 4 - 11 = 27 + 20 - 11 = 36

CD = 4x + 11 = 4 x 4 + 11 = 16 + 11 = 27

Thus,

The measure of the two line segments are 36 and 27.

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Answer:

Let's assume Tanner has "x" pants.

Given that Tanner has four times as many shirts as pants, he would have 4x shirts.

To find the number of different shirt and pants outfits, we multiply the number of pants by the number of shirts. In this case, it would be x * 4x = 4x^2.

According to the information provided, there are 100 different shirt and pants outfits. So we can set up the equation:

4x^2 = 100

To solve for x, we divide both sides of the equation by 4:

x^2 = 25

Taking the square root of both sides, we get:

x = ±5

Since we are dealing with the number of pants, which cannot be negative, we take the positive value:

x = 5

Therefore, Tanner has 5 pants.

Answer: 52

Step-by-step explanation:

Your question isn't complete. If Abby won 52 tickets, then she won 52 tickets. Please check your question and re type it. :)

Answer: 52-32=20

20 is naswer

Step-by-step explanation:

The correct option is target population.

In this situation, the 65 students would be considered Maria's sample.

A sample refers to a subset of individuals or elements that are selected from a larger population for the purpose of conducting a study or research.

The sample is typically chosen in a way that is representative of the larger population, allowing researchers to make inferences and draw conclusions about the population based on the data collected from the sample.

In Maria's case, she randomly selected 65 students from the list of students at Central Piedmont Community College.

These 65 students represent her sample, which she will ask to fill out her questionnaire.

By collecting data from this sample, Maria aims to gain insights into how students at the college balance academics and family commitments.

It's worth noting that the term "target population" refers to the entire group of individuals or elements that a researcher wants to study and make inferences about.

In this case, the target population would be all students at Central Piedmont Community College.

The sample (65 students) is drawn from this larger target population to represent it.

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Step-by-step explanation:

To determine how many weeks it took for Tom to have 15 cards collected, we need more information about the growth rate of his collection. The given information states that by week 5, Tom had collected 12 cards, but it doesn't provide details about the rate of card collection.

If we assume that Tom's card collection grows at a constant rate, we can calculate the rate of card collection per week using the given information. By week 5, Tom had collected 12 cards. This means that on average, he collected 12/5 = 2.4 cards per week up to that point.

Using this average rate, we can estimate how many weeks it would take for Tom to have 15 cards collected. We'll divide the total number of cards (15) by the average rate of card collection (2.4 cards per week):

15 cards / 2.4 cards per week ≈ 6.25 weeks.

Therefore, it would take approximately 6.25 weeks (or 6 weeks and 3 days) for Tom to have 15 cards collected, assuming a constant growth rate.

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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If f is a one-to-one function and g is the inverse of f, then (f°g)(x) = x and (g°f)(x) = x.

We have,

(f°g)(x) means applying the function f to the result of applying the function g to x.

Since g is the inverse of f, applying f to the result of applying g to x will give us back x.

(g°f)(x) means applying the function g to the result of applying the function f to x.

Since g is the inverse of f, applying g to the result of applying f to x will also give us back x.

In both cases, the compositions result in the original input value x.

Thus,

If f is a one-to-one function and g is the inverse of f, then (f°g)(x) = x and (g°f)(x) = x.

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The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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Sebastian's basis in the two assets are: $42,389 and $66,611

The computation of the Sebastian's basis in these two assets is shown below:

= Market value of the first piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($76300 ÷ $(76300 + 119900)) × $109,000

= $42,389

= Market value of the second piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($119,900 ÷ $(76300 + 119900)) × $109,000

= $66,611

The Total market value of two pieces of equipment

= $(76300 + 119900)

= $196,200

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Answer:

  3. see attached. Domain x > 1; Range all reals

  4. √15 ≈ 3.87298

Step-by-step explanation:

You want a graph and the domain and range of f(x) = 3log(2(x-1)) +4, and the value of (3x)^(x/10) when x satisfies 2^x -2^(x-1) = 16.

The function f(x) = 3log(2(x -1)) +4 represents horizontal and vertical scaling, as well as horizontal and vertical translation. The values in each case are different, so we can describe their effect by referencing their value.

1 — a horizontal right shift of the log function by 1 unit

2 — a horizontal compression of the log function by a factor of 2

3 — a vertical expansion of the log function by a factor of 3

4 — a vertical shift upward of the log function by 4 units.

Some points that you might graph for the parent log function would be (0.1, -1), (1, 0), (10, 1). The effect of these shifts is to transform them to ...

  (x, y) ⇒ (x/2 +1, 3y +4)

  (0.1, -1) ⇒ (1.05, 1)

  (1, 0) ⇒ (1.5, 4)

  (10, 1) ⇒ (6, 7)

The right shift 1 unit moves the domain to x > 1.

The range continues to be all real numbers.

We can solve the given equation as follows:

   2^x -2^(x -1) = 16

   2^(x-1) · (2 -1) = 16

  2^(x -1) = 2^4

  x -1 = 4

  x = 5

Then the expression you want the value of is ...

  (3·5)^(5/10) = 15^(1/2) = √15 ≈ 3.87298

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