Help me please!!!

Unit 8: Right Triangles & Trigonometry
Homework 1: Pythagorean Theorem
and its Converse

Answer:

The service tax paid was:

0.06 * RM180 = RM10.80

Step-by-step explanation:

To calculate the service tax paid by Mr. Lim, we need to first find the amount of the bill before the service tax was added.

Let's call the original bill amount "x".

After the 6% service tax was added, the total bill became x + (0.06 * x) = RM190.80.

So we can set up the equation:

x + (0.06 * x) = RM190.80

Expanding the right side of the equation:

x + (0.06 * x) = 190.80

Combining like terms:

1.06x = 190.80

Solving for x:

x = 180

So the original bill amount before the service tax was added was RM180.

The service tax paid was:

0.06 * RM180 = RM10.80

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.

A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:

Number of years = Number of months / 12

Number of years = 80 / 12

Number of years ≈ 6.67 years

So it would take approximately 6.67 years to pay off the vehicle through instalments.

To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:

Cash price = Total payment - Residual

Cash price = R303,007 - R80,180

Cash price = R222,827

So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:

Deposit = 0.1 x Cash price

Deposit = 0.1 x R222,827

Deposit = R22,282.70

So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.

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On solving the provided question we can say that  the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

A decagon in geometry is a decagon or not. A basic decagon has 144° of inner angles added up. A decagram is a self-intersecting regular decagon. A decagon is a polygon that has ten sides, ten internal angles, and ten vertices. A decagon or decagon is a shape that may be found in geometry. Furthermore, it has 10 horns and 10 horns. A 12-sided polygon is called a dodecagon. A regular polygon known as a regular dodecagon specifically has sides that are of the same length and angles that are uniformly spaced around a circle.

the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

'a = side length of the decagon

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The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and  a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.

Assuming the question is to graph the quadratic function y = 6x².

The x-intercept can be found by substituting y = 0

0 = 6x²

x = 0

x-intercept = (0,0)

y-intercept can be found by substituting x=0

y = 6 * 0

y = 0

y-intercept = (0,0)

The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).

The axis of symmetry is x = 0 i.e y-axis.

Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

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Answer:

where’s the options??

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3+2+7=12

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The required Length of the DC is 30.47 Units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

We have;

In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.

Then, In ΔABD

Sin∅ = BD/20

Sin(54°) = BD/20

BD = 0.809(20)

BD = 16.18

in ΔBDC

tan(28°) = BD/DC

DC = BD/tan(28°)

DC = 16.18/0.531

DC = 30.47 Units.

Thus, required Length of the DC is 30.47 Units.

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Answer:

Below

Step-by-step explanation:

Instead of x , I assume you want the angle For RIGHT triangles, remember

cos (angle ) = adjacent leg / hypotenuse

cos ( angle ) = 5 /12    

      angle = arccos( 5/12) = 65 °

You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.

Answer: A = 5

Step-by-step explanation:

So, we are given a function, with a point: we can substitute (x,y) from the coordinate into x and f(x) in the function. (recall that f(x) is just a fancy way of saying y).

so:

[tex]-1 = \frac{2(0) + 5}{0 - A}[/tex]

[tex]-1 = \frac{5}{-A}[/tex], (we can drop the negative sign from both sides here)

[tex]\frac{5}{5} = \frac{5}{A}[/tex], (recall 1 = x/x where x is literally any number)

hence we can see that A = 5

Ask questions in the comments if this doesn't make sense :)

<1 + <4 = 180 supplementary angles

180 - 95 = 85 degrees

Answer:

12

Step-by-step explanation:

First find the missing angle S

Three angles of a triangle add up to 180°

So m∠S + 81 + 42 = 180

m∠S + 123 = 180

m∠S = 180 - 123 = 57°

Using the law of sines which states that the ratio of each side to the opposite angle is the same for both sides we get

[tex]\dfrac{r}{\sin 42} = \dfrac{q}{\sin81} = \dfrac{15}{\sin 57}\\\\\sin 57 = 0.83867\\\\ \dfrac{15}{\sin 57}= \dfrac{15}{0.83867}\\\\= 17.88545\\\\[/tex]

Hence
[tex]\dfrac{r}{\sin 42} = 17.88545\\\\r = 17.88545 \times \sin 42\\\\r = 17.88545 \times 0.66913\\\\r = 11.9677\\\\r = 12 \textrm{ rounded to the nearest tenth}[/tex]

Answer:

  3 : 4

Step-by-step explanation:

You want to know the ratio of areas of a rectangle and square such that the rectangle is 50% longer and 50% narrower than the square.

A square that is 2 units on a side will be transformed to a rectangle that is 1.5×2 = 3 units long, and 0.5×2 = 1 unit wide.

The rectangle area is 3×1 = 3. The square area is 2×2 = 4.

The ratio of areas is ...

  rectangle area : square area = 3 : 4

The next term in the sequence of number 8, 4, 2, 1, 1/2 is 1/4

From the question, we have the following parameters that can be used in our computation:

The sequence of number 8, 4, 2, 1 -1/2

Express properly

The sequence of number 8, 4, 2, 1, 1/2

The above definitions imply that we simply divide the previous term by 2 to get the current term

Using the above as a guide,

Next term = (1/2)/2

Evaluate

Next term = 1/4

Hence, the next term is 1/4

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The number of pieces of candy that will be left on day 4 would be 2, 560 candies .

The number of pieces of candy left on day 8 would be 66 candies .

To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:

= Number of starting candy x ( 1 - Percent given away ) ^ number of days

= 100, 000 x ( 1 - 60 % ) ⁴

= 100, 000 x 40 % ⁴

= 2, 560 candies

On Day 8, this would be:

= 100, 000 x ( 1 - 60 % ) ⁸

= 66 candies

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The question is:

How many pieces of candy will be left on day 4? On day 8?

Answer:

----------------------------

Let the number of pizzas be x.

The average cost per pizza is:

If we need the average cost be at most $3.50, we need an inequality:

This is translated as:

The blanks are:

In the absence of trade between Glacier and Sequoia, Glacier would consume 8 million pairs of shorts and 48 million pounds of almonds, and Sequoia would consume 15 million pairs of shorts and 20 million pounds of almonds. However, if both countries decide to engage in trade, Glacier could specialize in producing shorts, using 1 million hours of labor per week, and Sequoia could specialize in producing almonds, using 1 million hours of labor per week. This specialization would result in Glacier producing 12 million pairs of shorts and Sequoia producing 24 million pounds of almonds. This would enable each country to consume more of both goods than they could produce in the absence of trade.

The lengths of the sides of the pentagon are;

12 Inches

13 inches

14 inches

15 inches

16 inches

The formula for the perimeter of a pentagon is expressed with the formula;

P = 5a

Given that the parameter are;

Since the sides are consecutive integers, then;

60 = 5(a)

expand the bracket

60= 5a

Make 'a' the subject

a = 12In

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Answer:

choice C.  y = -4/3x + 2

Step-by-step explanation:

slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.

m = -4/3  (negative reciprocal of 3/4)

Now use point-slope form to find the y-intercept (b):

y-2 = -4/3(x-0)

y = -4/3x + 2

Answer:

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.

Answer:

Step-by-step explanation:

6x4=24

another way of writing it is using addition

add 4, six times

so

4+4+4+4+4+4

6 boxes each has four cakes

Answer:

Step-by-step explanation:

To find the probability of rolling a 6 on two number cubes, we need to calculate the number of favorable outcomes (rolling a 6 on either or both of the cubes) divided by the total number of possible outcomes.

Each cube has 6 sides, numbered 1 through 6. So, the total number of possible outcomes when rolling two cubes is 6 x 6 = 36.

The number of favorable outcomes is 2, because there are two ways to roll a 6: either rolling a 6 on the first cube and a 6 on the second cube, or rolling a 6 on one of the cubes.

So, the probability of rolling a 6 is:

favorable outcomes / total outcomes = 2 / 36 = 1/18

Therefore, the probability of rolling a 6 on two number cubes is 1/18 or approximately 5.56%.

You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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The procedure for angle measurement by the protractor is mentioned below:

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To measure an angle using a protractor, follow these steps:

1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.

2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.

3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.

If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.

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The average of the three weighted points, A, B, and C, is (-1, 2.875).

A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.

weighted average = (w1 × x1 + w2 × x2 + w3 × x3) / (w1 + w2 + w3),

where wi is the weight of the ith point, and xi is the coordinate of the ith point.

Substituting the given values, we get:

weighted average = (1 × (-8, 5) + 3 × (8, 2) + 4 × (5, 4)) / (1 + 3 + 4)

= (-8, 5 + 3 × 2 + 4 × 4) / 8

= (-8, 23) / 8

= (-1, 2.875)

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Jenny's average jogging speed in the distance covered is; 10 miles/hr

Let x miles/hr be the speed that Jenny walks at

Then, 2x miles/hr is the speed that Jenny runs at

She jogs for  9.5 miles

2x miles = 1 hours

9.5 miles = a hours

a = 9.5/2x hours

She walks for 2.5 miles

x miles = 1 hour

2.5 miles = b

b = 2.5/x hours

Thus;

(9.5/2x) + (2.5)/x = 1.45

Multiply through by 2x to get;

9.5 + 5 = 2.9x

14.5/2.9 = x

x = 5 miles/hr

Jogging speed = 2 * 5 = 10 miles/hr

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Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

Answer:

$105

Step-by-step explanation:

Let x be the amount of money Carolina has in her checking account. Then, her savings account has x + $30. The total amount of money in both accounts is $180, so we can write the equation:

x + (x + $30) = $180

Expanding the left-hand side:

2x + $30 = $180

Subtracting $30 from both sides:

2x = $150

Dividing both sides by 2:

x = $75

Therefore, Carolina has $75 in her checking account and $75 + $30 = $105 in her savings account.

Answer:

Step-by-step explanation:

The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.

Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.

The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.

Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.

The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.

C. Only on the back of the check

A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.

The amount of check Elmo wrote Kris = $601.73

The amount Kris deposited into her checking account = The check Elmo issued to her

The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified  check is to be deposited into the checking account.

The correct option is therefore option C.

C. Only on the back of the check

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