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Please help me with #25 and 26​

Answer:

X=68m

Step-by-step explanation:

X²=40²+55²

X²=1600+3025

X²=4625

X=(4625)½

X=68m.

Answer:

f(10) = 3(10) - 5 = 30 - 5 = 25

f(-10) = 3(-10) - 5 = -30 - 5 = -35

The equation that shows the Pythagorean identity is true for θ = 270° and is in the form sin²θ + cos²θ = 1 is option  B. 0² + (-1)² = 1

The Pythagorean identity is a fundamental trigonometric identity that relates the sine and cosine functions. It states that for any angle θ, the sum of the squares of the sine and cosine of that angle is equal to 1: sin²θ + cos²θ = 1.

We are given θ = 270° and we need to select the equation that satisfies the Pythagorean identity in the given form.

Let's evaluate each option:

A. 0² + 1² = 1

In this case, sin²θ = 0² = 0 and cos²θ = 1² = 1. Adding them together, we get 0 + 1 = 1, which satisfies the Pythagorean identity.

B. 0² + (−1)² = 1

Here, sin²θ = 0² = 0 and cos²θ = (−1)² = 1. Adding them, we have 0 + 1 = 1, which satisfies the Pythagorean identity.

C. (−1)² + 0² - 1

In this equation, sin²θ = (−1)² = 1 and co

s²θ = 0² = 0. However, the equation does not satisfy the Pythagorean identity because 1 + 0 - 1 ≠ 1.

D. 1² + 0² = 1

For this option, sin²θ = 1² = 1 and cos²θ = 0² = 0. Adding them together, we get 1 + 0 = 1, which satisfies the Pythagorean identity.

Based on our evaluation, options A and B both satisfy the Pythagorean identity for θ = 270°. Therefore, either A or B can be selected as the correct equation.The correct answer is  b.

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The Question was Incomplete, Find the full content below :

Which equation shows that the Pythagorean identity is true for θ = 270°?

Select the equation that is in the form sin²θ+ cos²θ = 1.

A. 0² + 1² = 1

B. 0² + (−1)² = 1

C. (-1)² + 0² - 1

D. 1² + 0² = 1

The inverse of the equation is determined as [tex]y = \log_{6}(-3x)[/tex].

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

[tex]-3x = 6^y[/tex]

Take the logarithm of both sides of the equation with base -6:

[tex]\log_{6}(-3x) = y[/tex]

Finally, replace y with x to obtain the inverse equation as follows;

[tex]y = \log_{6}(-3x)[/tex]

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Given: Deposit = $120, Annual Interest = 7%, Compounded Annually, No additional deposits or withdrawals. After 8 years we need to calculate the balance of this account. To solve this question, we use the formula for compound interest. So, the balance of the account after 8 years will be $219.11.

Compound Interest FormulaThe compound interest formula is given as follows; A = P (1 + r/n)nt, Where, A is the amount earned after time t, P is the principal amount,n is the number of times interest is compounded every year,r is the annual interest rate,t is the time the money is invested in years.

Substituting the values in the given formula; P = $120, r = 7%, n = 1 (compounded Annually), t = 8 years

A = 120(1 + 0.07/1)^(1×8)A = $219.11. Therefore, the balance of the account after 8 years will be $219.11.

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Answer:

A) Line ZM is tangent to circle P.

Answer:

Θ = 23.9°

Step-by-step explanation:

Use inverse tangent in a calculator.

tan Θ = 23/52

tan Θ = 0.4423

tan^-1 0.4423 = 23.9°

Answer:

x = 5

Step-by-step explanation:

3x + 7 = 22 <-- Subtract 7 on both sides

3x = 15 <-- Divide both sides by 3 to isolate x

x = 5

The value of x is:

x = 5

Work/explanation:

The objective of this problem is to solve 3x + 7 = 22 by isolating x.

I begin by subtracting 7 from each side:

3x = 22 - 7

3x = 15

Next, I divide each side by 3:

x = 5

Hence, the value of x is 5.

Answer: (-5, -7)

Step-by-step explanation: To find the intersection of two functions, you need to set them equal to each other and solve for x.

In this case, we have:

2x + 3 = -4x - 27

Adding 4x to both sides, we get:

6x + 3 = -27

Subtracting 3 from both sides, we get:

6x = -30

Dividing both sides by 6, we get:

x = -5

Now that we have the value of x, we can find the corresponding value of y by plugging it into either of the original equations. Let's use f(x) = 2x + 3:

f(-5) = 2(-5) + 3 = -7

Therefore, the intersection of the two functions is (-5, -7).

Answer:

2/9

Step-by-step explanation:

Coin

A coin has 1 side heads and 1 side tails.

total number of possible outcomes = 2

desired outcome: heads

number of desired outcomes = 1

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(heads) = 1/2

Spinner

The spinner has 9 sections of equal size.

possible outcomes: the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9

total number of possible outcomes = 9

desired outcome: even number

number of desired outcomes = 4

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(even number) = 4/9

Combined probability

The coin and spinner are independent events. The overall probability of independent events is the product of the individual probabilities.

p(heads then even) = 1/2 × 4/9 = 4/18 = 2/9

Answer: 2/9

Answer:

[tex]\huge\boxed{\sf 44\ boys}[/tex]

Step-by-step explanation:

= Length × Width

Length = 32 m

Width = 11 m

Area of school room:

= Length × Width

= 32 × 11

= 352 m²

= 352 / 8

[tex]\rule[225]{225}{2}[/tex]

Janet's savings in January is $800

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Represent Mary's savings by x and Janet's savings by y

7/4 = x/y

40/100 × x = 40x/100 = 2x/5

New savings for Mary =

x -2x/5 = 5x - 2x)/5 = 3x/5

50/100 × y = y/2

New savings for Janet =

y + y/2 = 3y/2

3y/2 + 3x/5 = 2040

15y + 6x = 20400

7y = 4x

y = 4/7x

Substitute (4/7)x for y

15( 4/7) x + 6x = 20400

(60/7 )x + 6x = 20400

60x + 42x = 142800

102x = 142800

x = 142800/102

x = $ 1400

y = 4/7 × 1400

y = $800

Therefore, the savings for Janet in January is $800.

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Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Jolly Goods Limited may not be able to accept the order for 2,000 ornaments due to the limited capacity of the finishing department. While the cutting and assembling departments have the capacity to fulfill the order by working at 100% capacity, the finishing department cannot complete the required work within the given deadline. The company as a whole is operating at 85% of capacity, which suggests that the finishing department is already working close to its maximum capacity.

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Answer:

There are 14 blue marbles in the bag.

Step-by-step explanation:

Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.

First, we need to find the total number of parts in the ratio. That's 12+5+2=19.

Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:

2/19 (x + x + 112 + blue) = blue

Simplifying this equation, we get:

2x + 224 = 17blue

Now we can solve for blue:

blue = (2x + 224)/17

We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:

blue = (2(3) + 224)/17 = 14

Therefore, there are 14 blue marbles in the bag.

a) The force in the coupling between the first carriage and the locomotive can be found by analyzing the net force acting on the train. It is determined to be 100 N.

b) The force in the coupling between the first carriage and the locomotive is a tension force.

a) To find the force in the coupling between the first carriage and the locomotive, we need to analyze the forces acting on the train.

The forces acting on the train are:

The driving force applied by the locomotive: 700 N

The resistance force of each carriage: 400 N (assuming equal resistance forces for both carriages)

The force in the coupling between the first carriage and the locomotive (unknown)

Since the train comes to rest, the net force acting on the train must be zero. We can set up the equation for the net force as:

Net force = Driving force - Resistance force - Force in coupling = 0

Substituting the given values:

700 N - 2(400 N) - Force in coupling = 0

Simplifying the equation:

700 N - 800 N - Force in coupling = 0

-100 N - Force in coupling = 0

Therefore, the force in the coupling between the first carriage and the locomotive is 100 N (opposite in direction to the driving force).

b) The force in the coupling between the first carriage and the locomotive is a tension force. Tension forces act along a string, cable, or any stretched connection. In this case, the coupling acts as a connection between the locomotive and the first carriage, so the force in the coupling is a tension force.

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The approximate revenue obtained from selling the 7th unit of this product is $24,387.93.

To find the revenue from selling the 7th unit, we first need to determine the price at which the 7th unit will be sold. We can do this by substituting x = 7 in the given price function:

p(7) = 9000e^(-0.1*7) = 9000e^(-0.7) = 3483.99

Therefore, the price at which the 7th unit will be sold is approximately $3,483.99.

Now we can calculate the revenue obtained from the sale of the 7th unit as the product of the price and the quantity:

Revenue = 7 * 3483.99 = $24,387.93

Thus, the approximate revenue obtained from selling the 7th unit of this product is $24,387.93.

It is important to note that the given price function is an example of an exponential decay function, which is often used to model situations where the demand for a product decreases as the price increases. In this case, the function shows that as the price increases, the quantity demanded decreases at an accelerating rate (-0.1 is the rate of decay). The revenue function can be derived as the product of the price and the quantity, and the revenue can be maximized by finding the price that will result in the highest quantity of units sold. However, in this problem, we were given the quantity and asked to find the revenue, so we simply used the price function to determine the price of the 7th unit and multiplied it by 7 to find the revenue.

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Answer:

835.66m^2 (to 2d.p)

Step-by-step explanation:

Firstly split the shape up so you get a rectangle and 2 circles.
Find the area of the circle:
formulae = πr^2
14/2=7
7^2=49
49π*2 (as there is two circles)= 98
98π=307.876
Find the circumference of the circle
formulae = dπ
14π=43.98
43.98 is the height of the rectangle
43.98*12=527.79 (rounded to 1d.p)
Area of rectangle is 527.79
Area of two circles is 307.876
Add them together = 835.66m^2 (to 2d.p)

Answer:

836cm^2

Step-by-step explanation:

For the sides, do 14/2 to find the radius (r) which is 7.

7^2 x pi = 153.9380400259 (formula for area of a circle is pi x r^2)

Multiply this by 2 to account for both sides of the cylinder.

For the cross-section of the cylinder, do 2 x pi x the radius (7) x 12 (the length, or l) which gets you 527.787565803085.

527.787565803085 + (153.9380400259 x 2) = 835.663645854885, rounded to 836 centimetres squared.

Hope this helps :D

Answer:

  A.  p(t) = 16 -5t +2t²

Step-by-step explanation:

You want the interpolating polynomial for points (1, 13), (2, 14), and (3, 19).

The given system of equations can be solved by your favorite method to find ...

The interpolating polynomial is p(t) = 16 -5t +2t².

__

Additional comment

The points and the polynomial are graphed in the second attachment.

<95141404393>

The interpolating polynomial  is (a) p(t) = 13 - 2.5t +1.5t²

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

Points =  (1, 13), (2, 14), and (3, 19).

Using the general form of the quadratic formula, we have

a + b + c = 12

4a + 2b + c = 14

9a + 3b + c = 19

Subtract the equations to eliminate c

So, we have

3a + b = 2

5a + b = 5

Subtract the equations to eliminate b

So, we have

2a = 3

So, we have

a = 1.5

Next, we have

3a + b = 2

3(1.5) + b = 2

Evaluate

b = -2.5

Lastly, we have

4a + 2b + c = 14

4(1.5) + 2(-2.5) + c = 14

Evaluate

c = 13

So, the equation is p(t) = 13 - 2.5t +1.5t²

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The areas under the curve of the z-scores are 0.5098, 0.4357 and 0.1254

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

(a) z = -0.69 to 0.69

This is represented as

Area = P(-069 < z < 069)

Using a graphing calculator, we have

Area = 0.5098

(b) z = -1.52 to 0

This is represented as

Area = P(-1.52 < z < 0)

Using a graphing calculator, we have

Area = 0.4357

(c) z = -0.75 to -0.38

This is represented as

Area = P(-1.52 < z < -0.38)

Using a graphing calculator, we have

Area = 0.1254

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Answer:

372 March

360 April

372 May

390 June

403 August

1897 miles

Step-by-step explanation:

Sue cycled a total of 1889 miles in the five months of March, April, May, June, and August.

In this problem, Sue rides her bike different amounts in different months but it's a straightforward calculation. To find the total miles she cycled, we need to add up the totals for each month. In March, April and May, she cycled 12 miles per day. Each of these months has 30 or 31 days, so let's average that to 30.5 days per month. 12 miles/day * 30.5 days/month * 3 months = 1098 miles. In June and August, she cycled 13 miles per day. We'll use the same average of 30.5 days per month. 13 miles/day * 30.5 days/month * 2 months = 791 miles. Adding those up, 1098 miles + 791 miles, we get a total of 1889 miles.

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The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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The factoring of the polynomials gives;

1) Option C

2) Option A

3) Option B

4) Option C

5) Option A

6) Option B

7) Option C

8) Option C

9) Option B

10) Option B

1) 9x - 9

9(x - 1)

2) [tex]3x^2 - 9x[/tex]

3x(x - 3)

3) [tex]36x^2 - 1[/tex]

By the difference of two squares;

(6x + 1) ( 6x - 1)

4) [tex]x^2 - 4[/tex]

By the difference of two squares;

(x + 2) (x - 2)

5)

[tex]x^2 + 12x + 36\\x^2 + 6x + 6x + 36[/tex]

x(x + 6) + 6(x + 6)

(x + 6) (x + 6)

[tex](x + 6)^2[/tex]

6)

[tex]25x^2 - 20x + 4\\5x^2 + 2(5x) -2 + (-2)^2\\(5x - 2)^2[/tex]

7) [tex]x^2 - 3x - 54[/tex]

(x + 6) (x - 9)

8) [tex]2x^2 + 9x + 18 x+ 81\\ 2x^2 + 18 x + 9x + 81[/tex]

2x(x + 9) + 9 (x + 9)

(2x + 9) (x + 9)

9)

[tex]9y^2 + 18y + 8\\9y^2 + 12y + 6y + 8[/tex]

3y(3y + 4) + 2y(3y +4)

(3y + 2) (3y + 4)

10)

[tex]20z^2 - 3z - 9\\20z^2 - 15z + 12z - 9[/tex]

5z(4z - 3) + 3(4z - 3)

(5z - 3) (4z + 3)

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Answer:

695,512

Step-by-step explanation:

no explanation just x

The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.

Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.

Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

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The measure of angle LOP is given as follows:

m < LOP = 52º.

The segment OP bisects the angle O of the rhombus into two smaller angles, which are NOP and LOP.

.

A bisection means that the larger angle is divided into two smaller angles of equal measure.

The measure of angle NOP is given as follows:

m < NOP = 52º.

Hence the measure of angle LOP is given as follows:

m < LOP = 52º.

The final sentence is to find the measure of angle LOP.

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The yield to maturity for the ABC Inc. bonds is 4.95%.

The yield to maturity (YTM) represents the effective interest rate that an investor would earn if they hold the bond until its maturity date.

To calculate the YTM for the ABC Inc. bonds, we need to find the interest rate that equates the present value of the bond's cash flows (coupon payments and par value) to its current price.

Given that the bond has a $1,000 par value and an 8.40% coupon rate, it pays a coupon of $42 (8.40% × $1,000 / 2) semi-annually for 18 years, totaling 36 coupon payments. At maturity, the bond will also repay the par value of $1,000.

To calculate the YTM, we can use a financial calculator or a spreadsheet software. By inputting the cash flows and solving for the interest rate, we find that the YTM is approximately 4.95% (rounding to two decimal points).

Therefore, the yield to maturity for the ABC Inc. bonds is 4.95%.

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The rule used by the merchant is a function because it establishes a relationship between the cost of an item and its selling price

A function is simply described as a mathematical rule, law or expression that shows the relationship between two variables.

These two variables are known as;

From the information given, we have that;

Function assigns a unique selling price for every cost input

Input: cost

Output: selling price = cost + 10% of cost Formula: SP = C + 0.1C.

By following this rule, consistent selling prices can be determined efficiently based on cos

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