A recreational court is twice as long as it is wide. if the perimeter is 210 feet, find the width and length .

Corrected Question

Quadrilateral QRST is inscribed in circle W as shown below. The measure of ∠QRS is 12 degrees less than three times the measure of ∠QTS and

mRQT=mRST .

(a)Determine the measure of Angle QTS .

(b)What is the common measure of angles RQT and RST ?

Answer:

(a)48 degrees

(b)90 degrees

Step-by-step explanation:

Theorem: Opposite angles of a cyclic quadrilateral are supplementary.

(a)

Let the measure of ∠QTS=x

Therefore: m∠QRS=3x-12

∠QTS and ∠QRS are opposite angles of a cyclic quadrilateral. By the theorem above:

x+3x-12=180

4x=180+12

4x=192

x=48 degrees

The measure of angle QTS is 48 degrees.

(b)Since mRQT=mRST

mRQT and mRST are opposite angles of a cyclic quadrilateral

Therefore:

mRQT+mRST=180 degrees

2mRQT=180

mRQT=90 degrees

Therefore, the common measure of RQT and RST is 90 degrees.

Answer:

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

Find the difference of the initial and used amounts:

Answer:

\(\huge\boxed{\sf y = 30}\)

Step-by-step explanation:

Given that:

y ∝ x

Turning proportionality into equality by putting the constant 'k'

y = kx ---------------------(1)

We know that y = 24, when x = 8

24 = k(8)

Divide both sides by 8

24 / 8 = k

3 = k

OR

k = 3

Now, Finding y when x = 10

Put x = 10 and k = 3 in Eq. (1)

y = (3)(10)

y = 30

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

-2 11/35

GOOD LUCK!!

answer: 28561^2in the area involves multiplying by the 4 sides of the shaded square and the shaded is the colored square.

The value of the expression 4c² -9(c-1)/5c when c= 6 is 142.5

The value of an expression is the value which one gets after putting the value of the variables in the expression.

let 4x+ 2 be an expression and we want to know its value on x= 1 , then the value is 4(1)+2 = 6

Given an expression 4c² -9(c-1)/5c , then its value at c= 6 :

4(6)² -9(6-1)/5(6) =144 - 9(5)/5(6) = 144-3/2 = 285/2 = 142.5

The value of 4c² -9(c-1)/5c at c= 6 is 142.5

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#1

Domain

Here the arrows are going infinite directions

#2

Smae for range

Arrows approaching infinity

#3

It fails in horizontal line test and vertical line test

Also

Answer:

22

Step-by-step explanation:

22 is the area of the given traingle

Step-by-step explanation:

64 2/3 = 16

4 square root 256 = 64

16 3/2 =64

3 square root - 64 = - 24

16 - 24 64 64

Answer:

x= 5/12,y=− 5/4

​

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12

Answer:

y intercept when x is 0, so the answer is 3

Answer:

3 and one third %

3.3333%

Step-by-step explanation:

Answer:

5 units

Step-by-step explanation:

Notice that the x-coordinate is the same for both points, but that the y-coordinates differ by five units.  The distance between these two points is therefore 5 units.

Refer to the images attached. Edit: I realized after uploading this answer that the integral in terms of y is MUCH easier, so I attached that as well :) But at least you know it can be done both ways!

a) The rule that represents the height as a function of the number of bounces is described by H(n) = 1.5 · (71 / 100)ˣ⁻¹. (Correct choice: B)

b) The height at the top of the sixth path is equal to 0.27 meters. (Correct choice: B)

In this problem we need to derive the equation that represents maximum height as a function of the number of bounces:

H(n) = a · (r / 100)ˣ⁻¹

Where:

If we know that a = 1.5 m and r = 71, then the rule for the sequence is:

H(n) = 1.5 · (71 / 100)ˣ⁻¹

And the height at the top of the sixth path:

H(6) = 1.5 · (71 / 100)⁶⁻¹

H(6) = 0.27 m

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Answer:

27*n

Step-by-step explanation:

A theater has 27 rows with n seats in each row. Which expression shows how many seats are in the entire theater?

27n or 27*n

You got it right.

Ex: A theater has 27 rows with 2 seats in each row.  Which expression shows how many seats are in the entire theater?

27*2 = 54 seats

Hope this helps!

The expression showing the number of seats in the considered entire theater is given by: Option A: \(27 \times n\)

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as \(a\) and \(b\)

Then, their multiplication can be interpreted as:

\(a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}\)

For example,

\(5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}\)

Now, for the considered situation in the problem's statement, we are specified that:

So, total number of seats = n + n + ... + n (27 times) = \(27 \times n\)

Thus, the expression showing the number of seats in the considered entire theater is given by: Option A: \(27 \times n\)

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Answer:

perpendicular

Step-by-step explanation:

This question only asks about the slope of the line, so the intercept doesn't matter. You can see that the slope of one line is 3x and the other is -3x so they're perpendicular

Answer:

The athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

Step-by-step explanation:

Given that at first an athlete jogs at 4 miles per hour and then jogs at 6 miles per hour, traveling 8 miles in 1.5 hours, to determine how long does the athlete jogs at each speed the following calculation must be performed:

4 x 1.5 + 6 x 0 = 6

4 x 1 + 6 x 0.5 = 7

4 x 0.75 + 6 x 0.75 = 7.5

4 x 0.5 + 6 x 1 = 8

Therefore, the athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

The distance between the parallel lines y = -1/3x + 3 and y = -1/3x - 7 is approximately 9.49 units.

A parallel line is a pair of lines that never cross and are always spaced at the same distance apart. The y-intercepts are different, but they have the same slope. In other terms, two lines are parallel if they have the same slope but distinct y-intercepts. Due to their role in defining and producing forms like rectangles, parallelograms, and trapezoids, parallel lines play a crucial role in geometry and trigonometry. In the actual world, parallel lines are also used in things like roads, railroad tracks, and electrical cables.

The standard equation of the line is given as:

y = mx + c

where, m is the slope.

c is the y-intercept.

Comparing the equation with the given equation we have the slope of the parallel lines as:

y = -1/3x +3 and y =-1/3x -7

slope = m = -1/3

y-intercept of 1st line = (0, 3)

y-intercept of the 2nd line = (0, -7)

The distance between two parallel lines is the perpendicular distance between them.

To calculate the perpendicular distance we find the equation of the perpendicular line.

The slope of the perpendicular line is negative reciprocal of the slope of the two given lines, which is 3.

The point-slope form is:

y - y1 = m(x - x1)

Substituting the values:

y - 3 = 3(x - 0)

y = 3x + 3

The intersection of this perpendicular line with the other line.

3x + 3 = -1/3x - 7

10/3x = -10

x = -3

Substituting x = -3 into either equation of the parallel lines gives:

y = -1/3(-3) - 7 = -6

Using the distance formula we have:

d = √((x2 - x1)² + (y2 - y1)²)

d = √((-3 - 0)² + (-6 - 3)²)

d = √(9 + 81)

d = √(90)

d ≈ 9.49

Hence, the distance between the parallel lines y = -1/3x + 3 and y = -1/3x - 7 is approximately 9.49 units.

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The solution to the given quadratic graph will be -2 and 0 respectively

Quadratic equations are equations that has a leading degree of 2. The graph of a quadratic equation is always parabola in nature,

From the given graph, the solution to the given curve is the point where the curve intersects the x-axis. Since the parabola intersects the x-axis at two points, hence the quadratic equation will have 2 solutions.

The solution to the given quadratic graph will be -2 and 0 respectively

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Answer:

D

Step-by-step explanation:

f(x ) = \(x^{2} - 1\\\)

inverse ----> f(x) = y = x

x = \(y^{2}\) - 1

\(y^{2} = x + 1\)

y = ± \(\sqrt{x + 1}\)

Sequence 1: 13, 16, 19, 22, 25, Sequence 2: 15, 13, 11, 9, 7 and Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7).

what is sequence?

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.

A. Sequence 1: 13, 16, 19, 22, 25

Sequence 2: 15, 13, 11, 9, 7

Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B. Sequence 1: 1, 5, 17, 53, 161

Sequence 2: 6, 15, 33, 69, 141

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (161, 141)

C. Input (x) | Output

1 | 17,  2 | 19, 3 | 21, 4 | 23

D. Input (x) | Output

1 | 30, 2 | 15, 3 | 7.5

To find the outputs, we use the formula: output = 60 ÷ 2x.

For x = 1, output = 60 ÷ 2(1) = 30

For x = 2, output = 60 ÷ 2(2) = 15

For x = 3, output = 60 ÷ 2(3) = 7.5

E. Input (x) | Output

1 | 23, 2 | 30, 3 | 37, 14 | 102, 15 | 109, 16 | 116, 27 | 205, 70 | 498

To find the outputs, we use the formula: output = 16 + 7x.

For x = 1, output = 16 + 7(1) = 23

For x = 2, output = 16 + 7(2) = 30

For x = 3, output = 16 + 7(3) = 37

For x = 14, output = 16 + 7(14) = 102

For x = 15, output = 16 + 7(15) = 109

For x = 16, output = 16 + 7(16) = 116

For x = 27, output = 16 + 7(27) = 205

For x = 70, output = 16 + 7(70) = 498

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Answer:

12 yards

Step-by-step explanation:

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 2) and (1, -6)

The distance between them is

\(d = \sqrt{ ({ - 3 - 1})^{2} + ({2 + 6})^{2} } \\ = \sqrt{ ({ - 4})^{2} + {8}^{2} } \\ = \sqrt{16 + 64} \\ = \sqrt{80} \: \: \: \: \: \: \: \: \: \: \\ = 4 \sqrt{5} \: \: \: \: \: \: \: \: \: \: \\ = 8.9442719...\)

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

Answer:

100%

none are greater than 80

Step-by-step explanation: