In JKL, J = 7.9 inches, K = 2 inches and L =9.8 inches. Find the measure of K to the nearest degree

Answer:

m = 8

Step-by-step explanation:

4 x 2

you just have to multiply exponents

Answer:

pay rate £7.80

Step-by-step explanation:

28860 divide by 37 = 780

780 divided by 100 = 7.80

Thus, there are 169 different ways that a player could choose a diamond and a club.

A deck of 52 bridge cards contains 13 cards in each of the four suits—diamond, spade, club, and hearts—for a total of 52 cards. One of the earliest activities can be thought of as diamond choosing. \($A_1$\) and the second endeavour \($A_2$\) determines which club to join. Apply the adage "If two things, multiply them by two." \($A_1$\) and \($A_2$\) is possible to perform in \($n_1$\) and \($n_2$\) many methods, correspondingly. The total number of ways that are then \($A_1$\) then comes \($A_2$\) being able to be done \($n_1 \times n_2$\) "

Here, \($n_1=13$\) and \($n_2=13$\), In the following rule, change the values as follows:

\($$\begin{aligned}n_1 \times n_2 & =13 \times 13 \\& =169\end{aligned}$$\)

The user can choose a diamond and a club in one of 169 different ways. When I see a SPADE, I should square the item to the left, square the item to the right, add the two items, and then take the square root of that sum.

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The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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Answer:

No.

Step-by-step explanation:

A function should never have a shape like this.

Answer:

48 and 2/5 converted into decimal form is 48.4

Answer:

\(48.4\)

Step-by-step explanation:

\(48 \frac{2}{5} \\ \frac{242}{5} \frac{ \times 20}{ \times 20} = \frac{4840}{100} \\ = 48.4\)

Step-by-step explanation:

Answer is 99. I am pretty sure.

Answer:

try 21 x 21 plus 21 divided by 21 then add 21 x 21

Step-by-step explanation:

easy math

Answer:

\(y=7x-33\)

Step-by-step explanation:

\(m=\frac{9-(-5)}{6-4}\\m=\frac{14}{2}\\m=7\\y=7x+b\\b=-5-(7)(4)\\b=-33\\y=7x-33\)

Answer:

170

Step-by-step explanation:

17π/18 * 180/π

17*180/18

=170

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer:

a

Step-by-step explanation:

240

Answer:

-8$

Step-by-step explanation:

first, add 100 to 1,294

then multiply 350.50 by 4

and subtract them

Answer:

y(x) = -1/(x^2 + c_1 x)

Step-by-step explanation:

Solve Bernoulli's equation ( dy(x))/( dx) + y(x)/x = x y(x)^2:

Divide both sides by -y(x)^2:

-(( dy(x))/( dx))/y(x)^2 - 1/(x y(x)) = -x

Let v(x) = 1/y(x), which gives ( dv(x))/( dx) = -(( dy(x))/( dx))/y(x)^2:

( dv(x))/( dx) - v(x)/x = -x

Let μ(x) = e^( integral-1/x dx) = 1/x.

Multiply both sides by μ(x):

(( dv(x))/( dx))/x - v(x)/x^2 = -1

Substitute -1/x^2 = d/( dx)(1/x):

(( dv(x))/( dx))/x + d/( dx)(1/x) v(x) = -1

Apply the reverse product rule f ( dg)/( dx) + g ( df)/( dx) = d/( dx)(f g) to the left-hand side:

d/( dx)(v(x)/x) = -1

Integrate both sides with respect to x:

integral d/( dx)(v(x)/x) dx = integral-1 dx

Evaluate the integrals:

v(x)/x = -x + c_1, where c_1 is an arbitrary constant.

Divide both sides by μ(x) = 1/x:

v(x) = x (-x + c_1)

Solve for y(x):

y(x) = 1/v(x) = -1/(x^2 - c_1 x)

Simplify the arbitrary constants:

Answer: y(x) = -1/(x^2 + c_1 x)

a. Parameterize C₁ by

\((x(t),y(t)) = (1-t)(-13,-7) + t(0,6) = (-13+13t,-7+13t)\)

with 0 ≤ t ≤ 1. Then both dx = 13 dt and dy = 13 dt, so that the line integral along C₁ is

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_0^1 (-7+13t)^2(13\, dt) + (-13+13t)(13\,dt)\)

\(\displaystyle \int_C y^2\,dx + x\,dy = 13 \int_0^1 (169t^2 - 169t + 36) \, dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = 13 \left(\frac{169}3-\frac{169}2+36\right) = \boxed{\frac{611}6}\)

b. Parameterize C₂ by

\((x(t),y(t)) = (36-t^2,t)\)

with -7 ≤ t ≤ 6. Then dx = -2t dt and dy = dt, so the line integral is

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 t^2(-2t\,dt) + (36-t^2)\,dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 (36-t^2-2t^3) \, dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = \left(36\cdot6-\frac{6^3}3-\frac{6^4}2\right) - \left(36\cdot(-7)-\frac{(-7)^3}3-\frac{(-7)^4}2\right) = \boxed{\frac{5005}6}\)

Given:

Required:

To find the value of

Explanation:

We know that

Final Answer:

The difference quotient expression for the given function is

\(\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}\)

The expression in single-variable calculus is usually referred to as the difference quotient.

\(\frac{f(x+h)-f(x)}{h}\)

When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.

The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.

Consider the difference quotient formula,

\(\frac{f(x+h)-f(x)}{h}\)

Evaluate the function at x = x + h

replace the variable x with (x + h) in the given expression

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

simplify the result ,

\(f(x+h)=\sqrt{(x+h+1)(x+h-1)}\)

find the components of the definition,

\(f(x+h)=\sqrt{(x+h+1)(x+h-1)}\)

\(f(x)=\sqrt{(x+1)(x-1)}\)

plug in the components,

\(\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}\)

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Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

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Answer:

15 miles

Step-by-step explanation:

If there are 2.5 inches and 1 inch is 6 miles, then just multiply 6 by 2.5 to get 15

6*2.5=15

Answer:

B

Step-by-step explanation:

The length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple is 29.

Pythagorean triples are represented as the triple (a, b, c) where a represents the perpendicular side, b represents the base and c represents the hypotenuse.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

c² = a² + b²

Here a = 20, b = 21 and c = x.

x² = 20² + 21²

x² = 841

x = √841 = 29

Hence the length of the hypotenuse, x, is 29.

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

(4,8) and (6,10) are the pairs that could be included in the set so that it remains a function.

Answer:

15 green pieces.

Step-by-step explanation:

8x = 24

x = 3.

So you need 3 times the amount of green pieces for every yellow piece.

3 * 5 green pieces = 15 green pieces

Answer:

\(f(2.1) = 0.512195\)

\(f(2.05) = 0.506173\)

\(f(2.01)=0.501247\)

\(f(2.001) = 0.500125\)

\(f(2.0001) = 0.500012\)

\(f(1.9) = 0.487179\)

\(f(1.95) = 0.493671\)

\(f(1.99) = 0.498747\)

\(f(1.999) = 0.499875\)

\(f(1.9999) = 0.499987\)

Step-by-step explanation:

Given

\(f(x) = \frac{x^2 - 2x}{x^2 - 4}\)

Solve for f(x) for all given values of x

First, we need to simplify f(x)

\(f(x) = \frac{x^2 - 2x}{x^2 - 4}\)

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

\(f(x) = \frac{x(x - 2)}{(x- 2)(x + 2)}\)

\(f(x) = \frac{x}{x + 2}\)

When \(x = 2.1\)

\(f(x) = \frac{x}{x + 2}\)

\(f(2.1) = \frac{2.1}{2.1 + 2}\)

\(f(2.1) = \frac{2.1}{4.1}\)

\(f(2.1) = 0.512195\)

When \(x = 2.05\)

\(f(x) = \frac{x}{x + 2}\)

\(f(2.05) = \frac{2.05}{2 + 2.05}\)

\(f(2.05) = \frac{2.05}{4.05}\)

\(f(2.05) = 0.506173\)

When \(x = 2.01\)

\(f(x) = \frac{x}{x + 2}\)

\(f(2.01)=\frac{2.01}{2.01 +2}\)

\(f(2.01)=\frac{2.01}{4.01}\)

\(f(2.01)=0.501247\)

When \(x = 2.001\)

\(f(x) = \frac{x}{x + 2}\)

\(f(2.001) = \frac{2.001}{2.001 +2}\)

\(f(2.001) = \frac{2.001}{4.001}\)

\(f(2.001) = 0.500125\)

When \(x = 2.0001\)

\(f(x) = \frac{x}{x + 2}\)

\(f(2.0001) = \frac{2.0001}{2.0001 + 2}\)

\(f(2.0001) = \frac{2.0001}{4.0001}\)

\(f(2.0001) = 0.500012\)

When \(x = 1.9\)

\(f(x) = \frac{x}{x + 2}\)

\(f(1.9) = \frac{1.9}{1.9 + 2}\)

\(f(1.9) = \frac{1.9}{3.9}\)

\(f(1.9) = 0.487179\)

When \(x = 1.95\)

\(f(x) = \frac{x}{x + 2}\)

\(f(1.95) = \frac{1.95}{1.95 + 2}\)

\(f(1.95) = \frac{1.95}{3.95}\)

\(f(1.95) = 0.493671\)

When \(x = 1.99\)

\(f(x) = \frac{x}{x + 2}\)

\(f(1.99) = \frac{1.99}{1.99 + 2}\)

\(f(1.99) = \frac{1.99}{3.99}\)

\(f(1.99) = 0.498747\)

\(f(x) = \frac{x}{x + 2}\)

When \(x = 1.999\)

\(f(x) = \frac{x}{x + 2}\)

\(f(1.999) = \frac{1.999}{1.999 + 2}\)

\(f(1.999) = \frac{1.999}{3.999}\)

\(f(1.999) = 0.499875\)

When x = 1.9999

\(f(x) = \frac{x}{x + 2}\)

\(f(1.9999) = \frac{1.9999}{1.9999 + 2}\)

\(f(1.9999) = \frac{1.9999}{3.9999}\)

\(f(1.9999) = 0.499987\)

Note that all values of f(x) are approximated to 6 decimal places

Answer: 2, 3, 6, 7

Step-by-step explanation:

Supplementary is two angles adding up to 180. The angles above with angle 5 add up to 180.

Answer:

the numbers are going down by .5 nvm I answered this wrong.

Answer:

See below

Step-by-step explanation:

\(\displaystyle \frac{\sec x\sin x}{\tan x+\cot x}\\\\=\frac{\frac{1}{\cos x} \sin x}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin x \sin x}{\cos x \sin x} + \frac{\cos x \cos x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin^2 x}{\cos x \sin x} + \frac{\cos^2 x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2 x+\cos^2 x}{\cos x \sin x} }\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{1}{\cos x \sin x} }\)

\(=\frac{\sin x}{\cos x}\cdot \sin x \cos x\\ \\=\frac{\sin x \sin x \cos x}{\cos x}\\ \\=\sin^2x\)

Thus, the identity is proven. Match the options up accordingly to my step-by-step process.

Answer:

Ali has 1528. She has 1146 more cards than Max. In total, there are 1910 cards.

Step-by-step explanation:

382 x 4 = 1528

1528 - 382 = 1146

1528 + 382 = 1910

Answer: