Solve the following equation algebraically: Negative 16 = 16 x squared How many solutions does this equation have? Explain. a. Negative 1 = x squared; One solution because only -1 will satisfy the equation. b. Negative 1 = x squared; No real solution because there is no real number that, when squared, produces -1. c. 1 = x squared; Two solutions because the square root of 1 is positive 1 and negative 1. d. 1 = negative x squared; One solution because only -1 will satisfy the equation.

The length of the given golden rectangle is; 1.618 units

We are told that, for the golden rectangle;

Length = x units,

Width = (x - 1) units,

Area = 1 unit².

The area of this rectangle will have the formula;

A = x(x - 1)

Thus;

x(x - 1) = 1

Expanding gives;

x² - x - 1 = 0

Using online quadratic equation calculator, we have;

x = 1.618 or -0.618.

Length has to be positive and so we choose x = 1.618

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Its 48

33+15

Step-by-step explanation:11+11+11+15= Perimeter

33+15 = Perimeter

48 = Perimeter

Answer:

Decreasing

Step-by-step explanation:

Because the equation of that graph is Y=-X, and the - in the X represents that the graph is decreasing.

By using the given dimensions and volume of water, we will see that the height of the tank is 36.6cm

We know that 27,238 cm³ is the volume of water on the tank, and this is equal to 2/3 of the volume of the tank.

So we can write:

27,238 cm³ = (2/3)*V

Then the volume of the tank is:

V = (3/2)*27,238 cm³ = 40,992 cm³

The base of the tank measures 40cm by 28cm, then:

B = 40cm*28cm = 1,120 cm²

Then the height H is such that:

H*1,120 cm² = 40,992 cm³

Solving for H:

H = (40,992 cm³)/(1,120 cm²) = 36.6cm

The height of the tank is 36.6 centimeters.

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The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,

8/ Sin(30°) = 11/ Sin(θ)

Sin(θ) = [11 × Sin(30°)]/8

Sin(θ) = 0.6875

θ = Sin⁻¹ (0.6875)

θ = 43.4325° ≈ 43°

Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

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Answer:

Step-by-step explanation:

Area of the sector :

[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]

Finding the area given r = 30 ft. and θ = 60° :

⇒ Area = π × (30)² × 60/360

⇒ Area = π × 900/6

⇒ Area = 150π ft²

===========================================================

Length of the arc :

[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]

Finding the arc length given r = 30 ft. and θ = 60° :

⇒ Arc Length = 2 × π × 30 × 60/360

⇒ Arc Length = 60/6 × π

⇒ Arc Length = 10π ft.

Answer:

1. 150π ft²

2. 10π ft²

Step-by-step explanation:

Hello there!

Here is how we solve the given problem:

L = ∆°/360° ×2πr

From our problem,

∆ = 60°, r = 30ft

Lets substitute the values

1. A = (∆°/360°) × πr²

= 60°/360° × π × 30²

= 150π ft²

2. L = ∆°/360° × 2πr

= (60/360) × 2 × 30 × π

= 10π ft²

NOTE:

Use the formulas given below to be on a save side;

I hope this helps.

Have a nice studies. :)

Answer:

-3 1/5

Step-by-step explanation:

to find the slope of the line you use the equation (y2 - 1) / (x2 - x1)

when plugged in you get

(5 + 3) / (-2 1/4 - 1/4)

then you do what is inside the parenthesis

8 / -2 1/2

8 / -2.5

lastly you divide

you get -3 1/5

that is your answer

The area of the target that earns at least 30 points on a throw is 379.94 square inches

The target areas that earn at least 30 points on a throw are:

30-point, 40-point and 50-point

From the question, we have:

So, the total radius is:

r = 3 + 4 + 4

Evaluate the sum

r = 11

The area is then calculated as:

A = πr²

This gives

A = 3.14 * 11²

Evaluate

A = 379.94

Hence, the area of the target that earns at least 30 points on a throw is 379.94 square inches

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Answer:

49  square inches

Step-by-step explanation:

edmentum/ Plato hope this helps

THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Let's denote students

D = in the drama club ,

S = in a sports team

So, P(D) = 85/330

P(S) = 200/330

P(D and S) = 60/300

P(D or S) = P(D) + P(S) - P(D and S)  

P(D or S) = 85/330 + 200/330 - 60/330

P(D or S) = 15/22

P(neither D nor S) = 1- 15/22

P(neither D nor S) = 7/22

Thus, THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM ISNT IN DRAMA OR SPORTS is 7/22.

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Answer:

option c

Step-by-step explanation:

It’s extremely hard to tell, but it looks like it’s 3 over 2, which is 3/2.

3/2 is 1.5, or just 3/2. Since the line is going down, the slope would be negative, so -3/2.

Hope this helps!

Answer:

Step-by-step explanation:

-3/2 i think

THis might be wrong tho

The congruence theorem that can be used to prove that both triangles are congruent is: C. SSS.

The SSS congruence theorem is a triangle theorem which states that two triangle are congruent if they have three pairs of corresponding sides that are congruent.

The triangles in the image given have the following three corresponding sides that are congruent:

Therefore, the congruence theorem to prove they are congruent is: C. SSS.

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Answer:3,5,7,9

Step-by-step explanation:I’m pretty sure all the inputs are the domains

When accessing your credit card information online, you cannot makes purchase.

A credit card is a card that enables a card holder to buy or purchase things online on credit.

A credit card holder can carryout the following when accessing their credit card data online:

Therefore the correct option is C.

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Two six-sided fair dice are rolled simultaneously.... 6 and the sum of the two numbers is an odd number is mathematically given as

x=7/10

Generally, the equation for Number is mathematically given as

[tex]x=P\frac{E > 3}{Enot > 5}\\\\Therefore\\\\x=P\frac{E > 3}{E\leq5}\\\\x=P\frac{4\leq E \leq5}{E\leq5}\\\\x=P\frac{7/36}{10/36}[/tex]

x=7/10

In conclusion,  the sum of the two numbers

x=7/10

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Answer:

997

Step-by-step explanation:

Hope this helps a little.

Answer:

You can refer to the given attachment

The size of the crowd is 12,000

This is the portion covered by the shape.

Analysis:

Area of field = 100 x 300 = 30000 square feet

If 1 person covers 2.5 square feet of the file then 30000/2.5 = 12,000 persons will cover the whole field.

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The depth of the diver is 32 feet below sea level.

The angle of elevation is the angle between the observer's eyesight horizontal line and the object. The complete question can be seen in the image attached below.

The depth of the diver is the absolute value of -32 since it can't be negative.

= |-32|

= 32

Therefore, we can conclude that the depth of the diver is 32 feet below sea level.

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The English phrase can be written as the fraction:

   [tex]\frac{m}{n + p}[/tex]

Remember that the quotient between two numbers gives a fraction.

Now, we have the sentence:

"the quotient of m and the sum of n and p."

Then we know that the numerator is m, and the denominator is (n + p) (the sum of n and p).

So the expression will just be the fraction:

[tex]\frac{m}{n + p}[/tex]

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Answer:

1,290.6 in3                                                                                                                                                  

nut.

The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

In mathematics, sequences are sets whose elements observe at least a condition, which is represented by a recursion formula in this question:

f(n + 1) = f(n) + 3

Thus, the following term of the sequence is:

f(2) = f(1) + 3

f(2) = - 4 + 3

f(2) = - 1

The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

The statement is poorly formatted and reports typing mistakes. Correct statement is:

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3. The first term of the sequence is - 4. What is the next term in the sequence? a) - 7, b) - 1, c) 1, d) 7

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Answer:

it's 9

Step-by-step explanation:

type it in a calculater

The slope of AB is (0-4)/(-2-0)=2, so since perpendicular lines have negative reciprocal slopes, the slope of the perpendicular line is -0.5.

So, the equation of the line is:

y + 1 = -0.5(x - 5)

y + 1 = -0.5x + 2.5

y = -0.5x + 1.5

well, we know the discount is 4975 - 3781 = 1194.

if we take 4975 to be the 100%, what is 1194 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]

Answer:

0.76

Step-by-step explanation:

4975 × 0.76 = 3781

the discount percent given is .76%

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=y^2x+2 \cos(x)[/tex]

To find the derivative of the given equation, use implicit differentiation.

Add d/dx in front of each term:

[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x+\dfrac{d}{dx}\:2 \cos(x)[/tex]

Differentiate terms in x only (and constant terms) with respect to x:

[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]

Use the chain rule to differentiate terms in y only:

(in practice this means to differentiate with respect to y then place dy/dx on the end)

[tex]\dfrac{dy}{dx}\: =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]

Use the product rule on the term in x and y:

[tex]\textsf{let }u=y^2 \implies \dfrac{du}{dx}=2y \dfrac{dy}{dx}[/tex]

[tex]\textsf{let }v=x \implies \dfrac{dv}{dx}=1[/tex]

[tex]\implies u\dfrac{dv}{dx}+v\dfrac{du}{dx}=y^2+2xy \dfrac{dy}{dx}[/tex]

Therefore:

[tex]\dfrac{dy}{dx} =y^2+2xy \dfrac{dy}{dx}-2 \sin(x)[/tex]

Rearrange to make dy/dx the subject:

[tex]\dfrac{dy}{dx}-2xy \dfrac{dy}{dx} =y^2-2 \sin(x)[/tex]

[tex]\dfrac{dy}{dx}(1-2xy)=y^2-2 \sin(x)[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]

Answer:

B 695.187

because 7 in 468.705 has value 1/10

1/100×1/100 is 1/1000 which is 0.007.

Answer:

B. 695.187

Explanation:

In the number 468.705, the number 7 is in tenths place (0.1)

If the value of 7 in that number which is 0.1 has value of 1/100, then

0.1 × 1/100 = 0.001  (thousand place)

Then the number 7 will be in thousands place: 0.007

Among options, option B (695.187) has the value of 7 in thousands place.

Answer:

3.5 gallons of punch

Step-by-step explanation:

There are 4 quarts in 1 gallon.

Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.

Elijah made 3.5 gallons of punch.