What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7

The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Diving is the art of going down to the depth of the ocean. Divers usually go deep down in the ocean to study the dynamics of ocean life.

The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30

Therefore the equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.

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Exponential functions are typically organized in this format:

[tex]f(x) = a*c^x[/tex]

To find the equation given the graph of an exponential function:

Identify the horizontal asymptote

In this question, it appears to be x = 0.

Identify the y-intercept

The y-intercept is the value of y at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our a value. Plug this into [tex]f(x) = a*c^x[/tex]:

[tex]f(x) = 100*c^x[/tex]

Solve for c

We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for c:

[tex]f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}[/tex]

Plug c back into our original equation:

[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]

[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]

Answer: x≠±2, x<±2, x>1, x<1, and x>±2

explanation:

for this equation to be true

Case 1

either (x-1) should be a negative while (x²-4) should be positive

which gives:-

x-1<0

so, x<1

also, x²-4>0

so, x²>4

⇒x>±2

Case 2:-

x-1>0 and x²-4<0

which gives

x>1 and x²-4<0

so, x>1 or x<±2

Case 3:-

either way, the denominator can't be 0

so, x²-4≠0

which gives,

x≠±2

compiling all, we have,

x≠±2, x<±2, x>1, x<1, and x>±2

These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.

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The number of months before the complex would have 800 occupied units is 40 months.

The formula that can be used to determine the required value is:

(In FV / PV) / r

Where:

(In 800 / 15) / 0.1 = 40 months

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Answer: 47.3 months

Step-by-step explanation:

The circumference of this circle with a radius of 7 cm is equal to 44 cm.

Given the following data:

Mathematically, the circumference of a circle can be calculated by using this formula:

Circumference = 2πr

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

Circumference = 2 × 3.14 × 7

Circumference = 43.96 ≈ 44 cm.

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I have linked a picture with the intervel.

Answer:

Step-by-step explanation:

The volume of a cone is V = 1/3 [tex]\pi[/tex] * h * r^2

The height of the cone = the diameter of its circle.

Here is the expression:

Volume = 1/3 π * 2x * x^2

[tex]\frac{\pi *x^{2} *2x}{3}[/tex]

Hope I helped!

The distance between the points (0, 0) and (0, 6) on the coordinate plane will be 6 units. Then the correct option is D.

The shortest distance (length of the straight line segment's length connecting both given points) between points (p, q) and (x, y) is:

D² = (x – p)² + (y – q)²

Point M is 6 units away from the origin.

Take option D assuming correct, then the point will be (0, 6)

Then the distance between the points will be

D² = (0 - 0)² + (6 - 0)²

D² = 0² + 6²

D² = 0 + 36

D² = 36

D = 6 units

Then the correct option is D.

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Answer:

Step-by-step explanation:

To find the number of pages of the book in the given hour:

To find the number of pages in 2 1/5 hours, multiply the number of pages read in 1 hour by 2 1/5 hours.

[tex]\sf \text{ Number of pages read in 2 $\dfrac{1}{5}$ hours = $\dfrac{1}{3}*2\dfrac{1}{5}$ }[/tex]

                                                       [tex]\sf = \dfrac{1}{3}*\dfrac{11}{5}\\\\=\dfrac{11}{15}[/tex]

[tex]\sf \text{Number of pages read more in 2 $\dfrac{1}{5}$ hours = $\dfrac{11}{15}-\dfrac{1}{3}$}[/tex]

                                                                 [tex]\sf =\dfrac{11}{15}-\dfrac{1*5}{3*5}\\\\=\dfrac{11}{15}-\dfrac{5}{15}\\\\=\dfrac{6}{15}[/tex]

Answer:

see below

Step-by-step explanation:

Here is another way

1/3 book / hr   *  2 1/5 hr =

1/3 * 11/5 = 11/15 read in 2 1/5 hr    

1/3is the same as 5 /15          

   11/15 - 5 /15 = 6/15 = 2/5 more read in 2 1/5 hr that 1/3 hr

The probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

The number of particles follows a Poisson Distribution.

A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as  [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .

In the question, x = 12.

λ = 100*0.1 = 10.

To find : P(X > 12)

P(X > 12) = 1 - P(X ≤ 12) = 1 - poissoncdf(10,12)

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

Therefore, P(X > 12) = 1 - 0.79156 = 0.20844.

Therefore, the probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

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Answer:

Therefore, the y-intercept is (-12, 0)

Answer:

science type of food group : fibre

Let's first gather all the information we have:

 [tex]\rm\hookrightarrow Center: (-3, 2)\\\rm \hookrightarrow Radius: 5[/tex]

Let's put that into standard form [tex](x-h)^2+(y-k)^2 =r^2[/tex]

              [tex]\rm \hookrightarrow Equation: (x+3)^2+(y-2)^2 = 5^2[/tex]

To put that equation into general form:

 ⇒ expand all the quadratics on one side and move the radius squared

      to the same side as the quadratics

           [tex](x+3)^2+(y-2)^2 = 25\\x^2+6x+9+y^2-4y+4=25\\x^2+y^2+6x-4y-12=0[/tex]

Answer: x² + y² + 6x - 4y - 12 = 0

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Answer:

282.743 yd²

Step-by-step explanation:

Surface Area of the Cylinder: Top Base + Bottom Base + Side

Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²

Area of Bottom Base (Circle): same as top base = 25π yd²

Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =

2π(5 yd)*(4 yd) = 40π yd²

Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²

Answer:

bx=-3

Step-by-step explanation:

-2(bx-5)=16

Use distributive property.

-2bx+10=16

Now, subtract 10 from both sides.

-2bx=6

Divide -2 from both sides.

bx=-3

Hope this helps!

If not, I am sorry.

Answer: the answer is b

Step-by-step explanation:

Answer:

I know you said relevant so i have two answers.

1) (not so relevant).

You could use it to show how NASA and astronomers use it to calculate the distance between planets and connect it to building rockets and all that cool stuff.

2) (relevant).

For the one about music, you could connect it to sound engineers and use sine and cosine graphs to calculate wavelengths

Answer: Answers below.

Step-by-step explanation: Suppose you want to find the best angle to kick a soccer ball so that it enters the goal. A triangle can be formed with angle ζ facing the goal. Increasing ζ or decreasing ζ will allow you to see the best angle that is the maximum amount of time that you should wait until scoring the ball.

Sine, Cosine, and Tangent waves are used everyday in phones, tablets, computers, and in quantam and normal technology by imitating and creating waves that can be sent to a destination.

You can use inverse trigonometric functions to find the height of a roof, the height of a tree, the height of a pole, and more.

Light waves are, in reality, sine and cosine waves intertwined together.

You can even use trigonometry every day in work places, such as in software engineering. In fact, calculus 1 and 2, as well as Multivariate Calculus, which heavily and fundamentally uses trigonometry, is used widely across computer science. These help you to get $100,000 jobs.

Answer:

r(x)= 11x

c(x) = 6x + 20

p(x) = r(x) - c(x)

= 11x -( 6x + 20)

= 11x - 6x - 20

= 5x - 20

We know that if (x,y) lies on the graph of a function, then (y,x) lies on the graph of its inverse.

This means you need to draw the segment with endpoints (9,1) and (2,3).

The Venn diagram is given below. Then the number of students who have brother and sister will be 6.

A set is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

In a class of 20 students:

11 have a brother, 9 have a sister, and 6 have neither.

Then the Venn diagram will be

11 – a + a + 9 – a = 20 – 6

               20 – a = 14

                        a = 6

The Venn diagram is given below.

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Answer:

  £105

Step-by-step explanation:

The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:

  3/2 × £70 = £105

He would get paid £105 for an 18-hour job.

__

Here are a couple of other solution methods.

  pay/hours = ?/(18 hours) = £70/(12 hours)

Multiplying by 18 hours, we get ...

  ? = £70×(18 hours)/(12 hours) = £70×(18/12)

  ? = £105 . . . . pay for 18 hours

He would get paid £105 for 18 hours.

__

The equation for a directly proportional relationship is ...

  y = kx

If we let y represent pay and x represent hours, then we have ...

  70 = k(12)   ⇒   k = 70/12 = 35/6

Then for 18 hours, the pay is ...

  y = (35/6)x

  y = (35/6)(18) = 35(3) = 105

He would get paid £105 for 18 hours.

Step-by-step explanation:

thr standard form for a quadratic equation is:

ax²+bx+c

in this example, a=1, b=(-1), c=(-42)

Answer:

0.39??

Step-by-step explanation:

Answers:

(a) The ledge can support the plant box. It is safe to put it there.

(b) No the density would not change.

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

Explanation for part (a)

We'll need the volume of the cube.

volume = side*side*side

volume = 13*13*13

volume = 2,197

Or you could do

volume = (side)^3

volume = (13)^3

volume = 2,197

The volume of the cube is 2,197 cubic cm. Multiply this with the density to determine its weight.

1.33*2197 = 2,922.01

The soil weighs 2,922.01 grams which is below the 2400 gram weight limit. Therefore, the ledge can support the planter.

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

Explanation for part (b)

The weight would go down if you only put in half the soil, but the density would not change regardless of how much soil is in there. Why doesn't the density change? Because the density is the amount of stuff per unit volume. The density tells us how packed in a material is. We can scale the amount of material up or down, and retain the same density.

This is based off physics concepts which are bit beyond the scope of this math course, but different materials have different densities. It's common to use a reference table to look up densities of various materials. For instance, ice is less dense than water. This is why ice floats rather than sinks. As another example, gold is more dense than iron. So 1 cubic unit of gold will weigh more compared to 1 cubic unit of iron.