An electric current that alternates sinusoidally with a frequency of 60
cycles per second and is at maximum at t = 0.1 seconds can be described by
the equation
I(t) = 10cos(120πt - 12π) + 5,
where I is current in Amperes and t is time in seconds. What is the
approximate range of the current?

tan 5 = x / 35

0.0874 = x / 35

cross- mulltiply

x = 35 x 0.0874

x = 3 . 059 = 3. 06 feet

SOLUTION

From the what is given

We have the graph as shown below

We are told that the MAX is

Substituting these required points into the equation, our maximum becomes

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

Hence the surplus unit is

Hence the answer is 2

If the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is  15

The lines a and b are parallel lines

Here two parallel lines a and b are cut by a transversal t

The angles are

∠2 = 6x+20 degrees

∠8 = 8x-10 degrees

The angle 2 and angle 8 are called alternate exterior angles

When the two parallel lines are cut by a transversal, the formed alternate exterior angles are equal.

Then

6x+20 = 8x-10

Solve the equation

6x-8x = -10-20

-2x = -30

x = -30/-2

x = 15

Hence, if the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15.

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Answer:

13 storage boxes is the least

Step-by-step explanation:

What we know:

- We have 127 cd's

- We have boxes only able to hold 10

What we need to figure out:

- how many boxes at the least are we going to need

Step 1: Divide

Since we need to figure out how many times 10 goes into 127 we divide 127 by 10 so...

127/10 = 12 with a remainder of 7.

Step 2: Figure out the remainder

Since there are seven left over and you cannot put them in boxes already being used then we put them in a new box, not yet used. That would make it a total of 13 boxes needed at the least.

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The missing proof in the given congruence of triangle is;

∠FAB = ∠FBA.

For the given question;

The given data in the triangle FAB is;

In the step two,

FA = FB (Property of isosceles triangle)

Then, step 4 will be ∠FAB = ∠FBA.

Thus, the missing proof will be ∠FAB = ∠FBA.

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The time taken to completely fill the pool is 5/4 hour

From the question, the given parameters are:

Time =3/4 hour

Size of the pool = 3/5

The time to fill the pool is then calculated as

Time = Given time/Proportion of the pool

Substitute the known values in the above equation

So, we have the following equation

Time = 3/4 hour ÷ 3/5

Express the quotient as product

So, we have the following equation

Time = 3/4 hour x 5/3

Evaluate the products

Time = 5/4 hour

Hence, the time taken is 5/4 hour

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Given:

Aim:

We need to graph the given function.

Explanation:

Replace x =-4 in the given equation.

We get the point (-4, 4).

Replace x = 0 in the given equation.

We get the point (0,1).

Replace x =4 in the equation.

We get the point ( 4, -2).

Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.

Final answer:

The graph of the given eqaution:

The measure of ∠C is 121 degrees.

Given that:-

There is a triangle ABC.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

We have to find the measure of ∠C.

We know that,

The sum of all the angles of a triangle is 180 degrees.

Hence, we can write,

m∠A + m∠B + m∠C = 180 degrees

(x + 6)° + (3x - 15)° +  (5x + 36)° = 180 degrees

(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees

9x + 27 = 180 degrees

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

x = 17 degrees

Hence,

The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.

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Answer:

  y = 3x -4

Step-by-step explanation:

You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (8 -(-1))/(4 -1) = 9/3 = 3

The y-intercept can be found using the equation ...

  b = y1 -m(x1)

  b = -1 -3(1) = -4

The slope-intercept equation of a line has the form ...

  y = mx + b

Using the above values of m and b, this becomes ...

  y = 3x -4

__

Additional comment

Attached is a graph showing the points and the line the equation represents.

<95141404393>

Answer:

2(5*7) + 2(4*7) + 2(4*5)

Step-by-step explanation:

I can't really see all the values on the cuboid. I'm going to assume the dimensions are 5cm by 4cm by 7cm.

Surface area of this cuboid would be:

2(5*7) + 2(4*7) + 2(4*5)

Answer:

ASA

Step-by-step explanation:

ASA stands for Angle-Side-Angle which is the congruency theorem that states that if a triangle shares two congruent angles that have one line in between the two angles share a side length congruent to each other, then the two triangles are congruent.

Before you get very confused on the difference between AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle), let explain why these two triangles are ASA.

We are given that both triangles share a similar side length at KL where they are connected. We are also given that angle ∠JKL is congruent to angle ∠MKL. We are also given that angle ∠MLK is congruent to angle ∠JLK.

The most important part after deciding all the relationships is given to us, it is deciding what kind of congruence theorem we will use. We are given the options:

Because we are presented with two congruent angles and one congruent side, we know that this triangle congruency theorem is either ASA or AAS. To understand why these triangles are ASA, we have to look at where the two-given congruent sides are located. As we can see in the name and in our two triangles, the congruent side lengths are in between the two angles as it touches both angle ∠JKL and angle ∠JLK in triangle ΔJKL, while in on ΔMKL, the congruent side length is also found between angle ∠MLK and angle ∠MKL. So, these triangles share ASA because they share two congruent angles connected by one congruent line.

ORDER MATTERS WHEN YOU WRITE YOUR CONGRUENCY THEROMS

AAS is technically not the same as ASA and I will explain that in one moment.

An example of AAS is if instead being told that ∠JKL is congruent to angle ∠MKL, we are given that ∠KJL is congruent to angle ∠KML instead. now the congruent sides are not connected to angle ∠KJL or angle ∠KML. The side is no longer in-between the two congruent sides. The reason order matters here are because order matters between AAS and ASA because in another theorem, SAS, you will find out order matter because while SAS guaranties congruency SSA does not.  Technically, though, while both AAS and ASA both guaranty congruency, they are labeled separately, the way the remaining congruency thermos are.

Answer:

You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.

A: 40*5 = 200

Step-by-step explanation:

21 + 200 = 221

Height of the triangle is = 14m

Given,

Base of the triangle is 8m

Area of the triangle is = 56m^2

To find the height of the triangle.

Now, According to the question:

We know that

Area of the triangle is = 1/2 x b x h

where, b = base

h = height

Plug all the values of base and area in above formula:

56m^2 = 1/2 x 8m x h

56 x 2 / 8 = h

h = 14m

Hence, Height of the triangle is = 14m

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Answer: y=8x-58

Step-by-step explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58

Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.

A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where; base = length × breadth = 18ft²

The volume of the rectangular bathtub = 18h ......... (1)

Using differentiation to differentiate 18h with respect to t implicitly, then:

[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

When the rate of rising of the volume is 0.2 ft² / min

[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

substitute the values in the above equation, we get

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]

Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.

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The degrees of the following expression are

(7x-2)° => x = 2/7°

18y° =>  y = 0°

(11x - 34)° =>  x = 34/11°

Degrees:

Degree is the unit of measure is used to measure the magnitude of an angle.

1 degree = 1/360 of a complete revolution in magnitude.

Given,

Here we have the following expressions

(7x-2)°

18y°

(11x - 34)°

Now, we have to find the value of x and y from it.

In order to find the value x and y , we have to equate every equation with 0. then we get the value of variables x and y.

When we take the first expression, and then we have to equate it with zero, then we get,

(7x - 2)° = 0°

7x = 2°

x = 2/7°

Therefore, the value of x is 2/7°.

Now, we have to take the second one and equate it with zero, then we get,

18y° = 0

y = 0°

Therefore, the value of y is 0°.

Finally, the value of the expression in degrees,

11x - 34° = 0

11x = 34°

x = 34/11°

Therefore, the value of x is 34/11 degrees.

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Time taken by the smaller hose to fill the pool on its own = 75 minutes

Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes

Time taken by the larger hose to fill up the swimming pool = 50 minutes

Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.

In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.

In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.

It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.

Hence 1/30 = 1/x +1/50

⇒ 1/30 = (50+x)/50x

⇒ 30 = 50x/(50+x)

⇒ 30 (50 + x) = 50x

⇒ 1500 + 30x = 50x

⇒ 20x = 1500

⇒ x = 1500/20

⇒ x = 75 minutes.

Thus the smaller hose alone takes 75 minutes to fill up the pool.

The question is incomplete. Find the complete question below:

Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

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The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.

The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.

The given expression is  is 7 y = 2 x − 5

Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5

Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;

x = (7y +5)/2

Therefore, option A is correct because it is the expression that gives the x in terms of y.

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Check the missing options:

A. x = (7y +5)/2

B. y = (7x +5)/2

C. x=(7y +5)/3

Answer: using traditional algorithom

                                       23

                                   x  20

                                   __________

                                       0 0

                             +    4 6

                               ____________

                                   4 6  0

The exchange rate is 1 USD = 0.992714 EURO

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm).

Given:

1 US dollar = _________ euro.

As, the exchange rate between US dollar to Euros

1 USD = 0.992714 EURO

1 USD = 1 EURO

So, if we have to find 5 US dollar into EURO then

5 US dollar = 5.02 EURO = 5 EURO

Hence, the exchange rate is 1 USD = 0.992714 EURO

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If:

so:

Or:

0.32 liters

(b)

We need to find the volume of the rectangular prism, therefore:

However, we need to express the volume in liters, so:

Since we need to know the amount of mango juice:

SOLUTION

To get how many more stickers were shipped last month than this month, we simply subtract this month's shipment from last month's shipment.

This becomes

Therefore, the we have 1,000,000,000 to the nearest billion.

Option D is the correct answer

Squares are the numbers that are produced when a value is multiplied by itself.

If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].

The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.

The original number can be attained by multiplying the square root of an integer by itself.

Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.

Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]

[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]

therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

simplifying the given expression, we get

[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]

[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]

[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]

Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

The complete question is:

Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]

c) [tex]$6 \sqrt{5}$[/tex]

d) [tex]$6 \sqrt{9}$[/tex]

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SOLUTION:

Case: Transformation:

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Method:

1,

Transformation features:

Horizontal: None

Shift: None

Stretch/Compression: None

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5

2.

Transformation features:

Horizontal:

Shift: left by 9 units

Stretch/Compression: None

Vertical:

Shift: None

Stretch/Compression: Stretches by a factor of 7.

Final answer:

1.

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5.

2.

Horizontal:

Shift: left by 9 units

Vertical:

Stretch/Compression: Stretches by a factor of 7.

The function has an equation of f(x) = (x + 4)(x - 2)

The given parameters in the question are

Roots = -4 and 2

Point = (1, -5)

The above parameters can be rewritten as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

A quadratic equation can be represented as

f(x) = a * (x - Roots)

Where Roots: x = -4 and x = 2

The above parameters imply that we have the following equation

y = a(x + 4)(x - 2)

From the question, we have

(x, y) = (1, -5)

This gives

-5 = a(1 + 4)(1 - 2)

Divide

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

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

Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

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Answer: The answer would be A: f(x) = (x − 2)(x + 4)

Step-by-step explanation: I got it right on my test

If we round 81.244 to the nearest whole number then it would be 81.

For 65.33 is 65. Then, we sum.

Answer:

c and e

Step-by-step explanation:

(a)

x² - 4x + 3 = 0 ← is a quadratic and not linear

(b)

6x - 2y = 7 ← is a linear equation in 2 variables, x and y

(c)

3x - 1 = - 2x ( add 2x to both sides )

5x - 1 = 0 ← is a linear equation in 1 variable

(d)

pq - 3 = p ← is a linear equation in 2 variables , p and q

(e)

3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable

The approximate probability that between 70 and 90 is 0.728.

Using normal distribution,

Mean = xbar = np = 400 × 0.2 = 80

Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8

To ensure that the distribution is normal,

np ≥ 10

80 ≥ 10

And,

np(1-p) ≥ 10

80(0.8) = 320 ≥ 10

Hence, we use the z-tables for this

a) Convert 75 and 100 into standardized scores.

A value's standardized score is equal to the value minus the mean divided by the standard deviation.

z = (x - xbar) ÷ σ

For 75

z = (75 - 80) ÷ 8 = - 0.625

For 100

z = (100 - 80) ÷ 8 = 2.5

To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)

For these probabilities, use data from the normal probability table.

P(75 ≤ x ≤ 100)

= P(-0.625 ≤ z ≤ 2.5)

= P(z ≤ 2.5) - P(z ≤ -0.625)

= 0.994 - 0.266

= 0.728

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