Which of the following equations represent linear functions?
x² + y² = 1
x+y=14
y= 6/x
y=3(2x + 1)

The area of a parallelogram will be of 11 ft² when the multiplication of the base of the parallelogram by the height of the parallelogram is of 11 ft².

The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:

A = bh.

Then the area of a parallelogram will be of 11 ft² when the multiplication of the base of the parallelogram by the height of the parallelogram is of 11 ft², when both the base and the height are given in feet.

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The largest number which divides 70 and 125 , leaving remainders of 5 and 8 is 13.

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, we can follow these steps:

Subtract the remainders from their respective numbers:

70 - 5 = 65 and

125 - 8 = 117.

Find the factors of each resulting number:

Factor of 65 = 5 and 13

factor of 117 = 3 and 13

Determine the highest common factor (HCF) of the resulting factors:

The HCF of 5 = 1

the HCF of 13 = 1

the HCF of 3 = 3

the HCF of 13 = 13

Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, is 13.

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1. The frequency of the second harmonic is twice that of the fundamental frequency. The frequency of the second harmonic is, therefore, 120 Hz.

2. The 3rd, 9th, and 15th harmonics are triplen harmonics. Triplen harmonics are so-called because they are three times the fundamental frequency (50Hz). They are multiples of the third harmonic (150Hz) and are considered triplen harmonics.
3. A positive-rotating harmonic would be more damaging to an induction motor. Harmonics that rotate in the opposite direction to the fundamental frequency are referred to as negative-rotating harmonics. Positive-rotating harmonics are harmonics that rotate in the same direction as the fundamental frequency. Negative-sequence currents are created by negative-rotating harmonics, which cause a rotating magnetic field that rotates in the opposite direction to the fundamental frequency's magnetic field. This causes stator windings to heat up, which can cause a great deal of damage to an induction motor.
4. An ammeter should be used to determine what harmonics are present in a power system. An ammeter is used to determine the presence and quantity of current harmonics. It can also be used to compare the percentage of current distortion in the system with the maximum allowable percentage of current distortion, which is determined by the nature of the load.
5. The transformer's rating should be derated to avoid overheating. If an ammeter that indicates peak current is used instead of a true-RMS ammeter, the current reading is multiplied by 1.414 (the peak of the sine wave). The true-RMS current, on the other hand, is what creates heat in the transformer. The transformer should be derated to compensate for the current difference between the two meters. The derating factor can be found using the following equation:

true-RMS current/Peak reading x 100%. 94 A/204 A x 100%

= 46%.

The transformer should be derated by 46%.

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The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

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Answer:

x = -7 and x = 4

Step-by-step explanation:

Note, I am taking the polynomial equation as
\(x^2 - 28 = -3x\)

Otherwise it does not become a polynomial of one variable and cannot be solved

Zeros of a polynomial are the values of x where the polynomial value itself is 0

Standard equation for a polynomial of degree 2 is ax² + bx + c = 0 where a, b and c are constants

Degree is the highest exponent. Here the highest exponent is 2 so the polynomial has degree 2. Such a polynomial is called a quadratic polynomial

So we first have to convert
x² - 28 = - 3x into  this form ax² + bx + c

1. Add 3x to both sides
x² - 28 + 3x = -3x + 3x =0

==> x² + 3x - 28  = 0
With a = 1, b = 3 and c = -28

2. Factor x² + 3x - 28  = 0

Here a = 1, b = 3 and c = -28

Factoring means find two expressions x+a and x +b such that (x + a) (x + b) = x² + 3x - 28  = 0

Then we can state that
x + a = 0           ==> x = -a as one solution
x + b = 0           ==> x = -b as the other solution

To factor, find two numbers m and n(could be negative) such that mn = c and m + n = b

28 has factors 7 and 4 so that is a good start

-28 = -7 x 4 or could also be 7 x -4

How do we choose?
Add both and see what gives you +3

-7 +  4 = -3  Nope
7 + -4 = 7-4 = 3 YES

So the factors are 7 and -4

(x + m) = (x + 7)
(x + n)  = (x -4)

So the original quadratic polynomial becomes

(x + 7)(x -4) =

This means

x + 7 = 0 ==> x = -7

x -  4 = 0 ==> x = 4

So the solutions(also called roots) of x² + 3x - 28  = 0 are:

x = -7 and x = 4

Both the above values satisfy the quadratic equation

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour

Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.

Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

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Answer:

30 meters per second

Step-by-step explanation:

Step 1:

600 ÷ 20 = 30

Answer:

30 meters per second

Hope This Helps :)

Answer:

30 m /s

Step-by-step explanation:

We are looking for the speed

d/t = speed

600m / 20 second

30 m /s

Answer:

32 songs

Step-by-step explanation:

60 - 12 = 48

48 ÷ 1.5 = 32

32 songs

Answer:

m<a=41º

Step-by-step explanation:

a triangle has 180º total

180-98=82

since O is the center that makes OQ and OP radii and as such they are equally distanced

this means that the m<a and the measure opposite it are equal

so ÷82 by 2

a=41

The statement that is true is All rational numbers can be written as the quotient of Integers

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

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The statement that is true is All rational numbers can be written as the quotient of Integers

What are rational numbers ?

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

Answer:

0.980413

Step-by-step explanation:

The table for the deaths and death rate per 100,000 population is attached below ;

73 years fall in the 65 - 74 years category ; with 1958.7 deaths (Female)

Hence, the probability of living another year is :

Number of deaths per 100,000 population ;

P(death) = 1958.7 / 100,000 = 0.019587

Probability of living another year = 1 - P(death)

1 - 0.019587 = 0.980413

Answer:

C. 0.980413

FHKEDIbEDSAJFWBHES

Step-by-step explanation:

first- b

swcond- a

third- c

Answer:

5 1/3 + 9 2/3

Step-by-step explanation:

A number minus a negative number will be the same thing as addition

Answer:

The answer is A

Step-by-step explanation:

just got it right on edge :)

The images of the points are U' (-7, -4), V' (-4, 5), W' (5, 5)

A rotation is a type of transformation that rotates each point in a figure a specific number of degrees around a particular point.

When we rotate a point around the origin by 90° clockwise or anti-clockwise, (x,y) becomes (y,-x) .

- Then matrix of the rotation 90° is

\(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\)

We have the point U (-4, 7) and its image is

U' =\(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-4\\7\end{array}\right]\)

U' = \(\left[\begin{array}{ccc}-7\\-4\end{array}\right]\)

and, point V is (5, 4) and its image is

V' = \(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\) \(\left[\begin{array}{ccc}5\\4\end{array}\right]\)

V' = \(\left[\begin{array}{ccc}-4\\5\end{array}\right]\)

and, point W is (5, -5) and its image is

W' = \(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\) \(\left[\begin{array}{ccc}5\\-5\end{array}\right]\)

W' = \(\left[\begin{array}{ccc}5\\5\end{array}\right]\)

So, The images of the points are U' (-7, -4), V' (-4, 5), W' (5, 5)

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To solve the equation 2x^2 + 5x - 58 = 0, we can use the quadratic formula to find the value of x. The quadratic formula states that x = [-b ± √(b^2 - 4ac)]/2a, where a, b, and c are the coefficients of the equation. We can plug in the values of a, b, and c to find the value of x. In this case, a = 2, b

The equation of the line that passes through point (8,-5) and perpendicular to y = x - 2 is y = -x + 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that:

y = x - 2

To the equation of the line that passes through the point (8,-5) and is perpendicular to the line.

First, determine the slope of the initial line using the slope intercept-form. y = mx + b

y = x - 2

Slope m = 1

For the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/1

Slope m = -1

Next, find the equation of the perpendicular line, by using the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -1 ) and point (8,-5).

y - (-5) = -1( x - 8 )

y + 5 = -x + 8

y = -x + 8 - 5

y = -x + 3

Therefore, the equation of the line is y = -x + 3.

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Answer:

52.8 feets

Step-by-step explanation:

From the diagram :

The height of tree woulb be :

Height above the ground (at breakpoint) + hypotenus

Hypotenus, h cab be obtained using Pythagoras rule :

h² = opp² + adj²

h² = 39² + 12²

h² = 1665

h = sqrt(1665)

h = 40.804 feets

Height of tree to the nearest tenth ;

40.804 feets + 12 feets

= 52.804 feets

= 52.8 feets

Geometric sequence

an = a1 r ^(n-1)

____________________

f(n)=1/2*4^n, n≥0

in this case a1= 1/2

r = 4

n= 0 (you just replace n)

f( 0 )=1/2*4^0

f(0) = 1/2 =1/ 2

n f(n)

0 f(0) = 1/ 2 f( 0 )=1/2*4^0

1 f(1) = 2 f( 0 )=1/2*4^2 = 4/2

2 f(2) = 8 f( 0 )=1/2*4^2 = 16/2

3 f(3) = 32 f( 0 )=1/2*4^2 =64/2

4 f(4) = 128 f( 0 )=1/2*4^2 = 256/2

To find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval (-2/3, 5x /6), we need to use the definite integral. We can use the formula:
∫[a, b] f(x) dx

where a is the lower bound of the interval and b is the upper bound of the interval. In this case, a = -2/3 and b = 5x /6. Therefore, we have:
∫[-2/3, 5x /6] sin x dx
We can evaluate this integral using the substitution u = cos x. This gives us:

∫[-2/3, 5x /6] sin x dx = -cos x |[-2/3, 5x /6] = -cos(5x/6) + cos(2/3)
Finally, we can substitute in the values for the upper and lower bounds of the interval to get the exact answer:
Area = -cos(5x/6) + cos(2/3) = 0

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The probability that a randomly selected squirrel has a weight less than 3 pounds:  P(x < 3) = 0.0139

What is Probability?

Chance is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes certainty.

Given,

μ = 4.1

σ = 0.5

∴ P(x < 3) = P(z < (3 - μ) / σ)

= P(z < (3 - 4.1) / 0.5)

= P(z < -1.1/0.5)

P(x < 3) = P(z < -2.2)

P(x < 3) = 0.0139

As a result, P(x 3) = 0.0139 is the probability that a squirrel chosen at random weighs less than 3 pounds.

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Answer:

x=4

Step-by-step explanation:

5(2x-2)=30

divide both sides

2x-2=6

move the constant to the right

2x=6-2

caculate

2x=8

divide both sides

x=4

Answer:

reflexive property

Step-by-step explanation:

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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Answer:

ΔOGD ≅ΔPRC

Step-by-step explanation:

SAS

The person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).

Distance is the length of one point to the next.

Time refers to the hours or minutes consumed in making a displacement.

Speed shows the rate of the change in displacement resulting from the interaction of distance with time.

Speed measures the ratio of distance to time.

Thus, the person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).

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Answer:

71.70

Step-by-step explanation:

Answer:

71.70 for sure