HELP PLEASE, ANSWER ALL AND NUMBER.​

The steps to factor an equation with 5 terms is explained below.

In math the definition of equation is written as a mathematical statement that shows that two mathematical expressions are equal

Basically the equation with five terms in polynomial is known as Monomial.

The steps to factorize the monomial is explained below.

Here the very first steps is to factor By Grouping With 5 Terms

Then we have to take the common terms out of it, then factor out the GCF of the entire expression.

Then split the terms and it must be in the form of quadratic expression, and then use the quadratic formula to factor out the terms.

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Answer: 6

Step-by-step explanation:

    GCF is the greatest common factor of both values. First, we will list all factors of both numbers. Then, we will find the largest number that overlaps between both.

30 ➜ 1, 2, 3, 5, 6, 10, 15 and 30

54 ➜ 1, 2, 3, 6, 9, 18, 27 and 54

    The greatest common factor (GCF) is 6.

Answer:

the GCF of 30 and 54 is 6

Step-by-step explanation:

The greatest common factor (GCF) of two numbers can be found using the following steps:

For 30 and 54:

Prime factorization:

[tex]\sf:\implies{30 = 2 \times 3 \times 5}[/tex]

[tex]\sf:\implies{54 = 2 \times 3 \times 3 \times 3}[/tex]

Common factors:

[tex]\sf:\implies{2 \: and \: 3 }[/tex]

Multiply the common factors:

[tex]\sf:\implies{GCF = 2 \times 3 = 6}[/tex]

Therefore, the GCF of 30 and 54 is 6.

The value of k is 6.

The condition of the unique solution is

a1/a2[tex]\neq[/tex]b1/b2

Here a1=4,b1=k,a2=2,b2=3

4/2=k/3

k=6

The value of k is 6.

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The correct  question is below:

Find the value of k such that the following pair of linear equations has a unique solution.

4x+ky+8=0;          2x+3y+7=0

The equation of the line that passes through the points (36,-30) and (-12,34) is  y = - 4 / 3 x + 18.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the equation of the line  that passes through the points (36, -30) and (-12, 34).

Hence, the slope can be found as follow:

slope = y₂ - y₁ / x₂ - x₁

slope = 34 + 30 / -12 - 36

slope = 64 / -48

slope = - 8 / 6 = - 4 / 3

Therefore, let's find the y-intercept of the line using (-12, 34)

y = - 4 / 3 x + b

34 = - 4 / 3 (-12) + b

34 = 16 + b

b = 34 - 16

b = 18

Therefore, the equation is y = - 4 / 3 x + 18.

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In Mike's study, the sample is the group of 50 randomly selected professors from colleges or universities in Michigan that he is obtaining salary information from.

The sample is a smaller representative group of the larger population, which in this case is all the professors who work for colleges or universities in Michigan. The population is the group of individuals or objects that the researcher is interested in studying. In this case, the population is the group of all professors in Michigan and their salaries. The goal of the study is to make inferences about the population based on the sample data.

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Answer:78400

Step-by-step explanation:

They will be at same altitude is 171 minutes when their altitude will be 24300 feet.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Based on the information, to calculate the period when the airplane will be at same altitude will be:

51300 - 3000m = 2700m

Collect the like terms

-3000m - 2700m = -51300

-5700m = -51300

Divide

m = 51300 / 5700

m = 9

The number of minutes will be 9 minutes

The altitude will be:

= 2700m

= 2700 × 9

= 24300 feet

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The figure has an image of right triangle and the dimensions are solved to get

The right triangle's sides are solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

From the question it can be deduced that

opposite = 12 ft

adjacent = b

hypotenuse = c

Using tan, TOA the adjacent is solved

tan 30 = Opposite / Adjacent

tan 30 = b / 12 ft

b = 12 / tan 30

b = AC = 20.784 ft

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 20.784 / c

c = 20.784 / cos 30

c = AB = 24 ft

< A + < B + < C = 180 (angles in a triangle)

30 + < B + 90 = 180

< B = 60

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Answer: A quartile is a type of quantile that splits a data set into four equal parts. The first quartile (Q1) is also known as the lower quartile and is the value that separates the lowest 25% of the data from the rest. The second quartile (Q2) is also known as the median and is the value that separates the lowest 50% of the data from the highest 50%. The third quartile (Q3) is also known as the upper quartile and is the value that separates the lowest 75% of the data from the highest 25%.

In this case, the lower quartile (Q1) is 65, the median is 78, and the upper quartile (Q3) is 92.

Step-by-step explanation:

The solution is k = -257.57

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: k/6.3 + 99.8 = 55.9

We have to find the solution to k.

By applying simplification in the given equation we get the solution to k

k/6.3 + 99.8 = 55.9

k + 99.8 × 6.3 =  55.9 × 6.3

k + 628.74 = 352.17

k = 352.17 - 628.74

k = 276.57

Hence, the solution is k = 276.57.

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So, the area of the placemat is 155 square inches.

To find the area of the circular placemat, we can use the formula for the area of a circle, which is πr^2, where r is the radius of the circle.

We know that the placemat has 44 inches of braid around the edge, which represents the circumference of the circle. We can use the formula for circumference of a circle which is C = 2πr.

By substituting the value of C = 44 inches

C = 2πr

44 = 2πr

r = 44/(2π)

Now we have the value of the radius, we can substitute it into the formula of the area of a circle

A = πr^2

A = π(44/(2π))^2

A = (44^2)/(4π)

A = (1936)/(12.56) = 154.8 square inches

To the nearest square inch, the area of the placemat is 155 square inches.

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When the line is perpendicular to either the y-axis or the x-axis, the absolute value will be preferred above the distance coordinate formula.

How can I calculate the separation between two coordinates?

The formula used to calculate the separation between two coordinates is commonly represented as;

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

Now, this formula is particularly helpful when the line is parallel to either the y axis or the x axis and the two coordinates do not have identical x or y coordinates.

It is important to remember that opposites have the same distance from zero whether the line is parallel to either the y or the x axis when one coordinate is negative and the other is positive.

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The annual percentage yield is 3.40%.

To find the annual percentage yield (APY) given an interest rate and the compounding frequency, we can use the following formula:

APY = (1 + (interest rate / compounding frequency))^compounding frequency - 1

In this case, the interest rate is 3% and the compounding frequency is monthly, so we can plug these values into the formula:

APY = (1 + (0.03 / 12))^12 - 1

APY = (1 + 0.0025)^12 - 1

APY = (1.0025)^12 - 1

APY = 1.0340406779661017 - 1

APY = 0.0340406779661017 or 3.40406779661017%

Thus, the annual percentage yield is 3.40% (rounded to the nearest hundredth of a per cent).

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Adrian need to invest $2041.88,  to the nearest hundred dollars for the value of the account to reach $3900 in 14 years.

Let principal amount is x

And interest is y

Then, according to question

X + y = 3900    --------------eq(1)

and formula of interest

I = (P*t*R)/ 100

Y = (x * 14 * 6.5) / 100   ----------------------eq(2)

3900 – x = (x * 14 * 6.5) / 100  from eq(1) and eq(2)

390000 – 100x = 91x

191x = 390000

X = 2041.88

So, therefore principal amount = $2041.88

and interest = $1858.12

You can earn interest on interest by using compound interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

You get interest based on the amount you deposit when you add money to a savings account or other account of a similar nature. For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily. The account balance plus any interest that has accrued but has not yet been paid out are used by the bank to determine your daily interest earnings.

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The total amount with Siobhan is given by the equation S = $ 8.33

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount with Siobhan be represented as S

Let the amount with Priya be represented as P

Let the amount with James be J = $ 7.00

And , Priya makes 40% more than James

So , P = ( 40 / 100 ) x P + P

Substituting the values in the equation , we get

The amount with P = ( 0.40 ) ( 7 ) + 7

The amount with Priya P = 2.8 + 7

The amount with Priya P = $ 9.80

Now ,

Siobhan makes 15% less than Priya

So , the amount with Siobhan S = P - ( 15/100 )P

Substituting the values in the equation , we get

The amount with Siobhan S = 9.80 - ( 0.15 )( 9.80 )

On simplifying the equation , we get

The amount with Siobhan S = 9.80 - 1.47

The amount with Siobhan S = $ 8.33

Hence , the amount with Siobhan is $ 8.33

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The relationship between consecutive angles a and b is a° + b° = 180°

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are square, rectangle, parallelogram, kite etc.

A parallelogram is a quadrilateral in which opposite sites are equal and parallel to each other. All the angles sum up to 360 degrees and the diagonals bisect each other.

The opposite angles of a parallelogram are equal to each other while the consecutive angles are supplementary. Also, the perimeter is gotten by adding all the individual sides

a° + b° = 180° (consecutive angles)

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The type of graph of x = -2 is a vertical line.

Equations of the form x = a, where a is a constant, are represented by vertical lines, and the x-coordinate of that line is the value of a. Similarly, the equations of the form y = b, where b is a constant, are represented by horizontal lines and the y-coordinate of that line is the value of b.

x = -2 is a vertical line, the graph of this equation is a line that goes vertically through the point (-2,0) and extends infinitely in the upward and downward direction.

It is worth to note that if you want to graph an equation like x = -2 or y = -2, you only need to plot the point that satisfies the equation, and then extend that point infinitely in the direction of the other variable.

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Answer:

[tex]y=-\frac{4}{3} + 2[/tex]

Step-by-step explanation:

[tex]y=mx+b\\(-8)=-(\frac{4}{3} )(3)+b\\-8=-4 +b\\2=b\\y=-\frac{4}{3} + 2[/tex]

y - y1 = m(x - x1) Is the answer

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

First, calculate the slope of line joining points (-7 , 1) and (-3 , 9) :

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{y2 -y1 }{x2 - x1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{9 - 1}{ - 3 - ( - 7)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{8}{ - 3 + 7} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{8}{ 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = 2[/tex]

Slope of the line (m) = 2

Equation of line in point slope form :

[tex]\qquad \sf  \dashrightarrow \: y - y1 = m(x - x1)[/tex]

[ Put in the values ~ ]

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2(x - ( - 3))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2(x + 3)[/tex]

[ That's our required equation in point slope form ]

But it can be simplified further, it depends on it, if that's asked or not.

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 2x + 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 2x + 15[/tex]

It will travel a distance of 15 km in 20 minutes and it will cover a distance of 250 km in 3 hours and 20 minutes.

The given problem is a straightforward one involving time, speed, and distance. The given body travels at a constant 75 km/hr. According to the law of universal motion, the distance traveled by any body in any interval of time equals its speed times the elapsed time. Finding the distance the body must go in 20 minutes is the first step of the presented problem. This period of time is equal to one-third of an hour. Distance is now equal to speed multiplied by time. Using this relationship, we may calculate that the body travels 15 km in 20 minutes. Using the aforementioned relation once more, we can determine that it will take 3 hours and 20 minutes to travel 250 kilometers.

                                   [tex]Distance=speed*time[/tex]

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Answer:

The maximum height = 14 ft, and the time caught at 5 ft high = 1.5 seconds

Step-by-step explanation:

Used desmos.

2 and 3 has a multiplicative inverse of -3 and 2, which is 2. A number that, when multiplied by the inputted number, produces the result 1 is said to be the multiplicative inverse of that number.

When a number is multiplied by another, the result is 1, this is known as the multiplicative inverse of the original number . It is the reciprocal of a number per multiplicative inverse definition. A-1 or is used to denote the multiplicative inverse of a number "a".

According to the multiplicative inverse property, a multiplies with its reciprocal, 1/a, to get 1, for any number a. It follows that 1/a is a number's multiplicative inverse. The multiplicative inverse of 5, when applied to the integer 5, is 1/5, according to this characteristic. Dividing 1 by a real number yields the multiplicative inverse of that number. One fifth (1/5, or 0.2) and one-quarter (0.25, or 1 divided by 0.25, respectively) are examples of reciprocals.

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The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.

cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.

tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.

cosecant: Cosecant is a multiplicative inverse of sine.

secant: Secant is a multiplicative inverse of cosine.

cotangent: Cotangent is the multiplicative inverse of the tangent.

Thus, The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

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When we write a number in fraction with denominator 1, then we evaluate an expression with fractions like evaluating an expression with whole numbers.

But when we write a fraction with denominator other that 0 and 1, then we evaluate an expression with fractions is different from evaluating an expression with whole numbers.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We know that;

To evaluating an expression with fractions like evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator 1.

And, To evaluating an expression with fractions is different from evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator other that 0 and 1.

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The value of the car in 8 years after it has depreciated is $8,348.

To find the value of the car in 8 years, we can use the formula for the future value of a depreciating asset:

future value = original value * (1 - rate of depreciation)^number of years

In this case, the original value is $18,000, the rate of depreciation is 12% per year (or 0.12), and the number of years is 8. Plugging these values into the formula, we get:

future value = 18,000 * (1 - 0.12)^8

future value = 18,000 * 0.4630

future value = $8,348

So the value of the car in 8 years is $8,348.

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Acute angles can be measured with the help of a protractor.

Find the measure of x, y, and z?

The angles 2x x+2 =180°

2x+x+2=180°

3x+2=180°

3x=180-2

3x=178

x=178/2

X=88

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Answer:

Step-by-step explanation:

What you can do in this case is the following rule of three to find the result:

1 light year ---> 5.88 * 10 ^ 12 miles

3.2 * 10 ^ 2 light year ---> x

Clearing x we have:

x = ((3.2 * 10 ^ 2) / (1)) * (5.88 * 10 ^ 12)

x = 1.88 * 10 ^ 15 miles

answer:

In scientific notation, approximately it is 1.88 * 10 ^ 15 miles

The hypotenuse is 17 units.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The hypotenuse of a right triangle can be found using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs).

So the hypotenuse of a right triangle with legs 8 units and 15 units can be found by:

c = √(a² + b²)

Where c is the hypotenuse and a and b are the legs of the triangle.

c = √(8² + 15²) = √(64 + 225) = √289 = 17

So the hypotenuse of a right triangle with legs 8 units and 15 units is 17 units.

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A triangle's perimeter is determined by the sum of its three sides. The perimeter of triangle is 16

Sum of the three sides determines a triangle's perimeter.Additionally, the units used to measure the lengths of a triangle's sides and perimeter are the same.If the sides of it have lengths that are measured in various units, convert them to that unit first.

The lengths of all four side edges must be added up in order to determine the rectangle's perimeter.Since there are two of each side length, it is easy to accomplish this by simply multiplying the sum of the length and width by two.

(Length + Width)2 is the perimeter calculation formula.

The perimeter is the sum of the lengths of all sides.

Using the distance formula, determine the lengths of the sides:

d  = √ ( x2 - x1 ) ² + ( y2 - y1 )²

A = ( -3 ,0 ) , B= (0,4) C= (3,0)

AB = √ (0 - (-3)² + ( 4 - 0) ² = √ 25 =5\sAC = √ ( 3 (-3)²+ (0 -0)²  = √6² = 6

BC √ (3-0)² +(0 - 4) ² =  √ 25 =5

P = ( AB) + (AC)+ (BC) = 5+ 6+5

= 16

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Answer: the perimeter is 16