A plane travels 600 mph for the first three hours of the trip. Then, the plane travels at a constant speed of 300 mph for two hours. Calculate the plane's average speed.

The value of h(-2) is 65

A function can be defined as an expression, law , rule of hypothesis that explains or compares the relationship between two variables - the dependent and the independent variable.

Given the function;

h(x) = 2x^4 - x³ + 2x² - 7x + 3

To determine the function, h(-2)

We substitute the value of x as -2 into the function, we have;

h(-2) = 2(-2)^4 - (-2)^3 + 2(-2)^2 - 7(-2) + 3

expand the bracket

h(-2) = 2(16) - 2(-8) - 7(-2) + 3

h(-2) = 32 + 16 + 14 + 3

h(-2)= 65

Thus, the value of h(-2) is 65

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Part (a)

x = the missing value

The set is {81, 54, 77, 68, x}

Add up those values and divide by 5 to compute the mean. Set this equal to the 74.6 stated. Then solve for x like so:

(81+54+77+68+x)/5 = 74.6

(280+x)/5 = 74.6

280+x = 5*74.6

280+x = 373

x = 373-280

x = 93

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

Part (b)

In the previous part, we have n = 5 values and n-1 = 5-1 = 4 of them can be freely selected. The 5th final value is locked in based on what those previous four values are. That 5th value being x mentioned earlier.

This shows that the degrees of freedom is n-1

In other words, one value is determined by the other values in the set.

1) The decimal 0.31313131...as a fraction is; 310/990

2) The decimal 0.02020202 as a fraction is; 200/9990

3) The difference of the two numbers as a repeating decimal is; 0.29292929

We are given the decimals as;

0.31313131...

0.02020202...

1) The decimal 0.31313131... is repeating decimal.

If we write it as;

x = 0.31313131...

Multiply both sides by 10 to get;

10x = 3.131313  --- (1)

Multiply both sides of initial equation by 1000 to get;

1000x = 313.131313   ----(2)

Subtract eq 1 from eq 2 to get;

990x = 310

x = 310/990

2) The decimal 0.02020202 is a repeating decimal.

If we write it as;

x = 0.02020202...

Multiply both sides by 100 to get;

10x = 2.020202  --- (1)

Multiply both sides of initial equation by 10000 to get;

10000x = 202.0202 02  ----(2)

Subtract eq 1 from eq 2 to get;

9990x = 200

x = 200/9990

3) The difference of the two numbers as a repeating decimal is;

0.31313131 - 0.02020202 = 0.29292929

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The number of hours Alma volunteered is 46 hours.

The process of time conversion changing or converting the unit of time from one unit to another.

For example, it can be converting seconds to minutes, converting minutes to hour or converting hours to minutes or hours to seconds.

Basically, time can be converted from one unit to another.

The number of hours Alma volunteered is calculated as follows;

60 minutes = 1 hour

2,760 minutes = ?

= (2760 x 1) / 60

= 46 hours

Thus, the number of hours Alma volunteered is 46 hours.

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Answer:

Step-by-step explanation:

46

The equivalent expression of 14x2 +18x + 5 is 18x + 14x2 + 5, the correct option is D.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

The function  14x2 +18x + 5

Now,

18x + 14x^2 + 5

This expression is equivalent to 14x^2 + 18x + 5, because it has the same terms but in a different order. You can use the commutative property of addition to rearrange the terms in any order without changing the value of the expression. For example:

14x^2 + 18x + 5 = (14x^2 + 5) + (18x)

14x^2 + 18x + 5 = (18x) + (14x^2 + 5)

14x^2 + 18x + 5 = (18x) + (5) + (14x^2)

14x^2 + 18x + 5 = (5) + (18x) + (14x^2)

All of these expressions are equivalent to each other and to the original expression.

Therefore, the equation will be 18x + 14x^2 + 5.

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Answer:

18.33

Step-by-step explanation:

multiply 55×2 you get 110

then since it is +13-7 + is bigger than - ( positive is greater than negative)

it will be 6

so 110 ÷6 = 18.3333333 you put it into 4digits

The answer is 18.33

Hope it will help

Factors of the polynomial 2x² + 8x - 90 is Option (c) 2(x + 9)(x - 5).

Factorization is the method used to discover the factors of a given value or mathematical statement. A factor is an integer that is multiplied by another to create the original number. For instance, 2, 3, 6, 9, and 18 are the factors of 18. Likewise, in the case of polynomials, the factors are the polynomials that are multiplied to create the initial polynomial.

Given Equation: 2x² + 8x - 90

Step 1: Pull out like factors from the equation

 ⇒ 2x² + 8x - 90  =   2 • (x² + 4x - 45)

Step 2: Factorize by splitting the middle term of the equation (x² - 4x - 45)

   ⇒ x²+ 9x - 5x - 45

Step 3: Take Common factors from the two pairs of the equation

⇒ x(x + 9) - 5(x + 9)

Step 4: Rewrite the polynomial in factored form

  ⇒ 2(x + 9)(x - 5)

Therefore the factorization result is 2(x + 9)(x - 5).

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After reduction of original size of a document by [tex]30%[/tex]%, the reduction scale is 70% of original size i.e., [tex]70:100=7:10[/tex]

As per the question statement, A photocopier reduces the original size of a document by 30%. We are supposed to find out what is the reduction scale.

Let say the document original size to be [tex]100%[/tex]% and if 30% is reduced by the photocopier, the remaining 70% will be the original size.

Hence reduction scale = [tex]70:100 = 7:10[/tex]

Therefore the reduction scale is 70% of the original size.

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Answer:

83.5

Step-by-step explanation:

Median means middle. So in order to get that you need to write the numbers in order and then get the middle number. If the amount of numbers are even then take the 2 middle ones and add the together then divide by two.

89, 52, 78, 92, 98, 64 --> 52, 64, 78, 89, 92, 98

Since you have 2 middle numbers, you must take the middle 2 (78 and 89) and add them.

78 + 89 = 167

Now divide 167 by 2

167 / 2 = 83.5

Answer = 83.5

Answer:

The GCF (Greatest Common Factor) is the biggest factor common to both of these numbers, so we must determine the factors for each:

15--->1,15

         3,5

20--->1,20

         2,10

         4,5

As we can see, 1 and 5 are the common factors and 5 is the biggest (greatest). Therefore, we can "pull" out a 5 from both numbers and get a resulting equation of:

15 + 20--->5(3 + 4)

Hope this helps!

Step-by-step explanation:

The folded fabrics that can fit inside a shipping box with the dimensions of 1 foot by 1 foot by 2 feet will be 18.

It should be noted that 12 inches = 1 feet

Therefore, 432 cubic inches will be converted to feet and this will be:

= 432/12

= 36

Therefore the number of folded fabric will be:

= 36 / (1 × 1 × 2)

= 36/2

= 18

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After calculating equation we have come to find that the value of y is equal to 0.525 is true

An equation is formed by joining two expressions with the equal sign "=". The two expressions on either side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation.

Typically, the right-hand side of an equation is assumed to be zero. This does not reduce generality because we can balance it by subtracting the expression on the right-hand side from the expressions on both sides.

We have given 12y - 1 / 2 = 8y + 8 / 5

lets solve it

⇒ 12y - 1 / 2 = 8y + 8 / 5

⇒ 12y -8y = 8 / 5 + 1 / 2

⇒ 4y = 21/10

⇒ y = 21/40

⇒ y  = 0.525

Thus, the value of y is equal to 0.525 is true

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Full question

Which value of y makes this equation true?

12y - 1 / 2 = 8y + 8 / 5

Answer:

EF=22

LM=19

ML=

Step-by-step explanation:

Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]m\angle C+130^{\circ}=180^{\circ} \\ \\ m\angle C=50^{\circ}

[/tex]

Question 2

Drawing PR, we form congruent triangles PQR and PSR. Thus, using the sum of angles in a triangle,

[tex]55^{\circ}+24^{\circ}+m\angle Q=180^{\circ} \\ \\ m\angle Q=101^{\circ}[/tex]

Question 3

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]13x+6+70=180 \\ \\ 13x+76=180 \\ \\ 13x=104 \\ \\ x=8[/tex]

Question 4

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]11x+15+19x+15=180 \\ \\ 30x+30=180 \\ \\ 30x=150 \\ \\ x=5 \\ \\ m\angle B=11(5)+15=70^{\circ}[/tex]

Answer:1=a

             2=b

             3=c

Step-by-step explanation:

The equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)

Lines are represented by first grade polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept of the line, and x and y are the independent and dependent variables, respectively.

We can find the values of the slope and the y-intercept by knowing the location of two distinct points on Cartesian plane. If we know that (x₁, y₁) = (- 5, 0) and (x₂, y₂) = (0, - 2), then the equation of the line is:

- 5 · m + b = 0               (1)

b = - 2                           (2)

The solution to the system of linear equations is (m, b) = (- 2 / 5, - 2). Lastly, the equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)

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Answer:

x=82

Step-by-step explanation:

Because of Supplementary angles we know that x+10 degrees and x+6 degrees is 180 degrees. We combine this to form 16+2x=180

subtract 16 from both sides. 2x=164

divide both sides by 2

x=82

Answer:14 000

Step-by-step explanation:

Simple interest formula: A=P(1+in)

A= amount after interest is added

P= initial amount (10000)

i= interest rate (8%)

n= number of periods (5 years)

Now substitute what you have into the simple interest formula:

A=P(1+in)

A=10000(1+(8/100)(5))

A= 14 000

The reason why 8 is divided by 100 is that 8 is a percentage. Unless you have a percentage function on your calculator, I'd strongly encourage you to ALWAYS divide your percentages by 100.

Answer:

The answer is D. y=-2x+8

Step-by-step explanation:

Hope this helps!!

Answer:

Step-by-step explanation:

You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.

The area of a square is given by the formula ...

  A = s²

Solving for the side length (s), we find ...

  s = √A

The side length of a square with 250 ft² area is ...

  s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length

The area of a square that has 50% more area is ...

  (250 ft²) × (1 +50%) = 375 ft²

The side length of that square is ...

  √375 ft = 5√15 ft ≈ 19.36 ft . . . side length

The percentage change can be found from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%

The percentage increase in the length of one side is about 22.47%.

Answer:

104 mph

Step-by-step explanation:

The Phoenix International Raceway is 1 Mile so they did 312 miles in 3 hours.

Rate = Distance/Time

R = 312/3 = 104/1

The racers were traveling at 104 miles per hour.

Answer:

Step-by-step explanation:

+(-11) is -11. You're "adding" -11 when in reality you're taking away 11 unless:

the equation looks like: -6+(-11)

the answer would be -17 because you're adding a negative to a negative. Taking away from a negative number is simply moving further down the negative number line, which makes the negative numbers "increase" in value

But if an equation looks like: 6+(-11)

the answer would be -5 since you are taking away 11 from a positive number.

Hope this makes sense and answers your question.

The value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

It should be noted that an equation is simply used to show the relationship between the expression or variables.

From the information, 3x - 1 + 5 < 1.

Collect like terms

3x - 1 + 5 < 1.

3x < 1 + 1 - 5

3x < -3

Divide

3x / 3 < -3 / 3

x < 1

Therefore, the value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

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Answer:

Hi there The answer should be 11.45 miles

Step-by-step explanation:

I added 3.7 + 4.5 + 3.2 = 11.45

With a calculator.

hope this helps!

Answer:

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

Identities we will use:

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

Given expression:

Factorize it by completing the square and setting the difference of squares:

The Four-fifths is equal to ten-sixteenths of a number is x=32/25.

Given the statement is four-fifths is equal to ten-sixteenths of a number.

A mathematical statement is a meaningful component of words that can be  true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Four fifths means 4/5.          ......(1)

And ten sixteenths means 10/16.

It is also given that ten sixteenths of a number means is (10/16)x.      .......(2)

Now, we will equate equation (1) and equation (2) according to the given statement is

4/5=(10/16)x

Further, we will cross multiply both sides, we get

4×16=10x×5

64=50x

Now, we will divide both sides by 50, we get

64/50=50x/50

64/50=x

32/25=x

Hence, the number for the given statement "Four fifths is equal to ten sixteenths of a number" is 32/25.

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Answer:

C=0

Step-by-step explanation:

C = 5/9 (60-32)

C= 5/9 (28)

C=15.55555556 (round to the nearest tenth)

C=15.6   - ANSWER