What is the area of this composite figure?
10 ft
10 ft
6 ft
2 ft

a. In order to factor the equation, the vertex form needs to be expanded to the standard form first, to obtain the factors of the equation

b. The parabola is easily graphed with the information on the vertex given in the vertex form of the quadratic equation

c. The vertex, minimum or maximum of the parabola are easily obtained in the vertex form of the quadratic equation

d. The quadratic formula is defined based on the standard form of the quadratic equation

Answer:

[tex]\huge{\boxed{\text{A) Standard form}}}\\\huge{\boxed{\text{B) Vertex Form}}}\\\huge{\boxed{\text{C) Vertex Form}}}\\\huge{\boxed{\text{D) Standard Form}}}\\[/tex]

Step-by-step explanation:

Vertex form is represented as: [tex]f(x) = a(x-h)^2+k[/tex], where the vertex of the parabola is (h, k).

Standard form is represented as [tex]f(x) = ax^2+bx+c[/tex], where a, b, and c are constants.

A) When factoring an equation, the sum of the roots is equal to b and the sum of the roots is equal to c, meaning standard form is the beneficial.

B) When graphing a parabola, vertex form is extremely beneficial, as it provides the vertex of the parabola, and the direction in which it opens.  If "a" is positive, the vertex opens upward, while when "a" is negative, the vertex opens downward.  As such, graphing is greatly eased with this information.

C) As is evident from the name, vertex form is the best for identifying the vertex of a parabola, as it is explicitly shown via the constants h and k.

D) The quadratic formula directly uses the constants a, b, and c, so working in standard form is more beneficial, as it removes the effort of solving for each constant.

Hope it helps :) and let me know if you want me to elaborate.

The plane 13x + 11y + 20z = 39 is where the line x = t, y = 1 + t, and z = 1 t cross (2,3,-1).

A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions. In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used.

Here,

13t+11(1+t)+20(1-t)=39

13t+11+11t+20-20t=39

4t+31=39

4t=8

t=2

x=2, y=3, z=-1

The line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39 at (2,3,-1).

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The standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

As given,

(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )

=  ( 6.31 × 10 + 2.6 )

=  ( 63.1 + 2.6 )

=  ( 65.7 )

= 65.7 × 10⁴

Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.

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In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .

What is Standard Form of a Equation ?

Ax+By=C

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.

Given Equation :[tex]y = -\frac{4x}{3} + 2\\[/tex]

To convert it into Standard form , Multiply both sides with 3

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

[tex]3y = -4x + 6\\4x + 3y = 6[/tex]

Hence , In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .

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As per the concept of complex number, the equivalent expression to the given complex number is: –16 + 30i.

In math, the term complex number is defined as the following form:

=> a+bi,

where a and b are real numbers.  

where the variables: a is the real part and bi imaginary part.

Here we have given that the complex expression: (3+5i)²

And we need to find the equivalent expression for this one.

Here we know that the same properties used for real numbers can be applied to complex numbers.

According to this rule, we have to solve the operations math with these numbers, it is important to know that i²= -1.

As we know that the algebraic expressions are considered equivalent when they are equal.

Therefore, for solving this question, you should:

We have to apply the power rules and then  select the option that is equal to the result found.

= > (3+5i)²

Now it can be expanded like the following,

=> 9+30i+25i²

Apply the rule,

=> 9+30i+25*(-1)

=> 9+30i-25

=> -16 + 30i

Therefore, option (a) is correct.

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Therefore, the total cost of producing the first 16 units of a certain commodity is 28940.

The mathematical formula for a straight line on a graph is called a linear equation. Y = mx + b, where m is the line's slope  b seems to be the y-intercept, or the place where the line crosses the y-axis, is how it is expressed. Because they simply have one variable and no exponents, linear equations are comparatively easy to solve. They may be used to simulate a variety of real-world events, including population increase and the supply-demand connection in the economy. Generally speaking, linear equations are a fundamental algebraic tool produced and are used to represent and analyse a wide variety of data types.

How to solve?

dc/da = [tex]9x^{2} + 4x + 15x^(1/4) +10[/tex]

Differentiate with respect to x

dc/da = [tex]18x + 4 + 15/4 x^(-3/4)[/tex]

input the value 100 for the value of x,

dc/da = 1800 + 4.75

dc/da = 1808.75

To produce the first 16 units,

1808.75 × 16 = 28940

The cost of producing the first 16 units is 28940

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Answer:

False!

Step-by-step explanation:

See picture for examples.

Answer:

x = 7

Step-by-step explanation:

Compare the ratios of the longer side length to the shorter side length:

8 : 10 = (3x - 9) : 15

8*(3/2) : 15 = (3x - 9) : 15

Then, form an equation.

8 * (3/2) = 3x - 9

12 = 3x - 9

21 = 3x

7 = x

The value of x is 21.

If the ratios of the lengths of the respective sides of two figures are the same and their corresponding angles are congruent, then the figures are said to be similar.

Given that, the corresponding angles of the two trapezoids are equal, therefore, the trapezoids are similar.

Since the trapezoids are similar, the ratio of their corresponding sides are in proportional:

14/18 = x/27

x = 27× (14/18)

x = 21

Hence, the value of x is 21.

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The assumptions been met (0.6581,0.7819).

What is American adults?

In 2020, the U.S. Census Bureau counted 331.4 million people living in the United States; more than three-quarters (77.9%) or 258.3 million were adults, 18 years or older — a 10.1% increase from 234.6 million in 2010.

Given that.

[tex]$$\begin{aligned}& p=0.72 .(1-p)=1-0.72=0.28 \\& n=200 .\end{aligned}$$[/tex]

At [tex]$95 \%$[/tex] confidence level x value is 1.96

z=1.96

So r

A 95 % confidence interval bor percent of American adults who beleive in Aliens is,

[tex]$$\begin{gathered}p \pm 2 \sqrt{\frac{p \times q}{n}} \\\therefore 0.72+1.96 \sqrt{\frac{0.72 \times 0.28}{200}} \\\therefore 0.72 \pm 1.96 \sqrt{0.0010} \\0.72 \pm 0.0619 \\\therefore \quad(0.6581,0.7819)\end{gathered}$$[/tex]

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The description of each equation in comparison with its' right hand side is;

A) True for all values of x.

B) True for no values of x.

C) True for no values of x.

D) True for no values of x.

E) True for all values of x.

F) True for no values of x.

G) True for no values of x.

H) True for all values of x.

A) We are given the equation;

7x - 5

This can also be written as; -5 + 7x and so the right hand side is true.

B) We are given the equation as 5x - 7.

There is no 4 in the equation and so the right hand side is wrong.

C) We are given the equation as -3x + 5.

The coefficient of x is -3 and not -4 and so the right hand side is wrong.

D) We are given the equation as;

3x - 32 + 4(4x - 2463)

By basic inspection, the right hand side cannot be true because we can see a very huge value in this bracket.

E) We are given the equation as 7x - 9 + 3(6x + 3)

Expanding the bracket gives;

7x - 9 + 18x + 9 = 25x

Thus, the right hand side is correct.

F) We are given the equation as 3x + 9

The equation does not contain -4 and 20 and so the right hand side is wrong.

G) We are given the equation as 10(2x - 3)

Multiplying the bracket gives 20x - 30. Thus, the right hand side is wrong

H) We are given the equation as 4(4x + 3) - 3x

Multiplying out the bracket gives us;

16x + 12 - 3x = 13x + 12

Thus, the right hand side is correct.

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Answer:

Yes

Step-by-step explanation:

Since the point is in the intersection area (purple) of the lines it is a solution.

The factored form of the equation x² + 11x + 24  is  (x + 3)(x + 8).

A quadratic equation is an algebraic equation of the second degree in x. Quadratic equation can be represented in standard form as follows:

ax² + bx + c

where

Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.

Therefore, let's factor the equation x² + 11x + 24 as follows:

x² + 11x + 24

The two numbers we can add to get 11 and multiply to get 24 are 3 and 8.

Therefore,

x² + 3x + 8x + 24

x(x + 3) + 8(x + 3)

Hence, the factored form is (x + 3)(x + 8)

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Fraction of the sensors on the given satellite which have been upgraded is equal to  option D. 1/7.

As given in the question,

Total number of modular units = 30

Let 'n' be the total number of upgraded sensors available on the entire satellite

Number of non-upgraded sensors available on one unit = ( 1/5)n

                                                                                         = x/5

Number of non-upgraded sensors available on 30 modular unit

= 30n /5

= 6n

Total number of non- upgraded and upgraded sensors makes one unit

⇒n + 6n =  1

⇒7n = 1

Fraction of upgraded sensors are:

⇒ n = 1/7

Therefore, the fraction of the sensors available on the satellite and are upgraded is equal to option D. 1/7.

The above question is incomplete , the complete question is:

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

A. 5/6     B. 1/5      C. 1/6     D. 1/7        E. 1/24

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Answer: 8.20

Step-by-step explanation:

1kg = 1000g

take 650 divided by 1000 = 0.65kg

Then take 5.33 divided by 0.65 = 8.20

The remainder and quotient are written as the following partial fractions:

Quotient: [tex]4x + 1[/tex]

Reminder: [tex](18x - 3)[/tex]

Divide the leading term of the numerator by the leading term of the denominator to obtain the first term of the quotient:

[tex]\dfrac{8x^3} { 2x^2} = 4x[/tex]

Multiply the entire denominator by the first term of the quotient, then subtract it from the numerator:

[tex](4x)(2x^2 - x - 21) = 8x^3 - 4x^2 - 84x\\\\(8x^3 - 2x^2 - 67x - 24) - (8x^3 - 4x^2 - 84x) = 2x^2 + 17x - 24[/tex]

With the new numerator, repeat steps 1 and 2 [tex](2x^2 + 17x - 24)[/tex] and the original denominator [tex](2x^2 - x - 21)[/tex]:

[tex]\dfrac{2x^2} { 2x^2} = 1\\(1)(2x^2 - x - 21) = 2x^2 - x - 21\\(2x^2 + 17x - 24) - (2x^2 - x - 21) = 18x - 3[/tex]

The resulting numerator [tex](18x - 3)[/tex] is the remainder.

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Answer:y=-1/7x+26/7

Step-by-step explanation: y=mx+b substitute m=-1/7

y=-1/7x+b

The line passes through the point (-2,4)

This means x=-2 and y=4 must be substituted in the above equation

4=-1/7*-2+b

4=2/7+b

Solve for b

To get b on its own we need take 2/7 from both sides

4-2/7=2/7-2/7+b

26/7=b

Need to solve 4/1-2/7

Must make denominators the same

Multiply top and bottom by 7

4*7/1*7-2/7

28/7-2/7=26/7

Answer: I Do not know specifically but If we are talking about rates/per hour the answer is 55 Per hour

Step-by-step explanation:

165 miles ÷ 3 hours because It may be talking about rates. Per "HOUR"

A rectangle is transformed according to the rule R0, 90º.

What does parallelogram mean ?

A quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size.

                 Additionally, the internal angles on the same transverse side are supplementary. 360 degrees is the sum of all interior angles.

We are given that the rotation is

(x,y) --------> (x,y)

This means that the point is rotated back into its original position.

This means that full rotation occurred.

Since the full rotation is 360°,

For the other options:

Rotation 90° gives:

(x,y) ----------> (-y,x)

Rotation 180° gives:

(x,y) ----------> (-x,-y)

Rotation 270° gives:

(x,y) ---------> (y,-x)

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By using simultaneous linear equation, it can be calculated that-

200 adult tickets and 400 student tickets were sold

In another performance, ticket sale falls $1320 below the goal of $3300

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here, a simultaneous linear equation needs to be solved

Here, d represents the number of adult tickets and s represents the number of student tickets

Their auditorium holds 600 people

d + s = 600 ..... (1)

Price of adult ticket = $7.50

Price of student ticket = $4.50
Total price = $(7.50d + 4.50s)

By the problem,

7.50d + 4.50s = 3300

5d + 3s = 2200 ..... (2)

Multiplying (1) by 3

3d + 3s = 1800.... (3)

Subtracting (3) from (2)

2d = 400

[tex]d = \frac{400}{2}[/tex]

d = 200

Putting the value of d in (1)

200 + s = 600

s = 600 - 200

s = 400

Now,

At one performance there were two times as many student tickets sold as adult tickets.

Total tickets sold = d + 2d = 3d

By the problem-

3d = 360

d = [tex]\frac{360}{3}[/tex]

d = 120

s = 2 [tex]\times[/tex] 120 = 240

Number of student ticket sold = 240

Number of adult ticket sold = 120

Total cost = 240 [tex]\times[/tex] 4.50 + 120 [tex]\times[/tex] 7.50

                 = $1980

Fall in ticket sale = $(3300 - 1980) = $1320

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Last night, the two dinner specials at Dwayne's favorite restaurant were salmon filet and steak. The restaurant served 25 specials in all, 24 percent of which were salmon filets 6 salmon filets did the restaurant serve.

10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.

A percentage in mathematics is a figure or ratio that may be stated as a fraction of 100. If we need to determine a percentage of a number, we should divide it by 100 and multiply the result.

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Answer:

Step-by-step explanation:

For number 1, It is $52.4

Divide the cost by the number f days to get your constant

for number 2, It is 2

Just format it to y=mx+b

I do not know the answer to the third one

And the fourth one it is true with a 1/25 fraction

Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

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The probability is: 3/5

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

There are : 41 | 43 | 47 | 53 | 59 (5 primes)  Between 40 and 60.

41 + 12 =53 is a prime

43 + 12 =55 Not a prime

47 + 12 =59 is a prime

53 + 12 =65 Not a prime

59 + 12 =71 is a prime

Therefore, the probability is: 3/5

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Answer:

To make sure who ever want the job is reliable and suitable for it.

Step-by-step explanation:

Answer:

x=43

Step-by-step explanation:

Since the two interior angles of a triangle always add up to the exterior angle (d=a+b btw if u dont understand what i mean), x+90=133

x=133-90

x=43

The ratio of any two right-angled triangle sides may be used to compute trigonometric ratios.

Given details :

The measurement of the given angle is 30 degree.

Here we use trigonometric ratio rule which is sin theta= opposite/hypotenuse

Here theta = 30 degree, opposite =7 and hypotenuse =a

So we get

sin 30 = 7/a

a= 7/sin 30

And value of sin 30 = 0.5

So we get , a = 7/0.5 = 14

So the value of a is 14 .

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Answer:

Step-by-step explanation:

la première planche = 2x

la deuxième = x

la troisième = x-10

1ere planche + 2eme planche + 3eme planche = 50 pouces

donc :

(2x) + x + (x-10) =50

4x-10 = 50

4x-10+10 = 50 +10

4x = 60

4x diviser par 4 = 60 diviser par 4

x=15

la première planche = 30

la deuxième = 15

la troisième = 5

30+15+5=50

In the equation y = mx + b, the meaning of the m and the b is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + b

Information gotten from the question include

In the equation y = mx + b

m = ? and b = ?

y = mx + b

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

b = y intercept

therefore m and b are the slope and y intercept respectively

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