FACTOR:
b(a+1)^2 - 5(a+1)

a) By definition of standard form, a light-year is equal to 5.880 × 10¹² miles.

b) By simple rule of three, a magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

In this problem we need to convert a magnitude in miles to an equivalent magnitude in light-years and another magnitud in light-years to an equivalent magnitude in miles. Standard form is a notation used to represent both large and small number with no significant loss of precision. This form is described by the following form:

a.b × 10ⁿ

Where:

a) A light-year is equal to 5.880 × 10¹² miles.

b) The equivalent magnitude in miles is found by the following simple rule of three:

x = 4.25 ly × (5.880 × 10¹² mi / ly)

x = 2.499 × 10¹³ mi

A magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

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The interest of the CD account's of Ethan after 6 year is  $756.

For the given question;

Ethan deposit $7,000 into a certificate of deposit CD for 6 years.

The formula for finding the simple interest is;

SI = PRT/100

where,

Put the values in the formula,

SI = 7,000×1.8×6/100

Simplifying;

SI = 756.

Thus, the simple interest gained after 6 years will be $756.

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Answer:

5.2 × 10 to the power of 1

Step-by-step explanation:

IF AB=3x, BC=x+5 and AC=24 then the midpoint of AC is point B.

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

WE have given that AB=3x, BC=x+5 and AC=24. Since B is the midpoint, then we have:

AB = BC = AC/2

Now Substitute and solve for x:

AB = BC

x + 5 = 3x

x + -3x = -5

2x = 5

x = 5/2

AB = 3(5/2) = 15/2

BC = x + 5 = 5/2 + 5 = 15/2

Hence, the midpoint of AC is point B.

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Answer: x=8

Step-by-step explanation:

2x-3+x+5

2x-3+3=x+5+3 (Add 3 to both sides)

-2x=x+8

_____________

2x=x+8

2x-x=x+8-x (Subtract x from both sides)

_____________

Combine like terms

_____________

2x-x=x+8-x

1x=x+8-x

Multiply by 1

1x=x+8-x

x=x+8-x

_____________

Combine like terms

x=x+8-x

[x=8]

By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.

In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.

This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:

5 + 7 > 10

12 > 10 (True).

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Answer: 38.8g of sugar

Step-by-step explanation:

9.7 x 4= 38.8

a. The graph shows a positive correlation.

b. Using the line of best fit, his predicted score in his second paper could have been between 60 - 65.

A positive correlation is a type of correlation whereby two variables move in the same direction. That is, as one increases, the other increases also.

In a scatter plot, a positive correlation exist when both variables appear to move towards the same direction as the line of best fit slopes upwards from left to your right.

a. The scatter plot shows an upward trend on the line of best fit, therefore, the type of correlation shown by the graph is: positive correlation.

b. Using the line of best fit to make prediction, if he got 50 in his paper 1, then the score of the student in his paper 2 could have been between 60 and 65.

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The measure of the top, vertex angle of an isosceles triangle is option c 100 degrees

Given,

The base angle of an isosceles triangle = 40 degrees

We have to find the top, vertex angle:

Isosceles triangle:

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Here,

We know that total interior angle of a triangle is 180°

In an isosceles triangle base angles will be equal.

Here, base angle is 40 degrees.

Now, the top, vertex angle = total angle - base angle × 2

= 180 - 40 × 2

= 180 - 80

= 100

That is, the top, vertex angle of an isosceles triangle is 100°

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Answer: 15/16 is written as 0.9375 in decimal form.

Step-by-step explanation:

To convert any fraction to decimal form, we just need to divide its numerator by the denominator.

Here, the fraction is 15/16 which means we need to perform 15 ÷ 16.

This gives the result 0.9375

= 15/16

= 15 ÷ 16

= 0.9375

If the function 5x+ y = 1 has the domain {-2, 1, 6}, then {11, -4, -29}  is the corresponding range  and the  answer to your question is: letter D

Function   5x + y = 1

Domain        {-2, 1, 6}

Process

Domain is the possible values of the independent variable.

Range is the values of the dependent variable.

Evaluate the function with each of the domain values to get "y"

When x = -2

 5(-2) + y = 1

  -10 + y = 1

   y = 10 + 1

     y = 11

When x = 1

 5(1) + y = 1

 5 + y = 1

 y = -5 + 1

  y = -4

When x = 6

5(6) + y = 1

30 + y =1

 y = 1 - 30

y =  -29

Range = { 11, -4 , -29}

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Answer: x = -1 , F

Step-by-step explanation:

Hard to see your pic, but

[tex](-b+\sqrt{b^{2}-4ac } )/2a\\(-b-\sqrt{b^{2}-4ac } )/2a[/tex]

[tex](-5-\sqrt{5^{2}-16} ) / 8 = -1[/tex]

Your answer is: x = -1

Answer:

12 rolls, because 4.25 go into 20 , four times so u take 4 and multiply it by 3 and get 12.    

ALL THE SHAPES HERE ARE RECTANGLES AND THE AREA OF A RECTANGLE IS =L×B

TO GET THE AREA OF THE SHADED PART WE SAY THE AREA OF THE OUTSIDE SHAPE SUBTRACT THE AREA OF THE INNER SHAPE.

LET US FIND THE AREA OF THE OUTSIDE RECTANGLE FIRST.

[tex]a1 = (x + 5)(x - 1) \\ = {x}^{2} - x + 5x - 5 \\ a = {x}^{2} +4 x - 5[/tex]

NOW LET US FIND THE AREA OF THE INNER RECTANGLE.

[tex]a2 = (x + 1)(x - 4) \\ a = {x}^{2} - 4x + x - 4 \\ \\ a = {x }^{2} - 3x - 4[/tex]

the area of the shaded part is given by

[tex]a1 - a2 = ( {x}^{2} +4 x - 5) - ( {x}^{2} - 3x - 4) \\ = {x}^{2} + 4x - 5 - {x }^{2} + 3x + 4 \\ = {x}^{2} - {x}^{2} + 4x + 3x - 5 + 4 \\ areashaded = 7x - 1[/tex]

Answer:

2°C

Step-by-step explanation:

-3 + 5 = 11

Answer:

The temperature is 3°

Step-by-step explanation:

If we start at -3, then we go to -2, then -1, then 0, then 1 and then 2.

School A got 14 questions correct and School B got 14 questions correct.

The first step is to form a linear equations that represent the scores of the schools in the final round. A linear equation is an equation that has a single variable that is raised to the power of one. When graphed, a linear equation is usually a straight line.

Let x represent the number of correct and incorrect answers scored by School A

Total score at the end of the final round = beginning score + total scores of correct answers - total scores of incorrect answers

Total score at the end of the final round for School A :

87 + (12 ×x ) - (3 × x)

87 + 12x -3x

87 + 9x

Total score at the end of the final round for School B :

45 +  (12 ×x )

45 + 12x

If the two schools are tied, it means that both of the above expressions would be equal

45 +  12x = 87 + 9x

12x - 9x = 87 - 45

3x = 42

x = 42 / 3

x = 14

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Answer:

have a great day

Step-by-step explanation:

The zeroes of the equation f(x) is 3x² + 18x + 32 is x =  -18 -7.75/ 6 and x = -18 + 7.75/ 6

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

Given f(x) = 3x² + 18x + 32

3x^2 + 18x + 32 = 0

Here, a = 3

b = 18

c = 32

-b ±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

-18 ± [tex]\frac{\sqrt{18^2-4(3)(32)} }{2(3)}[/tex]

-18 ± [tex]\frac{\sqrt{324-84} }{6}[/tex]

-18 ± [tex]\frac{\sqrt{-60} }{6}[/tex]

-18 ± [tex]\frac{-7.75}{6}[/tex]

X = -18 (-7.75)/ 6 and x = -18 – (-7.75)/ 6

X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

Therefore, the zeroes of the polynomial are X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

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Answer:

44

Step-by-step explanation:

Let the number of eggs be N, and the weight be M

M is directly proportional to N.

.: M= kN

264 = 6k

.; k(the constant of proportionality is) = 264/6

k = 44.

1 small pizza and 4 large pizza feeds people according to the system of equations.

Let the number of small pizza be x and the number of large pizza be y.

So, we get the two equations as:

3 x + 4 y = 19 ...(1)

5 x + 5 y = 25 ...(2)

Taking 5 common from equation 2, we get that:

x + y = 5

x = 5 - y

Put it in equation 1, we get that:

15 - 3 y + 4 y = 19

15 + y = 19

y = 4

x = 5 - 4 = 1

Therefore, we get that, 1 small pizza and 4 large pizza feeds people according to the system of equations.

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The system of equations has one real solution (2,4).

The given system of equations is:

y = x²

y = 2x

Substitute the value of y in the second equation,

x² = 2x

x²- 2x = 0 ( Factorize it)

x(x - 2) = 0

x = 0 and x = 2

Putting the value of x in the equations to obtain the value of y,

y = x² = 0  

y = 2x = 2(0) = 0

y = x² = 2² = 4

y = 2x = 2(2) = 4

Therefore the system of equations has only one real solution (2,4).

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The x value will be 109°. The straight line formed a 180° angle. Solving the equation yields the angle.

Supplementary angles are two angels whose sum is 180°. When a straight line intersects a line, two angles form on each of the sides of the considered straight line.

Those two-two angles are supplementary angles in two pairs. That is, if two supplementary angles are adjacent to each other, their exterior sides form a straight line.

The straight line formed a 180° angle. The resulting equation is as follows:

⇒x+42°+29°=180°

⇒x=109°

Hence, the value of the x will be 109°

The complete question is:

AB is a straight line.

Work out the size of angle x.

Not drawn accurately

42°

Х

29°

А

B

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On multiplying by [3], the slope becomes 3 times the original slope and

y - intercept becomes 3 times of the original value.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

f(x) = ax + b, where [a] and [b] are nonzero real numbers. Now, the function f(x) is multiplied by 3.

The given straight line is -

y = f(x) = ax + b

After multiplied by [3], we get -

y' = 3f(x) = 3(ax + b) = (3a)x + (3b)

Therefore, on multiplying by [3], the slope becomes 3 times the original slope and y - intercept becomes 3 times of the original value.

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[Complete question - Given f(x) = ax + b, where a and b are nonzero real numbers, which of the following describes the differences between the graph of f and the graph of the output of f multiplied by 3 ]

The volume of sphere in terms of  is 288 cubic inches, if the sphere has a radius of 6 inches.

What is the volume of sphere?

In mathematics, the volume of the sphere defines the capacity of a sphere. It is measured in the cubic unit. Basically, it tells the amount of the air it can hold inside the sphere.

According to the question, the given data state that the sphere has a radius of 6 inches

Using standard formula for volume of sphere is,

Volume of the sphere = (4/3)πr³    

where, r - radius of sphere and it is 6 inches

Therefore, volume of sphere = (4/3)π(6)³ = (4/3)π(216) = 288 Cubic inches

Hence, the volume of sphere in terms of  is 288 cubic inches, if the sphere has a radius of 6 inches.

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The domain of any function represents the set of values of x for which the function is true.

The function shown in the graph starts at x=3 and continues towards +∞

The domain of the function is all values of x greater than or equal to 3.

√32 or 4√2 is the missing length of the right angle triangle whose other 2 legs measure 4 by 4 units.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Given the data in the diagram;

To determine the missing length, plug the given values into the formula above and solve for c.

c = √( a² + b² )

c = √( (4)² + (4)² )

c = √( 16 + 16 )

c = √( 32 )

Hypotenuse c = √32 or 4√2

Therefore, the missing length of the right angle triangle is √32.

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The length of each wooden board bought by Madelyn was 0.27 meters.

For the given question.

The number of wooden board bought by Madelyn = 7.

The length of all boards = 1.9 meters.

Thus, to find the length of each wooden board, simply divide the total length by the total board as each board is identical.

Each length = total length/number of boards

Each length = 1.9/7

Each length = 0.27 meter.

Thus, the length of each board bought by the Madelyn is 0.27 meters.

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Answer:

The correct answer is C.

Answer:

c = -10

Step-by-step explanation:

Hello!

According to the question we need to solve for c in the equation -49 = 2c - 29

-49 = 2c - 29

Flip the equation

2c - 29 = -49

Add 29 to both sides

2c - 29 + 29 = -49 + 29

2c = -20

Divide both sides by 2 to single out the variable

2c/2 = -20/2

c = -10

So, the value of c is -10