Mathematics High School

## Answers

**Answer 1**

There must be added one zero pair: -9, 9.

f (x) = x² - 6 x + 9 - 9 + 1 = (x² - 6 x + 9 ) - 8 =

=(x - 3 )² - 8 ( the vertex form)

**Answer 2**

Answer:

the answer is 8

Step-by-step explanation:

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## Related Questions

When a quadrilateral is inscribed in a circle, what is known about the opposite angles?

### Answers

The measure of the angle with vertex and the endpoints of the sides lying on the circle is half the measure of the intercepted arc. If the quadrilateral is inscribed in a circle, the sum of the measures of the intercepted arc is 360 degrees representing the whole circle.

This means that the sum of the opposite angles is 180 degrees.

18 months is the same as 1.5 years. a. True

b. False

is 18 months is the same as 1.5 years.

### Answers

One year has 12 months therefore...

18/12 = 1 6/12 = 1 1/2

1 1/2 is equivalent to 1.5

True

5x + 2y = 7 y = x + 1 What is the solution set of the given system?

### Answers

The solution set of the system of equation are, x = 5/7, y = 12/7

What is an expression?

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

We have to given that;

The system of equation are,

⇒ 5x + 2y = 7 .. (i)

⇒ y = x + 1 .. (ii)

Now, We can solve the system of equation as;

Here, The system of equation are,

⇒ 5x + 2y = 7 .. (i)

⇒ y = x + 1 .. (ii)

Substitute the value of y from (ii) in (i), we get;

⇒ 5x + 2y = 7

⇒ 5x + 2(x + 1) = 7

⇒ 5x + 2x + 2 = 7

⇒ 7x = 7 - 2

⇒ 7x = 5

⇒ x = 5/7

And, From (ii);

⇒ y = x + 1

⇒ y = 5/7 + 1

⇒ y = 12/7

Thus, The solution set of the system of equation are, x = 5/7, y = 12/7

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Answer: the solution set would be {(5/7,12/7)}

Step-by-step explanation: had this question on a quiz

Which products are negative? Choose all answers that are correct.

A.

–3.1 • (–4.2) • (–6) • (–1.5)

B.-1 1/4 x(-2 3/4)x(-3)

C.1/2 x(-1/4)x(-1/8)

D.

8 • (–1.1) • 5

### Answers

A product is negative when the number of negative numbers in the multiples is odd.

Therefore, options B and D gives negative products.

The ________ is the number of square units in the interior of a figure. composite

circumference

area

perimeter

### Answers

The area is the number of square units in the interior of a figure

Which products are negative? Choose all answers that are correct.

A.

–3 • 6.1 • 5

B.

5.1 • (–4.3) • (–3)

C.

–2 • (–1) • 5 • (–4) • (–7) • (–3)

D.

### Answers

A product is negative when the number of negative numbers in the multiples is odd.

Therefore, options A and C gives negative products.

What is the Greatest Common Factor of 8 and 36?

A. 2

B. 4

C. 6

D. 8

### Answers

Answer:

The greatest common factor is 4.

Step-by-step explanation:

The easiest way to do this exercise is to make two lists: one with all the factors of the number 8, and another with all the factors of 36. Thus,

Factors of 8 : {1, 2, 4, 8}

Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36}

Then, we found that the common factors are {1, 2, 4}. So, as the larger number in the last list is 4, we conclude that the greatest common factor is 4.

//List all the factors for both 8 and 36

8: 1, 2, 4, 8

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The highest number in both of these is 4, therefore B

Which equations illustrate the commutative property of multiplication? Choose exactly two answers that are correct.

A.

B.

–8 • (4 • 1) = (–8 • 4) • 1

C.

–4 • (5 + 7.1) = –4 • 5 + (–4) • 7.1

D.

–8 • (5 + 3.1) = (5 + 3.1) • (–8)

### Answers

Commutative law states that in multiplication a x b = b x a (i.e. the product remains the same irrespective of the order of presentation).

From the options

Option B illustrates associative property

Option C illustrates distributive property

Option D illustrates commutative property (i.e. -8 x (5 + 3.1) = (5 + 3.1) x (-8))

The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle. Always, sometimes, or never

### Answers

Answer:

Polygon: A polygon is a simple closed curve entirely made up of line segments.

1. As starting from triangle

Three kind of triangles: Isosceles, Scalene , and equilateral triangle

In none of these measure of an exterior angle at the vertex of the triangle equals the measure of the adjacent interior angle.

2. Quadrilateral = Parallelogram, Rhombus, Rectangle, Square, Kite, Trpzm

Apart from Rectangle and Square none other quadrilateral have The measure of an exterior angle at the vertex of the quadrilateral equals the measure of the adjacent interior angle.

we can also consider other polygons also like pentagon,hexagon,heptagon.

Decagon and found that it is not always possible that measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.

So, the correct option is Sometimes.

So an exterior angle at the vertex of a polygon not can being never equal the measure of the adjacent interior angle

A sphere-shaped water balloon can extend to a diameter of 3.5 inches before it explodes. How much water can the water balloon hold before it explodes.

Use 3.14 for π.

179.5 in3

5.6 in3

21.98 in3

22.44 in3

### Answers

Volume of a spehere=(4/3)πr³

Data:

diameter=3.5 in

π=3.14

1)we calculate the radius:

r=diameter/2=3.5 in / 2=1.75 in

2) we calculate the volume of this sphere:

volume=(4/3)*3.14*(1.75 in)³=22.4379...in³≈22.44 in³.

Answer: 22.44 in³

Answer:

The answer is 22.44 in³.

Step-by-step explanation:

I just did the quiz.

Which expression is equivalent to 2(m − 4) + 1? 2m − 7

2m − 3

2m + 9

2m + 10

### Answers

2(m - 4) + 1 = 2m - 8 + 1 = 2m - 7

Answer:

The expression 2(m − 4) + 1 is equivalent to 2m - 7 .

Step-by-step explanation:

As the expression given in the question is as follows

= 2(m − 4) + 1

Now first open the bracket of the above experession

= 2m - 8 + 1

Simplify the above

= 2m - 7

Therefore the expression 2(m − 4) + 1 is equivalent to 2m - 7 .

The diameter of a men's basketball is 24.2 centimeters. Compute the volume of the men's basketball.

Use 3.14 for π.

1854.2 cm3

5562.7 cm3

7416.94 cm3

59,335.5 cm3

### Answers

To solve for the volume of the sphere given its diameter use,

V = (πd^3) / 6

Substituting the given in the problem to the equation,

V = (3.14 x 24.2^3) / 6 = 7416.94 cm^3

Thus, the answer is7416.94 cm^3 which isthe third among the choices.

Answer:

The answer is 7416.94 cm^3

Step-by-step explanation:

I just did the quiz

Factor completely 4xy + 9x + 24y + 54. I am pretty sure this is D but i would appreciate if someone checks me!

A. (4y − 9)(x − 6)

B. (4y − 9)(x + 6)

C. (4y + 9)(x − 6)

D.(4y + 9)(x + 6)

### Answers

Answer:

(D ) ( 4y + 9 ) ( x + 6 ) is correct option.

Step-by-step explanation:

Given : 4xy + 9x + 24y + 54.

To find : Factor completely.

Solution : We have given that 4xy + 9x + 24y + 54.

Interchanging the terms 9x and 24 y.

4xy + 24y + 9x + 54.

Taking common 4 y from first two terms and 9 from last two terms .

4 y ( x + 6 ) + 9 ( x + 6 )

On grouping

( 4y + 9 ) ( x + 6 ).

Therefore, (D ) ( 4y + 9 ) ( x + 6 ) is correct option.

(x+6)(4y+9) yes it is D.

Which statement models this situation? The distance between two cars must be greater than 45 feet.

A.

d = 45

B.

d + 45 > 0

C.

d < 45

D.

d > 45

### Answers

The distance d must be greater than 45 feet

so this mean d > 45 ft

result choice D. is right sure

Factor completely 3bx2 − 9x3 − b + 3x. (b − 3x)(3x2 − 1)

(b + 3x)(3x2 + 1)

(b + 3x)(3x2 − 1)

Prime

### Answers

Hello,

answer A

3bx²-9x^3-b+3x=b(3x²-1)-3x(3x²-1)=(3x²-1)(b-3x)

Answer:

a is correct ty

Step-by-step explanation:

Isabella observed that everyone on her soccer team is older than 13. She wrote the inequality a > 13 to represent the possible ages of her teammates. Which numbers satisfy the inequality but make no sense in this situation?

Choose all answers that are correct.

A.

102

B.

96

C.

15

D.

13

### Answers

Of all the choices presented above, only letter D. 13 does not satisfy the inequality as the number should be higher than 13. Out of the choices that satisfy the inequality, only letter C. makes sense. Letter A and B satisfy the inequality but do not makes sense as this represent the ages of very old people already which are not capable of playing the sports.

Thus, the answer is letter A. 102 and letter B. 96.

Will upvote response and like any user that helps!! Factor completely 10xy + 3y + 20ax + 6a.

(10x − 3)(y − 2a)

(10x − 3)(y + 2a)

(10x + 3)(y + 2a)

(10x + 3)(y − 2a)

Factor completely 5ab + 3ay + 5b + 3y.

(5b + 3y)(a + 1)

(5b − 3y)(a + 1)

(5b + 3y)(a − 1)

Prime

### Answers

Hello,

1) Answer C

10xy+3y+20ax+6a=y(10x+3)+2a(10x+3)

=(10x+3)(y+2a)

2) Answer A

5ab+3ay+5b+3y=a(5b+3y)+1(5b+3y)

=(5b+3y)(a+1)

A printer can print 30 pages in 2.5 minutes. ￼Write and solve a proportion to find the number of pages that the printer can print in 5 minutes. Show your work

### Answers

The number of pages the printer can print and time are directly proportional. If we let x be the number of pages and t the time, this direct variation may be mathematically expressed as,

x = kt

where k is the constant of variation.

Substituting the given to the equation,

30 = k(2.5) ; k = 12

Solving for the number of pages printed after 5 minutes,

x = (12)(5) = 60

Thus, the printer can print 60 pages in 5 minutes.

What is the length of a side of a cube with a volume of 216 in3?

### Answers

Hello,

Side=∛216=6 (in)

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What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.

### Answers

We will use factoring:

x² - 7 = 0

x² = 7

x =

or x=

x² +2 = 0

x² = -2, this part of equation has no solutions.

Answer:

d on edge.

Step-by-step explanation: