Macon has 32 rocks in his collection. He has 4 times as many rocks as his brother. How many rocks does Macon’s brother have?

Answer:

[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex]

or

[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]

Step-by-step explanation:

we have

[tex]f(x)=8x^{2}-4x+11[/tex]

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

[tex]f(x)=8(x^{2}-\frac{1}{2}x)+11[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}[/tex]

[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}[/tex]

Rewrite as perfect squares

[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex] ----> equation in vertex form

or

[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]

The vertex is the point  (0.25,10.5)

Final answer:

To find the area of a circle with a radius of 7 units, use the formula A = πr². Substitute 7 for r to get A = π(7²), which calculates to approximately 153.93804 square units. We round it to 150 square units, to match the significant figures of the radius.

Explanation:

The expression representing the area of a circle with a radius of 7 units is A = πr², where 'A' is the area and 'r' is the radius of the circle. To solve for the area with a radius of 7 units:

Substitute the radius (7 units) into the expression: A = π(7²).

Square the radius: 7² = 49.

Multiply by π (approximately 3.14159): A = π(49) or A ≈ 3.14159 × 49.

Calculate the area, which gives approximately 153.93804 square units.

Since the radius is given in two significant figures, you should express the area in two significant figures: A ≈ 150 square units.

Answer:

y=4x-1

Step-by-step explanation:

4x-y=1

4x=y+1 then negative Y becomes positive after going to the other side of the equal sign.

4x-1=y the positive 1 becomes negative after going to the other side of the equal sign.

Answer:

y = 4x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

4x - y = 1 ( subtract 4x from both sides )

- y = - 4x + 1 ( multiply through by - 1 )

y = 4x - 1 ← in slope- intercept form

Answer:

is 24 a b c and d?

Step-by-step explanation:

Answer:

9 students ride the bus.

Step-by-step explanation:

First you take the amount of students which is 24 and divide the denominator which is 8. then you would get 3, meaning 1/8 = 3 students. Now you would multiply the 3 students making one 8 by three ( because there are 3/8 students taking the bus, and you would get 9 students.

Final answer:

To find how many students ride the bus in Ms Mull's class, multiply the fraction of bus riders (3/8) by the total number of students (24), resulting in 9 students who ride the bus.

Explanation:

The question asks to determine how many students in Ms Mull’s class ride the bus, given that 3/8 of the students use the bus and there are 24 students in total. To find the number of students who ride the bus, multiply the total number of students by the fraction that represents the bus riders.

Identify the total number of students: 24.

Calculate 3/8 of 24:
(3/8) × 24.

Multiply: 3 × 3 = 9 (since 24/8 = 3).

Conclude that 9 students in Ms Mull’s class ride the bus.

Answer:

x=4

Step-by-step explanation:

2(x+2)+2(x+4)=28

Simplify the equation

2x+4+2x+8=28

4x+12=28

4x=16

x=4

Answer:

answer is b

Step-by-step explanation:

look at the picture

Yo sup??

slope=y2-y1/x2-x1

just take any value of x1 x2 y1 and y2

let x1,y1=2,1

and

x2,y2=4,-2

plugging in the values

slope=-2-1/4-2

=-3/2

therefore your answer is option 2

Hope this helps

Answer:

The correct answer is 1 and 1/2  

Trust Me

Answer:

The correct option is A

Step-by-step explanation:

quiz

Answer:

First term: 5

Fourth term: 5 1/2

Tenth term: 6 1/2

Step-by-step explanation:

Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:

A(n) = 5 + (n-1) (1/6)

First term:

A(1) = 5 + (1-1) (1/6)

A(1) = 5 + (0) (1/6)

A(1) = 5

Fourth term:

A(4) = 5 + (4-1) (1/6)

A(4) = 5 + (3) (1/6)

A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)

Tenth term:

A(10) = 5 + (10-1) (1/6)

A(10) = 5 + (9) (1/6)

A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)

Answer:

200.52 m²

Step-by-step explanation:

A = 12² + π·6²/2

= 144 + 36π/2

= 144 + 18×3.14

= 144 + 56.52

= 200.52 m²

The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle ⇒ D

Step-by-step explanation:

The Pythagorean triple is:

A. 12, 16, 20

∵ 20 is the greatest number

∵ (12)² + (16)² = 144 + 256 = 400

∵ (20)² = 400

∴ (20)² = (12)² + (16)²

∴ The set of integers 12, 16, 20 is a Pythagorean triple

∴ 12, 16, 20 are the side lengths of a right triangle

B. 10, 24, 26

∵ 26 is the greatest number

∵ (10)² + (24)² = 100 + 576 = 676

∵ (26)² = 676

∴ (26)² = (10)² + (24)²

∴ The set of integers 10, 24, 26 is a Pythagorean triple

∴ 10, 24, 26 are the side lengths of a right triangle

C. 14, 48, 50

∵ 50 is the greatest number

∵ (14)² + (48)² = 196 + 2304 = 2500

∵ (50)² = 2500

∴ (50)² = (14)² + (48)²

∴ The set of integers 14, 48, 50 is a Pythagorean triple

∴ 14, 48, 50 are the side lengths of a right triangle

D. 27, 32, 45

∵ 45 is the greatest number

∵ (27)² + (32)² = 729 + 1024 = 1753

∵ (45)² = 2025

∴ (45)² ≠ (27)² + (32)²

∴ The set of integers 27, 32, 45 is NOT a Pythagorean triple

∴ 27, 32, 45 are NOT the side lengths of a right triangle

The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle

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Answer:

-12/13

Step-by-step explanation:

Final answer:

To simplify the expression 24 - 4.57 + (-4.62), add the negative numbers together and then subtract the sum from the positive number, resulting in a simplified answer of 14.81.

Explanation:

The question involves simplifying an expression, which is a basic arithmetic operation in mathematics. We are given the expression 24 - 4.57 + (-4.62). To simplify, we need to combine like terms and perform the addition and subtraction.

First, let's combine the positive and negative numbers separately:

Positive number: 24

Negative numbers: -4.57 and -4.62

We add the negative numbers together: -4.57 + (-4.62) = -9.19

Now, we subtract this sum from the positive number:

24 - 9.19 = 14.81

Therefore, the simplified result of the expression 24 - 4.57 + (-4.62) is 14.81.

Answer:

Divide each side of the equation by 2.

Step-by-step explanation:

(I took the test so i know its right) Basically, when doing the this by completing the square we need y^2 by itself, so we divide 2y^2-16y=6 by two first.

Answer:

Divide each side of the equation by 2.

Step-by-step explanation:

2y² – 16y = 6

Divide both sides by 2

y² - 8y = 3

Answer:

x=-11/6, y=7/6. (-11/6, 7/6).

Step-by-step explanation:

-2x+2y=6

4x+2y=-5

-----------------

2(-2x+2y)=2(6)

4x+2y=-5

----------------------

-4x+4y=12

4x+2y=-5

----------------

6y=7

y=7/6

4x+2(7/6)=-5

4x+14/6=-5

4x=-5-14/6

4x=-30/6-14/6

4x=-44/6

x=(-44/6)/4

x=(-44/6)(1/4)

x=-44/24

simplify

x=-11/6

Final answer:

The volume of the refrigerator is factored by dividing with the given height, resulting in a quadratic polynomial that provides the other two dimensions. Upon factoring, we discover that the other dimensions are x - 6 and x + 1, corresponding to option D.

Explanation:

The volume of the refrigerator is given by the polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex]. To find the other two dimensions of the refrigerator, we need to factor this polynomial using the given height of the refrigerator, which is x + 2. The goal is to divide the volume polynomial by the height polynomial to get the product of the remaining two dimensions.

We proceed with polynomial division or factoring:

Divide the volume polynomial by x + 2 using synthetic division or long division.

The result should be a quadratic polynomial that further factors into the product of two linear factors corresponding to the unknown dimensions.

Factor the quadratic polynomial to find the two missing dimensions.

In this case, the volume polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex] can be divided by x + 2 to yield [tex]x^2 - 5x - 6[/tex], which can then be factored into (x - 6)(x + 1). Hence, the other two dimensions are x - 6 and x + 1, making option D correct.

gregory is 19 years old  and daisy is 21 because 21 is two more that 19 but 19 +21=40

The correct answer is:

Gregory is 19 years old  and daisy is 21

Let,

Age of Gregory = x years

Age of Daisy = (x+2) years

An equation in term of x

x + (x+2) = 40

2x + 2 = 40

2x = 40 - 2

x = [tex]\frac{38}{2}[/tex]

x = 19

∵ 19+21=40

⇒ Gregory is 19 years old

⇒ daisy is 21 years old

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Answer:

A: -0.3 and C: 1/6

Step-by-step explanation:

Step 1. Since 1/6 is positive it is greater than all negative numbers including -0.33

Step 2. -0.33 and -0.3 have the same numbers they are both negative but in -0.33 there are more hundred.

-0.3 >- 0.33

Step 3. -3/9= 0.33333..... -0.33 and -3/9 have the same number of units, tenths  and hundredths and both are negative but, -3/9 has more thousandths, so it's farther below 0.

-3/9 < -0.33

Final Step 4. -0.3 and 1/6 are greater than-0.33

The correct options are A.-0.3 and C. 1/6

In mathematics, an interval can be defined as a set of real numbers that contains all real numbers lying within any two specific numbers of the set R.

Given here: -0.33  which is equivalent to -1/3

The numbers greater than -1/3 lie in the interval (-1/3, ∞)

Clearly out of the given options only -0.3 and 1/6 lie in this interval.

Hence, The correct options are A.-0.3 and C. 1/6

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Answer:235/3

Step-by-step explanation:

Two hundred and thirty five over three as an imperfections fraction

Answer:

235/3

Step-by-step explanation:

78 * 3 from denominator which equals 234 + 1 from the numerator.

Answer:

look down + pls give me brainiest

Step-by-step explanation:

Let x = number of people when she got on.

x -4+3 -5+1 -1 = 4

x -6 = 4

Solve for x to get x=10.

So there were 10 people when Paulina got on (including herself).

Answer:

store A

Step-by-step explanation:

Answer:

a^2b^2 - 3ab + 3ab - 9

a^2b^2 - 9

Step-by-step explanation:

Answer:

14.1cm (3s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

sine angle= opp/hyp

cosine angle= adj/hyp

Answer:

  f(x) = x² +2

Step-by-step explanation:

x-values are evenly spaced, and y-values decrease to a minimum of 2, then increase again. First differences are -1, 1, 3, 5, and second differences are constant at 2. This means that a 2nd degree polynomial can be used for the rule.

The minimum of f(x) occurs at x=0, so there is no horizontal shift of the vertex of the quadratic function. f(1) -f(0) = 1, so the vertical scale factor for the quadratic is 1.

The quadratic with a vertex of (0, 2) and a vertical scale factor of 1 is ...

  f(x) = 1·(x -0)² +2

  f(x) = x² +2 . . . . . . simplified

_____

Comment on differences

"First differences" are the differences between successive "y" values when the "x" values are evenly spaced. Here, they are 2-3 = -1, 3-2 = 1, 6-3 = 3, 11-6 = 5. These are not constant, so the function is not a linear function.

"Second differences" are the differences between successive first differences. Here, they are 1-(-1) = 2, 3-1 = 2, 5-3 = 2. These are constant, so the function is a quadratic (2nd-degree). When n-th differences are constant, the sequence can be modeled by a polynomial of degree n.

__

Comment on determining the rule

Once you know the rule is 2nd-degree, there are a number of ways you can find out what it is. One way is to write it as ...

  f(x) = ax^2 + bx + c

and fill in three different values for x and f(x). This will give you three linear equations in a, b, and c, which can be solved by any of the usual means for solving systems of linear equations.

Fortunately, this set of data includes the vertex of the function, making it easy to start with the vertex form:

  f(x) = a(x -h)^2 +k

where (h, k) is the vertex (minimum, in this case), and "a" is the vertical scale factor. The value of "a" is easily determined as being the difference between f(h+1) and f(h). Here, h=0, so that is f(1) -f(0) = 3-2 = 1.

Answer:

x² +2

Step-by-step explanation:

The coordinates of P' is [tex](7,-11)[/tex]

Explanation:

The coordinates of Point P is [tex](4,-9)[/tex]

It is given that the point P is translated according to the rule,

[tex]$(x, y) \implies(x+3, y-2)$[/tex]

Now, substituting, the values for x and y, we get,

[tex](4,-9)\implies(4+3,-9-2)[/tex]

Adding the values, we get,

[tex](7,-11)[/tex]

Thus, the coordinates of P' is [tex](7,-11)[/tex]

Answer:

Cuba

Step-by-step explanation:

Answer:

7/6 (= 1 1/6)

Step-by-step explanation:

5(3-2y)+4y=8   (by PEDMAS, expand distribute parenthesis first)

3(5) -2y(5) + 4y = 8

15 - 10y + 4y = 8

15 - 6y = 8   (subtract 15 from both sides)

-6y = 8 - 15

-6y = -7  (divide both sides by -6)

y = -7 / -6 = 7/6 = 1 1/6

Answer:

y = 10.5

Step-by-step explanation:

5 x (3 - 2y) + 4y = 8

5 x (3 + -2y) + 4y = 8

15 + -10y + 4y = 8

15 + -6y = 8

(15/6) (-6y/+6)

 2.5        Y

-Y + 2.5 = 8

10.5 - 2.5 = 8

To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication. The equivalent expression is 56x^2 + 59xy + 15y^2.

To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication over addition.

This means that each term in the first expression is multiplied by each term in the second expression.

Here are the steps:

Apply the distributive property to multiply 7x by each term in the second expression: 7x * 8x + 7x * 5y

Apply the distributive property to multiply 3y by each term in the second expression: 3y * 8x + 3y * 5y

Simplify each term: 56x^2 + 35xy + 24xy + 15y^2

Combine like terms: 56x^2 + 59xy + 15y^2

Therefore, the expression (7x + 3y)(8x + 5y) is equivalent to 56x^2 + 59xy + 15y^2.