Write a number of your choice, using the following clues:

a two digit number
greater than 40
divisible by both 2 and 3

Answer:

Step-by-step explanation:

(f-g)(x)​ = f(x)- g(x)

= 3x - 1 - ( x + 2)

=3x - 1 - x - 2

= 2x - 3

Answer:

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

a^2b^2 - 9

Step-by-step explanation:

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.

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)

Answer:

[tex]x=4\sqrt{6}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

[tex]z=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

[tex]x^2=y^2+(12-4)^2[/tex]

[tex]x^2=y^2+64[/tex]

[tex]y^2=x^2-64[/tex] ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

[tex]z^2=y^2+4^2[/tex]

[tex]z^2=y^2+16[/tex]

[tex]y^2=z^2-16[/tex] ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

[tex]12^2=x^2+z^2[/tex]

[tex]144=x^2+z^2[/tex] ----> equation C

step 4

Equate equation A and equation B

[tex]x^2-64=z^2-16[/tex]

[tex]x^2=z^2+48[/tex] -----> equation D

step 5

substitute equation D in equation C

[tex]144=z^2+48+z^2[/tex]

solve for z

[tex]2z^2=144-48[/tex]

[tex]2z^2=96[/tex]

[tex]z^2=48[/tex]

[tex]z=\sqrt{48}\ units[/tex]

simplify

[tex]z=4\sqrt{3}\ units[/tex]

Find the value of x

[tex]x^2=z^2+48[/tex]

[tex]x^2=48+48=96[/tex]

[tex]x=\sqrt{96}\ units[/tex]

[tex]x=4\sqrt{6}\ units[/tex]

Find the value of y

[tex]y^2=z^2-16[/tex]

[tex]y^2=48-16[/tex]

[tex]y^2=32[/tex]

[tex]y=\sqrt{32}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

For a.

Since there are already two angles given for the triangle, we can measure the last angle using this formula:

90 + 55 + a = 180

Now solve for "a".

90 + 55 + a = 180

145 + a = 180

a = 180 - 145

a = 35°

For b.

From the picture above, the two triangle's tip are touching and having to form vertical angles. This means that the angles are congruent to each other.

Now that we have two angles in the second triangle(35 and 120), we can use the same formula:

35 + 120 + b = 180

Now solve for "b":

35 + 120 + b = 180

155 + b = 180

b = 180 - 155

b = 25°

Answer:

a = 35     b = 25

Step-by-step explanation:

Triangles always add up to 180 degrees.  Knowing this we can first solve the triangle with the right angle.

55 + 90 + a = 180

Before we solve this, keep in mind that the reflective property will be used on angle a, giving the answer to the third angle in the second triangle.

145 + a = 180

-145        -145

a = 35

Now that we have a solved use the reflective property to get it on the second triangle.

120 + 35 + b = 180

155 + b = 180

-155        -155

b = 25

There you have your two angles.

Hope this helped you out.

The proportion that could be used to solve for the variable is [tex]\frac{16}{40}=\frac{3}{h}[/tex] ; h = 7.5 ⇒ answer b

Step-by-step explanation:

A proportional relationship: one variable is always a constant value times the other, that constant is called the constant of proportionality

The number of walls and the number of hours are increased or decreased together

∴ The number of walls and the number of hours are proportion

∵ 16 walls in 40 hours

∵ 3 walls in h hours

- By using the second rule above

∴ [tex]\frac{16}{40}=\frac{3}{h}[/tex]

The proportion that could be used to solve for the variable is  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

Let us solve it to find h

∵  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

- By using cross multiplication

∴ 16 × h = 3 × 40

∴ 16 h = 120

- Divide both sides by 16

∴ h = 7.5

The value of h is 7.5 hours

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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.

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:

Answer:

425

Step-by-step explanation:

just subtract, 750-325

You subtract 750 - 325 = 425. Your answer is 425.

Hope this helps!!!!!

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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:

The area of the orange ​band is 576 + 48x square inches

Step-by-step explanation:

Step 1: Area of the green square

The area of the green square =[tex]side^2[/tex]

The area of the green square  =  [tex]x^2[/tex] square inches

Step 2: Area of the orange square

The area of the orange square =[tex]side^2[/tex]

The side of the orange square  =  12+12 + x = 24 +x

Now the area of the orange square  =[tex](x+24)^2[/tex]

Step 3: The area of the orange ​band

Area of the orange ​band =  area of the orange square - area of the green square

Area of the orange ​band =   [tex](x+24)^2 - x^2[/tex]

expanding and solving the equation we get

[tex]x^2 + 24^2 +48x - x^2[/tex]

[tex]576 + 48 x[/tex] square inches

Final answer:

The area of the orange band surrounding the central green square on the rug is found by subtracting the area of the green square from the area of the entire rug. The formula for the area of the orange band is 48x + 576 square inches, where x represents the side length of the green square.

Explanation:

To find the area of the orange band on the rug, we need to calculate the area of the entire rug and subtract the area of the central green square. The width of the orange band is given to be 12 inches. Therefore, each side of the orange rug is increased by 2 times 12 inches (for both the left and the right side of the green square), making the total length of the rug's side x + 2(12) inches.

The area of the entire rug, which is a larger square, is[tex](x + 24)^2[/tex] square inches. The area of the central green square is [tex]x^2[/tex]square inches. To find the area of the orange band, we subtract the area of the green square from the area of the entire rug which is: [tex](x + 24)^2 - x^2[/tex].

Expanding the squared term we get: [tex]x^2 + 48x + 576 - x^2[/tex], which simplifies to 48x + 576 square inches. That's the area of the orange band surrounding the green square.

Answer: Angle X = 30

Step-by-step explanation: First and foremost, we should recognize that an isosceles triangle has two sides equal and the two angles subtended by the two equal sides are also equal in measurement.

This means. In the diagram on the left, line DE = line DF and that is 10cm.

The similar angles are the ones subtended by the lines identified as being equal, that is

Angle E = angle F and that is 75. If both angles measure a combined total of 150 the third angle can be derived simply as

180 - (75+ 75)

{Sum of angles in a triangle = 180}

180 - (150)

= 30

Therefore angle D = 30.

However having been given in the question that both triangles are similar and are isosceles, then

Angle D = Angle X and that is 30

Answer:

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:

b

Step-by-step explanation:

bc i just did it

Answer:

The interest rate was 2.5% per year.

Step-by-step explanation:

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:

Step-by-step explanation:

[tex]A_{5}=4+(-1)^5=4-1=3[/tex]

The fifth term of the sequence is 3.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Given to us,

Sequence,

An=4+(-1)^n

For fifth term,

n = 5,

now, we have,

Subsituting the value of n we get,

An=4+(-1)^n

A_5 = 4+(-1)^5

A_5 = 4+(-1)

A_5 = 4 -1

A_5 = 3

Hence, the fifth term of the sequence is 3.

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Answer:

The total of ways the buildings can be painted are  = 4 [tex]\times[/tex] 3  [tex]\times[/tex] 2  [tex]\times[/tex] 2  [tex]\times[/tex] 1 = 48 ways.

Step-by-step explanation:

i) color five buildings that are in a row.

ii) any two neighboring buildings must be different colors

iii) the first third and fifth buildings must be different colors.

iv) the number of ways to paint the fist building are 4.

v) the number of ways to paint the second building are 3.

vi) the number of ways to paint the third building are 2.

vii) the number of ways to paint the fourth building are 2.

viii) the number of ways to paint the last building are 1.

ix) therefore the total of ways the buildings can be painted are

   = 4 [tex]\times[/tex] 3  [tex]\times[/tex] 2  [tex]\times[/tex] 2  [tex]\times[/tex] 1 = 48 ways.

Answer:

84

Step-by-step explanation:

we can split it into 2 cases: 1 case is when you choose the last building first and the second case is when you choose it last: so it is 4x2x2x3 for the first case and 4x3x3x1 for the last. So it’s 36+48=84 total cases.

Answer:

What

Step-by-step explanation:

What is the missing variables

45 gallons of water used per person each month

Solution:

Given that,

The town of new London uses about 2,750,000 gallons of water each month

The population of new London is approximately 61,000

To find: Number of gallons of water used per person each month

From given,

Total gallons of water each month = 2750000

Population = 61000

Therefore,

[tex]Gallons\ of\ water\ per\ person = \frac{\text{Total gallons of water each month}}{population}[/tex]

[tex]Gallons\ of\ water\ per\ person = \frac{2750000}{61000}\\\\Gallons\ of\ water\ per\ person = \frac{2750}{61}\\\\Gallons\ of\ water\ per\ person =45.08 \approx 45[/tex]

Thus 45 gallons of water used per person each month

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:

The product of 5x + 3 and 8x2 - 2x + 5 is 3x2 and 8 + 3x + 5

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ((5x +  (3and8 • x2)) -  2x) +  5

Step  2  :

Trying to factor a multi variable polynomial :

2.1    Factoring    3x2and8 + 3x + 5

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

 3x2and8 + 3x + 5

Processing ends successfully

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Answer:

40X^3 - 34X^2 + 4X + 15

Step-by-step explanation:

Using Algebraic expansion, the first number in bracket with its coefficience multiplies the second bracket. Equally , the second number in the first bracket is also used to multiply the second bracket, taking note of the sign (addition and minus sign)

5x(8x^2 -2x +5) +3 (8x^2 -2x +5)

= 40X3 - 10X^2 + 10X -24X^2 - 6X + 15

= 40X^3 - 34X^2 + 4X + 15

Answer:

The scale factor is 3.

Step-by-step explanation:

Let the origin O(0,0) is the reference point and the coordinates of the point A are given by (3,-6).

Therefore, the distance OA is given by [tex]\sqrt{(3 - 0)^{2} + (- 6 - 0)^{2}} = 3\sqrt{5}[/tex] units.

Again, the coordinates of point A' are (1,-2).

Therefore, the distance OA' is given by [tex]\sqrt{(1 - 0)^{2} + (- 2 - 0)^{2}} = \sqrt{5}[/tex] units.

Hence, the scale factor is [tex]\frac{OA}{OA'} = \frac{3\sqrt{5} }{\sqrt{5}} = 3[/tex]. (Answer)

Answer:

es mi amigos senior le si nueve diez veite treinta Cien si onu fose locas

Step-by-step explanation:

Step-by-step explanation:

Given,

The product of two numbers = a

To find, the both numbers = ?

Let the two numbers = x

∴ x × x = a

⇒ [tex]x^{2}[/tex] =  a

⇒ [tex]x^{2} =\sqrt{a}^2[/tex]

Comparing the powers, we get

⇒ x = [tex]\sqrt{a}[/tex]

∴ First number = [tex]\sqrt{a}[/tex] and Second number = [tex]\sqrt{a}[/tex]

Thus, the product of two numbers is a,  [tex]\sqrt{a}[/tex] of both numbers.

Answer:

(2,-5)

Step-by-step explanation:

P(2,5)

(x,y)

Reflection over x-axis so the x coordinate stays the same while the y coordinate changes from a positive to a negative.

The point P(2, 5) reflected over the x-axis will have coordinates (2, -5), as the x-coordinate remains unchanged and the y-coordinate becomes negative.

When the point P(2, 5) is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Therefore, the coordinates of the resulting point, P', after reflection would be (2, -5). This is because reflecting over the x-axis means that we keep the horizontal position of the point the same (same x-coordinate), but flip the vertical position (change the sign of the y-coordinate).

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