wiple Choice which equation describes the relationship
20. Multiple
the table?
0 0 1 2 3 4 5 6
16 10 20 30 40 50 60 70
A. C= 10n
B. C= 10 +n
C. C= 10
D. C= 10 + 10n
​

Length of diameter is 2.86 cm

Solution:

Given that circumference of a circle is 8.97 cm

To find: length of diameter

We can use the formula for circumference of circle to find radius and then we can find diameter

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where "r" is the radius of circle and [tex]\pi[/tex] is a constant equals to 3.14

Substituting c = 8.97 and [tex]\pi = 3.14[/tex]

[tex]8.97 = 2 \times 3.14 \times r\\\\8.97 = 6.28 \times r\\\\r = \frac{8.97}{6.28}\\\\r = 1.4283[/tex]

Thus radius of circle is 1.4283 cm

Finding diameter of circle

diameter = 2(radius)

diameter = 2(1.4283) = 2.8566

On rounding to two decimal point we get, 2.86

Thus length of diameter is 2.86 cm

Answer:

The distance of frame from each side of the wall so that it is at centered is 7.5 feet

Step-by-step explanation:

Given as :

The measure of the wall = 17[tex]\dfrac{3}{4}[/tex] feet

i.e The measure of the wall =[tex]\dfrac{71}{4}[/tex] feet

The measure of the picture = 2[tex]\dfrac{3}{4}[/tex] feet

i.e The measure of the picture =[tex]\dfrac{11}{4}[/tex] feet

Let The distance from each side of wall so that frame at centered = x feet

Now, According to question

x = The measure of the wall - measure of the picture

Or, x = [tex]\dfrac{71}{4}[/tex] feet - [tex]\dfrac{11}{4}[/tex] feet

Or, x = [tex]\dfrac{71 - 11}{4}[/tex] feet

Or, x = [tex]\dfrac{60}{4}[/tex] feet

∴ x = 15 feet

Now, For each side so that frame st centered = [tex]\dfrac{15}{2}[/tex] feet

Or,  For each side so that frame st centered = 7.5 feet

Hence,The distance of frame from each side of the wall so that it is at centered is 7.5 feet Answer

Answer:

Out of every 5 trials, the desired outcome will occur approximately 2 times

Step-by-step explanation:

The first statements states that it will happen exactly two times, but probability never guarantee the outcome

The third and fourth statement states out of 7 which cannot be true as 2-5 basically means out of 5

Answer:

B: Out of every 5 trials, the desired outcome will occur approximately 2 times.

Step-by-step explanation:

Irene's list of factors for the number 88 is almost correct, but she forgot to include the number 1.

Irene wants to list the factors for 88 and she writes 2, 4, 8, 11, 22, 44, and 88. To verify if Irene is correct, we need to identify all of the numbers that can evenly divide 88 without leaving a remainder. Starting with the number 1, which is a factor of every number:

1 x 88 = 88, so 1 and 88 are factors.

2 x 44 = 88, so 2 and 44 are factors.

4 x 22 = 88, so 4 and 22 are factors.

8 x 11 = 88, so 8 and 11 are factors.

Since there are no other numbers between 1 and 88 that can multiply together to equal 88, the list that Irene wrote appears to be missing the number 1.

Therefore, Irene's list is almost correct, but for it to be complete, it should include the number 1. The full list of factors for the number 88 should be 1, 2, 4, 8, 11, 22, 44, 88.

Answer:  [tex]m=0[/tex]

Step-by-step explanation:

The slope can be calculated with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Notice that the formula shows the change in "y" for a unit change in "x"  on the line.

In order to solve this exercise, it is important to remember that:

1. If a line is increasing, then its slope is positive.

2. If a line is decreasing, then its slope is negative.

3. If the line is horizontal, its slope is zero.

4. If the line is vertical, it has no slope.

Therefore, since the given line that passes through the point [tex](3,-4)[/tex], is horizontal, its slope is:

[tex]m=0[/tex]

Final answer:

To find the total weight in Robbie's backpack, the weights of the history textbook (2 5/6 pounds) and lunch (1 2/3 pounds) are added, resulting in a total of 4 1/2 pounds.

Explanation:

The question involves finding the total weight of items in Robbie's backpack: a history textbook and his lunch. The history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds.

To find the total weight, we first convert the mixed numbers into improper fractions for easier addition. The history textbook's weight as an improper fraction is (2×6)+5 = 17/6 pounds. The lunch's weight is (1×3)+2 = 5/3 pounds.

Adding these two fractions gives us:

   17/6 + 5/3 = 17/6 + 10/6 = 27/6 pounds

Since 27/6 simplifies to 4 1/2 pounds, the total weight in Robbie's backpack is 4 1/2 pounds.

Answer:

True

Step-by-step explanation:

1 and 3 are vertical angles

Answer: False

<1 and <3 are Supplementary Angles

Step-by-step explanation:

You need to factor the numerator and denominator...

(2x^2+4x-2x-4)/(2x^2-2x-2x+2)

(2x(x+2)-2(x+2))/(2x(x-1)-2(x-1))

((2x-2)(x+2))/((2x-2)(x-1))  so the (2x-2)s cancel out leaving

(x+2)/(x-1)

Answer:

[tex]\large\boxed{\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{x+2}{x-1}}[/tex]

Step-by-step explanation:

[tex]\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{2(x^2+x-2)}{2(x^2-2x+1)}=\dfrac{x^2+x-2}{x^2-2x+1}\\\\=\dfrac{x^2+2x-x-2}{x^2-x-x+1}=\dfrac{x(x+2)-1(x+2)}{x(x-1)-1(x-1)}\\\\=\dfrac{(x+2)(x-1)}{(x-1)(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+2}{x-1}[/tex]

Answer:

-19

Step-by-step explanation:

4x-8(2-x)

4x-16+8x

12x-16

12(-1/4)-16

-12/4-16

-3-16

-19

Answer:

-19 I think lemme know if im right

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

y/4-9=-3

y/4=-3+9

y/4=6

y=6*4

y=24

Answer:

Step-by-step explanation:

                                        Solving equation A: y = x

Let us consider the given equation A:

                                                      y = x

y = x

y = 1    ∵ x = 1

Hence, (1, 1) is the ordered pair of  y = x

y = x

y = 2    ∵ x = 2

Hence, (2, 2) is the ordered pair of  y = x

y = x

y = 3    ∵ x = 3

Hence, (3, 3) is the ordered pair of  y = x

y = x

y = 4    ∵ x = 4

Hence, (4, 4) is the ordered pair of  y = x

y = x

y = 5    ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y                 x

1                  1

2                 2

3                 3

4                 4

5                 5

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

                                          Solving equation A: y = x +2

Let us consider the given equation A:

                                                         y = x + 2    

y = x + 2

y = 1 + 2 ⇒ 3  ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

y = x + 2

y = 2 +2 ⇒ 4   ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5    ∵ x = 3

Hence, (3, 5) is the ordered pair of  y = x + 2

y = x + 2  

y = 4 + 2 ⇒ 6   ∵ x = 4

Hence, (4, 6) is the ordered pair of  y = x + 2

y = x + 2

y = 5 +2 ⇒ 7    ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y                 x + 2

1                  3

2                 4

3                 5

4                 6

5                 7

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

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Answer:

.19 cent per egg

Step-by-step explanation:

15*12=180

34.20/180= .19

The unit cost per egg is $0.60 when a case of eggs costs $34.20.

The unit cost per egg is $0.60.

To find the cost per egg when a case contains 15 dozen eggs costing $34.20, you first calculate the cost per dozen by dividing the total cost by the number of dozens (15). Then, you divide the cost per dozen by 12 to find the cost per egg. In this case, $34.20 divided by 15 gives $2.28 cost per dozen. Finally, $2.28 divided by 12 equals $0.60, so each egg costs $0.60.

14 ft > [tex]4\frac{1}{2}[/tex] yards

Step-by-step explanation:

Given,

14 ft ____ 4 1/2 yd.

We will convert yards into feet to determine the inequality.

1 yard = 3 feet

[tex]4\frac{1}{2}[/tex] yards = [tex]3*4\frac{1}{2}[/tex]

[tex]4\frac{1}{2}[/tex] yards = [tex]3*\frac{9}{2}[/tex]

[tex]4\frac{1}{2}[/tex] yards = 3*4.5 = 13.5 feet

which is less than 14 feet, making 14 feet greater, therefore, we will use 'greater than' inequality.

14 ft > [tex]4\frac{1}{2}[/tex] yards

Keywords: inequality, conversion

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Answer:

>

Step-by-step explanation:

Answer:

About $90, because the trend line shows that value for $11.

Step-by-step explanation:

It is the only one that shows a constant rate of change.

Answer:

the first one ( the line closest to 90)

Step-by-step explanation:

Answer:

1.14

Step-by-step explanation:

hundreth = 0.01

so we ignore the 3 because it is in teh thousandths

hope this helps :)

Answer:

The answer is C. y=cos(0.4x)

Step-by-step explanation:

took the test

Answer: c

Step-by-step explanation:

y=cos(0.4x)

Answer:

The area of the circle is 3,8550 mm

Step-by-step explanation:

Diameter    (d) = 70 mm

Radius             (r) = (70/2) mm = 35mm

Π                   = 22/7

Area of circle x       =   πr^2

                  =   22/7 x 35^2

                  =   22/7 x 1225

                  =   26,950/7

                  =   3,850 mm

The length of rectangle will be 18 meters and width of rectangle will be 11 meters.

It is given that width of a rectangle is seven meters less than the length.

If perimeter of rectangle is 58 meters then find the value of length and width.

What are the area and perimeter of a rectangle ?

The area of rectangle is A = L × B and the perimeter is 2 ( L + B ) , where ; L = length and B = width.

Let's assume the length of the rectangle is x.

The width of the rectangle will be ;

= x - 7

Also ; the perimeter of triangle is given which is equal to 58 meters.

We know that ; the perimeter of triangle is given by ;

Perimeter = 2 × ( length + width )

So ;

58 = 2 [ x + (x - 7)]

58 = 2 ( 2x - 7 )

58 = 4x - 14

or

4x = 58 + 14

4x = 72

x = 72 ÷ 4

x = 18 meters

So ;

Length = 18 meters

and

Width = 18 -7 = 11 meters

Thus , the length of rectangle will be 18 meters and width of rectangle will be 11 meters.

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Answer:

C

Step-by-step explanation:

The diagonal of the square creates 2 right triangles with the diagonal as the hypotenuse.

Using Pythagoras' identity in either of the right triangles.

The square on the hypotenuse is equal to the sum of the squares of the other 2 sides.

Let x be the side of the square, then

x² + x² = 40², that is

2x² = 1600 ( divide both sides by 2 )

x² = 800 ( take the square root of both sides )

x = [tex]\sqrt{800}[/tex]

  = [tex]\sqrt{100(8)}[/tex]

=  = 10[tex]\sqrt{8}[/tex]

  = 10 × [tex]\sqrt{4(2)}[/tex]

  = 10 × 2[tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] → C

Answer:

1. The percent commission earned is 3%.

2. The loan period is 3.29 years.

Step-by-step explanation:

1. Salesman has $65,100 in sales. He earned $1,953 in commission.

Let the percent commission earn be x%

Therefore, x% of the sales equals $1,953

[tex]\frac{x}{100} of  $65,100 = $1,953[/tex]

[tex]\frac{x}{100}  * 65100 = 1953\\\frac{65100x}{100} = 1953[/tex]

We cross multiply

[tex]\frac{65100x}{100}  = 1953\\65100x = 1953 * 100\\65100x = 195300[/tex]

Divide both side by the coefficient of 'x' (65100)

[tex]\frac{65100x}{65100} =  \frac{195300}{65100} \\x = 3[/tex]

Therefore, the percent commission earned is 3%

2. Interest (I) = $299  Principal (P) = $1300   Rate (R) = 7%

The formula for finding interest is given as: [tex]I = \frac{PRT}{100}[/tex]

Therefore, substituting into the formula, we have:

[tex]299 = \frac{1300 * 7 * T}{100}[/tex]

We are finding the time it takes the loan to earn an interest of $299

[tex]299 = \frac{1300 * 7 * T}{100} \\299 = \frac{9100T}{100}[/tex]

We cross-multiply:

[tex]299 * 100 = 9100T\\29900 = 9100T[/tex]

Divide both side by the coefficient of T (9100)

[tex]\frac{29900}{9100}  = \frac{9100T}{9100}\\T = 3.29[/tex]

Therefore, the time taken for the loan to earn such interest is approximately 3.29 years

Answer:

90π units²

Step-by-step explanation:

(refer to attached)

Total Surface are off a right cylinder = area of its ends + area of curved surface

Given radius, r = 3 units and height, h = 12 units

Area of 2 ends,

= Area of 2 circles

= 2 x πr²

= 2π (3²)

= 2π (9)

=18π units²

Area of curved surface,

= 2πrh

= 2π(3)(12)

= 72π units²

Hence,

Surface area = 18π + 72π = 90π units²

The solution is, 90π units² is its surface area.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

A right cylinder has a radius of 3 and a height of 12.

we know that,

Total Surface are off a right cylinder = area of its ends + area of curved surface

Given radius,

r = 3 units and height, h = 12 units

Area of 2 ends,

= Area of 2 circles

= 2 x πr²

= 2π (3²)

= 2π (9)

=18π units²

Area of curved surface,

= 2πrh

= 2π(3)(12)

= 72π units²

Hence,

Surface area = 18π + 72π = 90π units²

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Answer:

4 tens 6 ones

Step-by-step explanation:

those are the only way

The number 46 can be expressed as 4 tens and 6 ones, representing the value 40 plus 6, utilizing the powers of ten place value system.

When expressing the number 46 in terms of tens and ones, we use the place value system which is based on powers of ten.

In this system, each place in the number represents a power of 10.

To represent 46 as tens and ones, we look for the highest power of ten that fits into the number without exceeding it.

In the case of 46, that value is 40, because 4 tens (4 x 10) equal 40, and there are 6 ones left over.

Therefore, we can say that 46 consists of 4 tens and 6 ones. This can be shown visually as:

Answer: B. 42 inches

Step-by-step explanation:

Answer:

42 inches

Step-by-step explanation:

The function states in its second row that for size 2, the range of x (a child’s height in inches) is 42 ≤ x < 44. Then, the option 41.9 is incorrect because is less than 42 and x is greater-or-equal-to 42; option 44 inches is incorrect because it is equal to 44 and the equality sign is not included; option 44.1 inches is greater than 44 and x is less than 44; and option 42 inches is correct  because x is greater-than-or-equal to 42, that is, the equal sign is included.

Answer:

Its 24 and 12

Step-by-step explanation:

Answer:

He's right

Step-by-step explanation:

Answer:getting rid of the constant

Step-by-step explanation:

Answer: simplify x + 7 = 2x + 5 - 4x by combining like terms so x+7= 5-2x

Step-by-step explanation:

Answer:

A) division

Step-by-step explanation:

4x=-4

4x/4=-4/4 (dividing by 4 on both sides)

x=-1

Answer:

We can say that equations 1 and 2 have no solutions.

Step-by-step explanation:

The equation 1 is |3x − 1| + 7 = 2 ........ (1)

⇒ |3x − 1| = - 5

This equation is invalid as the absolute value of (3x - 1) will always be positive and here it is - 5.

Therefore, this above equation has no solution.

The equation 2 is |2x + 1| + 4 = 3 ........ (2)

⇒ |2x + 1| = - 1

This equation is invalid as the absolute value of (2x + 1) will always be positive and here it is - 1.

Therefore, this above equation has no solution.

Hence, we can say that equations 1 and 2 have no solutions. (Answer)

Option B is correct. The required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

Composite functions are functions written inside another function e.g f(g(x))

Given the expressions

f(x) = 2/x

g(x) = 2/x

We are to find the composite function f(g(x))

f(g(x)) = f(2/x)

f(2/x) =  (2/(2/x))

f(2/x)  = 2 * x/2

f(2/x) = x

Hence the required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

[tex]1. \( (f \circ g)(x) = \frac{1}{x^2} \)\\2. \( (f \circ g)(x) = x \)\\3. \( (f \circ g)(x) = -x \)\\4. \( (f \circ g)(x) = \frac{1}{4}x - 1 \)[/tex]

let's break down each pair of functions and find their composition:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \):[/tex]

  To find [tex]\( (f \circ g)(x) \)[/tex], we substitute [tex]\( g(x) \) into \( f(x) \):[/tex]

  [tex]\[ (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2} \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{2}{x}\right) \).[/tex]

  When you substitute [tex]\( \frac{2}{x} \) into \( f(x) \),[/tex]  you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{2}{x}\right) = \frac{2}{\frac{2}{x}} = x \][/tex]

  So, [tex]\( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \):[/tex]

 [tex]\( (f \circ g)(x) = f(g(x)) = f(2 - 3x) \).[/tex]

  Substituting  [tex]\( 2 - 3x \) into \( f(x) \),[/tex]we get:

 [tex]\[ (f \circ g)(x) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x \][/tex]

  So, [tex]\( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{2}x + 2\right) \).[/tex]

  When you substitute [tex]\( \frac{1}{2}x + 2 \) into \( f(x) \),[/tex] you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{1}{2}x + 2\right) = \frac{1}{2}\left(\frac{1}{2}x + 2\right) - 2 = \frac{1}{4}x + 1 - 2 = \frac{1}{4}x - 1 \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]

So, summarizing:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \), \( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \), \( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \), \( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \), \( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]