The circumference of a circular pool is 7.8 meters. Find its diameter, rounded to one decimal place.

Answer:

14d + 21 = 7(2d + 3)

16 + 4w = 2(2w + 8)

Step-by-step explanation:

14d + 21

7(2d + 3)

14d + 21

14d + 21 = 7(2d + 3)

9(5r - 2)

45r - 18

14r - 7

9(5r - 2) ≠ 14r - 7

8(69 - 9)

552 - 72

489 - 72

8(69 - 9) ≠ 489 - 72

16 + 4w

2(2w + 8)

4w + 16

16 + 4w = 2(2w + 8)

32t + 16

16(2 - t)

32 - 16t

32t + 16 ≠ 16(2 - t)

The pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

To do this, we test each pair of expression.

This is done as follows

14d + 21 = 7(2d + 3)

Expand

14d + 21 = 14d + 21 --- this is true

9(5r - 2) = 14r - 7

Expand

45r - 18 = 14r - 7 --- this is false

8(69 - 9) = 489 - 72

Expand

552 - 72 = 489 - 72 --- this is false

16 + 4w = 2(2w + 8)

Expand

16 + 4w = 4w + 16 ---- this is true

32t + 16 = 16(2 – t)

Expand

32t + 16 = 32 - 16t --- this is false

Hence, the pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

Read more about equivalent expressions at:

https://brainly.com/question/2972832

#SPJ6

Answer:

4.25

Step-by-step explanation:

.50×8.5

price per pound times the number of pounds you are buying

Answer:

  61.03°

Step-by-step explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

  c² = a² +b² -2ab·cos(C)

Solving for angle C, we have ...

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

  C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

  C ≈ 61.03°

The angle of interest is about 61.03°.

__

Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

<95141404393>

Answer:

0/6 <--------------------------

Answer:

  (c)

Step-by-step explanation:

You want the graph that has a domain of x ≥ 5.

The domain of a function is the set of x-values for which the function is defined. A domain of x ≥ 5 means the function is defined for x-values at least 5. The graph of the function will extend from x=5 indefinitely to the right.

Graph C is like that.

Answer:

23n=65

Step-by-step explanation:

Answer: 6y + 36

Step-by-step explanation:

6(6+y)

= 6 * 6 + 6 * y

=36 + 6y

= 6y + 36

Answer: 23100 voters

Step-by-step explanation:

42*55000=2310000

2310000/100=23100 voters

Answer:

(-4,-1)

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

<95141404393>

Answer:

Step-by-step explanation:

To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:

11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:

1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.

2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:

2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.

ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:

10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.

123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:

1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.

Now, let's perform the arithmetic operations:

234 + 1090 + 2748 - 83 = 3989.

Therefore, the result of the given expression in decimal form is 3989.

Answer:

21

Step-by-step explanation:

you do 7x3

Answer:

  7. inverse relationship; equation: y = 16/x

  8. no relationship; no equation

Step-by-step explanation:

The attachment shows the support for the conclusions. The relationship can be chosen from those offered by looking at differences, ratios, or products of y-values for sequential x-values.

__

In the first problem, we note that the relationship between y-values varies inversely as the relationship between x-values: when x goes up by a factor of (n+1)/n, the value of y goes down by its inverse factor: n/(n+1). That same relationship is observed by noting that the product of x and y is a constant, 16.

 relationship: inverse

  y = 16/x

__

As we looked at the table, we thought this might be an exponential function. Each y-value seemed to be twice the one before—until we got to x=5. As x went from 4 to 5, the y-value increased by a factor of 16, not 2. This means there is no simple relationship between x and y, and no simple equation that will describe the sequence of y-values.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 7

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values are calculated by dividing 16 by the x-value.

\(\sf y=\dfrac{16}{x}\)

Question 8

As the x-value increases, the y-value increases.  

The y-value increases by a factor of 2 for each x-value increase of 1 unit from 1 ≤ x ≤ 4 and 5 ≤ x ≤ 6.

\(\sf y=2^x \ for \ 1\leq x\leq 4\)

\(\sf y=2^{(x+3)} \ for \ 5\leq x \leq 6\)

These are separate exponential relations for restricted domains.

So there doesn't appear to be one relationship for a non-restricted domain.

Answer:

the value of b is 12.

Step-by-step explanation:

To find the value of b, we can use the vertex form of a quadratic function, which is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Since we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8

Expanding this, we get f(x) = a(x^2 + 12x + 36) + 8

Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.

Therefore, the value of b is 12.

Answer:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

Step-by-step explanation:

Production:

                                      Flour      yeast     Almond paste      Profit $

Bear claws B  (x₁)            6 ou       1 ou            2 TS                   0.2

Almond-filled ( x₂)          3 ou       1  ou           4 TS                   0.3

Availability                    6600      1400           4800

The Model:

z  =   0.2*x₁   +  0.3*x₂       to maximize

Subject to

1.-Quantity of flour   6600 ou

6*x₁  +  3*x₂   ≤  6600

2.-Quantity of yeast  1400 ou

1*x₁   +   1*x₂   ≤  1400

3.-Quantity of Almond paste   4800 TS

2*x₁   +  4*x₂   ≤  4800

General constraints:

x₁ ≤  0    x₂  ≤ 0   both integers

After 6 iterations using an on-line solver. Optimal solution is:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

Answer:

36 ft by 32 ft

Step-by-step explanation:

36 by 32 = 9 by 8

Answer:

36 ft by 32 ft

Step-by-step explanation:

Because if divided by 4:

36/4= 9

32/4 8

Creating, 9:8

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

Learn more about triangle here

brainly.com/question/15833022

#SPJ1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

9 goals ===> 4 soccer games

average per game = ?

Step 02:

average per game = 9 goals / 4 games

= 2.25 goals / game

The answer is:

The average per game is 2.3 goals

If the average is 85 minutes, then on the seventh day he skated for 115 minutes.

For a set of N values {x₁, x₂, ..., xₙ} we define the average as:

A = (x₁ + ... + xₙ)/N

Here we know that for four days, he skated for 1hr + 25min = 85 min

Then for 2 days he skated for 1hr + 10min = 70 min

And the seventh day he skated x minutes.

We know that the average is 85 min, then we can write the equation:

(4*85 + 2*70 + x)/7 = 85

x = 85*7 - 2*70 - 4*85

x = 115

He scated for 115 minutes.

Learn more about averages at:

https://brainly.com/question/20118982

#SPJ1

Step-by-step explanation:

70 ÷ 3 = 23  1/3

a. Let \(d\) be the number of daytime calls Eshwa makes, and \(e\) the number of evening calls. Then the cost \(C\) (in pence) of making \(d+e\) calls is

\(C = \boxed{50d + 40e}\)

b. £1 = 100p, so the cost \(C'\) (in £) is 1/100 of the cost found in part (a),

\(C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}\)

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

\(C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}\)

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

\(C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}\)

d. Let \(e=40\) and \(C'=42\). Solve for \(d\).

\(42 = \dfrac d2 + \dfrac{2\cdot40}5\)

\(42 = \dfrac d2 + 16\)

\(\dfrac d2 = 26\)

\(d = \boxed{52}\)

What are the following statements?

The hikers in total travelled for \(13\frac{3}{4}\).

Addition in maths, a process of combining two or more numbers.

Given that, in the morning, a group of hikers hiked 3 3/4 miles, took a break, and then hiked another 2 3/4 miles. The group then stopped for lunch. In the afternoon, the group then hiked 4 3/4 miles, took another break, and then hiked 2 1/2 miles

\(3\frac{3}{4} +2\frac{3}{4} +4\frac{3}{4} + 2\frac{1}{2}\)

15/4+11/4+19/4+5/2 = 55/4

= \(13\frac{3}{4}\).

Hence, The hikers in total travelled for \(13\frac{3}{4}\).

For more references addition, click;

https://brainly.com/question/29464370

#SPJ2

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

reflecting over y just simply means counting the space between the shape and their points to the line and using that same number on the other side for example for the point -4,-4 is 2 spaces from the line then count 2 on the other side

Answer:

multiply 2h with h and (-2) and multiply 3 with h and (-2)

2h(h-2)+3(h-2)

2h²-2h+3h-6

2h²+h-6

Answer:

Option 2: \(f^{(-1)}(x) = -\frac{3}{4x}\) is the correct answer.

Step-by-step explanation:

Given function is:

\(f(x) = -\frac{3}{4x}\)

There are few steps to find inverse of a function. We will apply them one by one onto the function

Step 1: Replacing f(x) with y

\(y = -\frac{3}{4x}\)

Step 2: Replacing y with x and x with y

\(x = -\frac{3}{4y}\)

Step 3: Solving the equation in step 2 for y

\(x = -\frac{3}{4y}\\y = -\frac{3}{4x}\)

Step 4: Replacing y with inverse of f

\(f^{(-1)}(x) = -\frac{3}{4x}\)

Hence,

Option 2: \(f^{(-1)}(x) = -\frac{3}{4x}\) is the correct answer.

\( \sqrt[6]{x} . \sqrt[4]{ {y}^{3} } \\ = {x}^{ \frac{1}{6} } . {y}^{ \frac{3}{4} } \\ = {x}^{ - 6} . {y}^{ \frac{3}{4} } \)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

175 units cubed

Step-by-step explanation:

I think 7, 5, and 5 are the length, width, and height. multiply to find the volume and you have 175 units cubed.

have a great day and thx for your inquiry :)