question in the screenshot

The solution of the equation for b is b= 2d²/H

This involves taking a variable in an equation to stand alone

Note that this variable is different from the initial isolated variable

The equation is given as

1/2Hb = d²

Divide both sides of the equation by H

So, we have the following equation

1/2Hb/H = d²/H

Multiply both sides of the equation by 2

So, we have the following equation

2 * 1/2Hb/H = d²/H * 2

Evaluate the quotients and the products

b= 2d²/H

The above computation implies that:

We changed the subject of the formula in the equation 1/2Hb = d² from d² to b

This implies that solving for b is a concept of subject of formula

Hence, the solution is b= 2d²/H

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The solution to the system of equations as an ordered pair is (4, -3).

We are given a system of linear equations in two variables. The first equation is y = (-1/2)x-1. The second equation is (-1/4)x+y+4 = 0.

We need to find the solution of the system of equations. We will use the substitution method to solve for the values of "x" and "y".

y = (-1/2)x - 1

(-1/4)x + y + 4 = 0

Substitute the value of "y" from the first equation into the second equation.

(-1/4)x + (-1/2)x - 1 + 4 = 0

(-3/4)x+3 = 0

(3/4)x = 3

x = 4

Substitute the value of "x" back into the first equation to get the value of "y".

y = (-1/2)x - 1

y = (-1/2)4 - 1

y = -2 - 1

y = -3

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A. Mean = 71

B. Median = 75

C. Mode = 0

D. Mean is used to represent data, because mean measures central tendency.

From the given stem we have to write a data set ,

Data set = 35, 42, 43, 51, 55, 57, 62, 66, 68, 69, 74, 75, 76, 77, 78, 79 , 82, 84, 86, 88, 93, 94, 101

Mean = average

         = sum of all numbers / total number of values .

         = 1635 / 23

         = 71.08 = 71

Median = middle term

Total there are 23 terms so middle term is the 12th term .

So median = 75

Mode = Most repeated term or term that has high frequency.

Here no terms are repeating so mode = 0

By comparing mean , median and mode ,

Mean is used to represent data .Because, the mean is the most commonly used measure of central tendency because it averages all of the values in the data set.

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Answer:

8x=2

x=2/8

x=1/4

the co efficient of x is 8

to eliminate it

you divide both sides by the co efficient of x

Given the following exponential equation:

Note: the given equation is a quadratic equation

Let u = 3ˣ

So, the equation will be:

so,

The negative result will be rejected because the range of the exponential function is greater than zero

So, the exact value of x will be as follows:

The approximate solution using the calculator will be:

x = 2.40

Answer:

s-6

both of them are elements

but s is a letter while 6 is a number so these can not subtract each other because they are different values

The ratio is 5:1

What is a ratio?

An ordered pair of numbers a and b, written as a / b where b does not equal 0 is known as Ratio.

We are given

the ratio of 3m : 60cm

We known that 1m =100cm

Therefore 3m= 300cm

We have to find the ratio of 300 cm : 60cm

[tex]\frac{300}{60}=\frac{5}{1}[/tex]

On simplifying we get 5:1

Hence the ratio becomes 5:1

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Answer:

25 x 13 = 325

Bat = 20

Pumpkin = 5

Witch = 10

Leaf = 50

Ghost = 60

Step-by-step explanation: hope this helps :)

We need to find the amount Tommy is paid per hour. This is simple:

r = 189/21
r = 9

Now, to find the amount he is paid, the equation is as follows:

y = rx

For 40 hours, the equation is:

y = 9(40)
y = 360

Answer:

Step-by-step explanation:

r = 189/21

r = 9

Now, to find the amount he is paid, the equation is as follows:

y = rx

For 40 hours, the equation is:

y = 9(40)

y = 360

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$4635\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 0.6\%\to \frac{0.6}{100}\dotfill &0.006\\ t=years \end{cases} \\\\\\ 4635=4500[1+(0.006)(t)]\implies \cfrac{4635}{4500}=1+0.006t\implies \cfrac{103}{100}=1+0.006t \\\\\\ \cfrac{103}{100}-1=0.006t\implies \cfrac{3}{100}=0.006t\implies \cfrac{3}{0.6}=t\implies \boxed{5=t}[/tex]

Answer:

-1

Step-by-step explanation:

To find the mean average, add them all up and divide by the number of values (7):

-3 + -5 + 3 + 7 + -2 + -2 + -5 = -7

-7 / 7 = -1

Option D is the constructions that would construct a line of reflection from point A to point B. Make a line parallel to line AB.

A line parallel to line AB will generate a line of reflection that connects points A and B because a parallel line never intersects, resulting in direct imagery of Line AB.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect. They can be both horizontal and vertical in orientation.

We have,

-Make a perpendicular bisector of segment AB.

A perpendicular bisector does not create a line of reflection that connects points A and B, but rather divides the line AB into two equal parts.

-Draw a line through B that is perpendicular to segment AB.

A perpendicular line through B to segment AB WILL NOT Make a line of reflection from point A to point B.

-Build the line that connects A and B.

A line passing through A and B will NOT create a line of reflection that connects points A and B, but will instead create Line A and B and not its reflection.

Hence,

Make a line parallel to line AB.

A line parallel to line AB will generate a line of reflection that connects points A and B because a parallel line never intersects, resulting in direct imagery of Line AB.

To summarize

Option D is the constructions that would create a line of reflection from point A to point B.

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Answer:

-55

Step-by-step explanation:

hello

to solve for x, let's cross multiply both sides

step 2

divide both sides by -2

x = - 6

Answer:

x = -6

Step-by-step explanation:

Answer:

88888

88889

88898

....

2^5 = 32

83.59 is the solution of linear equation a- b .

What are examples of linear equations?

a = 86.4

b = 2.81

So,

Substitute = 86.4 - 2.81

Calculate the sum or difference = 83.59

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Answer:

Table C

Explanation:

Trust bro

The powers of the imaginary number gives:

etc...

We know that the imaginary number is defined as:

i = √(-1)

If we square it, then we get:

i²  = √(-1)² = -1

As the exponent 2 removes the square root.

With the exponent 3 we get:

i³ = √(-1)³ = √(-1)²*√(-1) = -1*i = -i

i³ = -i

Finally, the exponent 4 gives:

i⁴ = i²*i² = (-1)*(-1) = 1

And now the cycle repeats, we will have that:

i = i⁵

i² = i⁶

i³ = i⁷

i⁴ = i⁸

etc...

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Answer:

Answer is (f + g)(x) = 3x^2 - 4

Step-by-step explanation:

Using mathematical operations we can conclude that the area of the given figure is 40 units².

So, the area of the figure:

Where x = 4, so the expression will become:

Now, do the mathematical operations to get the area of the figure as follows:

'

Therefore, using mathematical operations we can conclude that the area of the given figure is 40 units².

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The equivalent expression is 9.45

How to find the equivalent expression?

Calculating the product,

(21.)5 (0.9) = 10.5 *0.9

                  = 9.45

Other equivalent expressions are:

[tex]\frac{189}{20} \text{ and } 9 \frac{9}{20}[/tex]

What is a product?

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The value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to  y = 2x - 5 is 6.

No matter how far we extend a parallel line, it will always remain straight. Take a look at the parallel lines in the following illustration. Lines "p" and "q" are parallel to each other as are lines "a" and "b."

We know that parallel lines have same slope, so the slope of y = 2x - 5 is 2 according the y intercept form, y = mx + b

Now using the point-slope form we will find the line parallel to Point B (6, 8)

y − y₁ = m(x − x₁)

Put m as 2, y₁ as 8 and x₁ as 6, and we wil get

y − 8 = 2(x −6)

y = 2x − 4 or

2 = (y + 4)/x           (slope)

We will us point-slope form for point A(n, 4) too

y − 4 = 2(x −n)

y = 2x − 2n + 8 or

2 = (y - 8 + 2n)/x

As slope 2 is same in both points it means their equations are same too

(y + 4)/x  =  (y - 8 + 2n)/x

Lest solve for n

(y + 4)/x  =  (y - 8 + 2n)/x

y + 4 =  y - 8 + 2n

4 = - 8 + 2n

4 + 8 = 2n

2n = 12

n = 12/2

n = 6

Thus, the value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to  y = 2x - 5 is 6.

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Answer:

$6,95

Step-by-step explanation:

3,19

1,45

2,31 +

————

6,95

An equation that shows the proportional relationship between cups (c) and tablespoons (n) is: B. c = 0.0625n

A proportion is an equation which is typically used to indicate the equality of two (2) ratios. Therefore, proportions can be used in mathematics to show that two (2) ratios are equivalent and then used to calculate or determine all of the unknown quantities.

Mathematically, a proportional relationship can be represented by the following equation:

y = kx

Where:

Let the cups be represented by c.

Let the tablespoons be represented by n.

Next, we would determine the constant of proportionality (k) as follows:

c = kn

Making k the subject of formula, we have:

k = c/n

k = 0.5/8 ≡ 1.5/24

k = 0.0625.

Substituting the parameters into the equation for a proportional relationship, we have;

c = kn

c = 0.0625n

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Answer:

C = (8/.5)n

Step-by-step explanation:

.5 = 8

1.5 = 24

C = (8/.5)n

Because  

8 divided by .5 = 16

16 * .5 = 8

Ex.2

8 divided by .5 = 16

16 * 1.5 = 24

The slope, starting, values and number of blocks in the figures, found using arithmetic progression are;

1. Slope= 2

Starting value = 1

Figure 100 has 211 squares

2. Slope = 3

Starting value = ³

Figure 100 has 303 squares

3. Slope = 2

Starting value = 1

Figure 100 has 101 squares

4. Slope = 2•n + 1

Starting value = 1

Figure 100 has 10201 squares

5. Slope = 3

Starting value = 4

Figure 100 has 304 squares

6. Slope = 2

Starting value = 2 squares and 3 triangles

Figure 100 has 200 squares and 3 triangles

An arithmetic sequence is one that is formed by the addition of a constant to the value of a term, to get the value of the next term.

1. The difference between the number of squares in subsequent figure is 5 - 3 = 7 - 5 = 2

Which gives;

The equation that gives the number of blocks in each figure is a linear equation of the form, y = m•x + c

Where;

m = The slope = The rate of change of the number of blocks = 2 more squares each subsequent figure

c = The y–intercept = The number of blocks when the figure is Figure 0 = The number of blocks at the start (The starting value)

Subtracting 2 (the slope) from the number of blocks in Figure 1, gives;

c = The starting value = Number of squares in Figure 0 = 3 - 2 = 1

Figure 0 has one square

Figure 4 has (2 × 4 + 1) blocks = 9 Squares

Figure 5 has (2 × 5 + 1) blocks = 11 Squares

Figure 100 has (2 × 100 + 1) blocks = 201 Blocks

2. Here, the slope, m = The rate of change = 3

The starting value, c = 6 - 3 = 3 = Figure 0

The number of blocks in each of the required figures are;

Figure 0 = 3 Squares

Figure 4 = 3 + 4 × 3 = 15

Figure 5 = 3 × 5 + 3 = 18

Figure 100 has (3 × 100 + 3) squares = 303 Squares

3. The slope, c = 7 - 5 = 5 - 3 = 2

The starting value = 3 - 2 = 1

Figure 0 has 1 block

Figure 4 has (2 × 4 + 1) blocks = 9 squares

Figure 5 has (2 × 5 + 1) blocks = 11 squares

Figure 100 has (2 × 100 + 1) blocks = 101 blocks

4. The number of blocks is (n + 1)²

The number of blocks increases by 2•n + 1

The slope = 2•n + 1

The starting value = 2×0 + 1 = 1

Figure 0 has 1 block

Figure 4 has (4 + 1)² blocks = 25 blocks

Figure 5 has (5 + 1)² blocks = 36 blocks

Figure 100 has (100 + 1)² blocks = 10,201 blocks

5. Slope = 13 - 10 = 10 - 7 = 3

The starting value = 7 - 3 = 4

Figure 0 has 4 block

Figure 4 has (3 × 4 + 4) blocks = 16 blocks

Figure 5 has (3 × 5 + 4) blocks = 19 blocks

Figure 100 has (3 × 100 + 4) blocks = 304 blocks

6. The slope = 2

Starting value = 2 blocks and 3 triangles

Figure 0 has 2 blocks and 3 triangles

Figure 4 has (2 × 4) blocks + 3 triangles = 6 squares + 3 triangles

Figure 5 has 10 blocks and 3 triangles

The figure in question 6 shows only the block part

Figure 100 has (2 × 100 = 200) blocks and 3 triangles

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264 cm² is surface area .

What is surface area and example?.

Surface area of triangle = 1/2  * 8 * 16

                                         = 4 * 16  ⇒  64 cm²

area of rectangle =   l * b

                              = 10 * 20

                             = 200 cm²

total surface area = Surface area of triangle +  area of rectangle

                              = 64 + 200

                              = 264 cm²

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The simplified expression is as follows;

The error was made because you didn't multiply the powers.

The expression can be simplified as follows;

[tex](x^{\frac{3}{5} } )^{\frac{7}{5} }[/tex]

Using the law of indices,

If a base variable is raised to a number (y) and the entire number raised to power (x), then it is equal to the base number raised to the multiplication of the two exponents (x × y) i.e.

Hence,

[tex](A^{x} )^{y} = A^{xy}[/tex]

Therefore, let's apply the rule,

[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{3}{5}.\frac{7}{5} }[/tex]

Hence,

[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{3}{5}.\frac{7}{5} } = x^{\frac{21}{25} }[/tex]

Therefore, using the law of indices,

[tex](x^{\frac{3}{5} } )^{\frac{7}{5} } = x^{\frac{21}{25} }[/tex]

The error was that he did not multiply the exponents.

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Answer:

Step-by-step explanation:

Let the initial price be x.

We have:

The price has decreased from x by 28% and become $455.76.

Set equation and solve for x:

Answer:

B. There is no solution

Step-by-step explanation:

35x - 21y = 10

 5x - 3y = 2

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

(5x - 3y = 2) × (-7)

= (-35x + 21y = -14)

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

35x - 21y = 10

-35x + 21y = -14

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

                 = (-4)

No Solution

I hope this helps!

The system of equation 35x - 21y =10 and  5x-3y=2 has no solution , Option B is correct.

Two or more expressions with an Equal sign is called as Equation.

The given system of equation is 35x - 21y =10 and  5x-3y=2

We can use elimination method to solve for x and y.

First, we can multiply the second equation by 7 to get:

35x - 21y = 10

35x - 21y = 14

Next, we can subtract the second equation from the first equation to eliminate the x terms:

35x - 21y - (35x - 21y) = 10 - 14

0 = -4

This is a contradiction, so there is no solution for x and y that satisfies both equations. The system is inconsistent.

Hence, the given system of equation 35x - 21y =10 and  5x-3y=2 has no solution , Option B is correct.

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