find the measure of side c.

Answer:

Compare your personal records to the bank's statement

The value of h for the expression will be -2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression is 17+4h+2=1−5h. The value of "h" will be calculated as below:-

17+4h+2 = 1-5h

4h+5h = 1-2-17

9h = -18

h = -2

Therefore, the value of h for the expression will be -2.

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Answer: 5/x+4

Step-by-step explanation: a pex

Answer:

The answer is 16.3

Step-by-step explanation:

For a random distribution with an specific mean and standard deviation, the most probable values are the ones that lie between the  ( means + or - standard deviation)

so in this case, the confidence range is:

Low = 15.5-1.5= 14

High = 15.5+1.5= 17

Values that lie between this range are more probable. So in this case 16.3, which is the only value in this range, has higher chance of occuring.

Answer:

a=-2 is extraneous solution.

Step-by-step explanation:

Given the equation

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]

we have to find the extraneous solution.

An extraneous solution is a solution to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}\\\\\frac{3a+2(a+2)}{a(a+2)}=\frac{4(a-1)}{a^2-4}\\\\\frac{5a+5}{a(a+2)}=\frac{4(a-1)}{a^2-4}[/tex]

On solving, we get

The solution is a=4 and a=-2

Here the solution a=-2 is the valid solution as it makes the denominator 0.

⇒ a=-2 is extraneous solution.

Option 1 is correct.

The inequality that represents the number decreased by 15 is at least 4 will be equal to x - 15 ≥ 4.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values.

Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given data in the question,

Let the number be x.

Number is decreased by 15 which is at least equal to 4.

Then, the inequality will be,

x - 15 ≥ 4

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Figure 1)

a) The area is A = 36( π - 2) ст²

b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]

Figure 2)

a) The area is A = 576 cm²

b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]

Figure 1)

a) To find the area of the figure 1 we have to do the substraction

The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.

The area of quarter circle is equal to

A = 2

we have

r = 12 cm

Put the  value r as given

A = (12)2

A = 36 [tex]cm^2[/tex]

Area of a triangle formula is

A = (b)(h)

Given information,

b=12 cm

h = 12 cm

substitute

A = (12) (12)

A = 72 cm²

therefore

The area of the figure is

A = (36π - 72) [tex]cm^2[/tex]

Simplify

A = 36(π -2) [tex]cm^2[/tex]

b)

The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle

The perimeter of a quarter of circle is formula

C = 2πr

simplify

C = r

we have

r=12 cm

substitute

C = (12)

C = 67 cm

Find the length side AC

Applying the Pythagorean Theorem

[tex]AC^2 = 12^2 + 12^2[/tex]

[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]

AC = 12√2 cm

P = (6π +12√2) cm

Taking 6 as a common multiplier we get

P = 6(π+2√2)

The perimeter of the figure 1 is

P = 6(π+2√2) cm

Part 2)

a) As we can see,

The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.

The figure's area and the square's area are equal.

A = [tex]24^2[/tex]

A = 576 cm²

b) Find the perimeter of the figure 2

we know that

The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles

The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle

P = 2(AB) + π D

P = 2(24) + π(24)

P = 48 +  π(24)

Take out 24

P = 24 (2 + π ) cm

Answer:

1. [tex]m\angle 1+m\angle 5=180^{\circ}[/tex] and [tex]m\angle 1+m\angle 4=180^{\circ}[/tex]; given

2. [tex]m\angle 1+m\angle5=m\angle 1+m\angle4[/tex]; substitution

3.[tex]m\angle5=m\angle4[/tex]; subtraction property of equality

4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.

Step-by-step explanation:

Given

[tex]m\angle1+m\angle5=180^{\circ}[/tex]

[tex]m\angle 1+m\angle4=180^{\circ}[/tex]

To prove that YZ is parallel to UV.

Proof:

1.Statement: [tex]m\angle 1+m\angle5=180^{\circ}[/tex] and [tex]m\angle1+m\angle4=180^{\circ}[/tex]

Reason; Given

2. Statement: [tex]m\angle1+m\angle5=m\angle 1+m\angle4[/tex]

Reason: By using substitution property

3.Statement: [tex]m\angle5=m\angle4[/tex]

Reason: Subtraction property of equality.

4.Statement: Ray YZ is parallel to Ray UV

Reason: If alternate interior angles equal, then lines are parallel.

To rewrite the inequality so that one side is 0, simply subtract x and add 1 to both sides, resulting in the inequality x² - 3x + 2 < 0.

To rewrite the inequality x² - 2x + 1 < x - 1 so that one side is 0, we follow these steps:

Bring all terms to one side of the inequality by subtracting x and adding 1 to both sides, resulting in x² - 3x + 2 < 0.

Now, the inequality is set up with one side equal to 0, and we can analyze or solve the inequality from here.

Final answer:

To find the equivalent expression to 6(2m - 1) - 4(m + 8), we first expand and simplify the given expression to 8m - 38, making option A the correct answer.

Explanation:

The question asks which expression is equivalent to 6(2m – 1) – 4(m + 8). To find the equivalent expression, we first expand both terms and then simplify the resulting expression.

Therefore, the expression that is equivalent to 6(2m – 1) – 4(m + 8) is 8m - 38, which corresponds to option A.

Answer:

Step-by-step explanation:

c

Answer:

Option D is correct.

value of x is 48

Step-by-step explanation:

Solve:  [tex]\frac{x}{64}=\frac{3}{4}[/tex]

Cross multiply in the given equation we get;

[tex]x \cdot 4 = 3 \cdot 64[/tex]

Simplify:

[tex]4x = 192[/tex]

Divide both sides by 4 we get;

[tex]\frac{4x}{4}=\frac{192}{4}[/tex]

Simplify:

[tex]x = 48[/tex]

Therefore, the value of x is 48

The given sequence is a geometric series.

Common ratio can be found as :

(-300/-600) = 0.5

(-150/-300) =0.5

So common ratio is 0.5

First term is -600

The attachment shows the required calculations.

Answer: Sum of eight terms is (-1195.31).

Answer:

The correct option would be 6 exterior angles in a Triangle.

Final answer:

The John Street Barber Shop pays a flat rate of $25 for the first 8,000 gallons of water, with an additional charge of $3.50 per thousand gallons above this threshold. Accordingly, the total costs for using 7,000 gallons is $25, for 10,000 gallons is $32, and for 13,000 gallons is $42.50.

Explanation:

The John Street Barber Shop pays $25 per month for the first 8,000 gallons of water and $3.50 per thousand gallons above 8,000 gallons. To calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons, we follow this methodology:

Thus, the total costs for using 7,000 gallons, 10,000 gallons, and 13,000 gallons are $25, $32, and $42.50 respectively.

Answer:

The answer is, the like terms are 7.5y and 2y.

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