Can someone give me a step-by-step on how to solve this, please?

The standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

The standard form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given a point (3,3) and a slope of -1/2, we can use the point-slope form to write the equation of the line as follows -

y - 3 = -1/2(x - 3)

To convert this equation to standard form, we can simplify the equation as follows -

y - 3 = -1/2x + 3/2

y = -1/2x + 3 + 3/2

y = -1/2x + 9/2

Hence, the standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

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The value of x would be 7 and perimeter of equilateral triangle would be 75.

What is Equilateral triangle and perimeter of equilateral triangle?

An equilateral triangle is one with the equal length on all three sides. To calculate the perimeter of an equilateral triangle given its area, we must first determine the length of its sides.

An equilateral triangle has three congruent sides, so if AABC is equilateral, we know that AB = BC = AC. We can use this information to write an equation for x, the length of one of the sides.

AB = BC = AC

given equations are,

4x-3 and 2x+11

as we know that, all sides of equilateral triangle are equal then,

4x-3 = 2x+11

2x = 14

x = 7

The perimeter of an equilateral triangle = 3 x side of equilateral triangle

Here, all sides of equilateral triangle are equal then sides = 25

Perimeter of an equilateral triangle = 3 x 25

Perimeter of an equilateral triangle = 75

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Answer:

Step-by-step explanation:

The function y = -2 is a constant function. It means that the output of the function is always equal to -2, regardless of the input value.

Here is a function table that shows the input and output values for y = -2:

x y

1 -2

2 -2

3 -2

4 -2

5 -2

As you can see, for any value of x, the output is always -2, since y = -2 is a constant function

There are 188 ways to pick one ace and next card as not a queen.

There are 4 aces in a normal 52 card deck, and once one is picked, there are 51 cards left.

If we want to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen, we can use the following formula:

Number of ways = (number of aces) x (number of cards not a queen)

In this case, the number of aces is 4, and the number of cards not a queen is 47 (52 cards total - 4 queens - 1 ace that has been picked).

So the number of ways to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen is 4 x 47 = 188.

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The length of one string of lights in feet is closest to 23 feet.

The problem states that students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached to the top of the flagpole, and the other end will be attached to the ground.

The flagpole is 15 feet tall and the distance from the base of the flagpole to the ground is 8 feet. Since the string of lights is attached at the top of the flagpole and at the ground, the length of the string of lights is equal to the height of the flagpole plus the distance from the base of the flagpole to the ground.

Therefore, the length of one string of lights can be calculated by adding the height of the flagpole (15 feet) to the distance from the base of the flagpole to the ground (8 feet), which results in:

15 feet + 8 feet = 23 feet

So the length of one string of lights is 23 feet.

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The coefficients of the terms on the right side of a binomial equation are the numbers in the triangle.

As the power increases, the expansion becomes more difficult to compute and takes longer. A binomial statement that has been raised to a very high power can be swiftly calculated using the binomial theorem. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.

The binomial theorem can be used to expand an expression that has been raised to any finite power. The binomial theorem is a helpful expansion method having applications in probability, probability theory, and algebra.

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The length of the ladder is 22 feet.

Let x = the height the ladder reaches on the wall.

Then 3x = the length of the ladder.

Substituting 15 for the foot of the ladder from the wall, we have:

15 + 3x = the length of the ladder

7 = 3x

x = 7/3

Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder we have:

15 + 3(7/3) = the length of the ladder

15 + 7 = the length of the ladder

22 = the length of the ladder

The length of the ladder can be determined by first figuring out how high the ladder reaches on the wall. Let x equal the height the ladder reaches on the wall. Then, the length of the ladder, 3x, can be determined. Since the foot of the ladder is 15 feet from the wall, the equation 15 + 3x = the length of the ladder can be written. In this equation, 7 is the known value for 3x, since the ladder is 7 feet less than three times longer than the height it reaches on the wall. Therefore, x = 7/3. Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder, the equation 15 + 3(7/3) = the length of the ladder can be written. Simplifying this equation, 15 + 7 = the length of the ladder can be written, which means the length of the ladder is 22 feet.

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The statistic is the average diameter of 100 bearings from the lot, which is 2.515 cm. This is outside the specified limits, resulting in the lot being mistakenly rejected.

The statistic in this case is the average diameter of the inspected bearings from the lot. The lot contains a boxcar of ball bearings, and the specified acceptance of the lot is that the average diameter must be 2.503 cm. The inspector happens to inspect 100 bearings from the lot and determines that the average diameter of these bearings is 2.515 cm, which is outside the specified limits. As a result, the lot is mistakenly rejected. The value of the statistic is the average diameter of the inspected bearings from the lot, which is 2.515 cm. This is the value that determined the lot's rejection, as it is outside the specified limits.

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The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.

we know that

In the right triangle XYZ

[tex]tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}[/tex]

In this problem,

Opposite side angle YZX= XY = 12.4cm

Adjacent side angle YZX= YZ = 15.1cm

substitute the values,

[tex]tan ( Y Z X) = \frac{12.4}{15.1}[/tex]

[tex]Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )[/tex]

Angle ( Y Z X) = 39.4°

So,  the approximate measure of angle YZX is 39.4°.

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The complete question is:

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

A .34.8°

B .39.4°

C .50.6°

D. 55.2°

He used five 40-cent stamps and eight 7-cent stamps.

Let x stand for how many 40-cent stamps he applied.

Let y stand in for the quantity of 7-cent stamps he applied.

41 cents = 40/100 = $0.40

7 cents = 7/100 = $0.07

To cover the $2.56 in postage, he uses 40-cent and 7-cent stamps. That implies

0.4x + 0.07y = 2.56

When you multiply something by 100, you get

40x + 7y = 256

7y = 256 -40x

The accompanying x and y values must both be whole numbers in order to satisfy the equation.

If x = 4,

7y = 256 - 40 × 4 = 96

y = 96/7 = 13.71

If x = 5,

7y = 256 - 40 × 5 = 56

y = 56/7 = 8

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Michael wants to place grass on the side of his lap pool, the area of the shaded region that he wants to cover with grass is 204 square yard.

We have to determine the area of the Shaded region that he wants to cover with grass.

By calculating the overall area and taking the area of the lap pool out, the area of the shaded area may be calculated.

We can see that the shape is the trapezium. So;

Area of trapezium = 1/2 × (Sum of parallel sides) × distance between them

Sum of parallel sides = 25 yd + (3 + 12) yd

Sum of parallel sides = 25 yd + 15 yd

Sum of parallel sides = 40 yd

Distance between them = 12 yd

Area of the trapezium = 1/2 × 40 × 12

Area of the trapezium = 40 × 6

Area of the trapezium = 240 square yd

Now finding the area of lap pool.

Area = length × width

Area = 12 × 3

Area = 36 square yd

Now finding the area of shaded region

Area = Area of the trapezium - Area of lap pool

Area = 240 - 36

Area = 204 square yard

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The two values which will make the given equation true are 17 and 4.

By using different processes, simplification refers to reducing the expression to a simpler form. The equation is simplified to its closest value using approximation, which is not perfectly accurate.

Simplification for the given equation:

Consider the given equation and substitute the values 17 and 4 in the blank space.

= 17y∛6y - 14∛48y⁴

= 17y∛6y - 14∛6 × 6y³y

= 17y∛6y - 14 × 2y∛6 × 2³y³y

Further simplifying,

= 17y∛6y - 14 × 2y∛6y

= 17y∛6y - 28∛6y

= - 11∛6y

Therefore, the values for which the 17y∛6y - 14∛48y⁴ = - 11∛6y are 17 and 4.

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I get to pay a total cost of $89.16 for the meal.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, multiplications and so on). Expressions are made up of terms. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is called a coefficient.

Pretax = 13% of meal cost

Tax = 7% of meal cost

Total = Meal cost + 13% of meal cost + 7% of meal cost

Total = $74.30 + (13/100 x $74.30) + (7/100 x $74.30)

Total = $74.30 + $9.659 + $5.201

Total = $89.16

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Answer:

x²y²(x²-2xy)

Step-by-step explanation:

they each include an x²y² so you take out the x²y² from each, and then write what's remaining & then add a bracket.

[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The given operations are

[tex]\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]

In the given operation, the operators used are addition and subtraction

[tex]\left[\begin{array}{ccc}13-3+6&10+2+10&7-6+15\\6-14+10&8+6+0&1-11+9\\2-8+1&5+12+0&0-9+7\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]

Hence, [tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

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The possible minutes Ali will run today can be represented by the inequality x ≥ 66.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Minutes taken to complete one lap = 6 minutes

Also, he will run at least 11 laps today.

This means that Ali will run laps greater than or equal to 11 laps.

Let x be the number of minutes taken by Ali today.

x ≥ 6 × 11

x ≥ 66

Hence Ali runs 11 laps in at least 66 minutes.

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The complete question is as follows :

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?

Answer:

3:2

Step-by-step explanation:

The time taken to cover the distance from the park to house with an average speed of 22km /h is 42 minutes.

Average speed is the directional speed of an object in motion as measured by a certain unit of time and seen from a particular point of reference. Average speed is a fundamental concept in kinematics, the branch of classical mechanics that investigates how bodies move.

Since average speed is a physical vector quantity, its magnitude and direction must be included in the definition. In the SI, speed is a coherent derived unit whose quantity is measured in metres per second (m/s), where speed is the scalar absolute value (distance) of average speed (metric system). The word "acceleration" describes a change in an object's speed, direction, or both.

we know that

distance = average speed × time

distance = 14×66/60 =15.4 km

now time = distance /average speed

time = 15.4×60/ 22 = 42 minutes

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The distance between  G and H on this number line  is 10

What is number line?

A range of line is a pictorial representation of numbers on a immediately line. It’s a reference for evaluating and ordering numbers. it is able to be used to symbolize any real variety that consists of each whole quantity and herbal quantity. simply to don't forget, the whole wide variety is a set of numbers that encompass all counting numbers (1, 2, three,four,5,6 …….) and zero (0), whereas the herbal number is the set of all counting numbers i.e. 1, 2, three, 4, five, 6……..

Given in the number line,

The number line is from the -12 to 7

And

we have to find the distance between G and H on this number line

GH = -2+12

GH = 10

Hence, The distance between  G and H on this number line  is 10

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The measure of the indicated angle is 33 degrees

It is important to note the properties of a triangle

The properties of a triangle are given as;

From the diagram shown, we have;

57° + K + 90° = 180°

Collect like terms, we get;

K = 180° - 147°

Subtract the numbers

K = 33°

Hence, the value is 33°

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The following are solutions to the inequalities;

7. c < 7

8. h < -4

9. r ≤ 55

Inequality is a relationship between two expressions or values that are not equal to each other. Lack of balance results in inequality.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.

7. 8c - 21 < 35

8c < 35 +21

8c < 56

c < 7

8. -6h + 17 > 41

-6h > 41 - 17

-6h > 24

h < 24/-6

h < -4

9. r/5 - 2 ≤ 9

Multiplying through by 5

r - 10 ≤ 45

r ≤ 45 + 10

r ≤ 55

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The value for the line segment FG represented by the algebraic expression 2x is equal to 4.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

The sum of the line segments FG and GH is equal to FH so;

2x + x + 4 = 10

3x + 4 = 10

3x = 10 - 4 {subtract 4 from both sides}

3x = 6

x = 6/3

x = 2

line segment FG = 2(2) = 4

line segment GH = 2 + 4 = 6

Therefore, the value for the line segment FG represented by the algebraic expression 2x is equal to 4.

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Answer:

A dependent variable represents a quantity whose value depends on how the independent variable is manipulated. y is often the variable used to represent the dependent variable in an equation.

Step-by-step explanation:

A short-run economic event like a recession is more likely to have aggregate demand rather than aggregate supply as its main cause.

The theory used in this question is the Keynesian Theory of Income and Expenditure,

It asserts that total spending (C + I + G + X - M) equals total output (Y), where C represents consumption, I represents investment, G represents government spending, X represents exports, and M represents imports.

Step 1: In order to solve for G, we must first recall the equation for calculating Gross Domestic Product (GDP):

GDP = C + I + G + (X - M)

Step 2: We have five of the six variables given in the equation and can solve for G by rearranging the equation to solve for G.

GDP - C - I - (X - M) = G

Step 3: Substitute the given values for each of the variables in the rearranged equation, starting with GDP.

900 - 500 - 300 - (200 - 200) = G

Step 4: To simplify the problem, subtract 500 from each side.

400 - 300 = G

Step 5: 300 should be subtracted from each side of the equation.

100 = G

Therefore, Government spending G = 100.

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Lila finds out the decimal equivalent of 3 divided by 16 is equal to 0.1875.

Lila knows that 3/16 means "3 divided by 16."

To find the decimal equivalent for 3/16, she would divide 3 by 16 using a calculator or long division. This would give her a decimal answer of 0.1875.

It's important to note that 3/16 is a fraction, which represents a ratio of two numbers, the numerator, and the denominator. The decimal equivalent is simply another way to represent the same value but in decimal form.

Lila understands that to convert fractions to decimals, she can divide the numerator by the denominator. And to convert decimals to fractions, she can write the decimal as a fraction with the denominator as a power of 10.

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Here is the stem and leaf plot:

Stem      Leaf

0            2, 3, 5, 9

1              2, 7, 7,, 8, 8

2

3                 0, 8

A stem-and-leaf plot is a table that is used to display a dataset.  A stem-and-leaf plot divides a number into a stem and a leaf.

The stem is the first number in the digit. In this question, the stem is the tens digit.  The leaf is the last number. In this question, the leaf is the units digit.  For example in the number 18, 1 would be the stem and 8 would be the leaf.

Here is the complete question:

Create a stem and plot diagram using the dataset provided: 3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12

Key: 30 = 30

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If Desi has a coupon  that entitles him to 35% off the regular price of a sweater , then another expression that represents the price Desi will pay is 0.65x .

the original price of the sweater is = x ;

the percent discount that Desi gets by applying the coupon is = 35% ;

Desi gets 35% discount , it means that Desi only need to pay the remaining 65% of the price .

So , the remaining price of the sweater to be paid by Desi is = 65% of "x" ;

= 0.65x  ...(because 65% = 0.65 ) .

Therefore , the another expression representing the situation is 0.65x .

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Answer:

  97.5% decrease

Step-by-step explanation:

You want the percentage change in noise intensity when it is reduced from 88 to 72 dB.

The intensity can be found by solving the given equation for I:

  [tex]\beta_1=10\log\left(\dfrac{I_1}{I_0}\right)\\\\10^{\beta_1/10}=\dfrac{I_1}{I_0}\\\\I_1=I_0\cdot10^{\beta_1/10}[/tex]

Similarly, the reduced intensity is ...

  [tex]I_2=I_0\cdot10^{\beta_2/10}[/tex]

The percentage change is found from ...

  percentage change = (I₂/I₁ -1) × 100%

Using the above expressions for I₁ and I₂, this becomes ...

  [tex]\text{\% change}=\left(\dfrac{I_0\cdot10^{\beta_2/10}}{I_0\cdot10^{\beta_1/10}}-1\right)\times100\%\\\\=(10^{(\beta_2-\beta_1)/10}-1)\times100\%=(10^{(72-88)/10}-1)\times100\%\\\\=(10^{-1.6}-1)\times100\% \approx -0.975\times100\% =\boxed{ -97.5\%}[/tex]

The noise intensity decreased by about 97.5%.

__

Additional comment

It can be useful to remember that log(2) ≈ 0.30103. That is, a reduction of 3 dB is a reduction by a factor of 2. Hence 16 db is a factor of about 40.

Answer:

97.49% (2 d.p.)

Step-by-step explanation:

Given equation:

[tex]\beta=10 \log\left(\dfrac{I}{I_0}\right)[/tex]

Divide both sides by 10:

[tex]\implies \dfrac{\beta}{10}= \log\left(\dfrac{I}{I_0}\right)[/tex]

Switch sides:

[tex]\implies \log\left(\dfrac{I}{I_0}\right)=\dfrac{\beta}{10}[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 10^{\frac{\beta}{10}}=\dfrac{I}{I_0}[/tex]

Multiply both sides by I₀:

[tex]\implies I=I_010^{\frac{\beta}{10}}\\[/tex]

Substitute the given value of I₀:

[tex]\implies I=10^{-12} \cdot 10^{\frac{\beta}{10}}\\[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies I=10^{\left(\frac{\beta}{10}-12\right)}\\[/tex]

Therefore, the value of I when β = 88 dB is:

[tex]\implies I=10^{\left(\frac{88}{10}-12\right)}\\[/tex]

[tex]\implies I=10^{-3.2}[/tex]

And the value of I when β = 72 dB is:

[tex]\implies I=10^{\left(\frac{72}{10}-12\right)}\\[/tex]

[tex]\implies I=10^{-4.8}[/tex]

Percent Decrease formula

[tex]\sf Percent\:decrease=\dfrac{original\:value-new\:value}{original\:value} \times 100[/tex]

Therefore, the percent decrease is:

[tex]\implies \dfrac{10^{-3.2}-10^{-4.8}}{10^{-3.2}} \times 100[/tex]

[tex]\implies 97.4881135...\%[/tex]

[tex]\implies 97.49\%\; \sf (2\; d.p.)[/tex]