A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?

Solution of the system of equations y - x²- 14x = 54 and 43 = y - 6x are

x = -4 ± √5 and y = ± 6√5 + 19

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given equations

y - x²- 14x = 54

y = x² + 14x + 54            -------------(1)

43 = y - 6x

y = 6x + 43                     ------------(2)

By equation (1) and (2)

6x + 43 = x² + 14x + 54

x² + 14x + 54 - 6x -43 = 0

x² + 8x + 11 = 0

a = 1, b = 8, c = 11

x = (-b ± √(b² - 4ac))/2a

x  = (-8 ± √(64 - 4.11))/2

x  = -4 ± √16-11

x = -4 ± √5

Putting value of x in equation (2)

y = 6(-4 ± √5) + 43

y = -24 ± 6√5 + 43

y = ± 6√5 + 19

Hence, x = -4 ± √5 and y = ± 6√5 + 19 are the solutions of equations

y - x²- 14x = 54 and 43 = y - 6x.

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answers are on the picture

Step-by-step explanation:

If the gross income per month is $4000 , then the monthly disposable income will be $2920   .

To find the monthly disposable income, we subtract the various taxes from the gross income.

The Federal tax is = 10% of $4000 = $400  ;

The State tax is = 7% of $4000 = $280  ;

The City tax is = 3% of $4000 = $120  ;

and the Social security tax is = 7% of $4000 = $280  ;

So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080  ;

We know that the Monthly disposable income = Gross income - Total tax ;

⇒ Monthly disposable income = $4000 - $1080  ;

⇒ Monthly disposable income = $2920  .

Therefore, the monthly disposable income after taxes is $2920.

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Answer:

[tex]\boxed{\checkmark}\;\;52 = 8n + 4[/tex]

[tex]\boxed{\checkmark}\;\;4(2n + 1) = 52[/tex]

[tex]\boxed{\checkmark}\;\;4 = 52 - 8n[/tex]

[tex]\boxed{\phantom{\checkmark}}\;\;4n = 48[/tex]

[tex]\boxed{\checkmark}\;\;n = 6[/tex]

Step-by-step explanation:

To determine if the equations are equivalent, solve the equations for n.

Option 1

[tex]\begin{aligned}\implies 52&=8n+4\\52-4&=8n+4-4\\48&=8n\\48\div 8&=8n \div 8\\6&=n\\n&=6\end{aligned}[/tex]

Option 2

[tex]\begin{aligned}\implies 4(2n+1)&=52\\8n+4&=52\\8n+4-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 3

[tex]\begin{aligned}\implies 4&=52-8n\\4+8n&=52-8n+8n\\4+8n&=52\\4+8n-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 4

[tex]\begin{aligned}\implies 4n&=48\\4n \div 4&=48 \div 4\\n&=12\end{aligned}[/tex]

Option 5

[tex]n=6[/tex]

Therefore, the equations that are equivalent are:

Step-by-step explanation:

use the pythagors theorm b square = h2 -p2

then the 10 cm is parallel so use area of right angled triange =1/2 b×p

Answer: Let's call Sarah's original amount of money as x. Then, Christine had 0.8x.

After they spent $684 altogether, Christine had 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x left.

Sarah had x - 684.

Since Christine had thrice as much money left as Sarah, we can write an equation:

0.6x = 3(x - 684)

Expanding the right side of the equation:

0.6x = 3x - 2052

Solving for x:

2.6x = 2052

x = 787.69

So Sarah originally had 787.69 dollars and spent 787.69 - 684 = 103.69 dollars.

Step-by-step explanation:

Answer:

the answer according to your question is that " b" is = -0.3

The slope-intercept form of a line is y=2/3x + 2, the line is perpendicular and shifted down 8 is y = -3/2x - 6.

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. In the given equation, y = 2/3x + 2, the slope is 2/3 and the y-intercept is 2.

To find a line that is perpendicular to this line, we need to find a line that has a slope that is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/3 is -3/2, so the slope of the new line will be -3/2.

Now we need to find the equation of the new line in slope-intercept form. We know the slope of the line (-3/2), so we can substitute this value for m in the slope-intercept form and get:

y = -3/2x + b

To find the value of b, which is the y-intercept of the new line, we need to use the fact that the line is shifted down 8 units. We can do this by subtracting 8 from the y-intercept of the given line (which is 2), to get:

b = 2 - 8 = -6

So the equation of the line that is perpendicular to y = 2/3x + 2 and shifted down 8 units is:

y = -3/2x - 6

This line has a slope of -3/2, which is the negative reciprocal of the slope of the given line, and a y-intercept of -6, which is 8 units lower than the y-intercept of the given line.

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The number of decimeters in  3.6 millimeters is 0. 0036 decimeters. Option D

Conversion of units is simply defined as the conversion that is between different units of measurement for a particular quantity.

it is carried out mostly through multiplicative conversion factors.

It may involve multiple steps of multiplication or division by  a conversion factor.

From the information given, we have that;

1 decimeter = 1000 millimeters

Then, x decimeter = 3.6 millimeters

Cross multiply the values

x = 3.6/1000

divide the values

x  = 0. 0036 decimeters

Hence, the value is  0. 0036 decimeters

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In a case whereby the distance between Dallas and Houston is about 364 kilometers the approximately measurement is closest to the number of miles between these two towns is A 227.5 miles.

The concept that will be used here is unit conversion. It should be noted that 1 Mile = 1.609344 kilometres.

Then                                 Xmile  = 364 kilometers

We can cross multiply to have

 Xmile  =364 kilometers/1.609344 kilometres.

=226.179

Hence the  closest to the number of miles is A 227.5 miles

Therefore, option A is correct.

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The number of multiplications for the power₁ is 3 multiplication power₂ is one multiplication and power₃ is 5 multiplications and the number of recursive calls will power2 and power3 make when computing 332 and  319 is 5.

First, let's look at power₁. This function can compute the power of a number by repeated multiplication. For example, to compute 3 to the 4th power, power₁ would perform three multiplications: 3 x 3 x 3 x 3 = 81.

Using this approach, we can see that to compute 3 to the 32nd power, power₁ would perform 31 multiplications (3 x 3 x 3... repeated 31 times). Similarly, to compute 3 to the 19th power, power₁ would perform 18 multiplications.

Next, let's consider power₂. This function uses a different strategy for computing powers. It relies on the fact that any number can be expressed as a power of 2

To compute 3 to the 32nd power using power₂, we would first express 32 as a sum of powers of 2:

=> 32 = 2⁵ + 2⁴ + 2³.

Then, we would use the fact that 3 raised to a power of 2 can be computed with just one multiplication: 3² = 9.

Using this fact repeatedly, we can compute 3 to the 32nd power with only 5 multiplications:

=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

For 3 to the 19th power, power2 would express 19 as 2⁴ + 2¹ and then use 4 multiplications:

=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.

Finally, let's look at power3. This function is similar to power2 but uses a more efficient algorithm called exponentiation by squaring. This algorithm works by repeatedly squaring the base and halving the exponent until the exponent is 1.

To compute 3 to the 32nd power using power₃, we would start with the binary representation of 32 (100000 in binary).

we can see that power₃ will only perform 5 multiplications to compute 3 to the 32nd power.

Similarly, to compute 3 to the 19th power, power₃ would start with the binary representation of 19 (10011 in binary) and use the exponentiation by squaring algorithm to perform only 6 multiplications.

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Complete Question:

How many multiplications will each of the functions power₁, power₂, and power₃ perform when computing 332? 319?

The function P(x) representing Ayden's total pay on a day on which  he sell x dollar worth of computers is P(x) = 0.01x + 90

The base pay amount of Ayden per regardless of sales = $90

The commission of Ayden = 1% of the dollar amount of sales

Consider the total sales amount in a day as x

The function is the mathematical expression that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will be independent variable.

Then the function will be

P(x) = 1% of x + 90

= 0.01x + 90

Therefore, the equation for the function P(x) = 0.01x + 90

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Answer:

2 * (M - 14) = 64

Step-by-step explanation:

Twice mean s two times the rest of M

The power in a significance test is the probability of detecting a true effect, while the probability of making a type II error is the complementary probability of power.

A significance test is a statistical method used to determine whether an observed difference or effect is statistically significant or simply due to chance.

Power is defined as the probability of detecting an effect in a significance test if an effect truly exists. In other words, it is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. The null hypothesis assumes that there is no significant difference between two groups, while the alternative hypothesis states that there is a significant difference.

Mathematically, power is calculated using the following formula:

Power = 1 - β

Where β is the probability of making a type II error, which is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. In other words, it is the probability of not detecting an effect when an effect truly exists.

Therefore, power and β are complementary probabilities. If power is high, β is low, and vice versa. A significance test with a low power has a higher chance of making a type II error, meaning that it can fail to detect a real effect. Conversely, a test with a high power has a lower chance of making a type II error, meaning that it can detect a real effect more accurately.

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The system of equations will have a unique solution.

A finite set of equations for which we searched for common solutions is referred to as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.

Given that the equations are:-

y=-2x+2 and 2y+4x=4

Convert the equations into general form,

2x + y = 2

4x + 2y = 4

If the ratio of a₁ / a₂ is not equal to the ratio of b₁ / b₂ the equation will have a unique solution. And if are equal than the equation will have infinitely many solutions.

2 / 4 = 1 / 2 = 2 /4

1 /2 = 1/ 2 = 1/ 2

The equation will have many solutions.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's start with eliminating choices first ~

The value decreases as years pass by, so the value multiplied by initial value should be an exponent on the value that is less than 1.

So, only the choices with exponent on 0.9 should be qualified, eliminating the choices A and C

Next, the initial value of motorcycle is 12000 according to table. so at x = 0, v(x) should be equal to 12000.

Now, let's check option B

[tex]\qquad \sf  \dashrightarrow \: v(x) = 12000(0.9) {}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000(0.9) {}^{0} [/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000(1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000[/tex]

And since choice B satisfy each and every condition, that's the correct answer ~

We solved the given inequality and found the values of x lie in the interval   ( -∞ , 4). This is graphed and shown on the number line as below.

What is meant by inequality?

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Given inequality is:

11x + 6 < 9x + 10

Solving,

11x - 9x < 10 - 6

2x < 4

x < 4

The values of x is in the interval : ( -∞ , 4)

The above inequality is shown below on the number line as well as on the graph.

We can see that all the values to the left of 4 but not including 4 can be taken as the value of x.

Therefore we solved the given inequality which is graphed and shown on the number line.

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The total number of red blood cells produced by human body in each minute is given by [ 1.2 × 10^8​ ] red blood cells

Number of red blood cells produced by human body = 4. 8 × 10^6

Time taken by human body to produce 4. 8 × 10^6 red blood cells

= 4×10^(−2)​ minute

Number of red blood cells produced by human body in one minute are :

4 × 10^(−2)​ minute = 4. 8 × 10^6 red blood cells

⇒ 1 minute =  [ 4. 8 × 10^6 / 4 × 10^(−2)​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 - (−2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 + 2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^8​ ] red blood cells

Therefore, total number of red blood cells produced by human body in one minute is equal to [ 1.2 × 10^8​ ] red blood cells.

The above question is incomplete, the complete question is:

The human body produces about4. 8×10^6​ red blood cells in 4×10^(−2)​ minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.

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Answer:70% chance they vote yes

Step-by-step explanation:

Answer:

3/10 for red people and 7/10 for blue people.

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

X=55

55+10=65

so

X+10=65

I hope that's what you meant.

By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.

Let x = number of seats on the main-floor

y = number of balcony seats

We know that if all the seats are sold, then the total income is $4,200, we can write the equation:

x*8 + y*5 = $4,200

And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:

0.25*x*8 + 0.4*y*5 = $1,200

x*2 + y*2 = $1,200

2(x + y) = $1200

x + y = $600

x = 600 - y

putting the value of x in equation1)

8(600-y) + 5y = 4200

4800 - 8y + 5y = 4200

3y = 600

y = 200

and x = 600 - 200 = 400

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The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.

To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.

Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:

11 = [tex]a * b^0[/tex]

Since [tex]b^0[/tex] = 1 for any value of b, we have:

11 = a * 1

So a = 11.

Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:

1375 = [tex]11 * b^3[/tex]

Dividing both sides of the equation by 11, we have:

125 = [tex]b^3[/tex]

By combining the cube roots of the two sides, we obtain:

b = 5

So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].

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The complete question is:

an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?

The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.

To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

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The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Solid A is dilated using a scale factor of 2/5, resulting in Solid B. Then the volume of solid A is given as,

(Scale factor)³ x (Volume of solid A) = Volume of solid B

(2/5)³ x Volume of solid A = 72

Volume of solid A = 1,125 km³

Solid B is also dilated using a scale factor of 2/5, resulting in Solid C. Then the volume of solid C is given as,

(Scale factor)³ x (Volume of solid B) = Volume of solid C

(2/5)³ x 72 = Volume of solid C

Volume of solid C = 4.608 km³

The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.

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According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...

To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.

On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:

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The value of x in the triangle is equal to: A. 21.

In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).

Note: x is the side opposite to the 60° angle.

The side opposite to the 60° angle, x = 7√3 × √3

The side opposite to the 60° angle, x = 7 × 3

The side opposite to the 60° angle, x = 21 units.

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Answer:36x^13

Step-by-step explanation:

We can solve this problem using the rule of exponents: (am)n = amn.

First, let's simplify the exponent on the first term:

(-3x^5)^2 = (-3x^5) × (-3x^5)

Next, let's multiply this by 4x^3:

(-3x^5)^2 × 4x^3 = (-3x^5) × (-3x^5) × 4x^3

Now, let's multiply the coefficients and combine the exponents:

(-3 × -3)x^(5 + 5 + 3) = 36x^13

Therefore, the answer is 36x^13.

Step-by-step explanation:

this is a 14.4 in × 10.2 in rectangle, were 2 identical half-circles (= 1 full circle) are removed.

so, in other words, the shaded area is

rectangle area - circle area

the rectangle area is length × width.

the circle area is pi×r². with r (radius) being half the diameter. the diameter is 10.2 in, so, r = 10.2/2 = 5.1 in.

so, the shaded area is

14.4 × 10.2 - pi × 5.1² = 146.88 - 3.14 × 26.01 =

= 146.88 - 81.6714 = 65.2086 ≈ 65.21 in²

remember, an area is always expressed in square units. a volume in cubic units. and a length in simple units.

Answer:

Step-by-step explanation:

chicken