If John solved the equation x² - 10x +8=0 by completing the square, one of the steps in his process would
be:
(z-5)² = 17
(z+4)² =10z+16
(z+4)² =10z
(2-5)² = -8

Answer:

Step-by-step explanation:

45

The length of segment EC is 24 in the given triangle

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

3x=2(x+4)

Apply distributive property on RHS

3x=2x+8

Subtract 2x from both sides

x=8

The segment EC =3x

=3(8)

=24

Hence, the length of EC is 24 in the given triangle

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Barrington pays 24 for 0 gallons of water and Barrington pays 55.9 for 11 gallons of water

Given that we have

P = 24 + 2.9w

When they used 0 gallons, we have

P = 24 + 2.9(0)

P = 24

When they used 11 gallons, we have

P = 24 + 2.9(11)

P = 55.9

Hence, the amount paid for 11 gallons is 55.9

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Answer: first do multiplcation for each part then add everythink to find total volume

Step-by-step explanation:

Answer:

w(w + 4) = 117

w^2 + 4w = 117

w^2 + 4w - 117 = 0

(w - 9)(w + 13) = 0

w = 9 meters

The width of the rectangle is 9 meters, and the length of the rectangle is 13 meters.

Answer:

487.20

Step-by-step explanation:

1. find the area of a rectangle ( length x width)

14ft x 12ft = 168ft²

2. Multiply the number of feet needed to becovered by the price of one foot of paper

168ft x 2.90 = 487.20

The volume of the cone with a diameter of 4ft and height 12ft is approximatelly 50.3 ft³

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The volume of a cone is expressed as;

V = (1/3)πr²h

The figure in the image is a cone.

Diameter of the base of the cone d = 4ft

Radius r = diameter/2 = 4/2 = 2ft

Height h = 12ft

Plug the given values into the above formula and solbr for the volume.

V = (1/3)πr²h

V = (1/3) × π × r² × h

V = (1/3) × π × (2 ft )² × 12ft

V = 50.3 ft³

Therefore, the volume is 50.3 ft³.

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The two numbers are 4 and 1.

To solve the problem, we will use algebraic equations.

We will call 2 numbers x and y. So, we know that:

------ x + y = 5 (equation 1)

------ xy = 20 (equation 2)

We will solve for y in terms of x:

y = 5 - x

We will substitute for y into equation 2 and simplify:

x(5 - x) = 20

5x - x^2 = 20

x^2 - 5x + 20 = 0

As a quadratic equation which will be solved using the quadratic formula, the solutions are x = 4 and x = 1. We can check that these solutions satisfy both equation 1 and equation 2.

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The value of x is, x = 6 ft

Now, We can formulate;

Area of the polygon = area of the square + 2(area of the triangle)

Here, We have;

Area of the polygon = 176 ft²

So, Area of the square = length × width

                                   = 16 × 8

                                  = 128

And, Area of the two triangles = 2( 1/2 x base x height)

                                               = 2(1/2 × x × 8)

                                               = 8x

Now, Plug in the above values into the equation for area of the polygon.

Thus: We get;

176 = 128 + 8x

Subtract 128 from each side

176 - 128 = 8x

48 = 8x

Divide both sides by 8

6 = x

x = 6 ft

Thus, The value of x is, x = 6 ft

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The equation of a line for the given graph is y=2x+5.

From the given graph, the coordinate points are (0, 5) and (1, 7)

Part A:

Slope = (7-5)/(1-0)

= 2

Part B:

The slope mean for the relationship between the number of races and the number of track meets 2 races per track

Part C:

Substitute m=2 and (x, y)=(0, 5) in y=mx+c, we get

5=2(0)+c

c=5

Part D:

Substitute m=2 and c=5 in y=mx+c, we get

y=2x+5

Therefore, the equation of a line for the given graph is y=2x+5.

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Answer:

Many buildings and structures around us involve transformed shapes in their design. For example, a skyscraper may have a rectangular base that is transformed into a triangular shape as it reaches higher levels. This transformation is achieved by using a technique called tapering, where the building's width gradually decreases as it goes up, resulting in a triangular shape at the top.

Another common transformation is the use of rotation, which is seen in the design of many cylindrical structures like water towers or chimneys. The cylinder is rotated around its axis to create a three-dimensional shape.

These transformed shapes contribute to the design of the object in many ways. For instance, the triangular shape of a skyscraper's top helps to reduce wind resistance and improve stability. Tapering also allows more sunlight to reach street level and reduces the impact of shadows on the surrounding area. In the case of cylindrical structures, rotation can provide structural stability while minimizing the amount of material used in the construction.

Overall, the use of transformed shapes in building and structure design helps to achieve specific aesthetic and functional goals, from stability to energy efficiency.

Step-by-step explanation:

Answer:

The Empire State Building is a skyscraper in Midtown Manhattan, New York City, on Fifth Avenue between West 33rd and 34th Streets. It has a roof height of 1,250 feet (381 m), and with its antenna spire included, it stands a total of 1,454 feet (443.2 m) high. Its name is derived from the nickname for New York, the Empire State.

The Empire State Building is an example of a transformed shape. The original shape is a square, but the architects transformed it into a triangle by adding a spire to the top. The spire adds height and visual interest to the building. It also helps to make the building more stable.

The use of transformed shapes in the design of the Empire State Building contributes to its overall aesthetic appeal. The building is both visually striking and structurally sound. It is a testament to the skill and ingenuity of the architects who designed it.

Here are some other examples of transformed shapes in buildings and structures:

* The Parthenon in Athens, Greece, is a rectangular building with a triangular pediment at each end. The pediments are decorated with sculptures that depict scenes from Greek mythology.

* The Eiffel Tower in Paris, France, is a wrought iron lattice tower that was built for the 1889 World's Fair. The tower is a transformed shape of a regular hexagon.

* The Gateway Arch in St. Louis, Missouri, is a stainless steel arch that spans the Mississippi River. The arch is a transformed shape of a catenary curve.

These are just a few examples of the many ways that transformed shapes are used in the design of buildings and structures. Transformed shapes can be used to add visual interest, create a sense of movement, or simply to make a building more structurally sound.

Step-by-step explanation:

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}[/tex]

The Taylor polynomial of degree 3 for sin(x) for x near 0 is,

sin (x) = x - 1/6 x³

The ratio is sin (x) / x = 1 - 1/6 x².

Limit is 1.

Given function is sin(x).

We have to find the Taylor Polynomial for sin (x).

We know that,

f(x) = sin(x), so f(0) = sin (0) = 0

f'(x) = cos (x), so f'(0) = cos (0) = 1

f''(x) = -sin (x), so f''(0) = sin (0) = 0

f³(x) = -cos (x), so f³(0) = -cos(0) = -1

Taylor polynomial is,

sin (x) = {[f(0) (x - k)⁰] / 0!} + {[f'(0) (x - k)¹] / 1!} + {[f''(0) (x - k)²] / 2!} + {[f³(0) (x - k)³] / 3!}

Here c = 0.

sin (x) = 0 + x + 0 + (-x³/6)

sin (x) = x - 1/6 x³

The ratio,

sin (x) / x = (x - 1/6 x³) / x = 1 - 1/6 x²

When x tends to 0 in the expression, 1 - 1/6 x², the value tends to 1 - 0 = 1.

Hence the required Taylor polynomial is sin (x) = x - 1/6 x³.

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The total cost to install new wood floor in a room is $164.64.

Given that, Khalil's dining room is 3 meters wide and 7 meters long.

We know that, area of a rectangle is Area = Length×Width

Area of a room = 7×3

= 21 square meters

Total cost = Total area × Cost of per square meter

= 21×7.84

= $164.64

Therefore, the total cost to install new wood floor in a room is $164.64.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{24}\\ a=\stackrel{adjacent}{22}\\ o=\stackrel{opposite}{MN} \end{cases} \\\\\\ MN=\sqrt{ 24^2 - 22^2} \implies MN=\sqrt{ 92 }\implies MN=2\sqrt{23}[/tex]

Answer:

  30°

Step-by-step explanation:

You want the measure of angle AEF in regular hexagon ABCDEF.

The interior angles of a regular hexagon are ...

  180° -(360°/6) = 120°

Angle AEF is 90° less than this, so is ...

  angle AEF = 120° -90°

  angle AEF = 30°

__

Additional comment

Angle AEF is also a base angle of isosceles triangle AEF, which has angle F = 120°. The base angles are (180° -120°)/2 = 30°.

Answer:

119

Step-by-step explanation:

Firstly, we need to solve the expression inside the parentheses, which is 23-11. This gives us 12. Then we need to carry out the division to get 48 divided by 12, which is 4. We can then multiply 4 by 14 to get 56. Finally, we add 56 to 63 which gives us the answer of 119. Therefore, the solution to the expression 63+48÷(23-11)×14 is 119.

The equations to represent the total cost C, for m miles on the hike for each guide are C(m) = 50 + 15m, C(m) = 200 and C(m) = 20m

From the question, we have the following parameters that can be used in our computation:

Larry

Initial fee = 50

Rate = 15 per mile

Connie

Initial fee = 200

Teo

Rate = 20 per mile

Represent the number of miles with m

So, we have

Larry

Initial fee = 50

Rate = 15 per mile

C(m) = 50 + 15m

Connie

Initial fee = 200

C(m) = 200

Teo

Rate = 20 per mile

C(m) = 20m

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The distribution that is positively skewed is Option C.

A positive skew is a statistical pattern, in which the majority of the data points are concentrated at one end within the range and wherein the tail is longer on the right side of the graph.

This phenomenon is also identified as a "right-skewed distribution," oppositely to its counterpart: the negative skew or "left-skewed distribution."

In conclusion, the distribution that is positively skewed is the third distribution or Option C.

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Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly to accumulate $83,000 in 7 years.

To determine how much Jasica should make in a sinking fund, we can use the formula for the future value of an annuity due:

FV = PMT x [tex](((1 + r/n)^nt[/tex] - 1) / (r/n))

Where:

FV = future value

PMT = monthly payment

r = interest rate (as a decimal)

n = number of compounding periods per year

t = number of years

In this issue, we are solving for PMT.

Given:

FV = $83,000,

r = 0.03 (3% expressed as a decimal),

n = 12 (monthly compounding),

t = 7 years.

Plugging in the values, we have:

$83,000 = PMT x [tex](((1 + 0.03/12)^(12*7)[/tex] - 1) / (0.03/12))

Simplifying:

$83,000 = PMT x (94.4523)

PMT = $83,000 / 94.4523

PMT = $878.84 (rounded to the nearest cent)

Therefore, Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly.

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Answer: so if it cosst 25,000,000 dollars to market a car and they sell it for 30,000 dollars they would need to sell 167 cars to get 5.1 million dollars or 166 for 5.0 million

Answer:

Step-by-step explanation:

1. the initial population at t=0 is 1

2. 16

well, first of all, you don't want to go into the oven, is too hot and you'll get burned, so you may not want to do that.

now, if we start to bake something at 3:40pm and it requires 35 minutes, it'll be done by 3:40 + 35, or 3pm and 40 + 35 minutes, or 3pm plus 75 minutes or 3pm plus 60 + 15 minutes, but since 60 minutes is 1hr, that'd be 3pm plus 1hr plus 15 minutes, 4:15pm.

Answer:

The answer is **FD = 1.52**.

Since triangle ABC ~ triangle DEF, we know that the ratio of their corresponding sides is equal. So, we have:

```

AB/DE = AC/DF = BC/EF

```

We are given that AB = 11, DE = 2.2, and AC = 7.6. Substituting these values into the first equation, we get:

```

11/2.2 = 7.6/DF

```

Cross multiplying, we get:

```

11 * DF = 2.2 * 7.6

```

```

DF = (2.2 * 7.6) / 11

```

```

DF = 1.52

```

Step-by-step explanation:

a) The range of chest measurements contains 68% which falls closest to the mean is between 38 inches and 42 inches

b) The chest measurements for the 2.5% of the men with the smallest chest measurements in the population to be approximately 36 inches

Given data ,

The Empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that describes the approximate distribution of data in a normal distribution.

Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ)

Approximately 95% of the data falls within two standard deviations of the mean (μ ± 2σ)

Approximately 99.7% of the data falls within three standard deviations of the mean (μ ± 3σ)

It would be within one standard deviation of the mean for the range of chest measures that accounts for 68% of the data and is closest to the mean. Since the standard deviation is 2 inches and the mean chest measurement is 40 inches, we can get the range as follows:

Mean - 1 standard deviation = 40 - 2 = 38 inches

Mean + 1 standard deviation = 40 + 2 = 42 inches

b)

We may look at the bottom end of the distribution to obtain the chest dimensions for the 2.5% of males with the smallest chest measurements in the population. The empirical rule states that 2.5% or less of the data goes outside of two standard deviations of the mean. So, using the following formula, we can get the chest size of the 2.5% of men:

Mean - 2 standard deviations = 40 - 2(2) = 36 inches

Hence , the standard deviations are solved

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The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).

The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.

To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.

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We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

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There are 6 different ways can the flags be arranged in a row.

We have,

Total number of flags = 6

So, to find the number of ways to arranged n object = n!

Then, the number of ways to arrange the flag

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

=120 x 6

= 720 ways

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Answer:

1km:100decameter(dam)

Step-by-step explanation:

so 35dam:0.35km

and 35dam:0.00035m

We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).

We have,

To show that the solution to the differential equation dp/dt = -0.1P is

P = 495e^(1.1t),

we can use separation of variables and integration.

Starting with the differential equation:

dp/dt = -0.1P

We can separate the variables by dividing both sides by P and multiplying both sides by dt:

dp/P = -0.1 dt

Integrate both sides:

∫ dp/P = -0.1 ∫ dt

Integrating the left-hand sid.

ln|P| = -0.1t + C

where C is the constant of integration.

To solve for C, we can use an initial condition.

Suppose that when t = 0, P = P0.

Then we have:

ln|P0| = -0.1(0) + C

ln|P0| = C

Substituting this value of C back into the equation for P.

ln|P| = -0.1t + ln|P0|

ln|P/P0| = -0.1t

Taking the exponential of both sides.

P/P0 = e^(-0.1t)

Multiplying both sides by P0.

P = P0 e^(-0.1t)

We can substitute P0 = 495 (since P(0) = 495 is given in the solution) and e^(-0.1t) = e^(1.1t)/e^t.

P = 495 e^(1.1t)/e^t

Simplifying the expression by combining the exponentials.

P = 495 e^(0.1t)

which is the same as the given solution.

Therefore,

We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).

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