Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why.

The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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

O = (3, 2)

A = (-7, 5)

B = (-7, 2)

The distance between (or length of) the coordinates is calculated as

Length = √[(x2 - x1)² + (y2 - y1)²]

Using the above as a guide, we have the following:

OB = √[(3 -- 7)² + (2 - 2)²]

OB = √[(3 -- 7)² + 0²]

OB = √[(3 -- 7)²]

OB = 3 -- 7

AB = √[(-7 -- 7)² + (5 - 2)²]

AB = √[0² + (5 - 2)²]

AB = √[(5 - 2)²]

AB = 5 - 2

Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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Answer:

[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]

[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]

Step-by-step explanation:

Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.

[tex]\large{\boxed{a^2+b^2=c^2}[/tex]

where:

From inspection of the given diagram:

Substitute these values into the formula and solve for x.

[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]

Substitute the found value of x into the expression for each side length.

[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]

[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]

Therefore, the exact side lengths of the given right triangle are:

[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]

The side lengths to the nearest hundredth are:

The number of bacteria present after 13 hours is 5,306.

The number of bacteria present after 13 hours is calculated by applying half-life equation.

N = N₀ x 2^(t / d)

Where:

Since the bacteria population grew from 3,000 to 3,600 in 6 hours, the value of d is calculated as follows;

3,600 = 3,000 x 2^(6 / d)

3600/3000 = 2^(6 / d)

1.2 = 2^(6 / d)

log2 (1.2) = 6/d

0.38 = 6/d

d = 6/0.38

d = 15.8 hours

The number of bacteria after 13 hours is calculated as follows;

N = 3,000 x 2^(13 / 15.8)

N = 5,306.5 ≈ 5,306

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The complete question is below:

A culture started with 3,000 bacteria. After 6 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present in 13 hours. round your answer to the nearest whole number.

The initial value (a) of the exponential function f(x) = 4ˣ is 1.

The standard form of an exponential equation is:

y = abˣ

where a is the initial value and b is the multiplication factor.

If b > 1, it is a growth function and if b < 1, it is a decay function.

Given the exponential function:

f(x) = 4ˣ

The initial value (a) = 1 and the multiplication factor (b) = 4.

The graph of the exponential function f(x) = 4ˣ is attached below.

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The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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(1) The result of the row operation R₂ ↔ R₃ is [ -5   1    0    8]

                                                                            [  8  8    -7   5 ]

                                                                            [ 2   2     6   -5]

(2) The result of the row operation  3R₁ ↔ R₁ is  [24  - 27   -21   - 18]

                                                                                [8       9      -4      -5]

                                                                                 [2       2       -7     -8]

The result of the row operation in the matrix is calculated as follows;

R₂ ↔ R₃, implies changing row 2 and row, and the result would be;

[ -5   1    0    8]

[  8  8    -7   5 ]

[ 2   2     6   -5]

The result of obtained from 3R₁;

3R₁ = [24  - 27   -21   - 18]

3R₁ ↔ R₁ is determined as; (the row interchange)

[24  - 27   -21   - 18]

[8       9      -4      -5]

[2       2       -7     -8]

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The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

The row operation R₁ - 6 — R₁ will be carried out as follows:

7 - 6 = 1 {row 1 column 1}

-4 - 6 = 5 {row column 2}

8 - 6 = -8 {row column 3}

Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

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The unknown number that is summed with 3 and double whose result is one less that the number would be = -7

To determine the unknown number, let the unknown number be = n

From the question statement;

2(n + 3) = n-1

2n + 6 = n-1

Bring the like terms together;

2n-n = -6-1

n = -7

Therefore, the number that represents the unknown number used in the statement above would be = -7.

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From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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Answer:

53yd

Step-by-step explanation:

SA1 = 2(4×2)

= 2×8

= 16

SA2 = 2(4×3)

= 2×12

= 24

SA3 = 2(3×2)

= 2×6

= 12

TOTAL SA

16+24+13

= 53

Answer:

7e+6

Step-by-step explanation:

biggest answer

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

Now,

From the given information,

The operation we are to carry out is:

Add -4(row 1) to row 3

This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)

Multiplying by -4

-4 × [ 1     2    1   | -5

     -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

Adding the results to corresponding elements in row 3

   4    -1     6  |  -8

+  -4   -8   -4  | 20

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

   0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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The height of the person on the ferris wheel can be modeled by the equation:

h = 20sin(π/4*t) + 21

where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.

The equation of the line parallel is y = mx + (1 + 2m).

We have,

The equation of the line.

y = mx + c

Slope = m

And,

(-2, 1) = (x, y)

So,

1 = m x -2 + c

c = 1 + 2m

Now,

y = mx + c

y = mx + (1 + 2m)

Thus,

The equation of the line parallel is y = mx + (1 + 2m).

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The values of missing variables are given by:

x = 51°, y = 105°, z = 90°.

We know that the sum of external and internal angles is 180°.

So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.

So, 75° + y° = 180°

y° = 180° - 75° = 105°

And also external angle is right angle that is 90° and the corresponding internal angle is z°.

So, z° + 90° = 180°

z° = 180° - 90° = 90°

This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°

According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.

So, 591° - x = 540°

x = 591° - 540° = 51°

Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.

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Step-by-step explanation:

| Equation | Solution |

| 6+x=15 | x = 9 |

| 9x = 18 | x = 2 |

The table would look like:

| Equation | Solution |

| 6+x=15 | X |

| 9x = 18 | X |

The surface area of the pyramid is approximately 74.24 square inches.

What is a pyramid?

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.

To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.

The area of each triangular face can be found using the formula:

Area = (1/2) * base * height

where the base is one of the sides of the square base and the height is the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

slant height² = height² + (1/2 * base)²

where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.

height = 7 in.

base = 4 in.

slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53

slant height = √53 ≈ 7.28 in.

Now we can find the area of each triangular face:

Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2

There are four triangular faces, so the total area of the triangular faces is:

4 * 14.56 = 58.24 in²

The area of the square base is:

Area = side² = 4² = 16 in²

Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:

Surface Area = 58.24 + 16 = 74.24 in²

Therefore, the surface area of the pyramid is approximately 74.24 square inches.

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The amount of the down payment and the mortgage amount are $61440 and $194560

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

Buy a $256,000 home with a down payment of 24%

This means that

down payment = 24% * 256,000

So, we have

down payment = 61440

Next, we have

mortgage amount = (1 - 24%) * 256,000

So, we have

mortgage amount = 194560

Hence, the mortgage amount is 194560

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In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the  formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

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complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

a.

3.99% compounded monthly

b.

4% compounded quarterly

c.

4.175% compounded annually

d.

4.2% simple interest

Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

<95141404393>

Answer:

x = 3,

y = -2

Step-by-step explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2

Answer:ina can row 6mph in still water and 2 mph in current

Step-by-step explanation:

Given that a₁ = 9 and aₙ = aₙ₋₁ + 2 , we can find the value of a5 by repeatedly applying the recursive formula to find a₂, a₃, a₄, and a₅.Using this method, we get a₅ is 17.

The given sequence is not defined explicitly. However, we can use the recursive formula to find the value of a5.

a₁ = 9 and aₙ = aₙ₋₁ + 2 for n > 1

To find a₂, we use the recursive formula

a₂ = a₁ + 2 = 9 + 2 = 11

To find a₃, we use the recursive formula

a₃ = a₂ + 2 = 11 + 2 = 13

To find a₄, we use the recursive formula

a₄ = a₃ + 2 = 13 + 2 = 15

To find a5, we use the recursive formula

a₅ = a₄ + 2 = 15 + 2 = 17

Therefore, the value of a₅ is 17.

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after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.

what is approximately ?

Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,

In the given question,

The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.

To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.

Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63

So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:

fraction remaining = (1/2)⁰°⁶³ ≈ 0.518

To find the remaining mass, we can multiply the fraction remaining by the initial mass:

remaining mass = fraction remaining x initial mass

remaining mass = 0.518 x 500 mg ≈ 259 mg

Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.

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The value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. It typically represents a mathematical relationship or formula and can be used to solve problems and make predictions.

Assuming you started with a value of 100, the value of the stock would be lower after these two weeks.

In the first week, the stock dropped by 60%, which means its value decreased to 40% of its original value. Therefore, the value of the stock at the end of the first week would be:

100 * 0.4 = 40

In the second week, the stock increased in value by 75%. Therefore, the value of the stock at the end of the second week would be:

40 * 1.75 = 70

Therefore, the value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.

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Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.

In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.

Here,

The equation of the parabolic trajectory of the golf ball is given by:

f(x) = 0.84x - 0.0033x²

where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b / 2a

where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:

a = -0.0033 and b = 0.84

Substituting these values into the formula, we get:

x = -0.84 / 2(-0.0033)

= 127.27

So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:

f(127.27) = 0.84(127.27) - 0.0033(127.27)²

f(127.27) ≈ 21.67

So the highest point of the trajectory is approximately 21.67 meters above the ground.

To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:

0 = 0.84x - 0.0033x²

0.0033x² = 0.84x

x = 0 or x = 254.55

So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.

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Answer: 70, 6

Step-by-step explanation:

(a)  For <F  that is the same as <D.  The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same

All of the angles are = 180   if you subtract <E, you are left with 140 to be split between <F and <D

<F= 70

(b) all of the sides are the same because all the angles are the same

so AB=6

The year in which  the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.

The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.

To derive the number of year,

140 = 2.86t + 112

Subtracting 112 from both sides gives:

28 = 2.86t

Dividing both sides by 2.86 gives:

t ≈ 9.79 years

See attached graph.

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The number for which the theoretical probability matches the experimental probability is 2.

Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.

Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.

Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.

In the given table;

For theoretical, P(2) = 1/4

For experimental, P(7) = 7/28 = 1/4

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needs more explanation