Suppose the solution set of a certain system of linear equations can be described as x_1 = 6 + 3x_3, x_2 = -2 - 5x_3, with x_3 free. Use vectors to describe this set as a line in R^3. Geometrically, the solution set is a line through parallel to

In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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The length of AC in this right-angled triangular prism is approximately 60.66 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Height²+Base²

However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.

If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:

AC² = AE²+ EC²

We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:

EC = 51 cm and ED = 45 cm

Substituting this into the equation above, we get:

AC² = 43² + 51²

AC² = 3680

AC ≈ 60.66 cm (to 1 decimal place)

Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.

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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.

Base is ED 51 cm and height is AE 43 cm of the prism."

A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.

A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:

1, 3, 5, 7, 9

3, 5, 1, 7, 9

The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.

Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each term in the sequence (starting with the third term) is the sum of the two preceding terms.

This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.

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What is the arrangement of objects in a definite order called?

The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.

A gardener will use up to 250 square feet for planting flowers and vegetables, hence:

x + y ≤ 250    (1)

She wants the area used for vegetables to be at least four times the area used for flowers. Hence:

y ≥ 4x     (2)

Plotting both equations using geogebra, the solution is the darker region.

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The option B, 0.0625, is the correct answer.

The probability that all children are boys is 1/2 × 1/2 × 1/2 × 1/2 = 1/16. The probability of the event is 0.0625. The probability that all the children are boys is 0.0625.Therefore, option B, 0.0625, is the correct answer.

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Using variation, the model for F = 42(m/p)

There is a direct variation between the two variables whenever one quantity directly influences the other, such as when one quantity increases relative to the other and vice versa. There is a connection between two variables when one of them is a constant multiple of the other. Because of their immediate connection, the two variables are referred to as directly proportional.

Inverse variation establishes a proportionality between two quantities that are inversely related. There are two separate proportionalities. They are the direct variation and inverse variation. The two quantities are said to be directly proportional if an increase or decrease in one generates an equal increase or decrease in the other. In an inverse variation, on the other hand, one quantity increases while the other falls.

Now as F is directly proportional to m and inversely to p, so we can form a model as:

F = 42(m/p)

So that F=36 when m =6 and p =7.

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[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20[/tex]

Answer:

I think is 500 hope it helps

We οbtain JN  44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly  44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.

The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.

The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.

Law of sines

sin(∠A)/a = sin(∠B)/b = sin(∠C)/c

Therefore,

39/sin(53°) = JN/sin(65°)

JN = (39×sin(65°))/sin(53°)

JN = 44.3

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The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

A simple randοm sample is a subset οf persοns picked at randοm, all with the same prοbability, frοm a larger set οf individuals. It is a methοd οf chοοsing a sample at randοm.

Here, we have

Given: a certain newspaper prοvides the net asset value, the year-tο-date percent return, and the three-year percent return fοr 882 mutual funds at the end οf 2017. assume that a simple randοm sample οf 12 οf the 882 mutual funds will be selected fοr a fοllοw-up study οn the size and perfοrmance οf mutual funds. use the third cοlumn οf the table οf randοm numbers, beginning with 71744, tο select the simple randοm sample οf 12 mutual funds.

The last three digits in each rοw οf cοlumn 6 less than 882 are

714, 041, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

Hence, The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488.

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Answer:

-7

Step-by-step explanation:

A negative number times a negative number is positive. Because -5 is negative and 35 is positive the other factor must be negative as well.

5 x 7 = 35

So, -5 x -7 also equals 35

The inflation rate in 2020, given the CPI in 2020 and the price in both years, would be 95. 5 %.

To find the inflation rate from the CPI (Consumer Price Index), subtract the beginning CPI from the end CPI. This gives you the increase in the price level over the time period.

Divide the increase in the price level by the beginning CPI. Multiply the result by 100 to get the inflation rate as a percentage. Basically, the formula is:

= (CPI in 2020 - CPI in 2019 ) / CPI in 2019

= ( 195.5 - 100 ) / 100

= 95. 5 %

Note : The CPI for 2020 is 195.5 and the assumed CPI for 2019 would be 100 as a base year.

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The cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

(a) 0.974

(b) 0.998

(c) 0.996

(d) 2.571

(a) To find the proportion of the area under the curve to the right of t = 2.015, we first calculate the cumulative probability of t = 2.015 from the t-distribution table. The cumulative probability of t = 2.015 is 0.974, which means that 0.974 or 97.4% of the area under the curve lies to the right of t = 2.015.

(b) To find the proportion of the area under the curve to the left of t = −3.365, we calculate the cumulative probability of t = −3.365 from the t-distribution table. The cumulative probability of t = −3.365 is 0.998, which means that 0.998 or 99.8% of the area under the curve lies to the left of t = −3.365.

(c) To find the proportion of the area under the curve between t = –4.032 and t = 4.032, we calculate the cumulative probability of t = 4.032 and subtract the cumulative probability of t = −4.032. The cumulative probability of t = 4.032 is 0.995 and the cumulative probability of t = −4.032 is 0.003. Subtracting the two gives us 0.996, which means that 0.996 or 99.6% of the area under the curve lies between t = –4.032 and t = 4.032.

(d) To find the value of t that cuts off the upper 2.5% of the distribution, we calculate the cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

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Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).

To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.

Let x be the length of the road connecting towns B and C. Then we have:

x^2 = 61^2 + 60^2

x^2 = 3721 + 3600

x^2 = 7321

x ≈ 85.6 km

Therefore, the length of the road connecting town B and C is approximately 85.6 km.

Step-by-step explanation:

Answer:

  996,250,626,076

Step-by-step explanation:

You want the value of the numerical expression 251^5+8-(9×20+3).

Your calculator will evaluate this properly if you enter it as shown. See the attachment.

If you're doing this in parts, the Order of Operations tells you to start with the parentheses, then do the exponentiation.

  251^5 +8 -(9·20 +3)

  = 251^5 +8 -183

  = 996,250,626,251 +8 -183 = 996,250,626,076

__

Additional comment

You can use a spreadsheet (or an on-line calculator) if your calculator only displays 10 digits.

By evaluating and simplifying f(x)=3x2 +3x+8, we get  f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8 and  (f(x + h) - f(x))/h = 6x + 3h + 3.

Given function is, f(x) = 3x² + 3x + 8

Evaluate f(x + h)

Expanding f(x + h) => f(x) + hf′(x) + h²/2f″(x)

Applying formulae in the given function f(x + h) = 3(x + h)² + 3(x + h) + 8=> 3x² + 6xh + 3h² + 3x + 3h + 8Now, f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8

Evaluate (f(x + h) - f(x))/h

Expanding both the terms f(x + h) and f(x) and simplifying, (f(x + h) - f(x))/h = [3x² + 6xh + 3h² + 3x + 3h + 8 - (3x² + 3x + 8)]/h=> [3x² + 6xh + 3h² + 3x + 3h + 8 - 3x² - 3x - 8]/h=> [6xh + 3h² + 3h]/h=> 6x + 3h + 3

Therefore, the required value is f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8and (f(x + h) - f(x))/h = 6x + 3h + 3.

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The work required to move q from the other vertex to the center of the line joining the fixed charges is (1/4π ε0) x 2 x q 2/a.

To solve this problem, we can use the principle of superposition to calculate the potential at the center of the equilateral triangle due to each of the two fixed charges, and then add them up to get the total potential.

Let's first find the potential due to one of the fixed charges at the center of the triangle. We can use the formula for the electric potential due to a point charge q at a distance r from it, which is given by:

V = k x q/r

In this case, the distance from one of the fixed charges to the center of the triangle is: r = a/2

So the potential due to one fixed charge at the center of the triangle is:

V1 = kq/r = kq/(a/2)

Next, let's find the potential due to the other fixed charge at the center of the triangle. Since the triangle is equilateral, the distance from the other fixed charge to the center of the triangle is also a/2. So the potential due to the other fixed charge at the center of the triangle is:

V2 = k x q/(a/2)

Now, the total potential at the center of the triangle due to the two fixed charges is simply the sum of the individual potentials:

V_total = V1 + V2 = kq/(a/2) + kq/(a/2) = 2kq/a

The work required to move a charge q from infinity to the center of the triangle is equal to the change in potential energy of the charge, which is given by:

W = q x (V_final - V_initial)

In this case, the initial potential is zero (since the charge is at infinity), and the final potential is 2kq/a (which we just calculated). So the work required is:

W = q x (2kq/a - 0) = 2kq 2/a

Substituting the given value of k, we get:

W = (1/4π ε0) x 2 x q2/a

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Answer: x = 100

Step-by-step explanation:

The position of a car driving along a straight road at time t in minutes is given by the function y = f(t).

The function y represents the position of the car in thousands of feet, while the variable t represents the time in minutes.

To find the position of the car at any given time, you simply need to plug in the value of t into the function and solve for y. For example, if you wanted to find the position of the car at 2 minutes, you would plug in 2 for t and solve for y:

y = f(2)

Once you have solved for y, you will have the position of the car in thousands of feet at 2 minutes. You can repeat this process for any value of t to find the position of the car at any given time.

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Answer:

5.1, 5 1/10

Step-by-step explanation:

(3.5 − 2/3) ⋅ (−2.8 + 4 3/5) =

= (7/2 - 2/3)(-14/5 + 23/5)

= (21/6 - 4/6)(9/5)

= (17/6)(9/5)

= (17 × 9)/(6 × 5)

= 51/10

= 5.1 = 5 1/10

The area of the composite figures are:

1: 106.28 sq. yd.

2: 79.27 sq. in.

3: 64.28 sq. m.

4: 44.82 sq. ft.

5: 406 sq. cm.

6: 629.46 sq. km.

To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

No. 1

Area = area of semicircle + area of rectangle + area of semicircle

Area = (1/2 * πr²) + (L*W) + (1/2 * πr²)

r = 6/2 = 3 yd, L = 13 yd and W = 6 yd

Area = (1/2 * π*3²) + (13*6) + (1/2 * π*3²)

Area = 14.14 + 78 + 14.14

Area = 106.28 sq. yd.

No. 2

Area = area of semicircle + area of triangle

Area = (1/2 * πr²)  + (1/2 *base* height)

r = 10/2 = 5 in, base = 10 in and height = 8 in

Area = (1/2 * π * 5²)  + (1/2 * 10 * 8)

Area = 39.27 + 40

Area = 79.27 sq. in.

No. 3

Area = area of square + area of semicircle + area of semicircle

Area =  L² + (1/2 * πr²) +  (1/2 * πr²)

L = 6 m,  r = 6/2 = 3 m

Area =  6² + (1/2 * π * 3²) +  1/2 * π * 3²)

Area =  36 + 14.14 + 14.14

Area = 64.28 sq. m.

No. 4

Area = area of semicircle + area of rectangle

Area =  (1/2 * πr²) + (L * W)

r = 5/2 = 2.5 ft, L = 7 ft and W = 5 ft

Area =  (1/2 * π * 2.5²) + (7 * 5)

Area =  9.82 + 35

Area = 44.82 sq. ft.

No. 5

Area = area of triangle + area of rectangle

Area =  (1/2 * base * height) + (L * W)

base = 10cm, height = 14 cm, L = 24 cm and W = 14 cm

Area =   (1/2 * 10 * 14) + (24 * 14)

Area =  70 + 336

Area = 406 sq. cm.

No. 6

Area = area of semicircle + area of triangle

Area =   (1/2 * πr²) + (1/2 * base * height)

r = 26/2 = 13 km, base = 28 km and height = 26 km

Area =   (1/2 * π * 13²) + (1/2 * 28 * 26)

Area =  265.46 + 364

Area = 629.46 sq. km.

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Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The first step in evaluating the expression 6 - (4/2 x 5)² is to simplify the expression inside the parentheses first.

An expression is a mathematical phrase that consists of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined according to certain rules to represent a mathematical calculation.

Following the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), as shown below:

4/2 = 2, so we can replace 4/2 with 2:

6 - (2 x 5)²

2 x 5 = 10, so we can replace 2 x 5 with 10:

6 - 10²

10² means 10 multiplied by itself, which equals 100:

6 - 100

Therefore, the expression simplifies to -94.

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Answer: first off i am not a nerd ur just a dummyboi second  this is simple math grade 4 really the answer is 24

Step-by-step explanation:

In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.

In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.

In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.

In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.

19+8=27 if ur making a 3x3 cube answer is 24

a) The continuous rate of growth of this bacterium population is 45%

b) Initial population of culture at t = 0 is 950 bacteria

c) number of bacterial cultures contain at t = 5 is 9013 bacteria

The number of bacteria in a culture is given by the function n(t) =950[tex]e^{0.450t}[/tex] Where t is measured in hours

what is the continuous rate of growth of this bacterium population

The number of bacteria in a culture is given by

n(t) = 950[tex]e^{0.45t}[/tex]

a) rate of growth is

Bacteria growth model N(t) = no[tex]e^{rt[/tex]

Where r is the growth rate

hence r = 0.45

             = 45%

b) Initial population of culture at t = 0

n(0) = 950[tex]e^0[/tex]

      = 950

      = 950 bacteria

c) number of bacterial culture contain at t = 5  

n(5)      = 950[tex]e^{0.45*5}[/tex]

     = 9013.35

     = 9013 bacteria

the complete question is-

The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent B) what is the initial population of the culture (at t=0) your answer is __ C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria

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a. The population in this question is all the Cheapo Coffee stores around the country.

b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.

In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.

However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.

The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.

We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.

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The interest compounded equation to model the given situation is A(t) = 4000[tex]e^{0.05t}[/tex].

To model the given situation, the interest compounded can be written as the given equation of:

A(t) = A0e^(rt)

Where:

A(t) is the amount of money after t years

A0 is the initial amount of money, in this case,

r is the interest rate expressed as a decimal

t is the time in years that the money is invested.

From the case, we know that:

Initial deposit = $4,000

Interest rate = 5%

Time period = t (undetermined)

So, substituting the values given in the problem, the equation to model the given situation is:

A(t) = A0e^(rt)

A(t) = 4000e^(0.05t)

Therefore, A(t) = 4000e^(0.05t) is the required equation that models the given situation.

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Tia's statement that the graph is a x^5 function is correct

The statements from the question are:

The zeros and the multiplicities in the format (zero, multiplicity) from the question are (-3, 1), (-1, 2), (2, 1) and (3, 1)

The equation of the polynomial can be expressed as

P(x) = (x - zero)^multiplicity

When the zeros and the multiplicities are substituted, we have

P(x) = (x + 3)(x - 3)(x - 2)(x + 1)^2

Expand

P(x) = (x^2 - 9)(x - 2)(x + 1)^2

When evaluated, we have

P(x) = x^5 - 12x^3 - 2x^2 + 27x + 18

The above is a x^5 function

Hence, Tia is correct

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If locked out of an account due to forgotten password and invalid email, try password recovery options or contact customer support, or create a new account.

If you've been locked out of your account. If you've forgotten your password and the email you used to sign up is not valid, it can be difficult to regain access to your account. Few steps you can try to recover your account:

It's important to note that in some cases, it may not be possible to regain access to your account. Always be cautious about the information you provide when signing up for online services and make sure to keep your login credentials in a safe and secure location.

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Answer:

a₉ = - 24

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁ = 8 and d = - 4 , then

a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24

Answer:

Tn = a + (n - 1)d

T9 = 8 + (9 - 1) × -4

T9 = (8 + 8) × -4

T9 = 16 × -4

T9 = -64