Drag each equation to its equivalent fact. DUE TODAY

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

The additive inverse of the polynomial is A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Given data ,

Let the polynomial be represented as A

Now , the value of A is

A = ( 1.3t³ + 0.4t² - 24t ) - ( 0.6t² + 8 - 18t )

On simplifying the equation , we get

A = 1.3t³ + 0.4t² - 24t - 0.6t² - 8 + 18t

A = 1.3t³ - 0.2t² - 6t - 8

Now , the additive inverse of the polynomial is

A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Hence , the polynomial is solved

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The acceleration of the runner is 0.2 m/s².

We can use the following equation to get the runner's acceleration:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

In this case, the initial velocity (u) is 0 m/s, the final velocity (v) can be calculated using the formula:

v = s / t

where t is the amount of time spent and s is the distance travelled.

The time taken (t) and the distance travelled (s) are both provided as 500 m.

Calculate the b (v):

v = 500 m / 50 s

v = 10 m/s

Plug into the formula for acceleration:

a = (10 m/s - 0 m/s) / 50 s

a = 10 m/s / 50 s

a = 0.2 m/s²

Therefore, the acceleration of the runner is 0.2 m/s².

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Answer:

5 > \(\sqrt{18\)

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

Answer:

B. Polygon ABCD was reflected over the x-axis and then reflected over the y-axis.

The standard deviation of the sample is 0.63

What is standard deviation?

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

To find the standard deviation of the sample, we need to first find the mean of the distribution. The mean of a distribution is given by the expected value of the random variable, which can be calculated as follows:

       \(E[X] = \int\limits {xf(x)dx}\)

Substituting the given pdf for f(x), we get:

     \(E[X] = \int\limits {x(x2 + Źosxs1)dx}\)

Evaluating the integral, we get:

   \(E[X] = (x3/3) + (Źosxs2/2) |0\\\\ E[X] = (1/3) + (0/2)\\\\ E[X] = 1/3\)

Next, we need to find the variance of the distribution. The variance of a distribution is given by the expected value of the squared deviation of the random variable from its mean, which can be calculated as follows:

\(Var[X] = E[(X - E[X])2]\)

Substituting the value of E[X] that we just found, we get:

Var[X] = E[(X - (1/3))2]

Var[X] = ∫((x - (1/3))2)(x2 + Źosxs1)dx

Evaluating the integral, we get:

Var[X] = ((x - (1/3))2)(x2 + Źosxs1) |0

Var[X] = ((1 - (1/3))2)(1 + 0) - ((0 - (1/3))2)(0 + 0)

Var[X] = (4/9)(1) - (1/9)(0)

Var[X] = 4/9

Finally, the standard deviation of the distribution is the square root of the variance, which is:

\(Std\ Dev[X] = \sqrt{Var[X]}\\\\ Std\ Dev[X] = \sqrt{(4/9) } \\\\Std\ Dev[X] = 0.63\)

Rounding off to the second decimal place, the standard deviation of the sample is 0.63.

Hence, The standard deviation of the sample is 0.63

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The inequality will be represented as y > 8(x – 3)(x + 12).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that the inequality in a factored form describes the set of values that is greater than the quadratic function with zeros –12 and 3 and includes the boundary point (–4.5, –450).

The inequality will be written as below,

y > 8(x – 3)(x + 12).

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The mean of a dataset is the sum of all data elements divided by the count of the elements.

The location of the 6th score relative to the mean is 5 points below the mean

Let:

\(\bar x \to\) Mean

\(a \to\) 5 scores

\(b \to\) 6th scores

Given that:

\(n = 6\)

The 5 scores that are 1 above the mean implies that:

\(a = \bar x + 1\)

The mean of a dataset is calculated using:

\(\bar x = \frac{\sum x}{n}\)

So, we have:

\(\bar x =\frac{5a + b}{6}\)

\(\bar x =\frac{5(\bar x + 1) + b}{6}\)

Open brackets

\(\bar x =\frac{5\bar x + 5 + b}{6}\)

Multiply both sides by 6

\(6\bar x =5\bar x + 5 + b\)

Make b the subject

\(b = 6\bar x -5\bar x - 5\)

\(b = \bar x - 5\)

This means that the 6th score is 5 points below the mean

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Answer:

c. -5/7

Step-by-step explanation:

See below for the distance between the points and the lines

Question 2

The line and the points are given as:

x = y

P = (4, -2)

Rewrite the equation as:

y = x

The slope of the above equation is

m = 1

The slope of a line perpendicular to it is

m = -1

A linear equation is represented as:

y = mx + b

Substitute m = -1

y = -x + b

Substitute (4, -2) in y = -x + b

-2 = -4 + b

Solve for b

b = 2

Substitute b = 2 in y = -x + b

y = -x + 2

So, we have:

x = y and y = -x + 2

Substitute x for y

x = -x + 2

Solve for x

x = 1

Substitute x = 1 in y = x

y = 1

So, we have the following points

(1, 1) and (4, -2)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(1 - 4)² + (1 + 2)²

Evaluate

d = 3√2

Hence, the distance between x = y and P = (4, -2) is 3√2 units

Question 3

The line and the points are given as:

y = 2x + 1

Q = (2, 10)

The slope of the above equation is

m = 2

The slope of a line perpendicular to it is

m = -1/2

A linear equation is represented as:

y = mx + b

Substitute m = -1/2

y = -1/2x + b

Substitute (2, 10) in y = -1/2x + b

10 = -1/2 * 2 + b

Solve for b

b = 11

Substitute b = 11 in y = -1/2x + b

y = -1/2x + 11

So, we have:

y = 2x + 1 and y = -1/2x + 11

Substitute 2x + 1 for y

2x + 1 = -1/2x + 11

Solve for x

x = 4

Substitute x = 4 in y = 2x + 1

y = 9

So, we have the following points

(4, 9) and (2, 10)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(4 - 2)² + (9 - 10)²

Evaluate

d = √5

Hence, the distance between the line and the point is √5 units

Question 4

The line and the points are given as:

y = -x + 3

R = (-5, 0)

The slope of the above equation is

m = -1

The slope of a line perpendicular to it is

m = 1

A linear equation is represented as:

y = mx + b

Substitute m = 1

y = x + b

Substitute (-5, 0) in y = x + b

0 = 5 + b

Solve for b

b = -5

Substitute b = 5 in y = x + b

y = x + 5

So, we have:

y = x + 5 and y = -x + 3

Substitute x + 5 for y

x + 5 = -x + 3

Solve for x

x = -1

Substitute x = -1 in y = x + 3

y = 2

So, we have the following points

(-1, 2) and (-5, 0)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(-1 + 5)² + (2 - 0)²

Evaluate

d = 2√5

Hence, the distance between the line and the point is 2√5 units

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Answer: how about 105/3 = 35, therefore the middle number is 35, and the 3 numbers are 33, 35, and 37.

Step-by-step explanation:

The probability of the event of a wafer to be conforming and from lot A are as follows;

(a) P(A) ≈ 0.15541

(b) P(C) ≈ 0.84

(c) P(AC) ≈ 0.159

(d) P(A|C) ≈ 0.86

(e) P(C|A) ≈ 0.185

(f) E1 and E2 are independent events

Probability is given by the ratio of the number of required outcomes divided by the number of possible outcomes.

(a) The number of wafers from lot A = 79 + 13 = 92

79+13+157+43+260+40 = 592

Which gives;

The probability that the wafer is from lot A is therefore;

(b) The conforming wafers = 79+157+260 = 496

Which gives;

(c) The conforming wafers in lot A are 79

Therefore;

The probability that the wafer is from lot A and conforming is therefore;

(d) The probability that the wafer is conforming, given that it is from lot A is therefore;

P(A|C) = 79/92 ≈ 0.86

(e) The number of conforming wafers = 496

The probability that the wafer is from lot A given that it is conforming is therefore;

(f) Independent events are events such that the occurrence of one does not impact the probability of the other.

Given that the occurrence of E1 changes the probability of event E2 if the wafer is not replaced, the events are not independent events.

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Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Given: ∠XAM = ∠YBM = 90°    and     AM = BM

To prove: BX ≅ AY

Proof:

In the triangle XAM and BYM:

From the ASA rule of congruency, we can say that: ΔXAM ≅ ΔYBM

Since ΔXAM ≅ ΔYBM: We can say that XM ≅ MY     [CPCT - Common Part of Congruent triangles]

In the Triangle AMY and XMB:

From the SAS rule of congruency, we can say that: ΔAMY ≅ ΔXMB

Since ΔAMY ≅ ΔXMB: We can finally say that BX ≅ AY    [CPCT]

Hence Proved!

Answer:

4/10 + 6/10 + 6/10 = 16/10 = 1 6/10

Step-by-step explanation:

1.

Looks like

\(y=2\sqrt[3]{x}+\dfrac1{x^2}+\pi\)

Write \(\sqrt[3]{x}\) as a fractional power, \(x^{1/3}\). This makes it more obvious that the power rule should be used here.

\(y'=(2x^{1/3})'+(x^{-2})'+\pi'\)

\(y'=\dfrac23x^{-2/3}-2x^{-3}\)

\(y'=\dfrac2{3\sqrt[3]{x^2}}-\dfrac2{x^3}\)

2.

\(y=(\sin(2x)+\tan(3x))^e\)

Power and chain rule:

\(y'=\left((\sin(2x)+\tan(3x))^e\right)'\)

\(y'=e(\sin(2x)+\tan(3x))^{e-1}(\sin(2x)+\tan(3x))'\)

\(y'=e(\sin(2x)+\tan(3x))^{e-1}(\cos(2x)(2x)'+\sec^2(3x)(3x)')\)

\(y'=e(\sin(2x)+\tan(3x))^{e-1}(2\cos(2x)+3\sec^2(3x))\)

Answer:

  1:30 pm

Step-by-step explanation:

You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.

The relation between time, speed, and distance is ...

  distance = speed × time

  time = distance / speed

Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...

  head start distance = (50 mi/h) × (0.5 h) = 25 mi

Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...

  time = distance / speed = 25 mi / (5 mi/h) = 5 h

So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.

Sahil catches Joaquin at 1:30 pm.

__

Additional comment

By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...

  distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi

In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.

Answer:

Holy Roman Emperor, was the ruler and head of state of the holy Roman Empire.

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer:

D

Step-by-step explanation:

Answer:19.3

Step-by-step explanation:add all angles of the shape that should give you 733

The minus 733 from 1080 because interior angles in a octagon add to 1080 this should give you 347 the add the the x together giving you 18x then divide 347 by 18 that give 19.27 rounded up to 19.3

Answer:

This report is biased because most people drive to gas stations.

Step-by-step explanation:

The distance to a gas station is often further than walking distance. Therefore, most people will take a car because it's quicker, and most people go to gas stations to get gas.

The rate of the first athlete is greater than the rate of the second athlete.

To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.

The average speed of an athlete is calculated by dividing the distance traveled by the time taken.

For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:

Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.

For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:

Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.

To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:

Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.

Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.

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Given the points on the graph:

(x, y) ==> (-1, 2), (0, 0), and (3, 1)

The graph represents a piece-wise function.

Let's write a definition for the function that best describes the graph.

Using the points, we have:

• (-1, 2) ==> f(x) = 2, when x = -1

• (3, 1) ==> f(x) = 1, when x = 3

Let's find the equation of each line.

• Equation of line segment with endpoints (-1, 2) and (0, 0)

Apply the slope intercept form:

y = mx + b

Use the slope formula to find the slope:

Therefore, the equation is:

y = -2x

• Equation of line segments with endpoints (3, 1) and (0, 0);

Therefore, the equation is:

y = 1/3x

Hence, the definition for the functions that best describe the left piece of the graph is:

f(x) = -2x, if -1 ≤ x ≤ 0

The definition for the right piece of the function is:

f(x) = 1/3x, if 0 ≤ x ≤ 3

ANSWER:

f(x) = -2x, if -1 ≤ x ≤ 0

Answer:

10 and 30

Step-by-step explanation:

The sum of 10 and 30 is 40.

30 is three times ten (10 x 3 = 30).

hope this helps!

The answer is 10 and 30

10 times 3 is 30, meaning 10 will be the number times 3 they wanted. 10 + 30 is 40, therefore the answer is 10 and 30

Step-by-step explanation:

Since we are told that 10 is a zero,

(x−10) must be a factor:

F(x)=2x3−14x2−56x−40

F(x)=(x−10) (2x2+6x+4)

F(x)=2(x−10)(x2+3x+2)

F(x)=2(x−10)(x+2)(x+1)

So the other two zeros are

x = -2 and x= −1

Answer:

AC = 49

Step-by-step explanation:

Using the Altitude - on - Hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

BC² = DC × AC, substitute values

14² = 4 × x

196 = 4x ( divide both sides by 4 )

49 = x

Thus AC = x = 49

Step-by-step explanation:

pythogoream theorem.(hyp^2=opp^2+adj^2)

hyp=14 adg=4 opp=?

since we have to find opp

opp^2=hyp^2-adj^2

opp^2=14^2-4^2

196-16=180

\( \sqrt{180} \)

BD= 13.41

(Q as theta)

sinQ= opp÷hyp

= 13.41÷14

Q=sin^-1(13.4÷14)

Q=73.33

cosQ=adj(AD)÷hyp(BC)

cos 73.33× 14 =adj

AD=4.01

Therefore, AC =AD +DC(4.01+4)

=8.01

I am not sure....but I got this much