The area of triangle ABC is 4√2 m².

Work out the value of x.
Give your answer correct
to 3 significant figures.
Note: Please make sure your final line says x =

Answer:

23

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

213.21/15.8 --->  ((213.21)100)/((15.8)100)

21321/1580 = 13 R 781.

781/1580 = 0.49~~~

We only need to be concerned about the tenth and hundredth place digits.

The decimal tells us that it rounds up from 4, so it's 5.

Thus, the answers 13+0.5, which is 13.5

For a circle k(O) with diameter AB and CD ⊥ AB, it is proved that AD·CB=AC·CD, using similarity of triangles.

Given:

circle k(O) with diameter AB

CD ⊥ AB

To Prove: AD·CB=AC·CD

Proof:

In ΔADC and ΔCDB,

∠ADC = ∠CDB = 90°  

[∵Both are right angle triangles]

CB = CB [Common side]

⇒ AC / CB = CD / DB

Thus, ΔACD is similar to ΔCDB by RHS similarity.

Therefore, we can write,

AD/CD = AC/CB [Since corresponding sides of similar triangles are proportional]

⇒ AD·CB = AC·CD

Hence proved.

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The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

According to the statement

we have to find the condition of the expected values in the case of testing of goodness-of-fit test.

So, For this purpose we know that the

The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.

So, The main condition of the expected value for the goodness of fit test is

For each​ category, the expected frequency is at least 5.

Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.

So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

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Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

Answer:

C = 10π ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

to find r use the area formula, that is

A = πr² = 25π ( divide both sides by π )

r² = 25 ( take square root of both sides )

r = [tex]\sqrt{25}[/tex] = 5

then

C = 2π × 5 = 10π ft

120=!3÷!6

!2-!5=!3

to 120 modes

Answer:

12.50h = 2500.75

Step-by-step explanation:

He earned $12.50 for 1 hour of work.

For 2 hours, he earned $12.50 × 2.

For 3 hours, he earned $12.50 × 3.

For h hours, he earned $12.50 × h which can be simply written as 12.50h

He earned altogether $2500.75, so 12.50h must equal 2500.75.

Answer: B 12.50h = 2500.75

Answer:

[tex]12.50 h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

12.50 x h = 2500.75

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

[tex]h=\frac{2500.75}{12.50}[/tex]

= 200.6 Hours

An equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

An equation can be defined as a mathematical expression which is used to show and indicate that two (2) or more numerical quantities are equal.

Mathematically, the equation of a hyperbola in standard form is given by:

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1[/tex]

Given the following data:

Center (h, k) = (0, 0)

Vertex (h+a, k) = (-5, 0)

Foci, F = (h+c, k) = (-6, 0) and F' = (6, 0)

Also, we can logically deduce that the value of a and c are -5 and -6 respectively.

For the value of b, we would apply Pythagorean's theorem:

c² = a² + b²

b² = c² - a²

b² = (-6)² - (-5)²

b² = 36 - 25

b² = 9.

b = √9

b = 3.

Substituting the given parameters into the equation of a hyperbola in standard form, we have;

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1\\\\\frac{(y\;-\;0)^2}{-5^2} - \frac{(x\;-\;0)^2}{3^2} = 1\\\\\frac{y^2}{-5^2} - \frac{x^2}{3^2} = 1\\\\\frac{y^2}{25} - \frac{x^2}{9} = 1[/tex]

y²/25 - x²/9 = 1.

In conclusion, we can logically deduce that an equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

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The frequency of the periodic function is given by: 0.0796.

From the graph, we have that the period is of 4pi hours, hence the frequency is:

f = 1/4pi = 0.0796.

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Step-by-step explanation:

1.

how many glasses of 0.32 liter can she fill ?

that means, how often does 0.32 fit into 1.45 ?

that is solved by division :

1.45 / 0.32 = 4.53125

so, she will need at least 5 glasses to completely empty the bottle. the 5th glass will be filled only partly, but that does not matter in that regard.

2.

he has 5.6 kg and adds 2.5 kg. that is 5.6 + 2.5 = 8.1 kg.

1 dough (that means 1 portion of dough as described by his recipe) uses 0.48 kg flour.

how many doughs can he make

so, again, how often does 0.48 fit into 8.1 ?

8.1 / 0.48 = 16.875

he can therefore make 16 full portions of dough. he does not have enough flour for a full 17th.

so, he uses

16×0.48 = 7.68 kg of flour for the 16 doughs.

and he has

8.1 - 7.68 = 0.42 kg of flour left.

The area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].

The area under a curve between two points exists seen by accomplishing a definite integral between the two points. To estimate the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. This area can be estimated by utilizing integration with given limits.

The equation that represents the curve exists

y = x² + 4

To estimate the area under the curve in the interval of [-3, 2] will be

[tex]$&\text { area }=\int_{-3}^{2} x^{2}+4 d x \\[/tex]

[tex]$&=\left[\frac{x^{3}}{3}+4 x\right]_{-3}^{2} \\[/tex]

[tex]$&=\frac{1}{3}\left[x^{3}\right]_{-3}^{2}+4[x]_{-}^{2} _{3} \\[/tex]

simplifying the above equation, we get

[tex]$&=\frac{1}{3}\left[(2)^{3}(-3)^{3}\right]+4[(2)-(-3)] \\[/tex]

[tex]$&=\frac{1}{3}[8+27]+4[2+3] \\[/tex]

[tex]$&=\frac{1}{3}(35)+20 \\[/tex]

[tex]$&=\left(\frac{95}{3}\right)[/tex]

Therefore, the area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].

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The factors illustrate they the sides of the rectangles are:

The first equation given is x² - 3x + 2.

= x² - 3x + 2.

= x² - x - 2x + 2

= x(x - 1) - 2(x - 1)

= (x - 1)(x - 2)

Therefore, the side lengths are (x - 1) and (x - 2).

In the rectangular figure, the length and width should be the expressions above.

The second equation given is 2x² + x - 6.

= 2x² + x - 6.

= 2x² + 4x - 3x - 6

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

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

Therefore, the side lengths are (2x - 3) and (x + 2).

In the rectangular figure, the length and width should be the expressions above.

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The values represent the robot facing east, south, and west are 1, -i, -1.

To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.

given that,

The robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now,

It is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1.

(as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.

Hence,The values represent the robot facing east, south, and west are 1, -i, -1.

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Answer:q = 6+43r/9

Step-by-step explanation:

Assuming R=9q-43r-6 is what you meant
R+6 = 9q - 43r
R + 6 + 43r = 9q
q = 6+43r/9

6) The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) The average depth of the water is 0.35 kilometers.

12) The dollar value of the deposit after 10 years is $ 1205.85.

13) Three horses need a consumption of 930 pounds of hay for the month of July.

14) The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) Anna has a mean time of 7.39 minutes.

In this question we must analyze and resolve on algebraic equations such as linear equations or conic sections. 6) We must use algebra properties to solve on the system of linear equations. First, we clear x in the first equation:

x = y - z

Then, we apply it in the two remaining equations:

- 5 · (y - z) + 3 · y - 2 · z = - 1

2 · (y - z) - y + 4 · z = 11

- 2 · y + 3 · z = - 1

y + 2 · z = 11

Second, we clear y in the second expression and we substitute into the first expression:

y = 11 - 2 · z

- 2 · (11 - 2 · z) + 3 · z = -1

- 22 + 7 · z = - 1

z = 3

y = 5

x = 2

The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) There is a function of the speed of a tsunami in terms of the average depth of the water. The former variable is known and we need to clear d in the formula to find the missing value:

145 = 356 · √d

d = (145 / 356)²

d = 0.345 km

The average depth of the water is 0.35 kilometers.

12) The compound interest model is shown below:

C' = C · (1 + r / 100)ˣ      (1)

Where:

If we know that C = 500, r = 4.5 and x = 20, then the resulting capital after 10 years is:

C' = 500 · (1 + 4.5 / 100)²⁰

C' = 1205.85

The dollar value of the deposit after 10 years is $ 1205.85.

13) The situations indicates a direct variation as the amount of hay is directly proportional to the number of days. Hence, we have the following linear model for the hay consumption of one horse:

y = m · x        (2)

y = 10 · x

Where:

The total consumption of three horses during July is equal to the product of the number of horses and consumed hay by one horse during one month:

y' = 3 · [10 · (31)]

y' = 930

Three horses need a consumption of 930 pounds of hay for the month of July.

14) There is the general equation of the circumference and we must transform it into its vertex form to find information about the radius. This can done by algebraic procedures:

x² + y² + 8 · y + 8 · y + 28 = 0

(x² + 8 · y) + (y² + 8 · y) = - 28

(x² + 8 · y + 16) + (y² + 8 · y + 16) = 4

(x + 4)² + (y + 4)² = 2²

The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) We need to sum all the times described in the table and divide it by the number of data to find the mean time for a 1-kilometer race:

x = (7.25 + 7.40 + 7.20 + 7.10 + 8.00 + 8.10 + 6.75 + 7.35 + 7.25 + 7.45) / 10

x = 7.39

Anna has a mean time of 7.39 minutes.

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The image on the left represents a function. The image on the right does not as a function cannot have multiple variables for a single X quantity.

Answer: A

Step-by-step explanation:

[tex](-5,3)\\(-3, 1)\\(-1,-1)\\(1, -1)\\(3, 1)\\(5, 3)[/tex]

Answer: 0.032, 18, 4224, 7.58

Step-by-step explanation:

5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]

5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L

6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box

400/23 = 17.4 so it takes 18 balls to overflow the water

7. 1 mL = 1 [tex]cm^{3}[/tex]

(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL

(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]

22 x 12 = 264

2000/264 = 7.58 cm

Answer: 1/2, 1/2, 1/4

Step-by-step explanation:

To find the fraction that the hour hand turns of a clockwise revolution, we have to find how long it is going then divide by 12

Ex. a) 11 - 5 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

b) 8 - 2 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

c) For this, we have to convert 1 into 13 as 1 - 10 is a negative number

13 - 10 = 3, 3/12 = 1/4 so the hour hand turns by 1/4 of a clockwise revolution

The answers are :

a) 1/2

b) 1/2

c) 1/4

To find the fraction of a clockwise revolution, take the ratio between hours covered and hours covered in one revolution.

a)

b)

c)

The lengths of the sides of the rectangles are;

a. (2•x + 3) and (x + 2)

b. (6•x + 2) and (x + 1)

c. (x + (2 + √3)) and (x + (2-√3))

The given functions are presented as follows;

a. 2•x² + 7•x + 6

By factoring of the above function we have;

2•x² + 7•x + 6 = (2•x + 3) × (x + 2)

The lengths of the sides of the rectangle are therefore;

b. 6•x² + 7•x + 2

The above function can be factored as follows;

6•x² + 7•x + 2 = (6•x + 2) × (x + 1)

The rectangle side lengths are;

c. x² + 4•x + 1

Using the quadratic formula, the above function can be factored to give;

x² + 4•x + 1 = (x + (2 + √3)) × (x + (2-√3))

The sides of the rectangle are therefore;

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The required length of the hypotenuse of the triangle is √19.

To find the required length of the hypotenuse of the triangle:

Legs in the right triangle refer to the perpendicular and base.

Hypotenuse:

[tex]= \sqrt{perpendicular^{2}+base^{2} } \\= \sqrt{3^{2}+\sqrt{10^{2} } } \\=\sqrt{19}[/tex]

Therefore, the required length of the hypotenuse of the triangle is √19.

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Answer:

1/50

Steps:

Recall 2 can divide 100

therefore

2/100 = 1/50

Answer:

  no solution

Step-by-step explanation:

The Law of Sines tells you the relationship between sides and angles of a triangle.

The Law of Sines tells you ...

  sin(A)/a = sin(B)/b = sin(C)/c

Using the given information, this would tell us ...

  sin(55°)/12 = sin(B)/b = sin(C)/27

Then angle C would be ...

  sin(C) = (27/12)sin(55°) ≈ 1.843

There is no angle whose sine is greater than 1. The triangle we seek does not exist. (Side BC is too short relative to side AB.)

Using a calculator, the critical value for the t-distribution with a confidence level of 99% and 49 df is of Tc = 2.4049.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level of 99% and 49 df is of Tc = 2.4049.

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[tex]f(x)=-\frac{3}{4}x-3[/tex]

A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. 5. A mathematical function or equation is shown by a curve or line, usually represented using a Cartesian coordinate system.

The equation for f (x):

[tex]y=f(x)=mx+b[/tex]

The slope of the line is m.

The point of intersection of the line with the y-axis is b.

To find the slope first by the following formula:

[tex]=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Two points of the line: [tex](x_{1} ,y_{1})=(x_{2},y_{2} )[/tex]

[tex](x_{1} ,y_{1})=(-4,0)[/tex]

[tex](x_{2} ,y_{2})=(0,-3)[/tex]

Substituting:

[tex]m=\frac{-3-0}{0-(-4)}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Find the y-intercept Looking at the graph, we find the line intercepts the y-axis at y=-3.

Therefore, b=-3.

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After finding the intercept form of the graph of the given straight line, it can be obtained that [tex]f(x)=-\frac{4}{5}x-3[/tex].

If the graph of a straight line cuts the x-axis at the point [tex](a,0)[/tex] and the y-axis at the point [tex](0,b)[/tex], then the equation of the straight line in intercept form will be [tex]\frac{x}{a}+\frac{y}{b}=1[/tex].

Here, in the given figure, we can see that the graph of [tex]y=f(x)[/tex] is a straight line.

From the graph, we can see that the straight line cuts the x-axis at the point [tex](-3\frac{3}{4},0)=(-\frac{15}{4},0)[/tex] and cuts the y-axis at the point [tex](0,-3)[/tex].

So, here, [tex]a=-\frac{15}{4}[/tex] and [tex]b=-3[/tex].

Hence, the equation of the straight line in intercept form is

[tex]\frac{x}{a}+\frac{y}{b}=1\\\frac{x}{-\frac{15}{4}}+\frac{y}{-3}=1\\\frac{y}{-3}=1+\frac{4x}{15}\\y=-\frac{4}{5}x-3[/tex]

Therefore, finding the intercept form of the given straight line, we obtain that [tex]f(x)=-\frac{4}{5}x-3[/tex].

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Answer:

C

Step-by-step explanation:

|-80 - 15| = 95

The distance between -80 and 15 is 95

80 to 0 plus 15.

Answer:

8/9

Step-by-step explanation:

I'm pretty sure it's that

The answer is 8/9.

First, find the HCF of 24 and 27.

Hence, the HCF of the numbers is 3.

Then, divide both sides of the fraction by 3.

The height of the rectangular pyramid is 7 ft.

First, we know that the volume of a rectangular pyramid is given by:

[tex]V = B*H/3[/tex]

Where B is the base, H is the height.

First, we know that the volume is 56 ft³, and the base is 24ft², then we can replace these two in the volume equation to get:

[tex]56 ft^3 = 24ft^2*H/3[/tex]

Solving that for H, we get:

[tex]H = 3*(56ft^3/24ft^2) = 7ft[/tex]

The height of the rectangular pyramid is 7 ft.

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The statement is false as the sample is a few ATMs of the total ATMs in US.

The sample is only 860 ATMs and not total ATMs in US thus, a sample of 860 ATMs have taken and conducted the survey.

Thus, the statement is false as the sample is a few ATMs of the total ATMs in US.

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