A ladder is leaning against the side of a 10 m. House. If the base of the ladder is 3 m. Away from the house, how tall is the ladder?.

Answer:

E. 2,850 ft²

Step-by-step explanation:

Answer:

OptionE)

Step-by-step explanation:

Area of a circle = [tex]\pi r^{2}[/tex]

[tex]3.14X30X30[/tex]

= [tex]2826[/tex]

Hence the closest is 2,850

Answer:

y = 2/3 x + 6

Step-by-step explanation:

I do not see a point C, so I guess you get to make your own point C.  I will make it at (06,)

The equation of the line seen is

y = 4/6x + 5  If you start at A and count up, you will get 4 unit and then count right you will be 6 units.  This is the slope 4/6.  the 5 is where the line crosses the x axis (0,5)

We can simplify  4/6 to 2/3

y = 2/3 x + 5

When lines are parallel, they have the same slope, but different y intercept.  

Since I made C (0,6)  The equation of this parallel line would be

y = 2/3 x + 6

Draw a line parallel to AB but make sure that it goes through the point (0,6)

The average rate of change of the trigonometric function f(x) = 3 · sin 2x on the interval [0, π / 4] is 12 / π. (Correct choice: D)

In this question we need to determine the average rate of change of a trigonometric function on the interval [0, π / 4]. Graphically speaking, the average rate of change is represented by a line secant to the curve of the function, whose definition is shown below:

m = [f(π / 4) - f(0)] / (π / 4 - 0)

If we know that f(x) = 3 · sin 2x, then the average rate of change is:

m = [3 · sin (π / 2) - 3 · sin 0] / (π / 4 - 0)

m = (3 - 0) / (π / 4)

m = 12 / π

The average rate of change of the function is 12 / π.

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Answer:

Answered Below :)

Step-by-step explanation:

To solve this problem, we can use the concept of similar triangles. Two triangles are similar if they have the same shape, but possibly different sizes. In other words, the angles in the two triangles are the same, and the lengths of their sides are in proportion to each other. In this case, we are given that the lengths of the sides of the first triangle are 3, 7, and 8, and the perimeter of the second triangle is 54. We are asked to find the length of the longest side of the second triangle.

To solve this problem, we first need to find the perimeter of the first triangle. Since the perimeter of a triangle is the sum of the lengths of its sides, the perimeter of the first triangle is 3 + 7 + 8 = 18. Now that we know the perimeter of the first triangle, we can use this information to find the scale factor between the two triangles. The scale factor is the ratio of the lengths of corresponding sides in the two triangles. Since the perimeter of the second triangle is 3 times the perimeter of the first triangle, we can say that the scale factor between the two triangles is 3. In other words, the lengths of the sides of the second triangle are 3 times the lengths of the corresponding sides of the first triangle.

Now that we know the scale factor between the two triangles, we can use it to find the length of the longest side of the second triangle. The longest side of the first triangle has length 8, so the longest side of the second triangle has length 8 * 3 = 24. Therefore, the length of the longest side of the second triangle is 24.

Note: It is important to realize that the scale factor between two similar triangles is always the same for all sides of the triangles. In other words, if one side of a triangle is x times the corresponding side of a similar triangle, then all sides of the second triangle are x times the corresponding sides of the first triangle. This means that if we know the scale factor between two triangles for any one side, we can use that scale factor to find the lengths of all sides of the second triangle.

the Answer: t=18, - 18

Answer:Cannot be factored

Step-by-step explanation:

Answer:

[tex]x(x+2)(x-4)[/tex]

Step-by-step explanation:

Given:

[tex]x^3-2x^2-8x[/tex]

Factor out the common term x:

[tex]\implies x(x^2-2x-8)[/tex]

Factor (x² - 2x - 8) by rewriting -2x as (-4x + 2x):

[tex]\implies x \left[ x^2-4x+2x-8 \right][/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x \left[x(x-4)+2(x-4) \right][/tex]

Factor out the common term (x - 4):

[tex]\implies x \left[ (x+2)(x-4) \right][/tex]

Therefore:

[tex]x^3-2x^2-8x=x(x+2)(x-4)[/tex]

The number of lines that can run through any two of these points is 66

What are Collinear Points?

Points that are on the same straight line are referred to as collinear points. They must lie on the same straight line, even if they don't have to be co-planar. The Latin terms "col" and "linear," where "col" means "together" and "linear" means "in the same line," are the source of the English word "colinear." Collinearity is the state of being shared by two points.

A group of three or more points that are located along the same straight line is called a collinear point. On separate planes, collinear points may exist, but not on different lines. Collinearity is the quality of two points being parallel to one another. Any three or more points are only considered to be collinear if they are situated along the same straight line.

12 points are given, not three of which are collinear.

∴ Number of lines formed = ¹² C ₂

= 12!/ 10!⋅2!

=66

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The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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The planes will both meet in 53 seconds based on the information.

From the information, Plane A is at an altitude of 5000 feet and Plane B is at an altitude of 4207 feet. Plane A is gaining altitude at 45.25 feet per second and Plane B is gaining altitude at 60.5 feet per second.

The equation will be:

5000 + 45.25f = 4207 + 60.5f

Collect the like terms

60.5f - 45.25f = 5000 - 4207

15.25f = 793

Divide

f = 793 / 15.25

f = 53

They'll meet in 53 seconds.

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An air traffic controller Is tracking two planes. To start, Plane A is at an altitude of 5000 feet and Plane B is at an altitude of 4207 feet. Plane A is gaining altitude at 45.25 feet per second and Plane B is gaining altitude at 60.5 feet per second. When will that meet

seconds:

feet:

The triangles that are congruent to (a) ΔCDE, and (b) ΔCDF include ΔBFG, ΔADG, ΔBDE, and  ΔABH, ΔBHCΔ, ΔGHE respectively

We should know that when two or more objects in geometry have the same shape and size, or if one has the same shape and size as the mirror image of the other, they are congruent.

From the object drawn the congruent triangles to ΔCDE include the following

ΔBDF

ΔABG

ΔBDE

ΔABI

ΔACH

ΔBCJ

ΔIHJ

All the triangle has side, side, right angle

The triangles that are congruent to ΔCDF include the following

ΔABG

ΔBHC

HGE

These triangles have SIDE, SIDE, SIDE (SSS)

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By applying the simple concept of algebra, the equation showing the number of Kenny's baseball cards (b) is b = 82 + 159. So it can be concluded that the number of Kenny's baseball cards is 241 cards.

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used, starting from simple mathematical operations, to financial planning, calculating time/mileage, and so on.

In the above questions, we can take some notes as follows:

Baseball cards sold (x) = 82 cards.

Remaining baseball cards (y) = 159 cards.

The number of baseball cards owned by Kenny (b):

b = x + y

  = 159 + 82

  = 241 cards

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The product of the value of each outcome and the likelihood that it will occur results in the expected value. The likelihood of each outcome occuring for the ticket wheel is inversely correlated to the number of points on the wheel for that outcome.

When N is the number of slots on the wheel for 15 tickets, for instance, the probability of winning 15 tickets is N/20.

So, the following is the expected value of the number of tickets won:

[tex](15 × \frac{N}{20} ) + (25 × \frac{N}{20} ) + (30 × \frac{N}{20} ) + (40 × \frac{N}{20} ) + (10 × \frac{2}{20} ) + (100 × \frac{6}{20} ) + (500 \times \frac{3}{20} )[/tex]

Simplifying this expression, we get:

[tex] \frac{(15N + 25N + 30N + 40N + 20 + 600 + 1500)}{20} [/tex]

Further simplifying, we get:

[tex]\frac{(100N + 2120)}{20} [/tex]

This expression can be further simplified by dividing the numerator and denominator by 5 to get:

[tex] \frac{(20N + 424) }{4} [/tex]

The response to the first query is that this expression is equal to the expected value of the quantity of tickets won. Therefore, (d) 102 tickets is the right response.

The percentage of data that falls within two standard deviations of the mean for all normal curves is what is being questioned in the second question. The correct response is (b) 95% because this is roughly 95% according to the Empirical Rule.

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7 is the value of x in the given figure.

A triangle is a three-sided polygon that consists of three edges and three vertices.

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

DE is the midsegment between AC and CB.

DE=1/2(AB)...*

From the figure, DE=2x+13 and AB=13x-37.

Now plug in the value of DE and AB in Equation (*).

2x+13=1/2(13x-37)

Apply distributive property on RHS.

2x+13=13/2x-37/2

2x-13/2x=-37/2-13

4x-13x/2=-37-26/2

-9x/2=-63/2

9x=63

Divide both sides by 9

x=7

Hence, the value of x in the figure is 7.

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Step-by-step explanation:

x/2 = 3×x/6

sin(x/2) = sin(3x/6)

cos(x/2) = cos(3x/6)

tan(x/2) = tan(3x/6) = sin(3x/6)/cos(3x/6)

looking up triple angle identities for trigonometric functions we find :

cos(3x) = 4cos³(x) - 3cos(x)

so,

cos(x/2) =

cos(3x/6) = 4cos³(x/6) - 3cos(x/6) = 4(3/5)³ - 3×3/5 =

= 4×27/125 - 9/5 = 108/125 - 9×25/125 =

= 108/125 - 225/125 = -117/125 =

= -0.936

sin(3x) = 3×sin(x) - 4×sin³(x)

so,

sin(x/2) =

sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6)

also remember,

sin²(x) + cos²(x) = 1

therefore,

sin²(x/6) + cos²(x/6) = 1

sin(x/6) = sqrt(1 - cos²(x/6)) = sqrt(1 - (3/5)²) =

= sqrt(1 - 9/25) = sqrt(25/25 - 9/25) =

= sqrt(16/25) = 4/5 = 0.8

so, again

sin(x/2) =

sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6) =

= 3×4/5 - 4×(4/5)³ =

= 12/5 - 4×64/125 = 12×25/125 - 256/125 =

= 300/125 - 256/125 = 44/125 =

= 3×0.8 - 4×0.8³ = 0.352

tan(x/2) = sin(x/2)/cos(x/2) =

= 44/125 / -117/125 = -44/117 =

= 0.352 / -0.936 =

= -0.376068376...

Line u and line v are perpendicular lines by the relation of their slopes.

Slope of a line is the ratio of the difference of the y coordinates of two points to the x coordinates of those points. Slope is commonly denoted by the letter 'm'.

If a line passes through the points (x₁, y₁) and (x₂, y₂), then slope of the line,

m = (y₂ - y₁) / (x₂ - x₁)

Slopes of two lines, m₁ and m₂, are equal if they are parallel ⇒ m₁ = m₂.

Slopes of two lines, if the lines are perpendicular have the relation,

m₁ × m₂ = -1.

First let's find the slopes of the given lines.

Let m₁ be the slope of line u and m₂ be the slope of line v.

Line u passes through (7, 2) and (10, 10).

m₁ = (10 - 2) / (10 - 7) = 8/3

Line v passes through (10, 8) and (2, 11).

m₂ = (11 - 8) / (2 - 10) = 3/(-8)

Slopes are not equal, so they are not parallel.

m₁ × m₂ = [tex]\frac{8}{3}[/tex] × [tex]\frac{3}{-8}[/tex] = -1.

So the lines are perpendicular.

Hence the given lines u and v are perpendicular.

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Answer:

x+9=2x-4

Step-by-step explanation:

it just has to be

age=x

9 years later =+9

x+9

will be is =

x+9=

4 less = -4

double of current age =2x

=x+9=2x-4

Answer:

The current age is X and 9 years later the age will be X+9

Step-by-step explanation:

And it was stated that in 9 years time the age will be 4 less than double of the current age

And the current age is X, double of the current age is 2×X= 2x and it was stated that the double of the age will be 4 less than the person age in 9 years time so the equation statement is

X + 9 = 2x + 4

Answer:

Step-by-step explanation:

25x6

37.96 sq units is the area enclosed by the graph [tex]y=\frac{20}{1+x^2}[/tex] and y=2

To calculate the area enclosed by 2 graphs we have to firstly find the intersection point of both graph

to find the intersection point we will equate given equation

=>    [tex]\frac{20}{1+x^2}[/tex] = 2

=>  [tex]1+x^2[/tex] = 10

=> [tex]x^2[/tex] = 9

=> x= 3,-3

so we have to find area of graph from x=-3 and x=3

so the formula for equation is given by:

[tex]\int\limits^b_a {\frac{20}{1+x^2} -2} \, dx[/tex]

where a=-3 and b=3

=>[tex]\int\limits^a_b {\frac{20}{1+x^2} } \, dx - \int\limits^a_b {2} \, dx[/tex]                      

[tex]\int\limits {\frac{1}{1+x^2} } \, dx = tan^-^1x[/tex] +c

=> 20 [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex]  [tex]tan^-^1x[/tex] - [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex]  2x

=> 20 (  [tex]tan^-^1 3 - tan^-^1 (-3)[/tex]  - 2*(3+3)

=>40 * 1.249 -12

=> 49.96 -12

=> 37.96

so the area enclosed by the given graphs is 37.96 sq. units

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The lines of the functions f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7 have slopes that are negative reciprocals and are said to be perpendicular lines.

The general formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the linear equations as; f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7

Now, when two lines are parallel, their slopes will be the same and equal. However, when two lines are perpendicular, their slopes will be a negative reciprocal of each other.

In our given functions, we see that the slope of g(x) is a negative reciprocal of the slope of f(x). Thus, both lines are concluded to be perpendicular to each other.

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The complete question is;

Consider the functions f(x) = ²/₃x - 5 and g(x) = -³/₂x + 7. what do the slopes indicate about the lines?

The length of the slide is 10 feet.

From the provided information, the height of the slide ladder is 8 feet and the distance between the bottom of the slide and the ladder is 6 feet. The three sides form a right-angle triangle.

Pythagoras theorem postulates that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides which are perpendicular and base. Hence,

Hypothenuse^2 = Base^2 + Perpendicular^2

The length of the slide using Pythagoras theorem is where length of the slide is the hypothenuse of the triangle,

Length^2 = 8^2 + 6^2 = 100

Length = √100 = 10 feet

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Answer:

narrower

Step-by-step explanation:

As [tex]|a|[/tex] increases, the parabola becomes narrower.

As [tex]|a|[/tex] decreases, the parabola becomes wider.

The probability P(A and B) has a value of 0.08

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

P(A) = 0.2

P(B) = 0.4

P(B|A) = 0.8

From the question, we have

Independent events

This means that

P(A and B) = P(A) * P(B)

So, we have

P(A and B) = 0.2 * 0.4

Evaluate

P(A and B) = 0.08

Hence, value is 0.08

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For a penny of diameter 19mm to be of the same apparent size as the moon it should be held at a distance of about 2.1m away from the eye.

Therefore, the answer is 2.1m.

Distance of moon from earth is 384,400km, that is 384,400,000m. Also 3,474.8km that is 3,474,800m.

For penny to have same apparent size as the moon, it should subtend equal angle as moon to the viewer. See the attached figure for reference. Thus ΔABC is similar to ΔEDB by AA criterion as ∠A is common and ∠BAC = ∠DEB as they are corresponding angles.

Let distance between penny and observer be x. Then

x/ ED = 384,400,000m/ AB

x/ 19mm = 384,400,000m/ 3,474,800m

x/ 19mm = 961000/ 8687

x = 961000/ 8687 × 19

x ≈ 2101.88mm

x = 2.1m

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Media tonelada son 500kg, con esa cantidad Rosa logra hacer 100 cajas de 5kg. En una semana ha vendido 125 kilos, es decir 25 cajas. Aún le quedan 375kg.

Para calcular los kilos de ropa que tiene Rosa debemos tener en cuenta que una tonelada equivale a 1000kg. De acuerdo con esto, media tonelada sería equivalente a 500kg.

1000kg / 2 = 500kg

Para saber cuántas cajas de 5kg hace con media tonelada debemos realizar la siguiente operación:

500 / 5 = 100

Para identificar cuántos kilos ha vendido Rosa, debemos identificar a cuántos kilos equivale 1/4 de media tonelada, para ello realizamos la siguiente operación.

500kg / 4 = 125kg

Para identificar a cuántas cajas equivale lo vendido por Rosa, debemos realizar la siguiente operación:

125kg / 5kg = 25 cajas

Para identificar cuántos kilos le faltan por vender, debemos realizar la siguiente operación:

500kg - 125kg = 375kg.

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Answer:

86.5

We add them together, which is 173, and since there are two terms, divide by 2

173/2=86.5

Answer:

86.5

127 + 46 / 2 = 86.5

I could be wrong but I believe this is correct.

The average speed should be almost 69 - 70 km/h.

To calculate average speed, divide the total distance traveled by the passing time. For instance, if a person is moving at a speed of one mile per minute, or 40 miles per hour, they would be traveling 20 miles north and then 20 miles south (60 mph).

The mean value of a body's speed over a period of time is its average speed. Since a moving body's speed is not constant over time and fluctuates, the average speed formula is required.

Time = distance / speed

Speed = Distance / Time

Speed = 600/8.66

Speed = 69.28 km/h

So the average speed should be almost 69 - 70 km/h

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