Berechne jeweils die Höhe der Pyramiden!
a) V = 140 cm3
G = 28 cm2
h = ?​

The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

With triangle C, no rotation would make it like A and B, with the same side lengths, hence it is not congruent to any of the triangles in this problem.

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Answer:

a. x=100 b. x=30

Step-by-step explanation:

A: <1 and <2 are supplementary by consecutive interior angles theorem

x + x-20 = 180

2x-20=180

2x=200

x=100

B: <1 and <2 are congrunt by corresponding angles postulate

3x-5=x+55

2x=60

x=30

The decimal fraction that represents the given fraction is: 0.36.

To convert the figure from the given form to the decimal fraction, you can choose to use the long division format or simply divide it with the common factors. Between, 9 and 25, there is no common factor, so the best method to use here will be long division. Thus, we can proceed as follows:

1. 25 divided by 9

This cannot go so, we put a zero and a decimal point as follows: 0.

Then we add 0 to 90

2. Now, 25 divided by 90 gives 3 remainders 15. We add 3 to the decimal: 0.3

3. 90 minus 75 is 15. we add a 0 to this and divide 150 by 25 to get 6. This is added to the decimal to give a final result of 0.36.

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24 represents the cost per gallon of paint.

The process of finding the rate of change of the value dependent variable of the function changes with respect to that of the variable independent variable.

Given that, The expression 102+24x represents the total amount, in dollars, a painter spends at a store to purchase paintbrushes and x gallons of paint.

The equation is 102+24x

Here, the slope of the equation is 24, which tells the rate of change.

Hence, 24 is the cost per gallon of paint

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Answer:

Step-by-step explanation:

AO = CO = radius

AO = CO  ⇒  AB = BC  and  m∠AOB = m∠BOC = ¹/₂m∠AOC

From BDOE:

m∠EOB + m∠OBC + m∠CDE + m∠DEO = 360°

(65° + 75°) + 90° + x + 90° = 360°

140° + 180° + x = 360°

x = 40°

we need to find the values of sin(10°) and cos(10°) to compute sin(20°).

To find the value of sin 20°, we can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ).

Given sin(θ) = √3/2 and 0° < θ < 90°, we can find the value of sin 20° as follows:

sin(20°) = 2sin(10°)cos(10°)

We need to find the values of sin(10°) and cos(10°) to compute sin(20°).

Given cos(θ) = -√2/2 and -π/2 < θ < 0, we can find the value of sin 20° as follows:

sin(20°) = 2sin(10°)cos(10°)

Similarly, we need to find the values of sin(10°) and cos(10°) to compute sin(20°).

Since you provided conflicting information for the values of sin 0 and cos 0, it is not possible to determine the value of sin 20° without accurate values for sin 0 and cos 0. Please provide the correct values, and I will be happy to help you further.

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Answer:

\(1a. \: = 20 + 200.( \frac{1}{2})^{ \frac{t}{10} }\)

\(1b. \: = 91^{o} c\)

\(1c. \: = 30 \: minutes\)

Step-by-step explanation:

\(1a. \: t = a + b. {c}^{t}\\ a = 20\)

\(t(0) = a + b = 220 = > b = 200 \\ c = (\frac{1}{2})^{ \frac{1}{10} } \)

\(t = 20 + 200.( \frac{1}{2} )^{ \frac{t}{10} } \)

\(1b.when \: t = 15 \\ t = 20 + 200.( \frac{1}{2})^{ \frac{15}{10} } \\ = 20 + 71 \\ = 91^{o}c\)

\(1c.when \: t \: = 45 \\ 20 + 200. (\frac{1}{2} )^{ \frac{t}{10} \: } = 45 \\200.( \frac{1}{2})^{ \frac{t}{10} } = 25 \\ ( \frac{1}{2} )^{ \frac{t}{10} } = \frac{1}{8} \\ \frac{t}{10} = 3\)

\(t = 30\)

Answer:

True

Step-by-step explanation:

|a+b|=|a|+|b|

=> a + b = a + b ✔

Therefore, this is true (Unsure).

Hoped this helped.

Answer:

51

Step-by-step explanation:

In an isosceles trapezoid, the two top angles are congruent and the two bottom angles are congruent

∠D and ∠G are angles that are both on top

Hence ∠D ≅ ∠G

Which means that because ∠D = 51°. ∠G also = 51°

Answer:

x=7, y=11

Step-by-step explanation:

Using simultaneous equations we can sub y in equation 1 into equation 2.

Equation 1. y=2x-3

Equation 2. x+y=18

Since y=2x-3 we can replace it so that

2'. x+2x-3=18

Now simplify

= 3x-3=18

Add 3 onto both sides to undo the subtraction of 3 so that,

3x=21

Now divide both sides by three to undo the multiplication of 3 so that,

x=7

Now sub in x (which is 7) into one of the equations to find y

7+y=18

To undo the five, subtract 7 from both sides so that

y=11

Answer:

5x²-11x-12=0

Step-by-step explanation:

1) the rule: if quadratic equation is ax²+bx+c=0 and x₁; x₂ are its roots, then x₁+x₂= -b and x₁*x₂=c. The value of 'a' can be calculated by 'b' and 'c'.

2) according to the rule above it is possible to make up the required equation:

b= -(-4/5+3)= -(-0.8+3)= -2.2 and c=(-4/5)*3= -2.4.

x²-2.2x-2.4=0; ⇔ 5x²-11x-12=0.

An atom is positively charged and therefore is referred to as a cation if one or more of its electrons have been lost. The charge of protons is positive (+).

A particle that is smaller than just an atom is what is known as a subatomic particle.

An atom is positively charged and thus is referred to as a cation if one or more of its electrons have been lost. The charge of protons is positive (+).

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Answer:

c

Step-by-step explanation:

I had to multiply 4 and 3 to get the answer

The height of the actual glass is equal to 10 cm.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as drinking glasses, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 2/2.5

For the height of the actual glass, we have:

2/2.5 = 8/x

x = (2.5 × 8)/2

x = 20/2

x = 10 cm.

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Formula:

\( \frac{5000}{2000} \)

\( = > \frac{5}{2} \)

\( = > 2.5\)

Hence, 5000 Pound is equal to 2.5 Ton.

Step-by-step explanation:

The unit of weight in the avoirdupois system equal to 2,000 pounds in the United States and 2,240 pounds in Britain. The metric ton used in most other countries is 1,000 kg, equivalent to 2,204.6 pounds.

Answer: 2 1/2

Step-by-step explanation:

Answer:

C is the correct answer

Step-by-step explanation:

A P E X

Answer: C. 870 is the correct answer

Step-by-step explanation:

Answer:

1/√6 or √6 /6

Step-by-step explanation:

√2/3 -√1/6 =√4/6 - √1/6

= (√4-√1)/√6

= (2-1)/√6

=1/√6 or √6 /6

The average speed of the bus can be calculated by dividing the total distance traveled by the total time taken. The average speed of the bus is 55 km/h.

First, let's calculate the total distance traveled by the bus. The bus traveled 200 km in 4 1/2 hours, and then it traveled another 240 km in 3 1/2 hours.

To find the total distance, we add the distances traveled in each leg of the journey:
200 km + 240 km = 440 km

Next, let's calculate the total time taken by the bus. The bus took 4 1/2 hours for the first leg of the journey and 3 1/2 hours for the second leg of the journey.

To find the total time taken, we add the times taken for each leg of the journey:
4 1/2 hours + 3 1/2 hours = 8 hours

Now that we have the total distance traveled (440 km) and the total time taken (8 hours), we can find the average speed of the bus.

Average Speed = Total Distance / Total Time

Substituting the values:

Average Speed = 440 km / 8 hours

Dividing 440 by 8:

Average Speed = 55 km/h

Therefore, the average speed of the bus is 55 km/h.

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Answer:

11/306

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to  the  number of total outcome.

Given that  there are 4 red, 8 yellow, and 6 blue socks in a drawer where the  probability of  picking a red, yellow and blue socks be  p(r), p(y), and p(b) respectively.

The probability of reaching into the drawer without looking and drawing out 2 blue socks

= 6/(4 + 8 + 6) * 5/(4 + 8 + 5)

= 6/18 + 5/17

= 11/306

According to the solving the slope of the ramp = 0.175.

shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:

find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

The given values are indeed the heights of a two beams and indeed the distance between them, which are:

Y₁ = 3.5ft

Y₂ = 10.5 ft

ΔX = 40 ft

To get the slope of both the ramp, enter the following values into the slope formula:

m = (Y₂ - Y₁)/ΔX

  = (10.5 - 3.5)/40

  = 7/40

= 0.175

According to the solving the slope of the ramp = 0.175

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a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

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Angles of elevation and depression are geometric and trigonometric terms used to describe the angle created between a line of sight and the horizontal plane.

       Angle of Elevation: The angle of elevation is the term used for the angle which is formed between the horizontal line of reference and the line of sight of observer when he/she is looking upwards. For example, when you look up at an airplane or at the tip of a pole, the angle between your line of sight and the horizontal line is the angle of elevation. It is measured in degrees.

       Angle of Depression: The angle of depression is the angle created between a horizontal line of reference and the line of sight of an observer when he/she is looking downwards. For example, when you look down from the top of a tall structure, the angle between your line of sight and the horizontal line is the angle of depression. It is also measured in degrees.

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To solve this problem, we need to use the normal distribution formula and standard deviation. We know that the mean score is 530.4 and the standard deviation is 25.7.

First, we need to standardize the score by calculating the z-score:

z = (534 - 530.4) / 25.7 = 0.141

Next, we can use a standard normal distribution table or a calculator to find the probability that a randomly chosen student scores 534 or higher:

P(z > 0.141) = 1 - P(z < 0.141)

Using a standard normal distribution table, we can find that P(z < 0.141) = 0.5564

Therefore,

P(z > 0.141) = 1 - 0.5564 = 0.4436

So the probability that a single student is randomly chosen from all those taking the test scores 534 or higher is 0.4436 or 44.36%.

In summary, the standard deviation and normal distribution formula are used to determine the probability of a student scoring 534 or higher on the SAT. The answer is calculated by standardizing the score, finding the area under the normal curve using a table or calculator, and subtracting from one to get the probability of a score above 534.

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Answer:

As the line EF intersects the line AB, angles ∠BHE and ∠AHF are vertically opposite angles. Therefore, according to the Vertical Angles Theorem, these two angles are congruent.

Assuming line AB and line CD are parallel, the line EF intersects parallel lines. Therefore, angles ∠AHF and ∠CGF are in the same relative position. Therefore, according to the Corresponding Angles Theorem, these two angles are congruent.

According to the Substitution Property of Equality, as ∠BHE ≅ ∠AHF and ∠AHF ≅ ∠CGF, then ∠BHE ≅ ∠CGF.

Step-by-step explanation:

When two straight lines intersect, the opposite vertical angles are congruent.

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

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As the line EF intersects the line AB, angles ∠BHE and ∠AHF are vertically opposite angles. Therefore, according to the Vertical Angles Theorem, these two angles are congruent.

Assuming line AB and line CD are parallel, the line EF intersects parallel lines. Therefore, angles ∠AHF and ∠CGF are in the same relative position. Therefore, according to the Corresponding Angles Theorem, these two angles are congruent.

According to the Substitution Property of Equality, as ∠BHE ≅ ∠AHF and ∠AHF ≅ ∠CGF, then ∠BHE ≅ ∠CGF.

Answer:

1st and 3rd answers are correct.

Step-by-step explanation:

\( \sf2x + 3 \leqslant x - 5\)

First, to take x left side, subtract x from both sides.

\( \sf2x + 3 - x \leqslant x - x - 5 \\ \sf \: x + 3 \leqslant - 5\)

To take 3 to the left side, subtract 3 from both sides.

\( \sf \: x + 3 - 3 \leqslant 5 - 3 \\ \sf \: x \leqslant 5 - 3 \\ \sf \: x \leqslant 2\)

Answer:

Step-by-step explanation:

First, lets simplify everything in the parenthesis.

(3×10^​2 ​​ )×(2×10^​−4 ​​ )= ​​

In the parenthesis, since exponents come before multiplication in the order of operations, we need to do the exponents first.

(3 • 100) • (2 • 1/10^4)

Now, we can just multiply everything from left to right to get:

6*10^-2

Or

.06

Answer:

$2/ hat

Step-by-step explanation:

Find the unit rate:

$ to hats

8 to 4

Divide by four to get the unit rate; over 1

2 to 1

So, $2 per hat

Hope this helps!

Answer:

A

Step-by-step explanation:

Given:

r (radius) = 2 in

h (height) = 8 in

Find:

A (surface area) - ?

.

First, we have to find the lateral area of the cylinder:

\(a(lateral) = 2\pi \times r \times h = 2 \times π\times 2 \times 8 = 32\pi \: {in}^{2} \)

Now, let's find the area of both bases (since a cylinder has 2 identical bases, we have to multiply the area of one base by 2):

\(a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times π\times {2}^{2} = 8\pi \: {in}^{2} \)

In order to find the surface area, we have to add both lateral and bases' areas together:

\(a(surface) =32\pi + 8\pi = 40\pi \: {in}^{2} \)