rhombus and a square have one and the same side of 6 cm. The area of the rhombus is 4/5 of the area of the square. Find the height of the rhombus.

Answer:

Her commission for the sale was $3,040

Step-by-step explanation:

A realtor sold a home costs = $380,000

She earns commission on the home she sells = 0.8%

Commission for the sale she earns = 0.8% of 380,000

[tex]\frac{0.8}{100}[/tex] × 380,000

0.008 × 380,000 = 3,040

Her commission for the sale was $3,040

Caitlin's reasoning is valid; in a triangle, the side opposite the largest angle is indeed the longest, according to the triangle inequality theorem.

Caitlin's reasoning that AC is the longest segment of fencing because it is opposite the largest angle measure in the figure is indeed valid. In any triangle, the longest side is always opposite the largest angle. This is due to the fact that the angles in a triangle are directly related to the lengths of their opposite sides.

The triangle side opposite the largest angle is the longest because of the triangle inequality theorem. So, if 68 degrees is the largest angle in the triangular piece of land that Caitlin is fencing, then segment AC, being opposite this angle, would be the longest side.

Caitlin's reasoning is valid based on the principle that in a triangle, the longest side is opposite the largest angle. The length of the third side can be determined using the cosine law or vector addition, depending on the given details.

The validity of Caitlin's reasoning is based on a principle in geometry that states the side opposite the largest angle in a triangle is the longest side. This fact is drawn from the Law of Sines which asserts that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Therefore, if AC is indeed opposite the largest angle, which is 68 degrees, then her reasoning is valid and AC would be the longest segment of fencing.

To calculate the length of the third side, one can use the cosine law or the vector addition method depending on the given information and the context of the question. If the internal angles and lengths of two sides are known, the cosine law allows for the calculation of the third side. In the context of vectors, the resultant vector, which in this case is the third side C, can be calculated by mathematically adding vectors A and B.

Final answer:

A triangle cannot have both a right angle and an obtuse angle, as the sum of its angles must always equal 180 degrees.

Explanation:

To convince your classmate that a triangle cannot have both a right angle and an obtuse angle, you should explain that according to Euclidean geometry, the sum of the angles in any triangle must equal two right angles, or 180 degrees.

If a triangle has a right angle (90 degrees), then the remaining two angles must sum up to 90 degrees as well. Introducing an obtuse angle, which is any angle greater than 90 degrees, would cause the total sum of the angles to exceed 180 degrees, which is impossible.

Therefore, the correct statement to use would be 'A. It is not possible because the sum of the angles in the triangle can't exceed 180 degrees.'

Final answer:

The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor. Madison and Centerville are 66 km apart in real life.

Explanation:

The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor:

Map distance = 6 cm

Scale factor = 1 cm : 11 km

Actual distance = 6 cm * 11 km = 66 km

Therefore, Madison and Centerville are 66 km apart in real life.

Answer:

Step-by-step explanation:

After the multiplication of the given fraction, the value obtained in terms of a fraction will be equal to 35/9.

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the information available in the question,

The given fraction is,

1 2/3 × 2 1/3

It can also be written as:

5/3 × 7/3 = 35/9 or 3 8/9.  

To know more about Fraction:

https://brainly.com/question/10354322

#SPJ2

Answer:

  98.4 inches

Step-by-step explanation:

You want the length 25.0 meters expressed in inches.

There are 0.254 m in an inch, so the distance d can be found from the proportion ...

  d/(25 m) = (1 in)/(0.254 m)

Multiplying by 25 m, we find ...

  d = 25/0.254 in ≈ 98.4252 in

The length is about 98.4 inches.

__

Additional comment

The value to convert is given to 3 significant figures. The conversion factor is exact. The answer is appropriately expressed using 3 significant figures.

Answer: two, line

Step-by-step explanation:

Answer:

The purchasing power is $7374

Step-by-step explanation:

We are given an equation [tex]y=10000(0.97)^x[/tex]

where,  

y represents purchasing power.

x represents the number of years.

We need to find purchasing power of $10000 after 10 years.

Put x=10 into equation and solve for y

[tex]y=10000(0.97)^{10}[/tex]

[tex]y=7374.24\approx 7374[/tex]

After 10 years the purchasing power of $10000 becomes $7374

As we can see the value of the product decrease.

Hence, The purchasing power is $7374

you were wrong, so I got it wrong...

QUESTION 1

The area of a triangle is given by

[tex]Area=\frac{1}{2}\times base\times heigth[/tex]

The length of the base of the triangle is [tex]6\:in.[/tex] and the vertical height is [tex]8\:in.[/tex].

We substitute these values into the formula to obtain,

[tex]Area=\frac{1}{2}\times 6\times 8[/tex]

[tex]Area=3\times 8[/tex]

[tex]Area=24\:in^2[/tex]

The area of the triangle is 24 square inches.

The correct answer is A

QUESTION 2

The company logo is made up of three triangles and a square.

The length of the square is [tex]7\:cm[/tex]

The area of a square is given by

[tex]Area=l^2[/tex]

[tex]\Rightarrow Area=7^2[/tex]

[tex]\Rightarrow Area=49cm^2[/tex].

The area of one of the triangles is

[tex]Area=\frac{1}{2}\times base \times height[/tex]

The height of the triangle is [tex]4cm[/tex].

The base of the triangle is on one side of the square, so it is [tex]7cm[/tex].

The area now becomes

[tex]Area=\frac{1}{2}\times 7 \times 4[/tex]

[tex]\Rightarrow Area=7 \times 2[/tex]

[tex]\Rightarrow Area=14cm^2[/tex].

Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.

[tex]Area\:of\:the\:three\:triangles=3\times14=42cm^2[/tex]

The area of the logo is equal to the area of the square plus the area of the three identical triangles.

[tex]Area\:of\:logo=49+42=91cm^2[/tex]

Hence the area of the logo is [tex]91cm^2[/tex]

QUESTION 3

Since the figure is made up of two rectangles and two right triangles, we find their areas and sum them to get the area of the figure.

The area of a rectangle is given by

[tex]Area=l\times w[/tex]

The width of the bigger rectangle is [tex]5[/tex] and the length is [tex]25[/tex].

[tex]Area\:of\:bigger\: rectangle=25\times 5[/tex]

[tex]Area\:of\:bigger\: rectangle=125\:square\:units[/tex]

The width of the smaller rectangle is [tex]8[/tex].

The length of the smaller rectangle is [tex]25-(6+6)=25-12=13[/tex].

[tex]Area\:of\:smaller\: rectangle=13\times 8[/tex]

[tex]Area\:of\:smaller\: rectangle=104\:square\:units[/tex].

The two triangles are identical, so we find the area of one and multiply by 2

[tex]Area\:of\:triangle=\frac{1}{2}\times base \times heigth[/tex]

[tex]Area\:of\:triangle=\frac{1}{2}\times 6 \times 8[/tex]

[tex]Area\:of\:triangle=3 \times 8[/tex]

[tex]Area\:of\:triangle=24\:square\:units[/tex]

[tex]\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units[/tex]

The area of the figure is

[tex]=125+104+48=277\:sqaure\:units[/tex]

The correct answer is C

The correct option is B) [tex]x=4.4[/tex]. The value of x to the nearest tenth is x=4.4.

To find the value of x, we need to apply the Law of Cosines to the given triangle. The Law of Cosines states that for any triangle with sides [tex]\( a \), \( b \), and \( c \),[/tex] and the angle opposite side c and [tex]\( \gamma \),[/tex] the following relationship holds: [tex]\[ c^2 = a^2 + b^2 - 2ab\cos(\gamma) \][/tex]

Let's denote the sides of the triangle as follows: the side opposite the right angle (hypotenuse) as c, the side opposite the 30-degree angle as b, and the side opposite the 60-degree angle as a. We are given that [tex]\( a = 2x \), \( b = x \), and \( c = 10 \).[/tex]

Using the Pythagorean theorem, we have:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

[tex]\[ 10^2 = (2x)^2 + x^2 \][/tex]

[tex]\[ 100 = 4x^2 + x^2 \][/tex]

[tex]\[ 100 = 5x^2 \][/tex]

[tex]\[ x^2 = \frac{100}{5} \][/tex]

[tex]\[ x^2 = 20 \][/tex]

[tex]\[ x = \sqrt{20} \][/tex]

[tex]\[ x = \sqrt{4 \cdot 5} \][/tex]

[tex]\[ x = 2\sqrt{5} \][/tex]

Now, we calculate the numerical value of x:

[tex]\[ x \approx 2 \cdot 2.236 \][/tex]

[tex]\[ x \approx 4.472 \][/tex]

Rounding to the nearest tenth, we get:  [tex]\[ x \approx 4.4 \][/tex]

Therefore, the value of x to the nearest tenth is 4.4, which corresponds to option B.

Final answer:

The probability that the observed pine tree is a foxtail pine is 0.94 or 94%, calculated by subtracting the probability of it not being a foxtail pine (0.06) from 1.

Explanation:

If the probability of not being a foxtail pine is 0.06, we can find the probability of a tree being a foxtail pine by subtracting this from 1 (since the sum of all probabilities for an event and its complement must equal 1). Therefore, the calculation to find the probability of the tree being a foxtail pine is 1 - 0.06.

Carrying out this subtraction gives us:

1 - 0.06 = 0.94.

Thus, the probability that the observed pine tree is a foxtail pine is 0.94, or 94%, when calculated to two decimals.

Answer:

r(p(x))=73

Step-by-step explanation:

To find the value of r(p(x)), the equation for p(x) which is 2x + 1, is substituted into every place that there is a x in the equation of r(x).

[tex]r(x)=4x-3\\r(p(x))=4(2x+1)-3\\r(p(x))=8x+4-3\\r(p(9))=8(9)+4-3\\r(p(9))=73[/tex]

Answer: the answer is 8n

The third side  of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n

The perimeter of any shape is total distance around the shape

In the triangle shown:

The perimeter = 17n  +  11

The first side = 5n + 6

The second side = 4n + 5

Let the third side be represented by M

The perimeter = (The first side) + (The second side) + (The third side)

Substitute perimeter = 17n  +  11, first side = 5n + 6, second side = 4n + 5, and third side = M into the equation above

17n  +  11    =   (5n  +  6)   +   (4n +  5)   +  M

M  =  17n  +  11   -  5n  -  6  -  4n  -  5

Collect like terms

M   =  17n  -  5n  -  4n  +  11  -  6  -  5

M   =  8n

Therefore, the third side  of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n

Learn more here: https://brainly.com/question/17539502