The graph of a line goes up and to the right when

The ratio of HD:HA in a triangle with sides 13, 14, and 15, where AD is the altitude, is 13:14.

The question involves finding the ratio of lengths HD:HA in a triangle with sides of lengths 13, 14, and 15, where AD is the altitude to the side of length 14.

According to the given theorem, if we consider AD as the altitude ha from vertex A and HD as ht, we are informed that a:ht=b:ha, where a and b are sides of the triangle.

Since triangle ABC has sides a=13, b=14, and c=15, we apply the theorem such that 13:HD=14:HA.

This gives us the ratio HD:HA as 13:14. Therefore, for every 13 units of height from H to D, there are 14 units of height from H to A.

Answer:

The variable "x" is the number of square tables and the variable "y" represents the number of round tables.

The committee needs 12 square tables.

Step-by-step explanation:

You know that the equation is 150 = 8*x + 6*y. You also know that 8 people can fit on a square table and 6 people can fit on a round table. Then 8 people multiplied by the amount of square tables plus 6 people by the amount of round tables should add 150 people. So in the previous equation the variable "x" is the number of square tables and the variable "y" represents the number of round tables.

If the number "y" of round tables is 9, you can replace this value in equation 150 = 8*x + 6*y, with 150 = 8*x + 6*9. Solving this last equation, you can calculate the value of the variable "x", that is, calculate the amount of square tables needed.

150= 8*x + 6*9

150= 8*x + 54

150-54= 8*X +54 - 54

96 = 8*x

[tex]\frac{96}{8} =\frac{8}{8} *x[/tex]

12=x

So, the committee needs 12 square tables.

The number of square tables that's needed will be 12 square tables.

The equation given is 150 = 8x + 6y and this represents the number of each type of table that's needed for 150 people.

Since 6 people are already give for the round tables, then to solve the square tables will be:

150 = 8x + 6y

150 = 8x + (6 × 9)

150 = 8x + 54

Collect like terms

8x = 150 - 54

8x = 96

Divide both side by 8

8x/8 = 96/8.

x = 12

Therefore, the number of square table that's needed will be 12 square tables.

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Answer is 32. hope i helped.

Answer:

32 units

Step-by-step explanation:

Verified by test results

Hope this helps:)

Final answer:

In the expression 3 to the power of 4, the base is '3', the exponent is '4', and the value of the expression is 81 after multiplying the base by itself for the number of times indicated by the exponent.

Explanation:

The expression given is 3 to the power of 4, which is written in mathematical terms as 34. The base of this expression is the number that is being multiplied by itself, which in this case is "3". The exponent is the number that indicates how many times the base is multiplied by itself, and here it is "4".

Finally, the value of the expression is the result of carrying out the multiplication that the exponent indicates, so for 3 raised to the 4th power, it's 3 x 3 x 3 x 3, which equals to 81.

Answer:

{I got 60} just took the test not 118 or 48 but thanks lol

Answer:

Option [tex]42.1\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle

see the attached figure to better understand the problem

Step 1

Find the area of the square

Remember that

The area of the square is

[tex]A=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=14\ in[/tex]

substitute

[tex]A=14^{2}=196\ in^{2}[/tex]

Step 2

Find the area of the circle

Remember that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex]

substitute

[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]

Step 3

Find the area of the region

[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]

Final answer:

After calculating the cost for 6 hours of bicycle rental on Saturday, we subtracted that from the total cost to determine the cost for Sunday. By dividing this amount by the hourly rate, we concluded that Mr. Scott rented the bicycle for an additional 6 hours on Sunday.

Explanation:

The question asks how many hours Mr. Scott rented a bicycle on Sunday. To solve this, we need to calculate the total rental hours using the cost information provided. We know that Mr. Scott rented the bicycle for 6 hours on Saturday, and the rental cost is $4 per hour. He paid a total of $48 for the entire rental period over the two days.

First, let's calculate the cost for Saturday's rental: 6 hours × $4 per hour = $24. Now we know that Mr. Scott spent $24 on Saturday, so the remaining $24 ($48 total - $24 for Saturday) must have been spent on Sunday's rental. Dividing the remaining cost by the hourly rate gives us the number of hours rented on Sunday: $24 ÷ $4 per hour = 6 hours. Therefore, Mr. Scott rented the bicycle for 6 hours on Sunday as well.

Answer: [tex]\dfrac{11}{50}[/tex]

Step-by-step explanation:

Given : When students at Luray Middle School were surveyed, 22% said they would like hamburgers at lunch rather than hotdogs.

We know that to convert a percent into a fraction , we need to divide the percent by 100 , we get

[tex]22\%=\dfrac{22}{100}[/tex]

Which can be written as :[tex]\dfrac{2\times11}{2\times50}[/tex]

Cancel out 2 from the numerator and the denominator , we get

[tex]\dfrac{11}{50}[/tex]

Hence, 22% rounded to the nearest compatible fraction [tex]\dfrac{11}{50}[/tex]

Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

Answer:

a conjecture, a postulate, and a definition

Step-by-step explanation:

A premise is an assumption something is true.  When completing a proof, we must use already established truths to get us from one step to another; these can be theorems, postulates, conjectures, or definitions.  However, premises themselves cannot be used to prove something.

Answer:

126

Step-by-step explanation:

No Following

you don't show the options but it should look something like this:

195 +15d = 360

answer:

subtract 195 from each side

15d = 165

d = 165/15  =11

 he needs to walk 11 dogs

The equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and number of dogs is 11.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Frank needs a total of $360 to cover his expenses of the week. He earns $195 a week working at a restaurant and also walks dogs to supplement his income, frank charges $15 per dog that he walks.

The equation, which can be used to find the number of dogs d that frank needs to walk to cover his expenses,

[tex]15d+195=360[/tex]

Solve it further to find the number of dogs d,

[tex]15d+195=360\\15d=360-195\\d=\dfrac{165}{15}\\d=11[/tex]

Thus, the equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and the number of dogs is 11.

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Final answer:

In an isosceles triangle, the angles opposite the two equal sides are themselves equal, and the sum of all angles always adds up to 180 degrees within plane geometry.

Explanation:

A rule about the angle measures of an isosceles triangle is that the angles opposite the two equal sides are themselves equal. An isosceles triangle has at least two sides of equal length, and the angles opposite these sides are called the base angles. Since the sum of angles in any triangle in Euclidean (plane) geometry must add up to 180 degrees, knowing two angles are the same allows us to easily calculate the third angle.

For example, if an isosceles triangle has two equal angles of 50 degrees each, the remaining angle must be 180 - (50 + 50) degrees, which is 80 degrees. This is different from a spherical triangle, where the sum of the angles can be greater than 180 degrees due to spherical geometry. It's also worth noting that these rules apply only to plane geometry, which is the study of shapes on a flat plane.

Answer:

the answer is negative 5

From the information, A is a right triangle, B is an acute triangle and C is an acute angle.

A polygon with three sides, angles, and vertices is called a triangle.

Given that, triangle side lengths, we need to identify the triangle as acute, right or obtuse,

How to solve the triangle?

It will be a right triangle if a² + b² = c², It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².

1) a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25

This is a right triangle.

2) a² + b² = 5² + 6²

= 25 + 36 = 61

c² = 7² = 49

61 > 49 = аcute triangle.

3) a² + b² = 8² + 9²

= 64 + 81 = 145

c² = 12² = 144

145 > 144 = аcute triangle.

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The volume of the cone is one-third the volume of the cylinder, if both shapes have the same radius and height

The volume of a cone is represented as:

v = 1/3[tex]\pi[/tex]r^2h

The volume of a cylinder is represented as:

V = [tex]\pi[/tex]r^2h

Substitute [tex]\pi[/tex]r^2h for V in the volume of the cone

v = 1/3V

The above means that:

The volume of the cone is one-third the volume of the cylinder

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To write the given numbers as words, you can break them down into groups of three digits from right to left and then write each group separately. For example, 38 is written as thirty-eight.

To write the numbers as words, we can break them down into groups of three digits from right to left. Here are the numbers written as words:

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To write the given numbers as words, we break them down into their place values. 38 can be written as thirty-eight, 116 as one hundred sixteen, 573 as five hundred seventy-three, 1.821 as one thousand eight hundred twenty-one, 754.322 as seven hundred fifty-four thousand three hundred twenty-two, and 6.615.010 as six million six hundred fifteen thousand ten.

In order to write the given numbers as words, we can break them down into their place values. Let's analyze each number:

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Final answer:

Joanna's wind chime is suspended from the centroid of the triangular piece, which is the intersection point of the triangle's three medians and serves as its center of gravity.

Explanation:

The anchor point where Joanna has suspended the flat wooden triangular piece of the wind chime is known as the centroid of the triangle. The centroid is the point where the three medians of the triangle intersect, and it is always located inside the triangle. A median of a triangle is a line segment connecting a vertex to the midpoint of the opposing side. The centroid is also the triangle's center of gravity, meaning it is the balance point where the triangle can be suspended and remain in equilibrium. For any given triangle, the centroid will be found at a point that is one-third of the distance from each vertex to the midpoint of the opposite side.