First write the ratio as a fraction. make sure both terms have the same unit of measure. note that 1 foot equals 12 inches 1 foot=12 inches. then divide the numerator and denominator by their greatest common factor (gcf) to write the ratio in simplest form. ok
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
From the information, A is a right triangle, B is an acute triangle and C is an acute angle.
What are triangles?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 sides of a triangle are of lengths 13, 14, 1nd 15. the altitude of the triangle meet at point h. if ad is the altitude to the side length 14, what is the ratio hd:ha
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.
Adjacent, right angles are complementary. always, sometimes, or never
Números write the numbers as words. 38 116 573 1.821 754.322 6.615.010
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.
Explanation: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:
38: thirty-eight 116: one hundred sixteen 573: five hundred seventy-three 1.821: one thousand eight hundred twenty-one 754.322: seven hundred fifty-four thousand three hundred twenty-two 6.615.010: six million six hundred fifteen thousand ten Learn more about Writing numbers as words here:
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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.
Explanation: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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What is a rule about the angle measures of an isosceles triangle?
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.
Solve. 10 = c/3 – 4 + c/6
Show steps
Please help me!
Write and solve the compound inequality
A student scored a 73 and 81 on their first
two tests. Write and solve a compound
inequality to find the possible values for a
3rd quiz score that would give them an
average between 80 and 85
my answer is 86<=x<=101, but I don't know if it is right
If a cone has the same radius and height as a cylinder, the volume of the cone is
one-fourth one-third half two-thirds
the volume of the cylinder. If a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, then the volume of the sphere is
one-fourth one-third half two-thirds
the volume of the cylinder.
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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Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. the diameter of the circle is 14 in. 10.5 in2 42.1 in2 153.9 in2 196 in2
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]
Y=3.6x. Tell whether this equation represents a direct variation. If so, identify the constant of variation
Joanna has a flat wooden triangular piece as part of a wind chime. the piece is suspended by a wire anchored at a point equidistant from the sides of the triangle. where is the anchor point located?
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.
When students at Luray Middle School were surveyed, 22% said they would like hamburgers at lunch rather than hotdogs. What is that percent rounded to the nearest compatible fraction?
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]
Solve the following equation 5x+3(x-1)=8(x+2)-10
A square piece of tile with sides 12 inches is cut along a diagonal, What is the length of the diagonal rounded to the nearest inch?
To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.
Explanation:To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:
Square the length of one side: 12 x 12 = 144
Multiply the result by 2: 144 x 2 = 288
Take the square root of the result: √288 ≈ 16.97 inches
Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.
Final answer:
The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.
Explanation:
The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the square are both 12 inches long. So, we have:
hypotenuse² = side1² + side2²
hypotenuse² = 12² + 12²
hypotenuse² = 144 + 144
hypotenuse² = 288
To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:
hypotenuse = √(288)
hypotenuse = 16.97 inches (rounded to the nearest inch)
Give two ways the unit "meter per second per second" can be abbreviated.
Identify the base, exponent, and the expression’s value. 3 to the power of 4 base= exponent= value=
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.
Two sides of a triangle are 9 cm and 12 cm long. What is the range of possible lengths for the third side? Enter your answer in the boxes below.
Answer:
Possible length range of third side is between 3<x<21.
Step-by-step explanation:
Sum of two sides of triangle cannot be equal or less than third side. Therefore, one side length of a triangle must be between subtract and sum of other two sides. Than, range of third side is:
[tex](12-9)<x<(12+9)\\3<x<21[/tex]
Let f(x)=2x-1 and g(x)=4-x^2. Find (f o g)(x).
What is the perimeter of a polygon with vertices at (3, 2) , (3, 9) , (7, 12) , (11, 9) , and (11, 2) ? Enter your answer in the box. Do not round any side lengths.
Answer is 32. hope i helped.
Answer:
32 units
Step-by-step explanation:
Verified by test results
Hope this helps:)
mr scott rented a bicycle for 6 hours on saturday and then several more hours on sunday. it cost $4 per hour to rent the bicycle, and he paid a total of $48 For many hours did mr scott rented the bicycle on sunday
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.
What can be used as a reason in a two-column proof? Select each correct answer. a premise a conjecture a postulate a definition
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.
The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people. The variable x represents the number of . The variable y represents the number of . If y = 9, find the value of x. The committee needs square tables.
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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Write 72.98 as a mixed number in simplest form. submit
Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°.
Find m∠ABC, m∠BAC, and m∠DBC.
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°.
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 which equation can be used to find the number of dogs d that frank needs to walk to cover his expenses and how many dogs is that
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.
What is an unknown variable?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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Daniel has 5 pieces of gum. If he splits the pieces between 6 people, how much will each person get
What is m∠A ?What is m∠A ?
Enter your answer in the box.
°
Answer:
{I got 60} just took the test not 118 or 48 but thanks lol
The number of chickens to the the number of ducks on a farm was 6:5. after 63 ducks were sold, there were three times as many chickens as ducks left. how many chickens were there on the farm
Answer:
126
Step-by-step explanation:
No Following
What is the value of y in the equation 2 + y = −3?
−1
−5
1
5
(I think its b)
Answer:
the answer is negative 5