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.
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.
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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Daniel has 5 pieces of gum. If he splits the pieces between 6 people, how much will each person get
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.
Write 72.98 as a mixed number in simplest form. submit
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.
Y=3.6x. Tell whether this equation represents a direct variation. If so, identify the constant of variation
Suppose that the distance D feet that a car travels in t seconds is given by d(t)=2t^2. Calculate the average speed (average rate of change.) in feet per second from t=5 to t=9. (An exact number.)
A rate of change is a rate that describes how one quantity changes in relation to another quantity, then d(t)=2t^2 is given, 28 feet is average speed in feet per second from t=5 to t=9.
What is Rate of change?A rate of change is a rate that describes how one quantity changes in relation to another quantity.
d(t)=2t^2 is given, we need to find average speed in feet per second from t=5 to t=9.
d(t)=2t^2.
The average rate of change is calculated by the formula: d(t2) - d(t1) / t2 - t1
So plug in 5 as t1 and 9 as t2.
d(9) - d(5) / 9 - 5 =
(2×81) - (2×25) / 9 - 5 =
162 - 50 / 4 =
112 / 4 = 28
Therefore the average speed is 28 feet.
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How do you solve x^2 - 16x -34 = 2 by completing the square?
Give two ways the unit "meter per second per second" can be abbreviated.
In which states of matter can materials take the shape of their containers?
A. liquid and gas
B. solid and liquid
C. solid and gas
In a test-cross of a heterozygous black guinea pig (bb), what is the probability that the first two (2) offspring will be white?
Solve. 10 = c/3 – 4 + c/6
Show steps
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]
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
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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Identify the 35th term of an arithmetic sequence when a1 = −7 and a 18 = 95
2 to determine the formula of a new substance one of the first steps is to find the
You solved a linear system with two equations and two variables and got the equation o=-8. how many solutions does the system of equations have
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.
Jack has twelve coins in his pocket made up of dimes and quarters. he has a total value of $1.95. how many of each are there
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]
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
Write the equation of a line with a slope of 4 and a y-intercept of −3.
A: 4x+y=-3
B: 4x-y=-3
C: y=3x+4
D: y=4x-3
Answer:
y = 4x − 3
Step-by-step explanation:
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
Kim is drawing a map of the different schools in her school district.she knows that her middle school is 10.6 miles away from the middle school that her best friend attends.if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map,to the nearest tenth of an inch
Answer:
4.24 inches.
Step-by-step explanation:
In the map,
2 inches represents 5 miles,
Thus, we can write,
[tex]5\text{ miles}=2\text{ inches}[/tex]
[tex]1\text{ mile}=\frac{2}{5}\text{ inches}-----(1)[/tex]
Since, the actual distance between the two schools is 10.6 miles.
Multiplying both sides by 10.6 in equation (1),
[tex]10.6\text{ miles}=10.6\times \frac{2}{5}=\frac{21.2}{5}=4.24\text{ inches}[/tex]
Hence, the distance between the two schools in the map is 4.24 inches.
The lengths of the sides of a triangle are in the extended ratio 5 : 7 : 10. The perimeter of the triangle is 88cm. What are the lengths of the sides?
The circumfrence is 16 pi. What is the are in terms of pi?