The other leg of the right triangle will be 16.5cm.
Legs of a right triangle:The side which shares the common/neighboring border to the right angle in a triangle is called legs.
Pythagoras theorem:It states that the sum of the areas of the two squares on the legs equals the area of the of the square on the hypotenuse.
According to the given question, we have
length of one leg of the right triangle is 13cm.
hypotenuse of the right triangle is 21 cm .
Let x be the length of the other leg.
Now, according to the Pythagoras theorem
We can write as
[tex](21)^{2} = x^{2} +(13)^{2}[/tex]
⇒ 441 = [tex]x^{2} +169[/tex]
⇒[tex]441-169 =x^{2}[/tex]
⇒ [tex]272 =x^{2}[/tex]
⇒ [tex]x = \sqrt{272}[/tex]
⇒[tex]x = 16.49[/tex] ≈ 16.5cm
Hence, the other leg of the right triangle will be 16.5cm.
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The width (l) of a sheet of plywood that is one half the length l
L=2+4W
W=L/2
f=3d
hope this is the right question????
Emma created the poster shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 36 cm, and the width is labeled as width equal to 24 cm. What would be the dimensions of the poster at fraction 1 over 4 times its current size?
Answer:
Length = 6 cm, width = 9 cm
Step-by-step explanation:
frank purchased a boat for $7,525. he made a down payment of $475. he applied for a six year installment loan with an interest rate of 8.4% in the amount of $7,050. what is the total cost of the boat after six years?
Answer:
$9474.40
Step-by-step explanation:
A spreadsheet can be used to calculate the amortization of the loan. The one attached uses rounding to the penny for all dollar amounts. The result is that the payment amount is rounded down, and the final payment is about 12¢ short. The total repaid on the loan will be slightly more than the product of payment amount ($124.99) and number of payments (72).
The total cost of the boat is the sum of down payment, loan amount, and interest amount. That sum is $9474.40.
How many points determine a unique line?
A.
1 point
B.
2 points
C.
any 3 points
D.
3 noncollinear points
I say 2 points!
Answer:
B. 2 points
Step-by-step explanation:
1 point is a dot in space, 2 can make a line
How much greater will Jennifer’s January finance charge be if the finance charge is calculated using the previous balance method than if it is calculated using the adjusted balance method? a. $0.48 b. $1.15 c. $0.67 d. $0.85
What is the x-intercepts of the graph of y = 12x-5x-2
Crystal has 81/100 of a dollar. What could be the coins crystal has?
what is the measure of BC
What is the measure of BC
Solution:
As per Inscribed Angle Theorem: If an angle is inscribed in a circle, then the measure of the intercepted arc is twice the value of the measure of the inscribed angle.
So, as we can see in the diagram the angle inscribed in the circle is 65°.
So, the measure of intercepted arc BC is twice ∠BDC
Or, BC=2*65°
BC=130° Answer
What is the approximate length of arc s the Circle? o
Answer:
c!
Step-by-step explanation:
Factor to find the zeros of the function defined by the quadratic expression.
7x2 + 14x − 105
Answer:
{-5, 3}
Step-by-step explanation:
7 is a factor common to all three terms of this polynomial function. Thus, after the first attempt to factor it, we have 7(x^2 + 2x - 15). The quadratic factors into (x + 5)(x - 3). Setting these = to zero individually, we get
x + 5 = 0, or x = -5, and
x - 3 + 0, or x = 3
Thus, the zeros of the given f(x) =7x2 + 14x − 105 are {-5, 3}.
Julia bought name tags for a party. Each name tag is 334 inches wide and 213 inches high. The formula for the area of a rectangle is A=bh. What is the area of one name tag?
Answer:the correct answer is 71142 just multiply 334 and 213
Step-by-step explanation:
please help asap !! ill mark brainliest but be corrrecct
Answer:
k=4
Step-by-step explanation:
Given
A line x=7
The line has only y-intercept which means that it is a vertical line.
As the two points are
A(10,2) and B(k,2)
The y-intercepts of both the points are same i.e. y=2 which means that the line fomed by joining A and B is a horizontal line.
As x=7 is a vertical line and bisects the horizontal line, the mid-point of line AB will be the point where first line (x=7) bisects the second which is (7,2).
The x-coordinate of mid-point is 7 because the vertical line has 7 as x-intercept and y-intercept is two because the horizontal line has y-intercept 2.
So,
Mid-point=((10+k)/2 ,2)=(7,2)
Comparing the x-coordinate
(10+k)/2=7
10+k=7*2
10+k=14
k=14-10
k=4
Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely with x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation.
1) y = kx . . . . . for some constant k
.. Here y is directly proportional to x , where k is the constant of proportionality
2) y = k/x . . . . for some constant k
.. Here y is inversely proportional to x , again k is the constant of proportionality.
3) y = 2x +52
..
Here y is linearly related to the x , it is neither directly proportional nor inversely proportional.
If quadrilateral ABCD rotates 90° counterclockwise about the origin, what are the coordinates of A′ in quadrilateral A′B′C′D′ ?
(2, 1)
(-2, -1)
(-2, -2)
(-2, 0)
I believe the answer is (-2,-1) after the original point (2,1) goes through the change of -y,x
Answer:
Option B is correct.
The coordinate of A' is (-2 , -1)
Explanation:
The coordinates of ABCD are A = (-1,2) , B(1,1) , C =(1,-1) and D(-2,-2).
Rotation means moving the shape around a fixed point clockwise or anticlockwise, and by a certain number of degrees.
Rule for 90° counterclockwise rotation about the origin: [tex](x,y) \rightarrow (-y,x)[/tex]
or we can say that switch x and y in the coordinates and make y value opposite.
Then, the coordinate of A' :
[tex]A(-1,2) \rightarrow A'(-2 ,-1) [/tex]
Therefore, the coordinate of A' in the quadrilateral A'B'C'D' is, (-2 ,-1)
you leave your house and walk for half an hour at a speed of 3 miles per hour. Then you run for 15 minuets at a speed of 7 miles per hour. You are now halfway to town. Write and solve an equation to find the distance from your house to town
Final answer:
To find the total distance to town, the distance walked (1.5 miles) and run (1.75 miles) were calculated, and it was found that the student is 3.25 miles away from home. This is halfway to town, so the total distance to town is 6.5 miles.
Explanation:
To solve the problem, we will calculate the distance traveled by walking and running and then use these to find the total distance to town.
Step 1: Calculate the distance walked
First, we convert the walking time into hours since the speed is given in miles per hour. Half an hour of walking at 3 miles per hour will cover:
Distance walked = Speed × Time = 3 mph × 0.5 hours = 1.5 miles
Step 2: Calculate the distance run
Since 15 minutes is a quarter of an hour, we can calculate the distance run at 7 miles per hour as:
Distance run = Speed × Time = 7 mph × 0.25 hours = 1.75 miles
Step 3: Determine the total half distance
Now, we combine the distances to find the halfway point to town:
Total half distance = Distance walked + Distance run = 1.5 miles + 1.75 miles = 3.25 miles
Step 4: Find the full distance to town
Since this is half the distance, the full distance to town is:
Full distance = Total half distance × 2 = 3.25 miles × 2 = 6.5 miles
Conclusion
Therefore, the total distance from the student's house to town is 6.5 miles.
Final answer:
The total distance from the house to town is found by doubling the sum of the distances walked and run, which were 1.5 miles and 1.75 miles, respectively. The full distance to town is 6.5 miles.
Explanation:
To solve for the distance from your house to town, we will use the information provided about your walking and running times and speeds. Since you walked for half an hour (0.5 hours) at a speed of 3 miles per hour and ran for 15 minutes (0.25 hours) at a speed of 7 miles per hour, and this brought you halfway to town, we can set up the following equation:
Distance walked = Speed walked × Time walked
= 3 mph × 0.5 hours
= 1.5 miles
Distance run = Speed run × Time run
= 7 mph × 0.25 hours
= 1.75 miles
The total distance you traveled to get halfway to town is the sum of the distance walked and the distance run:
Total distance halfway = Distance walked + Distance run
= 1.5 miles + 1.75 miles
= 3.25 miles
Since 3.25 miles is only halfway to town, the full distance to town is twice that amount:
Full distance to town = 2 × Total distance halfway
= 2 × 3.25 miles
= 6.5 miles
Therefore, the total distance from your house to town is 6.5 miles.
Daniel Potter bought a new car for $20,000.00. Two years later, he wanted to sell it. He was offered $14,650.00 for it. If he sold it for that amount, what was his depreciation rate?
x+2/x+8 divided by 2x/3
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the numberof nickels, n, and the number of quarters, q, Yolanda used?
Answer:
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
And the pair [tex](n,q)=(15,13)[/tex] is the solution.
Step-by-step explanation:
We know that Yolanda paid for her movie ticket using 28 coins. She only paid with nickels and quarters.
We also know that the ticket cost $4.
We need to form a linear equation system that solves this problem.
We have the following variables :
n : number of nickels
q : number of quarters
We know that she used 28 coins ⇒ the number of nickels plus the number of quarters must be equal to 28.
We have our first equation :
[tex]n+q=28[/tex] (I)
For the second equation we need to use the ticket price information.
We know that the ticket cost $4 and she only paid with nickels and quarters.
Therefore we can write the following equation that relates the variable ''n'' and the variable ''q'' :
[tex]n(0.05)+q(0.25)=4[/tex] (II)
This equation represents that the number of nickels ''n'' per its value plus the number of quarters ''q'' per its value is equal to $4 that it is the value of the movie ticket.
With (I) and (II) we form the linear equation system :
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
This linear equation system can be used to find the value of ''n'' and ''q''.
For example, in equation (I)
[tex]n+q=28[/tex]
we can solve it in terms of ''n'' :
[tex]n=28-q[/tex] (III)
If we use (III) in (II) :
[tex](28-q)(0.05)+q(0.25)=4[/tex]
[tex]1.4-(0.05)q+(0.25)q=4[/tex]
[tex]q(0.2)=2.6[/tex]
[tex]q=\frac{2.6}{0.2}=13[/tex]
[tex]q=13[/tex]
Now replacing this value of q in (III) :
[tex]n=28-13=15[/tex]
[tex]n=15[/tex]
We find that Yoland used 15 nickels and 13 quarters to paid the movie ticket .
) how many ways are there to divide a group of 10 kids into two groups of 5 to play soccer?
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
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]
Given the inequality below: x + 2y ≥ 10
The base and the height of sail b are x times greater than the base and the height of sail
a. how many times greater is the area of sail b? write your answer as a power.
When both the base and height of a shape are multiplied by x, the area increases by a factor of x^2. Therefore, the area of Sail B is x^2 times greater than that of Sail A.
Explanation:The area of a shape with a base and height is commonly found using the formula Area = 1/2 * Base * Height. If the base and the height of Sail B are x times greater than those of Sail A, then both the base and height of Sail B are multiplied by x, resulting in an area that is x^2 (x squared) times greater. This is because, in the formula, base and height are multiplied together, so if both are multiplied by x, the overall multiplication is by x*x, or x^2. Therefore, the area of Sail B is x^2 times greater than the area of Sail A.
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Kelly mixes the letters S E L E C T E and D thoroughly. Alex picks one letter. WHat is the probability that Alex will not select a consonant.
A. 3/8
B.3/5
C.5/8
D.1/2
Help I'm taking a k12 quiz 2.04: composite figures but, I can't figure these out can anyone help me?
Question. 1 What is the area of this polygon? (Picture 1)
Question. 2 What is the area of this polygon? 42.5 Units? 41.5 Units? 35.5 Units? 29.5 Units? (Picture 2)
Question. 3 This figure is made up of a rectangle and parallelogram.
What is the area of this figure? (Picture 3)
Question. 4 What is the area of this composite shape? (Picture 4)
Thank you angels who help me with these
Ten times the sum of a number and
15
is at least
26
.
Use the variable
b
for the unknown number.
An inheritance of $30,000 will be divided between sisters hannah and taylor. if hannah is to receive $4000 less than taylor, how much does each sister receive?
WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!!
Which pair of variables is the most likely to have both correlation and causation?
* the height of a person and the amount of work he does
* the number of hours spent exercising and the number of calories burned
* the length of a person's commute and the amount of money he earns
* the number of customers at a restaurant and the variety of soups ordered
Please help thank you. :P
for the love of God help me
(Economics) Select all that apply.
Select the items that apply to calculating the Gross Domestic Product.
a. final goods and services
b. intermediate goods and services
c. last year's products
d. new products
GDP calculations should include 'final goods and services' and 'new products' to reflect a nation's current economic activity accurately while preventing double counting.
Explanation:The question pertains to what should be included when calculating the Gross Domestic Product (GDP). The options given were a. final goods and services, b. intermediate goods and services, c. last year's products, and d. new products. According to the principles of economics, GDP is the market value of all final goods and services produced within a country in a given period of time.
It is crucial to understand that GDP calculations include only new products that are produced within the current year to reflect the nation's current economic activity. This method helps statisticians avoid the mistake of double counting, which would inflate GDP figures inaccurately. Consequently, the correct selections are a. final goods and services and d. new products.