Answers
It's an isosceles triangle 45° - 45° - 90°, therefore y = 5.
In that triangle, sides are in proportion 1 : 1 : √2.
Therefore we have x = 5√2.
Answer: B. x = 5√2, y = 5Other method.
You can use the Pythagorean theorem:
x² = 5² + 5²
x² = 25 + 25
x² = 2 · 25
x = √(25 · 2)
x = √25 · √2
x = 5√2
Answer: B. x = 5√2, y = 5Answer: Hello there!
You can see that this is a triangle rectangle, where one of the catheti is equal to 5, and we know all the angles (you can see that both lower angles are equal to 45°, then is safe to assume that both catheti are equal in length, but let's do the math):
we need to find the length of the other cathetus and the length of the hypotenuse.
A very useful thing to remember when you are working with a triangle rectangle is:
So-Ca -Toa
this means:
sin(a) = (opposite cathetus)/(hipotenuse)
cos(a) = (adjacent cathetus)/(hipotenuse)
tan(a) = (opposite cathetus)/(adjacent cathetus)
now, we can find y using the third relation:
tan(45°) = 5/x
y= 5/tan(45°) = 5
because tan(45°) = 1
and this has a lot of sence, because you can see that both cathetus are symetric.
Now we can find the value of x with the next Pythagorean theorem:
the square hypotenuse is equal to the sum of the squares of the cathetus:
x^2 = 5^2 + 5^2 = 2*(5^2)
x= (√2)*5
then the right answer is option B:
x = (√2)*5 and y = 5
Related Questions
A moving walkway at an airport moves at a pace of 1.75 feet per second. If you stand on the walkway as it moves, how long will it take to transport you 280 feet? CLEAR CHECK 160 seconds 278.25 seconds 490 seconds 625 seconds
Answers
Answer:
160 Seconds
Step-by-step explanation:
acceleration * seconds = distance
1.75 * (x) = 280
1.75x=280
x= 280/1.75
x= 160
In the given case, It will take 160 seconds to transport you 280 feet on the moving walkway.
To determine how long it will take to transport you 280 feet on a moving walkway, we can use the formula:
This formula is particularly useful in various scenarios, such as calculating travel time for a journey, determining how long it will take for an object to reach a certain location, or estimating the time it will take for a process to complete at a given speed.
Time = Distance / Speed
Plugging in the given values, we have:
Time = 280 feet / 1.75 feet per second = 160 seconds
Therefore, the correct answer is 160 seconds.
Learn more about Time calculation here:
https://brainly.com/question/30895034
#SPJ3
Write a numerical or variable expression for the quantity: the value in cents of n nickels
Answers
The value in cents of n nickels: 5n
The value in cents of d dimes and p pennies: 10d + p
The value in cents of w dollars: 100w
The next whole number following a whole number w: w + 1
The value in cents of n nickels can be written as a numerical or variable expression as 5n, with n representing the number of nickels. This is because each nickel is worth 5 cents.
Explanation:The quantity in cents of n nickels can be written as a numerical or variable expression. Because each nickel is worth 5 cents, you multiply the number of nickels, represented by n, by 5. This can be written as 5n. For example, if you have 4 nickels, you could calculate the total value in cents by multiplying 5 by 4, giving you 20 cents.
Learn more about Numerical Expression here:https://brainly.com/question/29778337
#SPJ3
Rod smokes 1 1/2 packs of cigarettes per day. Rod buys cigarettes by the carton. There are ten packs of cigarettes in each carton. If Rod pays $35.80 per carton, how much does it cost him for each day of smoking?
Answers
Answer:
It costs Rod $5.37 per day to smoke.
Step-by-step explanation:
If a carton costs 35.80 and there are 10 packs per carton
$35.80 /10 = 3.58 per pack
Rod smokes 1.5 packs per day
1.5 * 3.58 = $5.37
It costs Rod $5.37 per day to smoke.
B) around 5.38
David deposits $230 into a savings account that accrues 12% interest compounded quarterly each year. How much money will dave earn in interest after 3 years?
A. $97.93
B. $99.38
C. $327.93
D. $329.38
Answers
Answer:
C. $327.93
Step-by-step explanation:
The formula for interest compounded quarterly is
A = P(1 + r/n)nt where P is the principal
r is the rate
t is the time in years
n is the compoundings per year
p =230 r= .12 t= 3 n =4 since it is quarterly
Substituting these in
A = 230 (1+ .12/4)^(3*4)
= 230(1.03)^12
=327.93
Answer:
The answer is C. $327.93
Hope this helps and have a Merry Christmas.
P.S. Could you make me brainlest? It would help SO much. Thanks!
I need help with -5 -3w = 7w please!
Answers
Answer: W= 0.5
Step-by-step explanation:
You add 3w to both sides to get -5= 10w and then you divide everything by 10 to get w= 0.5
-5 - 3w = 7w
-5 - 3w+3w = 7w+3w <<--- add 3w to both sides
-5 + 0w = 10w
-5+0 = 10w
-5 = 10w
10w = -5
10w/10 = -5/10 <<--- divide both sides by 10 to isolate w
w = -5/10
w = -1/2 <<--- reduce; this is the answer in fraction form
w = -0.5 <<--- this is the answer in decimal form
A line passes through the point (2, -4) and has a slop of 0 what is the equation of the line. A.)y=2, B.) x=2, C.)y=-4 or D.)x=-2
Answers
52.85 ROUNDED AT NEAREST ONE
Answers
Answer: 53
52.85 is closer to 53, than it is to 52
The digit after the ones digit is 8, which is 5 or larger, so that tells us to round up from 52 to 53. We drop everything after the ones digit.
solve equation for x
Answers
Answer:
n-20
--------
3a
Step-by-step explanation:
(3ax - n)/5 = -4
The first step is to multiply each side by 5 to get rid of the fraction
(3ax - n)/5 * 5= -4* 5
3ax - n = -20
Then we need to add n to each side.
3ax -n+n = -20+n
3ax = n-20
Divide each side by 3a to isolate x
3ax/3a = (n-20)/3a
x = (n-20)/(3a)
Find greatest common factor of the following monomials
45m. 6m
Answers
Answer:
m
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values 45m and 6m. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:
45m: 1, 5, 9, 45, m
6m: 1, 2, 3, 6, m
Both have 1 and m as factors. Our GCF is these two factors multiplied which is 1m=m.
In 2005, joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear, what was the rate of the growth of the tree?
Answers
Answer:
2 feet per year
Step-by-step explanation:
First, we need to find the amount it grew:
13 - 3 = 10
So between 2005 and 2010 it grew 10 feet.
Now to find the yearly growth we need to divide the distance by time:
10 ÷ 5 = 2
So it grew 2 feet per year.
Hope this helps!
faith buys 3 pounds of flour. she uses 1/4 pound each day. in how many days does she use up the flour. ANWSER QUICK!!!!!
Answers
In the figure below , a cone is cut by a plane that passes through its vertex and it’s vertex and is perpendicular to its base. The height of the cone is 10 inches, and it’s diameter is 6 inches. What is the area of the cross section formed by the intersection
Answers
Answer:
The area of cross-section is [tex]30inch^2[/tex]
Step-by-step explanation:
we are given that
a cone is cut by a plane that passes through its vertex and it’s vertex and is perpendicular to its base
So, cross -section will be right angled triangle
whose base will be along diameter of cone
so, base of triangle = diameter of cone =6 inch
base =6 inch
Height of triangle will be same as height of cone
so, height of triangle =10inch
now, we can find area
[tex]Area=\frac{1}{2}\times 6\times 10[/tex]
[tex]Area=30inch^2[/tex]
The area of the cross-section formed by the intersection is 9π square inches.
How to determine the areaWhen a cone is cut by a plane passing through its vertex and perpendicular to its base, the resulting intersection is a triangle similar to the base of the cone.
Such that;
Height of the cone = 10 inchesRadius= diameter / 2 = 6 / 2 = 3 inches)Using the properties of similar triangles, the triangle formed by the intersection is similar to the base of the cone.
The area of the cross-section formed by the intersection is the area of a circle with radius 3 inches:
Area = πr²
Area = π × 3²
Area = π × 9
Area = 9π square inches
Learn about area at: https://brainly.com/question/25292087
#SPJ3
Clara has $67 in her piggy bank. She spent x dollars on a dog bowl and now has $57.4 remains.
A) 67+x=57.4
B) 57.4+x=67
C) x/67=57.4
D) x-57.4=67
Answers
Answer:
B) 57.4+x=67
Step-by-step explanation:
We take the amount in the piggy bank. Then we take the amount spent and add it to the amount she has left. These two amounts should be equal
piggy bank = spent + left
67 = x + 57.40
Which fraction is halfway between 3/7 and 10/21
A.) 7/15
B.) 19/42
C.) 15/42
D.) 4/9
Answers
Answer:
B) 19/42
Step-by-step explanation:
To find the fraction halfway between 3/7 and 10/21 we first find the difference between the fractions, half it, and then add it back on to the smaller one.
Because 10/21 > 3/7 we subtract in that order
[tex]\frac{10}{21} - \frac{3}{7} = \frac{10}{21} - \frac{9}{21} = \frac{1}{21}[/tex]
Half of 1/21 is 1/42 and so the fraction halfway between 3/7 and 10/21 is
[tex]\frac{3}{7} + \frac{1}{42} = \frac{18}{42} + \frac{1}{42} = \frac{19}{42}[/tex]
18 out of 20 is what percentage
Answers
I used Google and got 90%...if you simplify it you will get 9/10 which is a 90%
If 18 out of 20 is given. Then the percentage will be 90%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.
The given number statement is 18 out of 20.
Then the percentage will be
P = 18/20 x 100
P = 90%
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
PLEASE HELP! :( this table below shows the future value of a certificate of deposit (CD), after x years.Andre states the applied interest is simple interest.True or False? and why if you can?
Answers
Answer:
Andre states that the applied interest is simple interest, this statement is true.
Step-by-step explanation:
From the given table it is noticed that the value of y increased by 17.50 as the value of x increased by 1.
The rate of change is calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For first two years the rate of change is
[tex]m=\frac{535.00-517.50}{2-1}=17.50[/tex]
The rate of change for next two years is
[tex]m=\frac{552.50-535.00}{2-1}=17.50[/tex]
Similarly, the rate of change for all years in 17.50.
Since the rate of change is same for all years, therefore the future value is increased by a constant rate, therefore the applied interest is simple interest.
So, the statement "the applied interest is simple interest" is true.
Step-by-step explanation: (Apex) just did the quiz 9/26/19
An album contains x black-and-white photographs and y color photo graphs. If the album contains 24 photographs which of the following cannot be true?
A.x=2y
B.x=3y
C.x=4y
D.x=5y
Answers
x=4y, total phonographs are 5y
5y cannot be 24 if y is an integer.
A construction worker estimates that a kitchen remodel will take 1 person 120 hours. If 4 people work on the job for 6 hours a day, how many days will it take for them to complete the job?
Answers
it would take five days for them to complete their job if you want an explanation just ask
It will take 5 days for the 4 people working 6 hours a day to complete the kitchen remodel.
Let's calculate the total work hours required to complete the kitchen remodel and then determine how many days it will take for the 4 people working 6 hours a day to finish the job.
The estimated total work hours for one person to complete the remodel is 120 hours.
Total work hours required = 120 hours
Now, we have 4 people working on the job, and each person works 6 hours a day.
Total work hours per day with 4 people = 4 people * 6 hours/person = 24 hours
To find the number of days it will take to complete the job, we divide the total work hours required by the total work hours per day with 4 people:
Number of days = Total work hours required / Total work hours per day with 4 people
Number of days = 120 hours / 24 hours/day
Number of days = 5 days
It will take 5 days for the 4 people working 6 hours a day to complete the kitchen remodel.
To know more about days click here :
https://brainly.com/question/16034524
#SPJ2
p=2L+2W find p if L=10 and W=5
Answers
Answer:
30
Step-by-step explanation:
When l = 10, and w = 5
Plug in 5 for "w" and 10 for "l" inside the equation.
p = 2(10) + 2(5)
Solve for the variable "p". Simplify the equation. Remember to follow PEMDAS. First, solve the multiplication
p = 20 + 10
Next, add.
p = 30
30 is your answer for p in this problem
~
Sin (19pi/6)=_____ help please !!!
Answers
Answer:
sin(19pi/6)=-1/2
Step-by-step explanation:
a painter uses 4 gallons of paint to paint each apartment in a building. if the painter has 45 gallons of paint, how many apartments can be painted completely? how much paint will be left over?
Answers
Final answer:
The painter can completely paint 11 apartments with 45 gallons of paint and will have 1 gallon of paint left over.
Explanation:
A painter uses 4 gallons of paint for each apartment. With 45 gallons of paint, you would first divide the total gallons of paint by the gallons needed per apartment to determine how many apartments can be painted completely. Since 45 gallons ÷ 4 gallons per apartment equals 11.25, the painter can only completely paint 11 apartments, because you can't partially paint an apartment. The fractional part, .25, represents the leftover paint. To find out how much paint is remaining, you would then multiply the fractional part by the amount of paint used for one apartment, which is 4 gallons. So, 0.25 × 4 gallons equals 1 gallon. Therefore, the painter will have 1 gallon of paint left over after painting 11 apartments.
What is the domain and range for the following function and its inverse? f(x) = -x + 5
Answers
Answer:
Domain: [tex]\mathbb{R}[/tex]
Inverse: [tex]f^{-1}(x) = -x + 5[/tex]
Step-by-step explanation:
Since this is a linear function, the domain and range is simply the set of real numbers.
The inverse is obtain by switching the places of x and y, then solving for y.
Here,
y = -x + 5
So switching x and y,
x = -y + 5
Solving for y again,
y = -x + 5
Thus,
[tex]f^{-1}(x) = -x + 5[/tex]
Answer:
The domain of linear function is always the set of all real numbers
Range is also the set of all real numbers
[tex]f^{-1}=-x+5[/tex]
Step-by-step explanation:
[tex]f(x) = -x + 5[/tex]
Domain is the set of x value and range is the set of y value. There is no restriction for x and y in a linear function.
The domain of linear function is always the set of all real numbers
Range is also the set of all real numbers
Now find the inverse
[tex]f(x) = -x + 5[/tex]
Replace f(x) with y
[tex]y = -x + 5[/tex]
Replace x with y and y with x
[tex]x = -y + 5[/tex]
Subtract 5 from both sides
[tex]x-5=-y[/tex]
Divide both sides by -1
[tex]y=-x+5[/tex]
Replace y by f^-1
[tex]f^{-1}=-x+5[/tex]
A garden is 6 yards 24 inches wide and 6 yards long. Write the ratio of the width to the length as a fraction in simplest form.
Answers
Answer: 10/9
Step-by-step explanation:
On the width:
6 yards = 18 feet
24 inches = another 2 feet
Total width = 20 feet
On the length:
6 yards = 18 feet
Ratio of width to length = (20 feet) / (18 feet) = 10/9
The actual width of the garden is 72 inches, which is equivalent to 2 yards
To determine the actual width of the flower garden, we need to use the given scale of 1:12. This means that 1 inch on the plan represents 12 inches in reality. Given that the flower garden is 6 inches wide on the plan, we set up a proportion to find the actual width.
The proportion is:
1 inch on plan : 12 inches in reality = 6 inches on plan : x inches in reality
So we calculate:
(1 inch / 12 inches) = (6 inches / x inches)
Now we solve for x:
1/12 = 6/x
x = 6 * 12
x = 72 inches
Therefore, the actual width of the garden is 72 inches, which can be converted into yards by knowing that 1 yard equals 36 inches. Thus, 72 inches is equivalent to 2 yards (since 72 / 36 = 2).
24 is 4/5% of what number
Answers
Answer:
The number is 3000
Step-by-step explanation:
Is means equals
24 = 4/5 % *n
Lets change the percent to a decimal. To change percent, we move the decimal to places to the left.
4/5= .8
4/5 % = .8% = .008
24 = .008 *n
Divide each side by .008
24/.008 = .008n/.008
3000 = n
On Monday, Harry had 75\%75% as many toys as Teddy did. On Tuesday, after Harry acquired 3232 more toys and Teddy acquired 15\%15% more than he had on Monday, Harry had as many toys as Teddy did. How many toys did Harry have on Monday?
Answers
Let the number of toys Teddy has on Monday = x
On Monday Harry has = 75% of x or 0.75x
As given, On Tuesday, after Harry acquired 32 more toys and Teddy acquired 15% more than he had on Monday, Harry had as many toys as Teddy did.
Toys Teddy has = [tex]x+\frac{15x}{100}[/tex]
=[tex]\frac{100x+15x}{100} =\frac{115x}{100}[/tex] = 1.15x .... (i)
Toys Harry has = 0.75x+32 ...... (ii)
As both have equal toys now, so equation (i) equals equation (ii)
[tex]1.15x=0.75x+32[/tex]
[tex]1.15x-0.75x=32[/tex]
[tex]0.4x=32[/tex]
x=80
Hence, Teddy had 80 toys on Monday.
And Harry had 75% of 80 toys = 60 toys on Monday.
Find the value x that makes ABCD a parallelogram
Answers
Answer:
D.) 6
Step-by-step explanation:
A parallelogram needs supplementary consecutive sides. To make 150 supplementary, it needs to add 30 to make 180 degerees.
5 * 6 = 30.
Therefore, the value of [tex]x=6[/tex] degree i.e., option (D) is correct answer.
What is the parallelogram?
A parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
A parallelogram needs supplementary consecutive sides.
So, to make the supplementary angle i.e., [tex]150[/tex] degree .It requires to add [tex]30[/tex] to make [tex]180[/tex] degree.
[tex]x=6\\5(6)=30[/tex]
Hence, the value of [tex]x=6[/tex] degree i.e., option (D) is correct answer.
To know more about the parallelogram
https://brainly.com/question/28854514
#SPJ2
The Ratio of 3 numbers id 2:7:1. The sum of the numbers is 30. What are the 3 numbers?
Answers
Answer:
Three numbers are : 6 , 21 and 3
Step-by-step explanation:
Given,
Ratio of 3 numbers is 2:7:1 .
We can assume 3 numbers as : 2x ,7x and x respectively.
According to the problem :
2x + 7x + x = 30 {The sum of the 3 numbers is 30}
10x = 30
x = 3
Hence 3 numbers are, x = 3
2x = 2*3 = 6
7x = 7*3 = 21
Therefore we get three numbers as : 6 , 21 and 3
Remember , you can check their ratios to cross check the correct answer.
Answer:
6, 21, and 3
Step-by-step explanation:
i am a fraction greater than 1/2 and less than 6/8
Answers
Answer:
5/8
Step-by-step explanation:
it is 5/8 because if it is greater than1/2, which =to 4/8, and less than 6/8, it must be the number in between, which is 5/8
This month salesperson A made 11% of $67,530. Salesperson B made 8% of $85,740. Who made more commission this month? How much did that salesperson make?
Answers
Answer: Salesperson A made $7,428.30 in commission which is $569.10 more than Salesperson A.
Step-by-step explanation:
A: $67,530 * 0.11 = $7,428.30
B: $85,740 * 0.08 = $6,859.20
$ 569.10
At a school for performance art students 25 of the girls study music, 35 of the girls study dance, and 16 of the girls study music and dance. What fraction of those who study music also study dance?
Answers
25+35=60
Out of 60 students, 16 study both dance and music.
16/60
Divide both sides by 4, the GCF.
16/4=4
60/4=15
Your answer would be 4/15. Hope this helps! :)