You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane represents one inch.
Answers
Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.
Answer:
112.5 units²
Step-by-step explanation:
Area of the shelf = ½*base*height.
The base is the distance between Z(0, 5) and Y(15, 5)
The height is the distance between X(15, 20) and Y(15, 5).
Therefore area of the shelf = ½*ZY*XY
Use the distance formula to find ZY and XY.
Distance between Z(0, 5) and Y(15, 5):
[tex] ZY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] Z(0, 5) = (x_1, y_1) [/tex]
[tex] Y(15, 5) = (x_2, y_2) [/tex]
[tex] ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2} [/tex]
[tex] AB = \sqrt{(15)^2 + (0)^2} [/tex]
[tex] AB = \sqrt{225 + 0} = \sqrt{225} [/tex]
[tex] AB = 15 [/tex]
Distance between X(15, 20) and Y(15, 5):
[tex] XY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] X(15, 20) = (x_1, y_1) [/tex]
[tex] Y(15, 5) = (x_2, y_2) [/tex]
[tex] XY = \sqrt{(15 - 15)^2 + (5 - 20)^2} [/tex]
[tex] XY = \sqrt{(0)^2 + (-15)^2} [/tex]
[tex] XY = \sqrt{0 + 225} = \sqrt{225} [/tex]
[tex] XY = 15 [/tex]
Area of shelf = ½*15*15 = ½*225 = 112.5 units²
Related Questions
A rectangle has a length of 12 yards less than 10 times it’s width. If the area of the rectangle is 880 yards
Answers
Answer: The length is 88 yards and the width is 10 yards. Look into the steps for more information.
Step-by-step explanation:
The length is 12 yards less than 10 times the width so we can represent that by the equation L = 10w - 12
And the area is 880 so the width times the length has to equal 880. the width is w and the length is 10w -12
w( 10w -12 ) = 880 solve for w
10w^2 - 12w = 880 subtract 880 from both sides
-880 -880
10w^2 - 12w - 880 = 0 They share the same factors so dive each side by 2
5w^2 - 6w^2 - 440 = 0
a= 5 b = -6 and c=-440
The quadratic formula says that x= -b ± [tex]\sqrt{b^2- 4ac} / 2a[/tex]
x= 6 ±[tex]\sqrt{8836} / 5[/tex]
x= 6 ± 94 /10
x= 100 /10
x = 10
In this case the width is 10 yards.
The length is 12 less than 10 times the width .
So L = 10(10) - 12
L = 100- 12
l = 88
So the length is 88
The required length and width are 229 and 27 yards.
It is required to find the dimension of rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
A=l*w
w=width
10w-12=length
According to given question we have,
6183=(10w-12)(w)
6183=10[tex]w^{2}[/tex]-14w
9[tex]w^{2}[/tex]-14w-6183=0
By simplify we get,
(9w+229)(w-27)=0
w-27=0
w=27 yards
l=9*27-14=229 yards
Therefore, the required length and width are 229 and 27 yards.
Learn more details about rectangle here:
https://brainly.com/question/15019502
#SPJ2
Mateo He’s going to solve the equation below. Which of the following represents the equation after combining the terms? -8x +23-22+9=182
Answers
Answer:
-21.5
Step-by-step explanation:
-8x+23-22+9=182
-8x+1+9=182
-8x+10=182
-10 -10
-8x=172
x=172÷-8
x=-21.5
-21.5 IS THE ANSWER
if Xandy are integers and(x-y)=4, what is the main minimum possibile value of xy?
Answers
Answer:
-4
Step-by-step explanation:
Hello,
x-y=4 <=> x=y+4
so, xy=y(y+4)
[tex]y(y+4)=y^2+4y=(y+2)^2-4[/tex]
so this is minimum for y = -2 and the minimum value is -4
thanks
If you were 10 years old on
Earth, you would be 41.494 years old
on Mercury. Write the age on Mercury
as a mixed number in simplest form.
Answers
Answer:
[tex]41\frac{247}{500}[/tex]
Step-by-step explanation:
41.494
= [tex]41\frac{494}{1000}[/tex]
to simplify the fraction 494 /1000, we have to find and divide both numerator and denominator by the their highest common factor
494 = 2 x 13 x 19
1000 = 2 x 2 x 2 x 5 x 5 x 5
comparing the two, we can see that that the only common factor that both numbers share is 2, hence we divide both numerator and denominator by 2
41 494/1000
= [tex]41\frac{494}{1000}[/tex]
= [tex]41\frac{494/2}{1000/2}[/tex]
= [tex]41\frac{247}{500}[/tex]
If f(x)=(3+ X) over (X -3) what is f(a+2)
Answers
Answer:
5+a/a-1
Step-by-step explanation:
3+a+2/a+2-3=5+a/a-1
Find a parametrization of the circle of radius 3 in the xy-plane, centered at (−2,2), oriented counterclockwise. The point (1,2) should correspond to t=0. Use t as the parameter for all of your answers.
Answers
Answer:
x = 3*cos(t) - 2
y = 3*sin(t) + 2
Step-by-step explanation:
The equation for a circle of radius 3 and centered at the point ( h , k ) ( -2 , 2 ) is:
( x - h )² + ( y - k )² = r²
In this particular case
h = - 2 k = 2 and r = 3
Then to parametrizace the equation
x = r* cos(t) + h
y = r*sin(t) + k
x = 3*cos(t) + (- 2) ⇒ x = 3*cos(t) - 2
y = 3 *sin(t) + (2) ⇒ y = 3*sin(t) + 2
Now :
when t = 0 x should be 1
Then x = 3 cos(0) - 2 x = 3 - 2 x = 1
and t = 0 y should be 2
Then y = 3*sin(t) + 2 ⇒ y = 3*sin(0) + 2 y = 2
if f(x)=4x^2-6
find all x such that f(x)= 106
Answers
Answer:
50
Step-by-step explanation:
Answer:
[tex]2\sqrt7,-2\sqrt7[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=4x^2-6[/tex]
And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):
[tex]106=4x^2-6[/tex]
Add 6 to both sides:
[tex]112=4x^2[/tex]
Divide both sides by 4:
[tex]x^2=28[/tex]
Take the square root of both sides:
[tex]x=\pm\sqrt{28}[/tex]
Simplify the square root:
[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]
So, those are the two values that will satisfy our requirement.
And we're done!
write the sentence as an equation
the product of y and 6, add to 310 is y
Answers
y(6)+310=y
equals is =
product of is ×
add to is +
Pls answer the question I need it asap I'm literally crying
Answers
1. Which statement is true?
4.
A. 7.5 is 10 times as much as 750.
A
B. 0.2 is 1/10 of 2
E
C. 65 is 10 times as much as 0.065.
D. 70 is 1/10 of 7,000.
Answers
Answer:
B
Step-by-step explanation:
B is true because 0.2 x 10 = 2
The graph of the line 4x+3y= 12 is translated right 1 unit and down 3 units. What is the equation of the new line?
Answers
Answer: y = 7/3 - (4/3)*x
Step-by-step explanation:
First, let's write our line in the notation:
y = f(x)
So we must isolate y in the equation:
4x + 3y = 12
3y = 12 - 4x
y = 12/3 - (4/3)*x = 4 - (4/3)*x
Now, we have two translations, one horizontal and one vertical.
Let's define them in general cases:
Horizontal translation.
When we have y = f(x) and we want to do a horizontal translation of A units to the right (A positive) we have:
y = g(x) = f(x - A)
So we replace our variable x by x - A.
Vertical translation.
When we have y = f(x) and we want to do a horizontal translation of A units up (A positive) we have:
y = g(x) = f(x) + A.
Then in this case we have:
y = f(x) = 4 - (4/3)*x
then, the horizontal translation of 1 unit to the right is:
y = f(x - 1) = 4 - (4/3)*(x - 1)
And the translation of 3 units down (a vertical translation) is:
y = f(x - 1) - 3 = 4 - (4/3)*(x - 1) - 3 = 1 + 4/3 - (4/3)*x
y = 7/3 - (4/3)*x
This equation represents the new line.
(−8r5t8)(−5rt) Please help
Answers
Answer:
40r^6t^9
Step-by-step explanation:
Newton's Second Law states acceleration equals force
divided by mass, a = F/M. This graph shows f(x) = 5/x , an
acceleration based on a constant force of 5 Newtons
applied to different objects. How is f(x) transformed to
get g(x) and what is the new equation?
Answers
Answer:
2f(x); g(x) = 10/x
Step-by-step explanation:
The second option on edge
The new equation is, g(x) =2f(x), g(x) =10/x. Option B is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Given data in problem is;
a = F/M
f(x) = 5/x
We have to examine each option given and observe the graph for the function we got;
g(x) = 2f(x)
Substitute the values we get;
g(x) = 2×(5/x)
g(x)=10/x
The new equation is, g(x) =2f(x), g(x) =10/x.
Hence, option B is correct.
The complete question and graph are attached below.
To learn more about the graph, refer to the link;
https://brainly.com/question/14375099
#SPJ2
can someone help me with this?
Answers
Answer:
[See Below]
Step-by-step explanation:
✦ The pattern is y ÷ 8. (So just divided by 8 each time.)
✧ 512 ÷ 8 = 64
✧ 64 ÷ 8 = 8
✧ 8 ÷ 8 = 1
✧ 1 ÷ 8 = 0.125
✧ 0.125 ÷ 8 = 0.015625
✦ So then the next values would be:
✧ 8⁰ = 1
✧ 8⁻¹ = 0.125
✧ 8⁻² = 0.015625
~Hope this helps Mate. If you need anything feel free to message me.
If x =7/8 cm, y =1/4 cm, and z = 5/8 cm, what is the volume of the rectangular prism above?
Answers
what is 2k-3(2k-3)=45
Answers
Answer:
k = -9
Step-by-step explanation:
please help me
sec theta - cos theta= sin^2 theta/ cos theta
Answers
Answer:
Taking LHS
=1 by cos theta- cos theta
= (1- cos²0)/ cos0
= sin²0/ cos0 ( because 1-cos²0 is also equals to sin²0)
=RHS hence proved
Answer:
Step-by-step explanation:
Let theta be β.
So,
[tex]sec\beta - cos\beta = \frac{sin^2\beta }{cos\beta } \\=>\frac{1}{cos\beta } - cos\beta = \frac{1 - cos^2\beta }{cos\beta } \\=>\frac{1 - cos^2}{cos\beta } = \frac{1 - cos^2\beta }{cos\beta }[/tex]
Here , identity used = [tex]sin^2\beta + cos^2\beta = 1[/tex]
You start at (7, 1). You move right 3 units.
Answers
Answer:
4,1
Step-by-step explanation:
Express each rational number in decimal form
17)
[tex] - \frac{7}{4} [/tex]
Answers
Answer:
It is a negative 1.75. (-1.75)
An 8ft length of 4 inch wide crown molding costs $15. How much will it cost to buy 24 ft of crown molding?
Answers
Answer: 123$
Step-by-step explanation:
I dont even know but this gives me free five points
The sum of five and triple a number what is it please
Answers
Answer:
5 + 3a
Step-by-step explanation:
The expression is:
5 + 3a
15 POINTS
1. name two planes that intersect in WX in the figure to the right
plane UVR and plane XTS
plane UVW and plane UVR
plane UVW and plane XTS
plane VUX and plane VWS
Answers
Zx and Zy are supplementary angles. Zy measures 116º.
What is the measure of Z?
Answers
What is the base 2 equivalent of 6010? * 111101 base 2 111100 base 2 110000 base 2 110100 base 2
Answers
Answer:
111100 base 2
Step-by-step explanation:
The conversion of 60 base 10 to base 2
When converting a number from base 10 to base 2, the following steps are taken:
a) The number in base 10 is divided by 2 and the remainder is recorded, this continues until the remainder is less than 2.
b) The remainder from the bottom to the top are arranged so as to get the representation of the number in base 2.
60 base 10 to base 2
60 ÷ 2 = 30 remainder 0
30 ÷ 2 = 15 remainder 0
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
The remainder from bottom to top is 111100 base 2.
(60)₁₀ = (111100)₂
I need help with this pls ASAP
Answers
Answer: G.
Step-by-step explanation: you should divide both sides by 3. 3 divided by 3 is 0, and -12 divided by 3 is -4. therefore, your answer is (0,-4)
Answer: G (0,-4)
Step-by-step explanation:
You can use this website called "Desmos Graphing Calculator." The answer is G.(0,-4). It helps me a lot with graphing and graphing linear equations.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees. What is the value of y? y = 30 y = 50 y = 110 y = 130
Answers
Answer:
y=50
Step-by-step explanation:
look at photo attached
Answer:
y=50
Step-by-step explanation:
on edge2021
Benn Cornell and Tom Ingulli drove to Chicago a distance of 510 miles, their car gets 23 miles per gallon of gasoline. gasoline costs them $2.59 per gallon. how much did they spend for gasoline on there trip?
Answers
Answer:
about $57.42
Step-by-step explanation:
we know how many miles they drove in all (510) and how many miles they can drive per gallon (23)
we need to find out how many gallons of gas they used by dividing the total number of miles they drove (510) by the number of miles per gallon (23) which is about 22.17
510 ÷ 23 = 22.17
we then need to find out how much money they spent on the total number of gallons of gas they purchased by multiplying 22.17 by the amount of money for one gallon of gas ($2.59)
22.17 × 2.59 = $57.42
What are t + 8 + 3t terms and like
Answers
Answer:
t+8+3t
8+4t
Step-by-step explanation:
I guess the question is incomplete
2x² - (5 + 2x) + 6x²
Answers
Answer:
8x²-2x-5
Step-by-step explanation:
2x²-(5+2x)+6x²
2x²-5-2x+6x²
2x²+6x²-2x-5
8x²-2x-5
Hope this helps ;) ❤❤❤
Answer:
[tex]8 {x}^{2} - 2x - 5[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - (5 + 2x) + 6 {x}^{2} [/tex]
[tex]2 {x}^{2} - 5 - 2x + 6 {x}^{2} [/tex]
[tex]8 {x}^{2} - 2x - 5[/tex]
Michael bought a classic car for $8,500. He restored it then added 150% markup before advertising it for sale. What is the amount of markup? is it 21250? or I'm I wrong thank you
Answers
Answer:
$12750
Step-by-step explanation:
Initial price = $8500
Markup = 150%
Markup amount:
$8500*1.5 = $12750Selling price would be:
$8500 + $12750 = $21250