Mario writes the equation (x+y ) 2 = z 2 +4( 1 2 xy) (x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
Answer:
For the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The complete question related to this found on brainly (ID:16485977) is stated below:
Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
_____finds the area of the outer square by squaring its side length.
_____finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
Find attached the diagram of the question.
Step-by-step explanation:
Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.
Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
From the diagram of the question.
Hypotenuse = z
Opposite = y
Adjacent = x
z² = x² + y²
Area of outer square = area of inner square + 4(area of triangles)
area of inner square = length² = (x+y)²
Expanding area of the outer square:
(x+y)² = (x+y)(x+y) = x²+xy+xy+y²
(x+y)² = x²+y²+2xy
= z² + 2xy
Area of inner square = length² = z²
Area of triangle = ½ base × height
= ½ × x × y = ½ xy
Area of outer square = area of inner square + 4(area of triangles)
(x + y)² = z² + 4(½xy )
Therefore, it is a true equation.
( x + y )² finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
So for the drop down menu:
i) x + y
ii) z²
iii) ½ xy
what is -5c plus 2 less than or equal to 27. I need this for very difficult homework if anyone can help :)
Answer:
c ≥ -5
Step-by-step explanation:
-5c +2 ≤ 27
Subtract 2 from each side
-5c +2-2 ≤ 27-2
-5c ≤25
Divide by -5, remembering to flip the inequality
-5c/-5 ≥25/-5
c ≥ -5
Answer: [tex]x\geq 5[/tex]
Step-by-step explanation:
[tex]-5x+2\leq 27\\Subtract\\-5x\leq 25\\Divide\\x\geq 5[/tex]
It's important to remember that when you divide both sides of an inequality by a negative number to flip the sign.
Hope it helps <3
Doughnuts at one shop cost £1.20 each.
Doughnuts at a second shop cost 25% more.
What is the difference in the cost of doughnuts at the two shops?
Answer: 30p
Step-by-step explanation:
Cost of donuts in the first shop £1.20
Cost at the second shop at 25% higher
= 1.20 x 1.25 = 1.50
Difference in price
= 1.50 - 1.20 = 0.30
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answer:
165 students (hope it helps)
Step-by-step explanation:
300students - 45students = 255students
180students + 150students = 330students
330students / 2 = 165
Answer:
75 students watched both.
Step-by-step explanation:
150 students saw Zootopia
180 students saw Finding Dory
45 students saw nothing.
There are 300 students in total.
[tex]|(300-45)-150-180|=\\|255-150-180|=\\|105-180|=\\|-75|=\\75[/tex]
Bidmas 7+8 divided 5-2
Answer:
Step-by-step explanation:
7 + 8 = 15
5 - 2 = 3
∴ 7 + 8 ÷ 5 - 2
= 15 / 3
= 5
Hope this helps
plz mark as brainliest!!!!!!
Answer:
5
Step-by-step explanation:
:)
Solve: 3/x-4 >0 A.x -4 C.x>4 D.x<-4
Answer:
C. x>4
Step-by-step explanation:
3/(x-4) > 0
3>0, so
x-4 >0
x > 4
Graph the system of equations on the coordinate plane and determine the solution to
the system
y=-1/2x+5
y=2x-10
Answer:
(6,2)
Step-by-step explanation:
y=-1/2x+5
y=2x-10
-1/2 x+5 =2x-10 to find the solution y=y ( point of intersection of two lines)
-1/2 x-2x = -10-5 solve for x
-5/2 x=-15
x=-30/-5=6
y=2x- 10 substitute x in the equation to get y
y=2(6)-10
y=2
(2,3)
Dont put the other answer, it’s wrong I
did the math.
A car rental agency rents 210 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income?
Answer:
x=7.5
Step-by-step explanation:
Rental: R(x)=(27+x) dollar per day
Number of cars rented: N(x)
=(210-5x)
Income: I(x) =(27+x)(210-5x)
=5670 - 135x + 210x-5x^2
=5670+75x-5x^2
The maximum will be achieved when the derivative of
I(x) =zero.
I(x)=5670+75x-5x^2
dI(x)/dx=75-10x=0
75-10x=0
75=10x
x=75/10
=7.5
x=7.5
x=7.5 is the rate at which the car will be rented to produce maximum income.
The maximum income could be derived by using x=7 or x=8
27+7=$34 per day
27+8=$35 per day
When x=7
I(x)=5670+75x-5x^2
=5670+75(7)-5(7)^2
=5670+525-5(49)
=5670+525-245
=5,950
When x=8
I(x)=5670+75x-5x^2
=5670+75(8)-5(8)^2
=5670+600-5(64)
=5670+600-320
=5950
Either x=7 or 8 will yield the same income
Robert want to buy a sports cap that is on sale for 25% off if the original price is 35$ and the sales tax is 6% how much will robert need to pay for the cap
Answer: $27.825
Step-by-step explanation:
From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:
= Original price - Discount
= $35 - (25% × $35)
= $35 - (0.25 × $35)
= $35 - $8.75
= $26.25
We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:
= $26.25 + (6% × $26.25)
= $26.25 + (0.06 × $26.25)
= $26.25 + $1.575
= $27.825
Answer:
27.83
Step-by-step explanation:
Please answer this question fast in two minutes
Answer:
∠CGA or ∠DGF
Step-by-step explanation:
Supplementary angles add up 180°
∠CGD + ∠CGA = 180°
∠CGD + ∠DGF = 180°
Bottle A contains more soda than Bottle B. Pour from Bottle A into Bottle B as much soda as B already contains. Now pour from B into A as much soda as A now contains. Then pour from A into B as much soda as B now contains. Each bottle now contains 64 ounces. How many more ounces of soda were in Bottle A than Bottle B at the beginning?
Answer:
Bottle A started with 88 and bottle B started with 40
Step-by-step explanation:
To find out what they started with I got the ounces they finished with an the equation they did to get there.
Ended in 64 oz.
To get there:
A => B
B => A
A => B
Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.
B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.
Now you have this equation:
A => B
B => A
96 oz. => 32 oz.
64 oz.
I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.
Now you have this equation:
A => B
80 oz. => 48 oz.
96 oz. => 32 oz.
64 oz.
For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.
The Answer:
88 oz. => 40 oz.
80 oz. => 48 oz.
96 oz. => 32 oz.
Both will end up with 64 oz.
PLEASE HELP ME I WILL MAKE YOU THE FAMOUS
Which description matches the graph of the inequality y<-1/2x+5 A.a shaded region above a dashed boundary line B.a shaded region below a dashed boundary line C.a shaded region below a solid boundary line D.a shaded region above a solid boundary line
Answer:
B
Step-by-step explanation:
dashed line above the shaded area, shaded area below dashed boundary line
(-3)(-)-4+ (-2)(09-11)
Slove the problem
Answer:
The answer is -8
Step-by-step explanation:
(3)(-4)=-12 (-2)(-2)=4
Please help me with this question (Will get brainlist)
Answer:
169=169
Step-by-step explanation:
The pythagoras theorem states that if
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
Then the triangle is a right triangle
So
[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex]25 + 144 = 169[/tex]
[tex]169 = 169[/tex]
Therefore A is a right triangle
Answer:
Step-by-step explanation:
The pythagorian theorem :now the longest edge is 13 cm so : 13²must be equal to 5²+12²
5²+12²= 169[tex]\sqrt{169}[/tex]= 13so this triangle must be right angled
Solve for x. 7x=28 4x=48
Answer: x=4
x=12
Step-by-step explanation:
7x=28
divide 7 on both sides
28/7=4
x=4
4x=48
divide 4 on both sides
48/4=12
x=12
what is the slope intercept of the line y=2x+4
Answer:
Slope = 2
Y intercept = 4
Step-by-step explanation:
This is of the form y = mx + k
where m is the slope
K = y intercept
Hello! (:
y=2x+4
This equation is written in slope-intercept form:
y=mx+b
m is the slope (2) and b is the y-intercept (4)
Hope it helps!
If you have any question or query, feel free to ask! (:
~An excited gal
[tex]SparklingFlower[/tex]
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
-3(x-1) + 8(x-3) = 6x + 7 - 5x
Answer:
x=7
Step-by-step explanation:
-3(x-1)+8(x-3)=6x+7-5x
-3x+3+8x-24=6x+7-5x
5x-21=x+7
4x=28
x=7
Answer:
x=7
Step-by-step explanation:
-3(x-1) + 8(x-3) = 6x + 7 - 5x
Distribute
-3x +3 +8x -24 = 6x +7 -5x
Combine like terms
5x -21 = x+7
Subtract x from each side
5x-x-21 = 7
4x -21 =7
Add 21 to each side
4x-21+21 = 7+21
4x = 28
4x/4 = 28/4
x=7
The prime factorization of 324 can be written as 2^a x 3^b, where a = and b=
Answer: 2, 4 then c=4 also and B for the next one :)
Step-by-step explanation: Giving away 100 points be the first to comment on my " question " stay tuned!
25. En cada par de triangulos, las marcas iguales indican elementos congruentes. ¿Que par de triangulos es congruentre segun el criterio LAL? justifica 26.indica cual criterio se debe usar para determinar la congruencia de cada pareja de triangulos.
Answer:
i cant read spanish. sorry
Step-by-step explanation:
Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and they are both dimes. He says the probability of that occurring is 1 4 because 2 of the 8 coins are dime
Answer: No. Choosing two dimes are dependent events. The probability of choosing the first dime is 1/4 and the probability of choosing the second dime is 1/7. The probability that both coins are dimes is (1/4)(1/7) = 1/28.
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/8×1/7=1/28
Question is down below
Answer:
a ) [tex]2 / n[/tex],
b ) [tex]15[/tex]
Step-by-step explanation:
This is a nice and short question we have here.
Given that a bag has n counters, and that one counter is blue, respectively the rest is red, if two counters are taken at random there isn't a definite percentage that one of the counters chosen is red or blue, but there is a fractional representation of this.
We could express n ( number of counters ) to form a probability of 2 / n. As you can see, two counters are taken at random over n counters, and thus we derived this fraction.
a ) [tex]2 / n[/tex]
____
Now we have this second part -
[tex]2 / n = 2 / 16,\\16 - 1 = 15[/tex]
Therefore, there are 15 red counters. Hope that helps!
CAN SOMEONE TUTOR ME PLSSSSS ????
Answer:
[tex] \frac{105}{4} [/tex]
please see the attached picture for full solution..
hope it helps...
Good luck on your assignment..
how to solve: f(-1)=(1/4)^x
Answer:
f(-1) = (1/4)^x = 4
Step-by-step explanation:
When solving a f(x) equation, the x represents the number that will be used to replace x in the equation. So, from the equation, the value of x is -1. You would plug in -1 for x.
f(-1) = (1/4)^-1
Solve the exponent.
f(-1) = 4
So, the value of f(-1) is 4.
PLEASE HELP ME! can someone explain this to me pls?
Write the unit rate for the situation.
read 80 pages in 2 hours
20 pages/h
40 pages/h
8 pages/h
160 pages/h
Answer:
40 pages / hour
Step-by-step explanation:
Take the number of pages and divide by the number of hours
80 pages/ 2 hours
40 pages / hour
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed: Step 1. Declare the variable: Let x = the number of student signatures still needed. Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction. Step 3. Convert 25% to a decimal: 25% = 0.25. Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25. What is Jose’s error? In Step 1, x should be equal to the total number of students in the school. In Step 2, the ratio should be StartFraction x over 426 EndFraction. In Step 3, the decimal should be 0.025. In Step 4, the inequality should
Answer: Step 4
Step-by-step explanation:
1. Define variable x as student signatures still needed (Correct)
[tex]2)\ \dfrac{x+82}{426}[/tex] (Correct)
3. 25% = 0.25 (Correct)
[tex]4)\ \dfrac{x+82}{426}\leq 0.25[/tex] (Error)!
The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).
Answer:
In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.
¯\_ _/¯
( ﾉ ﾟｰﾟ)ﾉ ＼(ﾟｰﾟ＼)
Factor completely.
a 2 + 28 a + 27
Hey there! :)
Answer:
(x + 27)(x + 1)
Step-by-step explanation:
Given:
a² + 28a + 27
Find numbers that add up to 28 and multiply to 27:
We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:
(x + 27)(x + 1)
Answer:
(a+27)(a+1)Solution,
[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]
Hope this helps..
Good luck on your assignment..
The length of a rectangle is 2 less than 3 times its width. If the area of the rectangle is 96cm², what is the length of the rectangle?
Answer:
[tex] \boxed{\sf Length \ of \ the \ rectangle = 16 \ cm} [/tex]
Given:
Area of the rectangle = 96 cm²
Length of the rectangle = 2 less than 3 times it's width
To Find:
Length of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w'.
So,
Length of the rectangle = 3w - 2
[tex]\sf \implies Area \ of \ rectangle = Length \times Width \\ \\ \sf \implies 96 = (3w - 2) \times w \\ \\ \sf \implies 96 = 3 {w}^{2} - 2w \\ \\ \sf \implies 3 {w}^{2} - 2w = 96 \\ \\ \sf \implies 3 {w}^{2} - 2w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - (18 - 16)w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - 18w + 16w - 96 = 0 \\ \\ \sf \implies 3w(w - 6) + 16(w - 6) = 0 \\ \\ \sf \implies (w - 6)(3w + 16) = 0 \\ \\ \sf \implies w - 6 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 3w + 16 = 0 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: 3w = - 16 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: w = - \frac{16}{3} [/tex]
Width can't be negative. So,
Width of the rectangle = 6
Length of the rectangle = 3w - 2
= 3(6) - 2
= 18 - 2
= 16 cm
The length of the rectangle is 16 cm
The width of the rectangle is 6 cm
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be = 96 cm²
Let the length of the rectangle be = L
Let the width of the rectangle be = W
Now ,length of a rectangle is 2 less than 3 times its width
Substituting the values in the equation , we get
L = 3W - 2
Now , the area of the rectangle = L x W
So ,
96 = ( 3W - 2 ) x W
On simplifying the equation , we get
96 = 3W² - 2W
Subtracting 96 on both sides of the equation , we get
3W² - 2W - 96 = 0
3W² - 18W + 16W - 96 = 0
Taking 3W as the common factor , we get
3W ( W - 6 ) + 16 ( W - 6 ) = 0
( W - 6 ) ( 3W + 16 ) = 0
Now , the width of the rectangle cannot be negative , so
W - 6 = 0
Adding 6 on both sides of the equation , we get
W = 6 cm
Now , the length of the rectangle L = 3W - 2
L = 3 ( 6 ) - 2
L = 18 - 2
L = 16 cm
Therefore , the value of L is 16 cm
Hence , the length of the rectangle is 16 cm
To learn more about area of rectangle click :
https://brainly.com/question/15225905
#SPJ2
Here are two squares, A and B.
A
B
The length of the side of square A is 50% of the length of the side of square B.
Express the area of the shaded region of square A
as a percentage of the area of square B.
otal marks: 3
Submit Answer
The two squares and the shaded region of square A is in the attachment.
Answer: The shaded region of A is 12.5% of the area of B.
Step-by-step explanation: Assume that the length of side of square A is a and the length of side of square B is b.
Length a is half (50%) of length b:
a = [tex]\frac{b}{2}[/tex]
The shaded region is a triangle. The area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
b and h are the sides of the square A, so:
[tex]A_{1}[/tex] = [tex]\frac{\frac{b}{2}.\frac{b}{2}}{2}[/tex]
[tex]A_{1} = \frac{b}{2}.\frac{b}{2}.\frac{1}{2}[/tex]
[tex]A_{1} = \frac{b^{2}}{8}[/tex]
Area of square B is:
[tex]A_{2}[/tex] = b.b
[tex]A_{2} = b^{2}[/tex]
Comparing areas:
[tex]\frac{\frac{b^{2}}{8} }{b^{2}}[/tex] = [tex]\frac{b^{2}}{8}.\frac{1}{b^{2}}[/tex] = [tex]\frac{1}{8}[/tex]
As percentage:
[tex]\frac{1}{8}[/tex] × 100 = 0.125 × 100 = 12.5%
Comparing the shaded region of A to square B, the area of the first is 12.5% smaller than the second.