The legs of a right triangle measure 9 inches and 12 inches. What is the length of the hypotenuse of this triangle?

Answers

Answer 1

Answer:

The length of the hypotenuse of this triangle is 15 inches.

What is Pythagoras Theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

In this case, let's label the legs of the triangle as a and b, with a = 9 inches and b = 12 inches. Let c be the length of the hypotenuse that we want to find. Then the Pythagorean theorem can be written as:

c² = a² + b²

Substituting the values we know, we get:

c² = 9^2 + 12^2

c² = 81 + 144

c² = 225

Taking the square root of both sides, we get:

c = √225

c = 15

Therefore, the length of the hypotenuse of this triangle is 15 inches.

Learn more about Pythagorean theorem here:

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Answer 2

Answer: legs legnth a and b, and hypotnuse c
a^2+b^2=c^2
legs are 9 and 12
a=12
b=9
12^2+9^2=c^2
144+81=c^2
225=c^2
sqrt both sides
15=c

the legnth of the hyptonuse is 15 inches

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Find the possible values for s in the inequality 12s – 20 ≤ 50 – 3s – 25.

Answers

12s - 20 < 50 - 3s - 25

12s - 20 < 50 - 3s - 25
+3s +3s
15s - 20 < 50 - 25
+ 20 + 20
15s < 70 - 25

15s < 45
÷ 15 ÷15
s < 3

The value of s is less than or equal to 3. So s can be 3, 2, 1, 0, and negative numbers.

s = 3 ⇒ 12(3) - 20 < 50 - 3(3) - 25 ; 36 - 20 < 50 - 9 - 25 ; 16 < 16
s = 2 ⇒ 12(2) - 20 < 50 - 3(2) - 25 ; 24 - 20 < 50 - 6 - 25 ; 4 < 19

Sarah put raisins into 3/4 of the oatmeal cookie dough she was making. She put nuts into 2/5 of the oatmeal cookie dough with the raisins. What fraction of the entire batch has BOTH raisins and nuts.

Answers

The LCM (lowest common multiple) of 4 and 5 is 20, so convert them so that the denominator is 20:

3/4 = 15/20
2/5 = 8/20

I didn't quite read the question properly, but regardless. Since only 15/20 of the batch has raisins, of which only 8/20 has nuts, we can formulate this equation to solve:

1x15/20x8/20
=3/10

The table and the graph each show a different relationship between the same two variables, x and y:A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,180 and 4,240 and 5,300 and 6,360. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.

How much more would the value of y be in the table than its value on the graph when x = 11?

110
150
215
275

Answers

Answer:

The value of y be in the table is 275 more than its value on the graph when x = 11.

Step-by-step explanation:

The slope represent the changer is y with respect to change in x.

$Slope=(y_2-y_1)/(x_2-x_1)$

From the table it is noticed that the value of y increased by 60 as the value of x increased by 1. Therefore the slope of the function is 60. It is also calculated by the formula. The two points from the table are (3,180) and (4,240).

$Slope=(240-180)/(4-3)=60$

The point slope form is,

$y-y_1=m(x-x_1)$

The equation of function is,

$y-180=60(x-3)$

$y-180=60x-180$

$y=60x$

Put x=11

$y=60* 11=660$

Therefore the value of table is 660 at x=11.

The two points from the graph are (2,70) and (4,140).

$Slope=(140-70)/(4-2)=35$

The equation of line is,

$y-70=35(x-2)$

$y-70=35x-70$

$y=35x$

Put x=11

Therefore the value of line is 385 at x=11.

The difference between values of y at x=11 is,

$660-385=275$

Therefore the value of y be in the table is 275 more than its value on the graph when x = 11.

Answer:

the answer is 275.

i got it right on my test.

Please help me with this! I would appreciate it :)

Answers

1. b. Commutative Property of Addition
Reason: There is no multiplication used

2. a. 60
Reason: 36 + 24 = 60

3. b. 3d + 9
Reason: Simplification and combining like terms :)

4. b. 4,-1
Reason: Coefficients are the numbers in front of variables

5. b. 36m + 9
Reason: Just use distributive property (multiply 9 into both terms inside parenthesis)

6. b. 95.488
Reason: b = 165.288 - 39.7 - 30.1

7. The question is cut off, unanswerable

8. c. 5a, -3a
Reason: Like terms are things you can combine. So technically the answers could be b. and c. but just go with c. because they have variables.

9. b. 16
Reason: just add 4 to both sides to get the "a" by itself

Best of luck to you!

Which choice is equivalent to the expression below when y 0?√Y^+√9Y^3-3Y√Y

A.Y√10Y-3Y√Y
B.-2Y√11Y
C.Y√Y
D.√10Y^3-3Y√Y

Answers

$y√(y)+√(9y^3)-3y√(y)=y√(y)+\sqrt9\cdot√(y^2\cdot y)-3y√(y)\n\n=y√(y)+3y√(y)-3y√(y)=y√(y)\n\nAnswer:C.$

A stadium has 55,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,158,000 from each sold-out event. How many seats does each section hold?

Answers

A=number of seats in section A
B=number of seats in section B
C=number of seats in section C

We can suggest this system of equations:

A+B+C=55,000
A=B+C ⇒A-B-C=0
28A+16B+12C=1,158,000

We solve this system of equations by Gauss Method.

1      1     1    55,000
1 -1 -1    0
28 16       12    1,158,000

1      1     1    55,000
0 -2    -2    -55,000      (R₂-R₁)
0    12    16     382,000    (28R₁-R₂)

1 1 1 55,000
0    -2 -2    -55,000
0 0     4     52,000 (6R₂+R₃)

Therefore:

4C=52,000
C=52,000/4
C=13,000

-2B-2(13,000)=-55,000
-2B-26,000=-55,000
-2B=-55,000+26,000
-2B=-29,000
B=-29,000 / -2
B=14,500.

A + 14,500+13,000=55,000
A+27,500=55,000
A=55,000-27,500
A=27,500.

Answer: there are 27,500 seats in section A, 14,500 seats in section B and 13,000 seats in section C.

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$25;300%increse percent change