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sammy [17]
3 years ago
8

What is the value of s?

Mathematics
1 answer:
iris [78.8K]3 years ago
8 0

Answer:

17

Step-by-step explanation:

Since the triangle is a right triangle, we can use the Pythagorean theorem.

a² + b² = c²

The sum of the legs squared is equal to the hypotenuse squared.

15² + 8² = s²

225 + 64 = s²

289 = s²

√289 = s

17 = s

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Please help! i think the answer is 12 but any verification would be greatly appreciated!
ANEK [815]

Answer:

13.9 or 14

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + 13^2 = c^2

25 + 169 = 197

square root 197 to get c

c = 13.9 (14 rounded up)

Helpful thing to note is that the hyptoenuse will always be longer than your "long side" of the triangle

6 0
3 years ago
Read 2 more answers
1. Determine a rule that could be used to explain how the volume of a
Eva8 [605]

Answer:

See explanation

Step-by-step explanation:

Solution:-

- We will use the basic formulas for calculating the volumes of two solid bodies.

- The volume of a cylinder ( V_l ) is represented by:

                                  V_c = \pi *r^2*h

- Similarly, the volume of cone ( V_c ) is represented by:

                                  V_c = \frac{1}{3}*\pi *r^2 * h

Where,

               r : The radius of cylinder / radius of circular base of the cone

               h : The height of the cylinder / cone

- We will investigate the correlation between the volume of each of the two bodies wit the radius ( r ). We will assume that the height of cylinder/cone as a constant.

- We will represent a proportionality of Volume ( V ) with respect to ( r ):

                                  V = C*r^2

Where,

            C: The constant of proportionality

- Hence the proportional relation is expressed as:

                                 V∝ r^2

- The volume ( V ) is proportional to the square of the radius. Now we will see the effect of multiplying the radius ( r ) with a positive number ( a ) on the volume of either of the two bodies:

                                V = C*(a*r)^2\\\\V = C*a^2*r^2

- Hence, we see a general rule frm above relation that multiplying the result by square of the multiple ( a^2 ) will give us the equivalent result as multiplying a multiple ( a ) with radius ( r ).

- Hence, the relations for each of the two bodies becomes:

                              V = (\frac{1}{3} \pi *r^2*h)*a^2

                                          &

                              V = ( \pi *r^2*h)*a^2

8 0
3 years ago
Given SP = TP
balu736 [363]

Answer:

Step-by-step explanation:

              Statements                            Reasons

1). SP ≅ TP                                        1). Given

2). PQ bisects ∠SPT                        2). Given

3). ∠SPQ ≅ ∠TPQ                            3). Definition of angles bisector

4). PQ ≅ PQ                                      4). Reflexive property of congruence

5). ΔSPQ ≅ ΔTPQ                            5). SAS property of congruence          

7 0
3 years ago
1.
Eddi Din [679]

Answer:

a) y=\dfrac{5}{2}x

b) yes the two lines are perpendicular

c) y=\dfrac{5}{4}x+6

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form y = mx + c

5y = 7 - 2x

y = \dfrac{7 - 2x}{5}

y = \dfrac{7}{5} - \dfrac{2}{5}x

y = -\dfrac{2}{5}x+\dfrac{7}{5}

this is changed into the y = mx + c, and we easily see that -2/5 is in the place of m, hence m = \frac{-2}{5} is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

m_1m_2=-1.

here both slopesm_1 and m_2 are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

\dfrac{-2}{5}m_2=-1.

m_2=\dfrac{5}{2}.

Finally, we can find the equation of the line of the perpendicular using:

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

we know that the line passes through origin(0,0) and its slope is 5/2

(y-0)=\dfrac{5}{2}(x-0)

y=\dfrac{5}{2}x is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether m_1m_2=-1 ?

the slopes can be easily found through rearranging both equations to y=mx+c

Line:1

2x + 3y =6

y =\dfrac{-2x+6}{3}

y =\dfrac{-2}{3}x+2

Line:2

y = \dfrac{3}{2}x + 4

this equation is already in the form we need.

the slopes of both equations are

m_1 = \dfrac{-2}{3} and m_2 = \dfrac{3}{2}

using

m_1m_2=-1

\dfrac{-2}{3} \times \dfrac{3}{2}=-1

-1=-1

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be m=\dfrac{-4}{5} and the y-intercept is c=6 the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

m_1m_2=-1

\dfrac{-4}{5}m_2=-1

m_2=\dfrac{5}{4}

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

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

(y-6)=\dfrac{5}{4}(x-0)

y=\dfrac{5}{4}x+6

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0
3 years ago
The two-way table shows the number of students in a school who have rabbits and/or birds as pets:
kiruha [24]
It's 3 (total number of have rabbits that's 43 - Have rabbits which is 40) 43-40= 3

3 0
2 years ago
Read 2 more answers
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