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Ugo [173]
2 years ago
6

Write the equation of the line that passes through (0, 3) and is parallel to the line 3x + 5y = 6.

Mathematics
1 answer:
Pavel [41]2 years ago
3 0
Please, see the offered decision:
1) common equation for lines is y=kx+b. If k₁=k₂ (for line 1 and line 2) ⇒ 'line 1' || 'line 2'.
2) for line 3x+5y=6   k= -3/5. It means (according to item 1) for unknown line k is the same (-3/5).
3) using points (0;3) it is easy to find parameter b (x=0, y=3) via y=kx+b:
3=0*(-3/5)+b ⇔ b=3.
4) finaly (k=-3/5; b=3):
y=- \frac{3}{5}x+3 \ or \ 3x+5y=15
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Find the volume of a square based pyramid like you see below if the side of the base is 10 inches and the height of the the tria
Mekhanik [1.2K]

Answer:

The volume of a square based pyramid is <u>645.3 cubic inches</u>.

Step-by-step explanation:

Given:

The side of the base is 10 inches and the height of the the triangular face is 20 inches.

Now, to find the volume of square based pyramid.

Base side (a) = 10 inches.

Slant Height (s) = 20 inches.

Now, to get the height of pyramid by using pythagorean theorem:

Leg 1 = \frac{base}{2}=\frac{10}{2}=5\ inches.

Hypotenuse = 20 inches.

So,

Hypotenuse² = (leg 1)² + (leg 2)²

20^2=5^2+leg2^2\\400=25+leg2^2\\Subtracting\ both\ sides\ by\ 25 \ we\ get:\\375=leg2^2

<em>Using square root on both sides we get:</em>

<em />19.36=leg2<em />

<em>leg 2 = 19.36 inches.</em>

Thus, the height of pyramid = 19.36 inches.

Now, to get the volume of square pyramid we put formula:

h = 19.36 inches.

a = 10 inches.

Volume=a^2\frac{h}{3}

Volume=10^2\times \frac{19.36}{3}

Volume=100\times 6.453

Volume=645.3\ cubic\ inches.

<u><em>Hence, the volume to the nearest tenth is 645.3 cubic inches.</em></u>

Therefore, the volume of a square based pyramid is 645.3 cubic inches.

3 0
2 years ago
Austin drove 455 miles in 7 hours.
Effectus [21]

Answer:

9 hours

Step-by-step explanation:

455/7 gives you the mph

which is 65

then divide 585 miles by the mph (65)

585/65

= 9 hours

3 0
2 years ago
Find the length of the third side to the nearest tenth.<br> Hurry need help asap!!
gavmur [86]

Answer:

2.8

Step-by-step explanation:

6 0
2 years ago
Use the discriminant to find the number and type of solution for x^2+6x=-9​
likoan [24]

Answer:

D = 0; one real root

Step-by-step explanation:

Discriminant Formula:

\displaystyle \large{D =  {b}^{2}  - 4ac}

First, arrange the expression or equation in ax^2+bx+c = 0.

\displaystyle \large{ {x}^{2}  + 6x =  - 9}

Add both sides by 9.

\displaystyle \large{ {x}^{2}  + 6x + 9 =  - 9 + 9} \\  \displaystyle \large{ {x}^{2}  + 6x + 9 =  0}

Compare the coefficients so we can substitute in the formula.

\displaystyle \large{a {x}^{2}  + bx + c =  {x}^{2}  + 6x + 9 }

  • a = 1
  • b = 6
  • c = 9

Substitute a = 1, b = 6 and c = 9 in the formula.

\displaystyle \large{D =  {6}^{2}  - 4(1)(9)} \\  \displaystyle \large{D =  36 - 36} \\  \displaystyle \large{D =  0}

Since D = 0, the type of solution is one real root.

6 0
2 years ago
Philip did 14 setups on Monday 21 sit-ups on Tuesday and 28 sit-ups on Wednesday if the pattern continues how many sit-ups will
g100num [7]
So you add 7 every time so,

28+7=34
34+7=41

if he continues his pattern he will have done 41 sit-ups on Friday
7 0
3 years ago
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