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Xelga [282]
3 years ago
9

Factorise the following quadratic equations ​

Mathematics
2 answers:
vesna_86 [32]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

In 13 - 17

Consider the factors of the constant term which sum to give the coefficient of the x- term

13

x² - x - 42 = (x - 7)(x + 6)

15

x² + x - 6 = (x + 3)(x - 2)

17

x² - 27x + 50 = (x - 25)(x - 2)

19

r² - 25 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

r² - 25

= r² - 5² = (r - 5)(r + 5)

stich3 [128]3 years ago
4 0

1. (x+6)(x-7)

2. (x+3)(x-2)

3. (x-2)(x-25)

4. (x-5)(x+5)

I hope it helps

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Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.
SOVA2 [1]

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

X(-3, -5), Y(2, 6), Z(6, 3)

The vectors are;

z = \left \langle 2 - (-3), 6 - (-5) \right \rangle = \left \langle 5, 11  \right \rangle

y = \left \langle 6 - (-3), 3 - (-5)  \right \rangle = \left \langle 9, 8 \right \rangle

x = \left \langle 2 - 6, 6 - 3  \right \rangle = \left \langle -4, 3  \right \rangle

cos (\alpha ) = \dfrac{z \cdot y}{\left |  z \right | \times \left | y  \right |}

Therefore, we get;

cos (\alpha ) = \dfrac{5 \times 9  + 11 \times 8 }{\left |  \sqrt{5^2 + 11^2}  \right | \times \left | \sqrt{9^2 + 8^2}   \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = \left \langle -9, -8 \right \rangle

We get;

cos (\gamma) = \dfrac{-y \cdot x}{\left |  -y \right | \times \left | x  \right |}

Therefore;

cos (\gamma) = \dfrac{-9 \times -4  + -8 \times 3 }{\left |  \sqrt{(-9)^2 + (-8)^2}  \right | \times \left | \sqrt{(-4)^2 + 3^2}   \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

23.92°, 78.503°, and 77.577°

4 0
2 years ago
<img src="https://tex.z-dn.net/?f=3q%2B2p%2B7" id="TexFormula1" title="3q+2p+7" alt="3q+2p+7" align="absmiddle" class="latex-for
kirza4 [7]

Answer:

that seem pretty hard but i think ik it

6 0
3 years ago
- 2 + 0.8) ÷ (- 1.3) =<br><img src="https://tex.z-dn.net/?f=%20%28%20-%202%20%2B%200.8%29%20%5Cdiv%20%28%201%7D%5E%7B2%7D%20%20-
Nookie1986 [14]
(-2 + 0.8) ÷ (1²-1.3) =

(-1.2) ÷ (1-1.3)

(-1.2) ÷ (-0.3)

= 4
6 0
3 years ago
Round decimal to the nearest one . Then add 7.91+21.9=
Arte-miy333 [17]
7.91 = 8 21.9 = 22

8 + 22 = 30
7 0
3 years ago
Read 2 more answers
If there are 30 flower bouquets, 4/5 of the bouquets are daises, the rest are tulips. How many bouquets are tulips?
erastova [34]

Answer:

6 bouquets of tulips

Step-by-step explanation:

<h2><u>first find out the number of daisies.. </u></h2>

this is 4/5 * 30

= 24

there are 24 daises...

now to find the number of tulips are:

30 - 24 = 6

there a<u> 6 bouquets of tulips. </u>

4 0
3 years ago
Read 2 more answers
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