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Kitty [74]
1 year ago
10

Pls solve question 4b. Verrry urgent . Ok tyy

Mathematics
1 answer:
kodGreya [7K]1 year ago
8 0

Answer:

y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}

Step-by-step explanation:

Given equation:

y = 3x^2 - 9x + 17

Factor out 3 from the first 2 terms:

y = 3(x^2 - 3x) + 17

Divide the coefficient of x by 2 and square it:  (-3 ÷ 2)² = 9/4

Add this inside the parentheses and subtract the distributed value of it outside the parentheses:

y = 3\left(x^2 - 3x+\dfrac{9}{4}\right) + 17-\dfrac{27}{4}

Factor the parentheses and combine the constants:

y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}

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Given: AB || DE , AD bisects BE.<br> Prove: ABC = DEC using the ASA postulate.
Ket [755]

Answer:

As per ASA postulate, the two triangles are congruent.

Step-by-step explanation:

We are given two triangles:

\triangle ABC and \triangle DEC.

AD bisects BE.

AB || DE.

Let us have a look at two properties.

1. When two lines are parallel and a line intersects both of them, then <em>alternate angles </em>are equal.

i.e. AB || ED and \angle B and \angle E are alternate angles \Rightarrow \angle B = \angle E.

2. When two lines are cutting each other, angles formed at the crossing of two, are known as <em>Vertically opposite angles </em>and they are are <em>equal</em>.

\Rightarrow \angle ACB = \angle DCE

Also, it is given that <em>AD bisects BE</em>.

i.e. EC = CB

1. \angle B = \angle E

2. EC = CB

3. \angle ACB = \angle DCE

So, we can in see that in \triangle ABC and \triangle DEC, two angles are equal and side between them is also equal to each other.

Hence, proved that \triangle ABC \cong \triangle DEC.

8 0
3 years ago
Hurry please!
joja [24]

Answer:

Slope of the line x +2y =14 will be -1/2 since y = -1/2x+7, where m = -1/2 and c = 7.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none
Marysya12 [62]

Answer:  The required solution of the given system is

(x, y) = (3, 1)  and  (4, 0).

Step-by-step explanation:  We are given to solve the following system of equations :

x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

From equation (i), we have

x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

Substituting the value of y from equation (iii) in equation (ii), we get

y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.

When, x = 3, then from (iii), we get

y=4-3=1.

And, when x = 4, then from (iii), we get

y=4-4=0.

Thus, the required solution of the given system is

(x, y) = (3, 1)  and  (4, 0).

8 0
3 years ago
Mr. Hollins determines that he gives away $800 each month. If he gives away 16% of his budget, then how much is his overall budg
Fynjy0 [20]

Answer:

5000 dollars

Step-by-step explanation:

Let his budget be x

16% of x is 800 dollars

.16 * x = 800

Divide each side by .16

.16x/.16 = 800/.16

x=5000

His budget is 5000 dollars

6 0
1 year ago
At what point do the lines y = x + 7 and y = 5x - 13 intersect?​
borishaifa [10]
(x,y)
(3.5,10.5) this is where they meet
6 0
3 years ago
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