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jek_recluse [69]

4 years ago

11

Factorise the following equation:

x^2+17x+5" align="absmiddle" class="latex-formula">

1 answer:

RSB [31]4 years ago

8 0

Answer:

(3x+1)(2x+5) is the answer

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Find the area of triangle ABC with vertices A(2,1), B (12,2), C (12,8). Hence, or otherwise find the perpendicular distance from

Lapatulllka [165]

<h2>The area of a triangle is =54 square units</h2><h2>The perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$ </h2>

Step-by-step explanation:

Given a triangle ABC with vertices A(2,1),B(12,2) and C(12,8)

$x_1=2,y_1=1,x_2=12,y_2=2,x_3=12 and y_3=8$

The area of a triangle is= $\frac{1}{2} [x_1(y_2-y_3) +x_2 (y_3- y_1)+x_3(y_1-y_2)]$

= $|\frac{1}{2} [2(2-8+12(8-1)+12(1-2)]|$

= $|-54|$ = 54 square units

The length of AC = $\sqrt{(x_1-x_3)^{2} +(y_1-y_3)^2}$

= $\sqrt{(2-12)^{2} +(1-8)^2}$

= $\sqrt{149}$ units

Let the perpendicular distance from B to AC be = x

According To Problem

$\frac{1}{2} \times x \times \sqrt{149} = 54$

⇔ $x =\frac{108}{\sqrt{149} }$ units

Therefore the perpendicular distance from B to AC is = $\frac{108}{\sqrt{149} } units$

5 0

3 years ago

Identify whether the given numbers are perfect squares, perfect cubes, or neither.

Anna [14]

8- perfect cube. 2×2×2=8
9-perfect square. 3×3=9
21- neither.
27- perfect cube. 3×3×3=27
1331- perfect cube. 11×11×11=1331
1332- neither
100- perfect square. 10×10=100
1000- perfect cube. 10×10×10=1000
126- neither
125- perfect cube. 5×5×5=125
25-perfect square. 5×5=25
81-perfect square. 9×9=81

5 0

3 years ago

What is (+5) - (-1) - (-3)

maksim [4K]

+ = positive
Positive and positive makes a positive

Negative and negative makes a positive

- = negative
Negative and positive makes a negative

Positive and negative makes a negative

Your answer: +5 - (-1) = 6
+6 - (-3) = +9
Your answer that youre looking for is: 9

4 0

3 years ago

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of

Nesterboy [21]

Answer:

$P=400000(2^t)-40000t$

Step-by-step explanation:

The initial number of mosquitoes is 400000, and they double each day. This represents an exponential growth equation. If t represent days and P represent the population of the mosquitoes, hence this can be represented by the equation:

$P=400000(2^t)$

Also, the predators eat the mosquitoes at a rate of 40,000 mosquitoes/day. This means that each day, the mosquitoes reduce by 40000t, therefore this can be represented by:

$P=400000(2^t)-40000t$

8 0

3 years ago

What is the factored form of the expression. (2n^2 + 5n + 3) (4n - 5)

7nadin3 [17]

So firstly, <u>the factor (4n - 5) cannot be further factored, so we will be focusing on 2n² + 5n + 3.</u>

So for this, we will be factoring by grouping. Firstly, what two terms have a product of 6n² and a sum of 5n? That would be 2n and 3n. Replace 5n with 2n + 3n:

$(2n^2 + 2n + 3n + 3)(4n - 5)$

Next, factor 2n² + 2n and 3n + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(2n(n+1)+3(n+1))(4n-5)$

Now we can rewrite this expression as<u> $(2n+3)(n+1)(4n-5)$ , which is your final answer.</u>

7 0

3 years ago