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3 years ago

0.5a − 0.3 = 5 (solve for a)

Mathematics

2 answers:

Alla [95]3 years ago

3 0

0.5a - 0.3 = 5

Add 0.3 to both sides:

0.5a = 5.3

Divide both sides by 0.5:

a = 10.6

son4ous [18]3 years ago

3 0

$0.5a - 0.3 = 5 \ |\times 10 \\\\ 5a-3=50 \ |+3 \\\\ 5a=53 \ |:5 \\\\ a=\frac{53}{5} \\\\ a=10\frac{3}{5}\\\\ a=10.6$

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In the given figure find the value of x and y?<br>Show you works - Thank you!

Vaselesa [24]

<u>EXPLANATION</u><u>:</u>

In ∆ ABC , ∠ABC = 40°

∠CAB = x°
& ∠ACD = 50°

∠ACD is an exterior angle formed by extending BC to D

We know that

The exterior angle of a triangle formed by extending one side is equal to the sum of the opposite interior angles.

∠ACD = ∠CAB + ∠ABC

⇛50° = x° + 40°

⇛x° = 50°-40°

and

In ∆ ACD , AC = CD

⇛ ∠CDA = ∠CAD

Since the angles opposite to equal sides are equal.

Let ∠CDA = ∠CAD = A°

We know that

The sum of all angles in a triangle is 180°

In ∆ ACD,

∠CDA +∠CAD + ∠ACD = 180°

A°+A°+50° = 180°

⇛2A°+50° = 180°

⇛2A° = 180°-50°

⇛2A° = 130°

⇛A° = 130°/2

⇛A° = 65°

now,

∠CDA = ∠CAD = 65°

∠BAC + ∠CAD+y = 180°

Since angles in the same line

10°+65°+y = 180°

⇛75°+y =180°

⇛y = 180°-75°

<u>Answer</u><u>:</u> Hence, the value of “x” & “y” will be 10° and 105° respectively.

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3 years ago

Find the roots of:

Elena-2011 [213]

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Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

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So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

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Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

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Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

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2 years ago

Lily has two times as much money invested in 8% stocks as she has in bonds paying 6%. How much she has invested in stocks if her

EleoNora [17]

Answer:

Final answer is $4440.

Step-by-step explanation:

Let amount of money invested in 8% stock = x

Let amount of money invested in 6% stock = y

then total money invested $325.6 gives equation

8% of x + 6% of y = 325.6

0.08x + 0.06y = 325.6

8x + 6y = 32560...(i)

other equation will be x=2y...(ii)

plug (ii) into (i)

8x + 6y = 32560

8(2y) + 6y = 32560

16y+ 6y = 32560

22y = 32560

$y=\frac{32560}{22}$

y=1480

plug y=1480 into (ii)

x=2y=2(1480)=2960

Then total money invested in stocks = x+y= 1480+2960=4440

Hence final answer is $4440.

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3 years ago

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MAXImum [283]

Answer: the answer to ur question is A. Hope this helps plz mark brainliest:)

Step-by-step explanation:

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3 years ago