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3 years ago

A positive integer squared plus 3 times it’s consecutive integer is equal to 43

Mathematics

2 answers:

Jobisdone [24]3 years ago

5 0

Answer:

Step-by-step explanation:

let positive integer be x

x² + 3(x+1)=43

x²+3x+3-43=0

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x+8) - 5(x+8)=0

(x-5)(x+8)=0

x-5=0 or x+8=0

x=5. or x=-8

but the question says positive integer,

therefore, x=5

Eduardwww [97]3 years ago

3 0

Answer:

the integer is 5

Step-by-step explanation:

x^2+3(x+1)=43

x^2+3x+3=43

x^2+3x+(9/4)=43-3+(9/4)

(x+(3/2))^2=42 1/4

x+(3/2)=sqrt(42 1/4)

x+(3/2)=6 1/2

x=(6 1/2)-(3/2)

x=5

check:

5^2+3(6)=43

25+18=43

43=43

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I am in need of assistance.

Alex_Xolod [135]

Answer:

A. x = 6.08, x = -0.58

Step-by-step explanation:

$\displaystyle \frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24}=\frac{-3}{x-6}$

1. Factor the denominator.

$\displaystyle \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

2. Multiply the leftmost fraction by (x-6)/(x-6) to get common denominators.

$\displaystyle \Big ( \frac{x-6}{x-6} \Big ) \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

3. Simplify.

$\displaystyle \frac{2x^2-12x}{(x-4)(x-6)}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

4. Combine like terms.

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6}$

5. Multiply the right side of the equation by (x-4)/(x-4).

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6} \Big ( \frac{x-4}{x-4} \Big )$

6. Simplify.

$\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3x+12}{(x-6)(x-4)}$

7. "Cancel" out the denominators because they are equivalent.

$2x^2-14x+5=-3x+12$

8. Set the equation equal to 0.

$2x^2-11x-7=0$

Quadratic formula:

$\displaystyle x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}$

9. Factor using the quadratic formula.

$\displaystyle x = \frac{-(-11)\pm \sqrt{(-11)^2-4(2)(-7)} }{2(2)}$

10. Multiply and simplify.

$\displaystyle x = \frac{11 \pm \sqrt{177} }{4}$

11. Plug this into your calculator and solve for x.

$x=6.07603367 \approx 6.08$
$x=-0.57603367 \approx -0.58$

The correct answer is A. x = 6.08, x = -0.58.

8 0

3 years ago

Solve this puzzle !!

olganol [36]

3.
12 ÷ 2 = 6
27 ÷ 3 = 9
24 ÷ 4 = 6
30 ÷ 3 = 10
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7 0

4 years ago

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Bruce's hourly wage increased from $12.00 to $13.00. What is the percent of increase?

Tanya [424]

2% i think hopefully it's right

5 0

3 years ago

Each cube represents 1 cubic inch. What is the volume if the prism?

sashaice [31]

Answer:

12 in³

Step-by-step explanation:

Its made up of 12 (4×3 = 12) cubes of 1 in³ each

So 12 × 1 = 12 in³

6 0

3 years ago

A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of

tensa zangetsu [6.8K]

Answer:

<em>The height of the building is 21.38 m</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

$\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 22^\circ=\frac{H}{D+B}$

Multiplying by D+B:

$\tan 22^\circ(D+B)=H$

Dividing by tan 22°

$\displaystyle D+B=\frac{H}{\tan 22^\circ}$

Subtracting B:

$\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1]$

Applying to the smaller triangle:

$\displaystyle \tan 33^\circ=\frac{H}{D}$

Multiplying by D:

$\tan 33^\circ D=H$

Substituting from [1]:

$\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H$

Substituting values:

$\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H$

Operating:

$1.6074H-12.988=H$

$1.6074H-H=12.988$

$0.6074H=12.988$

$H = 12.988/0.6074$

H = 21.38 m

The height of the building is 21.38 m

3 0

3 years ago