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3 years ago

If 5x - 2y = 6 and 3x + 2y = 10, then find x

Mathematics

2 answers:

anastassius [24]3 years ago

6 0

Step-by-step explanation:

$\textsf{\large{\underline{Solution}:}}$

<h3>Given Equations:</h3>

→ 5x - 2y = 6 ----- (i)

→ 3x + 2y = 10 ---- (ii)

Adding (i) and (ii), we get:

→ 8x = 16

→ x = 16/8

→ x = 2

Substituting the value of x in (i), we get:

→ 5 × 2 - 2y = 6

→ -2y = 6 - 10

→ -2y = -4

→ y = -4/-2

→ y = 2

Therefore:

→ (x, y) = (2, 2) (Answer)

$\textsf{\large{\underline{Verification}:}}$

Put x = 2 and y = 2 in second equation, the LHS becomes:

= 5 × 2 - 2 × 2

= 10 - 4

= 6

= RHS

Put x = 2 and y = 2 in second equation, the LHS becomes:

= 3 × 2 + 2 × 2

= 6 + 4

= 10

= RHS

Hence, our answer is correct (Verified)

Hope this helps!!

Darina [25.2K]3 years ago

5 0

Answer:

x=2

Step-by-step explanation:

After solving with substitution, you would know x = 2

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A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

alukav5142 [94]

Answer:

0.17 °/s

Step-by-step explanation:

Since the ladder is leaning against the wall and has a length, L and is at a distance, D from the wall. If θ is the angle between the ladder and the wall, then sinθ = D/L.

We differentiate the above expression with respect to time to have

dsinθ/dt = d(D/L)/dt

cosθdθ/dt = (1/L)dD/dt

dθ/dt = (1/Lcosθ)dD/dt where dD/dt = rate at which the ladder is being pulled away from the wall = 2 ft/s and dθ/dt = rate at which angle between wall and ladder is increasing.

We now find dθ/dt when D = 16 ft, dD/dt = + 2 ft/s, and L = 20 ft

We know from trigonometric ratios, sin²θ + cos²θ = 1. So, cosθ = √(1 - sin²θ) = √[1 - (D/L)²]

dθ/dt = (1/Lcosθ)dD/dt

dθ/dt = (1/L√[1 - (D/L)²])dD/dt

dθ/dt = (1/√[L² - D²])dD/dt

Substituting the values of the variables, we have

dθ/dt = (1/√[20² - 16²]) 2 ft/s

dθ/dt = (1/√[400 - 256]) 2 ft/s

dθ/dt = (1/√144) 2 ft/s

dθ/dt = (1/12) 2 ft/s

dθ/dt = 1/6 °/s

dθ/dt = 0.17 °/s

8 0

3 years ago

If line ML is a midsegment of triangle IJK, find KJ

laila [671]

So what we're dealing with here is a similar triangle situation. Since ML is a midsegment, that means that IL and LJ are congruent. So, IL=LJ=13. This means that the whole side IJ is 26 (13+13=26). We also know that triangle IML and triangle IKJ are similar triangles, so their sides are proportional. This means that we can set up the ratio:
12/13 = x/26
and solve for x.
After multiplying 26 to both sides of the equation, we find that x=24, so KJ=24.

4 0

3 years ago

Read 2 more answers

The ratio of the ages (in years) of three children is 2:4:5. The sum of their ages is 33. What is the age of each child?

pickupchik [31]

We have 2x + 4x + 5x = 33 so 11x = 33 and x 3.

The children are 6, 12 and 15

5 0

3 years ago

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers

Maurinko [17]

Answer:

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(536.46, 603.54)

Step-by-step explanation:

Step:-1

Given that the mean of the Population = 540HP

Given that the size of the sample 'n' = 9

Given that the mean of the sample = 570HP

Given that the sample standard deviation = 30HP

Step(ii):-

Degrees of freedom = n-1 =9-1 =8

t₀.₀₀₅ = 3.3554

The 99% of a confidence interval for the average maximum HP for the experimental engine.

$(x^{-} - t_{\frac{0.01}{2} ,8} \frac{S.D}{\sqrt{n} } ,x^{2} + t_{\frac{0.01}{2},8 } \frac{S.D}{\sqrt{n} } )$

$(570-3.354\frac{30}{\sqrt{9} } , 570+3.354\frac{30}{\sqrt{9} } )$

(570 - 33.54 , 570+33.54)

(536.46 , 603.54)

Final answer :-

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(536.46, 603.54)

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3 years ago

75% of 32.2 is what number

Igoryamba

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3 years ago

If 5x - 2y = 6 and 3x + 2y = 10, then find x​

If 5x - 2y = 6 and 3x + 2y = 10, then find x