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hammer [34]
2 years ago
14

Solve the following using the elimination method and write the value of x.

Mathematics
1 answer:
yawa3891 [41]2 years ago
4 0

Answer:

the first one is ×=-2-3/5

the second one is ×=1-3y/2

hope it helps

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Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

10/20 is simplified to 1/2

k = 1/2

5 0
2 years ago
Three gardeners used different methods to estimate the diagonal length of a garden in feet.
Elden [556K]

Answer: C

Step-by-step explanation:

4 0
3 years ago
4 times the measure of the complement of an angle is equal to 2/3he measure of the original angle's supplement. what is the meas
Andrej [43]
Let x be the angle
Complement of x is (90 degrees-x)
Supplement of x is (180 degrees-x)

4•(90-x)= 2/3(180-x)
3•4(90-x)=2(180-x)
1080-12x=360-2x
1080-360=12x-2x
720=10x
720/10= x
So x = 72 degrees
3 0
3 years ago
What is the porosity of the gravel sample?(The sediment volume for each sample is 400ml. ) a. 23. 75% b. 28. 75% c. 55. 75% d. 8
Anna [14]

The porosity of the gravel sample is 28.75%

We have to determine.

What is the porosity of the gravel sample?

<h3>The porosity of the gravel sample;</h3>

Porosity is the term which is defined as the volume of voids present in the soil to the total volume of the soil.

The formula used to calculate the Porosity is;

\rm Porosity =\dfrac{Volume \ of \ voids \ present \ in soil}{Volume \ of \ soil}

A sponge is a case of a permeable fabric because it incorporates a huge number of purge spaces compared to its volume.

Porosity is the property of a question that communicates the entire volume of purge or pore space within the material.

Hence, the porosity of the gravel sample is 28.75%

Learn more about "porosity" :

brainly.com/question/2593663

4 0
2 years ago
PLS HELP ILL GIVE U BRAINLIST
SCORPION-xisa [38]
<h2>Answer:</h2>

B. |y| = 1.6

<h2>Step-by-step explanation:</h2>

A sketch of the vector is attached to this response.

As shown, the vector lies on the second quadrant and its horizontal and vertical components are given by x and y respectively.

Where;

|x| = v cos θ              -----------------(i)

|y| = v sin θ               -----------------(ii)

and

v = magnitude of the vector = 2.5km/hr

θ = angle that the vector makes with the +x axis = 90° + 50° = 140°

<em>To get the magnitude of the vector's vertical component</em>

<em>Substitute these values into equation(ii) as follows;</em>

|y| = 2.5 sin 140°

|y| =  2.5 x 0.6428

|y| = 1.607

|y| ≅ 1.6 km/hr

Therefore, the vertical component of the vector has a magnitude of 1.6 km/hr.

 

4 0
2 years ago
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