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3 years ago

Quadrilateral QRST is a parallelogram. Solve for x (3x+5) (9x-17)

Mathematics

1 answer:

Naddika [18.5K]3 years ago

5 0

Given:

Consider the below figure attached with this equation.

Quadrilateral QRST is a parallelogram.

To find:

The value of x.

Solution:

We know that the sum of two consecutive interior angles of a parallelogram is 180 degrees because they are supplementary angles.

In parallelogram QRST,

$m\angle Q+m\angle T=180^\circ$

$(3x+5)^\circ+(9x-17)^\circ=180^\circ$

$(12x-12)^\circ=180^\circ$

On comparing both sides, we get

$12x-12=180$

$12x=180+12$

$12x=192$

Divide both sides by 12.

$x=\dfrac{192}{12}$

$x=16$

Therefore, the value of x is 16.

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Find positive numbers x and y satisfying the equation xyequals12 such that the sum 4xplusy is as small as possible. Let S be the

WITCHER [35]

Answer:

The objective function in terms of one number, x is

S(x) = 4x + (12/x)

The values of x and y that minimum the sum are √3 and 4√3 respectively.

Step-by-step explanation:

Two positive numbers, x and y

x × y = 12

xy = 12

S(x,y) = 4x + y

We plan to minimize the sum subject to the constraint (xy = 12)

We can make y the subject of formula in the constraint equation

y = (12/x)

Substituting into the objective function,

S(x,y) = 4x + y

S(x) = 4x + (12/x)

We can then find the minimum.

At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0

(dS/dx) = 4 - (12/x²) = 0

4 - (12/x²) = 0

(12/x²) = 4

4x² = 12

x = √3

y = 12/√3 = 4√3

To just check if this point is truly a minimum

(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)

4 0

3 years ago

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis

Tju [1.3M]

The equations representing the circle having a diameter of 12 units and a center lying on y-axis are x² + (y – 3)² = 36, and x² + (y + 8)² = 36, making options 1, and 5 the two choices.

In the question, we are looking for the equations of the circle having a diameter of 12 units and a center lying on y-axis.

The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.

A circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.

A circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.

Thus, the equation of the circle, with a diameter of 12 units and the center lying on the y-axis takes the form:

x² + (y - k)² = 6², or, x² + (y - k)² = 36.

From the given options, the equations x² + (y – 3)² = 36, and x² + (y + 8)² = 36, are of this form.

Thus, the equations representing the circle having a diameter of 12 units and a center lying on y-axis are x² + (y – 3)² = 36, and x² + (y + 8)² = 36, making options 1, and 5 the two choices.

Learn more about equations of circle at

brainly.com/question/16039879

#SPJ4

The provided question is incomplete. The complete question is:

"Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

x² + (y – 3)² = 36
x² + (y – 5)² = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x² + (y + 8)² = 36."

8 0

2 years ago

Help!! Question on probability. Wi give brainliest!!

Aleks [24]

Answer:

$P = \frac{5}{282} = 0.0177$

Step-by-step explanation:

First we need to find the total amount of apples in the crate:

Total = 10 + 14 + 4 + 18 = 46 apples

The probability of the first apple being a golden delicious apple is the number of those apples over the total number of apples:

$P(golden) = \frac{N(golden)}{N(total)}$

$P(golden) = \frac{4}{48} = \frac{1}{12}$

Then, the probability of the second apple being a granny Smith apple is the number of those apples over the total number of apples, but now the total number of apples is one less, because one apple was removed from the crate:

$P(granny) = \frac{N(granny)}{N(total)-1}$

$P(granny) = \frac{10}{47}$

The final probability we want is the product of those two probabilities:

$P = P(golden) * P(granny) = \frac{1}{12} \frac{10}{47} = \frac{10}{564} = \frac{5}{282}= 0.0177$

7 0

3 years ago

Help! answer options included

lawyer [7]

Answer:

Y = [-6 6 6 -6]

Step-by-step explanation:

From the given matrices

If X - 2Y = Z

b - 2c = a ... 1

a -2d = c ...2

4+2a = 16.... 3

a + 2b = b .... 4

From3 ;

2a = 16-4

2a = 12

a = 6

From 4;

a + 2b - b = 0

a+b = 0

a = -b

6 = -b

b = -6

From1;

b - 2c = a

-6 - 2c = 6

-2c = 12

c = -6

also

a - 2d = c

6-2d = -6

-2d = -6-6

-2d = -12

d = 6

Hence the matrices Y = [-6 6 6 -6]

4 0

3 years ago

Which expression is equivalent to 3.3.3.3

nikdorinn [45]

Answer:

I'm not sure but i think it's 34y

Step-by-step explanation:

7 0

2 years ago