Find the value of each variable in the following parallelogram - show work

The possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

Given the gradient 2 for the point A and B, we have that;

gradient = (y₂ - y₁)/(x₂ - x₁)

so;

2 = (2t² + 7 - t)/(7 - 2)

2 = (2t² + 7 - t)/5

10 = 2t² + 7 - t {cross multiplication}

2t² + 7 - t - 10 = 0

2t² - t - 3 = 0

2t² + 2t - 3t - 3 = 0 {we rewrite the middle term}

2t(t + 1) -3(t + 1) = 0

(2t - 3)(t + 1) = 0 {factorization}

2t - 3 = 0 or t + 1 = 0

t = 3/2 or t = -1

Therefore, the possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

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Answer: A, D

Step-by-step explanation:

We have sinx cosx = -1/4. This means that either sinx = -1/2 and cosx = 1/2 or sinx = 1/2 and cosx = -1/2. In the first case, we get x = 7pi/6 + 2npi or x = 11pi/6 + 2npi. In the second case, we get x = 7pi/12 + 2npi or x = 17pi/12 + 2npi. Therefore, the solutions are x = 7pi/12 + npi and x = 11pi/12 + npi. So, options A and D are correct. Options B and C are not solutions to the given equation.

By solving it as a sequence, it will take 9 years for the club to plant 54 flowers in the courtyard.

The number of years will it take for 54 flowers to grow in the courtyard is determined by solving the planting method as a sequence.

The nth term of the sequence Z is given by:

Z = a1 + (n-1)d

where Z = 54

a1 = 6

n = ?

d = d

Solving for n:

54 = 6 + (n - 1) * 6

48 = (n - 1) * 6

8 = n - 1

n = 8 + 1

n = 9

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Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

Answer: 6 ≤ x ≤ 11

Step-by-step explanation:

Let x be the number of additional outfits that can be packed in the suitcase.

The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.

On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.

Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.

The sum of the first 9 terms of the arithmetic sequence is 81.

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.

To calculate the sum of the first 9 terms of the arithmetic sequence, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer: 44 degrees

Step-by-step explanation: 59+77+x=180

x=44

Answer:

the surface area of the cylinder is about 452.2 square centimeters.

Step-by-step explanation:

To find the surface area of a cylinder, you need to use the formula: A=2πr2+2πrh where A is the surface area, r is the radius of the circular base, and h is the height of the cylinder In this case, you are given the diameter of the base as 12 cm, so you need to divide it by 2 to get the radius: r=212​=6 cm

You are also given the height of the cylinder as 6 cm.

Plugging these values into the formula, you get: A=2π(6)2+2π(6)(6)

Simplifying, you get: A=72π+72π

Adding, you get: A=144π cm2

Using a calculator, you can approximate π as 3.14 and get: A≈452.16 cm2

Rounding to the nearest tenth, you get: A≈452.2 cm2

Answer:

here

Step-by-step explanation:

Answer:

Explanation:

-5 -4 -3 -2 -1 0 1 2 3 4 5

The coordinates that represents a point that is collinear with the given points: (4, -10) and (-2, 0) is (0, 10/3). So the correct answer is option C.

We must check to see if a point is on the straight line that connects two other points in order to determine if they are collinear.

Using the point-slope form of a line we can find the equation of the straight line passing through the points (4,-10) and (-2,0):

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

where (x1, y1) = (4, -10) and (x2, y2) = (-2, 0).

Substituting the values, we get:

(y + 10)/(x - 4) = (0 + 10)/(-2 - 4)

Simplifying, we get:

(y + 10)/(x - 4) = -5/3

Multiplying both sides by (x - 4), we get:

y + 10 = (-5/3)(x - 4)

Simplifying, we get:

y = (-5/3)x + (10 + 20/3)

y = (-5/3)x + (50/3)

So, any point that satisfies this equation is collinear with the given points.

Now checking all the three points whether they satisfy the equation:

(a) (2, -6)

Substituting the values in the equation, we get:

-6 = (-5/3)(2) + (50/3)

-6 = -10/3 + 50/3

-6 = 40/3, which is not true.

Therefore, the point (2, -6) is not collinear with the given points.

(b) (3, -3)

Substituting the values in the equation, we get:

-3 = (-5/3)(3) + (50/3)

-3 = -15/3 + 50/3

-3 = 35/3, which is not true.

Therefore, the point (3, -3) is not collinear with the given points.

(c) (0, 10/3)

Substituting the values in the equation, we get:

10/3 = (-5/3)(0) + (50/3)

10/3 = 50/3, which is true.

Therefore, the point (0, 10/3) is collinear with the given points.

Hence, the answer is (c) (0, 10/3).

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Correct Question

Which of the following coordinates represents a point that is collinear with the given points.

(4, -10) and (-2, 0)
(a) (2, -6)

(b) (3, -3)

(c) (0, 10/3)

The radius of a sphere with a volume of 10000 cubic meters is 13.36 meters

We know that the formula for the volume of sphere is :

V = 4/3 × π × r³

where r is the radius of the sphere

Here, a volume of the sphere is 10000 cubic meters.

V =  10000 cubic meters

we need to find the radius 'r'

V = 4/3 × π × r³

10000 = 4/3 × π × r³

r³ = 10000 × 3/4 × 1/π

r³ = 30000/4π

r³  = 2387.32

taking cube root,

r = 13.36 meters

Therefore, the radius is 13.36 meters.

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Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.

The formula used is:


Exposure Time = 8/ 2^((dBA-85)/3)

Since the decibel (dBA) given is 106


Exposure Time = 8/ 2^((106-85)/3)

= 8/2^1
= 8/ 128

= 0.0625 hours or 3 minutes, 75 seconds.

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Answer:

$4.20 / 7 erasers = $0.60 per eraser

So each eraser in the package costs $0.60.

Answer:

no not satisacl

Step-by-step explanation:

The lateral surface area of the cylinder is 376.8 sq ft

From the question, we have the following parameters that can be used in our computation:

Radius, r = 10 ft

Height, h = 6 ft

The lateral surface area of the cylinder is calculated as

Lateral area = 2 * 3.14 * rh

Substitute the known values in the above equation, so, we have the following representation

Lateral area = 2 * 3.14 * 6 * 10

Evaluate the products

So, we have

Lateral area = 376.8

Rounding the answer to the nearest tenth, we have

Lateral area = 376.8

Hence, the Lateral area is 376.8 sq ft

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Answer:v-14=42

Step-by-step explanation: Since Vidya’s age is v and when it is decreased by 14, v-14=42

The value of k is given as follows:

k = 10.

The quadratic function in the context of this problem is defined as follows:

y = 3x² - 8x + 2k + 1.

The coefficients are given as follows:

a = 3, b = -8 and c = 2k + 1.

The product of the roots of  quadratic function is given as follows:

c/a.

For this problem, the product is of 7, hence the value of k is obtained as follows:

(2k + 1)/3 = 7

2k + 1 = 21

2k = 20

k = 10.

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The simplified form of the fraction is A = -1 / (x - 2)

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = (6 - x) / (x² - 8x + 12)

On factorizing the denominator , we get

(x² - 8x + 12) = ( x - 6 ) ( x - 2 )

So , the new fraction is

A = ( 6 - x ) / ( x - 6 ) ( x - 2 )

A = - ( x - 6 ) / ( x - 6 ) ( x - 2 )

Taking the common factor out , we get

A = -1/ ( x - 2 )

Hence , the fraction is A = -1/ ( x - 2 )

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Answer:

Step-by-step explanation:

4

Answer:

Step-by-step explanation:

D 48 cubic ft

The surface area of the composite figure is 4364 sq. m.

A composite figure that consists of more than one shape. Thereby it is formed by joining two or more shapes.

In the given composite figure, we have;

i. area of one triangular surface = 1/2 x base x height

                                    = 1/2 x 25x13

                                    = 162.5

area of one of its triangular surfaces is 162.5 sq. m.

ii. area of rectangular surface 1 = length x width

                                           = 27 x 18

                                           = 486 sq. m.

iii. area of rectangular surface 2 = length x width

                               = 27 x 23

                                            = 621 sq. m.

iv. area of rectangular surface 3 = length x width

                                                     = 25 x 23

                                                     = 575 sq. m.

v. area of its base = length x width

                             = 27 x 25

                                              = 675 sq. m.

surface area of the composite figure = (2*162.5) + (2*486) + (2*621) + (2*575) + 675

                          = 4364

The surface area of the composite figure is 4364 sq. m.

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The length of piece of fabric is 6 cm.

Since, Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, Karen was cutting out some fabric for a friend. She cut a piece that was 6 centimeters wide and had an area of 36 square cm.

Here, area of rectangular shaped fabric is Area =Length × Width

36=Length × 6

Length =6 cm

Therefore, the length of piece of fabric is 6 cm.

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It will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

The formula for compound interest is:

[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]

where A is the future value of the investment, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, Boris has invested $6000 at an annual interest rate of 7%, compounded quarterly. Therefore, we have:

P = 6000

r = 0.07 (since 7% is the annual interest rate)

n = 4 (since the interest is compounded quarterly)

A = 8058

We can solve for t by rearranging the formula:

[tex]t =\dfrac{ ln(\dfrac{A}{P})} { n ln(1 + \dfrac{r}{n})}[/tex]

Substituting the values we have:

[tex]t = \dfrac{ln(\dfrac{8058}{6000}) }{ [4 ln(1 + \dfrac{0.07}{4})]}[/tex]

t ≈ 4.02 years

Therefore, it will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

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The angles and percentages have been calculated as shown below.

A pie chart for the information about the different make of cars is shown below.

For the total number of car makes, we have the following:

Total make of cars = 12 + 8 + 8 + 2 + 10

Total make of cars = 40.

Next, we would determine the angles and percentage as follows;

Toyota

12/40 × 360 = 108°

12/40 × 100 = 30%.

Nissan

8/40 × 360 = 72°

8/40 × 100 = 20%.

Datsun

8/40 × 360 = 72°

8/40 × 100 = 20%.

Volvo

2/40 × 360 = 18°

2/40 × 100 = 5%.

Peugeot

10/40 × 360 = 90°

10/40 × 100 = 25%.

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Step-by-step explanation:

a probability is always the ratio

"desired" cases / totally possible cases

the totally possible cases here are 100.

now, the question focuses on non-defective units.

how many out of the 100 are non-defective ?

well, 100 - 12 = 88 units.

so, the probability to select a non-defective (= working) unit is

88/100 = 22/25 = 0.88

in other words, as a mean and expected value, in 88 of 100 attempts, or in 22 of 25 attempts you will select a non-defective unit.

There are 100 DVRs in the inventory, and 12 of them are defective. Therefore, the number of non-defective DVRs is:

100 - 12 = 88

The probability of selecting a non-defective DVR can be found by dividing the number of non-defective DVRs by the total number of DVRs:

P(non-defective DVR) = number of non-defective DVRs / total number of DVRs

                     = 88 / 100

                     = 0.88

Therefore, the probability of randomly selecting a DVR that is not defective is 0.88, or 88%.

The distance will be in the decimal form is :41.34

Consider the triangle :

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

[tex]Hypotenuse^2 = Perpendicular^2 + Base^2[/tex]

[tex]c^2 = a^2 + b^2[/tex]

We have the points are:

15,-17 and -20, -5

To find the distance between them.

The distance of x- axis is:

15 - (-20)

= 15 + 20

= 35

The distance of y- axis is:

|17 - 5| = |-22| = 22

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:

[tex]x^2+y^2=(distance)^2[/tex]

[tex]35^2+22^2=distance^2[/tex]

[tex]1709= distance^2\\Distance = \sqrt{1709}[/tex]

In decimal form the distance would be around 41.34.

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The function represented by the graph given is equivalent to -

g(x) = (x - 4)².

The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -

f(x, y) → f(x - 4, y)

So, we can write the function as -

g(x) = (x - 4)²

So, the function represented by the graph given is equivalent to -

g(x) = (x - 4)²

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