Which equation could be used to solve the following system?

x+y=11
4x^2-3y^2=8



A. 4(y + 11)2 – 3y2 = 8

B. 4(11 – y)2 – 3y2 = 8

C. 4(y – 11)2 – 3y2 = 8

D. 4(–11y)2 – 3y2 = 8

Answer:

[tex]cos\Theta =\frac{4}{5}[/tex]

[tex]tan\Theta =\frac{3}{4}[/tex]

Step-by-step explanation:

Given : sin θ = 3/5

To Find : value of cos θ and tan θ

Solution :

use the identity:

[tex]sin^{2}\Theta +cos^{2}\Theta =1[/tex]

putting value of sin θ

⇒ [tex](\frac{3}{5})^{2} + cos^{2}\Theta =1[/tex]

⇒[tex]\frac{9}{25} +cos^{2}\Theta =1[/tex]

⇒[tex]cos^{2}\Theta = 1-\frac{9}{25}[/tex]

⇒[tex]cos^{2}\Theta = \frac{16}{25}[/tex]

⇒[tex]cos\Theta = \sqrt{\frac{16}{25}}[/tex]

⇒[tex]cos\Theta =\frac{4}{5}[/tex]

Thus , [tex]cos\Theta =\frac{4}{5}[/tex]

Now to find value of tan θ

Since we know that

⇒ [tex]tan\Theta =\frac{sin\Theta }{cos\Theta }[/tex]   (identity)

⇒[tex]tan\Theta =\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]

⇒[tex]tan\Theta =\frac{3}{5}\div \frac{4}{5}[/tex]

⇒[tex]tan\Theta =\frac{3}{5}\times  \frac{5}{4}[/tex]

⇒[tex]tan\Theta =\frac{3}{4}[/tex]

Thus , the value of

[tex]tan\Theta =\frac{3}{4}[/tex]

[tex]cos\Theta =\frac{4}{5}[/tex]

Final answer:

This detailed answer provides the values of cos θ and tan θ for an angle θ in the second quadrant given sin θ = 3/5. It explains the process using the Pythagorean identity and the characteristics of the second quadrant.

Explanation:

cos θ = -4/5

tan θ = -3/4

Given sin θ = 3/5 and the angle θ lies in the second quadrant, we can determine cos θ using the Pythagorean identity. Since sin θ = 3/5 is positive in the second quadrant, the x-coordinate in the triangle would be negative. Therefore, cos θ = -4/5. Similarly, tan θ can be calculated as tan θ = sin θ / cos θ = (3/5) / (-4/5) = -3/4.

The value of x is 12 and Shakeel got 18 points.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Adam scored x points. Imran scored 3 points fewer than Adam. Shakeel scored twice as many points as Imran. together they scored 39 points

Establishing the equation, we get

Adam scored x points.

Imran scored x-3 points.

Shakeel scored 2(x-3) points.

Together they scored 39 points:

x + (x-3) + 2(x-3) = 39

x + x -3 + 2x - 6 = 39

4x = 48

x = 12

∵ Shakeel scored = 2(x-3) points.

Putting x = 12, to get the marks scored by him,

Shakeel's score = 2(12-3) = 18

Hence, The value of x is 12 and Shakeel got 18 points.

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Answer:

yoo hoo

Step-by-step explanation: This was in 2016 but its 1/5

Answer:

You can find a width of 9 feet.

Step-by-step explanation:

The width of the rectangular shaped garden should be 9 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be P = 48 feet

We can use the equation given to solve for the width w of the garden:

2l + 2w = 48

Substituting l = 15, we get:

2(15) + 2w = 48

30 + 2w = 48

Subtracting 30 from both sides, we get:

2w = 18

Dividing both sides by 2, we get:

w = 9 feet

Hence , the width of the garden should be 9 feet

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Answer: The sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Step-by-step explanation:

Since we have given that

Number of runners = 4

Four runners are as follows:

Fran, Gloria, Haley, and Imani.

Since Haley is the first runner in the relay,

So, Sample space showing the possible order of the other three runners.

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Hence, the sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Answer:

False

Step-by-step explanation:

A five number summary consists of these five statistics: the minimum value, the first quartile, the median, the third quartile, and the maximum value of a set of numbers

A standard deviation is  a measure that is used to quantify the amount of variation or dispersion of a set of data values.

Std deviation is the square root of variance

Variance is the average of squares of deviations of each entry from the mean.

Hence from five point summary, we cannot calculated standard deviation of the distribution

1. Infinite many solution.

2. No solution

3. One solution

4. No solution

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Depending upon the situation we have three case

[tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

and, [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

and, [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

1. 3x = -12y + 15 and x+4y=5

3x + 12y - 15= 0 and x+ 4y- 5 = 0

So, [tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

2. 4x - y +3 = 0 and -8x + 2y -3 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

3. x+ 4y - 12= 0 and 5x - 20y -60 = 0

So,  [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

4. -5x + y +6 = 0 and -15x + 3y +12 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

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Aaron should pay $80 in the first month to satisfy the conditions of repaying $150 in 4 monthly installments, with each subsequent payment being half of the previous one.

Aaron needs to pay back a total of $150 in 4 monthly installments, with each payment being half the amount of the previous month. Let's denote the first payment amount as X. Then, the second payment would be X/2, the third would be X/4, and the fourth would be X/8. These four payments need to sum up to $150, which is the total amount Aaron borrowed.

To find the value of X, we can set up the following equation based on the aforementioned information:

X + X/2 + X/4 + X/8 = 150

To solve this equation, we should find a common denominator, which is 8 in this case, and rewrite the equation as:

8X/8 + 4X/8 + 2X/8 + X/8 = 150

Adding the numerators together gives us:

(8X + 4X + 2X + X) / 8 = 150

15X / 8 = 150

Multiplying both sides by 8 and then dividing by 15 gives us:

X = (150 × 8) / 15

X = 1200 / 15

X = 80

Thus, Aaron should pay $80 in the first month to repay the money on schedule as he promised.

Final answer:

The actual distance between two cities on a map with a scale of 1 cm:12 km, where the map distance is 6.8 cm, can be calculated as 6.8 cm × 12 km/cm, resulting in an actual distance of 81.6 kilometers.

Explanation:

Understanding Map Scale Problems

To calculate the actual distance between two cities on a map using the scale given, you would use the following steps:

First, identify the scale of the map provided; in this case, it is 1 cm : 12 km.

Next, measure the distance on the map between the two cities; the distance is 6.8 cm.

Finally, multiply the distance on the map by the scale factor to find the actual distance. That is, 6.8 cm (distance on the map) × 12 km/cm (scale factor) = 81.6 km (actual distance).

Therefore, the estimated actual distance between the two cities is 81.6 kilometers.

To find the marginal cost at the given production level x, differentiate the cost function C(x) and substitute the value of x. The units of measurement for the marginal cost are dollars per unit (x).

To find the marginal cost at the given production level x, we need to find the derivative of the cost function C(x) with respect to x. Let's differentiate the function:

C'(x) = 70 - 1,000/x^2

Now, substitute x = 100 into the derivative:

C'(100) = 70 - 1,000/100^2 = 70 - 1 = 69

The units of measurement for the marginal cost are dollars per unit (x).

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tan(θ) = -1/6.

Given that sec(θ) = √37/6 and sin(θ) < 0, we can find tan(θ) using the trigonometric identity:

sec²(θ) - tan²(θ) = 1

First, we need to find the value of tan(θ) using the given information:

Since sec(θ) = √37/6, we know that sec(θ) = 1/cos(θ), so cos(θ) = 6/√37.

Since sin²(θ) + cos²(θ) = 1, we can find sin(θ):

sin²(θ) + (6/√37)² = 1

sin²(θ) + 36/37 = 1

sin²(θ) = 1 - 36/37

sin²(θ) = (37-36)/37

sin²(θ) = 1/37

Given that sin(θ) < 0, sin(θ) is negative. Therefore, sin(θ) = -1/√37.

Now that we have sin(θ) and cos(θ), we can find tan(θ):

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-1/√37) / (6/√37)

tan(θ) = -1/6

Therefore, tan(θ) = -1/6.

The growth rate of the hedge maple tree is 0.75 feet per year, and the tree's original height when it was planted was 6 feet.

We are tasked with finding the growth rate of a hedge maple tree and its original height when it was planted based on the given data. The tree's height was recorded at two different times: Four years after it was planted, its height was 9 feet, and eight years after planting, its height reached 12 feet.

To calculate the growth rate per year, we take the difference in height over the difference in time:
Growth rate = (Height at 8 years - Height at 4 years) / (Time at 8 years - Time at 4 years)
Thus, Growth rate = (12 feet - 9 feet) / (8 years - 4 years) = 3 feet / 4 years = 0.75 feet per year.

To determine the original height when the tree was planted, we can subtract the total growth over the four years from the height at four years after planting:
Original height = Height at 4 years - (Growth rate * 4 years)
Original height = 9 feet - (0.75 feet/year * 4 years) = 6 feet.

Answer: x + 7/ 3

Assuming the said quantity is divided by 3x+15 as a denominator in fraction form.

After dividing, the simplest form, x + 7/ 3, can be found after dividing both the numerators and the denominators by the smallest common factor.

Proof of validity is shown below.

Answer:

D

Step-by-step explanation:

its reflected off the L-axis

Answer:

The coefficient of the term 13a is, 13

Step-by-step explanation:

Coefficient term are the numbers that multiply the variables or letters

In the given expression: [tex]13a+6b[/tex]

13a means 13 times a , and a is the variable,

so 13 is the coefficient .

6b means 6 times b , and b is the variable ,

so 6 is the coefficient .

therefore, the coefficient of the term 13a in the given expression is, 13.