Solve the system 2x + y = 5, x + 3y = 0 by graphing.

False, because The singles answer fits the description. All potential solutions are included in the solution set.

What makes up a linear system's solution set?

Is it true that a linear system's existence and uniqueness are two key issues? False or true?

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The value of y in expression is 14-2x/-9

The expression is written as

2x - 9y = 14

We are asked to calculate the value of y in the expression

2x - 9y = 14

-9y= 14-2x

Divide by the coefficient of y which is -9

y= 14-2x/-9

Hence the value of y is 14-2x/-9

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Answer:

"If chickens make eggs, then cows make milk."

Step-by-step explanation:

Answer: A:  If chickens make eggs, then cows make milk.

Step-by-step explanation: Hope that helped

Answer:

12/15

Step-by-step explanation:

Answer:

m <B = 41°

Step-by-step explanation:

Fact: complementary angles measures add to 90 degrees

Given: m < A = 2x-19,  and m <B = x+7

Find: m <B = ?

Find x

2x-19 + x+7 = 90

2x+x = 90 +19-7

3x = 102

x = 34

Find m <B

m <B = x+7

m <B = 34+7

m <B = 41

answer:

3/4

explanation:

the side lengths of preimage abcd are all four units, whereas image abcd's lengths are all three. from this, we can surmise the scale factor is 3/4.

how to calculate scale factor:

scale factor = dimension of the new shape ÷ dimension of the original shape

Answer:

-20/3

Step-by-step explanation:

Using point-slope form, the equation is

[tex]y+4=-\frac{2}{3}(x+1) [/tex]

Substituting x=3,

[tex]y+4=-\frac{2}{3}(3+1) \\ \\ y+4=-\frac{8}{3} \\ \\ y=-\frac{20}{3}[/tex]

Answer:

234

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [3, 6 ] , then

f(b) = f(6) = [tex]3^{6}[/tex] + 17 = 729 + 17 = 746

f(a) = f(3) = 3³ + 17 = 27 + 17 = 44 , then

average rate of change = [tex]\frac{746-44}{6-3}[/tex] = [tex]\frac{702}{3}[/tex] = 234

The value of g(-4) is 8.

A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.

Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.

g(x) = ax^2 + 24

⇒ g(4) = a (4)^2 + 24

⇒ 8 = 16a + 24

⇒ 8 − 24 = 16a

⇒ −16 = 16a

⇒ a = −1

Since, g(−4) = a(−4) ^2 + 24

∴ g(−4) = 16(−1) + 24

⇒ g(−4) = 8

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Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT = (R% of P)T

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).

Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,

6.5% of x + 9% of ($50,000 - x) = $3625

0.065x + 0.09(50,000 - x) = 3625

0.065x + 4,500 - 0.09x = 3,625

0.065x - 0.09x = 3625 - 4500

0.025 = 875

x = 875/0.025

x = 35,000

Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.

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πr² an example of a model.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

Here, the area of a circle is calculated by the use of formula πr² where π is a constant 3.14 and r is a variable. Therefore this formula is used to find the area.

Thus, πr² an example of a model.

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The height of the tower is approximately 46.765 feet

Step-by-step explanation:

The given parameters are;

The distance from the foot of the tower where the angle of elevation is

measured = 27 feet

The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°

Therefore, by trigonometric ratio, we have;

tan 60= the height of tower / distance from foot of tower

[tex]\sqrt{3}[/tex]= height of tower /27

1.73205 *27 = height of tower

46.765 feet is the height of tower

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We use import math when we want to use the sin function in the math library, x= math. sin(3.14).

Similar to #include header_file in C/C++, that how to import function in python. The import statement brings in code from one module into another program, where modules are files that contain python code, and modules are used to group related code in a program, instead of rewriting the code again, you can reuse the same code in different files. To import code from a module a parameter is to be followed import module name ( where the import word is the keyword and the module name is the module you want to import  ).

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πr2 is an example of (D) a model.

Therefore, πr2 is an example of (D) a model.

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The complete question is given below:

Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?

A. a robot

B. a car

C. a telescope

D. a model

Answer:

You would first move all of the y numbers to one side so it should look like this: 2y-4+5y+3y=4+5.  Then you would all the numbers that don't have y at the end to the other side: 2y+5y+3y=4+5+4.

Then you would add them all up:  10y=13

So your answer is 10y=13

Step-by-step explanation:

The ages of Olivia and her brother are 10 years and 11 years respectively

Let x₁, and x₂ be the ages of Olivia and her brother respectively.

Given that Olivia's brother is twice her age minus 9 years.

⇒ x₂ = 2x₁ - 9 → equation 1

Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.

⇒ x₂ = 1/2 × (x₁ + 12) → equation 2

Using equation 1 in equation 2, we get

2x₁ - 9 = 1/2 × (x₁ + 12)

⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)

⇒ 4x₁ - x₁ = 12 + 18

⇒ 3x₁ = 30

⇒ x₁ = 10 (dividing by 3 on both sides)

Using the value of x₁, in equation 1,

⇒ x₂ = 2(10) - 9

⇒ x₂ = 20 - 9

⇒ x₂ = 11

Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.

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The area in square feet that will be added to the garden is 44 square feet.

Length of square garden = 8 feet

Area of Square garden = [tex](side)^{2}[/tex] = [tex](8)^{2}[/tex] = 64 square feet

On enlarging the square to a rectangle, length rectangular garden is (8+4)feet i.e.,12feet and width of rectangular garden is (8+1)feet i.e.,9feet.

Area of rectangular garden = (length × width)

                                              = (12 × 9) square feet

                                              = 108 square feet

The area in square feet that will be added to the garden = (Area of rectangular garden - Area of Square garden)

= (108 square feet - 64 square feet)

= 44 square feet

The area in square feet that will be added to the garden is 44 square feet.

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The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

Luis has $420 to spend at a bicycle store for some new gear and biking outfits.

Therefore,

x = maximum number of outfits Luis can purchase while staying within his budget.

Hence, the inequality that can be used to represent the situation is as follows;

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:

r = √[(√11 / 6)² + (5 / 6)²]

r = √[(11 / 36) + (25 / 36)]

r = √(36 / 36)

r = √1

r = 1

By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

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Answer:

1 cm

Step-by-step explanation:

you multiply 3 by 1/3 and you get 3/3 which is 1

The answer to this question is:

Size of a square's side = 11 cm

A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.

Area of square = ( Side )²

Given that:

Area of square = ( Side )² = 121 cm²

Dimensions of a square's side = √ Area

so, the length of the square's side = √ 121

                                          = √ 11*11

                                          = √ ( 11 )²  

                                          = 11

Thus, side of the square = 11 cm

Therefore, side length of square = 11cm

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Step-by-step explanation:

-2x - 7 > 1

-2x > 8

-x > 4

x < -4

that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).

x - 2 >= -1

x >= 1

that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.

The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 3.9 and 6.1

The vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 5 )^2 + {-4)

substituting point ( 4, -1 ) from the graph we have:

-1 = a ( 4 - 5 )^2 - 4

-1 = a - 4

a = 3

substituting the known values to y = a ( x- h ) + k

y = 3 ( x - 5 )^2 - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x^2 - 10x + 25 ) - 4

y = 3x^2 - 30x + 75 - 4

y = 3x^2 - 30x + 71

The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 2 and 4

The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 3 )^2 + 2

substituting point ( 0, -16 ) from the graph we have:

-16 = a ( 0 - 3 )^2 + 2

-16 = a - 9 + 2

-16 = a - 7

a = -9

substituting the known values to y = a ( x- h ) + k

y = -9 ( x - 3 )^2 + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x^2 - 6x + 9 ) - 4

y = 3x^2 - 54x - 81 - 4

y = 3x^2 - 54x - 85

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Probability= 5/9

Even cards = 2,4,6,8

Odd cards = 1,3,5,7,9

The number of ways of choosing one odd and one even number is 5C1 * 4C1

            (  5!/ 1!* 4!) * (4!/1! * 3!)

            5* 4= 20

Total number of ways of choosing 2 cards out of 9 = 9C2

        9!/ 2! * (9-2)!

     = 9!/ 2! * 7!

     = 9*8/2

    = 9 *4= 36

Thus, Probability is = 20/ 36

                             = 5/9

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The equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is:

Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?

n = (1/2)(1/5)

n = (1/2)(5/1)

n = (1/2)(5)

n = (1/2)

From the data given in the question:

Let n be the fraction of a quart of grape juice n that is in each glass:

n = (1/2)(1/5)

Thus, the equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.

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Answer:

B is the correct answer.

Step-by-step explanation:

Add -2+e to both sides

v + f − e -2+e = 2 -2+e

Which will give you v + f -2 = e.