Solve the system algebraically.
2x-y=-5
y=1-3x

Answer:

  (a)  m^6·n^9

Step-by-step explanation:

You want to know an expression equivalent to (m^-2·n^-3)^-3.

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  [tex](m^{-2}n^{-3})^{-3}=m^{(-2)(-3)}n^{(-3)(-3)}=\boxed{m^6n^9}[/tex]

The true mean of the data-set is given as follows:

46.35.

The mean of a data-set is calculated as the sum of all observations divided by the number of observations.

In this problem, the sum is given by the multiplication of the mid-values by the number of students with each value, as follows:

S = 37.5 x 30 + 42.5 x 20 + 47.5 x 15 + 52.5 x 13 + 57.5 x 22 = 4635.

The total number of students is given as follows:

30 + 20 + 15 + 13 + 22 = 100.

Hence the mean is calculated as follows:

Mean = 4635/100 = 46.35.

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27kg is the weight of Barrys dog now,

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The weight of dog last time when Barry checked is 30kilograms.

Barry just measured his dog again and found out that it weighs 10% less now.

We need to find the weight of Barrys dog.

Convert 10% to decimal value

10/100=0.1

0.1×30=3

Now subtract 3 from 30

30-3

27

Hence, currently Barrys dog weight is 27kg.

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The correct statement as regards the transformation involving translation is

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformation is basically of two major divisions

Non rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation

In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are

Since the transformation point A and point B made are all translation which is a type of rigid transformation, the dimension of the length will remain same

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Answer: y=-[tex]\frac{5}{2}[/tex]x+2  or 5x+2y=4

Step-by-step explanation:

let’s make l1: 2x+5y=10,

then 5y=-2x+10

then y=-[tex]\frac{2}{5}[/tex]x+2

Answer: The answer is: a

Answer: [tex]g(x)=(x+3)^2[/tex]

Step-by-step explanation:

When shifting a function left [tex]3[/tex] units, [tex]f(x) \to f(x+3)[/tex].

Therefore, [tex]g(x)=(x+3)^2[/tex].

Step-by-step explanation:

part (a) - you plug 25 into the given function they give you and that'll be your answer

part (b) - 200 is your original amount given by the function so what is half of 200? 100. So set 100 on the right side of your function and solve for t to find the year

From the given statements about the linear graph, the correct ones are statements 1, 2 and 3 while the incorrect one is statement 4

The slope of a linear graph is simply the change in the y-values divided change in the corresponding x-values.

Now, from the graph, if we take two coordinates, we can easily say that;

Slope = (18 - 16)/(0 - 100)

Slope = -2/10 = -1/5

Statement 1; From the graph, the y-intercept is $18. This means that this is the cost of the book as that is where the cost starts decreasing for each weed she pulls. Thus, it is true.

Statement 2; The slope as we saw earlier was -1/5. Thus, it means that her grandma pays $1 for every 5 weed she pulls.

Statement 3; The x-intercept is 90 and it means after 90 weeds pulled, she no longer has to use her own money at all for the book. This is correct.

Statement 4; This is wrong because she needs to pull at least 90 weeds for her not to use her money.

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Answer: The value 550 represents the initial balance in the account, which means the account started with $550.

Step-by-step explanation:

The 550 represents the start balance that was put into the account. The (1+0.05t0 is the interest being added every t years/months.

The equations have no solution.

6x – 2 – 3x = 3x – 2

10 + 6x = 15 + 9x – 3x

11 + 3x – 7 = 6x + 5 – 3x.

We have determine from the given option which option has no solution.

When an equation has a solution?

An equation with no solution will be an equation when simplified, which will be a false statement.

The equation, 6x – 2 – 3x = 3x – 2

add like terms,

3x-2=3x-2

So we get,This equation has no solution

10 + 6x = 15 + 9x – 3x

10+6x=15+6x

add like terms we cannot find the value of x.

Therefore the given equation has no solution.

11 + 3x – 7 = 6x + 5 – 3x.

add like terms,

4+3x=3x-5

we cannot find the value of x.

So this equation has no solution.

Therefore, The equations 6x – 2 – 3x = 3x – 2,10 + 6x = 15 + 9x – 3x and 11 + 3x – 7 = 6x + 5 – 3x have no solution.

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The number of miles that you ran on the treadmill on Monday will be 3 miles.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

On Monday you run on the treadmill for thirty minutes at x mph and on Tuesday you walk a similar distance on the treadmill at 2 mph increasingly slow takes you three-fourths 60 minutes.

Then the distance is the same in both cases. Then we have

x × (1/2) = (x - 2) × (3/4)

Simplify the equation, then we have

x × (1/2) = (x - 2) × (3/4)

4x = 6(x - 2)

4x = 6x - 12

2x = 12

x = 6 miles per hour

The number of miles is given as,

D = 6 × 1/2

D = 3 miles

The number of miles that you ran on the treadmill on Monday will be 3 miles.

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The  equations that can be used to solve for the length of the room are

(b) y²-5y=750  ,    (c) 750-y(y-5)=0  and   (e) (y+25)(y-30)=0

Given that:

The area of rectangular room is 750 square feet.

Let the length of the rectangular room be y feet.

Since the width of the rectangular 5 less than the length of the room.

Then the width of the given rectangular room is (y-5) feet.

We know the area of a rectangular plot is = Length×width.

Thus , the area of the rectangular room is = y(y-5) square feet

According to problem,

area of the rectangular room =  750 square feet

⇒ y(y-5) =750.........(1)

⇒ y²-5y=750 .......(2)

⇒ y²-5y-750=0

⇒ y²-30y+25y-750=0

⇒ y(y-30)+25(y-30)=0

⇒ (y-30)(y+25)=0 ......(3)

⇒ y-30=0 or, y+25=0

⇒ y= 30, -25

∵ the length of a rectangle can't be negative.

So, y=30.

We can rewrite the equation (1) in form of

(i)

y(y-5) =750

⇒750= y(y-5)

⇒750-y(y-5)=0.......(4)

(ii)

y(y-5) =750

⇒y(y-5) -750=0.......(5)

Hence , the  equations that can be used to solve for the length of the room are

(b) y²-5y=750  ,    (c) 750-y(y-5)=0  and   (e) (y+25)(y-30)=0

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Given recursion function in options we have calculated values of f(1),f(2),f(3),f(4),f(5).

Find f(1), f(2), f(3), f(4), f(5) if f(0) = 3.

First recursive Function is given as

a) f(n+1) = -2*f(n)

f(1) = -2*f(0) = -2*3 = -6

f(2) = -2*f(1) = -2*(-6) =  12

f(3) = -2*f(2) = -2*12 = -24

f(4) = -2*f(1) = -2*(-24) = 48

f(5) = -2*f(4) = -2*(48) = -96

Second recursive Function is given as

b) f(n+1) = 3*f(n)+7

f(1) =  3*f(0)+7 = 3*3+7 = 16

f(2) = 3*f(1)+7 = 3*16+7=  55

f(3) = 3*f(2)+7 = 3*55+7 = 172

f(4) = 3*f(3)+7 = 3*172+7 = 523

f(5) = 3*f(4)+7 = 3*523+7 = 1576

Third recursive Function is given as

c) f(n+1) = [tex]f(n)^2-2*f(n)-2[/tex]

f(1) = f(0)*f(0)-2*f(0)-2 =3*3 - 2*3 - 2 = 1

f(2) = f(1)*f(1) - 2*f(1) - 2 = 1*1 - 2*1 - 2 =  -3

f(3) = f(2)*f(2) -2*f(2)- 2 =-3*(-3) - 2*(-3) - 2 = 13

f(4) = f(3)*f(3) -2*f(3)- 2 = 13*13 - 2*13 - 2 = 141

f(5) = f(4)*f(4) -2*f(4)-2 = 141*141 - 2*141 - 2 = 19597

Fourth recursive Function is given as

d) f(n+1) =  [tex]3^(f(n)/3)[/tex]

f(1) = 3^((f(0)/3) = 3^1 = 3

f(2) = 3^((f(1)/3) = 3^1 =  3

f(3) = 3^((f(2)/3) = 3^1 = 3

f(4) = 3^((f(3)/3) = 3^1 = 3

f(5) = 3^((f(4)/3) = 3^1 = 3  

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Each pass costs $17.77 and each student's lunch costs $8.81

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The school spends 746.34 dollars on passes for 40 students and 2 teachers.

So, Each pass costs = 746. 34/ 42 = $17.77

Now, The school also spends 352.40 dollars on lunch for just the students.

= 352.40/ 40

= $8.81

Hence, Each pass costs $17.77 and each student's lunch costs $8.81

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Answer:

it may be not

take an example x=(1) y={123) and define a relation of R as the set of pairs (1,1) (1,2)(1,3) so this not a function

Answer:

15 inches

Step-by-step explanation:

The shortcut for finding the side lengths on a 30°-60°-90° triangle is that the long leg is

the short leg × √3.

So for your question:

5√3 × √3

= 5 × √3 × √3

= 5 × 3

= 15

Just in case it comes up next, the other shortcut is that the hypotenuse is double the short leg. Hypotenuse =

2 × 5√3 = 10√3

Hello!

Let's use 'x' to represent the cost of the burger, and 'y' to represent the cost of the hotdog.

2x + y = 482

× + 2y = 370

2x + 47 = 740

-3y = -258

y = 86 cents

2x + 86 = 482

2x = 396

x = 198

A burger costs $1.98 and a hot dog costs $.86

I hope this didn't confuse you, I'm not very good at explaining!

The original price is $720.33 .

What is original price ?

Convert the percent discount to a decimal by dividing by 100% . Step 2: Set up the equation P=(1−d)x P = ( 1 − d ) x to find the original price of the item where P is the sale price, d is the discount as a decimal, and x is the original price of the item.You need to be aware of the selling price as well as the discount % in order to determine the item's original cost. The calculations contain a straightforward method that divides the sale price by the percentage-based result of 1 minus the discount. To determine an item's original or list price, use this formula.

SInce $194.49, is what is owed after the discount you will want to subtract 73 from 100 to get the percent of what is owed. Then you will set it up like a percent equation. 27/100 = 194.49/X where X = the original price. You will then multiply 194.49 by 100 and divide that answer by 1.9449. This equals $720.33 as the original price.

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The series of transformations of  triangle ABC to triangle CEF is shown.

For the given transformations from triangle ABC to triangle CEF are-

Translation:

Rotation: There is no rotation taken place.

Reflection: There is no reflection of the given triangle ABC.

Dilation: The dilation of the 2 times the original coordinates is taken place.

Thus, the series of transformations of  triangle ABC to triangle CEF is shown.

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Answer: Slope: 2, y-intercept: (0,-8)

Step-by-step explanation:

x | y
0  -8
1   -6

The equation of the number of dollar cins giuliana has,  is found to be

0.25(22 – d) + d = 10.75.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.

Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,

(1 x d) + (0.25 x (22-d)) = 10.75

d + 0.25(22-d) = 10.75

Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.

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The values of the angles for the given figure are m  ∠M=76°,

m ∠N=76°.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.

Given,

In ΔLMN,

m ∠L=28°

As we know that,

Angle sum in a triangle=180°

m ∠L+ m ∠M+ m ∠N=180°

From the figure,

m ∠M= m ∠N

So, m ∠L+ m ∠M+ m  ∠M=180°

28°+ 2 m  ∠M=180°

2 m  ∠M=180°-28°

2 m  ∠M=152°

m  ∠M=76°

So, m  ∠N=76°

Therefore, the values of the angles for the given figure are m  ∠M=76°,

m  ∠N=76°.

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7 is a value of k that transforms f into g, where g(x) = f(x) + k. Using the concept of x and y-axis:

A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.

The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.

From the graph it is observe that,

Graph of Function f(x) cut at y axis in the point 3

graph of function g(x)  cut y axis in the point 4

So, the difference between the cut of y axis is k

Thus, {g(x)-f(x)=k}

Hence, k = [4 - (-3)] = 7

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Answer:

No

Step-by-step explanation:

A function can have only  output for each input.  The input 3 has two outputs 3 and 5.  

The input 4 has two outputs 4 and 6.

Answer:

12.40mph

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

Answer:

Sym

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 + 3/8 = 7/8

2 x 7/8 = 7/4

2 + 5/8 = 9/8

2 x 9/8 = 9/4

2 + 6/8 = 8/8

2 x 8/8 = 16/8

2 + 7/8 = 15/8

2 x 15/8 = 15/4