sketch the solution to each system of inequalities.
y<=-x-2
y>=-5x+2

Answer:

  (b)  g(x) = 6√x +7

Step-by-step explanation:

You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.

A vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...

  f(x) = √x . . . . original square root function

  h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6

A translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...

  h(x) . . . . . original function

  g(x) = h(x) +7 . . . . . translation upward by 7 units

Our stretched and translated function is ...

  g(x) = 6√x +7

The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.

let

Number of small bowl = x

Number of large bowl = y

x + y = 63

2.25x + 3y = 159

From (1)

x = 63 - y

Substitute into (2)

2.25x + 3y = 159

2.25(63 - y) + 3y = 159

141.75 - 2.25y + 3y = 159

- 2.25y + 3y = 159 - 141.75

0.75y = 17.25

divide both sides by 0.75

y = 17.25 / 0.75

y = 23

Substitute y = 23 into (1)

x + y = 63

x + 23 = 63

subtract 23 from both sides

x = 63 - 23

x = 40

In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls

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The mass of the boy removed is 54.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

let's take the weight of five boys is x

so,

x/5 = 62

x = 310

and let's take the weight of four boys is y.

so,

y/4 = 64

y = 256

let's take the weight of a boy which is removed from them is z

so,

x - z = y

x - y = z

310 - 256 = z

z = 54

Hence, the mass of the boy removed is 54.

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Answer: Postulate

Step-by-step explanation:

Side-Side-Side (SSS) Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.

x² - 8x + 5 can be expressed as (x - 4)² - 11 in the form (x - a)² - b, where a = 4 and b = 11.

Let y = x² - 8x + 5 ..................( 1 )

Expanding (x - a)² - b we get,

x² - 2ax + a² - b ......................( 2 )

Equating ( 1 ) and (2), we get

x² - 8x + 5 = x² - 2ax + a² - b

Comparing the coefficient of x,

- 8  =  - 2a

a = 4

Comparing constants,

a² - b =  5

since we know a = 4

4² - b =  5

16 - b =  5

b = 11

Hence x² - 8x + 5  = (x - 4)² - 11

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The value of the variable 'y' will be 3. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the linear equation is given below.

2x - 5y = 1                ...1

-3x + 2y = - 18         ...2

Multiply equation 1 by 2 and equation 2 by 5, then we have

4x - 10y = 2

-15x + 10y = - 90

Add both equations, then we have

4x - 15x = 2 - 90

11x = 88

x = 8

Then the value of the variable 'y' is calculated as,

-3 (8) + 2y = - 18

- 24 + 2y = - 18

2y = 24 - 18

2y = 6

y = 3

The worth of the variable 'y' will be 3. Then the right choice is A.

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The equation of the required line is given as y = -23x - 92.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given problem can be solved as follows,

The equation of the line is  y = −23x + 32.

Then, its slope is given by -23.

Since the parallel lines have the same slope, the slope of the line parallel to  y = −23x + 32 is -23.

Now, the equation of the line passing through (4, -7) and parallel to the given line can be written as,

(y + 7)/(x - 4) = -23

=> y + 7 = -23x - 92

=> y = -23x + -99

=> y = -23x - 92

Hence, the equation of the line passing through (4, -7) and parallel to y = −23x + 32 is  y = -23x - 92.

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Answer:

Q14    x = 3

Q15    No unique solution

Step-by-step explanation:

Q14

The value of x where the line crosses the x axis is the solution for x

Here we see the line crosses the x axis at x = 3 so solution is x =3

Mathematically,

2x - 3 = 3

2x = 3 + 3  adding 3 to both sides

2x = 6

x = 6/2 = 3

Q15

This is a horizontal line which crosses the y-axis at y = 1

Since this does not cross the x axis but is parallel to it, there is no unique solution for x

Mathematically,
-4x + 2 = -4x + 1

Adding 4x to both sides we get the absurdity that 2 = 1 and that indicates no unique solution for x. Alternatively we can say that x has an infinite number of solutions

Answer:

22 rabbits and 50 hens

Step-by-step explanation:

Let H and R stand for the numbers of Hens and Rabbits.  Each hen has two feet and each rabbit has four feet.  Each only has 1 head.

We can set the quantities of feet and heads:

Hens:  2H feet and 1H heads

Rabbits:  4R feet and 1R heads

We are told that:

1.)  "The number of feet of the hens exceeds the number of feet of the rabbits by 12"  Rewrite this as an expression:

  2H - 4R = 12  [feet]

2)  "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"  This is written as:

  1H = 1R + 28  [heads]

Since each critter only has one head, this last expression will tell us, quickly, how many more Hens there are, which is 28.  But by substituting the first expression (the feet) into the second, we can detrermine the exact number of each animal.

Rearrange 2H - 4R = 12 to isolate one of the variables.  I'll choose H:

  2H - 4R = 12

  2H  = 12 + 4R

  H  = (12 + 4R)/2

   H =  6+2R

Now use this definition of H in the second equation:

1H = 1R + 28

1(6+2R) = 1R + 28

6 + 2R = 1R + 28

 R = 22   There are 22 rabbits

Use this in the second equation to find the number of hens:

1H = 1R + 28

1H = 22 + 28

 H = 50  There are 50 hens.

=================

Check:

1.)  "The number of feet of the hens exceeds the number of feet of the rabbits by 12."  

 Hens have 100 feet total.  Rabbits have 88 feet.    The hens have 12 more total feet:  This checks

2.)  "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"  

 There are 50 heans and 22 rabbits.  The number of hen heads exceed the number of rabbit heads by 28.  This also checks.

For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

4x-4y=12

16x-6y=-12

multiply equation 1 by 4,

16x-16y=48

-16x+6y=12

-10y=60

y=-10

-16x-60=12

-16x=72

x=72/16

x=4.5

The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.

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Answer:

9

Step-by-step explanation:

;)

answer:the answer for digital index of 23475 is 3

answer: 3

explanation: the digital index is 3 because 23475 is divisible by 3

The segments that could be the image of segment AB after a sequence of reflections, rotations, and/or translations include:

A. Line segment GH

D. Line segment NP

F. Line segment CD

From the information, the coordinates of the point A is (1, 2), the coordinates of the point B is (5, 2)

Therefore, the length of the line AB = 5 - 1 = 4 units

In this case, the transformations are, reflections, rotations, and/or translations which are rigid transformations, such that the length of the image of AB will be the same as the length of AB

Therefore, the possible images of AB are;

PN with coordinates P(5, -2) and N(9, -2) and length 9 - 5 = 4 units

HG with coordinates H(-4, -4) and G(-4, -8) and length -4 - (-8) = -4 + 8 = 4 units

CD with coordinates C(-4, 6) and D(-4, 2) and length 6 - 2 = 4 units

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Answer: The value of x is 0.625

Step-by-step explanation:

x=5/0.8

since figure A is scaled to 5 by 0.8, we divide 5 by 0.8 to find x.

x=0.625

Check the picture below.

so let's check the middle of the picture, inscribed angle "b" is intercepting the purple arc, wait a second!!! angle 22° is intercepting the same arc! ahaaa!.

now let's check the right of the picture, inscribed angle "a" is intercepting that brown arc, wait a second!!! angle 45° is intercepting the same arc!! ahaa!!.

well, you can see what's "c" and "d".

Step-by-step explanation:

here is your answer to your question

Answer: 20x^4 + 2x³ - 19x² - 28x + 6

Step-by-step explanation:

Your answer will be letter C [-4, ∞)

Answer:

10 and 8

Step-by-step explanation:

must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.

Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.

If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.

If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.

Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).

Answer: (6, -4)

Step-by-step explanation:

Because it translate right 4 units, so the x increase by 4, so x=6

It up 3, so y increase by 3, so y= -4

Answer:

Step-by-step explanation:

Answer:   -4608

========================================================

Explanation:

a = 9 = first term

r = -2 = common ratio

We multiply each term by -2 to generate the next term

The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)

If you tried plugging in say n = 2, you should find that,

9(-2)^(n-1)

9(-2)^(2-1)

9(-2)^1

9(-2)

-18

So that confirms the second term. I'll let you try the other values of n to confirm it further.

----------------------

From here, you plug in n = 10 to find the tenth term

9(-2)^(n-1)

9(-2)^(10-1)

9(-2)^9

9(-512)

-4608

Answer:

98-5 = 93

Step-by-step explanation:

Single bookcase units with two sides, top and bottom should be no wider than 36 inches without a center support.

Each shelf can hold 33 books

There are 1221 mystery books

Therefore the number of shelves he will need to build can be calculated as follows

= 1221/33

= 37

Hence Landon will need to build 37 shelves,

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Answer:

A- negative

B-positive

C- zero

Step-by-step explanation:

Going up= positive

Going down= negative

Horizontal line= zero

vertical line= undefined

Answer:

Step-by-step explanation:

12 x 3 = 36

answer is 36

Answer:

12 x 3 = 36

Step-by-step explanation:

The ratio of the radii of smaller circle to that of larger circle is 1/√2.

Let the Radius of smaller circle is "r".

So the area of the smaller circle will be π(radius)²=πr²

Let the Radius of the larger circle is "R".

So the area of the larger circle will be π(radius)²=πR².

In question it is given that, the area of the smaller circle is half of the area of larger circle.

That means,

area of smaller circle=1/2 area of larger circle

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2r/R=1/√2

Ratio of smaller circle to that of larger circle is 1/√2 .

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Answer: ($9.40) or (d)

Step-by-step explanation: