Which is a correct solution for the following system of Inequalities

Answer:

b or c

Step-by-step explanation:

126+6x=180

180-126=54

54/6=9

x= 9

The area of parks is 360 m² , base and height are respectively 30m and 24 m.

Given a triangle shaped park with sides 25m, 24m and 30 m.

The total area that is bounded by a triangle’s three sides is referred to as the triangle’s area.

We know that area of triangle = ½ * base * height

Clearly show that base is 30m and height is 24 m.

So, area of triangle = ½ * 30 * 24 = 720/2 = 360 m²

Therefore, area of triangle shaped park is 360m².

Base and height are respectively 30m and 24m.

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After performing the division , the missing term in the problem is (2x³ + 5x² + 9)/(x + 3) = (2x² -x +3) .

The problem is (2x³ + 5x² + 9)/(x + 3) ;

that means , we have to divide , the expression "2x³ + 5x² + 9" by "x + 3" ;

first we multiply (x+3) by 2x² ;

the expression becomes : 2x³ + 5x² + 9

                                           -2x³ - 6x²

                                                    -x²  +  9

next we multiply by -x :               -x²  - 3x                      

                                                             3x + 9

next we multiply by 3 :                        -3x - 9

                                                                      0   .

So , dividing the "2x³ + 5x² + 9" by "x + 3" , we get the remainder is 0 and the quotient is 2x² - x + 3 .

Therefore , the missing term is 2x² - x + 3 .

The given question is incomplete , the complete question is

Which is the missing term in this problem ?

(2x³ + 5x² + 9)/(x + 3) = ______  ;

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Answer:

x intercept = 1.66666...

y intercept = 2.5

The x intercept is approximate. The 6's go on forever. The y intercept is exact without any rounding done to it.

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

Explanation:

Plug in y = 0. Then solve for x to get the x intercept.

3x+2y = 5

3x+2*0 = 5

3x = 5

x = 5/3

x = 1.66666...

The 6's go on forever.

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

Plug x = 0 into the equation and solve for y. This will get us the y intercept.

3x+2y = 5

3*0+2y = 5

0+2y = 5

2y = 5

y = 5/2

y = 2.5

This value is exact without any rounding

To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.

First we can eliminate the y variable by adding the two equations together:

X + 3y = 14

2x - 3y = -8

3x = 6

Dividing both sides by 3:

x = 2

Now we have the value of x, we can substitute it back into one of the original equations:

X+3y=14

2 + 3y = 14

Subtracting 2 from both sides:

3y = 12

Dividing both sides by 3:

y = 4

So the solution of the system of equations is (x,y) = (2,4)

To check the solution, we can substitute the values back into the original equations:

x + 3y = 14

2 + 3(4) = 14

2 + 12 = 14

14 = 14

and

2x - 3y = -8

2(2) - 3(4) = -8

4 - 12 = -8

-8 = -8

As the equation holds true, the solution (2,4) is correct.

c=14+xh is the  equation that represents the relationship between h and c.

An expression is combination of variables, numbers and operators.

Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.

Let h represent the duration of a rental in hours and c represent the total cost of the rental.

We have to find the  relationship between h and c.

c=14+xh

Here x represents the dollar.

Hence, c=14+xh is the  equation that represents the relationship between h and c.

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The solution of the given fraction can be gotten through filling the boxes with the following values respectively;

8/100 + 9/10 = 98/100

A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.

The given fraction;

8/100 + 9/10 = ?

Find the lowest common multiple of the denominator = 100.

= 8/100 + 9/10

= 8 + 90/100

= 98/100

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The term is actually forming an AP.

On 2010 = $9 = a

[tex] \frac{1.5}{100} \times 9 \\ = \frac{13.5}{100} \\ = 0.135[/tex]

d = $0.135

now on 2020, that's 10 years after 2010.

n = 10

[tex]an = a + (n - 1)d \\ = 9 + (10 - 1)0.135 \\ 9 + 9(0.135) \\ = 9 + 1.215 \\ = 10.215[/tex]

For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-2 - (-11)]/[0 - (-3)]

(-2 + 11)/(0 + 3)

9/3

3

So, the slope point is obtained as m = 3.

The equation becomes - y =3x + b

To find the value of b substitute the values of x and y in the equation -

-11 = 3(-3) + b

-11 = -9 + b

b = -11 + 9

b = -2

So, the value for b is -2.

Now, the equation becomes -

y = 3x - 2

The graph is plotted for the function.

Therefore, the equation is y = y = 3x - 2.

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The length of the diagonal of the rectangle is 24cm.

The diagonal of the rectangle equals the square root of the width squared plus the height squared.

The width of the rectangle is indicated by the letter “w” and the length of the rectangle is indicated by "l".So, the diagonal of a rectangle formula is expressed as d = (l² + w²),

According to the question,

A rectangle is 22 inches long and 10 inches wide.

To observe the diagonal we use the Pythagorean Theorem:

Let, x = hypotenuse

22² + 10² = x²

⇒484 +100 =x²

⇒x = 24.14 =24

So, the length of the diagonal of the rectangle is 24cm.

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=> Convert feet into yards.

660 feet = 220 yards.

=> Convert feet into inches.

660 feet = 7920 inches.

Now, According to the question:

=> Convert feet into inches.

660 feet = 7920 inches

Formula: multiply the value in feet by the conversion factor '12'.

So, 660 feet = 660 × 12 = 7920 inches.

=> Convert feet into yards.

660 feet = 220 yards

Formula: divide the value in feet by 3 because 1 yard equals 3 feet.

So, 660 feet = 660/3

     660 feet = 220 yards.

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The distance between (-6 5) and (-6 -3.5) is 14.71 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-6, 5) and (-6, -3.5) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-6 - 6)² + (5 - -3.5)²}

d =√{144 + 72.25}

d = √216.25

d = 14.71 units

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C

Step-by-step explanation:

c,c is the answer i think so

The integers greater than 999 but not greater than 4000 is 375.

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.

The smallest number in the series is 1000, a4-digit number.

The largest number in the series is 4000, a4-digit number

The left most digits (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.

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335 students of fourth graders voted for the Falcon.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:

  Commutative and associative properties hold true for fractional       addition and multiplication

Using proportions, it is found that 335 students voted for the Falcon. In total, 536 students voted for a mascot. The proportion that voted for the Falcon is 5/8 of the total number of students. To find the number of students that voted for the Falcon, we multiply the proportion of 5/8 by the total of 536, thus: 335 students voted for the Falcon.

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The rate of change is given a 5 / 6. The values we have here are not linear

The rate of change (r.o.c) is the change in y (or the dependent variable) for every unit change in x (or the independent variable). In this case, the r.o.c is

(10-5) / (12-6) = 5/6.

This is not linear because linear is a relationship between a variable and a constant, here the relationship between y and x is not linear because the change in y is not constant with respect to the change in x.

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Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangle ΔABC, angle ∠B = 86° and ∠C = 55°, then angle ∠A is given as,

∠A + ∠B + ∠C = 180°

∠A + 86° + 55° = 180°

∠A = 39°

In triangle ΔDEF, angle ∠D = 55° and ∠F = 40°, then angle ∠E is given as,

∠E + ∠F + ∠D = 180°

∠A + 40° + 55° = 180°

∠A = 85°

Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.

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Answer:

$2837.04

Step-by-step explanation:

semi-annually = every 6 month

p=2000

i=6%

t=3 years = 6 periods

compound 6 times in 3years = (1+6%)^6 =1.418519

multiply principal of $2000 = 2837.04

For the inequality "2(34 + 12) > 5b" that contain a variable "b" , then the numbers that make this inequality true are (a) 16 , (b) 18 .

The inequality containing the variable "b" is ⇒ 2(34 + 12) > 5b  ;

simplifying the inequality ,

we have ;

⇒ 2×(46) > 5b  ;

⇒ 92 > 5b ;

(a) Substituting value of b = 16 ,

we get ; 92 > 5×16

⇒ 92 > 80 , TRUE  .

(b) Substituting value of b = 18 ,

we get ; 92 > 5×18

⇒ 92 > 90 , TRUE  .

(c) Substituting value of b = 19 ,

we get ; 92 > 5×19

⇒ 92 > 95 , FALSE  .

(d) Substituting value of b = 20 ,

we get ; 92 > 5×20

⇒ 92 > 100 , FALSE  .

Therefore , the inequality is TRUE for two values of b that are (a) 16 , (b) 18.

The given question is incomplete , the complete question is

This inequality 2(34 + 12) > 5b ;  contains a variable "b". Choose ALL numbers that make this inequality true.

(a) 16

(b) 18

(c) 19

(d) 20

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Answer:

1. y=29

2. m= -8

3. x=10

Step-by-step explanation:

1. Add the numbers

y+y+1+y+2=90

y+y+3+y=90

combine like terms

3y+3=90

Subtract 3 from both sides

3y+3-3+90-3

3y=87

Divide both sides by the same factor

3y/3 = 87/3

y=29

2. Distribute

5(m+4)=-20

5m+20=-20

Subtract 20 from both sides

5m+20=-20

5m+20-20+-20-20

Simplify

5m=-40

Divide both sides by the same factor

5m/5 = -40/5

m= -8

3. Add 8 to both sides

3x-8=2x+2

3x-8+8+2x+2+8

Simplify

3x=2x+10

Subtract 2x from both sides

3x=2x+10

3x-2x+2x+10-2x

x=10

Answer:

q= -3.25 and p= -6.25

Step-by-step explanation:

p=5q+10. p=q-3

p-5q=10. p-q=-3 subtract the two equations

-4q=13 q= -3.25 and p= -6.25

The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.

By definition, the mean value theorem is

f'(c) = [f(b) - f(a)]/b - a

So, in this case, we know that a = 2 and b = 7.

Now, we need to find f(2) and f(7) by replacing those values with the given function

f(x) = 9 - 14/x

f(7) = 9 - 14/7 = 9 - 2 = 7

So, f(b) = f(7) = 7.

f(x) = 9 - 14/x

f(2) = 9 - 14/2 = 9 - 7 = 2

So, f(a) = f(2) = 2

Then, we replace all values,

f'(c) = [f(b) - f(a)]/b - a

= (7 - 2)/(7 - 2)

= 5/5

= 1

Now, calculate the derivative of the function, which has to be equal to 1,

f(x) = = 9 - 14/x

f'(x) = 14/x² = 1

Now, we solve the equation to calculate the value of c,

14/x² = 1

x² = 14

x = √14

Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.

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The graph of the quadratic function y = x² + 2x - 5 is given by the image at the end of the answer.

The domain and range are given as follows:

The domain of a function is the set that contains all the possible input values for the function, hence in the graph it is composed by the values of x of the function.

The range of a function is the set that contains all the possible output values for the function, hence in the graph it is composed by the values of y of the function.

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Answer:

I think it is (8,16).

The probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.

There are 2 boys initially and an unknown number of girls in the nursery, so there were a total of 2 + x babies in the nursery, where x is the number of girls.

Since we know that one of those babies is a boy, there are a total of 2 + x - 1 = 1 + x babies left in the nursery.

So the probability of the nurse picking up a boy, given that the woman gave birth to a boy, is 1/(1+x).

P(boy | picked up boy) = P(picked up boy | boy) * P(boy) / P(picked up boy)

= (1/(1+x)) * 1/2 / (1/(1+x) * 1/2 + x/(1+x) * 1/2)

= 1/3

So the probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.

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Sylvan made a mistake computing the quotient in the problem.

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: 1.6 divided by 0.4

We know 1.6 can be expressed as 1.6=0.4×4

x ÷ y = z.

1.6÷0.4=4

Division method is nothing but the inverse of multiplication.

Divide 1.6 by number 0.4.

Solution:1.6÷0.4=1.6/0.4 with remainder zero

                          =4

Thus the quotient should have been 4

But according to Sylvan 1.6/0.4=0.4 which is not correct.

Hence, Sylvan computed the wrong quotient.

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The width of the swimming pool is 1.624yards.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Here, we have,

a swimming pool can hold 9.745 cubic yards of water.

i.e. V = 9.745

it has a length of 3 yards and a height of 2 yards.

i.e. l= 3

    h=2

so, width = w = V/(l*h)

i.e. w = 1.624

Hence, the width of the swimming pool is 1.624yards.

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Answer:

3 and 4

Step-by-step explanation:

numbers don't repeat in the X side

Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.

Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.

First, let's use the sine function to find the value of KL:

sin(40) = KL/ML

KL = (sin(40))(ML)

KL = (sin(40))(8)

Next, let's use the cosine function to find the value of MK:

cos(40) = MK/ML

MK = (cos(40))(ML)

MK = (cos(40))(8)

Finally, let's use the tangent function to find the value of mZK:

tan(40) = KL/MK

mZK = tan(40)

To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.

sin(40) = 0.766

cos(40) = 0.644

tan(40) = 1.193

KL = (0.766)(8) = 6.128 ≈ 6.1

MK = (0.644)(8) = 5.152 ≈ 5.2

mZK = 1.193

So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.

Answer:

To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.

Given:

angle K = 40°

ML = 8

KL = 2

We can use the sine function to find the value of angle M:

sin(M) = KL / ML

sin(M) = 2 / 8

sin(M) = 0.25

So M = arcsin(0.25) = 14.04 (approximately)

Next, we can use the cosine function to find the value of MK:

cos(M) = ML / KL

cos(M) = 8 / 2

cos(M) = 4

So MK = 4

Lastly, we can use the tangent function to find the value of angle L:

tan(L) = KL / MK

tan(L) = 2 / 4

tan(L) = 0.5

So L = arctan(0.5) = 26.57 (approximately)

So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.

John must work 8 hours walking the dog and 2 hours as a Maths tutor in order to earn at least $96.

Let us assume that m represents the number of hours he walks the dogs

and n represents the number of hours he works as a maths tutor

John wants to work no more than 10 hours.

As we know the statement 'No more' is represented by the inequality '≤'

So, we get an inequality

m + n ≤ 10             ...........(1)

Also, he also wants to earn at least $96.

As we know the statement 'at least' is represented by the inequality '≥'

So, we get an inequality

8m + n ≥ 96             ...........(2)

So, we get a system of inequalities:

m + n ≤ 10      

8m + n ≥ 96  

Now, we solve this system of inequalities.

Consider m + n = 10           .........(3)

and 8m + n = 96                    .........(4)

Substitute m = 10 - n for x in Equation 4

8(10 - n) + 16n = 96

80 - 8n + 16n = 96

8n = 96 - 80

n = 2

Substitute above value of n in  equation m = 10 - n

m = 10 - 2

m = 8

Thus, John must work 8 hours walking the dog and 2 hours as a Maths tutor.

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The complete question is:

John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this and solve.