Determine the constant rate of change

The solution of the given equations is x=-7 and x=3.

The given equation is x² + 5x - 12 = | x + 3| + 7.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values such that, when substituted for the unknowns, the equation becomes an equality.

Now, x² + 5x - 12 = | x + 3| + 7 can be rewritten as

x² + 5x - 12 = x + 3 + 7

⇒x² + 5x - 12 = x+10

⇒x² + 5x - 12 -x - 10=0

⇒x² +4x -22 =0

From the obtained graph, the solution of equations is x=-7 and x=3.

Therefore, the solution of the given equations is x=-7 and x=3.

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The k has interval notation(7,13).

Given that 5< k-2<11

Remove all of the teams from the inequality's center that don't contain k.

Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

So, 5+2<k<11+2

7<k<13

Therefore, The interval notation for k is (7,13).

Equations in mathematics are not always balanced on both sides using a 'equal to' symbol. Sometimes it's a 'not equal to' relationship, as though something is more than or less than the other. In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or other mathematical expressions. Inequalities are mathematical expressions that fall within the category of algebra.

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c. It is not linear because it has a constant rate of change.

Answer:

D

Step-by-step explanation:

this is showing a quadratic

The points awarded for striking the inner circle ought to be tripled.

What is the inner circle?

The formula for the area of a(one) circle is an inner circle for the external circle, use the formula also abate the value of the inner circle, to find the remaining area, which means that the area of the external circle is 3( three) times larger, making it 3( three) times more likely to hit the external circle.

Thus, The points awarded for striking the inner circle ought to be tripled.

[tex]\pi r^2 A =\pi 2^2 = 12.566 A\\[/tex]

so,

[tex]\pi 4^2 - 12.566 = 3(three)[/tex]

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Answer:

Step-by-step explanation:

For every "h" plug in "5", then follow the order of operations

2h+h-2(3)

2(5)+5-2(3)

10+5-6

15-6

=9

The answer is 9

In a survey where the ratio of students who prefer muffins to bagels is 4 to 5 and 420 prefer muffins, 525 students prefer bagels.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two ratios, such that

a : b = c : d

Given a proportion, the product of its means must be equal to the product of its extremes. That is:

ad = bc

If the ratio of students who prefer muffins to bagels is 4 to 5, and 420 students prefer muffins, the proportion can be written as:

4 : 5 = 420 : n

where n = number of students who prefer bagels

Solving for n,

4n = 5(420)

4n = 2100

n = 525

number of students who prefer bagels = 525

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Answer:

Step-by-step explanation:

Hi

[tex]2\frac{1}{2} ~~ : ~~ \cfrac{5}{8}\implies \cfrac{5}{2} ~~ : ~~ \cfrac{5}{8}\implies \cfrac{ ~~ \frac{5}{2} ~~ }{\frac{5}{8}}\implies \cfrac{5}{2}\cdot \cfrac{8}{5}\implies 4 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}~~ : ~~1\implies \cfrac{ ~~ \frac{1}{8}~~ }{1}\implies \cfrac{1}{8} ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]4~~ : ~~1\frac{1}{4}\implies 4~~ : ~~\frac{5}{4}\implies \cfrac{4}{ ~~ \frac{5}{4} ~~ }\implies \cfrac{4}{1}\cdot \cfrac{4}{5}\implies \cfrac{16}{5}~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}~~ : ~~3\frac{1}{2}\implies \cfrac{7}{8}~~ : ~~\cfrac{7}{2}\implies \cfrac{ ~~ \frac{7}{8}~~ }{\frac{7}{2}}\implies \cfrac{7}{8}\cdot \cfrac{2}{7}\implies \cfrac{1}{4}~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]4\frac{1}{3}~~ : ~~3\implies \cfrac{13}{3}~~ : ~~3\implies \cfrac{ ~~ \frac{13}{3}~~ }{3}\implies \cfrac{13}{3}\cdot \cfrac{1}{3}\implies \cfrac{13}{9} ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 2~~ : ~~\cfrac{1}{2}\implies \cfrac{2}{ ~~ \frac{1}{2} ~~ }\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4 ~~ \checkmark[/tex]

Answer: x=1

Step-by-step explanation:

2(8x-4y=7)

  3x+6y=12

16x-6y=7

3x+6y=12

19x/19 = 19/19

x=1

Step-by-step explanation:

8x-4y=7 3x+6y=12

8x-3x=7 4y+6y=12

5x=7 10y=12.

Lisa bowling score is 100.

John bowling score is 282.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Lisa and John are bowling.

Johns score is three times the difference of Lisa's score and 6.

The sum of their scores is 382.

Now, Let Lisa bowling score = x

Then, John bowling score = 3 (x - 6)

Since, The sum of their scores is 382.

Hence,

x + 3 ( x - 6 ) = 382

After solving,

x + 3x - 18 = 382

4x = 382 + 18

4x = 400

x = 100

Hence, Lisa bowling score = x = 100

And, John bowling score = 3 (x - 6)

                                       = 3 (100 - 6)

                                       = 3 × 94

                                       = 282

Therefore, Lisa bowling score is 100.

And, John bowling score is 282.

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Answer: 1.75 minutes

Step-by-step explanation:

6 gallons per minute.

14.5-4=10.5

10.5/6=1.75 minutes

Answer: 117in^3

Step-by-step explanation:

Answer:

Step-by-step explanation: 40 see attachment

Step-by-step explanation:

once we know what the domain and the range of a function is, this is very simple.

the domain is the interval or set of all valid x (input) values.

the game is the interval or set of all valid y (function result) values.

so, what are all the valid x values ? that means for how many months of collection can we use this function to see how many figurines he has ?

well, we can stay with 0 (what he currently has) and go up to 5 (because after 5 months he does not want to continue this behavior).

so, the domain is

0 <= x <= 5 if we allow also fractions of months as input (if this makes sense)

or

x € {0, 1, 2, 3, 4, 5} if we allow only whole numbers.

and the range ? what are the possible result values of the function ?

for x = 0 it starts with y (or f(x)) = 100.

x = 1 gives us 100 + 3×1 = 103

x = 2 gives us 100 + 3×2 = 106

x = 3, 100 + 3×3 = 109

x = 4, 100 + 3×4 = 112

x = 5, 100 + 3×5 = 115

so, the range is

100 <= y <= 115 if we allow fractions of months

or

y = f(x) € {100, 103, 106, 109, 112, 115} if we allow only whole months as values of x.

The critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).

Given that;

Number of residents, n = 7

Z*- value of 90% confidence level equals z* = 0.79

Mean x = 1.7 and deviation σ = 0.36

What is the standard deviation?

Standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.

Now,

Number of residents, n = 7

Z*- value of 90% confidence level equals z* = 0.79

Mean x = 1.7 and deviation σ = 0.36

The confidence interval for mean waste recycled per person is

[tex](x-z^{*} \frac{sigma}{\sqrt{n} } ; x+z^{*} \frac{sigma}{\sqrt{n} } )[/tex]

[tex](1.7 - 0.79*\frac{0.36}{\sqrt{7} } ; 1.7 + 0.79*\frac{0.36}{\sqrt{7} })[/tex]

[tex](1.592, 1.807)[/tex]

Hence, the critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).

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The slope of the line passing through the given points is 0.4 or 2/5.

From the table given below, we have (2, 23) and (5, 24.3).

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y-values over the change in the x-values.

Put the points (2, 23) and (5, 24.3) in the slope formula and find the slope.

That is, m=(24.3-23)/(5-2)

=1.3/3

=0.4

=4/10 = 2/5

Put m=2/5 and the coordinate points (2, 23) in y=mx+c.

That is, 23=2/5 (2)+c

⇒23 - 4/5 =c

⇒111/5 = c

⇒ c=22.2

Now, equation is y=0.4m+22.2

Therefore, the slope of the line passing through the given points is 0.4 or 2/5.

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Answer:

b

Step-by-step explanation:

 the answer is b because 50 + (11 x 9) = 149

75 + (8 x 9) = 147

Therefore, franks fiesta is less expensive for parties of 9 or more

Answer:

n <(_) -2

Step-by-step explanation:

We can start by doing this linearly.

First subtract 4 on both sides

-3n >(_) 6

Then divide both sides by -3. You have to switch the sign because you are dividing by a negative number.

n <(_) 6

The answer for "x" in 6^(x+2) = 10 is -0.715

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The number of tickets that can be bought with $40 is 4 tickets

It costs $9.50 to buy 1 tickets

The number of tickets that will be bought with $40 can be calculated as follows

= 40/9.50

= 4.2

Hence 4 tickets will be bought with $40

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Answer:

The slope is 4

Step-by-step explanation:

This equation is in slope intercept form

y = mx+b

where m is the slope and b is the y intercept

y = 4x-7

The slope is 4 and the y intercept is -7

The distance between points A and B  is 8 units.

We have been given two points A and B.

The coordinates of the points are A = (3,-7) B = (3,1)

We need to find the distance between points A and B.

Let d be the distance between points A and B.

Using distance formula,

d = √[(3 - 3)² + (1 - (-7))²]

d = √[0² + 8²]

d = √8²

d = 8 units

Therefore, the distance between points A and B  is 8 units.

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The computation shows that the time will be 11:05 am.

The friends entered the amusement park at 10:05 AM, the wait time it took 35 minutes to ride the FLIP-A-Trip and it took 23 minutes to ride the Slippery Slope.

Therefore, the time will be:

= 10.05 + 35 + 25

= 10:05 + 60 minutes

= 10:05 + 1

= 11:05

.It should be noted that 60 minutes= 1 hour. Therefore, you'll add 1 hour to the original time.

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Answer:

8 is 69

9 is 68

t is 99 i think

z is 80 i think

The first, second, and third numbers are 11, 80, and 20 respectively.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the first number is a second is b and the third one is c

Now,

The sum of the three numbers is 111

So,

a + b + c = 111

The first number is 9 less than the third

So.

a = c - 9

And the second number is 4 times third

So,

b = 4c

By substitution,

c - 9 + 4c + c = 111

c = 20

b = 4(20) = 80

a = 20 - 9 = 11

Hence "The first, second, and third numbers are 11, 80, and 20 respectively".

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The given question are incomplete , complete question is ;

The sum of the three numbers is 111. the first number is 9 less than the third. the second number is 4 times the third. what are the numbers?

The area of the shaded region based on the information will be 201cm².

It should be noted that the radius of the outer circle will be:

= Diameter / 2

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

= 24 / 2

= 12cm

The area of the circle = πr²

= 3.14 × 12²

= 3.14 × 144

= 452.16 cm²

The area of the circle with radius 8cm = 200.96 cm²

The area of the circle with radius 4cm =50.24cm².

The area of the shaded region:

= 452.16 - 200.96 - 50.24

= 200.96 cm²

Therefore, the area of the shaded region based on the information will be 201cm².

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Answer:

B

Step-by-step explanation:

_/25 can be rooted to 5. 5 is rational.

If we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

Given,

The total amount = $60

The ratio = 3:1

Then the amount given to first person = 3x

The amount given to the second person = x

Given that the total amount is 60

Then  the equation will become

x+3x=60

4x=60

x=[tex]\frac{60}{4}[/tex]

x=15

The amount given to the first person = 3x

Substitute the value of x in the equation

The amount given to the first person =3x

=3×15

= $45

The amount given to the second person =x

= $15

Hence, if we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

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The original price of a zip disk is; $1.4

Let cost of zip sticks bought by Ramon be x. Thus;

Cost that Ramon paid = 5x

Now, we are told that 2 days later the price increased by $1.5 per disc. Thus, new cost = x + 1.5

Leticia bought ten disks at the sale price and paid 22 more than ramon paid for 5 disks. Thus, equation here is;

10(x + 1.5) = 5x + 22

Expand the bracket to get;

10x + 15 = 5x + 22

10x - 5x = 22 - 15

5x = 7

x = 7/5

x = $1.4

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Answer: 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

it's the fourth number in the sequence