7<-(-k-3)+2 solve inequality

The composite function (f o g)(x) is found by substituting g(x) into the f(x) expression. Upon simplification, (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1) is: 1/(x² + 2x + 1) + 6/(x+1) + 5.

To find the composite function (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1), we substitute g(x) into f(x). That is, wherever you see 'x' in f(x), replace it with what g(x) is equal to.

Start with f(g(x)) = f(1/(x+1)). In f(x), replace x with 1/(x+1), which gives us: (1/(x+1))² + 6*(1/(x+1)) + 5. This is the composite function (f o g)(x).

To simplify further: the first term '(1/(x+1))²' becomes '1/(x² + 2x + 1)', the second term '6*(1/(x+1))' becomes '6/(x+1)', and the third term is just '+5'. So the composite function (f o g)(x) simplifies to: 1/(x² + 2x + 1) + 6/(x+1) + 5.

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Final answer:

Mridul will take 14.4 minutes to jog around a rectangular park for a total of 6 rounds, considering the total jogging distance of 2.16 kilometers at a pace of 9 kilometers per hour.

Explanation:

To calculate the time Mridul will take to jog around a rectangular park for 6 rounds, we need to compute the total distance he will cover and then use his speed to find the time. The perimeter of the rectangle is the sum of all its sides. Since the park is 100m by 80m, the perimeter will be (2 × 100m) + (2 × 80m), which equals 360 meters. For 6 rounds, the total distance will be 6 × 360 meters = 2160 meters or 2.16 kilometers.

Next, we use the formula for time:

Time = Distance / Speed

Given Mridul's jogging rate is 9 kilometers per hour, we can convert this speed into meters per second to match the distance units by multiplying by 1000 and dividing by 3600 (the number of seconds in an hour), which gives us 2.5 meters per second. Finally, to find the time taken:

Time = 2160 meters / (2.5 meters/second)

This calculation results in 864 seconds, which when converted to minutes is 14.4 minutes. Therefore, Mridul will take 14.4 minutes to jog 6 rounds around the park.

Answer:

The Option D (x ≥ - 53) is correct for the given graph.

Step-by-step explanation:

As shown in the graph blue part is from - 53 to -50 including -53.

therefore x ≥ - 53.

The correct conclusion based on the data is that 10% of all eighth-grade students at the High Achievers Charter School are reading below grade level.

Based on the information provided in the question, the most accurate conclusion we can make is that 10% of all eighth-grade students at High Achievers Charter School (HACS), specifically, are reading below grade level. This is because the sample data was only collected from eighth-grade students at HACS. Therefore,

answer C

is correct. That being said, these results only apply to this specific school and grade level and cannot be generalized for all students at HACS or all other schools.

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To divide the given polynomial by a binomial, use polynomial long division, resulting in a quotient of -2x² - 10x - 30 and a remainder of 92.

Dividing a Polynomial by a Binomial

To divide the polynomial -2x³ – 4x² + 3x + 2 by the binomial x - 3, we will use polynomial long division, which is a process similar to long division with numbers. It involves subtracting multiples of the divisor from the dividend to get a quotient and possibly a remainder.

First, divide the first term of the dividend, -2x³, by the first term of the divisor, x, to get -2x².

Multiply the divisor x - 3 by the first term of the quotient, -2x², to get -2x³ + 6x².

Subtract this result from the dividend to obtain the new dividend -4x2 (adjusting the original terms), which becomes -10x².

Repeat this process with the remaining terms of the new dividend.

Continue until all terms of the dividend have been divided.

This process results in the quotient -2x² - 10x - 30 and a remainder of 92. The complete division statement is -2x³ – 4x² + 3x + 2 = (x - 3)(-2x² - 10x - 30) + 92.

Answer:

The solution of the given system of equations is,

[tex]x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}[/tex]

Step-by-step explanation:

The given equations are :

x + ay = b          .......(1)

ax - by = c        .......(2)

We will use 'Substitution Method' to solve the given system of equations.

In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable  and then substitute that value in the other equation to find the value of the another variable.

Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).

Consider the equation (1), that is,

   x + ay = b ⇒ x = b - ay          ........(3)

Substitute the value of 'x' from (3) in (2), we get

  a(b - ay) - by = c

⇒ab - a²y - by = c

⇒-a²y - by = c - ab

⇒-y(a²+b) = c - ab

⇒y(a²+b) = ab - c

[tex]\implies y=\frac{ab-c}{a^{2}+b}[/tex]

Now, substituting the above value of 'y' in equation (3), we get

[tex]x=b-a(\frac{ab-c}{a^2+b})[/tex]

[tex]\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}[/tex]

[tex]\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}[/tex]

[tex]\implies x = \frac{b^2+ac}{a^2+b}[/tex]

Hence, the solution of the given system of equations is,

[tex]x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}[/tex]

Answer:

Step-by-step explanation:

105/5= 21

21m=b

feel free to ask any question

[tex]\[b = 21m\][/tex] This equation indicates that the number of blinks [tex]\( b \)[/tex] is equal to [tex]21[/tex]times the number of minutes [tex]\( m \)[/tex]

To find a linear equation that represents the number of times Maribel blinks in a given number of minutes, we can use the information provided and assume a constant rate of blinking.

Given:

Maribel blinks [tex]105[/tex] times in [tex]5[/tex] minutes.

To find the rate of blinking per minute, we divide the total number of blinks by the total number of minutes:

[tex]\[\text{Rate of blinking} = \frac{105 \text{ blinks}}{5 \text{ minutes}} = 21 \text{ blinks per minute}\][/tex]

Let [tex]\( b \)[/tex] represent the number of blinks, and let [tex]\( m \)[/tex] represent the number of minutes. Since Maribel blinks at a constant rate, the relationship between [tex]\( b \)[/tex] and [tex]\( m \)[/tex] is linear and can be described by the equation:

[tex]\[b = 21m\][/tex]

Answer:

1/52

Step-by-step explanation:

4/208=1/52

Answer:

58+54=112

Step-by-step explanation:

The solution is 112 objects

The total number of objects the 7 people from Pia's Pottery shop and Jason's Craft shop is A = 112 objects

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of objects be = A

Let the number of mugs in Pia's shop be = m₁

Let the number of bowls in Pia's shop be = b₁

Now , the value of m₁ = 29 mugs

The value of b₁ = 18 bowls

And ,

Let the number of mugs in Jason's shop be = m₂

Let the number of bowls in Jason's shop be = b₂

m₁ = m₂ and b₂ = 2 x b₁

Now , the value of m₂ = 29 mugs

The value of b₂ = 36 bowls

So , the total number of objects A = number of mugs in Pia's shop + number of bowls in Pia's shop + number of mugs in Jason's shop + number of bowls in Jason's shop

Substituting the values in the equation , we get

The total number of objects A = 29 + 18 + 29 + 36

The total number of objects A = 112 objects

Therefore , the value of A is 112 objects

Hence , the total number of objects is 112 objects

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Answer:

Yes, because (−1, −5) is below the line.

Step-by-step explanation:

The given inequality is [tex]y \leq  -\frac{3}{4} x - 1[/tex] .......... (1)

Now, rearranging this equality relation we get,

4y = - 3x - 4

⇒ 3x + 4y = - 4

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

This equation is in intercept form and the line represented by this equation passes through the x-intercept [tex](- \frac{4}{3}, 0)[/tex] and y-intercept (0,-1).

Now, it is clear that (0,0) point is above the equation.

But (0,0) point does not satisfy the inequality equation (1).

Hence, the solution of the inequality equation (1) is below and including line (2).

Now, point (-1,-5) is below the line (2) and hence, it is a solution of the inequality (1) as it is below the line. (Answer)

Answer:

the answer is [yes, because (-1, -5) is below the solid line].

Step-by-step explanation:

I took the test and got it right

Answer:

8.9 thats rounded if it wasnt rounded it'll be 8.944

Step-by-step explanation

AB = 14.42

If you plot these points on a graph, they will not be in a straight line, so we'll need to do a little more math here. Draw a diagonal line connecting both points, and use this line as the hypotenuse, so you can draw a right triangle. Count the lengths of each side (except the long, diagonal line called the hypotenuse). Use the equation a^2 + b^2 = c^2 to find the length of side c.

Since side a is 8 units long, square it to get 64.

And side b is 12 units long, and if we square it we get 144.

64 + 144 = 208.

One last step. Now we need to find the square root of 208.

It is 14.42.

So, the distance between points a and b is 14.42 units.

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

5/x = 4/x+3

5 * ( x+3) =  4 * x

5x + 15 = 4x

5x - 4x =  -15

x = ( -15)

Answer:

The fourth option

Step-by-step explanation:

48 is the minimum height, 42 is his current height, and h is the height he must grow. 42 +h is at least 48 so that rules out the first and third options. The second option would be around twice the required  height, so it must be the fourth option.

Answer:

False

Step-by-step explanation:

Image (graph) of y = Sinx is attached.

First, lets understand domain and range.

Domain is the set of all x-values for which a function is defined (x axis).

Range is the set of all y-values for which a function is defined (y axis).

We are said that range of y = Sin x is the set of all real numbers.

If we look at the graph and look at the y-values for which the function is defined, we see that the Sin Curve oscillates between y = -1 and y = 1.

So the range would be:

[tex]-1 \leq y \leq 1[/tex]

It is not defined for other values, certainly not for ALL REAL NUMBERS!

So, this statement is false.

Answer:

53.702

Step-by-step explanation:

You split the two numbers into two.

24, 0.41, 2, and 0,2

Then multiply each one by each other

2 x 24

2 x 0.41

0.2 x 24

0.2 x 24

24 x 2

24 x 0.2

0.41 x 2

then add all of them together and you get your answer

Answer:

8(3+4)

Step-by-step explanation:

simple use pemdas

parenthesis 3+4= 7

multiply 8x7=56 :)

Answer: 13

Step-by-step explanation: In this problem we're asked to rewrite as addition and then evaluate.

It's important to understand that minus a negative means the same thing as plus a positive so we can change 5 - (-8) to 5 + (+8).

Now we can simply add to get a sum of 13.

Therefore, 5 - (-8) or 5 + (+8) = 13

Answer: 13

Step-by-step explanation: We originally have the equation 5-(-8).

Flip everything around.

5 + (+8)

5 + (+8) = 13.

When it gives the keywords "rewrite as addition" you should know that you need the rewrite the equation an opposite way of what it was written.

In this case it was 5-(-8).

Flip the signs, 5+(+8).

Add 5 to 8 and get 13.

Answer:

0.0555555556

Step-by-step explanation:

Answer:

1/18 or 0.055...

Step-by-step explanation:

2/36=1/18

Answer:

9 lawns

Step-by-step explanation:

If she already has $25 of the $115 dollars needed for the ticket, she only needs to make $90 more. If she makes $10 each lawn, she would need to mow 9 lawns in order to get the $90 dollars.

Final answer:

To simplify the expression 7[63 ÷ (52 – 22) – 1], perform the operations inside the parentheses first, followed by division, subtraction, and multiplication in that order. The simplified form of the expression is 14.

Explanation:

To find the simplified form of the expression 7[63 ÷ (52 – 22) – 1], we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Within the parentheses, we first simplify the exponent, so we calculate 52 – 22 which is 25 – 4.

Perform the subtraction inside the parentheses: 25 – 4 equals 21.

Next, we divide 63 by 21, which equals 3.

Subtract 1 from 3 to get 2.

Finally, multiply 7 by 2 to get the simplified expression, which is 14.

Thus, the simplified form of the expression is 14.

Answer:

Dave:

$20 + 8% of 20 = $21.6

Dave payed a total of $21.6 for the basketball.

Mel

$28 + 8% of 28 = $30.2

Mel payed a total of $30.2 for the football.

$30.2 - $21.6 = $8.6

The difference is $8.6.

Answer:

The cost of 1 hat = $2.24

The coat of 1 pair of oven mitten = $2.06

Step-by-step explanation:

Let us assume the cost of 1 hat = $ x

The cost of 1 pair of oven mitten = $y

Case 1:   5 hat and 4 pairs of mittens for $30

Cost of 5 hats  =5 x ( cost of 1 hat) = 5 x    = $ (5 x)

Cost of 4 mittens  =4 x ( cost of 1 mittens) = 4 (y)    = $ (4 y)

Total cost of 5 hats + 4 mittens  = 5x  + 4 y

⇒ 5 x + 4 y = $30 ....... (1)

Case 2:   2 hat and 5 pairs of mittens for $30

Cost of 2 hats  =2 x ( cost of 1 hat) = 2 x    = $ (2 x)

Cost of 5 mittens  =5 x ( cost of 1 mittens) = 5 (y)    = $ (5 y)

Total cost of 2 hats + 5 mittens  = 2 x  + 5 y

⇒2 x + 5 y = $19 ....... (2)

Now, solving (1) and (2) , we get:

5 x + 4 y = $30     (multiply by -2)

2 x + 5 y = $19      (multiply by 5)

Add both equations, we get:

-10 x  - 8 y + 10 x + 25 y = -60 + 95

or, 17 y =  35

or, y =  35/17 =  2.05

or, y  = $2.06

Now, 5 x +  4y = 30

⇒ 5 x + 4 (2.06) = 30

or, 5 x = 30 - 8.24 =  21.76

so, x =  21.76/5 = 2.24

or, x =  $2.24

Hence, the cost of 1 hat = $2.24

And the coat of 1 pair of oven mitten = $2.06

Answer:

On that day 1500 children and 700 adults attended.

Step-by-step explanation:

Given:

There is a carnival. Children are $1.50 and adults are $4.

The total amount of money raised was $5050.

On this particular day there 2200 in attendance.

Now, to find the children and adults attended on that day.

Let the children attended be [tex]x[/tex].

And the adults attended be [tex]y[/tex].

The total number in attendance:

[tex]x+y=2200[/tex]

⇒ [tex]x=2200-y[/tex]........( 1 ).

Now, the total amount of money raised:

[tex]1.50x+4y=5050[/tex]

Putting the equation ( 1 ) in the place of [tex]x[/tex] we get:

⇒ [tex]1.50(2200-y)+4y=5050[/tex]

⇒ [tex]3300-1.50y+4y=5050[/tex]

⇒ [tex]3300+2.50y=5050[/tex]  

Subtracting both sides by 3300 we get:

⇒ [tex]2.50y=1750[/tex]

Dividing both sides by 2.50 we get:

⇒ [tex]y=700.[/tex]

The adults attended = 700.

Now, putting the value of [tex]y[/tex] in equation ( 1 ) we get:

[tex]x=2200-700[/tex]

⇒ [tex]x=1500.[/tex]

The children attended = 1500.

Therefore, on that day 1500 children and 700 adults attended.

Answer:

y = 2x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To fid c substitute (5, - 4) into the partial equation

- 4 = 10 + c ⇒ c = - 4 - 10 = - 14

y = 2x - 14 ← equation of parallel line

Answer:

C

Step-by-step explanation:

The diagram shows the system in equilibrium. Left part consists of 3 circles, 2 triangles and 6 squares. Right part consists of 2 circles, 5 triangles and 3 squares.

If this system is in equilibrium, then the mass of the left part is the same as the mass of the right part.

The mass of the left part:

[tex]3\cdot 3+2\cdot \triangle +6\cdot 2=2\triangle+9+12=2\triangle+21\ grams[/tex]

The mass of the right part:

[tex]2\cdot 3+5\cdot \triangle+3\cdot 2=5\triangle +6+6=5\triangle +12\ grams[/tex]

Hence,

[tex]5\triangle +12=2\triangle +21\\ \\5\triangle -2\triangle =21-12\\ \\3\triangle =9\\ \\\triangle =3\ grams[/tex]

The mass of the triangle is 3 grams.

Given information:

A circle has a mass of 3 grams and a square has a mass of 2 grams.

From the given diagram of a mass balance, it can be concluded that:

Now, the left and right sides are balanced. So, the mass of left side will be equal to the mass of right side.

Let x be the mass of a triangle shape.

So, the value of x can be calculated as,

[tex]\texttt{mass of left side = mass of right side} \\6\times 2+2x+3\times 3=3\times 2+5x+2\times 3\\12+9+2x=6+6+5x\\3x=9\\x=3[/tex]

Therefore, the mass of the triangle is 3 grams.

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Answer:

it should be a 50:1 gas oil ratio.

Step-by-step explanation:

Answer:

Commutative Property of Addition.

Step-by-step explanation:

The Commutative Property of Addition states that no matter what order you add the numbers, the outcome (answer) will all be the same.

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x+y=8 and 25x+10y=170 are the linear equations.

x+y≤8 and 25x+10y≤170 are the inequalities.

Step-by-step explanation:

Given,

Worth of coins = $1.70 = 1.70*100 = 170 cents

Number of coins = 8

1 quarter = 25 cents

1 dime = 10 cents

Let,

x represent the number of quarters

y represent the number of dimes

1. Write an equation to represent the amount of coins Karen has.

x+y = 8

2.Write an equation to represent the value of the coins Karen has.

25x+10y=170

x+y=8 and 25x+10y=170 are the linear equations.

For inequalities, the amount cannot increase number of coins and worth but it can be less, therefore,

x+y≤8

25x+10y≤170

x+y≤8 and 25x+10y≤170 are the inequalities.

Keywords: linear equations, addition

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