Which of the following is NOT equivalent to the formula d=rt? The options are in the picture.

Answer:

[tex]\textsf{1. \quad $x < -4$ or $x > 2$}[/tex]

[tex]\textsf{2. \quad $-2 < x < 6$}[/tex]

[tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}[/tex][tex]\textsf{3. \quad $x < -1$ or $x > \dfrac{8}{5}$}[/tex]

Step-by-step explanation:

The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.  

If the leading coefficient of a quadratic function is positive, the parabola opens upwards.

If the leading coefficient of a quadratic function is negative, the parabola opens downwards.

Therefore, to find the intervals on which each quadratic function is positive:

Given function:

[tex]y=x^2+2x-8[/tex]

Factor the given function:

[tex]\implies y= x^2+4x-2x-8[/tex]

[tex]\implies y=x(x+4)-2(x+4)[/tex]

[tex]\implies y=(x-2)(x+4)[/tex]

Substitute y = 0 to find the zeros:

[tex]\implies (x-2)(x+4)=0[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

[tex]\implies x+4=0 \implies x=-4[/tex]

The leading coefficient is positive, so the parabola opens upwards.  

Therefore, the interval on which the function is positive is:

Given function:

[tex]y=-x^2+4x+12[/tex]

Factor the given function:

[tex]\implies y=-(x^2-4x-12)[/tex]

[tex]\implies y=-(x^2-6x+2x-12)[/tex]

[tex]\implies y=-(x(x-6)+2(x-6))[/tex]

[tex]\implies y=-(x+2)(x-6)[/tex]

Substitute y = 0 to find the zeros:

[tex]\implies -(x+2)(x-6)=0[/tex]

[tex]\implies (x+2)(x-6)=0[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies x-6=0 \implies x=6[/tex]

The leading coefficient is negative, so the parabola opens downwards.  

Therefore, the interval on which the function is positive is:

Given function:

[tex]y=5x^2-3x-8[/tex]

Factor the given function:

[tex]\implies y=5x^2-8x+5x-8[/tex]

[tex]\implies y=x(5x-8)+1(5x-8)[/tex]

[tex]\implies y=(x+1)(5x-8)[/tex]

Substitute y = 0 to find the zeros:

[tex]\implies (x+1)(5x-8)=0[/tex]

[tex]\implies x+1=0 \implies x=-1[/tex]

[tex]\implies 5x-8=0 \implies x=\dfrac{8}{5}[/tex]

The leading coefficient is positive, so the parabola opens upwards.  

Therefore, the interval on which the function is positive is:

The solution to the given linear inequality expression is equivalent to x < 8

Inequality expressions are expressions that are not separated by an equal sign. They are separated by the signs <, >, ≤ and ≥.

Given the inequality below:

0.35x – 4.8 < 5.2 – 0.9x

Collect the like terms;

0.35x + 0.9x  < 5.2 + 4.8

Simplify the result to have:

(0.35+0.9)x < 10.0

1.25x < 10.0

Divide both sides by 1.25

1.25x/1.25 < 10.0/1.25

x <8

This gives the solution to the linear inequality shown.

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Answer: 12.5 pounds

Step-by-step explanation:

How many times greater, 75=6x

divide by 6

Answer: None

Step-by-step explanation: Trick question the total is 110 and none took both math and physics

Using a proportional relationship, it is found that:

a) The independent variable is x.

b) The dependent variable is y = 12x.

c) The domain is of 0 ≤ x ≤ 25.

d) The range is of 0 ≤ y ≤ 300.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as shown below:

y = kx

In which:

For this problem, Jennifer makes $12 an hour, hence the constant is of k = 12 and the equation is:

y = 12x.

She can work between 0 and 25 hours, hence:

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The population of the city next year, after decreasing, will be 359,778

Here, we are given that the population of a city decreases by 1.7 percent per year.

This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.

The population of the city this year is given to be 366,000.

Thus, next year, the population will decrease by-

1.7% of 366,000

= 1.7/100 × 366,000

= 17/10 × 3,660

= 17 × 366

= 6,222

Thus, the city's total population next year will be-

366,000 - 6,222

= 3,59,778

Hence, the city's population to the nearest individual comes out to be 359,778.

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Answer:

5.48

78.541

97

42.111...

(all of above)

Step-by-step explanation:

because a rational number is a number that can be written as a fraction

a decimal number that ends can be written as a fraction (ex: 5/4 = 1.25)

a decimal number that has a repeating number after the decimal point can also be written as a fraction (ex: 10/3 = 3.33...)

Answer:

6, -2, and-1

Step-by-step explanation:

f(2) means that x is 2, so looking in the left column find x as 2, and then find the corresponding number beside it.

f(x)=0 so look for 0 in the right column and find the number corresponding to it in the left.

Answer:

#8 is equal to 6

#9 is equal to -2

#10 is equal to -1

Step-by-step explanation:

If you look in the x column for 2 the outcome is 6

If you look in the f(x) column for 0 the income is -2

If you look in the f(x) column for 1.5 the income is -1

Answer:

1 solution

Step-by-step explanation:

By using percentage, we conclude that the total cost of the stereo equipment is $114.8.

The worth of stereo equipment is $112 and there is a 2.5% processing fee for using a credit card.

Whenever we purchase anything with a credit card we have to pay a processing fee that a Bank charges.

To find the total cost of the stereo equipment, we have to add the worth of the stereo equipment and processing fee for using a credit card.

And to find the processing fee for using a credit card, we have to calculate 2.5% of the worth of the stereo equipment.

So, 2.5/100 x 112 = 2.8

Therefore, the required processing fee for using a credit card is $2.8.

The total cost of the stereo equipment = $112 + $2.8 = $114.8

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Answer:

k = 4

Step-by-step explanation:

g(x) higher than by 4 units

Answer:

k = 4

Step-by-step explanation:

'k' represents the vertical translation

Answer:

[tex]\textsf{1.} \quad 3x^2-4x+12[/tex]

[tex]\textsf{2.} \quad 3x^2-8x+4[/tex]

[tex]\textsf{3.} \quad 6x^3-8x+32[/tex]

[tex]\textsf{4.} \quad \dfrac{3x^2-6x+8}{2x+4}[/tex]

[tex]\textsf{5.} \quad 12x^2+36x+32[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x^2-6x+8\\g(x)=2x+4\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The composite function (f + g)(x) means to add function f(x) and g(x):

[tex]\begin{aligned}\implies (f+g)(x) & = f(x)+g(x)\\&=(3x^2-6x+8)+(2x+4)\\ &=3x^2-6x+2x+8+4\\ &=3x^2-4x+12\end{aligned}[/tex]

The composite function (f - g)(x) means to subtract function g(x) from function f(x):

[tex]\begin{aligned}\implies (f-g)(x) & = f(x)-g(x)\\&=(3x^2-6x+8)-(2x+4)\\&=3x^2-6x+8-2x-4\\ &=3x^2-6x-2x+8-4\\ &=3x^2-8x+4\end{aligned}[/tex]

The composite function f(x) · g(x) means to multiply functions f(x) and g(x):

[tex]\begin{aligned}\implies f(x)\cdot g(x) & =(3x^2-6x+8)(2x+4)\\ &=3x^2(2x+4)-6x(2x+4)+8(2x+4)\\&=6x^3+12x^2-12x^2-24x+16x+32\\&=6x^3-8x+32\end{aligned}[/tex]

The composite function f(x)/g(x) means to divide function f(x) by function g(x):

[tex]\begin{aligned}\implies \dfrac{f(x)}{g(x)} & = \dfrac{3x^2-6x+8}{2x+4}\\\end{aligned}[/tex]

The composite function f(g(x)) means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}\implies f(g(x))&=3(g(x))^2-6(g(x))+8\\&=3(2x+4)^2-6(2x+4)+8\\&=3(2x+4)(2x+4)-12x-24+8\\&=3(4x^2+16x+16)-12x-16\\&=12x^2+48x+48-12x-16\\&=12x^2+48x-12x+48-16\\&=12x^2+36x+32\end{aligned}[/tex]

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The highest common factor of N and 500 is 2²x5² and The lowest common multiple of N and 500 is [tex]2^{3}[/tex]x[tex]5^{3}[/tex]x7.  p, q and r is p =2 , q =2 , r =1

Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers by "prime factorizing" it.

Given that : Written as product of their prime factors N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] and 500= 2² x 5³ The highest common factor of N and 500  is 2² x 5³? The lowest common multiple of  N and 500 is  2²x5²x7.

N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]

500= 2² x 5³

highest common factor of N and 500  is 2²x5²

p ≥ 2

q = 2

r ≥ 0

The lowest common multiple of  N and 500 is  2²x5²x7.

HCF x LCM = N * 500

=> 2²x5²  x 2²x5²x7 =  [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]  x 2² x5³

=>  2²x5x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]

p = 2

q = 1  but q = 2 as per HCF

r = 1

There is mistake in data

As LCM should have [tex]5^{3}[/tex] atleast as 500 has 5^2

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Answer:

y = 15x - 35

Step-by-step explanation:

STANDARD PLAN information:

Define the variables:

If it costs $40 for the first 5GB then y = 40 when 0 ≤ x ≤ 5.

It costs $15 per GB after the first 5GB. Therefore:

Therefore:

⇒ y = 40 + 15(x - 5)

⇒ y = 40 + 15x - 75

⇒ y = 15x - 35

Jeweler needs 144 inches of silver chain to make the necklaces and 108 inches of silver chain to make the bracelets.

For the given question;

The total length of silver chain jeweler had = 36 inches.

Length of silver chain required to make necklaces = 4 times.

So, multiply 36 with 4 to get the result;

36 x 4 = 144.

Thus, the silver chain required to prepare the necklaces is 144 inches.

For the making of bracelets = 3 times the length of silver chain.

So, multiply 36 with 3 to get the result.

36 x 3 = 104

Thus, the length of silver chain required to prepare bracelets is 104 inches.

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Answer:

X = 31

Step-by-step explanation:

180 = 2x + 9 + 3x +16

180 = 5x + 25

180 + -25 = 5x

155 = 5x

5x/5 = 0 (Cancel out)

155 /5x = 31

X = 31

Check math by :

2 x 31 = 62 + 9 = 71

3 x 31 = 93 + 16 = 109

109 + 71 = 180

Therefore, X = 31

Therfore we can derive the equation:

[tex]2x+3x+9+16 =180[/tex]

[tex]5x+25 = 180[/tex]

5x = 155

[tex]x = 31[/tex]

The angle between the line PV and the plane PTWS is 29.4°

In this question we have been given a cuboid PQRSTUVW

We need to find the angle between the line PV and the plane PTWS.

First we find the length of the line PW which is diagonal of rectangular surface PTWS.

In right triangle PWS by Pythagoras theorem,

PW² = PS² + SW²

PW² = 19² + 16²

PW² = 361 + 256

PW² = 617

PW = 24.84 cm

now, consider a right triangle PWV.

Consider tangent of angle VPW

tan(∠VPW) = VW / PW

tan(∠VPW) = 14 / 24.84

∠VPW = tan^{-1}(0.5636)

∠VPW = 29.4°

Therefore, the angle between the line PV and the plane PTWS is 29.4°

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Answer:

y = -5/6x + c

Step-by-step explanation:

line equation is:

y = mx + c

y = -5/6x + c

sub in values:

1 =-5/6(6) + c

1 = -5 + c

6 = c

equation of line:

y = -5/6x + 6

As per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.

As given in the question,

Liquid storage container is being filled at a constant rate.

Rate of filling a container = 1/3 gallon per 1/4 minute

Unit rate = (1/3 gallons)/ (1/4 minutes)

              = (4/3) gallons per minute

Equivalent rate for 4 minutes is equal to

= [ ( 4 / 3) × 4 ] gallons per 4 minutes

= ( 16 / 3) gallons

Therefore, as per unit rate of storing liquid in a container , the equivalent rate for 4 minutes is equal to (16/3) gallons.

The complete question is :

A liquid storage container is being filled at a constant rate. The container is being filled at a rate of 1/3 gallon per 1/4 minute.

Unit rate = (1/3 gallons)/ (1/4 minutes)

              = (4/3) gallons per minute

Find the equivalent rate for 4 minutes.

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Answer:

29041

Step-by-step explanation:

1995-1990

300×5=1500

27541+1500=29041

Correct option is C, The solution is set of all real numbers.

When x=0, 0=0 and 24 Equals 24 when x = 4.

This equation holds true for all real numbers since both sides of the equation are the same. When 0=0, the solution reveals that the equation is an identity, a specific kind of equation that is true regardless of the value of x.

Identity equations are described as equations that are true regardless of the value of the inserted variable.

3(x+4)=3x+12

3x+12=3x+12

When x = 0

3(0)+12=3(0)+12

12=12

When x = 4

12+12=12+12

The set of all real numbers is the answer as a result.

Y - = m is an equation for a line given a slope and a point ( x - )

or y - 7 = 1 ( x - 1) ( x - 1)

or y - 7 = x -1

or y = x + 6

Consequently, a line parallel to the line y = x + 4 has the equation y = x + 6.

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Answer:

f= 37 / 4

Step-by-step explanation:

I am using ( / ) to show a fraction

Let's solve your equation step-by-step.

f(4)=7(4+2)−5

Step 1: Simplify both sides of the equation.

f(4)=7(4+2)−5

4f=42+−5

4f=(42+−5)(Combine Like Terms)

4f=37

4f=37

Step 2: Divide both sides by 4.

4f / 4 = 37 / 4

f= 37 / 4

Answer:

f= 37 / 4

Hope this helps! :)

Answer:

The quadratic function is x²-5x+4=0

Step-by-step explanation:

To find a quadratic equation whose roots are given we use

x²-(sum of roots)x + (product of roots) =0

x²-(4+1)x + (4×1)=0

x²-5x+4=0

let us check if it is correct

x²-5x+4=0

x²-1x-4x+4=0

x(x-1)-4(x-1)=0

(x-4)(x-1)=0

(x-4)=0 and (x-1)=0

x=4 and x=1

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A line of best fit (linear equation) to model this data is y = 27x + 699.43

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the game would be plotted on the x-axis of the scatter plot while the attendance would be plotted on the y-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a linear equation for the line of best fit is given by:

y = 27x + 699.43

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Answer:

3 teaspoons.

Step-by-step explanation:

500/2=250 grams per teaspoon

750/250=3

3 teaspoons

The mathematical statement of the expression 9 + 11g is the sum of 9 and 11g

Expressions are mathematical statements that are represented by variables, coefficients and operators

The algebraic expression is given as

9 + 11g

The above mathematical representation is an algebraic expression that is already in its most simplified form

This means that the algebraic expression cannot be further simplified

However, the algebraic expression can be rewritten as a mathematical statement

Recall that, we have

9 + 11g

The pronunciation of the above expression is:

9 plus 11g

In expressions, plus represents sum

So, we have

9 + 11g can be represented as the sum of 9 and 11g

Hence, the representation of the algebraic expression given as 9 + 11g is the sum of 9 and 11g

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Using linear function concepts, the interpretation of the slope of the model is:

The slope indicates that the Fuel Efficiency decreases by an amount of 0.15 mpg for every 1 mile per hour increase of speed.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, the model is given as follows:

Fuel Efficiency = 32 - 0.15Speed.

The slope is of m = -0.15, meaning that for each mph that the average velocity increases, the fuel efficiency decays by 0.15 mpg.

The model is missing, and is given as follows:

Fuel Efficiency = 32 - 0.15Speed.

The units are as follows:

It asks for the interpretation of the slope.

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Triangle B is a reflection of triangle A across the axis y=-1

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The graph A is the original graph and it is transformed to B. Triangle B is a reflection of triangle A across the axis y=-1

Hence  Triangle B is a reflection of triangle A across the axis y=-1

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Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.

What is Average speed?

The average speed is the total distance traveled by any object in a particular time interval.

Given that;

Distance covered by Roger = 13.2 miles

Time is taken by Roger = 1.6 hours

Distance covered by Ana = 10.85 miles

Time is taken by Ana = 1.4 hours

Now, Calculate the speed of Roger and Ana as;

Speed = Distance / Time

For Roger,

Speed = 13.2/1.6 = 8.25 mph

For Ana,

Speed = 10.85/1.4= 7.75 mph

Hence, Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.