Montraie bought snacks for his team's practice. He bought a bag of popcorn for $2.45
and a 18-pack of juice bottles. The total cost before tax was $29.99. How much was
each bottle of juice?

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:

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

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.

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:

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]

Answer:

3 teaspoons.

Step-by-step explanation:

500/2=250 grams per teaspoon

750/250=3

3 teaspoons

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

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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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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1. The algebraic expression that represents the amount left on her card after Laqueta buys 7 songs is 50 - 7s

2. The money that will be left on her card if each song costs $1.25 is $41.25.

From the information given, Laqueta has a $50 gift card for an online music store and each song costs s dollars.

In this case, the algebraic expression that represents the amount left on her card after Laqueta buys 7 songs will be:

= Total amount - Cost of songs

= 50 - (7 × s)

= 50 - 7s

where s = number of songs

The money that will be left on her card if each song costs $1.25 will be:

= 50 - 7s

= 50 - (7 × 1.25)

= 50 - 8.75

= $41.25

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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 three of the following expenses which the student aid cover include the following below:

This is referred to as the type of funding which is required to cover the cost of post-secondary education and are usually in the form of scholarships, grants, etc. It is awarded by government or private institutions and most times the highest scorers in an exam determines who will get it.

This aid covers different types of school expenses which are the most important ones such as tuition, school supplies etc thereby making it the correct choice.

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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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Answer:

18 red and 6 other color

Step-by-step explanation:

A box of 24 ornaments contains 3/4 red ornaments. How many red ornaments are in the box? How many ornaments are another color than red?

3/4 × 24 = red ornaments

= 18 red

24 - 18 = 6 other color

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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The goalposts are 6.92m tall.

Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.

Both angles  ( θ) are equal, as seen in the attached image.

m<ABC = mADC = 90° - θ

m<ACB = mECD = 90°

detailed explanation?

Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.

Both angles  ( θ) are equal, as seen in the attached image.

m<ABC = mADC = 90° - θ

m<ACB = mECD = 90°

Thus, the ABC triangle and the EDC triangle will both be similar.

Their corresponding sides will also be proportionate due to the property of comparable triangles

AB/BD  =  CB/CD.

1.15/ED  =  2.0/12.5

ED  =   1.15  *   12.05 /2.0

ED=  6.92

ED = ED = 6.92 m

The goalposts are 6.92m tall.

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Answer:

1 solution

Step-by-step explanation:

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:

1.divide

2.minus

3.times

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...)

375π litters of water is needed to fill the cylindrical tank with a diameter of 1.0m and height of 1.5m.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi.

Given the data in the question;

Plug the given values into the formula above and solve for V, to determine the liters of water that will fill the tank.

V = π × r² × h

V = π × ( 0.5m )² × 1.5m

V = π × 0.25m² × 1.5m

V = 0.375π m³

Next, convert cubic meters to liters.

V = 0.375π m³ = ( 1000 × 0.375π )L

Volume V = 375π L

Therefore, a volume of 375π litters is needed to fill the tank.

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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:

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: 12.5 pounds

Step-by-step explanation:

How many times greater, 75=6x

divide by 6

Answer: 7(30 + c) min

Step-by-step explanation:

Total time spent in gym = (30 + c)

Total day went to gym = (3 + 4) = 7 day

Net time = 7(30 + c) min

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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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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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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