What does 1/4 of a can of coffee cost if 4 cans of coffee cost $1.60

To complete the square for the equation x^2 - 9x = 8, the number 81/4 must be added to both sides, resulting in x^2 - 9x + 81/4 = 113/4.

To complete the square for the equation x^2 - 9x = 8, we need to find a number that when added to x^2 - 9x makes it a perfect square trinomial. The formula to complete the square is to take the coefficient of the x term (which is -9), divide it by 2, and square it. The process looks like this:

(-9/2)^2 = 81/4

Therefore, the number to add to both sides of the equation is 81/4. The equation then becomes:

x^2 - 9x + 81/4 = 8 + 81/4

Which simplifies to:

x^2 - 9x + 81/4 = 32/4 + 81/4

x^2 - 9x + 81/4 = 113/4

By adding 81/4 to both sides, we have successfully completed the square.

1)

v - 6 ≥ 4

  +6   +6

v      ≥ 10

Graph: 10 -----------------→  the dot at 10 is filled in because of the "equal to" symbol

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2)

-5x < 15

[tex]\frac{-5x}{-5} > \frac{15}{-5}[/tex]  divided by a negative so the symbol flipped

x > -3

Graph: -3 o------------------→ the dot at -3 is NOT filled in because it's NOT "equal to"

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3)

3k > 5k + 12

-5k  -5k      

-2k >          12

[tex]\frac{-2k}{-2} < \frac{12}{-2}[/tex]   divided by a negative so the symbol flipped

k < -6

Graph: ←------------o -6   the dot at -6 is NOT filled in because it's NOT "equal to"

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5)

2t ≤ 4      or    7t ≥ 49

[tex]\frac{2t}{2} \leq\frac{4}{2}[/tex]      or    [tex]\frac{7t}{7} \geq \frac{49}{7}[/tex]

 t ≤ 2      or      t ≥ 7

Graph: ←------- 2        7 ---------→   the dots at 2 and 7 are filled in

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6)

| n + 2 | = 4

n + 2 = 4      or     n + 2 = -4

    -2   -2                 -2   -2

n      = 2        or     n       = -6

Answer: n = {2, -6}

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7)

| 2x - 7 | > 1

2x - 7 > 1       or     2x - 7 < -1

     +7  +7                 +7   +7

2x      > 8       or     2x     <  6

    [tex]\frac{2x}{2} > \frac{8}{2}[/tex]             or       [tex]\frac{2x}{2} < \frac{6}{2}[/tex]

    x > 4          or         x < 3

Graph: ←----------o 3      4 o------------→

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8)

A = {1, 2, 3, 4, 5, 6, 7, 8, 9}    B = {2, 4, 6, 8}

A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9}    union combines both sets

A ∩ B =  {2, 4, 6, 8}   intersection includes only those that are in BOTH sets

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9)

P = {1, 5, 7, 9, 13}   R = { 1, 2, 3, 4, 5, 6, 7}    Q = {1, 3, 5}

P ∩ R ∩ Q = {1, 5}

P ∩ R = {7}  disregard 1 & 5 since they are already in P∩Q∩R

R ∩ Q = {3}  disregard 1 & 5 since they are already in P∩Q∩R

P ∩ Q = { }  disregard 1 & 5 since they are already in P∩Q∩R

P no intersection = {9, 13)

R no intersection = {2, 4, 6}

Q no intersection = {  }

If you can't figure out how to draw it based on the information I provided, please see the attached diagram. Note: Usially, you would only identify P, Q, R.  I identified the intersections so you would understand why those specific numbers are placed in the designated sections.

4, 12, 16, 48, 52, 156, 160, ______, _______, _______

x3  +4  x3  +4  x3    +4

That pattern is: multiply by 3, add 4, multiply by 3, add 4, ...

160 x 3 = 480

480 + 4 = 484

484 x 3 = 1452

Answer: 480, 484, 1452

The next 3 numbers are 480, 484, 1452

The given sequence is:

4,12,16,48,52,156,160,_,_,_

The rule of the sequence is:

The last three terms are the 7th, 8th, and 9th terms

The 7th term is:

[tex]T_7=3T_6\\\\T_7=3(160)\\\\T_7=480[/tex]

The 8th term is:

[tex]T_8=T_7+4\\\\T_8=480+4\\\\T_8=484[/tex]

The 9th term is:

[tex]T_9=3T_8\\\\T_9=3(484)\\\\T_9=1452[/tex]

Therefore, the next 3 numbers are 480, 484, 1452

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THE ANSWER IS:

the measure of the arc FH is 48 degrees

and btw I flipping love killing stalking :)

Answer:

[tex]48^{\circ}[/tex]

Step-by-step explanation:

Consider we need to find [tex]m\widehat{FH}[/tex],

Since, if two chords of a circle intersect outside the circle then the measure of intercepted angle is half of the difference of the measures of intercepted arcs.

Thus,

[tex]m\angle ADJ = \frac{m\widehat{AJ}-m\widehat{BE}}{2}[/tex]

By the diagram,

[tex]37^{\circ}=\frac{m\widehat{AJ}-38^{\circ}}{2}[/tex]

[tex]74^{\circ}=m\widehat{AJ}-38^{\circ}[/tex]

[tex]\implies m\widehat{AJ}=74^{\circ}+38^{\circ}=112^{\circ}[/tex]

Now,

[tex]m\angle AGJ = \frac{m\widehat{AJ}-m\widehat{FH}}{2}[/tex]

[tex]32^{\circ}=\frac{112^{\circ}-m\widehat{FH}}{2}[/tex]

[tex]64^{\circ}=112^{\circ}-m\widehat{FH}[/tex]

[tex]\implies m\widehat{FH}= 112^{\circ}-64^{\circ}=48^{\circ}[/tex]

Hence, SECOND OPTION would be correct.

Answer:

Option B 0.11

Step-by-step explanation:

Given that  the population proportion of 0.58, a simulation of 200 trials is run, each with a sample size of 50 and a point estimate of 0.42. The minimum sample proportion from the simulation is 0.31, and the maximum sample proportion from the simulation is 0.53.

This gives an idea that confidence interval is

(0.31, 0.53) with mean being in the middle of this interval

Margin of error = 1/2 (length of this interval)

Length of confidence interval =[tex]0.53-0.31 =0.22[/tex]

Margin of error =± 1/2(0.22) = ±0.11

Hence option B is correct

Find where the equation is undefined ( when the denominator is equal to 0.

Since they say x = 5, replace x in the equation see which ones equal o:

5-5 = 0

So we know the denominator has to be (x-5), this now narrows it down to the first two answers.

To find the horizontal asymptote, we need to look at an equation for a rational function: R(x) = ax^n / bx^m, where n is the degree of the numerator and m is the degree of the denominator.

In the equations given neither the numerator or denominators have an exponent ( neither are raised to a power)

so the degrees would be equal.

Since they are equal the horizontal asymptote is the y-intercept, which is given as -2.

This makes the first choice the correct answer.

In this mathematical context, 'f' represents a vehicle's fuel efficiency in miles per gallon, and the given inequality f > 40 mpg indicates that the vehicle's fuel efficiency is higher than 40 miles per gallon.

The problem refers to a situation where a vehicle achieves fuel efficiency of more than 40 miles per gallon. This efficiency is quantified using the variable 'f'.

Considering f as the vehicle's fuel efficiency in miles per gallon, you are expressing a relationship where f > 40 mpg.

Using an example: if we consider a vehicle that achieves 43 miles per gallon, this can be represented as: f = 43 mpg. This efficiency is indeed more than 40 miles per gallon, thus confirming that f > 40 mpg in this case. It's important to understand that in this context, the fuel efficiency varies from one vehicle to another. For instance, vehicles become more fuel efficient over the years due to advancements in technology and heightened fuel economy standards.

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Answer:

This equation is a line

Step-by-step explanation:

We can tell it's a line because both the x and y values are raised to the first power. In order for it to be any of the others, one or both of the variables would have to have a non-one exponent.

Answer:

It is a line.

Step-by-step explanation:

Since, the general equation of,

A line is ax + by = c

A circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]

An ellipse is [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

A parabola is [tex]y^2=4ax[/tex] or [tex]x^2=4ay[/tex]

A hyperbola is [tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

Where, a, b and c are constants.

Here, the given equation is,

x + y = 5

Which is the type of ax + by = c

Hence, x + y = 5 is a line.

Based on the graph of the relationship given between time and the amount of popcorn popped, the relationship doesn't yield a straight line, hence, the relationship isn't proportional.

A proportional relationship is one in which there is a constant change in one variable as the value of the other variable is varied.

A proportional relationship will always yield a straight line with either a positive or negative slope.

Since, the trend line isn't straight, then the relationship isn't proportional.

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The actual question is not about the popcorn machine but about testing the hypothesis on mean differences of relaxed and jumping times for eight girls. To assess this, statistical methods like the paired t-test are used to examine the existence of a direct relationship between the two sets of times.

The relationship between time and the amount of popcorn popped could be considered directly proportional if the rate of popping remains constant over time. However, this question appears to be based on a misunderstanding, as it incorrectly states that Rachel had a popcorn machine. Instead, the actual task given is to test the hypothesis that the mean difference between jumping and relaxed times for eight girls at a party would be zero.

To test this hypothesis, a statistical test like a paired t-test could be used to determine if there is a significant difference between the two mean times. Proportionality in the question should be related to rates or ratios. For instance, when data shows a positive correlation as one variable increases, so does the other. This is seen when graphing data that results in a straight line, which signifies a direct relationship.

Therefore, to determine the relationship between two quantities, the concept of direct and indirect proportionalities is important, and having a direct relationship would mean that the variables increase together linearly.

You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.

Thus, height of specified volcano is 4214 meters.

The height of volcano above sea level

You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.

Thus:

Height of volcano above sea level = total height of volcano - depth of volcano below sea level

[tex]\text{Height of volcano above sea level} = 10207 - 5993 = 4,214 \: \rm meters[/tex]

Thus, height of specified volcano is 4214 meters.

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The graph of this relation is four points on the coordinate plane (see attached diagram).

A function is a special relation, where each input x has a single output y.

This relation is not a function, because for one x (x=-1), here are two different possible y (y=3 or y=2). If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2). This means that option D is true.

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y

x= 18 y=11

Step-by-step explanation:

We know that MNQ= 8x+12

PNQ=78 and MNP is equal to PNQ

Therefore, PNQ=MNP

So since these two angles make up MNQ,

Add 78+78 which is 156

So now we need to find x

The equation to find x is 8x+12=156

8x+12=156

8x=144

x=18

Now that we know x it is time to find y.

So we know that RNM=3y-9

And we know that MNQ is equal to 156

RNM an MNQ form a straight line which means that it is equal to 180 degrees

So the equation to find y is 3y-9+156=180

3y-9+156=180

3y+147=180

3y=33

y=11

So in conclusion, x=18 and y=11

Hope this helped! :3

Answer:

2x-3y=20

12x+8y=-192

Solution

In the determinant of the matrix to find the variable "x" [Ax], we replace the coefficients of "x" (2 and 12) by the independent terms (20 and -192 respectively).

In the determinant of the matrix to find the variable "y" [Ay], we replace the coefficients of "y" (-3 and 8) by the independent terms (20 and -192 respectively).

d = r * t

                               time                rate                       distance

Downstream:           2                   8 + c                     d = 2(8 + c)

Upstream:                3                   8 - c                      d = 3(8 - c)

Since the distance is the same, we can set the distance equations equal to each other and solve for c.

2(8 + c) = 3(8 - c)

16 + 2c = 24 - 3c

16 + 5c = 24

      5c = 8

        c = [tex]\frac{8}{5}[/tex]

        c = 1.6

Answer: 1.6 mph

y = | 3x - 7 |

x-intercept is when y = 0

0 = | 3x - 7 |

0 = 3x - 7

+7       +7

7 = 3x

[tex]\frac{7}{3} = \frac{3x}{3}[/tex]

 [tex]\frac{7}{3} = x[/tex]

[tex](\frac{7}{3}, 0 )[/tex]

y-intercept is when x = 0

y = | 3(0) - 7 |

y = | 0 - 7 |

y = | -7 |

y = 7

(0, 7)

Answer: [tex](\frac{7}{3}, 0 )[/tex] and (0, 7)

To factor a number out of an expression means to divide each term of the expression by that number.

So, if you want to factor [tex] a [/tex] from the expression [tex] x+y+z [/tex], you'll write it as

[tex] a\left(\dfrac{x}{a}+\dfrac{y}{a}+\dfrac{z}{a}\right) [/tex]

So, in your case, when you divide both terms by -5 you get

[tex] -10a \div (-5) = 2a,\quad -25\div (-5) = 5 [/tex]

So, the expression becomes

[tex] -10a-25 = -5(2a+5) [/tex]

The inequality x>35 represents the problem

more than is: >

A bank balance in excess of $35. Julia wishes to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The inequality symbol should she use to match the phrase “more than” is >.

A bank account with a balance of greater than $35. Julia wants to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Hence, x >35 is the correct answer.

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Marshall can use x = 8 and y = 0 to show that 8² = 64 using the polynomial identity (x−y)^2=x^2−2xy+y^2.

Marshall can use any values for x and y to show that (x−y)^2=x^2−2xy+y^2. However, he specifically wants to show that 8² = 64. In this case, Marshall can choose x = 8 and y = 0.

Using the polynomial identity (x−y)^2=x^2−2xy+y^2, we substitute x = 8 and y = 0 to get (8 − 0)^2 = 8^2 − 2(8)(0) + 0^2. Simplifying, we have 8^2 = 64 − 0 + 0, which simplifies further to 8^2 = 64.

So, Marshall can use the values x = 8 and y = 0 to show that 8² = 64 using the given polynomial identity.

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4x³ - 20x² + 24x = 0

4x(x² - 5x + 6) = 0

4x(x - 2)(x - 3) = 0

4x = 0        x - 2 = 0          x - 3 = 0

 x = 0            x = 2              x = 3

Answer: 0, 2, 3  

Factoring and solving a quadratic equation, it is found that the roots of the equation are:

[tex]x = 0[/tex]

[tex]x = 2[/tex]

[tex]x = 3[/tex]

The equation given is:

[tex]4x^3 - 20x + 24x = 0[/tex]

Factoring the common term:

[tex]4x(x^2 - 5x + 6) = 0[/tex]

For the roots:

[tex]4x = 0 \rightarrow x = 0[/tex]

Or

[tex]x^2 - 5x + 6 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = -5, c = 6[/tex], and then:

[tex]\Delta = (-5)^{2} - 4(1)(6) = 1[/tex]

[tex]x_{1} = \frac{-(-5) + \sqrt{1}}{2} = 3[/tex]

[tex]x_{2} = \frac{-(-5) - \sqrt{1}}{2} = 2[/tex]  

Thus, the other two roots are [tex]x = 2[/tex] and [tex]x = 3[/tex].

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Answer:

When you join points D(2,3),O(0,0)and E(5,1) which are not collinear it will form a triangle.

Now , Adjacent of ∠ DOE are [ ∠ ODE and ∠OED] .

As we know that  Sum of three interior angles of a triangle is 180°.

∠ DOE + ∠OED+∠EDO = 180°

∠DOE=180°- (∠OED+∠EDO)

Supplementary ,of ∠DOE is  (∠OED+∠EDO).

Answer: angle DOF, with F (-5,-1) and angle EOF, with F(-2,-3)

It seems that you are trying to find the length of hair of Florencia on Tuesday.

Given that length of the hair of Florencia on Monday = h centimeters

On Tuesday, she got hair cut.

So new length of the hair of Florencia on Tuesday = 75% of Monday value

= 75% of (h)

= 0.75* (h)

= 0.75h

Hence final answer is the length of the hair of Florencia on Tuesday is ( 0.75h ) centimeters.

Answer:

3/4h and 0.75h

Hi, here is the solution.

The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)

There 1000 toothpicks in a regular box.

The jumbo box hold  8 *1000 = 8000 toothpicks.

Thank you.

8,5 and 6,1

The slope is 2