I need explanation with this problem been struggling and it's practice for my exam coming up this semester

Answer:

1) -2

2) -2

3) -2

4) -3

5) -4

6) -15

7) -13

8) 3

1b) -9

2b) -2

3b) 7

4b) 17

5b) -4

6b) -9

7b) -16

8b) 0

1c) -5

2c) -3

3c) 0
4c) -2

5c) -8
6c) -11
7c) -3
8c) 15

Jeez, I hope this helps xD

If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (130 - 65) / (2 - 1)

Slope for speed= 65 / 1

Slope for speed= 65 mph

Determining Roger's starting position if Roger distance is 65.

Hence,

Mile of head start = Slope of speed - Roger distance

Mile of head start = 65 mph - 65 miles

Mile of head start = 0 miles

Rita  starting position if Rita distance is 93

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (158 - 93) / (2 - 1)

Slope for speed = 65 / 1

Slope for speed = 65 mph  

Mile of head start = Slope of speed - Rita distance

Mile of head start =  93 - 65

Mile of head start= 28 miles

Therefore we can conclude that Rita has a head start of 28 miles.

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Answer:

Rita had a 28-mile head start.

Step-by-step explanation:

EDGE

The equation for finding the length between two points is:

where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).

We assign A to be point 1 and B be point 2

Therefore,

The value of x for the given logarithm equation  log(x^2 + 7) base 4 = 2​ is x = ± 3.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

It is known that [tex]log_{a}b[/tex] = c can be written as [tex]a^{c}[/tex] = b.

Given that, log(x^2 + 7) base 4 = 2​

Therefore, x² + 7 = 4²

x² + 7 = 16

x² = 16 - 7 = 9

x² = 9

x = ±3

Hence "The value of x for the given logarithm equation  log(x^2 + 7) base 4 = 2​ is x = ± 3".

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Albert borrowed $17 from his friend.

Given,

Albert brought some items:

Cost of blanket = $32.75

Cost of pillow = $12.75

Cost of glove = $16.25

Amount paid by Albert = 50

Amount borrowed by Albert from his friend = x

Cashier gave back the change = $5.25

We have to find the amount borrowed by Albert from his friend:

This is simply arithmetic operations:

Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75

Total amount given to the cashier = 61.75 + 5.25 = 67

Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert

x = 67 - 50

x = 17

That is,

Albert borrowed $17 from his friend.

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Answer:

No, the cross products to not equal

Step-by-step explanation:

[tex]\frac{12}{8}[/tex] = [tex]\frac{2}{1}[/tex]

12(1) = 8(2)

12 [tex]\neq[/tex] 16

Or make them both into decimals

12/8 = 1.5

[tex]\frac{2}{1}[/tex] = 2  They do not equal each other.

Given the data shown in the table, you can identify that these two points are on the line:

By definition, the Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

You can find the slope of the line using this formula:

Where these two points are on the line:

The equation 5.5x - 2.1 = 3 + 5.5x has no solution. Then the number of the solution is zero.

The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a direct consequence.

Simplicity is the quality of making anything less complicated and more manageable in terms of both execution and comprehension.

The equation is given below.

5.5x - 2.1 = 3 + 5.5x

Subtract 5.5x on both sides, then simplify the equation.

5.5x - 5.5x - 2.1 = 3 + 5.5x - 5.5x

0x - 2.1 = 3

The equation 5.5x - 2.1 = 3 + 5.5x has no solution. Then the number of the solution is zero.

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Answer:

You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.

A: 40*5 = 200

Step-by-step explanation:

21 + 200 = 221

Answer:

1/2

Step-by-step explanation:

75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:

= 100% - 75%

= 25%

The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:

= 75% - 25%

= 50%

= 1/2

Since the 1st brand is 70% pure antifreeze

Since the 2nd brand is 95% pure antifreeze

Since we need to obtain 110 g of a mixture that contains 85% pure antifreeze

Let the quantity of the first is x and the second is y

Then

Now let us solve the two equations to find x and y

Multiply equation (2) by -0.7

Add equations (1) and (3)

Divide both sides by 0.25

Substitute the value of y in equation (2) to find x

Subtract 66 from both sides

First brand: 44 gallons

Second brand: 66 gallons

1) Considering e =2.72

Then let's plug it in the inequality, and calculate the natural logarithm.

2) Then option 5 is the answer

X≥ 1.52

Answer:

70

Step-by-step explanation:

Answer: 3, 9, and 9

Step-by-step explanation:

X+3x+3x=217x=21x=33, 9, 9=21

a) the maximum error in surface area  and  the relative error  is 25.4 cm² and 1.25%

b) the maximum error in the volume and  the the relative error  is 162.1 cm³ and 1.875%

As we know  the  formula for surface area is

                                    Surface Area , S= 4*π*r^2.

So  differentiating both sides we get

                                     dS/dr = 8*π*r .....1

and  the  formula for  the circumference is :2*π*r

, so the error on the circumference will be respect to radius

=> Δc = 2*π*Δr  

=> Δr = ΔC / (2*π)

substituing the value ofΔr in  the equation 1, we get

The maximum error in surface area which is :

ΔS = 8*π*r*Δr = 4*r*Δc

      = (2/π)*c*Δc.

    = 25.4

where for the relative error

                 ΔS/S = 4*r*Δc/(4*π*r^2)

                          = Δc/(π*r)

                          = 2*Δc/c

                        = 1.25%

Now Since  the formula for  the volume of a sphere  is :

                                       V = 4/3*π*r^3

dofferentiating both sides we get ,

                           => dV/dr = 4*π*r^2.

So,  the   the maximum error in the calculated volume  will be :

ΔV = 4*π*r^2*Δr

       = 2*r^2*Δc

       = 1/(2*π^2)*c^2*Δc

      =162.1

Where as the relative error for the volume will be

ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%

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ANSWER:

We can see the answer in the drawing.

STEP-BY-STEP EXPLANATION:

In this case, we make the diagram as follows:

In general, one can obtain the volume of a sphere and a cube using the formulas below

In our case, we need to subtract the volume of the hollow sphere from the volume of the cube, as shown below

Rounding to the nearest hundredth,

The answer is 2778.37in^3

In the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .

In the question ,

the data set is given as {30,45,49,50,63,75,75,77,84}

as the data set has 9 terms , the median will be the central term that is 5th term .

so the median is 63 .

For finding the lower and upper quartile , we break the set into two half .

lower half = {30,45,49,50}

the lower quartile will be the central value ,that is (45+49)/2 = 47

so, the lower quartile(Q₁) is 47 .

upper half = {75,75,77,84}

the upper quartile will be the central value ,that is (75+77)/2 = 76

so, the upper quartile(Q₃) is 76 .

Therefore , in the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .

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The car will catch up with cyclist in 3 hours

Time refers to the interval in seconds , minutes or hours it took for an event to take place

Information given for the question include

A cyclist has average speed of 9 miles per hour

A car leaves has average speed of 21 miles per hour

following same route when

The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already

Calculation of distance covered by the cyclist

average speed = distance / time

distance = 9 mph *  (x + 4)

Calculation of distance covered by the car

average speed = distance / time

distance = 21 mph *  x

equating both gives

9 mph *  (x + 4) = 21 mph *  x

9x + 36 = 21x

36 = 21x - 9x

12x = 36

x = 3

hence the car will meet the cyclist in 3 hours

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The total cost for 8 hours of work is $425.

The total cost for 10 hours of work is $525.

The total amount the plumber earns is made up of a fixed charge and a variable charge. A fixed charge is a charge that remains constant regardless of the number of hours the plumber works. The fixed charge is $25. The variable charge is the charge that increases per hours worked. The variable charge is $50 per hour.

Cost = fixed charge + variable charge

C = $25 + $50h

The total cost for 8 hours

$25 + $50(8)

$25 + $400

= $425.

The total cost for 10 hours

$25 + $50(10)

$25 + $500

$525.

The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.

The cost function is given by:

C(x) = 2x² - 32x + 678

The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.

Take the derivative:

C'(x) = 4x - 32 = 0

4x = 32

x = 32/4 = 8

Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.

Substitute x = 8 into the cost function:

C(8) = 2(8)² - 32.(8) + 678 =  550

Complete question:

The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar

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In a performance there will be 5 songs and 3 dances

Total objects 5+3 = 8

Number of ways of arranging this objects is 8! = 40,320...........(1)

If all the dances must be next to each other than all dances should take as an object as 3!

Number of ways of arranging performing taking dance to each other

is = (5+1)! 3!

    = 6! 3!

    = 4320 ....................(2)

Number of ways to arrange the shows if all dances can not be next to each other = (1) - (2)

         = 40320-4320

         = 3600 ways

Number of ways to arrange the shows if all the dances must be next to each other is 4320 ways.

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In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).

So we can equate them and solve for x.

So, m∠2 is

According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°

Therefore, the measure of m∠1 is 147°

A triangle has all three angles summing up to 180. If two of the sides measure 40 degrees and 50 degrees, then the third side measures as follows;

The third angle, which is labelled as angle A measures 90 degrees, and that means the triangle is a "right angled triangle."

The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.

Given that,

The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.

We have to calculate the probability that a light bulb will survive at most 533 hours.

We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,

z = (x - µ)/σ

Where

x = life of light bulbs.

µ = mean lifetime

σ = standard deviation

From the information given,

µ = 520 hours

Variance = 225

σ = √variance = √225

σ = 15

The probability that a light bulb will last for no more than 560 hours is given by

P(x ≤ 533)

For x = 533

z = (533 - 520)/15 = 0.86

According to the normal distribution table, 0.86 represents the probability for the z score.

Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.

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Given:

percentage decerease = 25%

current price of the grill = $496

Let the original price of the grill be x

We can calculate percentage decrease using the formula:

Substituting the given values we have:

Cross-Multiply:

Hence, we can conclude that the original price of the grill is approximately $661.33

Answer:

$661.33

Answer:

x/1

Step-by-step explanation:

8=-4x-4

4=-4x

(divide by -4)

1=x

Answer:

[tex]-1\geq x[/tex]

Step-by-step explanation:

[tex]8\leq -4(x-1)[/tex]

[tex]8\leq -4x+4[/tex]

[tex]8-4=-4x+4-4[/tex]

[tex]4\leq -4x[/tex]

[tex]\frac{4}{-4} \leq \frac{-4x}{-4}[/tex]

Inequality is reversed:

[tex]-1\geq x[/tex]

Hope this helps

The answer for the equation:

7x+31 = 8x -1/3(27x+3) is x=-4

Answer: 0-10

1-9

2-8

Step-by-step explanation: