solve this equation
y= 2x
x= -y + 6

Final answer:

To calculate the cost per second for a $4 million Super Bowl ad that runs for 30 seconds, divide the total cost by the number of seconds, yielding a cost of approximately $133,333.33 per second.

Explanation:

The question asks us to calculate the cost per second for Super Bowl commercial air time when 30 seconds of air time sold for $4 million. To find the price per second, we divide the total cost by the total number of seconds.

Price per second = Total cost ÷ Number of seconds

Price per second = $4,000,000 ÷ 30 seconds

Price per second = $133,333.33 (rounded to the nearest cent)

Therefore, the price per second for Super Bowl commercial air time was approximately $133,333.33.

Answer:

The density of oak is 0.695 grams per cubic centimeter.

Step-by-step explanation:

Given:

Oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters.

Now, to find the density of oak in grams per cubic centimeter.

Mass (m) = 2.85 kilograms.

So, using conversion factor we convert into grams:

[tex]2.85\times 1000=2850\ grams.[/tex]

Volume (v) = 4100 cubic centimeters.

Now, to get the density by using formula:

[tex]Density=\frac{mass}{volume} \\Density=\frac{m}{v}[/tex]

[tex]Density=\frac{2850}{4100}[/tex]

[tex]Density=0.695\ grams\ per\ cubic\ centimeter.[/tex]

Therefore, the density of oak is 0.695 in grams per cubic centimeter.

Final answer:

The speed of the skater is 18 km/h.

Explanation:

To find the speed of the skater, we can set up a proportion using the information given. Let's let the speed of the skater be x km/h. Since the cyclist traveled 9 km/h faster than the skater, the speed of the cyclist would be x + 9 km/h. Now, we can set up the proportion:

(x + 9 km/h)/(45 km) = x km/h)/(30 km).

To solve this proportion, we can cross-multiply and solve for x:

(x + 9 km/h)(30 km) = (x km/h)(45 km)

30x + 270 = 45x

270 = 45x - 30x

270 = 15x

x = 18

Therefore, the speed of the skater is 18 km/h.

Answer:

1 - Avenue A is perpendicular to South St.

2 - 70°

Step-by-step explanation:

1 - North, Center, and South St. are parallel lines. Therefore Ave A will be perpendicular to the three lines.

2 - Ave B and Center street forms a 70° angle. Since Center and South St. are parallel lines, they have corresponding angles. Therefore, Ave B and South St also form a 70° angle. The same is true for Ave B and North St.

Answer:

For the first one, x is 9 and y is 2. 9 + 3(2) = 15. The second is y = 3.75

The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.

The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.

Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.

Answer:

The second number is 225.

Step-by-step explanation:

Consider the provided information.

Let the first number is x.

Second number

[tex]\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x[/tex]

Third number is:

[tex]\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x[/tex]

Fourth number is:

[tex]\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x[/tex]

The sum of 4 numbers is 771.

[tex]x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771[/tex]

[tex]50x+75x+60x+72x=38550[/tex]

[tex]257x=38550\\x=150[/tex]

First number is 150.

[tex]\text{Second number}=\dfrac{3}{2}\times150=225[/tex]

Hence, the second number is 225.

The value of the second number is 165.21.

Step 1: Understand the problem.

We have four numbers whose sum is 771. The ratios between consecutive numbers are given. We need to find the value of the second number.

Step 2: Construct equations using the provided ratios.

Let the four numbers be represented as 2x, 3x, 4x, and 5x respectively (using the smallest common multiple of the ratios).

Step 3: Create an equation using the total of the numbers.

2x + 3x + 4x + 5x = 771

Step 4: Solve for x.

[tex]\(2x + 3x + 4x + 5x = 771\)[/tex]

[tex]\(14x = 771\)[/tex]

[tex]\(x = \frac{771}{14}\)[/tex]

[tex]\(x = 55.07\)[/tex]

Step 5: Find the value of the second number.

The second number is 3x.

[tex]\(3x = 3 \times 55.07 = 165.21\)[/tex]

So, the value of the second number is 165.21.

Answer:

-5 3/4, -5, 5/12, 1 1/5

Step-by-step explanation:

Negatives are opposite of positives when least to greatest

Answer:

It can be anything

Step-by-step explanation:

It just has to be grater.

Answer:

∠1 ≅ ∠2

Step-by-step explanation:

As shown in the figure:

We need to prove e ∥ f using the congruent angle.

So, check the options:

A) ∠2 ≅ ∠4 ⇒ (Wrong)

B) ∠1 ≅ ∠2 ⇒ (True) because a ∥ b (Given)

C) ∠2 ≅ ∠3 ⇒ It is required to prove that to prove e ∥ f , it can't be used.

D) ∠1 ≅ ∠4 ⇒  (Wrong)

The complete sentence will be:

We see that ∠1 ≅ ∠2 by the alternate exterior angles theorem.

Therefore, angle 2 is congruent to angle 3 by the transitive property.

The missing information in the paragraph proof is: ∠2 ≅ ∠4.

In the given proof, it is correctly established that angle 1 is congruent to angle 3 because lines a and b are parallel, and this is due to the alternate exterior angles theorem.

Furthermore, it is correctly deduced that angle 2 is congruent to angle 3 through the transitive property.

However, to conclude that lines e and f are parallel using the converse alternate exterior angles theorem, it is essential to establish that angle 2 is congruent to angle 4.

Without this information, the proof is incomplete because it doesn't demonstrate the congruence between the corresponding angles on lines e and f at their intersection with line b.

To complete the proof, you would need to show that ∠2 ≅ ∠4, thereby demonstrating that all pairs of corresponding angles between lines e and f are congruent.

This additional congruence statement would justify the application of the converse alternate exterior angles theorem, allowing you to conclude that e ∥ f.

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Answer:

12x+60

Step-by-step explanation:

12 gets multiplied with x

12 gets multiplied with 5

Which gives 12x + 60

volume of the speaker= 22 cubic inches

Step-by-step explanation:

The total cost of the sweater will be $36.75.

Percentage is a number or ratio which is a fraction of hundred.

Given,

Cost price of sweater =$35.

Sales tax= 5%.

The total cost of the sweater can be calculated as,

Total cost price = CP of sweater + sales tax

                          = 35 + (5/35)*100

                          =$36.75

Hence, The total cost price of sweater would be $36.75.

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Answer: 7%

Step-by-step explanation:

Answer:

6 days

Step-by-step explanation:

Data given:

Vancouver is in the British Columbia

3/5 of the vacation was spent in British Columbia

1/2 of the time spent in British Columbia was spent in Vancouver.

The whole vacation was 20 days long

total days spent in British Columbia = 3/5 *20

total days spent in British Columbia = 12

Since the 1/2 of the time in British Columbia was spent in Vancouver then

time spent in Vancouver = 1/2 * 12

time spent in Vancouver =6 days

Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver. If her vacation lasted 20 days, she spent 6 days in Vancouver.

 Mara spent [tex]\(\frac{3}{10}\)[/tex]of her vacation in British Columbia. While in British Columbia, she spent [tex]\(\frac{1}{2}\)[/tex] of her time in Vancouver.

To find the fraction of her entire vacation that Mara spent in Vancouver, we multiply the two fractions:

[tex]\[ \text{Fraction of vacation in Vancouver} = \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} \][/tex]

So, Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver.

Next, to find out how many days she spent in Vancouver, we take the total number of days of her vacation, which is 20 days, and multiply it by the fraction of the vacation spent in Vancouver:

[tex]\[ \text{Days in Vancouver} = 20 \times \frac{3}{10} \][/tex]

[tex]\[ \text{Days in Vancouver} = 6 \][/tex]

 Therefore, Mara spent 6 days in Vancouver.

Answer:

(x - 4, y + 3)

Step-by-step explanation:

This is because when you follow the movement of the individual points you can see that they have moved 3 spaces up which is shown as y + 3, and they have moved 4 spaces to the left which is shown as x - 4

Answer:

The correct answer is: D

Step-by-step explanation:

(x - 4, y + 3)

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Answer:

56.52

Step-by-step explanation:

C=3.14 * D

Name the property the equation illustrates

(ab)3 = a(b3)

A. Commutative property of addition

B. Associative property of Multiplication

C. Associative Property of Addition

D. Inverse Property of Multiplication

Associative property of Multiplication

From given equation

(ab)3 = a(b3)

We have to find the property used here

We find the brackets are interchanged

So here, given is a multiplication equation

Therefore, Associative property of Multiplication  is used

This property says that when we are multiplying it does not matter where you put the parenthesis

The result will be same wherever we put the parenthesis in multiplying two or more numbers

Which means,

[tex]a \times (b \times c) = (a \times b) \times c[/tex]

Therefore, from given,

[tex]a \times (b \times 3) = (a \times b) \times 3[/tex]

Thus associative property of multiplication is used

Answer:

3/5

Step-by-step explanation:

0.6 is actually 6/10 as a fraction. You divide bot the 6 and the 10 by 2 to get 3/5

Answer:

7

Step-by-step explanation:

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

a+6=3a−8

Step 1: Subtract 3a from both sides.

a+6−3a=3a−8−3a

−2a+6=−8

Step 2: Subtract 6 from both sides.

−2a+6−6=−8−6

−2a=−14

Step 3: Divide both sides by -2.

−2a

−2

=

−14

−2

a=7

Answer:

a=7

Answer:

2i

Step-by-step explanation:

The square root of -4 is equal to 2i.

The square root of -4 can be simplified using the imaginary number i. Since the square root of a negative number is not defined in the set of real numbers, we use i to express it, where i is defined as the square root of -1. Thus, the square root of -4 is calculated as follows:
√-4 = √(-1*4)
= √(-1) * √(4)
= i * 2
= 2i

This result shows that 2i is the simplified form of the square root of -4 using the imaginary number i.

Answer:

x = 5/4 or 1.25.

Step-by-step explanation:

10x + 4 = 6x + 9

10x - 6x = 9 - 4

4x = 5

x = 5/4.

Answer: x = 5/4 or 1.25 or 1 1/4

Step-by-step explanation:

Step 1: Subtract 6x from both sides.

10x+4−6x=6x+9−6x

4x+4=9

Step 2: Subtract 4 from both sides.

4x+4−4=9−4

4x=5

Step 3: Divide both sides by 4.

4x/4 = 5/4

Step-by-step explanation:

x+13÷2×2=4×2

x+13=8

x+13-13=8-13

x=8-13

x=-5

Answer:-2.5

Step-by-step explanation:

13/2=6.5. 4-6.5 =-2.5

Answer:

m=5

Step-by-step explanation:

Since we know that triangle ABC is similar to QRS, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.

Choose whole numbers to make the division easier

[tex]\frac{QR}{AB} = \frac{QS}{AC} \\\frac{10}{6} = \frac{m}{3} \\\frac{10*3}{6} =m\\m=10*3/6 = 5[/tex]

The missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].

The missing side length, [tex]$m$[/tex], can be found using the fact that triangles [tex]$ABC$[/tex] and[tex]$QRS$[/tex] are similar. This means that their corresponding side lengths are proportional. We can set up a proportion like this:

(m)/(3)=(10)/(6)

Cross-multiplying, we get:

[tex]$$6m[/tex] =[tex]30$$[/tex]

Solving for [tex]$m$[/tex], we get:

[tex]$$m[/tex] =[tex]5$$[/tex]

Therefore, the missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].

Answer:

$10,500 in the 8% interest account,

$31,000 in the 15% interest account

Step-by-step explanation:

Let

x ---> the amount invested in the 8% interest account

41,500-x ----> the amount invested in the 15% interest account

we know that

The amount  invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490

so

The linear equation that represent this problem is

[tex]0.08x+0.15(41,500-x)=5,490[/tex]

solve for x

[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]

so

[tex]41,500-x=41,500-10,500=\$31,000[/tex]

therefore

$10,500 in the 8% interest account,

$31,000 in the 15% interest account

Answer:

y=3x-13/2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1/2)=3(x-2)

y+1/2=3x-6

y=3x-6-1/2

y=3x-12/2-1/2

y=3x-13/2

By using the information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference, we calculate that it can travel 11.8 miles with 0.1 gallons and 1180 miles with 10 gallons.

To complete the table and find the number of miles the scooter can travel for other amounts of gasoline, we can use the given information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference point. We can calculate the mileage for different amounts of gasoline using this information.

Here's how we can complete the table:

Gallon 0.1:

We can calculate the distance for 0.1 gallons by taking 10% of the mileage for 1 gallon:

0.1 * 118 miles = 11.8 miles

Gallon 10:

Similarly, we can calculate the distance for 10 gallons by multiplying the mileage for 1 gallon by 10:

10 * 118 miles = 1180 miles

So, the completed table would look like this:

Gallon 0.1: 11.8 miles

Gallon 1: 118 miles

Gallon 10: 1180 miles

This table provides the number of miles the scooter can travel for different amounts of gasoline, including 0.1 gallons, 1 gallon, and 10 gallons.

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Answer:

a.  [tex]$ \frac{\textbf{17}}{\textbf{4}} $[/tex]

b.  [tex]$ \frac{\textbf{3}}{\textbf{8}} $[/tex]

Step-by-step explanation:

a. [tex]$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $[/tex]

A mixed fraction of the form [tex]$ a\frac{x}{y} = a + \frac{x}{y} $[/tex]

[tex]$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $[/tex]

[tex]$ = 4 + \frac{1}{4} $[/tex]

[tex]$ = \frac{\textbf{17}}{\textbf{4}} $[/tex]

b. [tex]$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $[/tex]

A mixed fraction of the form [tex]$ -c\frac{a}{b} = - c - \frac{a}{b} $[/tex]

[tex]$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $[/tex]

[tex]$ = 1 - \frac{5}{8} $[/tex]

[tex]$ = \frac{8 - 5}{8} $[/tex]

[tex]$ = \frac{\textbf{3}}{\textbf{8}} $[/tex]

Hence, the answer.

Answer:

17 pies and one half pie

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

X/100% x 140 = 50.4

X x 140 = 50.4 x 100

X x 140 = 5040

X = 5040/140

X = 36