Final answer:
To solve for x in the equation X + 6y = 29, subtract 6y from both sides to isolate x, resulting in x = 29 - 6y. The solution for [tex]\( x \)[/tex] in the first equation is [tex]\( x = \frac{19}{2} \).[/tex]
Explanation:
To solve for [tex]\( x \)[/tex] in the first equation [tex]\( x + 6y = 29 \)[/tex], we can isolate [tex]\( x \)[/tex] by subtracting [tex]\( 6y \)[/tex] from both sides of the equation:
[tex]\[ x + 6y - 6y = 29 - 6y \][/tex]
[tex]\[ x = 29 - 6y \][/tex]
Now, we can substitute this expression for [tex]\( x \)[/tex] into the second equation [tex]\( 2x - 4y = -6 \):[/tex]
[tex]\[ 2(29 - 6y) - 4y = -6 \][/tex]
First, distribute the 2:
[tex]\[ 58 - 12y - 4y = -6 \][/tex]
Combine like terms:
[tex]\[ 58 - 16y = -6 \][/tex]
Next, isolate the term with [tex]\( y \)[/tex] by adding [tex]\( 16y \)[/tex] to both sides:
[tex]\[ 58 - 16y + 16y = -6 + 16y \][/tex]
[tex]\[ 58 = -6 + 16y \][/tex]
Now, isolate [tex]\( y \)[/tex]by subtracting 6 from both sides:
[tex]\[ 58 - 6 = 16y \][/tex]
[tex]\[ 52 = 16y \][/tex]
Finally, solve for [tex]\( y \)[/tex] by dividing both sides by 16:
[tex]\[ \frac{52}{16} = y \][/tex]
[tex]\[ y = \frac{13}{4} \][/tex]
Now that we have found the value of [tex]\( y \)[/tex], we can substitute it back into the expression we found for[tex]\( x \)[/tex]:
[tex]\[ x = 29 - 6\left(\frac{13}{4}\right) \][/tex]
[tex]\[ x = 29 - \frac{39}{2} \][/tex]
[tex]\[ x = \frac{58}{2} - \frac{39}{2} \][/tex]
[tex]\[ x = \frac{19}{2} \][/tex]
Therefore, the solution for [tex]\( x \)[/tex] in the first equation is [tex]\( x = \frac{19}{2} \).[/tex]
what is the distance between 16 and 52
How do you complete a square root problem?
What is the value of negative 3.25 times negative 1.56
if z=2 what is z+6? This is a practice question.
brett hoped to get 100 pumpkins from his garden this year. since the weather was favorable 20% more pumpkins grew then he xpected. unfortuntely animals ate 30% of all the pumpkins the grew A) how many pumpkins were left B) is the final number of pumpkins more than or less then he hoped?
A produce stand sells a basket of 12 apples for $6. If the unit price of an apple is the same , what is the price for a basket of 18 apples?
Community Gym charges a $40 membership fee and a $50 monthly fee. Workout Gym charges a $210 membership fee and a $40 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?
To find the number of months it will take for the total amount of money paid to both gyms to be the same, set up an equation and solve for x. After 17 months, the total amount paid to both gyms will be $870.
Explanation:To find the number of months it will take for the total amount of money paid to both gyms to be the same, we need to set up an equation and solve for x. Let x represent the number of months.
For Community Gym, the total cost after x months is: 40 (membership fee) + 50x (monthly fee).
For Workout Gym, the total cost after x months is: 210 (membership fee) + 40x (monthly fee).
Setting up the equation:
40 + 50x = 210 + 40x
10x = 170
x = 17
After 17 months, the total amount of money paid to both gyms will be the same, which is $870.
7 teachers share 1 liter of cappuccino. If you make 3 litters of cappuccino, how many teachers can drink cappuccino? If you need to make enough cappuccino for 74 teachers, how many liters would you need to make?
If 3 liters of cappuccino are made, 21 teachers can drink it. To have enough cappuccino for 74 teachers, approximately 10.57 liters would be needed.
Explanation:To answer the first part of the question, we can use a proportion to find out how many teachers can drink cappuccino if 3 liters are made. Since 7 teachers share 1 liter, we can set up the proportion: 7 teachers / 1 liter = x teachers / 3 liters. Solving for x, we get x = 21 teachers. Therefore, 21 teachers can drink cappuccino.
For the second part of the question, we can use a similar proportion to find how many liters of cappuccino would be needed for 74 teachers. From the previous proportion, we know that 7 teachers share 1 liter. So, we can set up the proportion: 7 teachers / 1 liter = 74 teachers / x liters. Solving for x, we get x = 10.57 liters. Therefore, you would need to make approximately 10.57 liters to have enough cappuccino for 74 teachers.
Please be 100 correct! I'll give brainiest to who's correct.
if you needed to triple a recipe, would the ratio change? Explain.
A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = -16t2 + 112t + 30 How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary
Answer:
3.5 s; 226 ft is correct.
Step-by-step explanation:
An employee earns $255 for 15 hours of work. Assuming he is paid by the hour, how much will he earn in 8 hours?
Two stores sell the same television for the same original price. Store A advertises that the television is on sale for 30% off the original price. Store B advertises that it is reducing the television’s price by $250. When Allison compares the sale prices of the television in both stores, she concludes that the sale prices are equal. Let p represent the television’s original price. Which equation models this situation? 0.7(p−250)=p 0.3=p−250 0.7p=p−250 0.3p = p + 250
30% off so sale price is 70%
so 0.7p = p-250
Answer:
Musiclover10045 is correct! I took the test and the correct answer is in fact:
0.7p = p - 250!
Thanks, mate!
Cheers!
The number 9 has only one prime Factors, 3. What is another number less than 50 with only one prime factor
7x + 55 ≥ 300. Solve this inequality for x.
identify a number of pages that the student could read per day in order to have at least 300 pages of the novel read in a week.
The number of pages is 35
To solve the inequality 7x + 55 ≥ 300 for x, we first subtract 55 from both sides to isolate the term with x:
7x + 55 - 55 ≥ 300 - 55
7x ≥ 245
Divide by 7 to solve for x:
x ≥ 35
This means the student needs to read at least 35 pages per day to have 300 pages of the novel read in a week.
explain why two employees at a company, earning the same gross pay, might have different net pays.
Step-by-step explanation:
Gross pay:
Gross pay can be define as the wage before paying any taxes and all other deductions.
Net pay:
Net pay can be define as the wages after paying all taxes and all other deductions.
So we can say that
Gross pay = Net pay + taxes and all other deductions
So from above equation we can say that ,even two employees have same gross pay but can have different net pays .Because maybe they are paying different taxes and other deductions.
line r is parallel to line t. find m<6. The diagram is not to scale
All movies until 4:00 p.m require a discount ticket, and all movies after 4:00 p.m require a regular-price ticket.Each theater at the movieplex seats 98 people. What is the least number of showings the theater could have shown after 4:00 p.m last Saturday ? Explain how you found your answer. The discount ticket is 208 the regular price is 1248
What is the slope of the graph?
100 POINTS IF YOU ANSWER CORRECTLY Rotate these coordinates 180 around the origin and then translate 6 units to the left.
Hello!
When you flip the coordinates and move them 6 units to the left your coordinates would be: (-4, 8) (0, 8) (5, 1) (1, 3)
The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length of the other leg.
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored points in the game. what is the expression (what is the numeric form) in this equation?
what multiplication expression can you use to solve 2 divided by 8 4/5?
The Jensen family took a trip in September. Sally is calculating the gas mileage in miles per gallon for her dads SUV. When he fills the tank ,her dad records the miles on the SUV as 24033. Her dad pays $83.58 I fill up the empty gas tank of the SUV. At the destination, there was a quarter tank of gas left in the vehicle and the miles where recorded as 24,297. Use a ratio equation to determine the gas mileage in miles per gallon for the trip. Round your answer to the nearest whole.
Answer:
The gas mileage formula in miles per gallon (mpg) is:
[tex]gas mileage=\frac{miles driven}{gallons used}[/tex] (1)
We know that Sally’s dad filled the tank when it was empty and the miles recorded in the SUV were 24033 miles.
We also know that at the destination, there was a quarter tank of gas left in the vehicle and the miles were recorded as 24297 miles.
This means that the miles driven during the whole trip were 894 miles:
[tex]24927 miles-24033 miles=894 miles[/tex]
If at the beginning the tank was full and at the end is left with a quarter tank ([tex]\frac{1}{4}[/tex]), this means that the car wasted [tex]\frac{3}{4}[/tex] of the tank:
[tex]\frac{4}{4}-\frac{1}{4}=\frac{3}{4}[/tex]
Now, SUVs come in so many different sizes and models, hence it is difficult to assume an average size for a SUV gas tank. It may vary from the smaller ones that hold 16.5 gallons to larger SUVs that hold from 28 to 33.5 gallons.
In this case let’s assume that the tank holds 28 gallons
Then, if 1 tank holds 28 gallons, [tex]\frac{3}{4}[/tex] of a tank holds 21 gallons.
Knowing this, let’s apply the mileage formula ( equation 1):
[tex]\frac{894 miles}{21 gallons}=42.571mpg[/tex]
If we round the result we have, the gas mileage in miles per gallon for the Jensen’s SUV is 43mpg
Domain, first element, and y -value all have the same meaning.
True Or False
Answer:
False
Step-by-step explanation:
Hi there!
The domain refers to the possible x-values in a function.
The first element refers to the first member in a set of data (example: In the set {1, 2, 3}, 1 is the first element).
The y-value of a coordinate refers to the y-coordinate (example: In the ordered pair (4,9), 9 is the y-value or y-coordinate).
Therefore, the three terms all have different meanings.
I hope this helps!
a car travels an average speed of 64 miles per hour. how many miles does it travel in 5 hours and 15 minutes?
0.249 in expanded form
Final answer:
The expanded form of the number 0.249 is the sum of each digit multiplied by its place value, which is 0.2 + 0.04 + 0.009.
Explanation:
The question asks to write the number 0.249 in expanded form. The expanded form of a number is the sum of each digit multiplied by its place value. For the number 0.249, the expanded form is:
2/10 + 4/100 + 9/1000
This can also be written as:
0.2 + 0.04 + 0.009
Breaking down the number 0.249 into its decimal place values helps one understand how each digit contributes to the overall value of the number.
Serena uses chalk to draw a straight line on the sidewalk. The line is 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?
Evaluate 10s 3t for s = 3 and t = 7.
An online retailer sells two packages of protein bars. Package 10−pack of 2.3 ounce bars 12−pack of 1.6 ounce bars Cost ($) 17.35 16.97 Which package has the better price per bar?
Answer:
Package 10−pack of 2.3 ounce bars has the better price per bar
Step-by-step explanation:
Case 1) Package 10−pack of 2.3 ounce bars Cost ($) 17.35
Cost of Package 10−pack of 2.3 ounce bars = 17.35
Cost of Package 1−pack of 1 ounce bars = [tex]\frac{17.35}{10 \times 2.3}[/tex]
= [tex]0.7543[/tex]
2) 12−pack of 1.6 ounce bars Cost ($)16.97
Cost of Package 12−pack of 1.6 ounce bars = 16.97
Cost of Package 1−pack of 1 ounce bars = [tex]\frac{16.97}{12 \times 1.6}[/tex]
= [tex]0.8838[/tex]
Hence Package 10−pack of 2.3 ounce bars has the better price per bar