Final answer:
The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.
Explanation:
The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:
Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.
Solve log 4x + log 13 = 0. Round to the nearest thousandth if necessary. a.0.019 b. 52 c.3.25 d. 0.311 Mathematics
Jim bought a $576 TV with the cash in his wallet. He now has $137 in his wallet. Write and solve an equation that shows how much he originally had in his wallet.
Final answer:
Jim originally had $713 in his wallet before purchasing the TV. We found this by setting up the equation x - $576 = $137, which represents the situation before and after the purchase, and solving for x.
Explanation:
Jim bought a $576 TV with the cash in his wallet and now has $137 left. To find out how much money Jim originally had, we can write and solve a simple equation. Let's denote the amount of money Jim originally had as x. After buying the TV, he spent $576, so the money left is $137. This gives us the equation x - $576 = $137.
To solve for x, we add $576 to both sides of the equation, which gives us x = $137 + $576. Therefore, x = $713. So, Jim originally had $713 in his wallet before buying the TV.
Li is making beaded necklaces for each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length. Write an equation to find how many beads Li needs for each necklace.
A. Input variable
B. Output variable
C. Equation
The output variable B (total number of beads needs for each necklace) equals 27 (number of spacers used) plus 5 times the input variable A (length of the necklace in inches). The resulting equation is B = 27 + 5A.
Explanation:In this question, we're trying to find out the total number of beads Li needs to create each necklace.
Let's define two variables:
A is the input variable, representing the length of the necklace in inches. B is the output variable, which stands for the total number of beads Li needs for each necklace.Li uses 27 spacers for each necklace regardless of its length and there are 5 beads for every inch of necklace. Given these facts, we can create an equation as follows:
B = 27 + 5A
In this equation, 27 is the number of spacers used, while 5A indicates that 5 beads are strung for each inch of the necklace.
To use this equation, simply replace the variable 'A' with the desired length of the necklace in inches. The result will give the total number of beads Li needs for that particular length of necklace.
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is the line through points P(1,9) and Q(9,6) perpendicular to the line through points R(-6,0) and S(-9,8)? Explain?
To determine if two lines are perpendicular, we can calculate their slopes. The line through P(1,9) and Q(9,6) has a slope of -3/8, and the line through R(-6,0) and S(-9,8) has a slope of -8/3. The product of these slopes is -1, indicating that the lines are perpendicular.
Explanation:To determine whether the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8), we can calculate the slope of each line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).
For the line through P(1,9) and Q(9,6), the slope is (6 - 9) / (9 - 1) = -3/8.
For the line through R(-6,0) and S(-9,8), the slope is (8 - 0) / (-9 - (-6)) = 8/-3 = -8/3.
If the two lines are perpendicular, the product of their slopes should be -1. Let's check: (-3/8) * (-8/3) = 1. Therefore, the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8).
Need help! Would greatly appreciate help
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3 −1 ?
When you do a negative number minus a negative number do you get a positive?
What is m∠SVT?
Enter your answer in the box.
Normally I am not one to make long answers
but if you want an explanation in case you have the same question with different numers, here is an explanation
Plug in the eequation and solve for x
Doing quick math the equation would be 8y-33 = 5y+9
I plugged this into m a t h w a y and got y=14
Then I subsituted y with 14
5 x 14 = 70 70 + 9 =79
Then I did a double check by making sure they were both equal
8 x 14 = 112 112 - 33 = 79
79 = 79
Therefore your answer is 79
Hope this helped, have a great day :)
I NEED QUICK HELP QUICK!!! PLEASE HELP ME SOMEONE!! THANK YOU!!
Which graph does NOT represent a function?
Answer:
ITS B!!!
Step-by-step explanation:
alphametic FOOD+FOOD=SHOP
Maddie throws a baseball from third base to first base. The four 90-foot lines between the bases form a square. Which number is the best estimate of how far Maddie throws the baseball?
What is the height of the ramp, to the nearest foot?
Question 4 options
90 feet
130 feet
150 feet
180 feet
A cyclist pedals up a hill that has a 13° angle. If the cyclist pedals up the hill for 10 kilometers, what is the change in her elevation, x ?
0.22 kilometer
9.7 kilometers
2.2 kilometers
45.0 kilometers
PLEASE HELP PLEASE PLEASE PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Evan earns $12 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime.
Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours.
Part C: Evan earned $510 in 1 week. How many hours (regular plus overtime) did he work?
Let's say we have a circle with a radius of 17 inches. What is the circumference of this circle in inches? Round your answer to the hundredths place.
54.78
86.23
91.1
106.81
Why is looking at cash flow an important step in a good financial plan?
Answer:
To keep knowing how much money you have i recommend credit karma to help but money is very important
Step-by-step explanation:
ASAP PLEASE ANSWER
Given △ABC≅△JKL, m∠B=55°, and m∠L=25°, what is the measure of ∠J? Enter your answer in the box. °
Answer: [tex]\angle{J}=100^{\circ}[/tex]
Step-by-step explanation:
Given: △ABC≅△JKL,
m∠B=55°, and m∠L=25°
We know that if two triangles are congruent then their corresponding angles are equal.
∴ m∠A=m∠J
m∠B=m∠K=55°
m∠C=m∠L=25°
Now, by angle sum property in triangle JKL we have
[tex]\angle{J}+\angle{K}+\angle{L}=180^{\circ}\\\\\Rightarrow\angle{J}+55^{\circ}+25^{\circ}=180^{\circ}\\\\\Rightarrow\angle{J}=180^{\circ}-55^{\circ}-25^{\circ}\\\\\Rightarrow\angle{J}=100^{\circ}[/tex]
Find two numbers whose difference is 168 and whose product is a minimum
The two numbers whose difference is 168 and whose product is a minimum will be -50 and 50.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, two numbers whose difference is 168 and whose product is a minimum.
Suppose the two numbers are x and Q respectively.
If x - Q = 100, then Q = 100 + x
The function of their product is minimum,
F(x) = xQ
F(x) = x (100 + x)
F(x) = x² + 100x
Find the equation's lowest point on a graph. At x, the lowest point is -50,
f(x) = -2500
If,
Q = 100 + x
Q = 100 + (-50)
Q= 50
The product of the number is,
xQ = 50 × -50
xQ = -2500
Thus, the two numbers whose difference is 168 and whose product is a minimum will be -50 and 50.
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Which transformation is not isometric?
The average value of the function v(x)=6/x2 on the interval [1,c] is equal to 1. find the value of
A student has some $1 and $5 bills in his wallet. He has a total of 14 bills that are worth $38. How many of each type of bill does he have?
mnmn if m=8m=8 and n=3n=3.
Answer: 8x8x8=512
Step-by-step explanation:
The set of all x values that make up the function is called the
ms.snork brought two steaks that weighed 2.96 lb and 3.48 lb. If the meat cost $3.60 per pound, what was the total cost of the steaks ?
The total cost of the steaks that Ms. Snork brought will be $23.184.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ms. Snork brought two steaks that weighed 2.96 lb and 3.48 lb. If the meat cost $3.60 per pound. Then the total cost of the steaks will be given as,
⇒ 2.96 x $3.60 + 3.48 x $3.60
⇒ $10.656 + $12.528
⇒ $23.184
The total cost of the steaks that Ms. Snork brought will be $23.184.
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Find points on the line 3x+5y=15 that are equidistant from the coordinate axes.
Final answer:
Points on the line 3x+5y=15 which are equidistant from the coordinate axes are (15/8, 15/8) and (-15/8, -15/8).
Explanation:
To find points on the line 3x+5y=15 that are equidistant from the coordinate axes, we need a point where the x and y coordinates are equal because the distances to the x-axis and y-axis from any point (x, y) are |x| and |y|, respectively. Since the line is equidistant from both axes, we require |x| = |y|.
Substituting y for x in the equation of the line, we get 3x + 5x = 15, which leads to 8x = 15, and therefore x = 15/8. Since we are looking for points equidistant from the axes, we have to check the signs of x and y to ensure they are at equal distances from both axes. Thus, the possible points are (15/8, 15/8) and (-15/8, -15/8).
Jared needs 2.4 micrograms of vitamin B-12 each day. Today, Jared drank a serving of milk containing 0.44 micrograms of B-12 and ate a lamb chop containing 1.224 micrograms of B-12. Which method can Jared use to find the number of micrograms of vitamin B-12 he still needs?
Answer:
the answer is d
Step-by-step explanation:
A private plane leaves the airport and flies 1.3 hours at 110 mph on a bearing if 40 degrees. Then it turns and continues another 1.5 hours at the same speed, but in a bearing if 130 degrees. Through what angle did the plane have to turn to head back to the airport?
A sample of size n is selected at random from an infinite population. as n increases, the standard error of the sample mean increases.
a. True
b. False
When Seb reconciles his accounts, what is the first step he should take?
Answer:
Seb should check if all is records are accurate and he should include all the transactions.
Step-by-step explanation:
When Seb reconciles his accounts, what is the first step he should take?
We can say that reconciling an account means proving that an account balance is correct.
For this, we need all the correct and accurate transactions and figures.
So, Seb should check if all is records are accurate and he should include all the transactions.
If a certain number is added to both the numerator and denominator of the fraction 7 6 76, the result is 3 2 32 . find the number.
If two angles share a vertex then they are adjacent true or false
The given statement is true"If two angles share a vertex then they are adjacent".
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
If two angles in geometry share a side and a vertex, they are said to be adjacent. In other words, consecutive angles do not overlap and are placed side by side.
When an angle's vertex and side are shared by another angle, the two angles are said to be adjacent angles. The vertex of an angle is the point where the rays come to a stop and form the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complementary or supplementary angles.
Thus, the given statement is true"If two angles share a vertex then they are adjacent".
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The school baseball team wants to have each player's name imprinted on the player's jacket. the cost is $75 plus $8.50 for each name. write a function to represent the cost c(n) for n names. what is the cost to have names printed on 25 jackets