What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.
Final answer:
The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.
Explanation:
The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.
Ben walks at a rate of 3 miles per hour. he runs at a rate of 6 miles per hour. in one week, the combined distance that he walks and runs is 210 miles.
b. (using 3x + 6y = 210 with x representing walk and y representing run) ben runs for 25 hours. for how many hours does he walk?
The length of a rectangular garden is 7 feet longer than its width. if the garden's perimeter is 182 feet, what is the area of the garden in square feet?
A $50,000 investment earns 18% annually. If B represents the balance and t represents the number of years, determine an expression that gives the account balance, B, after t years. Also, determine an equivalent expression that displays the effective monthly interest rate.
Answer:
usa test prep its B
Step-by-step explanation:
Which ordered pair is the best estimate for the solution of the system of equations?
y=−34x−2y=x+6
(−4.25,1.5)
(−4.75,1.75)
(−4.5,1.5)
(−4.5,1.75)
The best estimate for the solution of the system of equations is (-4.5, 1.5).
Explanation:The system of equations given is:
y = -34x - 2
y = x + 6
To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.
Let's check each option:
For (-4.25, 1.5):
1.5 = -4.25 + 6
1.5 = 1.75 (not equal)
This is not a solution for the system.
For (-4.75, 1.75):
1.75 = -4.75 + 6
1.75 = 1.25 (not equal)
This is not a solution for the system.
For (-4.5, 1.5):
1.5 = -4.5 + 6
1.5 = 1.5 (equal)
This is a solution for the system.
For (-4.5, 1.75):
1.75 = -4.5 + 6
1.75 = 1.5 (not equal)
This is not a solution for the system.
Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).
What is 5% in a decimal and a fraction?
Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.
−1
−0.75
−0.5
−0.25,
Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa
75 less than twice a number
How to find x in this math problem?
Suppose that a system has 5000 grasshoppers. how many hawks would be expected?
The explicit rule for a sequence is an=14-9n
What is the recursive rule for the sequence?
The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]
Let us put n=1, we get
[tex] a_{1}=14-(9 \times 1)=5 [/tex]
Now let n=2,
[tex] a_{2}=14-(9 \times 2)=-4 [/tex]
Let n=3,
[tex] a_{3}=14-(9 \times 3)=-13 [/tex]
Similarly, in this manner we obtain a sequence as
5, -4, -13, -22,.....
Since we can clearly observe that the first term is '5' and common difference is '-9'.
So, we get recursive rule for the sequence as:
[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].
Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2 . What is the value of x?
Please explain it and tell me how u got the answer
Thx
what is y−4=−2(x+7) written in standard form?
Justin lives in saint paul and goes to school in minneapolis. in the morning, he has 333 transportation options (bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home. if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?
Answer:
2/9
Step-by-step explanation:
TRUST ME THIS GUY ABOVE ME IS A DING DONG
What context clue in the paragraph best helps in understanding the meaning of the word native?
Question 2 options:
"much in America"
"lived in Nantes, France"
"first in France"
"born in Louisiana"
How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?
The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;
to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.
A system of linear equations can be solved by three major methods which are;
- Elimination method
- Substitution method
- Graph method
Now, in this question we want to know how substitution method is done.
Let us say we have two simultaneous equations which are;
2x + 3y = 8 ----(eq 1)
x + 5y = 11 ----(eq 2)
Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.
In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;
x = 11 - 5y
In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.
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Perform the indicated operation. (r + s)(r2 - rs + s2)
The operation in the equation, (r + s)(r2 - rs + s2), is solved by distributing the multiplication of the binomial across each term in the trinomial. When the multiplications are complete and the terms are added, the resulting solution is r3 + s3.
Explanation:The indicated operation in the question is the multiplication of the binomial, (r + s), and the trinomial, (r2 - rs + s2). This can be performed by using the distributed property of multiplication over addition. In this case, you would multiply each term in the binomial by each term in the trinomial, then add the products. So the solution will be:
r3 - r2s + rs2 + r2s - rs2 + s3 = r3 + s3
Note: the terms -r2s and r2s cancel each other out, as do the terms rs2 and -rs2, which is why the final result is r3 + s3.
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Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0
Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]
We can use following formulas to solve this problem :-
1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]
2. sin(2∅) = 2·sin(∅)·cos(∅)
Solving the given equation :-
[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]
Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].
Which fraction is NOT equivalent to 8 1/2 ? A) 2 3 B) 24 36 C) 4 6 D) 6 10
What is 5 x 2/3?
A) 3 1/3
B) 3 2/5
C) 5 2/3
D) 10/15
Find the simple interest. $7,064 at 6.5% for 8 months
Simple Interest can be calculated using the formula I=Pr t
Here I= interest earned ,P= Principal ,R= rate of interest ,t= time in years.
It is given Principal P=$7,064
Rate r=6.5% =0.065
Time t= 8 months =[tex] \frac{8}{12} =\frac{2}{3} [/tex] years
Substituting these values in I = P r t
I =(7064)(0.065)([tex] \frac{2}{3} [/tex])
Solving for I
I=306.11
interest earned on $7,064 at 6.5% for 8 months is $306.11
Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.
which do you think would seat more people a 4ft by 6 ft rectangular table or a circular table with a diameter of 6 ft? How many people would sit at each table? Explain your reasoning.
Final answer:
Comparing a 4ft by 6ft rectangular table and a circular table with a 6ft diameter, the circular table can seat more people (approximately 9) due to more efficient use of its perimeter, compared to the rectangular table which can seat 6 people.
Explanation:
The question asks which table would seat more people: a 4ft by 6ft rectangular table or a circular table with a diameter of 6ft. To answer this, we need to compare the arrangements and sizes of the two tables.
The rectangular table measures 4 feet by 6 feet. Typically, a person needs about 2 feet of space at a dining table to sit comfortably. Therefore, on the longer sides (6 feet), you can seat 3 people on each side, for a total of 6. On the shorter sides (4 feet), it's not practical to seat anyone due to space constraints and leg room. So, the rectangular table can seat 6 people.
The circular table has a diameter of 6 feet. Placing chairs around a circle often allows for more efficient use of space. If we assume each person requires the same 2 feet of space, roughly, the circumference of the table (which is π * diameter) dictates how many people can sit around it. The circumference of a 6-foot diameter table is about 18.85 feet (π * 6). Dividing this by 2 feet per person, you can seat approximately 9 people around the circular table.
In conclusion, a circular table with a diameter of 6 ft would seat more people, approximately 9, compared to a 4ft by 6ft rectangular table, which would seat 6 people. This is due to the circular table's ability to more efficiently use the perimeter for seating.
10 points!
Which graph represents the solution to the system of inequalities?
2x – y ≥ 3
x + 2y < 4
Answer:
graph c is the correct answer hope this helps you get an A.
A roped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of Native American artifacts. The combined area of the display and the roped-off is 120 square feet. Find the width.
The width of the roped off area around the museum display is 4 feet.
To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:
Area of display + Area of roped-off region = Total Area
(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120
24 + (24 + 4x + 12x + 4x2) - 24 = 120
Simplifying, we get:
4x² + 16x - 96 = 0
Divide by 4:
x² + 4x - 24 = 0
Factor the quadratic equation:
(x + 6)(x - 4) = 0
Setting each factor equal to zero gives us two potential solutions:
x + 6 = 0
or
x - 4 = 0
Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:
x = 4 feet
The width of the roped-off area is 4 feet.
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is a hope this helped
Answer:
answer is d
Step-by-step explanation:
If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)
A. $10.59
B. $8.76
C. $10.80
D. $18.25
Find the zeros of the function. f(x)=9x^2-12x-5
Please answer this and thank you
If DE=4x+10, EF=2-1, and DF=9x-15, find DF.