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?
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].
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).
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
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"
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.
Solve for z. 7-~-3z+2=4 What is the root? If there is no root, choose none.
Desmos is Function Calculator is a great tool for this, the correct answer is z= 7/3
7/3= 2.333~ and so √(3*2.333~) + 2= 2.9999999833333~
Now 7- 2.9999999833333~= 4.0000000166667~ but I don't know the true infinate sign for this so thats why my numbers look a little werid, just plug (7/3) in for z and you will get 4, trust me
The root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, an equation 7-[tex]\sqrt{3z+2}[/tex] = 4
Solving for z,
7-[tex]\sqrt{3z+2}[/tex] = 4
[tex]\sqrt{3z+2}[/tex] = 3
Squaring both sides,
3z + 2 = 9
3z = 9-2
3z = 7
z = 7/3
Hence, the root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3
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Please help!
Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? Are these events independent?
A. 1/17: no, they are dependent events
B. 1/16: yes, they are independent events
C. 25/52: yes, they are independent events
D. 3/52: no, they are dependent events
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
draw a number line from 0 to 2 write 3\8 1 and 3\4 and 1.25 on the number line,
What is the number of pi?
Pi is a very special number in math and it’s so special that it even gets its own symbol. Mathematicians found out that when you try to write down what pi is, the decimal points keep going and going. This means that it’s impossible to find all the digits of pi.
I will only write down some digits.
π = 3.1415926535897932384626
In the triangle below, 4/5 represents which ratio?
A lab is conducting a test to see if people prefer chocolate A or chocolate B. The steps in the test are outlined below: Step 1. Recruit one hundred volunteers and tell them the purpose of the study. Step 2. Give them chocolate A and ask them to rate the flavor. Step 3. Give them chocolate B and ask them to tell how delicious it is. Step 4. Reveal which chocolate they preferred. Which step could lead to biased results?
Answer:
Step 3
Step-by-step explanation:
By asking the participants how delicious chocolate B is, you can possibly create bias in the test. It is a leading question; these should not be asked to avoid creating bias.
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].
Please explain it and tell me how u got the answer
Thx
Overdraft protection means the bank will loan you the money needed to cover the check that cannot be covered by funds in the account. True or false ASAP HELP PLEASE
True. Overdraft protection is a service offered by banks to their customers. When your account does not have enough money to cover a transaction, overdraft protection allows the bank to loan you the necessary funds to complete the transaction.
If you make a purchase or withdrawal that exceeds your account balance, the bank will cover the shortfall by lending you the needed amount. This ensures the transaction goes through, but typically comes with fees or interest. While convenient, it can lead to extra costs if used frequently.
Overdraft protection may apply to debit card purchases, checks, or automatic bill payments, depending on the account settings. Some banks offer this service automatically, while others require customers to opt in. It's a useful safety net but should be used responsibly to avoid accumulating unnecessary charges.
Which point lies in the plane represented by the equation 2x + 7y + 3z = -25?
(–3, 3, –2)
(–6, –4, 5)
(6, 1, –3)
(6, 1, 2)
The point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.
What is an equation of plane?The equation of the plane is defined as the plane has three variables. Having the coordinates in all three dimensions. The general form of the equation of the plane is ax + by + cz = d.
The given equation of plane is 2x + 7y + 3z = -25.
Check the point which satisfies the equation of the plane. Take the point ( -6,-4,5).
2x + 7y + 3z = -25.
2 ( -6 ) + 7(-4) + 3(5) = -25
-12 - 28 + 15 = -25
-40 + 15 = -25
-25 = -25
Therefore, the point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.
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BRAINLIEST ANSWER RN!!!!!!! HELP ME PLZZ!!!!!
A cylinder tube with caps on both ends is used to safely carry a rolled up poster. The tube is 42 inches tall with a radius of 1.5 inches. If one mini can of spray paint covers 150 square inches, how many mini spray cans of red paint would be needed to cover the entire tube?
A. 3
B. 2
C. 1
D. 4
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.
How to find x in this math problem?
what is y−4=−2(x+7) written in standard form?
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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what is the missing number in the synthetic division problem below?
(everything in picture)
In the given problem , missing number in the synthetic division is equal to [tex]10[/tex].
What is synthetic division?" Synthetic division is defined as simplified way of dividing a polynomial by another polynomial of first degree by writing its coefficient and changing usual subtraction into addition."
According to the question,
As shown in the given synthetic division,
[tex]4 + 20 = 24\\\\-2 + 6 = 4[/tex]
Therefore,
Missing number in the given synthetic division [tex]= 2+ 8[/tex]
[tex]=10[/tex]
Hence, Option (C) is the correct answer.
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Suppose an investment of $2,300 doubles in value every decade. The function gives the value of the investment after x decades. f(x)=2300*2^x How much is the investment worth after 2 decades?
(1 point)$2,355,200
$92,000
$46,000
$9,200
The investment is worth $9,200 after 2 decades.
Explanation:To find the value of the investment after 2 decades, we can substitute x = 2 into the function f(x) = 2300 * 2^x.
So, f(2) = 2300 * 2^2 = 2300 * 4 = 9200.
Therefore, the investment is worth $9,200 after 2 decades.
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Find an angle between 0 and 2π that is coterminal with 27 pi/10
Please answer this and thank you
If DE=4x+10, EF=2-1, and DF=9x-15, find DF.
Will mark brainliest ⭐️⭐️⭐️⭐️⭐️
is a hope this helped
Answer:
answer is d
Step-by-step explanation:
Please help me on this....
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.