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,
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].
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 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.
To know more about an equation of plane follow
https://brainly.com/question/14976724
#SPJ2
In the triangle below, 4/5 represents which ratio?
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 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.
Please explain it and tell me how u got the answer
Thx
Suppose that a system has 5000 grasshoppers. how many hawks would be expected?
How to find x in this math problem?
Please help me on this....
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.
Read more at;https://brainly.com/question/19770914
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.
Learn more about synthetic division here
brainly.com/question/11850611
#SPJ2
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.
Learn more about Investment worth here:https://brainly.com/question/32802960
#SPJ12
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"
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?
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
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
Learn more about equations, click;
https://brainly.com/question/29657988
#SPJ2
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.
Will mark brainliest ⭐️⭐️⭐️⭐️⭐️
is a hope this helped
Answer:
answer is d
Step-by-step explanation:
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:
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
draw a number line from 0 to 2 write 3\8 1 and 3\4 and 1.25 on the number line,
what is y−4=−2(x+7) written in standard form?
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.
Please answer this and thank you
If DE=4x+10, EF=2-1, and DF=9x-15, find DF.
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
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
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).