Answers
n = 12
Related Questions
Find the zeros of the function. f(x)=9x^2-12x-5
Answers
You can use the quadratic formula or you can do any method that your teacher teaches you (box, etc.)
Explanation:
1) Set the given function equal to 0: 9x^2 - 12x - 5 = 0
2) make 9x^2 = (3x)^2 and 12x = 4(3x)
=> (3x)^2 - 4(3x) - 5 = 0
3) Factor the polynomial:
(3x - )(3x + ) first stept of factoring.
Now find two numbers that sum - 4 and their product of - 5, those are -5 and + 1: =>
(3x - 5) (3x + 1) = 0
4) Set the two factors equal to 0:
3x - 5 = 0 => 3x = 5 => x = 5/3 ↔ one root
3x + 1 = 0 => 3x = - 1 => x = - 1/3 ↔ the other root.
Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now?
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We know Maura is five years younger than Cara. In symbols that is, M - 5 = C
We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols: [tex]M-7= \frac{1}{2}(C-7) [/tex]
Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:
[tex]M-7= \frac{1}{2}(C-7) [/tex]
[tex]C-5-7= \frac{1}{2}(C-7) [/tex]
[tex]C-12= \frac{1}{2}C-( \frac{1}{2})(7) [/tex]
[tex]C-12= .5C-3.5[/tex]
[tex].5C-12= -3.5[/tex]
[tex].5C= 8.5[/tex]
[tex]C= 17[/tex]
Cara is 17. Since Maura is 5 years younger she is 12.
As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.
To solve this problem, set up equations based on the given information. M = C - 5 and M - 7 = (C - 7) / 2. Solve the system of equations to find Maura's age (19).
Explanation:To solve this problem, we can set up equations based on the given information. Let's let M represent Maura's age and C represent Cara's age.
The first clue tells us that Maura is 5 years younger than Cara, so we can write the equation M = C - 5.
The second clue tells us that seven years ago, Maura was half as old as Cara. So seven years ago, Maura's age was M - 7 and Cara's age was C - 7. We can write the equation M - 7 = (C - 7) / 2.
Now we can solve this system of equations to find Maura's age. Substituting the value of M from the first equation into the second equation, we get (C - 5) - 7 = (C - 7) / 2. Simplifying and solving for C, we find that Cara's current age is 24. Substituting this value back into the first equation, we find that Maura's current age is 19.
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
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find the area of the circle .Leave your answer in terms of pie (3.14) the area is 4.1m .I need help on this question
Answers
Answer:
Area of the circle = 1.3π m²
Step-by-step explanation:
Area of the circle is given by the formula A = πr²
It is given that area of the circle is 4.1 m² and we have to convert it in the terms of π.
Now to convert the area in terms of π we will multiply the area by π and divide the area by 3.14.
⇒ Area×π / 3.14 = 4.1 × π/3.14 = 1.30π
Therefore answer is area of the circle = 1.30π m²
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
Answers
The answer for the second question is A. 3 1/3. 5/1 x 2/3 =10/3 10/3=3 1/3
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.
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FV=P(1+r/100)^t
FV is the future value
P is the principle
r is the rate
t is the time
the formula that gives the account balance after t years will be:
FV=50000(1+18/100)^t
FV=50000(1.18)^t
The formula for effective monthly interest rate will be:
monthly interest rate=(annual rate)/(number of months)
annual rate=18%
number of months in a year=12 months
rate=18/12=1.5%
Answer:
usa test prep its B
Step-by-step explanation:
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.
Answers
x----------> width a roped off area
we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0
using a graph tool---------> to calculate the quadratic equation
see the attached figure
the solution is
x=3 ft
the answer is
the width a roped off area is 3 ft
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 HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER!
Answers
Our expression is 5/x^-2y^5
The first thing we notice is that we have a negative exponent in the denominator. This is easily solved if we switch the term with the negative exponent into the numerator.
Our expression now looks like this: 5x^2/y^5
Now, there aren't any other terms that cancel out, so our simplified expression is 5x^2/y^5.
5 times the sum of p and r
A.5(p+r)
B.5p+r
C.5pr
D.5+p+r
Answers
Option: A is the correct answer.
The mathematical representation of the given statement is:
[tex]5(p+r)[/tex]
Step-by-step explanation:We are asked to represent the given expression in words to numerical expression.
The statement is:
5 times the sum of p and r
The sum of p and r is: (p+r)
and now 5 times the sum of p and r i.e. 5 is multiplied to the sum of p and r.
i.e.
[tex]5(p+r)[/tex]
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.
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For the rectangle, you will find the perimeter:
P = 2l + 2w
2 x 6 + 2 x 4
P = 20 feet
For the circle you will find the circumference:
C = pi x d
3.14 x 6
C = 18.84 feet
The rectangle would seat more people because the distance around the table is longer.
You would be able to fit about 7-8 people around the rectangular table and 6-7 people around the circular table.
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.
What needs to happen before you can use the reason CPCTC?
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Explanation:
1) CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.
2) Therefore, to use that reason you first need to prove that the the triangles are congruent.
3) Once, it has been stated that the triangles are congruent, then you can use the reason to state the the corresponding segments are congruent which will let you to state the length of any side of one triangle known the corresponding side of the other triangle, because they are congruent (have the same length).
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?
Answers
Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:
24/(x-2) = 20/5
Cross multiply:
24*5 = 20(x-2)
Use the distributive property:
120 = 20x - 40
Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x
Divide both sides by 20:
160/20 = 20x/20
8 = x
Find the simple interest. $7,064 at 6.5% for 8 months
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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
How do I find the holes for this function?
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x^2 - x - 2 factors into (x - 2)(x + 1) both of which can be crossed out or canceled with the factors in the numerator. That creates very really tiny holes at x = 2 and x = - 1.
[tex] {x}^{2} - x - 2 \: = > (x + 1)(x - 2)[/tex]
Which leaves is with the equation:
[tex]y = \frac{(x - 5)(x + 1)(x - 2)}{(x + 1)(x - 2)} [/tex]
We can see that we have the common factors of (x+1) and (x-2), so these cancel out in the numerator and denominator:
[tex]y = \frac{(x - 5)}{1} [/tex]
a.k.a: y = x - 5
So if x+1 and x-2 cancel out, then the x values of the holes are:
x+1=0
x= -1
And
x-2=0
x= 2
Now we plug in each of these numbers into our simplified equation:
y = x - 5
y=(-1)-5
y= -6
This gives us the coordinate (-1,-6)
y = x - 5
y=(2)-5
y= -3
This gives us the coordinate (2,-3)
So the holes are at (-1,-6) and (2,3)
Suppose that a system has 5000 grasshoppers. how many hawks would be expected?
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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?
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Answer:
2/9
Step-by-step explanation:
TRUST ME THIS GUY ABOVE ME IS A DING DONG
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
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Phil is a commercial fisherman. He keeps 5 salmon for every 8 cod he catches. If Phil keeps 15 salmon, how many cod will he keep?
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3 * 8 = 24 cod
Please help me please
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_____
The other selections are nonsense.
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?
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A population of 80,000 toads is expected to shrink at a rate of 9.2% per year.
What will the toad population be in 20 years?
3632
7360
11,609
72,640,
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How many real number solutions does the equation have?
0=5x^2+2x-12
A- one solution
B- two solution
C-infinity many solutions
D-no solutions
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x=(-b+sqrt(b^2-4ac))/2a and x=(-b-sqrt(b^2-4ac))/2a
Substituting using the equation 0=5x^2+2x-12
x=(-2+sqrt(2^2-4(5)(-12)))/(2(5)) and x=(-2+sqrt(2^2-4(5)(-12)))/(2(5))
Since the sqrt(244) is a real number, there are two real solutions.
75 less than twice a number
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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.
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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.
(0.2,3),(0.4,6) what is the slope? 10,15,20,25
HELP PLEASE
Answers
Answer:
15
Step-by-step explanation:
Use the slope formula to find the slope m.
m= y2-y1 / x2-x1
m= 6-3/0.4-0.2
m=15
Perform the indicated operation. (r + s)(r2 - rs + s2)
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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.
Learn more about Polynomial Multiplication here:https://brainly.com/question/20121808
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Will mark brainliest ⭐️⭐️⭐️⭐️⭐️
Answers
is a hope this helped
Answer:
answer is d
Step-by-step explanation:
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,
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AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
=[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
= [tex] \sqrt{4+49} [/tex] =
= √53
- Hence, we know that the distance between point A and the point C to be found is:
AC = √53 / 4
- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:
y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4
This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)
- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
=[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
=[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
=[tex] \sqrt{(53/4) x^{2} } [/tex] =
=+/-(√53/2)x
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)
Since point C is towards point B, we have to take the negative answer:
x = -(1/2)
- Therefore the correct answer is C: -0.5
Please explain it and tell me how u got the answer
Thx
Answers
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
___
The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1
What is 5% in a decimal and a fraction?
Answers
That is, 5% means 5/100. This is your fraction. It can be reduced to 1/20.
As a decimal, of course, 5/100 = .05, a number with 5 in the hundredths place.