The expressions equivalent to (2n+6)(n+3) are Options C and F, E, F.
To determine which expressions are equivalent to (2n+6)(n+3), we can first expand this expression using the distributive property (also known as the FOIL method for binomials). This gives us:
[tex]2n \times n = 2n^2\\2n \times 3 = 6n\\6 \times n = 6n\\6 \times 3 = 18[/tex]Combining like terms (6n + 6n) gives us the expression [tex]2n^2 + 12n + 18[/tex]. Therefore, option C is equivalent to (2n+6)(n+3).
Looking at option F, [tex]2(n+3)^2[/tex] is indeed the same as (2n+6)(n+3) because if we expand[tex](n+3)^2[/tex], we get [tex]n^2 + 6n + 9[/tex], and multiplying the whole expression by 2 yields [tex]2n^2 + 12n + 18[/tex], which matches our previous result.
Option B, [tex]2n^2+6n+18[/tex], is not equivalent because it lacks the combined coefficient for the n terms that should be 12n rather than 6n. Option A is also correct. Option E, 2(n+3)(n+3), is just a different way of writing option F and is therefore equivalent. Option D, 12n+18, doesn't have the [tex]n^2[/tex] term, so it's not equivalent to the original expression.
A town has a population of 20000 and grows at 2.5% every year. To the nearest year, how long will it be until the population will reach 24700?
Answer:
9 years
Step-by-step explanation:
Its right
Using the exponential growth formula, it will take approximately 8 years for a population of 20,000 growing at 2.5% per year to reach 24,700.
Explanation:To determine how long it will take for a town with a population of 20,000 to grow to 24,700 with an annual growth rate of 2.5%, we can use the formula for exponential growth: P = P0ert, where P is the future population, P0 is the initial population, r is the growth rate, and t is time in years.
First, we convert the growth rate to a decimal, so 2.5% becomes 0.025. Our equation will look like this: 24,700 = 20,000e(0.025t). Taking the natural logarithm of both sides gives us ln(24,700/20,000) = 0.025t.
We can use a calculator to find that ln(24,700/20,000) ≈ 0.2112, and so 0.2112 = 0.025t. Dividing both sides by 0.025 gives us t ≈ 8.448. We round this to the nearest whole number to find that it will take approximately 8 years for the population to reach 24,700.
Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is StartFraction 2 d minus 6 Over 2 d minus 4 EndFraction. The width is StartFraction 4 Over d minus 4 EndFraction. The length is StartFraction d minus 2 Over 3 d minus 9 EndFraction.
We know that the volume of a prism is defined by:
[tex]V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}[/tex]
Substituting values:
[tex]V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}[/tex]
[tex]Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}[/tex]
The volume of the given prism in simplified form is [tex]V = \frac{4}{3(d - 4)}[/tex].
To find the volume of the prism, we use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Given the dimensions of the prism:
l = \frac{d - 2}{3d - 9}
[tex]l = \frac{d - 2}{3d - 9}\\\\w = \frac{4}{d - 4}\\\\h = \frac{2d - 6}{2d - 4}[/tex]
We substitute these into the formula:
[tex]V = \left(\frac{d - 2}{3d - 9}\right) \left(\frac{4}{d - 4}\right) \left(\frac{2d - 6}{2d - 4}\right)[/tex]
Now we simplify this expression step-by-step:
Simplify the height term:
[tex]\frac{2d - 6}{2d - 4} = \frac{2(d - 3)}{2(d - 2)} = \frac{d - 3}{d - 2}[/tex]
Substitute the simplified height term:
[tex]V = \left(\frac{d - 2}{3(d - 3)}\right) \left(\frac{4}{d - 4}\right) \left(\frac{d - 3}{d - 2}\right)[/tex]
Combine and cancel common terms:
[tex]V = \frac{4}{3(d - 4)}[/tex]
This gives us the volume of the prism in its simplest form.
Complete question:
Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown.
The height is (2 d - 6) / (2 d - 4).
The width is 4 / (d - 4 ).
The length is StartFraction (d - 2) / (3 d - 9 ).
11/20+ c=3/4 what is the answer
Answer:
Step-by-step explanation:
Given that,
11/20 + c = 3/4
Subtract 11/20 from both sides of the equation to eliminate 11/20
11/20-11/20+c=3/4-11/20
c= (15-11)/20
c=4/20
c=1/5
For the following right- triangle find the side length x 8 12
Answer:
4[tex]\sqrt{13}[/tex] or 4[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Pythagorean theorem:
your solution will differ based on which side is the hypotenuse
x = [tex]\sqrt{12^{2} -8^{2} }[/tex] =4[tex]\sqrt{5}[/tex]
or x = [tex]\sqrt{8^{2}+12^{2} }[/tex] = 4[tex]\sqrt{13}[/tex]
Find values of x and y
Answer:
3 = x, 2 = y
Step-by-step explanation:
Opposite sides in a parallelogram are always congruent, so 2y+3=y+5 and 4y+1=4x-3
The first equation, when solved, shows that y = 2
When you plug that into the second equation, you get 4(2) + 1 = 4x - 3
This means that 12 = 4x, so 3 = x
Juanita has 3 1/4 pounds of sugar. How many ounces of sugar does she have? Explain how you know?
Answer:
12 ounces
Step-by-step explanation:
3
Final answer:
To find out how many ounces Juanita has from 3 1/4 pounds of sugar, we convert the 1/4 pound into ounces and add it to the full pounds after converting them into ounces. The calculation shows that she has 52 ounces of sugar in total.
Explanation:
To answer how many ounces of sugar Juanita has from 3 1/4 pounds, we must first understand the relationship between pounds and ounces. There are 16 ounces in 1 pound. Since Juanita has 3 1/4 pounds, we will first convert the 1/4 pound to ounces and then add that to 3 times 16 ounces.
Here's the calculation step by step:
Convert 1/4 pound to ounces: 1/4 pound = 0.25 × 16 ounces = 4 ounces.
Multiply the whole number of pounds (3) by 16 to get ounces: 3 × 16 = 48 ounces.
Add the ounces from the fractional pound to the ounces from the whole pounds: 48 ounces + 4 ounces = 52 ounces.
Hence, Juanita has 52 ounces of sugar.
convert 34 base five to 34 base ten
34 base five to 34 base ten is 19.
Step-by-step explanation:
Basically , In order to convert 34 from base 5 to base 10 , We skip consecutive 5 numbers after counting 5 numbers as shown below in table in base-5 table and , just increment 1 in base-10 table
Base- 5 Base-10
1 1
2 2
3 3
4 4
10 5
12 6
13 7
14 8
20 9
....... ....
34 19
34 base five to 34 base ten is 19.
Write the multiples of 5 (1,5,25,125,....) based on the no.of digits given. Then multiply and add to convert it into base 10
5 1
------------
3 4
------------
5 (3)+ 1(4) = 15+4 = 19
HELPPPPP PLEASEEEEEE
Gabby assigned a number to each of the 120 athletes at her school and
put the numbers in a box. She randomly chose 25 numbers and found that
10 athletes were female. Use this sample to make an inference about how
many athletes at Gabby's school are female.
Answer:
48
Step-by-step explanation:
[tex] \frac{10}{25} [/tex]
athletes are female. Now, we need to find what
[tex] \frac{x}{120} [/tex]
athletes are female.
10 ÷ 25 = 0.4
0.4 × 100 = 40 so
[tex] \frac{10}{25} = 40\%[/tex]
40% is the experimental probability for the number of female athletes in the sample. 40% of 120 should be about the number of female athletes in the whole school.
120 × 0.4 (or 40%) = 48.
You can infer that 48 athletes in the school are female.
Answer:
Step-by-step explanation:48
add at the park there's a pool shaped like a circle with a diameter 22 yards. A ring shaped path goes around the pool. it's width is 5 yards.
Answer:
424 yards²
Step-by-step explanation:
Diameter 22, radius 11
Outer circle: radius = 11+5 = 16
Area of the path:
Pi× (16²-11²)
= 135pi yards²
Or, 424 yards² (3 sf)
Answer:
135pi
Step-by-step explanation:
(I'm guessing you want to know the ring's area)
Diameter = 22 yards, meaning Radius = 11 yards
[tex](11+5)^{2}\pi[/tex] = 256pi = Outer Ring + Pool
[tex](11)^{2}\pi[/tex] = 121pi = Pool
Outer Ring = 256pi - 121pi = 135pi
The 6-foot man casts a shadow that is 10 feet
long. If the pyramid casts a 48 feet long
shadow, how tall is the pyramid?
Answer:
80 feetStep-by-step explanation:
6:10 ratio
6x8=48 10x8=80
If an employer lacked 6 days of working twice as many days as did his employee and the sum of the days they worked is 42, how many days did each work
Answer:
Step-by-step explanation:
2x-6=48
2x=42+6
2x=48days
x=24days
The employee worked 16 days and the employer worked 26 days to reach the total of 42 days both worked.
Explanation:
This problem can be solved using algebraic expressions. Let's denote the number of days the employee worked as 'e'. According to the problem, the employer worked (e+6) days, since he lacked 6 days of working twice as many days as his employee (2e-6). Then, combining these gives the equation (2e-6) + e = 42 (the total number of days they both worked). We can simplify this equation by adding like terms and getting 3e - 6 = 42. Solving for 'e' will give us the number of days the employee worked. First, add 6 to both sides of the equation making it 3e = 48. Then, divide both sides by 3 to solve for 'e'. Thus, e = 16. This means the employee worked 16 days. The employer, having worked (2e-6) days, worked (2*16-6) = 26 days.
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If f(3) = -4, f'(3) = 4, g(3) = 2, and g'(3) = 0, find (f + g)'(3).
Final answer:
The derivative of the sum of functions f and g at x = 3 is calculated by adding the derivatives of f and g at 3. Given that f'(3) = 4 and g'(3) = 0, the derivative (f + g)'(3) equals 4.
Explanation:
The student is asking about the derivative of a sum of two functions at a specific point, which is a concept covered in calculus. From the given information, we know that:
f(3) = -4, f'(3) = 4g(3) = 2, g'(3) = 0To find (f + g)'(3), we apply the rule for the derivative of a sum of functions, which states that:
(f + g)'(x) = f'(x) + g'(x)
Therefore, (f + g)'(3) is:
(f + g)'(3) = f'(3) + g'(3)
(f + g)'(3) = 4 + 0
(f + g)'(3) = 4.
Thus, the derivative of the sum of functions f and g at x = 3 is 4.
Suppose you are a carpenter and need to buy the best deal available on framing nails for your next construction job. What is the savings per nail between the best deal and worse deal? NAIL PRICES Box of 75 for $6.50 Box of 200 for $15.50 Box of 500 for $36.00 Box of 1000 for $78.00 A) 2¢ B) 3¢ C) 4¢ D) 5¢
Answer:C
Step-by-step explanation:
The best deal can be calculated by dividing the cost of the nail by the total amount of nails present in the pack.
A = $6.50/75 = $0.076
B = $15.50/200 = $0.0775
C = $36.00/500 = $0.072
D = $72.00/1000 = $0.078
From the above, the best deal is C (500 nails for $36.00) and the worst deal is D (1000 nails for $72.00).
Answer:
It´s A not C
Step-by-step explanation:
What is the slope of the line passing through the points (-2, -8) and (-3, -9) ?
Answer: answer is 1
Step-by-step explanation:
Slope(m) of the line = change in y/change in x
y2 - y1/x2 - x1
Locate the coordinates points: (-2, -8) and (-3, -9) ?
X1= -2, X2=-3
Y1= -8, y2= -9
Slot in the values into the equation:
m = -9 - (-8)/-3 - (-2)
-9 + 8/ -3 +2
= -1/ -1
=1
I hope this helps.
-1(n2 + 3) if n = -3.
Answer:
3
Step-by-step explanation:
Answer:
n = 3
Step-by-step explanation:
-1(n2 + 3) if n = -3.
from the question
-1(n2 + 3)
we are then asked to find n if its equals to -3
solution
-1(n2 + 3) .................. we are going to open the bracket with-1 according to BODMAS rule
we have,
-n²-3
when the value of n = -3
we have,
= (-3)² - 3
= 9 - 3
= 3
therefore when n = -3 in the expression -1(n2 + 3) the value of n = 3
to check if your answer is correct you will put the value of n which is 3 into the -1(n2 + 3) then you will see that the right handside = lefthandside
which is
3=3...........proved.
the simple interest on a certain sum of money for two years at 6% per annum is Rs 900. what will be the compound interest on that sum at the same rate and for the same period?
Answer:
Rs 927.
Step-by-step explanation:
For simple interest we have:
I = PRT/100 where I = interest, P = amount invested, R = the rate and T = the time.
900 = P*6* 2 / 100
P = 900*100/ 12
P = Rs 7500
The formula for the amount after t years when investing P amount at a rate of r% is:
A = P(1 + r/100)^t
A = 7500(1 + 6/100)^2
= Rs 8427.
So the compound interest is 8427 - 7500
= Rs 927.
6x-3=3x+12 what is X
Answer:
6x-3=3x+12
+3 . +3
6x=3x+15
-3x=-3x
3x=15
X=5
Step-by-step explanation:
Answer:
x = 5
Step-by-step explanation:
6x - 3 = 3x + 12
Combine like terms
6x - 3x = 3 + 12
3x = 15
Divide both sides by 3
3x/3 = 15/3
x = 5
A New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 in. tall. The scale of the model to the actual statue is 1:232. What is the height of the actual statue to the nearest foot?
About 151. That seems pretty close. If it is incorrect, sorry.
Evaluate - x - 4 when x = - 7 and y=5
Answer: 3
Step-by-step explanation: Plug in x = -7
How can I this math equation -5 -x =-8
Answer: x = 3
Step-by-step explanation:
-5 -x = -8
-× = -8 + 5
-x = -3
x = 3
Explain how you would distribute 4 ones into 5 groups.
Answer:
To distribute 4 ones into 5 groups, you have a few options. Here are three possible ways to distribute the 4 ones evenly among the 5 groups:
Option 1:
- Give each group 1 one: 1 1 1 1 0
Option 2:
- Give three groups 1 one, and leave two groups with 0 ones: 1 1 1 0 0
Option 3:
- Give one group 2 ones, and the other four groups 1 one each: 2 1 1 1 1
These are just a few examples, and there may be other ways to distribute the 4 ones into 5 groups. The important thing is to ensure that each group receives the same number of ones, if possible, or as close to equal as possible.
29.91 – 1.35p=-5.7(-6p - 4)
Answer:
p = 0.2
Step-by-step explanation:
Step 1: Distribute
29.91 - 1.35p = -5.7(-6p - 4)
29.91 - 1.35p = 34.2p + 22.8
Step 2: Add 1.35p to both sides
29.91 - 1.35p + 1.35p = 34.2p + 22.8 + 1.35p
29.91 = 35.55p + 22.8
Step 3: Subtract 22.8 from both sides
29.91 - 22.8 = 35.55p + 22.8 - 22.8
7.11 = 35.55p
Step 4: Divide both sides by 35.55
7.11 / 35.55 = 35.55p / 35.55
0.2 = p
Answer: p = 0.2
I need some help with this please I will give u heart....
Answer:
11/12
Step-by-step explanation:
Simple addition.
1/4 + 2/3
=
3/12 + 8/12 =
11/12
Answer:
11/12
Step-by-step explanation:
All you have to do is simply add 1/4 and 2/3 leaving you with
3/12 + 8/12 then add them to get the answer 11/12
Hopefully this helps.
Btw Can i get my heart?
What does AB represent in this figure
Answer:
B. Ray
Step-by-step explanation:
When they ask what does AB represent because they put the A first this means that the line is going from A to B and because there is an arrow and the end of B this means its a ray.
A ray is a half-infinite line. AB represents a ray.
What is a ray?A ray is a half-infinite line (sometimes called a half-line) in which one of the two points A and B is assumed to be at infinity.
As we can see that AB has a point on one side while the other side of the line has an arrow, therefore, AB represents a ray.
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Dan, Angad & David share some money in the ratio 1 : 1 : 3.
In total, Dan and David receive £52.
How much does Angad get?
Solution:
Given that,
Dan, Angad & David share some money in the ratio 1 : 1 : 3
Let the share of Dan be 1x
Let the share of Angad be 1x
Let the share of David be 3x
In total, Dan and David receive £52
Therefore,
1x + 3x = 52
4x = 52
x = 13
Therefore,
share of angad = 1x = 13
Thus share of Angad is £ 13
is 8 4\5 greater than 8.08
Yes.
8 4/5 = 8 8/10 = 8.8
8.8 is greater than 8.08
Answer:
yes
Step-by-step explanation:
4/5 as a fraction is 8/10 and 8/10 as a decimal is 0.8 and 0.8 is greater than 0.08
For the geometric series
2+6+ 18 +54 + 162
what is the value
The given series is a geometric series. The sum of this series can be calculated using the formula for the sum of a geometric series, Sn = a(Rn-1)/(R-1). By substituting the given values into the formula, the sum of the series is found to be 242.
Explanation:The series given is a geometric series. A geometric series is a series of numbers where each term after the first is found by multiplying the previous term by a constant.
The series is 2+6+18+54+162, where each successive term is 3 times the previous term. Hence, the common ratio (R) is 3.
The sum of the first 'n' terms (Sn) of a geometric series can be found using the formula: Sn = a(Rn-1)/(R-1), where a is the first term, R is the common ratio and n is the number of terms.
Here, 'a' = 2 and 'R' = 3. The total number of terms (n) is 5 in this case. Substituting these values into the formula gives: S5=2(35-1)/(3-1)= 2*(243-1)/2= 242
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What is the ordered pair solution to the system y= -4x and y=2x+12 ??
The solution to the system of equations y = -4x and y = 2x + 12 is found by setting the two equations equal to each other, solving for x, and then finding y. The ordered pair solution is (-2, 8).
Explanation:To find the ordered pair solution to the system of equations y = -4x and y = 2x + 12, we need to set the two equations equal to each other since they both describe y in terms of x. This gives us:
-4x = 2x + 12
Now, we will solve for x by combining like terms:
-4x - 2x = 12
-6x = 12
To get x by itself, divide both sides by -6:
x = -2
Next, we substitute x = -2 back into one of the original equations to find y. For example:
y = 2(-2) + 12
y = -4 + 12
y = 8
Therefore, the solution to the system of equations is the ordered pair (-2, 8).
The roots of the quadratic equation z^2 + az + b = 0 are -7 + 2i and -7 - 2i. What is a+b?
The required value of a + b = -14.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
The standard quadratic function is given by as f(x) = ax² + b x + c.
The roots of the quadratic equation z² + az + b = 0 are -7 + 2i and -7 - 2i,
As we know that the sum of roots is -b/a for the standard quadratic function.
So the sum of these roots, -7 + 2i + (-7 - 2i) = -14, is equal to -a/2.
Hence, a = -28, and the sum of the coefficients, a + b = -28 + b = -14.
So, a + b = -14.
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Final answer:
The sum of the coefficients a and b from the quadratic equation with roots -7 + 2i and -7 - 2i is 67.
Explanation:
The roots of the quadratic equation z2 + az + b = 0 given are -7 + 2i and -7 - 2i. These roots are complex conjugates of each other. According to the properties of quadratics, the sum of the roots (given by -a) is equal to -7 + 2i + (-7 - 2i), which simplifies to -14. Therefore, the coefficient a is 14. To find b, we use the fact that the product of the roots is b. Thus, b equals (-7 + 2i) x (-7 - 2i), which expands to 49 + 4, giving us b = 53. The question asks us for the sum of a and b, which is 14 + 53 = 67.