For this case we must find the product of the following expression:
[tex](n ^ 3) ^ 2 * (n ^ 5) ^ 4[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Rewriting the expression we have:
[tex]n ^ 6 * n ^ {20} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]n^{6 + 20} =\\n^{26}[/tex]
Answer:
[tex]n^{26}[/tex]
Answer:
n^26
Step-by-step explanation:
Is (x+7) a factor of f(x) x3-3x2+ 2x-8?
Answer:
(x+7) is not a factor
Step-by-step explanation:
we know that
If (x+7) is a factor of f(x)
then
For [tex]x=-7, f(-7)=0[/tex]
Verify
we have
[tex]f(x)=x^{3}-3x^{2} +2x-8[/tex]
Substitute x=-7
[tex]f(-7)=(-7)^{3}-3(-7)^{2} +2(-7)-8[/tex]
[tex]f(-7)=-343-147 -14-8[/tex]
[tex]f(-7)=--512[/tex]
[tex]-512\neq 0[/tex]
therefore
(x+7) is not a factor
Which is a quadratic function having a leading coefficient of 3 and a constant term of –12? f(x) = –12x2 + 3x + 1 f(x) = 3x2 + 11x – 12 f(x) = 12x2 + 3x + 3 f(x) = 3x – 12
For this case we have that a quadratic equation is of the form:[tex]ax ^ 2 + bx + c = 0[/tex]
Where:
a: is the main coefficient because it accompanies the quadratic variable.
b: It is the linear coefficient
c: It is the constant term.
Then, a quadratic function with a main coefficient of "3" and a constant term of "-12" is:
[tex]f (x) = 3x ^ 2 + 11x-12[/tex]
Answer:
Option B
[tex]f (x) = 3x ^ 2 + 11x-12[/tex]
Answer:
It is B. f(x) = 3x2 + 11x – 12
Step-by-step explanation:
If this question is on Edg, then it is B, & B is Correct.
Solve the equation -5x+31+3x=3
Answer:
Step-by-step explanation:
-5x+31+3x=3
move everthing to one side
-5+31+3x-3=0
add and subtract common terms
-2x+28=0
divide across by common denominator
-x+14=0
Solve for x
x=14
Select the true statement.
A.
Only function g is even.
B.
Only function f is even.
C.
Neither function is even.
D.
Both functions are even.
Answer:
A.
Only function g is even
Option: A is the correct answer.
A. Only function g is even.
Step-by-step explanation:We know that the graph of a even function is such that both the ends of a graph points in the same direction and the graph of a odd function is such that both the ends of the graph points in the opposite direction.Also, the graph of the even function is symmetric about the y-axis .whereas the graph of the odd function is symmetric about the origin i.e. it has rotational symmetry about the origin.Here by looking at the graph we observe that the graph of function g satisfies the condition of even function.
( whereas the graph of function f is not symmetric about the y-axis and hence function f is not even )
Hence, the function g is an even function.
Solve the equation: -3(h+5)+2=4(h+2)-9
For this case we must solve the following equation:
[tex]-3 (h + 5) + 2 = 4 (h + 2) -9[/tex]
We apply distributive property to the terms of parentheses:
[tex]-3h-15 + 2 = 4h + 8-9[/tex]
We add similar terms:
[tex]-3h-13 = 4h-1[/tex]
We add 13 to both sides of the equation:
[tex]-3h = 4h-1 + 13\\-3h = 4h + 12[/tex]
Subtracting 4h on both sides of the equation:
[tex]-3h-4h = 12\\-7h = 12\\h = - \frac {12} {7}[/tex]
ANswer:
[tex]h = - \frac {12} {7}[/tex]
Answer:
[tex]h=-\frac{12}{7}[/tex]
Step-by-step explanation:
To solve the equation for h follow the next steps
[tex]-3(h+5)+2=4(h+2)-9[/tex]
Subtract 4(h+2) on both sides of the equality
[tex]-3(h+5)+2-4(h+2)=4(h+2)-4(h+2)-9[/tex]
[tex]-3(h+5)+2-4(h+2)=-9[/tex]
Subtract 2 on both sides of the equality
[tex]-3(h+5)+2-4(h+2)-2=-9-2[/tex]
[tex]-3(h+5)-4(h+2)=-11[/tex]
Apply the distributive property
[tex]-3h-15 -4h-8=-11[/tex]
[tex]-7h-15 -8=-11[/tex]
[tex]-7h-23=-11[/tex]
Sum 23 on both sides of equality
[tex]-7h-23+23=-11+23[/tex]
[tex]-7h=12[/tex]
Divide by -7 on both sides of the inequality
[tex]\frac{-7}{-7}h=-\frac{12}{7}[/tex]
[tex]h=-\frac{12}{7}[/tex]
help please???!!!! 20p
Answer:
SA = 952 ft²Step-by-step explanation:
We have:
two squares 10ft × 10ft
three rectangles 14ft × 10ft
two rectangles 9ft × 14ft
two triangles with base 10ft and height 8ft
The formula of an area of a reactangle l × w (square s × s) :
[tex]A=lw\qquad(s^2)[/tex]
Substitute:
[tex]A_1=10^2=100\ ft^2\\\\A_2=(14)(10)=140\ ft^2\\\\A_3=(9)(14)=126\ ft^2[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{(base)(height)}{2}[/tex]
Substitute:
[tex]A_4=\dfrac{(10)(8)}{2}=40\ ft^2[/tex]
The Surface Area:
[tex]SA=2A_1+3A_2+2A_3+2A_4[/tex]
Substitute:
[tex]SA=(2)(100)+(3)(140)+(2)(126)+(2)(40)=952\ ft^2[/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used
Match each situation to its corresponding expression.
Reading from top to bottom. Answers are as follows:
1. 7(2)^t
2. 3000(0.93)^t
3. 300(1.015)^t
4. 300(0.985)^t
We know that the exponential function is given by:
[tex]f(x)=ab^x[/tex]
where a is the initial amount.
and b is the change in the amount and is given by:
[tex]b=1+r[/tex] if the function is increasing by a rate of r
and [tex]b=1-r[/tex] if the function is decreasing by a rate of r.
a)
The initial amount of fish in the trout are: 7
i.e. a=7
Also, the population doubles every year.
This means that that b=2
Hence, the population after t years is given by the function P(t) as:
[tex]P(t)=7(2)^t[/tex]
b)
The original amount of the machine is: $ 3,000
i.e. a=3,000
Also, the value of machine decreases by a rate of 7%
i.e.
[tex]r=7\%\\\\i.e.\\\\r=0.07[/tex]
Hence, we have:
[tex]b=1-r\\\\i.e\\\\b=1-0.07\\\\i.e.\\\\b=0.93[/tex]
Hence, the function which represent the price of the machine after t years i.e. P(t) is given by:
[tex]P(t)=3000(0.93)^t[/tex]
c)
The initial population of colony of ants i.e. a=300.
The number of ants increases at a rate of 1.5% every month.
i.e. [tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]
i.e.
[tex]b=1+r\\\\i.e.\\\\b=1+0.015\\\\i.e.\\\\b=1.015[/tex]
Hence, the function P(t) which represents the population of ants after t months is given by:
[tex]P(t)=300(1.015)^t[/tex]
d)
The initial infected cells i.e. a=300
The infected cells are decaying at a rate of 1.5% per minute.
i.e.
[tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]
Since, there is a decay hence,
[tex]b=1-r\\\\i.e.\\\\b=1-0.015\\\\i.e.\\\\b=0.985[/tex]
Hence, the function P(t) which represents the number of infected cells after t minutes is given by:
[tex]P(t)=300(0.985)^t[/tex]
If you run for 4 hours at 8 miles an hour and walk 8 hours at 2 miles an hour, how far will you have gone at the end
of 12 hours?
Make a Selection:
A. 48 miles
B. 50 miles
C. 32 miles
D. 60 miles
Answer:
4 hours at 8 miles an hour: 8(4) = 32 miles in total
8 hours at 2 miles an hour: 2(8) = 16 miles in total
Miles in total: 32 + 16 = 48
The answer is A. 48 miles
Answer: 48
Step-by-step explanation:
8 (MPH) x 4 (H) = 32 miles covered in 8 hours.
2(MPH) x 8 (H) = 16 miles covered in 8 hours.
32 + 16 = 48 MPH
A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile.
How many deer live in the county? Round to the nearest whole number, if necessary.
deer
Answer:
5852 deer.
Step-by-step explanation:
That would be 11 * 532
= 5852 (answer).
Answer:
There are 5852 deer live in the county.
Step-by-step explanation:
The population density of deer in the county is 11 deer per square mile.
That means, there are 11 deer in 1 square mile in that county.
Given that, the total area of that county is 532 square miles.
For getting the total number of deer, we just need to multiply the 'population density' by the 'total area'.
So, the total number of deer [tex]=(11\times 532)= 5852[/tex]
what is the product? 6(x^2-1) • 6x-1/6(x+1)
Konichiwa~! My name is Zalgo and I am here to help you out on this amazing day. I believe the answer that you would be looking for is (x-1) (6x-1).
I hope that this answer helps! :3
"Stay Brainly and stay proud!" - Zalgo
(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Arigato~! XP)
In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population had increased to
approximately 1884 bears. If this trend continues and the bear population is increasing exponentially,
how many bears will there be in 2018?
Answer:
[tex]8,101\ bears[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
x ----> is the number of years since 2009
y ----> is the population of bears
a ----> is the initial value
b ---> is the base
step 1
Find the value of a
For x=0 (year 2009)
y=1,570 bears
substitute
[tex]1.570=a(b)^{0}[/tex]
[tex]a=1.570\ bears[/tex]
so
[tex]y=1.570(b)^{x}[/tex]
step 2
Find the value of b
For x=1 (year 2010)
y=1,884 bears
substitute
[tex]1,884=1.570(b)^{1}[/tex]
[tex]b=1,884/1.570[/tex]
[tex]b=1.2[/tex]
The exponential function is equal to
[tex]y=1.570(1.2)^{x}[/tex]
step 3
How many bears will there be in 2018?
2018-2009=9 years
so
For x=9 years
substitute in the equation
[tex]y=1.570(1.2)^{9}[/tex]
[tex]y=8,101\ bears[/tex]
Answer:
Step-by-step explanation:
Question 15
1 / 1 pts
In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population had increased to approximately 1884 bears. If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?
ANSWER = 8,101 GOT IT RIGHT ON TEST
what is the Distance between (-4, -8) and (10, -8)??
Answer:
The distance between both points would be 14.
Step-by-step explanation:
The y coordinate or -8 stays the same for both points on a coordinate grid. However the x coordinate changes from -4 to 10, which is 14 places away on a coordinate grid. Therefore the distance between these two points is 14.
Answer:
14
Step-by-step explanation:
Use the distance equation:
d² = (x₂ − x₁)² + (y₂ − y₁)²
d² = (10 − -4)² + (-8 − -8)²
d² = 14² + 0²
d = 14
Which expression is equivalent to
2x^2+2x-4/2x^2-4x+2
Answer: A is correct (x+2)/(x-1)
Step-by-step explanation:
Divide the top and bottom by 2, to simplify
[2(x^2+x-2)]/[2(x^2+2x+1)]
The 2's cancel each other out, since 2/2 would be 1.
Now factor (x^2+x-2)/(x^2+2x+1)
[(x+2)(x-1)]/[(x-1)(x-1)]
Now you can cancel out one of the (x-1) on top and bottom. All that's left is (x+2)/(x-1) which is your answer. Hope this helps!
Solve the following system of equations using the substitution method
y = 4/5x - 3
y = -7
Answer: [tex]x=-5\\y=-7[/tex]
Step-by-step explanation:
Given the system of equations:
[tex]\left \{ {{y=\frac{4}{5}x-3 } \atop {y=-7}} \right.[/tex]
You can apply the Substitution method.
You need to substitute the second equation which gives the value of the variable "y" into the first equation and solve for the variable "x", then:
[tex]y=\frac{4}{5}x-3\\\\-7=\frac{4}{5}x-3\\\\-7+3=\frac{4}{5}x\\\\-4=\frac{4}{5}x\\\\(-4)(5)=4x\\\\x=\frac{-20}{4}\\\\x=-5[/tex]
Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 – 3x – 20x + 4. Her work is shown below. (15x2 – 3x) + (–20x + 4) 3x(5x – 1) + 4(–5x + 1) Talia noticed that she does not have a common factor. What should she do?
Answer:
Factor out a -1 from one of the terms so they are the same
Step-by-step explanation:
15x^2 – 3x – 20x + 4
(15x2 – 3x) + (–20x + 4)
3x(5x – 1) + 4(–5x + 1)
Talia should notice that the terms in the parentheses are opposites of each other and factor out a -1 out of the second term
3x(5x-1) +4 (-1) (5x-1)
Now the terms have a common factor
(5x-1) (3x+(-1)4)
(5x-1) (3x-4)
Answer:
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Step-by-step explanation:
[tex]15x^2 - 3x - 20x + 4[/tex]
Group first two terms and last two terms to factor it
[tex](15x^2 - 3x)+(- 20x + 4)[/tex]
Now we factor out GCF
GCF of 15x^2-3x is 3x
GCF of -20x+4 is -4 because first term should be positive
[tex](15x^2 - 3x)+(- 20x + 4)[/tex]
[tex]3x(5x- 1)-4(5x-1)[/tex]
Talia needs to factor out negative so that the binomials will be same (5x-1)
(this is my sister on my acc I'm letting her) True or False? When you use a pulley you use less force to pull up a load.Explain your thinking below. btw im in grade four so no fancy words.
Answer:
True depending on what you are comparing it to.
Step-by-step explanation:
A pulley would help lighten the load that you are trying to pull up, which may make it easier for you to get the load to your designated area. The more complicated it is, usually the more 'lighter' it becomes, or the less force you have to exert.
For example, you will have to give a 100% energy in trying to life a heavy box. However, if you use a simple pulley (only one), you may only have to exert 75% more energy, for the weight is significantly lower.
~
A road has a 10% grade, meaning increasing 1 unit of rise to every 10 units of run.
a) What is the elevation of the road to the nearest degree?
b) If the road is two km long, how much does it rise? Round your answer to the nearest tenth?
Answer:
Part a) The elevation of the road is [tex]6\°[/tex]
Part b) The rise is [tex]0.2\ km[/tex]
Step-by-step explanation:
Part a) What is the elevation of the road to the nearest degree?
Let
y-----> the rise of the road ( vertical distance)
x ----> the run of the road (horizontal distance)
we have
y/x=1/10
we know that
The ratio y/x is equal to the tangent of the angle of the elevation of the road
Let
[tex]\theta[/tex] ----> angle of the elevation of the road
[tex]tan(\theta)=y/x[/tex]
[tex]tan(\theta)=1/10[/tex]
[tex]\theta=arctan(1/10)=6\°[/tex]
Part b) If the road is two km long, how much does it rise?
using proportion
[tex]1/10=y/2[/tex]
[tex]y=2/10=0.2\ km[/tex]
how many weeks are in 3 years
Answer:
156.429
Step-by-step explanation:
52.1428571 in one year x 3
Find the coordinates of the vertices of polygon H´J´K´L´ after polygon HJKL is dilated using the given scale factor. H(–1, –6), J(1, –3), K(–5, –1), and L(5, –5); scale factor 3
ANYONE PLEAAAAASE
Answer:
[tex]H'(-3,-18)\\\\J'(3,-9)\\\\K'(-15,-3)\\\\L'(15,-15)[/tex]
Step-by-step explanation:
We know the coordinates of the polygon HJKL:
H(-1,-6), J(1,-3), K(-5,-1), and L(5,-5)
We know that the polygon HJKL is dilated using the scale factor 3. This means that, to find the coordinates of the vertices of polygon H'J'K'L', we need to multiply the x-coordinate and the y-coordinate of each vertex by this scale factor.
Then:
[tex]H'=(-1(3),-6(3))=(-3,-18)\\\\J'=(1(3),-3(3))=(3,-9)\\\\K'=(-5(3),-1(3))=(-15,-3)\\\\L'=(5(3),-5(3))=(15,-15)[/tex]
n triangle ABC, m∠A = 35° and m∠B = 40°, and a=9. Which equation should you solve to find b?
Answer:
[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex] should be used to find b.
Step-by-step explanation:
We are given that in a triangle ABC, ∠A = 35°, ∠B = 40° and side a = 9 and we are to find the side length b.
Now using sine rule to find b:
[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex]
[tex]\frac{sin 40}{b} = \frac{sin 35}{9}[/tex]
[tex]b=\frac{sin 40 \times 9}{sin 35}[/tex]
b = 10.1
Answer:
The equation is 9/sin(35) = b/sin(40) , The length of b = 10.086
Step-by-step explanation:
* Lets explain how to solve the triangle
- In ΔABC
- a, b, c are the lengths of its 3 sides, where
# a is opposite to angle A
# b is opposite to angle B
# c is opposite to angle C
- m∠A = 35°
- m∠B = 40°
- a = 9 ⇒ the side opposite to angle A
* To solve the triangle we can use the sin Rule
- In any triangle the ratio between the length of each side
to the measure of each opposite angle are equal
- a/sinA = b/sinB = c/sinC
∴ The equation which used to find b is a/sinA = b/sinB
∵ a = 9 , m∠A = 35° , m∠B = 40°
∴ 9/sin(35) = b/sin(40) ⇒ by using cross multiplication
∴ b = 9 × sin(40) ÷ sin(35) = 10.086
* The length of b = 10.086
Simplify 9x + 12 –x + 4.
Answer:
8x+16
Step-by-step explanation:
What is the distance between points A and B?
8 -7
-6
-5
4
-3
-2
-1
0
1
2
3
4
5
6
7
8
units
Answer:
6 units
Step-by-step explanation:
We require to calculate the absolute value so as to consider the measure both ways, that is
AB = | 1 - (- 5) | = | 1 + 5 | = 6
BA = | - 5 - 1 | = | - 6 | = 6
A bird leaves its nest and travels 14 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour slower and has 6 miles left after x hours.
a. What is the distance of the entire trip?
miles
b. How long does the entire trip take? (In Hours Minutes and Seconds
Answer:36
Step-by-step explanation:
The given parameters include;
The speed of the bird in the forward trip = 20 m/hTime of motion = xThe speed of the bird in the backward trip in x hours = (20 - 4)m/h = 16 mi/h.Distance remaining to complete the backward trip = 6 miles.The time to complete each trip is calculated as;
distance =[tex]speed $\times$ time[/tex]
forward distance = backward distance
[tex]&20 x=16 x+6 \\[/tex]
[tex]&20 x-16 x=6 \\[/tex]
[tex]&4 x=6 \\[/tex]
[tex]&x=\frac{6}{4} \\[/tex]
[tex]&x=1.5 h r[/tex]
The total time of the motion for the entire trip exists calculated as follows;
Time = time for forward + time for backward
[tex]\text { time } &=1.5 \mathrm{hr} r_{\text {forward }}+1.5 \mathrm{hr} \text { backward }+\frac{6 \mathrm{mi}}{16 \mathrm{mi} / \mathrm{hr}} \text { backward } \\[/tex]
time [tex]&=2(1.5) \mathrm{hr}+0.375 \mathrm{hr} \\[/tex]
time[tex]&=3.375 \mathrm{hr}[/tex]
The time for the entire trip is 3.375 hours.
The total distance of the trip exists calculated as follows;
total distance = forward distance + backward distance total distance [tex]$=20 \times 1.5+16 \times 1.5+6$[/tex] miles
Total distance =60 miles
Therefore, the total distance of the trip is 60 miles.
To learn more about The total distance of the trip refer to:
https://brainly.com/question/1788514
#SPJ2
given the numbers 6, 8, 10, and 20, what number when added would make the average of all five numbers 12? 1. (4) 2. (10) 3. (16) 4. (22) 5. (28)
Answer:
16
Step-by-step explanation:
6+8+10+20=44+16= 60 divided by 5 is 12
What equation represents an exponential function that passes through the point (2, 80)?
Answer:
[tex]f(x) = (4\sqrt{5})^{x}[/tex]
Step-by-step explanation:
The exponential function looks like the following: [tex]f(x) = b^{x}[/tex].
If the function passes through the point (2, 80), then:
[tex]f(x) = b^{x}[/tex] → [tex]80 = b^{2}[/tex]
Solving for 'b':
[tex]b = \sqrt{80}[/tex] →[tex]b=4\sqrt{5}[/tex]
Then, the equation of exponential function that passes through the point (2, 80) is: [tex]f(x) = (4\sqrt{5})^{x}[/tex]
Determine the area of a triangle with (see picture below)
Answer: c. area ≈ 5 units²
Step-by-step explanation:
Step 1: Use Law of Sines to find b:
[tex]\dfrac{sinC}{c}=\dfrac{sinB}{b}\\\\\\\dfrac{sin44.9}{4}=\dfrac{sin107.3}{b}\\\\\\b=\dfrac{4sin107.3}{sin44.9}\\\\\\b=5.4[/tex]
Step 2: Use SAS formula to find the area of the triangle:
[tex]Area = \dfrac{1}{2}bcsinA\\\\\\Area=\dfrac{1}{2}(5.4)(4)sin27.8\\\\\\Area = 5.05[/tex]
What’s the area of a rectangle measuring 13 inches times 12 inches ?
Answer:
156 square inches
Step-by-step explanation:
We are given the two quantities
Let
length = l = 13 inches
and
Width = w = 12 inches
The formula for the area of rectangle is:
[tex]Area=l*w[/tex]
where l is length and w is width
Putting the values of both that are given
[tex]Area = 13*12\\=156[/tex]
so the area is 156 square inches ..
Can someone help me plz
Answer:
The division was completed in the wrong order
Step-by-step explanation:
To convert [tex]\frac{5}{8}[/tex] to a percent
The numerator is divided by the denominator, that is
0.625
8 | 5.0
Multiply 0.625 × 100% = 62.5%
Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour. Which function represents Wayne’s distance in miles from Milwaukee in terms of the number of hours he drives?
A.
y = 420x
B.
y = 470 + 50x
C.
y = 50 − 470x
D.
y = 50 + 470x
E.
y = 470 − 50x
Let the number of hours driven equal x.
You would multiply the number of hours by his speed, so you would have 50x
You would then want to subtract that from the total miles to see how many more miles he needs to drive.
The answer would be E. y = 470 - 50x
NEED HELP ASAP
The equation yˆ=−2.5x+222.5 models the amount of cholesterol, LDL , for a person, in mg/dl , where x is the time spent exercising per day, in minutes.
According to the regression equation, what is the amount of cholesterol for a person exercising 20 minutes a day?
A. 61.5 mg/dl
B. 81.5 mg/dl
C. 172.5 mg/dl
D. 272.5.5 mg/dl
Answer:
172.5 mg/dl
Step-by-step explanation:
Given the equation y= -2.5x + 222.5, where 'x' is the time spent exercising in minutes. If we want to know the amount of cholesteron for a person exercising 20 minutes a day, we just have to subtitute 20 into the equation for x.
So we have: y= -2x + 222.5 → y= -2.5(20 minutes) + 222.5 = 172.5 mg/dl
Answer:
172.5
Step-by-step explanation:
Confirmed on test