We know: 9 = 3²
Therefore [tex]\dfrac{1}{9}=\dfrac{1}{3^2}[/tex]
We know the property:
[tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]
Therefore [tex]\dfrac{1}{9}\cdot3^x=\dfrac{3^x}{3^2}=3^{x-2}[/tex]
We must find f(5). Put x = 5 to the equation of the function:
[tex]f(5)=3^{5-2}=3^3=3\cdot3\cdot3=27[/tex]
Answer: f(5) = 27.The value of f(5) is 27 of function f(x) = 1/9(3)ˣ
What is the function?The function is defined as mathematics expression defines a relationship between one variable and another variable. When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that value of x determines what value of y will be. This relationship can be expressed as follows: y = f (x)
What is Exponential Function?An exponential function is defined as function has a constant as its base and a variable as its exponent.
In mathematical form an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function.
For the function f defined by f(x) given as :
f(x) = 1/9(3)ˣ ,
To determine the value of f(5).
f(x) = 1/9(3)ˣ,
Substitute the value of x = 5 in the function,
f(5) = 1/9(3)⁵ , [ 3⁵ = 243 ]
f(5) = 1/9(243),
f(5) = 27
Hence, the value of f(5) is 27.
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Pls help! I will mark brainliest!!
Total: 2p + 50 < 150
-50 -50
2p < 100
[tex]\frac{2p}{2} < \frac{100}{2}[/tex]
p < 50
Answer: 2p + 50 < 150 , p < 50
in order to obtain energy animals must do what?
A. consume food
B. produce food
C. make new cells
D. get sunlight
Answer:
A. consume food
Step-by-step explanation:
The food they eat has energy. One eaten the energy the food had is passed along to the animal.
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. The proportion of wolves that are neither female nor hunt in medium-sized packs is
Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.
If y = 7x, what happens to x when y is increased by 5 times its original value?
A) x decreases 5 times its original value
B) x increases to 11/5 its original value
C) x also increases 5 times its original value
D) x decrease to 4/5 of its original value
Answer:
C) x also increases 5 times its original value
35/5=7
70/10=7
Step-by-step explanation:
write the number three hundred sixty five ten thousandths in standard form
0.0365 is the standard form for this
A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m(x), where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay $1.50 per square foot of mulch. This cost is represented by the function g(m), where m is the area requiring mulch. Which expression represents the cost of the mulch based on the radius of the circle?
If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.
Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.
The top angle of each triangle is obtained by dividing the full angle by 8.
So, each top angle = [tex]\frac{360}{8}[/tex]
= 45°
Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.
This altitude OC bisects the top angle 45°.
Therefore, ∠ AOC = 22.5°.
Now, in Δ AOC,
[tex]sin 22.5=\frac{AC}{OA}[/tex]
[tex]=\frac{AC}{x}[/tex]
So, AC = x sin 22.5°
Note that, AB = 2 AC.
Therefore, AB = 2x sin 22.5°.
Also, [tex]cos 22.5=\frac{OC}{OA}[/tex]
[tex]=\frac{OC}{x}[/tex]
So, OC = x cos 22.5°.
Area of Δ AOB = [tex]\frac{1}{2}(AB)(OC)[/tex]
= [tex]\frac{1}{2}[/tex] × (2x sin 22.5°) × (x cos 22.5°)
= [tex]\frac{1}{2} x^{2}[/tex] (2 sin 22.5° cos 22.5°)
= [tex]\frac{1}{2} x^{2}[/tex] sin 45°
= [tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex]
Area of the octagonal gazebo = 8 × one triangular area
= 8 × ([tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex])
[tex]=2\sqrt{2} x^{2}[/tex]
[tex]=2.828x^{2}[/tex]
Area required for mulch = circular area - area of the gazebo
[tex]=3.14x^{2} -2.828x^{2}[/tex]
[tex]=0.312x^{2}[/tex]
Now, cost per unit area = $1.50.
Hence, total cost g(m) = area × cost per unit area
Total cost g(m) = [tex]0.312x^{2}[/tex] × 1.5
[tex]=0.468x^{2}[/tex]
Hence, total cost g(m) = [tex]0.468x^{2}[/tex].
Answer:
1.50(piexsqared-2root2xsqared) or on edge A
Step-by-step explanation:
i just did it
Help me please.......
Area of the horizontal rectangle.
A = L *W
L = 8cm
W = 3 cm
Area = 8 * 3 = 24 cm^2
Area of the Vertical Rectangle
The vertical rectangle has the same dimensions
L = 8 cm
W = 3 cm
Area = L * W
Area = 8 * 3
Area = 24 cm^2
Combined Area
Area = 24 + 24
Area = 48 cm^2 <<< Answer
Hey there!!
In order to solve for the area, let's divide this figure into two rectangles.
Area of a rectangle = Length × Breadth
First rectangle at the top - Length = 8 and width = 3
Hence, the area would be = 24cm²
The second triangle measures : Length = 3 and the width = 5
Area = 3 × 5
... 15cm²
Total area = 24cm² + 15cm²
... 24 + 15 cm²
... 39cm²
Hope my answer helps!!
What’s the answer to number one ? Solve please !!
Originally Dan has X amount of base ball cards.
So the equation would be
(x+6)/2=29
multiply both sides by 2
x+6=58
subtract 6
x=52
Check your work: 52+6=58/2=29
the number of units in the perimeter of a square is less than or equal to the number of square units in the area of the square which side length of a square provides a counterexample?
Answer:
2
Step-by-step explanation:2+2
The side lengths of a square in which the perimeter of a square is greater than its area is 1 unit, 2 units, and 3 units.
What is a square?A square is a 2D figure of which all sides are equal.
We know that the perimeter of a square is the sum of the lengths of all the sides and the area of a square is (side)².
Assuming a square has a side length of 4 units.
Therefore the perimeter of the square is 4×side = 4×4 = 16 units.
Now the area of the square will be (4)² = 16 sq units.
Now assuming the side length of the square is 2 units.
The area of the square is (2)² = 4 units and the perimeter is (2×4) = 8 units.
∴ The side length which provides a counter-example is 2 units.
Basically, we have to determine the numbers that when multiplied by 4 are greater than it's square such numbers are 1, 2, 3.
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HELP :(
ill give ya 5 stars and a thanks and if it lets me ill give you brienlest or what ever its called
There is 1 solution, which is 3/4.
To show this, you actually have to solve the equation. First, you distribute -1 into(9 - 3h) and distribute -3 into (h + 2). In doing so, you should be left with "6h - 9 + 3h = 6 - 3h - 6". Next you combine like terms on each side, so you add 3h to 6h and you subtract 6 from 6. Now you should have "9h - 9 = -3h". Then, you start to solve by subtracting 9h from both sides. You should have -9 = -12h, which you divide -12 on both sides to get h by itself. Finally, you have h = 9/12 (since the negatives on the top and bottom cancel out) which simplified (divided by 3/3) is 3/4. Thus meaning there is only 1 answer.
I hope this helps!
URGENT! PLEASE HELP NOW!
Jasmine is 23 years old. Three years less, 20, half is 10. If I am correct, George is 10.
Numbers 38 and 40 pls and thanks
38a) $10.50 To get this answer, you need to multiply $1.50 by 7
38b) $25.50 To get this answer, you need to subtract $10.50 from $36
40) The answer would be $13.7694 and it could be rounded to $13.77. To get this answer .you need to multiply $12.99 by 1.06 since it has a 6% sales tax.
find the perimeter....
The perimeter is adding all the outside edges together:
4 + 1 +4 +1 + 3 + 1 = 14 cm.
I reallly need help quick with this
you can do that on here
fraction-1/3
decimal- 0.3333333333333333333333333333333333333333333333333333333333333333333333
(they are equal)
-hope this helps
-i hope u get the 0.3 part it will never end its just that i since it never ends i can't but th e whole thing
Sue scored a total of 45 points in two games . She scored 8 times as many points in the second game as the first. How many more points did she score in the 2 nd game?
There are 11 candidates for homecoming king and 12 candidates for homecoming queen. How many possible outcomes are there for homecoming king and queen ? 156, 182, 132, 210 ?
Answer should be 132
6 and 2/3 in simplest form
The different forms you can convert 6 2/3 to would be 20/3 and 6.6 but I'd have to say 20/3 would be the simplest form to convert it to. Hope this helps <3
20/3 thats the exact form
I need help with this Algebra question, if someone could explain how to solve this I'd appreciate it.
See the attached picture:
Given equation: 3 + x/2 = 10
1st step subtract 3 from each side:
x/2 = 7
2nd step multiply both sides by 2:
x = 14
Step 1)
3 + x/2 = 10 ..............This is given
Step 2)
x/2 = 7 ....................... Multiplication property of equality.
This step is wrong. This step is called "Subtraction property of equality". This means you have to subtract 3 from both sides
3 + x/2 - 3 = 10 - 3
Simplifying
x/ 2 = 7
Step 3)
x = 14 ....This is called "Multiplication property of equality" because you multiply both sides by 2.
Hope that helps.
What is the slope of a line perpendicular to the line in the graph?
A. −3/2
B. −2/3
C. 3/2
D. 2/3
The slope of a line from the given graph is -2/3. Therefore, option B is the correct answer.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
From the given graph,
Slope (m) = Rise/Run
= -1/1.5
Multiply both numerator and denominator by 2, we get
= -2/3
Therefore, option B is the correct answer.
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Literal Equations Answer 5 and Ill mark brainliest!
3.- 5x-6=y
First you leave the variable alone along with 5 and you pass to the other side number 6 with the opposite sign
5x=y+6
then as 5 is multiplying you pass it dividing
y+6 x= 5
4.-2x-3y=8
First you leave the variable with 3 alone and you pass the 2x to the other side subtracting
-3y=8-2x
Then as -3 is multiplying you pass it dividing
y= 8-2x/-3
12.-7x-y=14
First you leave the variable with the 7 alone and you pass the -y to the other side adding
7x=14+y
then as 7 is multiplying you pass it dividing
x=14+y/7
18.-12x-4y=20
First you leave the variable y with the -4 alone and you pass the 12x to the other side subtracting
-4y=20-12x
Then as -4 is multiplying you pass it dividing
y= 20-12x/-4
20.- R-C/N=P
First you leave the R and the C alone and as N is dividing you pass it multiplying
R-C=PxN
Then as C is subtracting you pass it adding
R= (PxN)+C
I haven't done these types of problems in forever, so I did a few of the easier ones before I went onto a few of the harder ones. Sorry if 20 is incorrect, I wasn't too sure.
Judy planted vegetables on a piece of land. The land is in the right-angled triangular shape. Given the longest side of the land is y metre. The other two sides of the land are 2x metre and (2x+6) metre respectively. He fenced the land with 72 metres of barbed wire. Find the length, in metre , of each side of the land.
We know that the perimeter is 72 meters, so we have
[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]
Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:
[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]
Expand the squares to get
[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]
Bring everything to the right hand side to get
[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]
Divide both sides by 8:
[tex] x^2 - 69x + 540 = 0 [/tex]
This equation has solutions [tex] x=9,\ x=60 [/tex]
This solutions would yield the following side lengths:
[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]
[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]
Since we can't have negative side lengths, we can only accept the solution x=9.
In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.
[tex] 18^2+24^2=30^2 [/tex]
Which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)
Answer:
(1+2i)(1-2i)
Step-by-step explanation:
Answer:
(1+2i)(1-2i)
Step-by-step explanation:
Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
A. [tex](1+2i)(8i)= 8i+16i^{2}[/tex]
=[tex]8i-16[/tex]
B. [tex](1+2i)(2-5i)=2-i-10i^{2}[/tex]
=[tex]12-i[/tex]
C. [tex](1+2i)(1-2i)=1^{2}-4i^{2}[/tex]
=[tex]5[/tex]
D. [tex](1+2i)(4i)=4i+8i^{2}[/tex]
=[tex]4i-8[/tex]
Since, A,B,D contains the term "i" which means they are not real valued, therefore option C that is (1+2i)(1-2i) has a real number product.
PQ=RQ?
Someone who is smart in math help me.
Answer:
a=43
Step-by-step explanation:
90+47=137 180-137=43
What is the probability of drawing 1 red marble out of a bag containing 4 red marbles 3 green marbles 2 blue marbles and 1 purple marbles?
4/10 Probability
-Hiadamcom
Answer:
2/5
Step-by-step explanation:
4 ÷ 10= 2/5
(4 ÷10 is for 4/10 which is red marbles to the total marbles)
The probability of the compliment is 3/5(for edge students)
What is the measure of angle 1?
SOLUTION: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures. Question 345899: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures.
PLEASE!!! HELP?!? Find two consecutive even integers such that the smaller added to two times the larger gives a sum of 28. The numbers are?
Does the point (2, √6) lie on the circle shown? Help please ASAP
Answer:
Option D is the answer.
Step-by-step explanation:
The circle given on the graph has the center at origin (0, 0).
We have to find the point (2, √6) lies on the circle or not.
If the point lie on the circle then distance of this point from origin = radius of the circle.
Given from the graph radius = 3 units
Now distance of point (2, √6) from (0, 0) = [tex]\sqrt{(2-0)^{2}+(\sqrt{6}-0)^{2}} =\sqrt{4 + 6}=\sqrt{10}=3.16[/tex]
Distance between the point and origin is more than radius 3 units.
Therefore point doesn't lie on the circle.
Option D is the answer.
You earned $96.15. You would like to buy some new T-shirts. Estimate the number of T-shirts you can buy if each one costs $13.75.
By dividing the total amount of $96.15 by the cost of one T-shirt at $13.75, you can estimate buying approximately 7 T-shirts. You round down to the nearest whole number, so you can purchase 7 T-shirts.
Explanation:To estimate the number of T-shirts you can buy with $96.15, when each T-shirt costs $13.75, you first divide the total amount of money earned by the cost of one T-shirt.
$96.15 ÷ $13.75 = approximately 7 T-shirts
Since you can't buy a fraction of a T-shirt, you will round down to the nearest whole number. Therefore, you can purchase 7 T-shirts with $96.15, assuming there is no sales tax or additional costs.
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[tex] {x}^{2 }+3x + 2 = (x + 2) \times (answer)[/tex]
x² + 3x + 2 = (x + 2)(x + 1)
consider the factors of the constant term ( + 2 ) which sum to give the coefficient of the x- term ( + 3)
These are + 2 and + 1
x² + 3x + 2 = (x + 2 )(x + 1)
I need help with these 3
First of all remeber that "a number" means we don't know the number or it could be many but not all numbers, so it is represented by x.
5. 1/2x + 6 > 20
6. 12 + 3x < -11 (They asked for the opposite of 11, the opposite of a positive number is always the negative of that number, and the opposite of a negative number is the positive of that number).
7. 2x - 8 < 5
Answers:
5) 1/2n + 6 > 20
6) 12 + 3n < -11
7) 2x - 8 < 5
Hope this helps :-)