[tex]\bf \begin{array}{ccll} \$&hour\\ \cline{1-2} 5.5&1\\ x&3\frac{1}{3} \end{array}\implies \cfrac{5.5}{x}=\cfrac{1}{3\frac{1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{3\cdot 3+1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{10}{3}}\implies \cfrac{5.5}{x}=\cfrac{\frac{1}{1}}{\frac{10}{3}} \\\\\\ \cfrac{5.5}{x}=\cfrac{1}{1}\cdot \cfrac{3}{10}\implies \cfrac{5.5}{x}=\cfrac{3}{10}\implies 55=3x\implies \stackrel{\textit{about 18 bucks and 33 cents}}{\cfrac{55}{3}=x\implies 18\frac{1}{3}=x}[/tex]
Answer:
$18.3
Step-by-step explanation:
If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, you should earn $18.3.
3 1/3 hours
$5.50 and hour
$5.50 x 3 = $16.5
$5.50 / 3 = $1.8
$16.5 + $1.8 = $18.3
Therefore, you are owed $18.3.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 20% salt and
Solution B is 80% salt. She wants to obtain 180 ounces of a mixture that is 30% salt. How many ounces of each solution should she use?
The scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.
To obtain 180 ounces of a 30% salt mixture, the scientist should use 90 ounces of Solution A (20% salt) and 90 ounces of Solution B (80% salt) by solving a system of two equations.
To solve the problem, we need to create a system of equations based on the quantities of salt in each solution and the desired final mixture. We want to mix Solution A (20% salt) and Solution B (80% salt) to get 180 ounces of a mixture that is 30% salt. Let the amount of Solution A be x ounces and the amount of Solution B be y ounces.
The two equations representing the system are:
Equation for total mixture: x + y = 180 (total ounces of the mixture)Equation for salt content: 0.20x + 0.80y = 0.30 *180 (total ounces of salt in the mixture)Now, we solve this system of equations. Multiplying the second equation by 100 for simplicity, we get:
20x + 80y = 54 * 100
Using the first equation to express y in terms of x, we get y = 180 - x. Substitute y into the second equation:
20x + 80(180 - x) = 5400
Opening parentheses and simplifying gives us:
20x + 14400 - 80x = 5400
Subtract 20x from each side:
-60x + 14400 = 5400
Solving for x, we find that:
x = (14400 - 5400) / 60 = 90
Substituting x into y = 180 - x, we get y = 180 - 90 = 90.
Therefore, the scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.
Find the value of x for which line a is parallel to line b. (21)
f(x) = 3x^4 is even or odd?
Answer:
Step-by-step explanation:
it's even because f(-x)=f(x)
Answer:
even function
Step-by-step explanation:
recall that:
a function is EVEN if and only if f(-x) = f(x) for all x in the domain of f
a function is ODD if and only if f(-x) = -f(x) for all x in the domain of f
we observe that for the function
f(x) = 3x^4
because x has been raised to an even power, that f(x) will always be positive (or zero), regardless of whether x is negative or positive.
i.e
f(x) = f(x) and f(-x) = f(x)
This behavior is described by the definition of an EVEN function (given above)
Hence f(x) is an even function
Select one answer for part A and one answer for part B
Tre determines the solution to the equation 3.57x + 1.61 = 4.71 - 2.63x is x = 0.5. He verifies his solution using the steps below.
Equation: 3.57x + 1.61 = 4.71 - 2.63x
Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5)
Step 2: 1.785 + 1.61 = 4.71 - 1.315
Step 3: 3.395 = 6.025
Which statement most accurately describes Tre’s error?
A. Tre made an error when determining the original solution of x = 0.5.
B. Tre made an error when substituting the solution in for x.
C. Tre made an error when multiplying each coefficient by 0.5.
D. Tre made an error when adding or subtracting.
Answer:
Option D. Tre made an error when adding or subtracting
Step-by-step explanation:
we have the equation
[tex]3.57x + 1.61 = 4.71 - 2.63x[/tex]
Solve for x
Group terms that contain the same variable and move the constant to the other side
[tex]6.2x= 4.71 - 1.61[/tex]
Combine like terms
[tex]6.2x=3.1[/tex]
[tex]x=0.5[/tex]
Verify
Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5) ---> is correct
Step 2: 1.785 + 1.61 = 4.71 - 1.315 ----> is correct
Step 3: 3.395 = 6.025 ---> is not correct
because
4.71-1.315=3.395 instead of 6.025
therefore
Tre made an error when subtracting
Answer: The answer is d
Step-by-step explanation:
what is the surface area of the rectangular pyramid
Answer:
41.74 m²Step-by-step explanation:
We have:
rectangle 4.8 m × 3.8 m
two triangles with base b = 4.8 m and height h = 2.6 m
two triangle with base b = 3.8 m and height h = 2.9 m.
The formula of an area of a rectangle l × w:
[tex]A = lw[/tex]
Substitute:
[tex]A_1 = (4.8)(3.8) = 18.24\ m^2[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_2=\dfrac{(4.8)(2.6)}{2}=6.24\ m^2\\\\A_3=\dfrac{(3.8)(2.9)}{2}=5.51\ m^2[/tex]
The Surface Area:
[tex]S.A.=A_1+2A_2+2A_3\\\\S.A.=18.24+2(6.24)+2(5.51)=41.74\ m^2[/tex]
Answer:
GIVE THE OTHER DUDE BRAINLISET
Step-by-step explanation:
Using the linear combaination method what is the solution to the system of linear equations 7x-2y=-20and9x+4y=-6
Answer:
x=-2 y=3
Step-by-step explanation:
7x-2y=-20
9x+4y=-6
Multiply the first equation by 2
2(7x-2y) = 2 * -20
14x - 4y = -20
Add this to the second equation
14x - 4y = -40
9x+4y=-6
--------------------------
23x = -46
Divide by 23
23x/23 = -46/23
x = -2
Now we solve for y
9x+4y=-6
9(-2) +4y = -6
-18 + 4y = -6
Add 18 to each side
-18+18 +4y = -6+18
4y = 12
Divide by 4
4y/4 = 12/4
y=3
If f(x) = x/1 + x, what is the value of f(x+h)
Answer:
[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]
Step-by-step explanation:
Given function is:
f(x) = x/1 + x
In order to find f(x+h) we have to put x+h in place of x
[tex]f(x)=\frac{x}{1+x} \\f(x+h)=\frac{x+h}{1+x+h}[/tex]
Therefore,
[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]
Answer: B
Got it right lol
help please
1) Which of the following is not a line segment in the drawing?
2) Which of the following does not name the same line?
The option "KM" does not represent a direct line segment in the drawing as there is no straight path connecting points K and M without passing through another point.
The figure contains various labeled points connected by lines representing different segments except for NK; hence option NK does not name an existing line segment in the drawing.
1) In this case, all options refer to line segments except for "KM." The points K and M are not connected by a straight line; instead, point N lies between them. Therefore, KM is not a direct line segment in this drawing.
It's essential to understand that a line segment is named after its end points and consists of these points and all the points on the line between them. Since there is no direct path from point K to M without passing through another point (N), KM cannot be considered as a single, uninterrupted line segment.
2)The image you provided contains a geometrical diagram with five labeled points: J, K, L, M, and N. Line segments are drawn connecting these points forming an X shape. The options given are JL, MN, JK, and NK.
Upon careful examination of the image, it is evident that line segments JL (from point J to L), MN (from point M to N), and JK (from point J to K) are present in the drawing. However, NK (from point N to K) is not a line segment depicted in this drawing.
what is the value of the expression g * (g+1)^2 for g=2
Answer:
18Step-by-step explanation:
[tex]\text{Put}\ g=2\ \text{to the expression}\ g(g+1)^2:\\\\2(2+1)^2=2(3)^2=2(9)=18[/tex]
A data set with less variation will have a smaller ____________________.
A. minimum
B. mean
C. interquartile range
D. median
Answer: Option C
A data set with less variation will have a smaller __ interquartile range__.
Step-by-step explanation:
The datasets that have less variation are those that have smaller dispersion or variation measures.
Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.
Then the answer is the option C
A new dolphin tank is being built outside of Houston. The tank will be a cylinder with a depth of 42 feet and a radius of 240 feet. How many cubic feet of water will the tank hold? Use π = 3.14
A. 30,400,564 ft³
B. 7,596,288 ft³
C. 31,667 ft³
D. 3,237,000 ft³
Answer:
B. 7,596,288 ft³
Step-by-step explanation:
volume of cylinder = π * r^2 * h
volume = 3.14 * (240 ft)^2 * 42 ft
volume = 7,596,288 ft³
Answer: B . [tex]7,596,288 ft^3[/tex]
Step-by-step explanation:
The volume of a cylinder is given by :_
[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.
Given : A new dolphin tank is being built outside of Houston. The tank will be a cylinder with a depth of 42 feet and a radius of 240 feet.
i.e. r=240 and h = 42
Now, the volume of tank will be :_
[tex]\text{Volume}=(3.14) (240)^2 (42)=7,596,288[/tex]
Hence, the tank will hold [tex]7,596,288 ft^3[/tex] water.
As Rainsford struggles in the water, the boat travels onward without him. Quickly, he retains his wits. Instead of panicking, he decides to head toward the sound of the gunshots. He does so _________ he realizes where there are gunshots, there are people. Hopefully, these people will be willing and able to help him.
Which transition best fills in the blank?
specifically
absolutely
because
later
Answer:
the answer is 'because'
Can somebody please help me. I don’t understand it at all.
Step-by-step explanation:
Just pick a bunch of values of x, and use the formula to find the corresponding value of y.
For example
When x = 0, y = 0+5 = 5 ----> Plot the point (0,5) on graph paper
When x = 1, y = 1+5 = 6 ----> Plot the point (1,6) on graph paper
When x = 2, y = 2+5 = 7 ----> Plot the point (2,7) on graph paper
Then connect the dots to get a linear graph. You should get a graph that looks like the one attached.
You first make a table with x and y
like this: x | y
then you think of possible values for x then solve for y
it needs to be positive , 0, and a negative like:
under x, you do:
2
0
-3
then you take the equation and solve for y.
after, with the y values, create a Cartesian plane and plot the points
so the points would be (2,7), (0,5), and (-3,2)
then you connect the points and draw arrows on both ends.
then label the line w/ the equation
-------------------------------------------------------
hey btw, i learned this just yesterday. lol
great timing
A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs
$8. Each additional inch costs $1.50, and each additional topping costs $0.75. Write an equation
that represents the cost of a pizza. Be sure to specify what the variables represent
Answer: [tex]T=8+ 1.50 x+0.75y[/tex] , where 'x' denotes the number of additional inch to the pizza and 'y' denotes the number of additional toppings.
Step-by-step explanation:
Let 'x' denotes the number of additional inch to the pizza and 'y' denotes the number of additional toppings.
Given : A 10-inch cheese pizza costs $8.
i.e. Fixed cost = $8
Each additional inch costs $1.50, and each additional topping costs $0.75.
∴ Cost of additional inch = $1.50 x
∴ Cost of additional topping = $0.75y
Then The Total cost of any pizza would be :
Total cost = Fixed cost + Cost of additional inch + cost of additional topping
= $8+ $1.50 x+$0.75y
⇒ Equation that represents the cost of a pizza :
[tex]T=8+ 1.50 x+0.75y[/tex]
An equation that represents the cost of a pizza will be C = 8 + 1.50x + 0.75y
Fixed cost = $8Cost of additional inch = 1.50xCost of additional topping = 0.75y
Total cost (C) will then be:
= 8 + (1.50 × x) + (0.75 × y)
C = 8 + 1.50x + 0.75y
Therefore, the equation to represent the cost is C = 8 + 1.50x + 0.75y
Read related link on:
https://brainly.com/question/12336191
How do you find the base area of a rectangular prism and a cylinder? Please help
Answer:
See explanation.
Step-by-step explanation:
The 'base' of a rectangular prism refers to only one side of the rectangular prism, which is a rectangle.
The formula for the area of a rectangle is as follows:
[tex]A=lw[/tex]
Where A = area, l = length, and w = width.
The 'base' of a cylinder refers to only one side of the cylinder, which is a circle.
The formula for the area of a circle is as follows:
[tex]A=\pi r^2[/tex]
Where A = area and r = radius.
Just in case you typed your question incorrectly and were asking for surface area, here is the formula for surface area for both as well:
Rectangular prism: [tex]A=2(wl+hl+hw)\\[/tex]
Cylinder: [tex]A=2\pi rh+2\pi r^{2}[/tex]
how to create an equation with infinitely many solutions.
Answer:
See below.
Step-by-step explanation:
An equation with infinite solutions is, strictly, an identity.
An example is 2(x + 3) = 4x + 6
Simplifying we get 4x + 6 = 4x + 6. We can replace by any value of x and the equation will hold true.
A rectangular prism has a base that is 5cm by 7cm and a height of 12cm if all dimensions are doubled what happens to the volume?
Answer:
The volume increased eightfold.Step-by-step explanation:
The formula of a volume of a rectangular prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have l = 5cm, w = 7cm and h = 12cm.
Substitute:
[tex]V=(5)(7)(12)=420\ cm^3[/tex]
Doubled the dimensions:
l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.
Calculate the new volume:
[tex]V'=(10)(14)(24)=3360cm^3[/tex]
Calculate the quotient [tex]\dfrac{V'}{V}[/tex]
[tex]\dfrac{3360}{420}=8[/tex]
Generalization:
V = lwh - the volume of a prism l × w × h
2l × 2w × 2h - new dimensions
V' = (2l)(2w)(2h) = 8lwh = 8V - new volume
If the quadratic formula is used to find the solution set of 3x2 + 4x - 2 = 0, what are the solutions?
Answer:
[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]
Step-by-step explanation:
Compare [tex]ax^2+bx+c[/tex] to [tex]3x^2+4x-2[/tex].
We have [tex]a=3,b=4,c=-2[/tex].
The quadratic formula is for solving equations of the form [tex]ax^2+bx+c=0[/tex] and is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
So we are going to plug in our values in that formula to find our solutions,x.
If you want to notice it in parts you can.
Example I might break it into these parts and then put it in:
Part 1: Evaluate [tex]b^2-4ac[/tex]
Part 2: Evaluate [tex]-b[/tex]
Part 3: Evaluate [tex]2a[/tex]
------Let's do these parts.
Part 1: [tex]b^2-4ac=(4)^2-4(3)(-2)=16-12(-2)=16+24=40[/tex].
This part 1 is important in determining the kinds of solutions you have. It is called the discriminant. If it is positive, you have two real solutions. If it is negative, you have no real solutions (both of the solutions are complex). If it is 0, you have one real solution.
Part 2: [tex]-b=-4[/tex] since [tex]b=4[/tex].
Part 3: [tex]2a=2(3)=6[/tex].
Let's plug this in:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
or in terms of our parts:
[tex]x=\frac{\text{Part 2} \pm \sqrt{\text{Part 1}}}{\text{Part 3}}[/tex]
[tex]x=\frac{-4 \pm \sqrt{40}}{6}[/tex]
40 itself is not a perfect square but it does contain a factor that is. That factor is 4.
So we are going to rewrite 40 as [tex]4 \cdot 10[/tex].
[tex]x=\frac{-4 \pm \sqrt{4 \cdot 10}}{6}[/tex]
[tex]x=\frac{-4 \pm \sqrt{4} \cdot \sqrt{10}}{6}[/tex]
[tex]x=\frac{-4 \pm 2\cdot \sqrt{10}}{6}[/tex]
I'm going to go ahead and separate the fraction like so:
[tex]x=\frac{-4}{6} \pm \frac{2 \cdot \sqrt{10}}{6}[/tex]
Now I'm going to reduce both fractions:
[tex]x=\frac{-2}{3} \pm \frac{1 \cdot \sqrt{10}}{3}[/tex]
[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]
Final answer:
Using the quadratic formula with a=3, b=4, and c=-2, the solution set for the quadratic equation 3x^2 + 4x - 2 = 0 is x = (-4 + 2√(10)) / 6 and x = (-4 - 2√(10)) / 6.
Explanation:
To find the solution set of the quadratic equation 3x2 + 4x - 2 = 0, we can use the quadratic formula:
x = (-b ± √(b2 - 4ac)) / (2a)
Here, comparing with the standard form ax2 + bx + c = 0, we identify a = 3, b = 4, and c = -2. Substituting these values into the quadratic formula gives us:
x = (-(4) ± √((4)2 - 4(3)(-2))) / (2(3))
x = (-4 ± √(16 + 24)) / 6
x = (-4 ± √(40)) / 6
x = (-4 ± 2√(10)) / 6
Which simplifies to two solutions:
x = (-4 + 2√(10)) / 6
x = (-4 - 2√(10)) / 6
These are the two solutions to the given quadratic equation.
Myra owns a car service that charges a $5 flat rate and an additional $0.50 per mile, which is represented by the equation y = 0.5x + 5, where x is the number of miles and y is the total cost.
How much is the total cost for a car with 30 miles?
$10
$15
$20
$35
Answer:
Option C is correct.
Step-by-step explanation:
The equation given is y = 0.5x +5
where x is the number of miles and y is the total cost.
We need to find total cost y if the car has traveled 30 miles
so, x=30
Putting value of x in the given equation:
y = 0.5x +5
y = 0.5(30) + 5
y = 15 + 5
y = 20
So, the total cost is $20
Option C is correct.
Answer:
the answer is $20 i just did that one :))
Step-by-step explanation:
good luck!
!PLEASE HELP!
y + x = 3
Does the line increase or decrease? How do I find this without graphing the line?
Answer:
Decreasing
Step-by-step explanation:
y=mx+b is called slope-intercept from because it tells you the slope,m, and the y-intercept,b.
If the slope is positive then the line is increasing.
If the slope is negative then the line is decreasing.
If the slope is zero then the line is horizontal or constant.
So let's solve our equation for y:
y+x=3
Subtract x on both sides:
y=-x+3
The slope is -1.
Therefore the line is decreasing.
just a quick addition to @Freckledspots' great reply above.
y + x = 3
y = 3 - x
if we pick any random "x" value, and then pick another value larger than the one before for "x", to get a "y" value, if "y" is decreasing, the the first value of "y" will be larger, else it's increasing, let's do so, say using hmmm x = 2 and x = 7.
x = 2
y = 3 - 2
y = 1
x = 7
y = 3 - 7
y = -4
as "x" moves to the right, from 2 to 7, "y" moved down, from 1 to -4, thus is decreasing.
When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!
The other degree amount is 90 in a clockwise rotation.
what is the slope of the line shown below? (5, 11) (-5, -1)
Answer:
-6/-5 is the slope
Step-by-step explanation:
Y2 - Y1 / X2 - X1 so
-1 - 11 / -5 - 5 = -12 / -10 simply it and get -6 / -5
Slope equals rise over run
Answer:
6/5
Step-by-step explanation:
What is the measure of E, in degrees?
O A. 1550
O B. 1300
O
C. Cannot be determined
O
D. 125°
Answer:
B. 130
Step-by-step explanation:
Since both sides of the triangle are 10, given that angle D is 25. We can conclude that angle F is also 25.
Total angle of triangle is equal to 180.
angle D + angle F + angle E = 180
25 + 25 + E = 180
50 + E = 180
E = 180 - 50
angle E = 130
Simplify 6 / (7+3i).
Answer:
To simplify the following expression: 6 / (7+3i), we're going to multiply and divide the entire expression by (7+3i), as follows:
[tex]\frac{6 (7-3i)}{ (7+3i)(7-3i)} = \frac{42-18i}{58} = 0.72 - 0.31i[/tex]
Now, the denominator has NO imaginary numbers.
Answer:
21/29 - 9/29i
Which of the following polynomials represents a difference of squares? x^2-1,x^2-8,4x^2+16,9x^2-18
Answer:
[tex]x^{2} -1[/tex]
Step-by-step explanation:
we know that
Every difference of squares problem can be factored as follows:
[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
If the polynomial represent a difference of squares every number must be a perfect square (Remember that a number is a perfect square if its square root is an integer.)
Verify each case
case 1) we have
[tex]x^{2} -1[/tex]
In this case both numbers are perfect square
so
[tex]x^{2} -1=(x+1)(x-1)[/tex]
therefore
The polynomial represent a difference of squares
case 2) we have
[tex]x^{2} -8[/tex]
In this case 8 is not a perfect square
therefore
The polynomial not represent a difference of squares
case 3) we have
[tex]4x^{2} +16[/tex]
[tex]4x^{2}+16=4(x^{2}+4)[/tex]
In this case both numbers are perfect square
but is a sum of squares
therefore
The polynomial not represent a difference of squares
case 4) we have
[tex]9x^{2}-18[/tex]
[tex]9x^{2}-18=9(x^{2}-2)[/tex]
In this case 2 is not a perfect square
therefore
The polynomial not represent a difference of squares
what is the solution of this equation
w+9=14
Answer:
w=5
Step-by-step explanation:
14-9=5
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{ w + 9 = 14}[/tex]
[tex]\huge\text{SUBTRACT by the \#9 on your sides! }[/tex]
[tex]\huge\text{Like: w + 9 - 9 = 14 - 9}[/tex]
[tex]\huge\text{Cancel out: 9 - 9 because it equals 0}[/tex]
[tex]\huge\text{Keep: 14 - 9 because it helps us solve for w}[/tex]
[tex]\huge\text{w = 14 - 9}[/tex]
[tex]\huge\text{14 - 9 = w}[/tex]
[tex]\huge\text{14 - 9 = 5}[/tex]
[tex]\huge\text{w = 5}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: w = 5}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
what is the soultion to 40(0.9-x)
Answer:
Step-by-step explanation:
(40*0.9)+(40*-x)
36-40X
Answer: 36-40X
Answer:
[tex]\displaystyle =36-40x[/tex]
Step-by-step explanation:
Distributive property:
↓
[tex]\displaystyle A(B+C)=AB+AC[/tex]
A= 40, B=0.9, and C=x
[tex]\displaystyle 40*0.9-40x[/tex]
Then multiply numbers from left to right.
[tex]40*0.9=36[/tex]
[tex]\displaystyle 36-40x[/tex], which is our answer.
What was done to the quadratic parent function F(x) = xto get the
function G(X) = x2 - 3? 0
A.Shifted 3 units to the right
B. Vertically stretched by multiplying by 3
C.Shifted 3 units down
D.Shifted 3 units to the left
Answer:
Step-by-step explanation:
Given the function f(x), the function g(x) = f(x) + k represents the function f(x) shifted k units downwards.
In this case, given that k=-3 (k<0). The graph is shifted 3 units down. Therefore, we can conclude that the correct option is Option C.
3^8 a^10 b^-5 c^2 over 3^12 a^7 b^-3 c^-2 when a =4 b= 8 and c= 3
[tex]\bf \cfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\implies \cfrac{a^{10}a^{-7}c^2c^2}{3^{12}\cdot 3^{-8}b^{-3}b^5}\implies \cfrac{a^{10-7}c^{2+2}}{3^{12-8}b^{-3+5}}\implies \cfrac{a^3c^4}{3^4b^2}~\hfill \begin{cases} a=4\\ b=8\\ c=3 \end{cases}[/tex]
[tex]\bf \cfrac{4^3\cdot ~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 8^2}\implies \cfrac{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1[/tex]
Answer:
1Step-by-step explanation:
[tex]\dfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=3^{8-12}a^{10-7}b^{-5-(-3)}c^{2-(-2)}=3^{-4}a^3b^{-2}c^{4}\\\\\text{substitute:}\ a=4,\ b=8,\ c=3:\\\\(3^{-4})(4^3)(8^{-2})(3^4)=(3^{-4}\cdot3^4)\bigg(2^2\bigg)^3\bigg(2^3\bigg)^{-2}\\\\\text{use}\ (x^n)(x^m)=x^{n+m}\ \text{and}\ \bigg(x^n\bigg)^m=x^{nm}\\\\=(3^{-4+4})\bigg(2^{(2)(3)}\bigg)\bigg(2^{(3)(-2)}\bigg)=(3^{0})(2^6)(2^{-6})\\\\\text{use}\ x^{-n}=\dfrac{1}{x^n}\ \text{and}\ (x^n)(x^m)=x^{n+m}[/tex]
[tex]=(1)\left(2^{6+(-6)}\right)=2^0=1\\\\\text{Used}\ a^0=1\ \text{for any real value of}\ a,\ \text{except 0}.[/tex]