Answer: 9xy3
Step-by-step explanation:
STEP
1
:
y
Simplify ——
x5
Equation at the end of step
1
:
y
(((3xy)2) • (x4)) • ——
x5
STEP
2
:
Equation at the end of step
2
:
y
(32x2y2 • x4) • ——
x5
STEP
3
:
Multiplying exponential expressions :
3.1 y2 multiplied by y1 = y(2 + 1) = y3
Dividing exponential expressions :
3.2 x6 divided by x5 = x(6 - 5) = x1 = x
Final result :
9xy3
Bacteria in a petri dish doubles every 10 minutes. (Express in exponential function)
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
Answer:
a)1280 bacteria
Step-by-step explanation:
We find the function in t hours first
Bacteria in a petri dish doubles every 10 minutes. (Express in exponential function)
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
The formula to use is given as
y = Ab^t
Where
y = Total Population of bacteria
B= initial population of the bacteria
r =
t = time in hours
The bacteria doubles in the petri dish every 10 minutes, we have 10 bacteria
10 minutes in hours = 10/60= 1/6 hours
10 × 2 = 10b^10/60
20 = 10b ^1/6
2 = b^1/6
Multiply both sides by Power of 6
2^6 = b
b = 64
Hence, y = 10×(64)^t
a) If there are 10 bacteria initially, how many are there after 120 minutes?
120 minutes in hours = 2
y = 10(64)²
y = 1280
There would be 1280 bacteria after 120 minutes
b) If there are 10 bacteria initially, when would there be a million bacteria?
y= 1,000,000
A = 10 bacteria
b = 64
t = ???
1000000 = 10 × (64)^t
Divide both sides by 10
100000 = (64)^t
Find the area of the following
trapezoid:
12 cm
10 cm
8 cm
22 cm
A = [?] cm2
Answer:
136 cm^2
Step-by-step explanation:
The area of a trapezoid is found by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 12+22) *8
= 1/2 (34) * 8
= 136 cm^2
Answer:
144
Step-by-step explanation:
The inverse of G(x) is a function.
Answer:
This is False.
Step-by-step explanation:
I hope this helped you! :)
Answer: false
Step-by-step explanation:
What is the angle of rotation from figure D to figure D’? Assume that the center of rotation is the origin. A. 270° clockwise B. 90° clockwise C. 90° counterclockwise D. 180° counterclockwise
Answer:
the answer is B. 90°clockwise
Answer:
B. 90 Clockwise
Step-by-step explanation:
The lines graphed below are perpendicular. The slope of the red line is 3. What is the slope of the green line?
Answer:
Hey there!
The slope of the green line is -1/3.
Perpendicular lines have opposite reciprocal slope.
Hope this helps :)
→Answer:
-1/3
→Step-by-step explanation:
Well this is pretty simple.
2 lines that are perpendicular to each other are both reciprocals of each other.
So what’s the reciprocal of 3?
Ans: -1/3
Find dy/dx of (3 - 2x)-1/2
Answer:
Step-by-step explanation:
To evaluate the derivative of this function you need the chain rule. The pattern I teach to my calculus students is to find
u =
u' =
f(u) =
f'(u) =
First pick your "u". u will be the inner function, the one inside the parenthesis.
u' will then be the derivative of u.
f(u) is the function in terms of u, and
f'(u) is the derivative of the function in terms of u.
The derivative then, finally, will be u' * f'(u). Let's begin.
Our u, or the part of the function inside the parenthesis is 3 - 2x; hence,
u = 3 - 2x
The derivative, u', then is
u' = -2
f(u) is the function in terms of u, so
f(u) = [tex]u^{-\frac{1}{2}[/tex] and the derivative in terms of u is
f'(u) = [tex]-\frac{1}{2}u^{-\frac{3}{2}[/tex]
u' * f'(u) then is
[tex]-\frac{1}{2}u^{-\frac{3}{2}*(-2)[/tex] Simplify that by subbing back in for u and multiplying -2 by -1/2 to get
[tex]y'=(3-2x)^{-\frac{3}{2}[/tex]
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
Nick, Paul and krutika share £80 in a ratio 1:1:2 how much money does each person get
Answer:
£20
Step-by-step explanation:
First you add 1 ,1 ,2 which =4
Next you divide 80 by 4 which give you the answer 20.
If z is a standard normal variable, find the probability.
P(Z < 0.97)
0.1660
0.8340
0.8315
0.8078
Answer:
the correct option is A
Step-by-step explanation:
hope this helps
Using the standard normal distribution table, the probability of having a Zscore less than 0.97 would be 0.8340
To obtain the probability z P(Z < 0.97) ; we use a standard normal distribution table or a Z probability calculator ;
Using a normal distribution table :
P(Z < 0.97) = 0.8339Therefore, the most appropriate option is 0.8340
Learn more : https://brainly.com/question/23105648
factor the trinomial below x^2 - 2x - 48
Answer:
( x-8) ( x+6)
Step-by-step explanation:
x^2 - 2x - 48
What two numbers multiply to -48 and add to -2
-8*6 = -48
-8+6 = -2
( x-8) ( x+6)
Find the area of the triangle.
Answer:
76 ft squared
Step-by-step explanation:
First, you need to find the height of the triangle using the Pythagorean theorem. By adding a line down the middle from point P to the center of line RQ you create a right triangle with 16 as a hypotenuse and a leg with the length 5 (half of the length of line RQ, 10) you can then plug this into the equation to get 5^2+b^2=16^2. Then you get 25+b^2=256, then b^2=231. You then take the square root of both sides to get a height of about 15.2. Now you can find the area of the triangle with the equation A=1/2(bxh). You multiply the base times the height so 10 times 15.2 to get 152, then multiply by 1/2, or divide it by 2, to get 76 feet squared as the area.
Answer:
Length of missing side: 14.7 (rounded to nearest tenth)
Step-by-step explanation:
1/2 * (base) * (height) = area
Memorize this: SOH CAH TOA
sine (degrees) = opposite length/hypotenuse
sin(67 degrees) = x/16
x = 14.7 (rounded to nearest tenth)
x = missing side = 14.7
Find the ordered pairs for the x- and y- intercpets of the equations 3x-2y=18 and select the appropriate option below
Answer:
ordered pairs for the
x-intercept : (6,0)
y- intercepts :(0,9)
Step-by-step explanation:
Given equation : 3x-2y=18
X- intercept on coordinate plane is point where the line intersect the x- axis.
The coordinate of point y is 0 for x-intercept.
Based on this let the coordinate of X- intercept be (x,0)
we will plug this value in equation 3x-2y=18, to find value of x and hence we will get x-intercept
3x-2y=18
3x -2*0 =18
=> 3x = 18
=> x = 18/3 = 6
Thus, coordinate of x-intercept is (6,0)
________________________________________________
Y- intercept on coordinate plane is point where the line intersect the y- axis.
The coordinate of point x is 0 for y-intercept.
Based on this let the coordinate of X- intercept be (0,y)
we will plug this value in equation 3x-2y=18, to find value of y and hence we will get y-intercept
3x-2y=18
3*0 -2y =18
=> 2y = 18
=> y = 18/2 = 9
Thus, coordinate of y-intercept is (0,9)
Mrs. Boiler is three times as old as her son, William. Mr. Boiler is 4 years older than his wife. If William's age will be x years old in 5 years, express the sum of their current ages, in terms of x.
Answer:
william's age=x-5, mrs boiler=3 (x-5), mr boiler=4+3 (x-5) the sum=7x-31
Answer the geometry question in the pic and save my life...
Answer:
The answer should be A'(-9,3) B'(12,-6)
Step-by-step explanation:
If you dialate, you multiply every coordinate by 3. -3 x 3= -9. 1 x 3=3. 4 x 3= 12. -2 x 3= -6. So, the last option is correct.
Wendy is creating a large soup based on a recipe. Her recipe calls for of a pint of milk, but she only has of a pint of milk, so she can only make a portion of her soup. Wendy can only make _____ of her recipe with the amount of milk that she has.
Answer:
She can only make 5/6 of her recipe with the amount of milk that she has.
Step-by-step explanation:
Some data of this problem is missing, the data missing is:
Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.
Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:
[tex]\frac{5}{8}[/tex] ÷[tex]\frac{3}{4}[/tex]
When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:
[tex]\frac{5}{8}[/tex]÷[tex]\frac{3}{4}=\frac{5}{8}[/tex]×[tex]\frac{4}{3} =\frac{20}{24}[/tex]
If we simplify this last expression we have:
[tex]\frac{20}{24}=\frac{10}{12} =\frac{5}{6}[/tex]
Thus, she can only make 5/6 of her recipe with the amount of milk that she has.
Note: In case the data missing is different, you can apply this same procedure with the fractions you have.
Given: ∆KLM, KL ≅ LM A∈ KM , B ∈ KM AK ≅ BM Prove:△AKL ≅ △BML ΔALB is isosceles
Answer:
ΔAKL is congruent to ΔBML by the Side Angle Side rule of congruency and ΔALB is isosceles as two of its sides [tex]\overline {AL}[/tex] and [tex]\overline {BL}[/tex] are congruent
Step-by-step explanation:
The given parameters are;
The given triangle ΔKLM has sides [tex]\overline {KL}[/tex] ≅ [tex]\overline {LM}[/tex], Given
ΔKLM is isosceles Δ (two equal segments), Definition of isosceles Δ
∠LKM ≅ ∠LMK, Base ∠s of isosceles Δ are ≅
Point A is on segment [tex]\overline {KM}[/tex], Given
Point B is also on segment [tex]\overline {KM}[/tex], Given
Segment [tex]\overline {AK}[/tex] ≅ segment [tex]\overline {BM}[/tex], Given
ΔAKL ≅ ΔBML, SAS rule of congruency
Segment [tex]\overline {AL}[/tex] ≅ segment [tex]\overline {BL}[/tex], CPCTC
ΔALB is isosceles (two equal segments), Definition of isosceles Δ
Where:
SAS = Side Angle Side
CPCTC = Congruent parts of congruent triangles are congruent.
Answer:
m∠AKL=m∠BML | Base Angle Theorem (Base ∠ TH.)
Step-by-step explanation:
KL=LM | Given
A ∈ KM | Given
B ∈ KM | Given
AK=BM | Given
m∠AKL=m∠BML | Base ∠ TH.
Question 8 Multiple Choice Worth 1 points)
(02.05 LC)
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
In the graph the line shifted down by 3 units, so k=3. Therefore, option B is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the given graph,
The coordinates of line red are (0, 5) and (3, 6)
Here, slope (m) = (6-5)/(3-0)
= 1/3
Substitute m=1/3 and (x, y)=(0, 5) in y=mx+c, we get
5=1/3 (0)+c
c=1/3
Now, g(x)=1/3 x
The coordinates of line blue are (0, 2) and (3, 4)
Here, slope (m) = (4-2)/(3-0)
= 2/3
Substitute m=2/3 and (x, y)=(0, 2) in y=mx+c, we get
2=2/3 (0)+c
c=0
So, f(x)=2/3 x
From the graph the line shifted down by 3 units
Therefore, option B is the correct answer.
To learn more about the function visit:
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Emanuel was charged $32 for a 14 2/9km taxi ride What was the cost per kilometer?
Serena wants to wrap ribbon around the edge of the picture frame represented in the drawing. Which is the simplified form of the expression representing the length of ribbon Serena will need? A. 9x – 13.2 B. 4.5x – 6.6 C. 9x – 14.8 D. 2(3.5x – 7) + 2(x + 0.4)
Answer:
A.9x – 13.2
Step-by-step explanation:
2*(3.5x-7+x+0.4)=2*(4.5x-6.6)=9x-13.2
Answer:
It is A
Step-by-step explanation:
Steve Fossett is approaching the shores of Australia on the first successful solo hot air balloon ride around the world. His balloon, the Bud LightTM Spirit of Freedom, is being escorted by a boat (directly below him) that is 108 meters away. The boat is 144 meters from the shore. How far is Fossett's balloon from the shore?
Answer:
180 meters
Step-by-step explanation:
Distance from the balloon to the boat = 108 meters
Distance from the boat to the shore = 144 meters
Since the boat is directly below the balloon, the problem forms a right triangle in which the distance from the balloon to shore is the hypotenuse.
Let the length of the hypotenuse = l
Using Pythagoras Theorem
[tex]l^2=108^2+144^2\\l^2=11664+20736\\l^2=32400\\l=\sqrt{32400} \\l=180$ meters[/tex]
The distance from Fossett's balloon to the shore is 180 meters.
Fossett's balloon is 180m from the shore
data;
escort boat to the ballon = 108mboat from the shore = 144mdistance between the ballon and the shore = xPythagoras TheoremTo solve this problem we can assume this is situation forms a right angle triangle and we can solve this using pythagoras theorem.
[tex]x^2 = y^2 + z^2\\[/tex]
Let's substitute the values and solve
[tex]x^2 = y^2 + z^2\\x^2 = 108^2 + 144^2\\x^2 = 32400\\x = \sqrt{32400} \\x = 180m[/tex]
Fossett's balloon is 180m from the shore
Learn more on pythagorean theorem here;
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Plz help similarity in right triangle
Answer:
similar triangles have there corresponding sides proportional and corresponding angles equal
Is the function f(x) =(4)^x -2 an exponential function. If so, identify the base. If not, why not?
Answer:
Yes.
Base: 4
Step-by-step explanation:
Since we have 4 to the power of x, we do indeed have an exponent. The -2 just signifies vertical movement down.
HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Answer:
This is equation 1.
Step-by-step explanation:
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
Someone please help thanks!!!
Answer:
-3/2
Step-by-step explanation:
The slope of a line is calculated by dividing the difference in the y-coordinates by the difference in the x-coordinates.
Here, the given ordered pairs are (-6, -8) and (-14, 4), so the slope is:
slope = m = (4 - (-8)) / (-14 - (-6)) = 12 / (-8) = -3/2
The answer is thus -3/2.
~ an aesthetics lover
Answer:
m= -3/2
I hope this helps.
please someone help me with my work i will give you brainly if it is correct :)
Answer:
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Step-by-step explanation:
[tex]\frac{21x^{6}y^{5} }{14x^{2}y^{9} }[/tex]
→ First simplify the numbers
[tex]\frac{3x^{6}y^{5} }{2x^{2}y^{9} }[/tex]
→ Now simplify the x powers, remember when dividing indices, you subtract them away from each other so,
[tex]\frac{3x^{4}y^{5} }{2y^{9} }[/tex]
→ Now simplify the y powers, remember when dividing indices, you subtract them away from each other so,
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Answer:
simplify.
Step-by-step explanation:
If at the same rate of interest, in 2 years, the simple interest is Rs. 40 and compound interest is Rs. 41, then what is the principal
Answer:
Simple Interest for 1 year = 40/2 = 20
CI for 2 years = 20 + 20 + 1
The difference of Re 1 is due to the interest received on this interest.
Hence interest rate = 1/20 * 100 = 5
Interest for 1 year at 5% = 20
Hence principal = 20*100/5 = 400
Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo's equation is missing, as shown below. Negative (x minus 1) + 5 = 2 (x + 3) minus box Which could be the missing term that Leonardo put into the box? x 3x 1 5
Answer:
The missing term is 3x
Step-by-step explanation:
Given
-(x - 1) + 5 = 2(x + 3) - _
Required
Find _
For proper identification of the parameters, represent _ with Z
So, the equation becomes
-(x - 1) + 5 = 2(x + 3) - Z
Open bracket (start from the left hand side)
-x + 1 + 5 = 2(x + 3) - Z
-x + 1 + 5 = 2x + 6 - Z
Solve like terms
-x + 6 = 2x + 6 - Z
Subtract 6 from both sides
-x + 6 - 6 = 2x + 6 - 6 - Z
-x = 2x - Z
Subtract 2x from both sides
-x - 2x = 2x - 2x - Z
-3x = -Z
Multiply both sides by -1
-3x * -1 = -Z * -1
3x = Z
Reorder
Z = 3x
Hence, the missing term is 3x
Answer:
answer is 3x
Step-by-step explanation:
Simplify : (-7/18 × 15/-7) - (1 × 1/4) + (1/2 × 1/4)
Answer:
17/24
Step-by-step explanation:
This expression simplifies to the following:
-7 15 1 1
---- * ----- - ----- + -----
18 -7 4 8
Reducing the product, we get
15 1
-------- - -----
18 8
and this simplifies further:
5 1
----- - -----
6 8
The LCD is 24. Thus, we have:
20 3 17
------ - ----- = -----
24 24 24
If x, y, z, are integers such that 2^x*3^y*7^z=329, Then what is x, y, and z? PLZZZZ HELP THANK YOU
Answer:
I just answered this question lol but the answer is 2^0*3^0*7^47=329. Hope this helps!!
Step-by-step explanation:
A landscaper designs a garden border to run along the inside perimeter of a piece of property that is shaped like a
rectangle.
The garden border that runs along the edge of the property has a width of x meters and surrounds the entire
property. The area inside of the garden border has a width of 39 meters and a length of 21 meters as shown by the
diagram.
The total area of the property, in square meters, is a function of the distance, x, in meters.
Enter the quadratic function, A(x), in standard form that represents the total area of the property in square meters.
If your answer includes exponents, use the symbol. For example, if your answer is 42, enter it like this: 4344
please help me
Answer:
A = 4x^2 + 120x
Step-by-step explanation:
(39+2x)(21+2x)-(39*21) = 819 + 78x + 42x + 4x^2 - 819
A = 4x^2 + 120x