You have the following expression:
[tex]-6\sqrt[3]{256x^7y^8}[/tex]by simplifying the previous expression you obtain:
[tex]\begin{gathered} -6\sqrt[3]{256x^7y^{8}}=-6\cdot\sqrt[3]{4\cdot64x\cdot x^{6}y^{6}y^{2}}=-6\cdot4x^2y^2\sqrt[3]{4xy^{2}} \\ =-24x^2y^2\sqrt[3]{4xy^2} \end{gathered}[/tex]where you have taken into account to factorize the variables inside the root in a way you can simplify it.
For the system of equations below, which of the variables will be eliminated by adding/ subtracting the two equations together? -8x-5y=145x+5y=10
The variable that will be eliminated is variable y
It will be eliminated by adding the two equations
The reason it will be eliminated is because the
Sally receives a bill from the medical clinic for services totaling $350.000A 10% discount is offered to patients who pay their bill within 60 days.How much would Sally save by paying her bill within 60 days? 10% isfigured by multiplying by 0.10 (x0.10), or by moving the decimal point oneplace to the left.
If Sally pays within the 60 she will have a 10% discount, as mentioned in the statement of the question, the 10% is figured by multiplying the given amount by 0.1. Then if Sally has to pay $350.00 she would save the following amount:
Money saved = 350×0.1 = 35
Then, she would save $35
Classify the following triangle. Check all that apply15.823025O A. IsoscelesO B. ObtuseC. AcuteD. RightE. EquilateralO F. Scalene
Since no two sides of the triangle are the same lenght, it is not an isoceles triangle.
Since no angle in the triangle is greater than 90°, it is not obtuse. This means it is acute.
No angle measures 90°, so it isn't a right triangle.
Once again, the sides are all different lenghts, so it is not equilateral.
Suppose q is directly proportional to the square root of h and inversely proportional to the cube of j, and q=24 when h= 16 and j=2. Find q when h=9 and j=1/2
When h=9 and j=1/2 the q value is 1152.
Given that:
q is directly proportional to the square root of h and inversely proportional to the cube of j, and q=24 when h= 16 and j=2.
q ∝ [tex]\sqrt{h}[/tex]/[tex]j^{3}[/tex]
q = k [tex]\sqrt{h}[/tex]/[tex]j^{3}[/tex]
24 = k [tex]\sqrt{16}[/tex]/[tex]2^{3}[/tex]
24 = k 4/8
k = 24 *2
k = 48
q = 48 [tex]\sqrt{h}[/tex]/[tex]j^{3}[/tex]
substitute h = 9 and j = 1/2
q = 48[tex]\sqrt{9[/tex]/[tex]1/2^{3}[/tex]
q = 48 * 3/1/8
q = 48 * 3 * 8
q = 48 * 24
q = 1152
Therefore when h=9 and j=1/2 the q value is 1152.
Learn more about the directly proportional and square root here:
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can you please help me with #1 a and b.
Answer:
a. All real numbers between 0 and 7.5, except s = 5.5
b. The approximate speed of her current trip, if she takes 6 hours, is 4 kilometers per hour.
As we can see from the graph, we have a vertical asymptote at s = 5.5. This means that at x = 5.5, the given function is not defined. Therefore, the domain that Jada use instead is:
[tex]D\colon\mleft\lbrace s\mright|s\in R,0[tex]\text{ }[/tex]Or:
[tex]0The domain is all real numbers except s = 5.5
Next, let us find her approximate speed if the current trip takes 6 hours. As we can see from the graph, as y approaches 6, x is approaching 4. Since y = T(s), or the time, and s is the speed, we can assume that the approximate speed of her current trip, if she takes 6 hours, is 4 kilometers per hour.
This table shows the cost per-unit of printing a given number of copies of a book.
We can perform a scatter plot of this data as:
It seems that there is an inverse relation between the cost per unit and the number of copies.
The cost per unit approaches an asymptote, so it may correspond to a total cost that is equal to a fixed cost plus a variable cost depending on the number of copies.
We can then calculate the total cost for each option by multiplying the unit cost by the number of copies and we will get:
Then, if we transform the data, we can see a positive correlation between the total cost and the number of copies.
This correlation can not be seen just by looking at the unit cost per copy.
Answer:
- If we consider the transformed data (total cost vs. number of copies), we can see a positive correlation.
- If we ony consider the original table (unit cost vs. number of copies), we can not see any correlation.
Hello, will you please tell me how to solve step by step? This is evaluating functions from an equation. We have: f(x)=x2 + 3 (that is x squared) g(x)=x + 1 h(x)=2How do I solve these? 1. f(g(2))=2. g(f)(0))=3. f(g(h(1)))=4. f(y)=5. g(w)=6. h(z)=
1. f(g(2))
Find g(2); evaluate g for x=2
[tex]\begin{gathered} g(2)=2+1 \\ g(2)=3 \end{gathered}[/tex]Find f(g(2)) or f(3)
[tex]\begin{gathered} f(g(2))=f(3)=3^2+3 \\ f(g(2))=9+3 \\ f(g(2))=12 \end{gathered}[/tex]2. g(f(0))
Find f(0)
[tex]\begin{gathered} f(0)=0^2+3 \\ f(0)=3 \end{gathered}[/tex]Find g(f(0)) or g(3)
[tex]\begin{gathered} g(f(0))=g(3)=3+1 \\ g(f(0))=4 \end{gathered}[/tex]3. f(g(h(1)))
Find h(1): (All the values of h are euqual to 2
[tex]h(1)=2[/tex]Find g(h(1)) or g(2):
[tex]g(2)=3[/tex]Find f(g(h(1))) or f(3):
[tex]\begin{gathered} f(g(h(1)))=f(3) \\ f(g(h(1)))=12 \end{gathered}[/tex]4. f(y); substitute the x in f by y:
[tex]f(y)=y^2+3[/tex]5. g(w); substitute the x in g by w:
[tex]g(w)=w+1[/tex]6. h(z); substitute the x in h by z:
[tex]h(z)=2[/tex]If you originally paid $125 for Pokémon cards and then sold them for $175 what was the markup rate you earned on the sale?
Markup rate is the percentage difference between the selling price and the cost price of a product.
[tex]r=\frac{s-c}{c}\times100\text{\%}[/tex]Applications Involving Rational Equations Create an equation that represents each scenario. Then use that equation to solve the given problem.
Miriam needs 8 consecutive throws to win
Here, we want to calculate the number of throws consecutively that Miriam must make into the cup to beat Ishak
Since Ishak made 48% already, Miriam must make 52%
Out of 30, she made 12;
This represents a percentage of;
[tex]\frac{12}{30}\text{ }\times\text{ 100\% = 40\%}[/tex]Let the number of throws needed be x;
So;
[tex]\begin{gathered} \frac{x+12}{30+x}\text{ }\times\text{ 100 = 52} \\ \\ 100(x+12)\text{ = 52(30+x)} \\ \\ 100x\text{ + 1200 = 1560+52x} \\ \\ 100x-52x\text{ = 1560-1200} \\ \\ 48x\text{ = 360} \\ \\ x\text{ = }\frac{360}{48} \\ \\ x\text{ = 7.5 which is approx 8} \end{gathered}[/tex]So what this mean is that, out of 38 throws, 20 would enter, with the last 8 being consecutive
Michael Phelps has been working on improving his time in the 500 yard freestyle competition.His first time was 4 minutes and 25 seconds. He improved his time by 13 seconds. The next timehe swam, he improved his time by 16 seconds. At the competition, he got his best time when heimproved by 8 more seconds. What was Michael's best swimming time?
Initial time = 4 minutes and 25 seconds
first improve = 13 seconds
second improve = 16 seconds
third improve = 8 seconds
First, we have to add all the improvements:
13+16+8 = 37 seconds
Then we have to subtract the result to the initial time:
4m 25 sec -37 sec =
Since 1 minute = 60 seconds
4 minutes x 60 = 240 seconds
240 + 25 sec = 265 seconds
4m 25 sec = 265 seconds
Back with the subtraction:
265 sec-37 sec = 228 seconds
Michaels best swimming time was 228 seconds.
To convert it into minutes:
228 /60 = 3.8 minutes
of 7. Jon ran around a track that was a mile long. He ran around the track 24 times. How many miles did Jon run?
Question:
Solution:
If Jon ran around the track 24 times, then we have that Jon ran:
[tex]\frac{1}{8}\text{ x }24\text{ = 3 miles}[/tex]then the correct answer is
3 miles.
Answer:
he ran 3 miles
Step-by-step explanation:
this is a multiple choice question so please don't make the explanation long
Slope means inclination level of the line
slope is defined by
m= Y/X. Where Y = y - y'. And X = x - x'
then m= ( 0-8)/(8-0) = -8/8 = -1
then this means slope is NEGATIVE
find the missing side length of a square given the area of the square
The area of a square is given by the following formula:
[tex]A=s^2[/tex]To find the sidelength of the square, solve the equation for s:
[tex]s=\sqrt[]{A}[/tex]Replace the given value in the equation to find the sidelength:
[tex]\begin{gathered} s=\sqrt[]{\frac{16}{49}} \\ s=\frac{4}{7} \end{gathered}[/tex]The sidelength is 4/7cm.
find the value of x ( 94 , 45, & x)
Explanation
We are given a triangle
and then asked to determine the value of x
To do so, we know that the total angles in a triangle are 180 degrees
Thus
[tex]\begin{gathered} x+94+45=180 \\ \\ x+139=180 \\ x=180-139 \\ x=41^0 \\ \end{gathered}[/tex]The value of x is 41 degrees
, I need to find the domain and the functions of two different f of x and G of x
To find g o f(x), we need to replace each x in g(x) for f(x), this is:
[tex]\begin{gathered} g\circ f(x)=g(f(x)) \\ g\circ f(x)=\sqrt[]{-(f(x))-2} \\ g\circ f(x)=\sqrt[]{-(2x-3)-2} \end{gathered}[/tex]Its domain must contain the numbers that make the function be real. In this case the function can be indefinite when having a negative root, it means that the domain of this function is:
[tex]\lbrack\frac{1}{2},\infty)[/tex]Do the same procedure to find f o g(x):
[tex]\begin{gathered} f\circ g(x)=f(g(x)) \\ f\circ g(x)=2\cdot(g(x))-3 \\ f\circ g(x)=2\cdot(\sqrt[]{-x-2})-3 \end{gathered}[/tex]The domain of this function is:
[tex](-\infty,-2\rbrack[/tex]9) A computer generates a random, 3-digit number from 100-999. How many numbers can be generated that are divisible by 2 and 7?
Let consider the numbers between 100 to 199;
The numbers which are divisible by 2 and 7 are 112, 126, 140, 154, 168, 182 and 196.
Total 7 numbers.
Similarly, between 200 to 299, 300 to 399, 400 to 499, 500 to 599, 600 to 699, 800 to 899 and 900 to 999; have 7 such numbers. And between 700 and 799 8 numbers including 700.
So there are (8 x 7) + 8 = 64 numbers
every pair of supplementary angle includes one obtuse angle .
The given statement is
"Every pair of supplementary angle includes one obtuse angle".This statement is false since there's a counterexample when those angles are 90° each, then the statement is not true for that case.
Therefore, the answer is "false".Solve for x:x/6+3≥ −2
The function g(x) is a transformation of f(x). Graph g(x) on the given coordinate plane.
For the point 19, we need to note that the function g(x) is the function f(x) moved 2 units to the left in the x-axis and moved 4 units upward in the y-axis, then we need to return this transformation to get back to f(x), then what we need to do is to move the graph two units to the right and 4 units down, and the result will be:
For the point 20, what we are going to do is to look at each of the points and transform them to the preimage. for example:
since g(-3)=2 then 2f(-3-3)-2=2 then f(-6)=2
since g(-2)=4 then 2f(-2-3)-2=4 then f(-5)=3
since g(0)=1 then 2f(0-3)-2=1 then f(-3)=1.5
since g(1)=3 then 2f(1-3)-2=3 then f(-2)=2.5
since g(3)=3 then 2f(3-3)-2=3 then f(0)=2.5
now we can graph these points to obtain the new graph:
For the point 21:
since g(-3)=2 then 1/2f(-(-3))-4=2 then f(3)=12
since g(-2)=4 then 1/2f(2)-4=4 then f(2)=16
since g(0)=1 then 1/2f(0)-4=1 then f(0)=10
since g(1)=3 then 1/2f(-1)-4=3 then f(-1)=14
since g(3)=3 then f(-3)=14... and now we can do the third graph:
Evaluate the following expression with a calculator.arccot(−3.5)Express your answer in degrees, and round to the nearest hundredth. When you enter your answer, do not enter a degrees symbol or θ= - just enter the numerical value.
Value = -3.5
[tex]\text{arccot(}-3.5)\text{ = }-15.95\text{ degree}[/tex]The answer would be -15.95°
Rounded
The answer would be -16°
Word problem involving a sine or cosine function: Problem type 1
Given:
a.) Amplitude = 9 cm
b.) Period = 0.5 seconds
c.) At time = 0, displacement from rest is -9 cm
The general equation for displacement as a function of time is:
[tex]\text{ d = -A }\cdot\text{ Cos}(\text{Bt - C) }+\text{ D}[/tex]The amplitude is given by A. Here, since amplitude is 9 cm, so we have:
A = 9
The period of the object is 0.5 seconds, so we have:
[tex]\text{ Period = 2}\frac{\text{ }\pi}{\text{ B}}[/tex][tex]\begin{gathered} 0.5\text{ }=\frac{1}{2}\text{= 2}\frac{\pi}{\text{ B}} \\ \text{ B = }(\text{ 2}\frac{\pi}{\text{ B}})(2) \\ \text{ B = 4}\pi \end{gathered}[/tex]Since the minimum displacement is at t = 0, so there is no phase shift.
Therefore, C = 0
Also since there is no vertical shift, so D = 0.
In Summary, we get: A = 9, B = 4π, C = 0 and D = 0
Thus the equation modeling the displacement d as a function of time t is given by:
[tex]\text{ d = -A }\cdot\text{ Cos}(\text{Bt - C) }+\text{ D}[/tex][tex]\text{ d = -9 }\cdot\text{ Cos}(4\pi\text{t - 0) }+0[/tex][tex]\text{ d = -9Cos}(4\pi\text{t)}[/tex]Therefore, the equation is:
[tex]\text{ d = -9Cos}(4\pi\text{t)}[/tex]write a sinusoid equation for the given situation and clearly explain how you determined the AMPLITUDE, VERTICAL and PHASE SHIFT.( the equation should have exact values no decimal of approximations. your equation should be in radians.)Centennial Colorado averages the maximum amount of daylight hours in June at 15 hours and the least amount in December at 9.4 hours. Assume that the number of hours of daylight varies sinusoidally over a period of 12 months. Develop a model for the number of hours of daylight as a function of time
y = A sinX
Maximum value= 15
Minimum value= 9.4
Amplitude= ( 15 - 9.4 )= 5.6/2 hours
Vertical shift = 15 - 2.8= 12.2 hours
Phase shift
June = 6th month
December= 12th month
X + delta
when x= 15 , sin ( 6 /12+ delta) = 1
and. x = 9.4 ,. Sin (12/12 + delta) + 2.8 = 0
then
Sin ( 6 /12 + delta) = 1
arcsin 1= 90°
Sin (12/12 + delta) = 2.8/12= 0.23
Then arcsin 0.23= 13.29 °
Then answer is
y = 15• Sin ( X + 0.5)
How to count 100 dollar bills
There are different ways to count 100 dollars
One of them is count 100 individual 1$dollar
Other possible way is count 20 individual $5 dollar
Other possible way is count 10 individual 10$ dollar
other possible way is count 5 individual $20 dollar
And the other possibility is just have one $100 dollar
You could count the dollar bills individually or in sections for example:
1x100
5x20
10x10
20x5
I think its 3 I just need them to tell me I’m right not a whole explanation if I’m wrong then explain, just need you to check my answer thank you.
Outliers are observations that are significantly distant from the rest of the data set. They represent experimental errors or atypical observations.
In the scatter plot, you can consider being outliers any dot that is apart from the rest of the data set.
In the given scatter plot there are three observations that can be considered outliers.
three angles are congruent and adjacent and form a line. each angle measures____?
Answer:
60 degrees
Explanation:
Given three adjacent and congruent angles that form a line as illustrated in the diagram below:
Let each of the angles = x
The sum of angles on a line = 180 degrees.
Therefore:
[tex]\begin{gathered} x+x+x=180 \\ \implies3x=180 \\ \implies x=\frac{180}{3} \\ x=60\degree \end{gathered}[/tex]Each of the angles measures 60 degrees.
If pH = -log [H+], and the pH of lemon juice is 2.2, what is the concentration of hydrogen ions [H+] in gram atoms per liter? Round to the nearest ten thousandths.
The pH is calculated using the formula:
[tex]pH=-\log[H^+][/tex]The question gives the pH of lemon juice to be 2.2.
Hence, the formula is written to be:
[tex]2.2=-\log[H^+][/tex]Multiply both sides by -1:
[tex]\log[H^+]=-2.2[/tex]Since the log is in base 10, we have:
[tex]\log_{10}[H^+]=-2.2[/tex]Apply the law of log
Alex’s coach needs to buy 30 jersey costs $29. How much will the total cost for the 30 jerseys be
He needs to buy 30 jerseys and each jersey costs $29. Therefore, to find how much will the total cost will be, we need to to de the next operation:
Total cost = jerseys cost * amount need of jerseys
Therefore:
Total cost = 29* 30 - This is the equation
Total cost =870
Hence, the total cost will be $870.
Find the y-intercept of the function y = -3(x+2)(x-1)(x+3)
The y-intercept of a function happens when the function "cuts" the y-axis.
This can be calculated as the value of the function f(x) when x=0.
Then, if we replace x by 0, we get the y-intercept:
[tex]\begin{gathered} f(x)=-3\mleft(x+2\mright)\mleft(x-1\mright)\mleft(x+3\mright) \\ f(0)=-3(0+2)(0-1)(0+3) \\ f(0)=-3\cdot2\cdot(-1)\cdot3 \\ f(0)=18 \end{gathered}[/tex]The y-intercept for this function is f(0)=18.
4.7 x 10^-2 in standard form.
To write in standard form, Since the exponent is negative 2, move the decimal point two units to the left.
[tex]0.047[/tex]How do you solved this?
7-×=10
Answer:
X = -3
Step-by-step explanation:
Since the given equation cannot be done with minus, X must be equivalent to a minus.
The correct equation would be [tex]7+6=10[/tex], however, in this current state, the equation would be [tex]7-(-3)=10[/tex]