let s be the side of the cube
Volume of cube = s³
From the the question volume = 729 cubic inches
Substitute into the formula;
729 = s³
Take the cubic root of both-side of the equation
[tex]\sqrt[3]{729}=s[/tex][tex]S=\sqrt[3]{729}[/tex]What is that rounded to the nearest tenth as a decimal
(I had a tutor helping me but the app randomly logged me off so can someone please help)Solve and graph each compound inequality.a.5x+1>11 or x-1<-4b. -5x > 20 or x-2>7
Answer
a) x > 2 OR x < -3
b) x < -4 OR x ≥ -5
Explanation
The compound inequalities to be solved and graphed include
a) (5x + 1) > 11 OR (x - 1) < -4
b) (-5x) > 20 OR (x - 2) ≥ -7
The first step is to solve these expressions
a) (5x + 1) > 11 OR (x - 1) < -4
5x + 1 > 11
Subtract 1 from both sides
5x + 1 - 1 > 11 - 1
5x > 10
Divide both sides by 5
(5x/5) > (10/5)
x > 2
OR
x - 1 < -4
Add 1 to both sides
x - 1 + 1 < -4 + 1
x < -3
So, the solution for this is x > 2 OR x < -3
b) (-5x) > 20 OR (x - 2) ≥ -7
(-5x) > 20
Divide both sides by -5
Note that dividing both sides by a negative number causes the inequality sign to change
(-5x/-5) < (20/-5)
x < -4
OR
(x - 2) ≥ -7
Add 2 to both sides
x - 2 + 2 ≥ -7 + 2
x ≥ -5
So, the solution for this is x < -4 OR x ≥ -5
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
(a) An angle measures 48°. What is the measure of its complement? (b) An angle measures 65°. What is the measure of its supplement? measure of the complement: 5 ? measure of the supplement:
(1) Complementary angles always add up to 90 deg, if one angle is 48 deg then another one will be 90-48 = 42 deg
(2) Supplementary angles on the other hand always add up to 180 deg or half a circle so if one angle is 65 deg then another angle is 180-65 =115 deg
This is the answer.
what is the unit rate or price per oz. of chips at ingles
$1.98 ------------------>5oz
$x----------------------->1oz
Using cross multiplication:
[tex]\begin{gathered} \frac{1.98}{x}=\frac{5}{1} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{1.98}{5}=0.396 \end{gathered}[/tex]How does the graph of y = f(x + 2) differ from the graph of y = f(x - 3)?
Two graphs are differenced by the way x variable is changing
Firts find the difference between two variables (x+2)
which of the following equation does not have a solution
Step 1
Solve the equations to know which of them has no solution
[tex]\begin{gathered} A)x+4=2(x+4) \\ x+4=2x+8 \\ 2x-x=4-8 \\ x=-4 \\ \text{Option A has a solution} \end{gathered}[/tex][tex]\begin{gathered} B)3x+1=2x+5 \\ 3x-2x=5-1 \\ x=4 \\ \text{Option B has a solution} \end{gathered}[/tex][tex]\begin{gathered} C)\text{ 4(x-1)+2x=6x+5} \\ 4x-4+2x=6x+5 \\ 6x-6x=5+4 \\ 0=9 \\ \text{Option C has no solution} \end{gathered}[/tex][tex]\begin{gathered} D)3x+7=3x-6 \\ 3x-3x=-6-7 \\ 0=-13 \\ \text{Option D has no solution} \end{gathered}[/tex][tex]\begin{gathered} E)\text{ }4x=5x \\ 4x-5x=0 \\ -x=0 \\ x=0 \\ \text{Option E has solution} \end{gathered}[/tex][tex]\begin{gathered} F)x+1=2x \\ 2x-x=1 \\ x=1 \\ \text{Option F has solution} \end{gathered}[/tex][tex]\begin{gathered} G)x=x+7 \\ x-x=7 \\ 0=7 \\ G\text{ has no solution} \end{gathered}[/tex][tex]\begin{gathered} H)10x+1=5x-6 \\ 10x-5x=-6-1 \\ 5x=-7 \\ \frac{5x}{5}=-\frac{7}{5} \\ x=-\frac{7}{5} \\ H\text{ has a solution} \end{gathered}[/tex]Hence C,Dand G has no solution
4y^2-28y+49factor each polynomial completely.If polynomial Prime, state this.
We are given the following polynomial
[tex]4y^2-28y+49[/tex]Let us factor out the above polynomial.
We need to break the middle term into two numbers such that their sum is equal to -28 and their product is equal to 196
How about -14 and -14?
-14 -14 = -28
-14×-14 = 196
[tex]\begin{gathered} 4y^2-28y+49 \\ 4y^2-14y-14y+49 \\ (4y^2-14y)+(-14y+49) \\ 2y(2y-7)-7(2y-7) \\ (2y-7)(2y-7) \\ (2y-7)^2 \end{gathered}[/tex]As you can see, the polynomial is completely factored.
Also, notice that the polynomial is not a prime since it has more than 2 factors.
Use the given information to solve right triangle ABC for all missing parts. Find all parts missing A=31.5°, a =8 1/4 in.
We know two angles and one side of a right triangle. We can find the missing angle as shown below (knowing that the sum of the inner angles of a triangle is equal to 180°)
[tex]\begin{gathered} 180=A+B+C=31.5+B+90 \\ \Rightarrow B=58.5 \end{gathered}[/tex]Finally, we can use the following two trigonometric identities to find the lengths of the missing sides.
[tex]\begin{gathered} \sin A=\frac{a}{c},\tan A=\frac{a}{b} \\ \Rightarrow c=\frac{a}{\sin A},b=\frac{a}{\tan A} \\ \end{gathered}[/tex]Thus,
[tex]\Rightarrow c=15.79,b=\text{13}.46[/tex]The answer are B=58.5°, b=13.46in, c=15.79in
if XYZ equals ABC what is the scale factor to enlarge XYZ to create ABC
step 1
Find out the scale factor
The ratio between corresponding sides is equal to the scale factor
so
scale factor=9/6
scale factor=1.5
therefore
the answer is 1.5Round each number to the nearest ten, hundred and thousand:6,999
ANSWER
[tex]\begin{gathered} Tens:7,000 \\ \\ Hundreds:7,000 \\ \\ Thousands:7,000 \end{gathered}[/tex]EXPLANATION
We want to round the given number to the nearest ten, hundred, and thousand.
To round a number to any given place, if the number in the place value after the given place is greater than or equal to 5, round up but if the number is less than 5, round down.
To round the number to the nearest ten, apply the rule above to the number in the units place value:
[tex]6,999\approx7,000[/tex]To round the number to the nearest hundred, apply the rule to the number in the tens place value:
[tex]6,999\approx7,000[/tex]To round the number to the nearest thousand, apply the rule to the number in the hundreds place value:
[tex]6,999\approx7,000[/tex]That is the answer.
PartBecause his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, X? Donot combine like terms.BFont SizeA- A
The biker needs to travel 65mi in four days and each day he needs to ride 1.5 the distance he did the day before.
In Part A you found that:
Day 1: 8 mi
Day 2: 1.5 (8mi)=12mi
Day 3: 1.5(12mi)=18mi
Day 4: 1.5(18mi)=27mi
This was just a recompilation of our previous results
Regarding part B
So, if x represents the distance traveled during the first day, once we add up each day we obtain the next expression:
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))[/tex]Notice that the first term corresponds to the distance he bikes on the first day, the second term corresponds to the second day, and so on.
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=d[/tex]d represents the total distance during the 4 days
And remember, do not combine like terms!
This represents how much distance he will ride during the 4 days given the first-day distance
And, as you found in part A, if x=8, then 8.125(8)=65. So, our result is consistent.
Regarding Part C
Now, as our goal is to ride during 65mi, we only need to do d=65mi, giving us:
[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=65[/tex]Regarding part D:
First, let's remember what 'like terms' mean:
An easy example of like terms is the next set: x, 2x, -7x
Notice that all of them share the term x, so they are 'like terms'
Going back to part C, we have that our final expression is:
[tex]x+1.5x+2.25x+3.375x=65[/tex]As you can see, the left side of the equation contains terms that involve the x-factor, so all the terms on the left side are 'like terms' involving x
[tex]x,1.5x,2.25x,3.375x[/tex]which of these expressions is equivalent to -2(x-5)?a. -2x-5b. -2x+5c. -2x+10d. -2x-10
To find a equivalent expression you apply the distributive property on the given expression:
Distributive property:
[tex]a(b+c)=ab+ac[/tex]For the given expression:
[tex]\begin{gathered} -2(x-5)=-2\cdot x+2\cdot5 \\ \\ =-2x+10 \end{gathered}[/tex]As you can see the equavalent expression is option Cif abcd equals wxyz and the scale factor is 3/2, find the dimensions of rectangle wxyz
AB is similar to XW 2 * 3/2 = 6/2 = 3 XW = 3
BC is similar to WZ 3* 3/2 = 9/2 = 4.5 WZ = 4.5
BC is similar to YZ 2*3/2 = 6/2 = 3 YZ = 3
AD is similar to XY 3 *3/2 = 9/2 = 4.5 XY = 4.5
done
Which two values of x are roots of the polynomial below?x2 + 3x + 5A. *= -3 + /292.O B. X=-3+/-112D.C. X=-3-v-11-3--11D. x= -3+, VTTE x=-3-DE. =-3-1129
Answer:
Options B and C
Step-by-step explanation:
Finding the roots of a quadratic equation:
Suppose that we have a quadratic equation in the following format:
ax² + bx + c = 0
The roots are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this question:
x² + 3x + 5 = 0
So a = 1, b = 3, c = 5
The roots are:
[tex]x=\frac{-3\pm\sqrt[]{3^2-4\ast1\ast5}}{2}=\frac{-3\pm\sqrt[]{-11}}{2}[/tex]So
[tex]x=\frac{-3+\sqrt[]{-11}}{2},x=\frac{-3-\sqrt[]{-11}}{2}[/tex]Options B and C
A fraction whose _____ and ______ are integers, is considered a rational number.
A fraction whose numerators and denominators are integers, is considered a rational number.
A rational number is a number in the form
[tex]\begin{gathered} \frac{a}{b},b\neq0 \\ \text{where a and b are integers.} \end{gathered}[/tex]Myiah rides her bike from home to the park to meet a friend. When she arrives at the park, Myiah and her friend sit at a park bench and talk. Myiah then rides her bike home at a slower rate. Which graph represents this situation?
Myiah rides her bike from home to the park so there is a distance from home, then she and her friends stay some time at the park, then the distance vs time is a horizontal line because they don't move while the time is moving. Finally, she rides her bike home at a slower rate, so she takes more time to get home.
In conclusion, the graph that represents this situation is the third.
THE CORNER POINTS OF THE SHADED REGION IN A LINEAR PROGRAMING PROBLEM ARE (7,0) (9,-1) (9,5) (8,6) AND (0,6) IF THE COST FUNCTION WAS GIVEN BY C=3X+Y WHAT WILL THE MINIMUM COST BE?
Given:
The shaded region are (7,0) (9,-1) (9,5) (8,6), and (0,6).
The cost function is
[tex]C=3x+y[/tex]Required:
We need to find the minimum cost.
Explanation:
Consider the point (7,0).
Substitute x =7 and y=0 in the given function.
[tex]C=3(7)+0=21[/tex]Consider the point (9,-1).
Substitute x =9 and y=-1 in the given function.
[tex]C=3(9)+(-1)=27-1=26[/tex]Consider the point (9,5).
Substitute x =9 and y=5 in the given function.
[tex]C=3(9)+5=27+5=32[/tex]Consider the point (8,6).
Substitute x =8 and y=6 in the given function.
[tex]C=3(8)+6=24+6=30[/tex]Consider the point (0.6).
Substitute x =0 and y=6 in the given function.
[tex]C=3(0)+6=6[/tex]We know that the lowest value of 21, 26, 32, 30, and 6 is 6.
The minimum cost will be 6.
Final answer:
The minimum cost will be 6.
Complete the table . On the coordinate plane below , plot the points represented by the pairs of coordinates from table . 3x - y = 1
EXPLANATION
Given the table, we can see that the appropiate points are:
x y
-2 -2
-1 -1
0 0
1 1
2 2
Now, we can plot this on the coordinate plane as shown as follows:
I’m new to this math and could use some help.
The operation A U B means "A union B" for which the elements of A is combined with the elements of B
Given that
A = {3,4,5,6,7,8,9,10,11,12} and B = {8,10,12,14,16,18}
Combine all the elements, and list the repeat elements from both sets A and B (such as 8, 10 and 12) only once.
Therefore, A U B = {3,4,5,6,7,8,9,10,11,12,14,16,18}.
Evan is picking marbles out of a bag. The results are recorded below. Red 24 Blue 16Yellow 10 Green 22Black 8 What is the experimental probability of picking a black marble? A. 90% B. 10% C. 1%
Answer:
Choice B: 10%.
Explanation:
The experimental probability of an event is the probability determined from the results of the experiment.
Now, in our case the experimental probability of picking a black marble would be the number of black marbles picked divided by the total number of marbles:
Experimental probability =( # black marbles / # total marbles ) x 100%
Now,
# total marbles = 24 + 16 + 10 + 22 + 8 = 80 marbles
and
# black marbles = 8 black marbles
Therefore,
Experimental probability =( 8 / 10 ) X 100%
Experimental probability = 10%
Hence, the correct choice is B.
Not sure on how to do this. Could really use some (quick) and easy help.
Okay, here we have this:
Considering the provided cone, we are going to calculate the requested volume, so we obtain the following:
So to calculate the volume of the oblique cone, we will substitute in the following formula:
Volume=(π*radius^2*height)/3
Volume=(π*(6ft/2)^2*4ft)/3
Volume=(π*9ft^2*4ft)/3
Volume=(π*9ft^2*4ft)/3
Volume=(36π ft^3)/3
Volume=12π ft^3
Finally we obtain that the volume of the cone is 12π cubic ft.
I need help with this math problem question number 2 please
The first question is true because a one-to-one function always has a different value in y.
For the second you need to find the inverse function to conclude that the function that they give you is correct. So
The first step is to replace the x with y and the y with x:
[tex]y=4x+3[/tex][tex]x=4y+3[/tex][tex]4y=x-3[/tex][tex]y=\frac{x-3}{4}[/tex]We find the same function as g(x). So the question is true.
For question 3, to discard a slant asymptote subtract the grade of the denominator from the numerator, if it is one we have a slant asymptote, else we don't have a slant asymptote:
[tex]2-2=0[/tex]We don't have slant asymptote, now find the vertical asymptotes
Equal the denominator to 0 and solve:
[tex]9x^2-6=0[/tex][tex]9x^2=6[/tex][tex]x^2=\frac{6}{9}[/tex][tex]x^2=\frac{2}{3}[/tex][tex]x=\sqrt{\frac{2}{3}},-\sqrt{\frac{2}{3}}[/tex]We have vertical asymptotes in these 2 values of x
Finally for horizontal asymptotes:
Find the limit of the function when x tends to infinity:
[tex]\lim _{x\to \infty }\left(\frac{-5x+2x^2}{9x^2-6}\right)[/tex]Divide for the denominator with the greatest potency:
[tex]\lim _{x\to \infty \:}\left(\frac{-\frac{5}{x}+2}{9-\frac{6}{x^2}}\right)[/tex]Separate terms
[tex]\frac{\lim _{x\to \infty \:}\left(-\frac{5}{x}+2\right)}{\lim _{x\to \infty \:}\left(9-\frac{6}{x^2}\right)}[/tex]Solve each one:
[tex]\lim_{x\to\infty\:}\left(-\frac{5}{x}+2\right)=-\lim_{x\to\infty\:}\left(\frac{5}{x}\right)+\lim_{x\to\infty\:}\left(2\right)=0+2=2[/tex][tex]\lim_{x\to\infty\:}\left(9-\frac{6}{x^2}\right)=\lim_{x\to\infty\:}\left(9\right)-\lim_{x\to\infty\:}\left(\frac{6}{x^2}\right)=9-0=9[/tex]Replace:
[tex]\frac{\operatorname{\lim}_{x\to\infty}(-\frac{5}{x}+2)}{\operatorname{\lim}_{x\to\infty}(9-\frac{6}{x^{2}})}=\frac{2}{9}[/tex]So have a horizontal asymptote in 2/9
A boxplot for a set of 68 scores is given below.How many scores are represented in the blue section of the boxplot?
Remember that the line inside the box represents the median of the data set; thus, 50 percent of the data set is to the left, and the remaining part of the data set is to the right of that line.
On the other hand, the right side of the box represents the upper quartile and marks 75% of the data.
Thus, between the upper quartile and the median, we can find 75%-50%=25% of the data.
Therefore, since the data set consists of 68 scores, the answer is
[tex]68\cdot0.25=17[/tex]The answer is 17 scores
how do I put these in slope intercept form?2y=x+10and3y=3x+15
we equalize the equations
[tex]\begin{gathered} x+5=\frac{1}{2}x+5 \\ x-\frac{1}{2}x=0 \\ \frac{1}{2}x=0 \\ x=0 \end{gathered}[/tex]the intersection is x=0
replace x on any equation to find y
[tex]undefined[/tex]on rectangle DEFG, it D is located at (-1 -1) and F is located at (4 -8), what is the length of GE
First we have to notice that the lenght GE is the same as the length DF, this comes from the fact that the diagonals in any rectangle have the same length. Now that we know that we have to remember that the distance between two points is given as:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In this case we have that:
[tex]\begin{gathered} d(G,E)=d(D,F)=\sqrt[]{(4-(-1))^2+(-8-(-1))^2} \\ =\sqrt[]{(5)^2+(-7)^2} \\ =\sqrt[]{25+49} \\ =\sqrt[]{74} \end{gathered}[/tex]Therefore the distance between GE is
[tex]\sqrt[]{74}[/tex]this is appoximately 8.602
Try once more Booker's father sells computer software and earns a 4.25% commission on every software package he sells. How much commission would he eam on a software package that sold for $15.725? Round to the nearest cent
He will earn the following amount:
[tex]x=(15.725)(0.0425)\Rightarrow x=0.6683125\Rightarrow x\approx0.67[/tex]So, he will earn a commission of approximately $0.67.
***Explanation***
*Since we are given that he will earn the 4.25% commission for each sale and he sold $15.725 we will operate as follows:
*The $15.725 will represent 100% of the price of the sale, and we will want to find what is 4.25% of that:
*We then multiply the total cost of the sale ($15.725) times the percentage we want to obtain (4-25%) and divide that by the percentage that the whole sale represents (100%), that is:
[tex]x=\frac{15.725\cdot4.25}{100}\Rightarrow x=15.725\cdot(0.0425)\Rightarrow x=0.6683125[/tex]So, we round to the nearest cent:
[tex]\Rightarrow x\approx0.67[/tex]So, the commission that he will earn for the $15.725 sale is approximately $0.67.
About 16% of drivers are uninsured. There were approximately 196 million drivers in the United States in 2003.* How many of these drivers were likely uninsured?
Answer:
Given that,
There were approximately 196 million drivers in the United States in 2003.
About 16% of drivers are uninsured.
To find the number of drivers were likely uninsured
we get,
the number of drivers were likely uninsured is,
[tex]\frac{\text{percent \%}}{100}\times Total\text{ number}=\frac{16}{100}\times196=31.36\text{ million}[/tex]the number of drivers were likely uninsured is 31.36 million.
what would be the correct solution for 7x=42
The given equation is
[tex]7x=42[/tex]We just have to divide the equation by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{42}{7} \\ x=6 \end{gathered}[/tex]Therefore, the solution is 6.7) Ryan wants to go to Launch Trampoline Center. The entrance fee is $5 plus $1.25 for every minute on the trampoline floor. He has a total of $80 in his wallet. a) Write an equation to determine x, the total number of minutes he can use the trampoline floor (3 pts). b) Solve your equation (3 pts). YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT c) What does your solution represent in this situation? (2 pts) 2 is also true for the
Ryan has a total of $80
It costs $5 and $1.25 for every minute on the trampoline floor
If the total cost = y and every minute is x
The required equation hence is
$y = $5 + $1.25x
Since, he has $80 in his wallet y = $80
1) $80 = $5 + $1.25x----------- required equation
2) we solve the equation thus
80 = 5 + 1.25x
80-5 = 1.25x
75 = 1.25x
75/1.25 = 1.25x/1.25
x =60 minutes
3) The solution represents the fact that it will cost Mr. Ryan 60 minutes to exhaust his $80 at Launch Trampoline center
Let (c) t be the number of customers In any restaurant t hours after 8 AM . Explain the meaning of each statement.c(n)=29
Let t = n
c(n) = 29 means that after n hours after 8AM, the number of customers in a restaurant is 29.