Answer:
16
Step-by-step explanation:
first primes: 2,3,5,7,11,13,17,19,23,29,31,37,41
then,cube 2 and square 3 to get 3.6510032e+15 which has 15+1=16 digits
Anya is wrapping gift boxes in paper. Each gift box is a rectangular prism. The larger box has a length, width, and height twice as large as the smaller box. Which statement shows the relationship between the surface areas of the gift boxes?A. The larger gift box has a surface area 2 times as large as the smaller gift box.B. The larger gift box has a surface area 4 times as large as the smaller gift box.C. The larger gift box has a surface area 6 times as large as the smaller gift box.D. The larger gift box has a surface area 8 times as large as the smaller gift box.thank you ! :)
The surface area of a rectangular prism is calculated using the formula:
[tex]\begin{gathered} SA=2LW+2LH+2WH \\ or \\ SA=2(LW+LH+WH) \end{gathered}[/tex]Let us assume that this is the surface area of the smaller box.
Now, let's represent the surface area of the bigger box by doubling the dimensions of the smaller box.
[tex]SA_{big}=2(2L\cdot2W+2L\cdot2H+2W\cdot2H)[/tex]Let's simplify this by factoring out the common factors.
[tex]\begin{gathered} SA_{b\imaginaryI g}=2(2L\cdot2W+2L\cdot2H+2W\cdot2H) \\ \\ SA_{b\imaginaryI g}=2\cdot2\cdot2(L\cdot W+L\cdot H+W\cdot H) \\ \\ SA_{big}=4\cdot2(LW+LH+WH) \\ \\ SA_{big}=4SA \end{gathered}[/tex]So the answer is option B (The larger gift box has a surface area 4 times as large as the smaller gift box).
Consider the following equation for line 1. Find the distance between I and the point V (5, -6) 1 —> y = -1
We must find the distance between the line y = -1 and the point V(5, -6).
Plotting a graph of the line and the point, we get:
From the graph, we see that the distance between the line and the point is d = 5 units.
Answer5 units
Jane has $10 more than Bill, Bill has $17 more than Tricia, and Tricia has $21 more than Steve. If the total amount of all their moneyis $171, how much morley does each have?Steve has $Tricia has $Bill has $and Jane has $
Jane has $10 more than Bill, Bill has $17 more than Tricia, and Tricia has $21 more than Steve. If the total amount of all their money
is $171, how much morley does each have?
Steve has $
Tricia has $
Bill has $
and Jane has $
Let
x ------> amount that Steve has
y -----> amount that Tricia has
z ----> amount that Bill has
w ----> amount that Jane has
we know that
x+y+z+w=171 -------> equation A
w=z+10 -----> equation B
z=y+17 ------> equation C
y=x+21 -----> equation D
step 2
isolate variable y in equation C
y=z-17 ------> equation E
substitute equation E in equation D
z-17=x+21
isolate the variable x
x=z-17-21
x=z-38 ------> equation F
step 3
substitute equation F, equation E, and equation B in equation A
so
(z-38)+(z-17)+(z+10)+z=171
solve for z
4z-45=171
4z=171+45
4z=216
z=$54
Find the value of x
x=z-38 ------> equation F
x=54-38=$16
Find the value of y
y=z-17 ------> equation E
y=54-17=$37
Find the value of w
w=z+10 -----> equation B
w=54+10=$64
therefore
Steve has $16Tricia has $37Bill has $54and Jane has $64I need help on 13 pls help Round each number to the place of the underlined digit
13)
The place of the underlined digit is the hundredth. We would consider the next digit to the right of the underlined digit. If it is lesser than 5, the value of the underlined digit remains the same but if it is greater than or equal to 5, the underlined digit increases by 1. Since it is 5 in this case, rounding to the nearest hundredth, it is
905.26
Solve the system by substitution. -10x + 4y = -18 x — у Submit Answer
You have the following system of equations:
-10x - 4y = -18
x = y
In order to solve the previous equation, replace x = y into the first equation, and solve for y, just as follow:
.10(y) - 4y = -18
-10y - 4y = -18 simplify left side
-14y = -18 divide by -14 both sides
y = 18/14
consider x = y:
x = y = 18/14
Complete the table for the properties of each quadrilateral
Step 1
State properties of each diagram by construction.
Given u=<-3.0,-9.5> and z=<-5.3,5.8>, what is the value of u times s
u.z = <-15.9, -55.1>
Explanation:Given
u = <-3.0, -9.5> and
z = <-5.3, 5.8>
u.z = <-3.0 * -5.3, -9.5 * 5.8>
= <-15.9, -55.1>
Does the graph have a minimum? Yes or NoThe minimum point is: (-3, 0) or noDoes the graph have a maximum? Yes or NoThe maximum point is: (, ) or noThe domain is:The range is:The relation is / is not a function.
• The graph does not have a minimum point
,• No
,• The graph has a maximum point.
,• The maximum point is (0,3)
,• The domain is {-3,3}
,• The range is {-4,3}
,• The relation is not a function since it fails the vertical line test.
Note: In the vertical line test, if a horizontal line drawn touches the graph at two points, it is not a function.
I need help, Solve the system of equations x=-2y and x-y=9
Given
x = -2y
and
x - y = 9
Replace 2nd equation with the 1st:
x - y = 9
(-2y) - y = 9
-2y - y = 9
-3y = 9
y = 9/ -3
y = -3
So, now we know x = -2y, thus
x = -2(-3) = 6
So, the solution is:
(6,-3)
For a line on a coordinate plane line with point A at (7,10) and point B at (4,6): 9) How long is the line?
A (7, 10)
B (4, 6)
Distance between two points = squared root (y2 - y1)2 + (x2 - x1)2
= squared root (6 - 10)^2 + (4 - 7)^2
= squared root (-4)^2 + (-3)^2
= squared root (16 + 9)
= squared root (25)
= 5
The line measures 5 units
Evaluate 6c if c = 4
To solve the exercise you can replace c = 4 in the given expression and then operate. So, you have
[tex]\begin{gathered} c=4 \\ \text{ Replacing} \\ 6c \\ 6(4)=24 \end{gathered}[/tex]Therefore, the value of 6c is 24, if c = 4.
word problem: Solve I=prt for t
Then
[tex]t=\frac{l}{pr}[/tex]19. For the simple interest loan whose terms are given below, find the principal required to reach the given future value at the end of the specified time. Future value: $9000 Interest rate: 3.2% Time: 5 years Principal: $
We will use the following formula:
[tex]PV=\frac{FV}{(1+i/12)^{12n}}[/tex][tex]undefined[/tex]Select the response that best represents the x - intercept
The points that best represents the x-intercept is E.
This comes from the fact that the x-intercept is the point where the graph cuts the x-axis.
5. Solve the division expression from the problem above (4 + 3). 4 3 A. 12 B. 1 c. 13 D. 14 3
A division as follow:
[tex]\frac{4}{3}[/tex]Can be solve as:
4/3 is equal to sum 1/3 four times:
[tex]\frac{4}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}[/tex]As 3/3 is equal to 1 unit:
[tex]=1+\frac{1}{3}[/tex]Writen as a mixed number:
[tex]1\frac{1}{3}[/tex]Question 9: Identify the co-vertices. *A. (-3, 4) and (-3, -2)B. (0, 1) and (-6, 1)C. (1, 1) and (-7, 1)D. (4, -3) and (-2, -3)
The general equation for a hyperbola is
[tex]\frac{(y-h)^2}{b^2}\text{ + }\frac{(x-k)^2}{a^2}\text{ = 1}[/tex]The equation we are considering is a hyperbola with the following parameters:
[tex]\begin{gathered} (k,\text{ h) = (-3 , 1)} \\ a^2\text{ = 9 } \\ \text{a = 3} \\ b^2\text{ = 16} \\ b\text{ = 4} \end{gathered}[/tex]The co-vertices can be obtained by locating the vertices along the x-axis
[tex]\begin{gathered} (-3\text{ + 3, 1) and (-3 -3 , 1)} \\ (0,\text{ 1) and (-6 , 1)} \end{gathered}[/tex]This corresponds to option B
(a) Find h(- 2), h(0), h(2) , and h(3) (b) Find the domain and range of h.(c) Find the values of x for which h(x) = 3 .(d) Find the values of x for which h(x) <= 3 .(e) Find the net change in h between x = - 3 and x = 3 .УА3h-303X
To find values of the function h at different x values, we go straight to that x value and find the corresponding y value of the graph.
From the graph, we have:
[tex]\begin{gathered} h(-2)=1 \\ h(0)=-1 \\ h(2)=3 \\ h(3)=4 \end{gathered}[/tex](b)The domain of a function is the set of x-values for which the graph of the function is defined.
The range of a function is the set of y-values for which the graph of the function is defined.
Looking at the graph, we see that from
x = - 3 to x = 4, the function is defined.
Also, from
y = - 1 to y = 4, the function is defined.
Thus, we can write the domain and range as >>>>>
[tex]\begin{gathered} D=-3\leq x\leq4 \\ R=-1\leq y\leq4 \end{gathered}[/tex](c)h(x) = 3 means y = 3
We will draw a horizontal line at y = 3 and see the points at which that line and curve crosses. Then, we will draw a perpendicular from that point to the x-axis. These are the values of x for which y = 3.
The graph:
We see from the graph drawn that for x = - 3, x = 2, and x = 4, the value of the function h is 3.
So,
[tex]x=-3,2,4[/tex](d)The values of x for which the function is ≤ 3 can be found by again drawing a line y = 3 and finding the places where the graph is BELOW that line.
Graph:
So, we can see that from x = - 3 to x = 2, the function is less than or equal to 3.
Thus,
[tex]-3\leq x\leq2[/tex](e)From x = - 3 to x = 3, the function changes several values. But the net change can be found by finding the respective values of the function at x = - 3 and at x = 3 and finding the difference.
At x = - 3, the function has a value of "3".
At x = 3, the function has a value of "4".
Thus, the net change is 4 - 3 = 1
Net Change = 1
A lake is stocked with 20 carp. If the carp population grows at a rate of 7.5% per month, when will the pond contain 500 carp? Round your answer to the nearest hundredth.
We have a lake with 20 carp and a gowth rate of 7.5% per month, so the equation of the population at time t is:
[tex]\begin{gathered} P(t)=P_0\cdot(1+\frac{7.5}{100})^t \\ \text{Where t is the time in months, P}_0\text{ is the initial population (t=0) and P(t) is the population at time t.} \end{gathered}[/tex]So, we need to find the value of t when P(t)=500 and P0 (the initial population) is 20:
[tex]\begin{gathered} P(t)=500=20\cdot(1+\frac{7.5}{100})^t \\ \frac{500}{20}=1.075^t \\ \log (25)=\log (1.075^t) \\ \log (25)=t\cdot\log (1.075) \\ t=\frac{\log(25)}{\log(1.075)}=44.51 \end{gathered}[/tex]The lake contain 500 carp in 44.51 months.
5 Explain how the graph can be used to check that the ratios are equivalent.
Here, we want to use the graph to check that the ratios are equivalent
To do this, we need to establish that there is a linear relationship between the width and the length
We identify the points given and plot them on the graph
After plotting, we join the points with a straight line passing through the points
Now, after joinin the points with a straight line, we identify the length 20 and trace it to the line. At the point that it touches the line, we get the corresponding width value
We do same for the length 10
Then we fill in the values on the table, then reduce the terms to the lowest values
We will deduce that the lowest value for the points we got through th graph will be the same as that already on the table
Then, with this we can conclude that the ratios are equaivalent and we have succeeded in using the graph to show this
Solve the quadratic equation by the square root method and write the solutions in radical forms simplify the solutions
Given the following quadratic equation:
[tex](8x+20)^2=50[/tex]We will solve the equation by the square root method.
Taking the square root of both sides:
[tex]\begin{gathered} \sqrt{(8x+20)^2}=\pm\sqrt{50} \\ \\ 8x+20=\pm\sqrt{50} \\ Note:\sqrt{50}=\sqrt{25*2}=5\sqrt{2} \\ \\ 8x+20=\pm5\sqrt{2} \end{gathered}[/tex]Subtract 20 from both sides
[tex]\begin{gathered} 8x+20-20=-20\pm5\sqrt{2} \\ 8x=-20\pm5\sqrt{2} \end{gathered}[/tex]Divide both sides by 8
[tex]x=\frac{-20\pm5\sqrt{2}}{8}[/tex]So, the answer will be:
[tex]x=\frac{-20+5\sqrt{2}}{8};or;\frac{-20-5\sqrt{2}}{8}[/tex]Select the correct answer from each drop-down menu.y 110+8C46+4+2BАAB-5-448--2AABC goes through a sequence of transformations to form AA'BC. The sequence of transformations involved is afollowed by a
The Solution.
It was a translated 2 units right, and then reflected over the y- axis.
Which of the following shows the simplified function of sine squared x over the quantity 1 plus cosine x end quantity question mark
Answer
Explanation
Given:
[tex]\frac{sin^2x}{1+cosx}[/tex]To determine the simplified function of the above given, we first use the Pythagorean identity:
[tex]cos^2(x)+sin^2(x)=1[/tex]Hence,
[tex]sin^2x=1-cos^2x[/tex]We plug in what we know:
[tex]\begin{gathered} \frac{s\imaginaryI n^{2}x}{1+cosx}=\frac{1-cos^2x}{1+cosx} \\ Simplify\text{ and rearrange} \\ =\frac{-(cos^2x-1)}{1+cosx} \\ =\frac{-(cosx+1)(cosx-1)}{1+cosx} \\ =-(cosx-1) \\ =-cosx+1 \\ =1-cosx \end{gathered}[/tex]Therefore, the answer is:
[tex]1-cos\text{ }x[/tex]The price per share of a certain stock fell from $46.44 to close at $43.00. Find the percent of decrease in price. Round to the nearest tenth as needed
Original price: $46.44
Price after variation: $43
Variation= 46.44-43 = $3.44
46.44 x = 3.44
Solve for x:
x= 3.44/46.44
x= 0.07407
Multiply by 100:
0.074 x 100 = 7.4%
I have trouble with system of equations. I always get one right and one wrong
To solve the system of equations above:
1. Rewrite the second equation to be similar to the frist equation:
[tex]\begin{gathered} \text{Add 2 in both sides of the equation:} \\ -x+2y-2+2=0+2 \\ -x+2y=2 \end{gathered}[/tex]2. Multiply the equation you get in step 1 by -1:
[tex]\begin{gathered} -1(-x+2y=2) \\ x-2y=-2 \end{gathered}[/tex]As you get that both equations in the system are the same (x-2y= -2) (the lines are the same) the system has infinitely many solutions (all the values of x and y are solutions for the system)
[tex]\begin{gathered} -2y=-2-x \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]It’s an essay with five point explain how to use an estimation to help find the product of two decimals give an example with both estimated an actual answers it is in math
In mathematics, estimation means approximating a quantity to the required accuracy. This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.
To approximate numbers,
We can give the following examples
Example 1
[tex]8.9\times2.1[/tex]We can approximate the numbers as follow
[tex]\begin{gathered} \text{For 8.9} \\ we\text{ will round 9 up to give 1} \\ \text{This is then added to 8 to give 9} \\ \text{Thus} \\ 8.9\cong9 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 2.1 \\ we\text{ will round down 1 to 0} \\ So\text{ that 2.1}\cong2 \end{gathered}[/tex]Thus, we will have
[tex]8.9\times2.1\cong9\times2=18[/tex]Therefore, the approximated value is 18
The actual answer is
[tex]8.9\times2.1=18.69[/tex]We can look at another example
[tex]11.23\times36.06[/tex]Thus
[tex]\begin{gathered} 11\times36=396 \\ \end{gathered}[/tex]The actual answer is
[tex]11.23\times36.06=404.95[/tex]In both cases, we can see that the approximated values and the actual values are not so far from each other.
Find the value of 3y-4 given that 2y-6=8Simplify your answer as much as possible
Given:
[tex]2y-6=8[/tex]is given expression
Required:
We need to find the value of
[tex]3y-4[/tex]Explanation:
First simplify the given expression
[tex]\begin{gathered} 2y-6=8 \\ 2y=14 \\ y=7 \end{gathered}[/tex]now put the value of y in reauired
[tex]3y-4=2*7-4=21-4=17[/tex]Final answer:
Required value is 17
If BD= 4x+3, find x. Round your answer to answer to the nearest tenth if necessary BC= 37CD = x-3
ok
BD = 4x + 3
BC = 37
CD = x - 3
37 + x - 3 = 4x + 3
37 - 3 - 3 = 4x - x
37 - 6 = 3x
31 = 3x
x = 31/3
That's all
Hello :) Can you help me understand this and break it down for me after solving please thanks in advance
The domain of a function is the set of x-values that you can put into any given equation. For the equation:
[tex]g(x)=\sqrt[3]{x+8}[/tex]There are no restrictions, therefore, the domain is all real numbers:
[tex]D\colon(-\infty,\infty)[/tex]---------------------------------------------------
[tex]\begin{gathered} x=16 \\ g(16)=\sqrt[3]{16+8}=\sqrt[3]{24}\approx2.88 \end{gathered}[/tex]adding and subtracting polynomials find each sum or differenceplease do minimum steps
Solve the sums or differences between similar terms.
[tex]\begin{gathered} 5ax^2+3ax^2+3a^2x-5ax-5x+7x \\ 8ax^2+3a^2x-5ax+2x \end{gathered}[/tex]The vertices of ABC are A(2, - 2), B(-2, - 2), and C(4,4). For the translation below, give the vertices of AA'B'C'. T(2.4 (ABC) The vertices of AA'B'C'are A' . B and O? (Simplify your answers. Type ordered pairs.)
The vertices of triangle A'B'C' are A' (4, 2), B'(0, 2) and C'( 6, 8)
Explanations:The vertices of ABC are A( 2, -2), B(-2, -2), and C(4, 4)
[tex]\begin{gathered} \text{The translation T}_{<2,\text{ 4>}}\text{ means that }\Delta ABC\text{ is translated by 2 units to the right and } \\ 4\text{ units upwards} \end{gathered}[/tex]All the vertices will be translated by 2 units in the +ve x direction and 4 units in the +ve y direction.
If a vertex M(x, y) is translated by 2 units in the x-direction, and 4 units in the y-direction, the new coordinates will become M'(x+2, y+4)
Therefore, the vertices of triangle ABC will become:
A' (2+2, -2+4) = A'(4, 2)
B'(-2+2, -2+4) = B'(0, 2)
C'(4+2, 4+4) = C'(6, 8)