Part A)
According to the text, the equation that relates x and y is:
[tex]y=\frac{14}{x}[/tex]Substitute x=21 to find the value of y when x=21:
[tex]y=\frac{14}{21}[/tex]Simplify the expression:
[tex]\frac{14}{21}=\frac{7\cdot2}{7\cdot3}=\frac{2}{3}[/tex]Therefore, the value of y when x=21 is:
[tex]\frac{2}{3}[/tex]Part B)
To find the value of x when y=28, substitute y=28 and solve for x:
[tex]\begin{gathered} y=\frac{14}{x} \\ \Rightarrow28=\frac{14}{x} \\ \Rightarrow28x=14 \\ \Rightarrow x=\frac{14}{28} \\ \therefore x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of x when y=28 is:
[tex]\frac{1}{2}[/tex]Part C)
Since the pressure P is inversely proportional to the volume V, then:
[tex]P=\frac{k}{V}[/tex]Solve for k and substitute P=250kPa and V=1.7m^2 to find the constant of proportionality:
[tex]\begin{gathered} \Rightarrow k=PV \\ =(250\text{kPa})(1.7m^3) \\ =425\text{kPa}\cdot m^3 \end{gathered}[/tex]Therefore, the constant of proportionality for this situation is:
[tex]425\text{ kPa}\cdot m^3[/tex]Part D)
Substitute the value of k into the equation that shows the inverse relation between P and V:
[tex]\begin{gathered} P=\frac{k}{V} \\ \Rightarrow P=\frac{425\text{ kPa}\cdot m^3}{V} \end{gathered}[/tex]Therefore, the inverse variation equation model for this situation, is:
[tex]P=\frac{425\text{ kPa}\cdot m^3}{V}[/tex]Part E)
Substitute V=3.2m^3 to find the pressure under those conditions:
[tex]\begin{gathered} P=\frac{425\text{ kPa}\cdot m^3}{3.2m^3} \\ =132.8\text{kPa} \end{gathered}[/tex]Therefore, the pressure would be:
[tex]132.8\text{kPa}[/tex]Part F)
Isolate V from the equation and substitute P=150kPa:
[tex]\begin{gathered} V=\frac{425\text{ kPa}\cdot m^3}{P} \\ =\frac{425\text{ kPa}\cdot m^3}{150\text{ kPa}} \\ =2.83m^3 \end{gathered}[/tex]Therefore, the approximate volume would have to be equal to:
[tex]2.83m^3[/tex]Part G)
Since the temperature has decreased, the pressure must be lower according to the description provided in the text. Then, an inequality to model this situation would be:
[tex]P<\frac{k}{V}[/tex]Part H)
Substitute the value of k and V=3m^3:
[tex]\begin{gathered} P<\frac{425\text{ kPa}\cdot m^3}{3m^3} \\ \Rightarrow P<141.7\text{ kPa}^{} \end{gathered}[/tex]Part I)
Mathematically, all numbers under 141.7 satisfy the inequality from part H. Nevertheless, negative pressures do not have a physical meaning under the context of the Ideal Gas Law. Therefore, we must include the condition that P is greater than 0:
[tex]0Hi, can you help me answer this question please, thank you
The confidence interval 219.9 ± 57.6 is just equal to:
219.9 - 57.6 = 162.3
219.9 + 57.6 = 277.5
The confidence interval 219.9 ± 57.6 can also be written as between 162.3 and 277.5. In trilinear inequality, it is:
[tex]162.3<\mu<277.5[/tex]A survey of visitor at national park was conducted to determined the preferred activity. The survey results are shown in the table. Based on this information which prediction about the preferred activity for the next 200 visitors to the park is the most reasonable.
Given:
A survey of visitors at a national park is shown in the table.
a) The number of visitors who preferred champing is 28.
The number of visitors who preferred hiking tails is 22.
And The number of visitors who preferred champing is 6 more than visitors who preferred hiking tails.
Option a) is incorrect.
b) Hiking trails - water sports= 22-14=8
c) Water sports - biking trails = 14-16= -2
Option c) is incorrect.
d)
[tex]\begin{gathered} \text{Camping}=2\times water\text{ sports} \\ =2\times14 \\ =28 \end{gathered}[/tex]From the given options b) and d) shows the correct predictions.
Amoung these two options most reasonable is option d) for next 200 visitors.
Which method of finding probabilities do you prefer: lists, binompdf, binomcdf, nCr, etc.? Why?
For BinomPDF and BinomCDF we have a distribution that gives you the probability to have some number of successes, the difference is that PDF gives you only one specific number of successes, and the CDF gives you a range of successes probabilities.
Lists are the basic form to find a probability, you have to write all the cases and count the different groups of them, then divide by the total of cases.
NCR and NPR are the classic counting method to reach the number of combinations or permutations that a situation could have, is very useful and very quick to calculate the interest data or the number of combinations that may have a group of cases.
Which of these equations has infinitely many solutions? 3(1-2x + 1) = -6x + 2. 4 + 2(x - 5) = 1/2 {(4x - 12) (5x + 15) 3x - 5 = 5= 1/(5x () which statement explains a way you can tell the equation has infinitely many solutions? It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign. It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign. It is equivalent to an equation that has different variable terms on either side of the equation.
Answer
The equation with infinite solutions is Option B
4 + 2 (x - 5) = ½ (4x - 12)
The key way to know if an equation has infinite solutions is shown in Option B
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
Explanation
The key way to know if an equation has infinite solutions is when
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
So, we will check each of the equations to know which one satisfies that condition.
2x + 1 = -6x + 2
2x + 6x = 2 - 1
8x = 1
Divide both sides by 8
(8x/8) = (1/8)
x = (1/8)
This is not the equation with infinite solutions.
4 + 2 (x - 5) = ½ (4x - 12)
4 + 2x - 10 = 2x - 6
2x - 6 = 2x - 6
2x - 2x = 6 - 6
0 = 0
This is the equation with infinite solutions.
3x - 5 = (1/5) (5x + 15)
3x - 5 = x + 3
3x - x = 3 + 5
2x = 8
Divide both sides by 2
(2x/2) = (8/2)
x = 4
This is not the equation with infinite solutions.
Hope this Helps!!!
9. (a) The diagram below, not drawn to scale, shows a circle, where two lines intersect at point C. The points A, B, D and I lie on the circumference of the circle Note that ABDE is a right-angled triangle and BD is the diameter of the circle. A 66° D 78° C E B Determine, giving a reason for your answer, (1) ВСЕ 121 (ii) BDE 121 (iii) DBE 121
(i)
The angle 78° is supplementary to the angle BCE. Then we have:
[tex]\begin{gathered} 78\degree+B\hat{C}E=180\degree \\ B\hat{C}E=180\degree-78\degree \\ B\hat{C}E=102\degree \end{gathered}[/tex](ii)
When the vertex of a angle formed by two segments is located on the circle, the corresponding arc formed by the two segments is the double of the angle. Then we have:
[tex]\begin{gathered} B\hat{A}E=B\hat{D}E=\frac{arc\text{ BR}}{2} \\ B\hat{A}E=66\degree \\ \therefore B\hat{D}E=66\degree \end{gathered}[/tex](iii)
Since BDE is a right triangle, we have:
[tex]\begin{gathered} D\hat{B}E+B\hat{D}E+90\degree=180\degree \\ D\hat{B}E+66\degree+90\degree=180\degree \\ D\hat{B}E=180\degree-90\degree-66\degree \\ D\hat{B}E=24\degree \end{gathered}[/tex]A person who wants to get in shape goes to a local gym that advertises 31 training sessions for $1908. Find the cost of 133 training sessions. Round your answer to the nearest cent.
According to the given data we have the following:
31 training sessions=$1908
In order to calculate the cost of 133 training sessions we would have to apply the 3 rule.
So, if 31 training sessions__________________$1908
133 training sessions______________________x
Therefore, x=(133 training sessions*$1908)/31 training sessions
x=$253,764/31 training sessions
x=$8,186
The cost of 133 training sessions would be $8,186
Which of the following equations represents the line that passes throught the points (2, -6) and(-4,3)?A.y= -3/2x - 7B.y= -2/3x - 3C.y= -2/3x + 1/3D.y= -3/2x - 3
Given two points (x1, y1) and (x2, y2), the slope (m) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (2, -6) and (-4, 3), we get:
[tex]m\text{ = }\frac{3-(-6)}{-4-2}=\frac{9}{-6}=-\frac{3}{2}[/tex]slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
Replacing with point (2, -6) and m = -3/2, we get:
-6 = -3/2(2) + b
-6 = -3 + b
-6 + 3 = b
-3 = b
Finally, the equation is:
y = -3/2x - 3
Robert is selling his bulldozer at a heavy equipment auction. The auction company receives a commission of 5%of the selling price. If Robert owes $122,230 on the bulldozer, then what must the bulldozer sell for in order forhim to be able to pay it off?Select one:a.123,000b. 122,230C. 128,664d. 130,786
Answer:
Explanation:
The auction company receives a commission of 5% of the selling price.
Let the sale price of the bulldozer = x
[tex]\begin{gathered} \text{ Sale Price}=\text{ The amount Robert owes + Commision} \\ x=122,230+0.05x \end{gathered}[/tex]The equation is then solved for x:
[tex]\begin{gathered} x-0.05x=122230 \\ 0.95x=122230 \\ \text{ Divide both sides by 0.95} \\ \frac{0.95x}{0.95}=\frac{122,230}{0.95} \\ x=128663.20 \\ \text{ Round up} \\ x\approx128,664 \end{gathered}[/tex]The bulldozer must sell for $128,664 n order for him to be able to pay off the a
What is (4x ^ 2 + 14x + 6) ÷ (x+3)
Hello!
We have the expression:
[tex]\frac{4x^2+14x+6}{x+3}[/tex]Note that all numbers in the numerator are even. So, we can put 2 in evidence, look:
[tex]\frac{2(2x^2+7x+3)}{x+3}[/tex]Now, let's rewrite 7x as 6x+x:
[tex]\frac{2(2x^2+6x+x+3)}{x+3}[/tex]The first and second terms are multiples of 2x, so let's rewrite it putting it in evidence too:
[tex]\frac{2(2x(x+3)+x+3)}{x+3}[/tex]Another term appears twice: (x+3). So, we'll have:
[tex]\frac{2(x+3)(2x+1)}{x+3}[/tex]Canceling the common factors:
[tex]\frac{2\cancel{x+3}(2x+1)}{\cancel{x+3}}=2(2x+1)=\boxed{4x+2}[/tex]Answer:4x +2.
Find the derivative :f(x) = 6x⁴ -7x³ + 2x + √2
We need to find the derivative of the function
[tex]f\mleft(x\mright)=6x^{4}-7x^{3}+2x+\sqrt{2}[/tex]The derivative of a polynomial equals the sum of the derivatives of each of its terms.
And the derivative of each term axⁿ, where a is the constant multiplying the nth power of x, is given by:
[tex](ax^n)^{\prime}=n\cdot a\cdot x^{n-1}[/tex]Step 1
Find the derivatives of each term:
[tex]\begin{gathered} (6x^4)^{\prime}=4\cdot6\cdot x^{4-1}=24x^{3} \\ \\ (-7x^3)^{\prime}=3\cdot(-7)\cdot x^{3-1}=-21x^{2} \\ \\ (2x)^{\prime}=1\cdot2\cdot x^{1-1}=2x^0=2\cdot1=2 \\ \\ (\sqrt[]{2})^{\prime}=0,\text{ (since this term doesn't depend on x, its derivative is 0)} \end{gathered}[/tex]Step 2
Add the previous results to find the derivative of f(x):
[tex]f^{\prime}(x)=24x^{3}-21x^{2}+2[/tex]Answer
Therefore, the derivative of the given function is
[tex]24x^3-21x^2+2[/tex]The perimeter of the triangle PQR is 94cm. What is the length of PQ?
the length of PQ is 33 cm
Explanation:The perimeter of the triangle = 94 cm
The triangle is an isosceles triangle as two of its sides are equal
From the diagram:
PQ = RQ
Perimeter of triangle = PQ + PR + RQ
PR = 28 cm
94 = PQ + 28 + RQ
94 = 2PQ + 28
94 - 28 = 2PQ
66 = 2PQ
divide both sides by 2:
66/2 = 2PQ/2
PQ = 33
Hence, the length of PQ is 33 cm
Heads= 24Tails= 21Based on the table, what is the experimental probability that the coin lands on heads? Express your answer as a fraction
ok
Total number of results = 24 + 21
= 45
Probability that the coins lands on heads = 24/45
= 8/15
Result = 8/15
Use the sample data and confidence level given below to complete parts (a) through (d)A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1047 and x = 545 whosaid "yes." Use a 95% confidence level.A. find the best point of estimate of the population of portion p.B. Identify the value of the margin of error E. (E= round to four decimal places as needed.)C. Construct the confidence interval. (
a. The best point of estimate of the population of portion p is given by the formula:
[tex]p^{\prime}=\frac{x}{n}[/tex]where x is the number of successes x=545 and n is the sample n=1047.
Replace these values in the formula and find p:
[tex]p^{\prime}=\frac{545}{1047}=0.521[/tex]b. The value of the margin of error E is given by the following formula:
[tex]E=(z_{\alpha/2})\cdot(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}})[/tex]Where z is the z-score at the alfa divided by 2, q'=1-p'.
As the confidence level is 95%=0.95, then alfa is 1-0.95=0.05, and alfa/2=0.025
The z-score at 0.025 is 1.96.
Replace the known values in the formula and solve for E:
[tex]\begin{gathered} E=1.96\cdot\sqrt[]{\frac{0.521\cdot(1-0.521)}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.521\cdot0.479}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.2496}{1047}} \\ E=1.96\cdot\sqrt[]{0.0002} \\ E=1.96\cdot0.0154 \\ E=0.0303 \end{gathered}[/tex]c. The confidence interval is then:
[tex]\begin{gathered} (p^{\prime}-E,p^{\prime}+E)=(0.521-0.0303,0.521+0.0303) \\ \text{Confidence interval=}(0.490,0.551) \end{gathered}[/tex]d. We estimate with a 95% confidence that between 49% and 55.1% of the people felt vulnerable to identity theft.
A text book store sold a combined total of 347 history and physics textbooks in a week. The number of history textbooks sold was 79 more than the number of physics textbooks sold. How many textbooks of each type were sold?
Let the number of history textbooks be h and the number of physics textbooks be p.
It was given that the bookstore sells a combined total of 347 books. Thus we have:
[tex]h+p=347[/tex]It is also given that the number of history textbooks sold was 79 more than the number of physics textbooks. This gives:
[tex]h=p+79[/tex]We can substitute for h into the first equation:
[tex]p+79+p=347[/tex]Solving, we have:
[tex]\begin{gathered} 2p+79=347 \\ 2p=347-79 \\ 2p=268 \\ p=\frac{268}{2} \\ p=134 \end{gathered}[/tex]Substitute for p in the second equation, we have:
[tex]\begin{gathered} h=p+79 \\ h=134+79 \\ h=213 \end{gathered}[/tex]Therefore, there were 134 physics textbooks and 213 history textbooks.
whats the length of RS,UW,UVwhat is the value of x and y
In the given triangle,
it is given that,
U is the midpoint of RS, V is the midpoint of ST and W is the midpoint of RT
so,
UR = US
VT = VS
WT = WR
put the values,
UR = US
12 = US
so, RS = 2 x UR = 2 x 12 = 24
VT = VS
11 = 2x
x = 11/2
x = 5.5
so, TS = 2 x 11 = 22
WT = WR
3y = 15.9
y = 15.9/3
y = 5.3
so, RT = 2 x 15.9 = 31.8
also, UV = 1/2 RT
UV = 1/2 x 31.8 = 15.9
UW = 1/2x TS
UW = 1/2 x 22 = 11
VW = 1/2 RS
VW = 1/2 x 24 = 12
There were two candidates in a student government election for 7th gradeTreasurer, Kaya and Jay. Out of 322 total votes, Jay received 112 votes andKaya received 210. What percentage of the students voted for Kaya? Roundto the nearest tenth, if necessary.53.3%O 187.5%O 34.8%0 65.2%
Given:
There were the two candidate in the students governement election : kaya and jay.
Total votes=322
jay received 112 votes and Kaya received 210 votes.
To calculate the percetage of votes for kaya,
[tex]\begin{gathered} P=\frac{parts}{\text{whole}}\times100 \\ P=\frac{210}{322}\times100 \\ P=65.2 \end{gathered}[/tex]Answer: 65.2% of the students voted for Kaya.
If 9:x=x:4, then x = 3618246
Answer
Option D is correct.
x = 6
Explanation
9 : x = x : 4
To solve this, we know that ratios can be written in fraction form
(9/x) = (x/4)
[tex]\begin{gathered} \frac{9}{x}=\frac{x}{4} \\ \text{Cross multiply} \\ x^2=9\times4 \\ x^2=36 \end{gathered}[/tex]Take the square root of both sides
√(x²) = √(36)
x = 6
Hope this Helps!!!
Madelyn incorrectly followed the set of directions when she transformed pentagon PENTA.The directions are listed below the coordinate plane. What was the error Madelyn made?A. She rotated, but not 180°B. She reflected over the x-axis instead of the y-axisC. She translated 4 units to the left instead of the rightD. She did not make a mistake
Solution:
Given the transformation below:
Given the directions:
[tex]\begin{gathered} Rotate\text{ 180 degrees} \\ Reflect\text{ over the y-axis} \\ Translate\text{ 4 unnts to the right} \end{gathered}[/tex]Step 1: Give the coordinates of the vertices of pentagon PENTA.
Thus,
[tex]\begin{gathered} P(-5,5) \\ E(-3,\text{ 5\rparen} \\ N(-4,\text{ 4\rparen} \\ T(-3,\text{ 2\rparen} \\ A(-5,\text{ 2\rparen} \end{gathered}[/tex]step 2: Rotate the pentagon 180 degrees.
For 180 degrees rotation, we have
[tex]\begin{gathered} A(x,y)\to A^{\prime}(-x,\text{ -y\rparen} \\ where \\ A^{\prime}\text{ is an image of A} \end{gathered}[/tex]Thus, the coordinates of pentagon becomes
[tex]\begin{gathered} P(5,\text{ -5\rparen} \\ E(3,\text{ -5\rparen} \\ N(4,\text{ -4\rparen} \\ T(3,\text{ -2\rparen} \\ A(5,\text{ -2\rparen} \end{gathered}[/tex]The image is shown below:
step 3: Reflect over the y-axis.
For reflection over the y-axis, we have
[tex](x,y)\to(-x,y)[/tex]This, we have the image to be
step 4: Translate 4 units to the right.
For translation by 4 units to the right, we have
[tex](x,y)\to(x+4,\text{ y\rparen}[/tex]This gives
Hence, the mistake Madelyn made was that she reflected over the x-axis instead of the y-axis.
The correct option is B.
Find the missing sides of the following without using calculator
The missing sides are 3 and 3√3
Explanation:Let the opposite sides be represented by x, and the other missing side be y, then
[tex]\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]Using the above, we have:
[tex]\begin{gathered} \sin 60=\frac{x}{6} \\ \\ x=6\sin 60 \\ =6\times\frac{\sqrt[]{3}}{2} \\ \\ =3\sqrt[]{3} \end{gathered}[/tex]And
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \\ \cos 60=\frac{y}{6} \\ \\ y=6\cos 60 \\ =6\times\frac{1}{2} \\ \\ =3 \end{gathered}[/tex]The missing sides are 3 and 3√3
To raise money for charity, Bob and some friends are hiking across the continent of Asia. While out on the trail one day, one of his Jordian friends asks Bob for the temperature. He glances at his precision sports watch and sees that the temperature is -12.9 F. What is this temperature in degrees C Celsius ()?
ANSWER
[tex]-24.9[/tex]EXPLANATION
Given;
[tex]-12.9F[/tex]To convert to degree Celsius, we use the formula;
[tex]\begin{gathered} \frac{5}{9}(F-32) \\ \\ \end{gathered}[/tex]Substituting F;
[tex]\begin{gathered} \frac{5}{9}(-12.9-32) \\ =\frac{5}{9}\times-44.9 \\ =-\frac{224.5}{9} \\ =-24.94 \\ \cong-24.9 \end{gathered}[/tex]cam you show me the conversion from mm to cm to m to dm to km please
To determine the conversion from mm to cm to m to dm to km:
[tex]\begin{gathered} \operatorname{mm}\text{ => Millimtere} \\ \operatorname{cm}=>\text{centimetre} \\ m\Rightarrow\text{ metre} \\ dm\Rightarrow\text{ decimetre} \\ \operatorname{km}-\text{kilometre} \end{gathered}[/tex]Conversion from mm to cm =
[tex]10\text{ mm }\Rightarrow\text{ 1 cm}[/tex]Conversion from cm to m
[tex]100\operatorname{cm}\Rightarrow\text{ 1m}[/tex]Conversion from m to dm
[tex]1m\Rightarrow\text{ 10dm}[/tex]Conversion from dm to km
[tex]10000dm\Rightarrow\text{ }1\text{ km}[/tex]Hence the correct conversion are
10 mm = 1 cm
100 mm = 1 dm
1000 mm = 1 mm
1000000 mm = 1 km
Points A, B, and C are collinear and point B lies in between points A and C. If AB = 3x + 1, BC = 15, and AC = 7x + 1, find AC. Show work please
Answer:
AC = AB + BC + AC
AC= 3×+1+15+7×+1
AC= 3x+7×+1+15+1
AC=10×+17
ExplanationCheckX3(a) Move the cubes so that each stack has the same number of cubes.Then give the number of cubes in each stack.(b) What is the mean of 8, 6, 8, 4, and 9?(These are the numbers of cubes in the original stacks.)0(c) Are the values you found in parts (a) and (b) the same? Why or why not?No. But it didn't have to turn out that way. When the stacks are made equal,the number of cubes in each stack may be the mean of the original stacks.I need help with this math problem.
a. After moving the cubes so that each stack has the same number of cubes, we got 7 cubes in each stack.
Explanation:
In total, there are 35 cubes. Since there are 5 stacks, we divide 35 by 5 and got 7. Hence, there must be 7 cubes in each stack.
b. To determine the mean, simply do the same process above. Add the given numbers and divide the sum by the total numbers given.
[tex]8+6+8+4+9=35[/tex]Since there are 5 numbers, divide 35 by 5.
[tex]35\div5=7[/tex]Hence, the mean is 7.
c. Yes, the values in parts a and b are equal. When we make the stacks equal, the number of cubes in each stack must be the mean of the original stacks because the mean is the average of the number of stacks. (Option 3)
12. On Monday, a museum had 150 visitors. On
Tuesday, it had 260 visitors.
a. Choose Efficient Methods Estimate the
percent change in the number of visitors to
the museum.
b. About how many people would have to visit
the museum on Wednesday to have the same
percent change from Tuesday to Wednesday
as from Monday to Tuesday? Explain your
answer.
a. The percent change in the number of visitors to the museum is 73.33%
b. The people that would have to visit the museum on Wednesday to have the same
percent change is 450.
How to calculate the percentage?From the information given, on Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors. It should be noted that the increase will be:
= 260 - 150
= 110
The percentage increase will be:
= Increase in value / Original value × 100
= 110/150 × 100
= 73.33%
The number of people that should visit in Wednesday will be:
= 260 + (73.33% × 260)
= 260 + 190
= 450
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
A diver ascended 9/10 of a meter in 1/10 of a minute. What was the diver's rate of ascent?Show your work.
According to the given data we have the following:
A diver ascended 9/10 of a meter in 1/10 of a minute, hence a full minute=10/10 becuase 9/10*1/10=10/10
Therefore, in order to calculate the diver's rate of ascent we would make the following calculation:
diver's rate of ascent=9/10*10
diver's rate of ascent=9
Therefore, the rate would be 9 meters per minute
(3 x 10–6) x (7.07 x 1011)
we have
(3 x10^-6)x(7.07x10^11)
remmeber that adds the exponents
so
(3x7.07)x10^(-6+11)
(21.21)x10^5 ---------> 21.21)x10^5x(10/10)
2.121x10^6
what represents the factorization of the trinomial below?[tex] {x}^{2} - x - 20[/tex]
The expression given is,
[tex]x^2-x-20[/tex]Factorize the expression above
[tex]\begin{gathered} Break\text{ the expressions into two groups} \\ \left(x^2+4x\right)+\left(-5x-20\right) \\ Factorize\text{ out the common terms} \\ =x\left(x+4\right)-5\left(x+4\right) \\ \mathrm{Factor\:out\:common\:term\:}x+4 \\ =\left(x+4\right)\left(x-5\right) \end{gathered}[/tex]Hence, the answer is
[tex]\left(x+4\right)\left(x-5\right)[/tex]Which of the following names the figure in the diagram below?
O A. Triangle
O B. Prism
O C. Polygon
O D. Pyramid
O E. Cylinder
O F. Cube
Step 1
A triangular prism is a 3D shape that looks like an elongated pyramid. It has two bases and three rectangular faces.
Step 2:
A triangular prism has two triangular bases and three rectangular sides and is a pentahedron because it has five faces. Camping tents, triangular roofs and "Toblerone" wrappers -- chocolate candy bars -- are examples of triangular prisms.
Final answer
B. Prism
Find the angle of elevation from the base of one tower to the top of the second
This system can be represented by a triangle with base 350 m length and height 100 m length
The angle of elevation is given by:
[tex]\tan ^{-1}(\frac{100}{350})=\tan ^{-1}(\frac{2}{7})\approx0.28\text{ rad }\approx\text{ 16\degree}[/tex]Find a degree 3 polynomial that has zeros -3,3, and 5 and in which the coefficient of x^2 is -10.The polynomial is: _____
Given the polynomial has zeros = -3, 3, 5
so, the factors are:
[tex](x+3),(x-3),(x-5)[/tex]Multiplying the factors to find the equation of the polynomial:
So,
[tex]\begin{gathered} y=(x-3)(x+3)(x-5) \\ y=(x^2-9)(x-5) \\ y=x^2(x-5)-9(x-5) \\ y=x^3-5x^2-9x+45 \end{gathered}[/tex]But the coefficient of x^2 is -10.
So, Multiply all the coefficients by 2
So, the answer will be:
The polynomial is:
[tex]2x^3-10x^2-18x+90[/tex]