Given:
Rita earns scores of 83, 87, 85, 88, and 90 on her five-chapter tests for a certain class.
And a grade of 82 on the class project.
First, we will find the average of the scores of the five tests
[tex]5-tests\text{ }average=\frac{83+87+85+88+90}{5}=\frac{433}{5}=86.6[/tex]The overall average for the course is computed as follows:
30% of the course grade ⇒ Rita get 86.6
30% of project grade ⇒ Rita get 82
40% of the final exam ⇒ let Rita get x
We will find the value of x provided that Rita will earn a "B" score
a "B" is an overall score greater than or equal to 80, but less than 90
So, we will find (x) as follows:
[tex]\frac{30*86.6+30*82+40*x}{100}\ge80[/tex]Solve the inequality to find (x):
[tex]\begin{gathered} 5058+40x\ge8000 \\ 40x\ge8000-5058 \\ 40x\ge2942 \\ x\ge\frac{2942}{40} \\ \\ x\ge73.55 \end{gathered}[/tex]And the upper limit will be as follows:
[tex]\frac{30\times86.6+30\times82+40x}{100}<90[/tex]Solve to find (x):
[tex]\begin{gathered} 5058+40x<9000 \\ 40x<9000-5058 \\ 40x<3942 \\ x<\frac{3942}{40} \\ \\ x<98.55 \end{gathered}[/tex]So, the answer will be:
To obtain a "B", Rita needs to score between 73.55 and 98.55
Find the missing the side length leave the answer as radical form. Question 3.
In order to calculate the value of x, we can use the cosine relation of the angle 60°.
The cosine is equal to the length of the adjacent leg to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \cos(60°)=\frac{2}{x}\\ \\ \frac{1}{2}=\frac{2}{x}\\ \\ x=4 \end{gathered}[/tex]Now, to calculate the value of y, we can use the tangent relation of the angle 60°.
The tangent is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan(60°)=\frac{y}{2}\\ \\ \sqrt{3}=\frac{y}{2}\\ \\ y=2\sqrt{3} \end{gathered}[/tex]a surveyor locating the corners of a four-sided of property started at one corner and walk 200 feet in the direction of N80°E 5o reach the next corner he turned and walked to north 160 feet to the next corner of the property he did turn and walk due west to get to the 4th corner of the property finally he walked in the direction S15°E to get back to the starting point. What is the area of the property is in square feet?
we have three figures, we must find the area of each one and at the end, add them
lower triangle
we must find x and y to calculate the area, we will use trigonometric ratios
[tex]\begin{gathered} \sin (80)=\frac{x}{200} \\ \\ x=200\sin (80) \\ x=197 \end{gathered}[/tex][tex]\begin{gathered} \sin (10)=\frac{y}{200} \\ \\ y=200\sin (10) \\ y=34.73 \end{gathered}[/tex]now calculate the area
[tex]\begin{gathered} A_{T1}=\frac{b\times h}{2} \\ \\ A_{T1}=\frac{y\times x}{2}=\frac{34.73\times197}{2} \\ \\ A_{T1}_{}=3420.9 \end{gathered}[/tex]the area of the triangle is 3420.9 square feet
Rectangle
we have the height (160ft) and the base we calculate it in the previous step (x=197ft)
the area is
[tex]\begin{gathered} A_R=b\times h \\ A_R=197\times160 \\ A_R=31520 \end{gathered}[/tex]the area of the rectangle is 31520 square feet
Left Triangle
we must use trigonometric ratios to calculate Z
[tex]\begin{gathered} \tan (15)=\frac{Z}{160+34.73} \\ \\ Z=194.73\tan (15) \\ Z=52.18 \end{gathered}[/tex]and the area of the triangle is
[tex]\begin{gathered} A_{T2}=\frac{b\times h}{2} \\ \\ A_{T2}=\frac{Z\times(160+34.73)}{2}=\frac{52.18\times194.73}{2} \\ \\ A_{T2}=5080.5 \end{gathered}[/tex]Total area
[tex]\begin{gathered} A=A_{T1}+A_R+A_{T2} \\ A=3420.9+31520+5080.5 \\ A=40021.4 \end{gathered}[/tex]the total area is 40,021.4 square feet
Solve using the elimination method:4x + y + 5z = -40-3x + 2y + 4z = 10x - y - 2z = -2
Let's take
4x + y + 5z = -40 (Eq1)
-3x + 2y + 4z = 10 (Eq2)
x - y - 2z = -2 (Eq3)
Now create a new system using elimination
-2* (4x + y + 5z = -40) (Eq1)
1* (-3x + 2y + 4z = 10) (Eq2)
----------------------------------
-11x - 6z = 90 (Eq4)
Use elimination again
1* (-3x + 2y + 4z = 10) (Eq2)
2* (x - y - 2z = -2) (Eq3)
---------------------------------------
-x = 6 (Eq5)
From Equation 5 we have that
x = -6
Replace the value of x in Equation 4 and clear z
-11(-6) - 6z = 90
-6z = 90 - 66
-6z=24
z = 24/-6
z = -4
Replace x and z in equation 3 and clear y
-6 - y - 2*(-4) = -2
-y + 8= -2 +6
-y = 4 - 8
-y= -4
y = 4
Determine if the measures create aight triangle.13m5m12m
use the pythagorean theorem to see if the measurements create a right trinangle.
remember the addition of the squared shorter sides must be equal to the largest side squared
[tex]a^2+b^2=c^2[/tex][tex]5^2+12^2=13^2[/tex][tex]\begin{gathered} 5^2+12^2=169 \\ 13^2=169 \\ \\ 169=169 \end{gathered}[/tex]How to create a table like the following for the following problem:
We have to graph the function:
[tex]y=-\frac{5}{2}+\cos \lbrack3(x-\frac{\pi}{6})\rbrack[/tex]We can start from known points of the cosine function and then find the values of y.
We know the exact values of cosine for the following angles:
[tex]\begin{gathered} \cos (0)=1 \\ \cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2} \\ \cos (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2} \\ \cos (\frac{\pi}{3})=\frac{1}{2} \\ \cos (\frac{\pi}{2})=0 \\ \cos (\frac{2\pi}{3})=-\frac{1}{2} \\ \cos (\frac{3\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \cos (\frac{5\pi}{6})=\frac{-\sqrt[]{3}}{2} \\ \cos (\pi)=-1 \end{gathered}[/tex]We have half the cycle here. We will complete the values later.
We then can find the value of x that matches the arguments of the known vlaues of the cosine as:
[tex]\begin{gathered} \alpha=3(x-\frac{\pi}{6}) \\ x=\frac{\alpha}{3}+\frac{\pi}{6} \end{gathered}[/tex]where α is the argument of the known values of cosine (0, π/6, π/4, ...).
We then can calculate the values of x for each one as:
[tex]\begin{gathered} x_1=\frac{0}{3}+\frac{\pi}{6}=\frac{\pi}{6} \\ x_2=\frac{1}{3}\cdot\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{18} \\ x_3=\frac{1}{3}\cdot\frac{\pi}{4}+\frac{\pi}{6}=\frac{\pi}{12}+\frac{\pi}{6}=\frac{3\pi}{12}=\frac{\pi}{4} \\ x_4=\frac{1}{3}\cdot\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{9}+\frac{\pi}{6}=\frac{5\pi}{18} \\ x_5=\frac{1}{3}\cdot\frac{\pi}{2}+\frac{\pi}{6}=\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{3} \\ x_6=\frac{1}{3}\cdot\frac{2\pi}{3}+\frac{\pi}{6}=\frac{2\pi}{9}+\frac{\pi}{6}=\frac{7\pi}{18} \\ x_7=\frac{1}{3}\cdot\frac{3\pi}{4}+\frac{\pi}{6}=\frac{\pi}{4}+\frac{\pi}{6}=\frac{5\pi}{12} \\ x_8=\frac{1}{3}\cdot\frac{5\pi}{6}+\frac{\pi}{6}=\frac{5\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{9} \\ x_9=\frac{1}{3}\pi+\frac{\pi}{6}=\frac{\pi}{2} \end{gathered}[/tex]We then can calculate the value of y for each of this points, using the known values of the cosine, as:
[tex]\begin{gathered} x=\frac{\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \\ x=\frac{4\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{3}}{2}=\frac{\sqrt[]{3}-5}{2} \\ x=\frac{\pi}{4}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{2}}{2}=\frac{\sqrt[]{2}-5}{2} \\ x=\frac{5\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{1}{2}=-\frac{4}{2}=-2 \\ x=\frac{\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{7\pi}{18}\Rightarrow y=-\frac{5}{2}-\frac{1}{2}=-\frac{6}{2}=-3 \\ x=\frac{5\pi}{12}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{2}}{2}=\frac{-5-\sqrt[]{2}}{2} \\ x=\frac{4\pi}{9}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{3}}{2}=\frac{-5-\sqrt[]{3}}{2} \\ x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \end{gathered}[/tex]We can repeat this process for the rest of the cycle, but in this case, we will only graph the mean value (when cosine is 0) and the extreme values (when cosine is -1 or 1).
We can list this as:
[tex]\begin{gathered} \cos (\pi)=-1 \\ \cos (\frac{3\pi}{2})=0 \\ \cos (2\pi)=1 \end{gathered}[/tex]We can relate this values to x using the formula we used before:
[tex]\begin{gathered} x_{10}=\frac{1}{3}(\pi)+\frac{\pi}{6}=\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{2} \\ x_{11}=\frac{1}{3}(\frac{3\pi}{2})+\frac{\pi}{6}=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2\pi}{3} \\ x_{12}=\frac{1}{3}(2\pi)+\frac{\pi}{6}=\frac{2\pi}{3}+\frac{\pi}{6}=\frac{5\pi}{6} \end{gathered}[/tex]Now, we calculate the values of y as:
[tex]\begin{gathered} x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \\ x=\frac{2\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{5\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \end{gathered}[/tex]Using this particular values for the complete cycle we can complete the table as:
Points W, X, and Y are collinear. WY = 25 andthe ratio of WX to XY is 2:3. Find WX.wY
WX is 10
Explanation goes as follows:
WY = 25 from the question given
adding the ratios together, we will have 2+3= 5
WX : XY = 2: 3
To find WX, we will simply say;
WX = 2/5 multiplied by 25
WX = 2/5 x 25
WX = 50/5
WX=10
Like-wise to find WY
we will simply say;
WY = 3/5 multiplied by 25
WY = 3/5 x 25
WY = 75/5
WY =15
During 7 1/2 months of hibernation, a black bear experienced a weight loss of 64.4 lbs. on average what was the bears weight change per month. Round to the nearest tenth.
Hibernation time: 7 1/2 months = 15/2 months
Weight loss: 64.4 lbs
We can calculate the average weight change per month using the equation:
average_weight_loss = weight_loss / time
We know that:
weight_loss = 64.4 lbs
time = 15/2 months = 7.5 months
Then, using the equation above:
average_weight_loss = 64.4 lbs / 7.5 months
average_weight_loss = 8.5867 lbs/month
To the nearest tenth, the average monthly weight loss of the black bear was 8.6 lbs/month.
After how many cakes will their savings be the same for both? b) What will their savings be?
Let "s" represent the amount saved in the bank account and "c" the number of cakes sold.
Jane (J)
Has a starting balance of $70 and she sells "c" cakes for $25 each, you can symbolize the earnings of the cake sales as 25c
You can express the total amount saved using the following expression
[tex]s_J=70+25c[/tex]Miriam (M)
Has a starting balance of $100 and shells cakes for $20 each, you can symbolize the total earnings for her cakes sales as 20c
So the total amount saved can be expressed as:
[tex]s_M=100+20c[/tex]a) To determine how many cakes they must sell so that their savings will be the same, you have to equal both expressions and calculate the value of c:
[tex]\begin{gathered} s_J=s_M \\ 70+25c=100+20c \end{gathered}[/tex]To calculate for c, the first step is to pass the term containing the variable to the left by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 70+25c-20c=100+20c-20c \\ 70+5c=100 \end{gathered}[/tex]Repeat the process to pass 70 to the right side of the expression
[tex]\begin{gathered} 70-70+5c=100-70 \\ 5c=30 \end{gathered}[/tex]And divide both sides by 5 to reach the value of c
[tex]\begin{gathered} \frac{5c}{5}=\frac{30}{5} \\ c=6 \end{gathered}[/tex]After selling 6 cakes both Jae and Miriam will have saved the same amount.
b)
To determine what will their savings be, you have to replace either one of the expressions with c=6 and calculate for s:
[tex]\begin{gathered} s_J=70+25c \\ s_j=70+25\cdot6 \\ s_j=220 \end{gathered}[/tex]If you solve it using Miriam's expression the result must be the same:
[tex]\begin{gathered} s_M=100+20c \\ s_M=100+20\cdot6 \\ s_M=220 \end{gathered}[/tex]As you see using either equation we arrived to the same result, after selling 6 cakes their total saves will be $220
why is this correct?
Trapezoid area = (7+3)/2• height = 10/2 •height
Parallelogram area= 5 • height
Then ,Candy is correct ,both areas are EQUAL
The area of parallelogram is 5•H
The area of trapezoid is 10•H divided by 2 ,or. 5•H
Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true?
If f is an even function, then f can't have an inverse, because even functions don't have inverses. Therefore the correct answer is A.
12. A local poll finds that 0.35 of all citizens approve of the mayor's policies. What fraction of citizens approve? Write the answer in lowest terms. O 3/5 035/100 O 7/20 O 35/50
Explanation:
Writing 0.35 as a fraction we have:
[tex]\frac{35}{100}[/tex]And we can simplify dividing both numerator and denominator by 5:
[tex]\frac{\frac{35}{5}}{\frac{100}{5}}=\frac{7}{20}[/tex]Answer:
7/20
Sharon Nguyen has $25,000 to invest and believes that she can earn 8% compounded semiannually. Find the amount if she invests for 10 years
Solution:
Given:
[tex]\begin{gathered} P=\text{ \$25,000} \\ r=8\text{ \%}=\frac{8}{100}=0.08 \\ t=10\text{years} \\ n=\text{twice a year(semiannually),}n=2 \end{gathered}[/tex]
To get the amount, we use the compound interest formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substituting the given values into the formula,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=25000(1+\frac{0.08}{2})^{2\times10} \\ A=25000(1+0.04)^{20} \\ A=25000(1.04)^{20} \\ A=25000\times1.04^{20} \\ A=\text{ \$54,778.08} \end{gathered}[/tex]
Therefore, the amount after 10 years is $54,778.08
how do i findFind the domain of f ∘ g in the equation
First, we need to find the composite function of f ∘ g.
We need to write the function f(x) in terms of g(x).
Then:
[tex]\begin{gathered} (fog)(x)=\frac{6}{g(x)+7}=\frac{6}{x+5+7} \\ =\frac{6}{x+12} \end{gathered}[/tex]Now, to find the domain we need to look at the x values that the function can take.
The function is a rational function, then the domain is given using the denominator because it can be equal to zero.
x+12 = 0
x=-12
Therefore, the domain is the interval (-∞.-12)U(-12,∞)
2. Ashley purchased a new television for$2400 and a surround sound for $980.The sales tax is 7%. Find the totalamount of money that Ashley will payfor her two items including tax.
Ashley has to pay $2400 + $980 = $3380 for both items.
We need to calculate the 7% of this amount to find how much she has to pay in taxes.
[tex]3380\cdot\frac{7}{100}=236.6[/tex]Finally, the total amount she has to pay is $3380 + $236.6 = $3616.6
Billy is comparing gasoline prices at two different gas stationsAt the first gas station the equation c = 2.80g gives the relationship between g the number of gallons of gasoline and c the total cost in dollarsAt the second gas station the cost of 2.5 gallons of gasoline is $8.30 and a cost of $5 of gasoline is $16.60how much per gallon would Billy save by going to the less expensive gas station
Answer
Billy would save $0.52 by going to the less expensive gas station (which is the first gas station).
Explanation
At the first station,
c = 2.80g
c = cost of gasoline
g = number of gallons of gasoline
The cost of 1 gallon of gasoline at this station will be obtained by putting in g = 1
c = 2.80g
g = 1 gallon
c = 2.80 (1)
c = 2.80 dollars per gallon
Cost per gallon = 2.80 dollars
At the second station,
2.5 gallons = 8.30 dollars
5 gallons = 16.60 dollars
The cost of 1 gallon at this station will be
1 gallon = (8.30/2.5) = (16.60/5) = 3.32 dollars
Cost per gallon = 3.32 dollars
We can see that gasoline is cheaper at the first station and the difference in price per gallon (which is the amount that will be saved by going to the less expensive gas station) is
3.32 - 2.80 = 0.52 dollars
Hope this Helps!!!
if I can...give me any word problems that have to deal with multiply and dividing rational numbers
Determine whether the given numbers are rational or irrational.
(a) 1.75 (b) 0.01 (c) 0.5 (d) 0.09 (d) √3
So, rational can be any fraction number, but it can not be in under root form.
Thus the only option (d) is irrational number. all other are rational number.
[tex]\begin{gathered} \text{The product of rational number }\frac{4}{7}\text{ and }\frac{3}{5\text{ }}is? \\ \Rightarrow\frac{4}{7}\times\frac{3}{5} \\ \Rightarrow\frac{12}{35} \end{gathered}[/tex]you Owens 15 books before Christmas,but after Christmas you now own 21 books. is this a decrease or increase explain.find the percent of change
Let's begin by listing out the given information:
Before Christmas: 15 books
After Christmas: 21 books
This is an increase
The percentage increase is given by % increase = Increase ÷ Original Number × 100:
[tex]\begin{gathered} \text{\%}increase=Increase\div OriginalNumber\times100\text{\%} \\ \text{\%}increase=\frac{21-15}{15}\times100\text{\%} \\ \text{\%}increase=\frac{6}{15}\times100\text{\%}=40\text{\%} \\ \text{\%}increase=40\text{\%} \end{gathered}[/tex].The 9th-grade students are sellingI chocolate bars for a fundraiser.Each student is encouraged tosell at least 12 chocolate bars.Pam sells 3 bars on Monday and4 bars on Tuesday. Write andsolve an inequality to find the remainingpossible number of bars Pam cansell to reach the goal.
Answer:
The possible number of bars Pam can sell to reach the goal must be at least 5 bars.
Explanation;
Let the remaining number of bars Pam can sell to reach the goal be "x"
If Pam sells 3 bars on Monday and 4 bars on Tuesday, the total number of bars sold will be 3 + 4 = 7bars
Also if each student is encouraged to sell at least 12 chocolate bars, the required inequality expression to solve will be:
[tex]\begin{gathered} 4+3+x\ge12 \\ 7+x\ge12 \\ x\ge12-7 \\ x\ge5 \\ \end{gathered}[/tex]This shows that the possible number of bars Pam can sell to reach the goal must be at least 5 bars.
Content attributionQUESTION 5.1 POINTTranslate and solve: 6 greater than b is greater than 84.Give your answer in interval notation.Provide your answer below:
6 greater than b is
[tex]=b+6[/tex]6 greater than b is greater than 84. is represented as
[tex]b+6>84[/tex]Step :Subtract 6 from both sides
[tex]\begin{gathered} b+6>84 \\ b+6-6>84-6 \\ b>78 \\ \end{gathered}[/tex]Therefore,
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: b>78\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(78,\: \infty\: \mright)\end{bmatrix}[/tex]Hence,
The interval notation is (78,∞)
Select the correct choices to complete the sentence.
AIR SHOW At a flight demonstration, two planes are flying in a synchronized pattern. The planes start their demonstration at (−20,−15) and (5, −15) . Select the transformation that represents the planes’ flight pattern to their final destinations at (−30, 20) and (0, 20) .
Options:
A. (-2, 7)
B. (-10, 35)
C. (-12, 48)
Answer:
The coorect option is letter C
Which scenario has more arrangements?:2:• 5 letter arrangements using the letters from the word CHAMPION.• 4 letter arrangements using the letters from the word ABRUTPING.. The total number of ways the word EDMONTON can be arranged.Prepare your work on paper, take an image and post in the answer box provided.s:ParagraphVB1UAVLato (Recom19pxVEa5 с:
This is a simple question to solve. Let's first calculate all the arrangements for the first case to understand the logic:
As we can see above, once we have 8 letters, and we need to calculate the numbers of arrangements with 5 letters, for the first letter we have 8 possible letters, for the second letters we have 7 possible letters once one letter was used for the first one. For the third letter we have 6 possible letters, for the fourth, 5 possible letters and for the fifth, 4 possible letters. So, we just multiply 8*7*6*5*4 = 6720 possible arrangements.
For the second situation we can follow the same logic:
And finally for the third situation we have:
As we can see above, the third scenario has more arrangements.
In how many ways can a committee of four Democrats and five Republicans be formed from a group of seven Democrats and eleven Republicans?
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall.In the House, there are now 20 standing committees and 1 permanent select committee. Please visit the Clerk of the House website for the most recent committee information.Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.To learn more about standing committees refer to:
https://brainly.com/question/2609442
#SPJ1
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.
The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall. In the House, there are now 20 standing committees and 1 permanent select committee.
Please visit the Clerk of the House website for the most recent committee information. Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.
To learn more about standing committees refer to:
brainly.com/question/2609442
#SPJ1
an open-top box is to be constructed from a sheet of tin that measures 22 inches by 14 inches by cutting out squares from each corner. let V(x) denote the volume of the resulting box. step 1 of 2: write V(x) as a product of linear factorsstep 2 of 2: among the values of x for which V(x)=0, which are physically possible?
It is given that an open-top box is to be constructed from a sheet of tin that measures 22 inches by 14 inches by cutting out squares from each corner
Let x be the measure of the side of the square.
Length of the resulting box =22-2x
Width of the resulting box=14-2x
Height of the resulting box=x
The volume of the box is
[tex]V=\text{length }\times width\times height[/tex]Substitute values, we get
[tex]V(x)=(22-2x)(14-2x)x[/tex][tex]=(22-2x)(14x-2x^2)[/tex][tex]=22\mleft(14x-2x^2\mright)-2x\mleft(14x-2x^2\mright)[/tex][tex]=22\times14x-22\times2x^2-2x\times14x-(-2x)2x^2[/tex][tex]=308x-44x^2-28x^2+4x^3[/tex][tex]V(x)=4x^3-72x^2+308x[/tex]Putting V(x)=0, we get
[tex]4x^3-72x^2+308x=0[/tex][tex]4x(x^2-18x+77)=0[/tex][tex]4x=0,(x^2-18x+77)=0[/tex]Here x is not zero
[tex]x^2-18x+77=0[/tex][tex]x^2-11x-7x+77=0[/tex][tex]x(x^{}-11)-7(x-11)=0[/tex][tex](x^{}-11)(x-7)=0[/tex][tex](x^{}-11)=0\text{ or }\mleft(x-7\mright)=0[/tex][tex]x^{}=11\text{ or }x=7[/tex]The height of the box is 11 or 7
If the height is 11 inches, substitute x=11 in the length equation, we get
[tex]\text{length =22=2x=22-2}\times11=22-22=0[/tex]we get a length is 0, so it is not possible to make the box.
Setting x=7, the height of the box is 7 inches.
[tex]\text{Length =22-2x=22-2}\times7=22-14=8inches[/tex][tex]\text{width =14-2}\times7=14-14=0[/tex]we get a width is 0, so it is not possible to make the box.
Hence among the values of x for which V(x)=0 is not physically possible.
1. Which of the following pairs of figures are congruenta which are not ? How do you know Be sure to use the following vocabulary words congruent .
Congruent and similar goes by:
Two figures are congruent if they have the same shape and size.
and,
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Now, check the images.
First figure (two houses) are congruent.
Second figures (two triangles) are not congruent.
State what additional information is required in order to know that the triangles are congruentfor the reason given.11) SSS12) SAS
11) SSS
The Side Side Side (SSS) theorem states that if three given sides of one triangle are equal to the three sides of another triangle, both triangles are congruent.
Since we are given two equal sides (VC = DC) and one common side(CE), to prove this SSS theorem, the additional information required is to indicate the third side of both triangles are equal (VE = DE).
We have the figure below:
Where:
VC = DC
CE = CE
The additional information required is:
VE = DE
ANSWER:
VE = DE
Nicole can run 4
laps in 2/5 hour.
How long will it
Hake her to run 5
laps?
Answer:
1/2 hour
Step-by-step explanation:
Each lap is 1/10 hours times that by 5 and you get 5/10 and simplified is 1/2
how do I find which coordinate pairs represent vertices of P'Q'R'S after these two transformations?
We have two transformations.
We will apply them to a generic point P=(x,y), and then we can replace them with any coordinates as inputs.
First transformation: translating 6 units to the right.
This changes the x-coordinate by adding 6 units (x=0 becames x'=6, for example), so we can write:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x+6,y)[/tex]Second transformation: rotate 90 degrees clockwise.
This changes both x and y coordinates. We can look at a drawing to understand the transformation.
The x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative x-coordinate.
We can then write:
[tex]P^{\prime}=(x+6,y)\longrightarrow P^{\prime}^{\prime}=(y,-x-6)[/tex]So now we know that the final image of a point (x,y) after the two transformations is (y,-x-6).
Then, we can list all four points:
[tex]P=(-3,7)\longrightarrow P^{\prime}^{\prime}=(7,-(-3)-6)=(7,-3)[/tex][tex]Q=(4,12)\longrightarrow Q^{\prime}^{\prime}=(12,-4-6)=(12,-10)[/tex][tex]R=(4,-2)\longrightarrow R^{\prime}^{\prime}=(-2,-4-6)=(-2,-10)[/tex][tex]S=(-3,-7)\longrightarrow S^{\prime}^{\prime}=(-7,-(-3)+6)=(-7,-3)[/tex]Final coordinates: (7,-3), (12,-10), (-2,-10) and (-7,-3).
The equation d=16t^2 gives the distance in feet that a golf ball falls in t seconds.How many seconds will it take the gol to drop to the ground from a height of 4 feet?64 feet?
We are given the following function of distance in terms of time:
[tex]d=16t^2[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ t=\text{ time} \end{gathered}[/tex]We are asked to determine the time when the distance is 4ft. To do that we will solve for "t". First, we will divide both sides by 16:
[tex]\frac{d}{16}=t^2[/tex]Now, we take the square root to both sides:
[tex]\sqrt{\frac{d}{16}}=t[/tex]Simplifying we get:
[tex]\frac{1}{4}\sqrt{d}=t[/tex]Now, we substitute the value of the distance:
[tex]\frac{1}{4}\sqrt{4}=t[/tex]Solving the operations:
[tex]\begin{gathered} \frac{1}{2}=t \\ \\ 0.5=t \end{gathered}[/tex]Therefore, the time is 0.5
The same procedure is used to determine the time for 64 feet.
How is seeing the parts of a partitioned number line the same as seeing the parts of a partitioned rectangle? How is it different?
Partitioning a number line:
If you have a number line, you can partition into fractions. This is done by dividing the number lines into equal portions and summing up the portions to give the total part that you need.
For example, to partition a number line into 3/4 portion of a number line, you can partition the number line into 4 portions of 1/4 each and take 3 portions out of the four to get 3/4.
The same strategy is used for a rectangle:
To divide a rectangle into two portions of 3/4 and 1/4, you can use similar method as above:
Difference:The difference is that in a number line, you only have the length and you can partition only across the length
In a rectangle you can partition both the length and the width of the shape
g(n) = 2n^2 - 4; Find g(-2)
ANSWER
g(-2) = 4
EXPLANATION
We are given the function g(n) as:
[tex]g(n)=2n^2\text{ - 4}[/tex]To find g(-2), we have to replace n with -2 in g(n) and simplify it.
[tex]\begin{gathered} g(-2)=2(-2)^2\text{ - 4 = 2}\cdot4\text{ - 4} \\ g(-2)\text{ = 8 - 4} \\ g(-2)\text{ = 4} \end{gathered}[/tex]That is the value of g(-2)