The equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
What is meant by binomial equation?A binomial number is an integer that can be produced by evaluating a homogeneous polynomial with two terms in mathematics, more specifically in number theory. It is a Cunningham number that has been generalized.
Let the equation be (2x + 5)² + (x -2)(x- 2)
By using binomial formula we get,
(a + b)³ = a³ + 3a²b + 3ab² + b³
The coefficient multipliers are located in row 3 of Pascal's triangle.
(2x + 5)³ + (x - 2)(x - 2)
= 8x³ + 60x² + 150x +125(x - 2)(x - 2)
8x³ + 60x² + 150x + 125 + x(x - 2) - 2(x-2)
8x³ + 60x² + 150x + 125 + x² - 2x - 2x +4
simplifying the above equation, we get
8x³ + 60x² + 150x + 125 + x² - 4x +4
8x³ + 60x² + 150x +129 + x² - 4x
8x³ + 60x² + 150x + 129 - 4x
8x³ + 60x² + 146x + 129
= 8x³ + 60x² + 150x +129
Therefore, by simplifying the equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
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trey is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
Given the graph represents the amount of water in the aquarium versus time.
A) As shown in the graph :
as the time increases the amount of water in the aquarium decreases
The rate of water decreasing =
[tex]\frac{480}{8}=60[/tex]so, the rate = 60 litres per minute
Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.9 ft13 ft6 ft
The area of the triangle is 27 square feet
Explanation:The area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]Where b and h are the base and height of the triangle respectively
[tex]\begin{gathered} A=\frac{1}{2}(9\times6) \\ \\ =27ft^2 \end{gathered}[/tex]What is the solution to the linear equation 2/5+p=4/5+3/5p
Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets
What rule describes the translation that was applied to triangle JKM to create triangle J’K’M’, Initial directions with the pic below.
Given a point (x, y), let's evaluate the transformations:
- Translation 6 units to the right.
Means moving the point 6 units in the horizontal direction; to the right.
The new point will be (x + 6, y).
- Translation 2 units down.
Means moving the point 2 units down; in the vertical direction.
The new point will be (x + 6, y - 2).
Answer: (x + 6, y - 2).
if f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which of the following
Answer:
The correct answer is the third option:
[tex]\lim_{x\to4}(\sqrt{x}-2)[/tex]Explanation:
We have the function:
[tex]f(x)=\frac{x-4}{\sqrt{x}-2}[/tex]In the numerator, we have x - 4. We can rewrite it as a difference of squares, since:
[tex]\begin{gathered} x=(\sqrt{x})^2 \\ 4=2^2 \end{gathered}[/tex]Thus:
[tex]x-4=(\sqrt{x}-2)(\sqrt{x}+2)[/tex]Then, the limit:
[tex]\begin{gathered} \lim_{x\to4}(\frac{(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)} \\ \end{gathered}[/tex]We can cancel out the terms, since we are taking limit, this is, numbers that infinitely close to 4, bt never 4. This way we can cancel the terms, and get:
[tex]\lim_{x\to4}(\sqrt{x}+2)[/tex]
Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle ABC and triangle PQR .
Consider the triangle ABC and triangle PQR .
we can see that
(i) angle C = angle R .....given in the figure
(iii) angle B = angle Q .... given in the figure
(ii) side BC = side QR ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔPQR
both the triangles KLM and PQR are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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Alexa read a total of 54 books over 9 months. If Alexa has read 120 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
If the relation between the book read by Alexa and the number of months she takes to read them is directly proportional, then, if x is the number of months she took to read 120 books, you can write:
[tex]\frac{x}{120}=\frac{9}{54}[/tex]By solving for x and simplifying, you obtain:
[tex]\begin{gathered} x=\frac{9}{54}\cdot120 \\ x=20 \end{gathered}[/tex]Hence, Alexa read 120 books in 20 months
f(×) = 3× + 7 f(1) =
f(1) = 10
Explanation:Given f(x) = 3x + 7
To find f(1), replace x by 1 in the equation above
f(1) = 3(1) + 7
= 3 + 7
= 10
someone please help I don't get it!!
Answer:
which one
Step-by-step explanation:
don't forget to follow rate like
D − 37 = 40D =Check your solution.− 37 = 40
We have to solve this equation:
[tex]D-37=40[/tex]We can solve it for D by adding 37 on both sides of the equation as this won't change the equality:
[tex]\begin{gathered} D-37+37=40+37 \\ D=77 \end{gathered}[/tex]Answer: D = 77
1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables fill in the missing cells on table and make sure to reduce your fraction.
Horizontal addition
Row 1 a + 12 + b +6 =37
[tex]\begin{gathered} a+12+b+6=37 \\ a+b+18=37 \\ a+b=37-18 \\ a+b=19 \end{gathered}[/tex]Row 2
[tex]\begin{gathered} 8+c+16+11=d \\ c+35=d \end{gathered}[/tex]Row 3
[tex]\begin{gathered} 17+5+e+18=f \\ 40+e=f \end{gathered}[/tex]Row 4
[tex]\begin{gathered} g+34+45+h=143 \\ g+h+79=143 \\ g+h=143-79 \\ g+h=64 \end{gathered}[/tex]Now Let us add the columns
Column 1
[tex]a+8+17=g[/tex]Column 2
[tex]\begin{gathered} 12+c+5=34 \\ c+17=34 \\ c=34-17 \\ c=17 \end{gathered}[/tex]Column 4
[tex]\begin{gathered} 6+11+18=h \\ h=35 \end{gathered}[/tex]Column 2
[tex]\begin{gathered} b+16+e=45 \\ b+e=45-16 \\ b+e=29 \end{gathered}[/tex]Hence, Video games under 10-12 is c=17, gotten from column 2
Vertical total under 16-18 is h=35 gotten from column 4
Hence, the horizontal total of the video game is 52
Since h is gotten, we can solve for 7 to 9 vertical total
[tex]\begin{gathered} g+h=64 \\ g=64-h \\ g=64-35 \\ g=29 \end{gathered}[/tex]Hence, the 7 to 9 vertical total is 29
[tex]\begin{gathered} a+25=g \\ a=g-25 \\ a=29-25 \\ a=4 \end{gathered}[/tex]Hence, Darts under 7 to 9 is 4
Darts under 13 to 15 is b
[tex]\begin{gathered} a+b=19 \\ b=19-a \\ b=19-4 \\ b=15 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 15
Basket ball under 13 to 15 is e
[tex]\begin{gathered} b+e=29 \\ e=29-b \\ e=29-15 \\ e=14 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 14
Video Games Horizontal total is d,
[tex]\begin{gathered} c+35=d \\ 17+35=d \\ d=52 \end{gathered}[/tex]Hence, the Horizontal total of the Video game is 52
Basketball horizontal total is f
40+e=f
[tex]\begin{gathered} 40+e=f \\ 40+14=f \\ 54=f \end{gathered}[/tex]Hence, the horizontal total of the Video game is 54.
Hence, the above table fill the empty space
Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?
We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.
We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:
[tex]v=\frac{d}{t}[/tex]where v is speed, d is distance and t is time, we know that for the first jet:
[tex]x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1[/tex]Where d₁ represents the distance of the first jet from the starting point. For the second jet:
[tex]x=\frac{d_2}{4}\Rightarrow4x=d_2[/tex]Where d₂ represents the distance of the second jet from the starting point.
We also know that:
[tex]d_1+d_2=6000[/tex]As:
Thus, we have that:
[tex]\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}[/tex]This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).
im on a bit of a time crunch so please hurry :)
Answer
39 child tickets were sold that day
Step-by-step explanation
Variables
• x: child tickets sold
,• y: adult tickets sold
Given that four times as many adult tickets as child tickets were sold, then:
[tex]y=4x[/tex]If 1 child ticket cost $5.70, then x child tickets will cost 5.7x dollars.
If 1 adult ticket cost $9.20, then y adult tickets will cost 9.2y dollars.
Given that the theater sold tickets for $1657.50, then:
[tex]5.7x+9.2y=1657.5[/tex]Substituting the first equation into the second one and solving for x:
[tex]\begin{gathered} 5.7x+9.2(4x)=1,657.5 \\ 5.7x+36.8x=1,657.5 \\ 42.5x=1,657.5 \\ \frac{42.5x}{42.5}=\frac{1,657.5}{42.5} \\ x=39 \end{gathered}[/tex]Now finish solving the equation. What is the value of m?-(m - 6) = 3m + 14-m + 6 = 3m + 14-m + 6 - 3m = 3m + 14 - 3m-4m + 6 = 14m=
Find the equation for the line that passes through the point (3.-5), and that is perpendicular to the line with the equation x = -2
• Line x = -2 is a vertical line that passes through point x = -2
Given the point ( 3;-5)
• We know that perpendicular lines have opposite reciprocal slopes , so the slope of the line will be
,• m = 1/2
• so , the standard formula for a line : y = mx +c
at point ( 3-5) , we will have :
-5 = 1/2(3) + c
Therefore c = -5 -3/2
= -13/2
• Our y- intercept will be -13/2
• Finally , our equation of the line will be :
y = 1/2x -13/2
-2( 4 - 6h ) +9-8 - 12h + 9-12h + 1Explain the error in the work.
The error is in the distribution property application, in the way the signs are multiplied.
We will look at it in detail:
[tex]\begin{gathered} -2(4-6h)+9 \\ \lbrack(-2)(4)+(-2)(-6h)\rbrack+9 \\ (-8+12h)+9 \\ 12h+1 \end{gathered}[/tex]When (-2) is multiplied by (-12h) it should end with a positive sign, as (-a)*(-b)=a*b
Can you help me with number 11? Thank you I am having trouble with it.
N 11
Remember that
The law of sines
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]In this problem
[tex]\frac{14.9}{\sin X^o}=\frac{25.5}{\sin 71^o}[/tex]Solve for x
sinX=(14.9*sin71)/25.5
what is the value of x to the nearest tenth on problem 5
Answer:
Explanation:
In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).
So, by Pythagorean theorem, we can write the following equation
[tex](x+8)^2=x^2+16^2[/tex]Now, we can expand the left side
[tex]\begin{gathered} x^2+2(8)(x)+8^2=x^2+16^2 \\ x^2+16x+64=x^2+256 \end{gathered}[/tex]Then, subtract x² from both sides
[tex]\begin{gathered} x^2+16x+64-x^2=x^2+256-x^2 \\ 16x+64=256 \end{gathered}[/tex]Subtract 64 from both sides
[tex]\begin{gathered} 16x+64-64=256-64 \\ 16x=192 \end{gathered}[/tex]Finally, divide by 16
[tex]\begin{gathered} \frac{16x}{16}=\frac{192}{16} \\ \\ x=12 \end{gathered}[/tex]Therefore, the value of x is 12
The USDA collects and distributes a wide variety of data about agriculture in the United States. One statistic reported each year is the number of milk cows (in thousands) in each state. A random sample of 10 states is selected, with the number of milk cows reported in both 2011 and 2015.
State 2011 2015 Difference
North Dakota 19 16 -3
California 1769 1778 9
Nevada 29 29 0
Ohio 268 267 -1
New Hampshire 14 14 0
Colorado 128 146 18
Minnesota 468 460 -8
Oklahoma 53 39 -14
Utah 93 96 3
Washington 260 277 17
mean 310.1 312.2 2.1
sd 532.857 535.367 10.159
An agricultural researcher wants to conduct a paired difference test to determine if the mean number of milk cows (in thousands) in the US changed between 2011 and 2015.
Round all calculated values to 4 decimal places as appropriate.
1. Which hypotheses should be used to conduct the test?
A. H0:μdiff=0 vs. Ha:μdiff≠0
B. H0:μdiff<2.1 vs. Ha:μdiff>2.1
C. H0:μdiff=0 vs. Ha:μdiff<0
D. H0:μdiff=0 vs. Ha:μdiff>0
2. Assume the conditions for the hypothesis test are met and find the test statistic and the p-value.
test statistic =
p-value =
3. Based on the p value we have
?
evidence that the null model is not a good fit for our observed data.
4. Construct a 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015.
1. The hypothesis tested are given as follows: A. H0:μdiff=0 vs. Ha:μdiff≠0.
2.
The test statistic is of: t = 0.65.The p-value is of: 0.26603. Based on the p-value, we do not have enough evidence that the null model is not a good fit for our observed data.
4. The 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015 is of (-8.34, 12.54).
What are hypothesis tested?At the null hypothesis, it is tested if there has not been change, that is, if the mean is of zero, hence:
H0:μdiff=0
At the alternative hypothesis, it is tested if there has been change, hence:
Ha: μdiff≠0
Considering a two-tailed test, as we are testing if the mean is different of a value, with 10 - 1 = 9 df, and a significance level of 1 - 0.99 = 0.01, the critical value is of:
|t| = 3.25.
What is the test statistic?The test statistic for the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters in this problem are given as follows:
[tex]\overline{x} = 2.1, s = 10.159, n = 10, \mu = 0[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{2.1 - 0}{\frac{10.159}{\sqrt{10}}}[/tex]
t = 0.65.
What are the p-value and the conclusion?Considering a two-tailed test, with t = 0.65 and 10 - 1 = 9 df, the p-value is of:
0.2660.
What is the confidence interval?The confidence interval is given as the estimate plus/minus the multiplication of the critical value and the standard error.
Hence the lower bound of the interval is of:
2.1 - 3.25x10.159/sqrt(10) = -8.34.
The upper bound of the interval is of:
2.1 + 3.25x10.159/sqrt(10) = 12.54.
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The volume of gas kept at a constant pressure varies inversely with the temperature T. If the temperature is 50 degrees, the volume is 20 quick feet. What will the volume be when the temperature is 100 degrees. V= , Temperature=. . Solution
Given that the volume of gas kept at constant pressure varies inversely with the temperature T and when the temperature is 50 degrees, the volume is 20 cubic feet.
We have to find the volume of gas when the temperature is 100 degrees.
Since it is given that volume varies inversely with the temperature. It means
[tex]T_1V_1=T_2V_2[/tex]Substitute T1 = 50, V1 = 20, T2 = 100.
[tex]\begin{gathered} 50\times20=100\times V_2 \\ 1000=100\times V_2 \\ \frac{1000}{100}=V_2 \\ 10=V_2 \end{gathered}[/tex]Thus, the volume of gas when the temperature is 100 degrees is 10 cubic feet.
Rewrite the area formula with the info given from the problem then find the value of x , then how many feet of fencing should me Korber buy ?
Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:
[tex]A=\frac{1}{2}x^2[/tex]Now, let's use the given area and solve it for x:
[tex]\begin{gathered} 4232=\frac{1}{2}x^2\\ \\ x^2=8464\\ \\ x=92\text{ ft} \end{gathered}[/tex]Since the "path" already has fence, the amount of fence needed is 2x:
[tex]2x=2\cdot92=184\text{ ft}[/tex]lax and tip word pr You might need: 3 Calcu The sales tax in your city is 4.4%. and an item costs $3 before tax. How much tax would you pay on that item?
Tax = $0.13(nearest hundredth)
In the image below, line ris perpendicular to both lines p and q. Lines p and p and r. are parallel to one another. Transversal s goes through lines p 28° s What is the value of x? A 62 OB. 72 O C 152 OD. 162 Sign out INTL 2
In this problem we have that
m by supplementary angles
so
mmtherefore
the answer is
x=52 degreesPart 2
the transformations that produce triangle ABC are
1) A dilation from the with scale factor of 2
2) A reflection across the x-axis
3) A translation of
I need help on this, I need it answered in steps
Let's solve the given logarithmic expression:
[tex]\text{ log}_4(64)\text{ = m}[/tex]We get,
[tex]\text{ log}_4(64)\text{ = m}[/tex][tex]\mathrm{Factor\: the\: number\colon\: }\: 64=4^3[/tex][tex]=\log _4\mleft(4^3\mright)[/tex][tex]\mathrm{Apply\: log\: rule}\colon\quad \log _a\mleft(a^x\mright)=x[/tex][tex]\log _4\mleft(4^3\mright)\text{ = 3 = m}[/tex]Therefore, m = 3.
aThecity of Huntsville, TX has approximately 25,000 registered voters. There are two candidates forcity council in an upcoming election: Brown and Solano. The day before the election, a telephone pollof 550 randomly selected registered voters was conducted. 243 said they'd vote for Brown, 253 saidthey'd vote for Solano, and 54 were undecided.give the simple statistic for the proportion of voters surveyed
The surveyors are really interested in all registered boters in Huntsville, therefore the first answer is F.
Since they are only doing a sample of people with phones the real population is all registered voters with telephones, therefore the second answer is C.
The sample for this survey is the 550 voter surveyed.
To find the proportion of people who said they vote for brown we divide the number of this people by the total of people surveyed:
[tex]\frac{243}{550}=0.4418[/tex]Therefore the proportion was 0.4418
Given: the function f defined by f(x) = 3x^2. Which statement is true?
The given function is
[tex]f(x)=3x^2[/tex]If we evaluate the function when x = 0, we get
[tex]f(0)=3(0)^2=3\cdot0=0[/tex]Hence, the first option is correct.Marcus is playing dodge ball with hisfriends. He catches 2 out of every 5 ballsthrown in his direction. If he catches14 balls, how many balls were thrownat him?balls
Step 1
Given;
[tex]\begin{gathered} \text{Marcus is playing dodge ball with his friends.} \\ He\text{ catches 2 out of every 5 balls thrown in his direction.} \end{gathered}[/tex]Required; To find out how many balls are thrown at him if he catches 14 balls.
Step 2
There are two approaches to determine the number of balls thrown at Marcus
Approach 1
[tex]\begin{gathered} \text{Marcus catches 2 balls for every 5 balls thrown in his direction.} \\ we\text{ can draw up a table and add up 2 balls caught and 5 balls } \\ \text{thrown respectively until we arrive at 14 balls caught.} \end{gathered}[/tex]Draw the table;
we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.
Answer=35 balls
Approach 2
[tex]\begin{gathered} We\text{ will use the ratio} \\ \frac{2\text{ balls caught}}{14\text{ balls caught}}=\frac{5\text{ balls thrown }}{x\text{ balls thrown}} \\ \text{cross multiply} \\ 2x=5(14) \\ \text{simplify} \\ 2x=70 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{70}{2} \\ x=35\text{ balls thrown} \end{gathered}[/tex]Hence, 35 balls were thrown at Marcus
PQR is a right triangle. If PQ=8, what is PR?
Sine formula
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hypotenuse}}[/tex]Considering angle Q = 60°, the opposite side is PR, and the hypotenuse is PQ = 8. Substituting this information into the formula, we get:
[tex]\begin{gathered} \sin (m\angle Q)=\frac{PR}{PQ} \\ \sin (60\degree)=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}\cdot8=PR \\ 4\sqrt[]{3}=PR \end{gathered}[/tex]Lynn got a $50 gift card to an online music store she uses the gift cards to buy an album for 9.99 she also wants to use the gift card to buy some songs. Each song cost 1.29. What equality is described the situation where n is the number of songs like monster by
ANSWER
B. 9.99 + 1.29n ≤ 50
EXPLANATION
The total amount of money she spends at the store has to be at most, the value of the gift card $50. This is the cost of the album, 9.99, and then 1.29 for each song. If the total number of songs is 'n', then for n songs, she'll spend 1.29n. In total she spends: 9.99 + 1.29n at the store. The equation is
[tex]9.99+1.29n\le50[/tex]A 3 dimensional shape is created when the shape isrotated around the y-axisFind the volumen of shape
By rotating the shape of the graph, we get the following cylinder:
So we have a cylinder with:
• radius r = 4,
,• height h = 6.
The volume of the cylinder using π = 3.14 is given by:
[tex]V=\pi *r^2*h=3.14*4^2*6=301.44.[/tex]AnswerThe solid obtained is a cylinder of volume 301.44.