I vaguely remember how to do this although I am familiar with all. All I need is a quick review explanation and I’ll be good. Thanks!
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We have to calculate the perimeter of a pen that has an area expressed as
A = 3x²-7x+2.
We assume it is a rectangular pen, so it will have two different sides.
The area will be the product of this two side lengths, while the perimeter will be 2 times the sum of the lengths of the two sides.
Then, we start by rearranging the expression of A as a product of two factors.
We can do it by factorizing A.
To do that, we calculate the roots of A as:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot3\cdot2}}{2\cdot3} \\ x=\frac{7\pm\sqrt[]{49-24}}{6} \\ x=\frac{7\pm\sqrt[]{25}}{6} \\ x=\frac{7\pm5}{6} \\ \Rightarrow x_1=\frac{7-5}{6}=\frac{2}{6}=\frac{1}{3} \\ \Rightarrow x_2=\frac{7+5}{6}=\frac{12}{6}=2 \end{gathered}[/tex]Then, we can now express A as:
[tex]\begin{gathered} A=3(x-\frac{1}{3})(x-2) \\ A=(3x-1)(x-2) \end{gathered}[/tex]Then, we can consider the pen to be a rectangle (or maybe square, depending on the value of x) with sides "3x-1" and "x-2".
Then, we can now calculate the perimeter as 2 times the sum of this sides:
[tex]\begin{gathered} P=2\lbrack(3x-1)+(x-2)\rbrack \\ P=2(3x-1+x-2) \\ P=2(4x-3) \\ P=8x-6 \end{gathered}[/tex]Answer: we can express the perimeter as 8x-6.
Related Questions
what is 8 × 2000? and
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simple, it's a multiplication
I multiply the number of atoms with the weight of each one to find the total weight of the gas
[tex](5.04\times10^{23})\times(1.67\times10^{-24}^{})[/tex]We group
[tex](5.04\times1.67)\times(10^{23}\times10^{-24})[/tex]and solve
[tex]\begin{gathered} (8.4168)\times(10^{-1}) \\ =0.84168 \end{gathered}[/tex]the result is: 0.84 grams
question number 2! I already have the answer of the number one
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If we have f(x) = sin(x), then:
[tex]f(2x)=\sin2x[/tex]f(2x) = sin(2x) is a vertical shrink if we compare it with f(x) = sin(x). Then, the graph of each function is:
It is equally probable that the pointer on the spinner Shown will land on any one of the eight regions number one through eight if the pointer lands on the borderline spin again. find the probability that the pointer will stop on an even number or number greater than three
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SOLUTION
The even numbers here are 2, 4, 6 and 8. That is 4 numbers.
The numbers greater than 3 are 4, 5, 6, 7, and 8, that is 5 numbers.
And we have a total of 8 numbers.
Let P(A) be the probability of the pointer landing on an even number
Let P(B) be the probability of the pointer landing on a number greater than 3
Let P(A or B) be the probability that the pointer stops on an even number or number greater than three
From the probability formula,
[tex]P(\text{A or B) = P(A) + P(B) - P(A}\cap B)[/tex][tex]\text{ P(A}\cap B)\text{ means probability of A and B}[/tex]Hence
[tex]\begin{gathered} P(A)=\frac{4}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{ For P(A}\cap B)\text{ we can s}ee\text{ that betwe}en\text{ } \\ \text{the even numbers 2, 4, 6, 8 and } \\ n\text{umbers greater than 3, which are 4, 5, 6, 7, 8} \\ \text{what is common is 4, }6,\text{ 8} \\ So,\text{ } \\ \text{P(A}\cap B)=\frac{3}{8} \end{gathered}[/tex]Therefore, P(A or B) becomes
[tex]\begin{gathered} \frac{4}{8}+\frac{5}{8}-\frac{3}{8} \\ \frac{4+5-3}{8} \\ \frac{6}{8} \\ =\frac{3}{4} \end{gathered}[/tex]The numbers of products a store sold on 4 consecutive days were x,x+5,x+3 and x+12. if the daily average of the products sold was 13. What is the value of x?
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Answer:
x = 8
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
given daily average is 13 , then
[tex]\frac{x+x+5+x+3+x+12}{4}[/tex] = 13 ( multiply both sides by 4 to clear the fraction )
4x + 20 = 52 ( subtract 20 from both sides )
4x = 32 ( divide both sides by 4 )
x = 8
I need to find how much does is his monthly payment.
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The total amount Christian will pay is given by:
[tex]A=P(1+rt)[/tex]where P is the principal, r is the interes rate and t is the time. In this case we have that P=15000, r=0.07 and t=2. Then we have:
[tex]\begin{gathered} A=15000(1+0.07(2)) \\ A=17100 \end{gathered}[/tex]Hence he will pay $17,100 in total. Now, to find the monthly amount we divide the total by the number of months; in this case 24:
[tex]\frac{17100}{24}=712.50[/tex]Therefore he will pay $712.50 each month.
3. B 8 cm 9 cm D F 5 cm x cm A CITO 4 CM Α' ο cm D' F O 75 cm o Scale Factor: Scale Factos
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Scale factor on a map
Suppose a spherical snowball is melting and the volume is decreasing at a constant rate, changing from 12 in^3/min to 10in^3/min in 30min. How fast is the radius changing when the volume is 8in^3/min? (Answer in terms of pi)
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The radius changing when the volume is 8in^3/min by: -512π /30 in³ /min.
How to find the radius?First step is to find the radius changing over time at a constant rate
dr/dt = 10-12 /30
= -2/30 in/min
Now let find the how fast is the radius changing using this formula
dV/dt = 4πr²(dr/dt)
Where,
r =8
Hence,
dV/dt = 4π (8in)² × -2/30 in/min
dV/dt = 4π (64in) × -2/30 in/min
dV/dt = -512π /30 in³ /min
Therefore the change in radius is -512π /30 in³ /min.
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7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
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Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
If there are four independent events E1, E2, E3, and E4, then the probability P(E1 and E2 and E3 and E4) equals ____________________.
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Answer:
The probability of having all four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Explanation:
Given that there are four independent events E1,E2,E3 and E4.
[tex]E_1,E_2,E_3,E_4[/tex]The probability of having all the four events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)[/tex]would be the product of the probability of each of the events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)=P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Therefore, the probability of having all the four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]sin(??? ) O A. O V3 ОВ. 2 Oc. O D.
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The correct option is D
[tex]-\frac{1}{2}[/tex]Explanation:[tex]\sin(\frac{7\pi}{6})=-\frac{1}{2}[/tex]ProbabilityHello need help Thank you. A phone number in Cameroon consists of 9 digits. From the theoretical capacity of the Cameroonian telephone network, say whether the 4 current operators (CAMTEL MTN, NEXTTEL and ORANGE) can meet a demand for 150 million subscriptions. 1) How many different ways can you arrange four people in four numbered chairs? 2)How many ways can you distribute 10 balloons to 3 children, 4 for the first and 3 for each of the other two?
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Answer:
1) 24
2)66
Explanation:
1) How many different ways can you arrange four people in four numbered chairs?
Answer: we have 4 people ands 4 chairs, so we use the factorial of 4 to find the number of ways that we can arrenge the people:
[tex]4!\text{ = 4}\cdot3\cdot2\cdot1=24[/tex]we can arrange 4 people in 4 chairs in 24 different ways
2)How many ways can you distribute 10 balloons to 3 children?
To distribute "n" objects to "r" people (in this case n=10, and r = 3) we use the following combinarions formula:
[tex]C(n+r-1,r-1)[/tex]substituting our values we get:
[tex]C(10+3-1,3-1)[/tex][tex]C(12,2)[/tex]and since C(a,b) is defined as:
[tex]C(a,b)=\frac{a!}{b!(a-b)!}[/tex]For C(12,2) we get the following:
[tex]C(12,2)=\frac{12!}{2!(12-2)!}[/tex]which simplifies to:
[tex]C(12,2)=\frac{12!}{2!(10)!}=66[/tex]We can distribute 10 balloons to 3 people in 66 ways
kiran ran 1/5 the length of the road which is 9 miles how many miles did he run?
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Answer:0.02
Step-by-step explanation:
How do I simplify -88/4
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Solve: x^3= -65 This is for homework
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Step 1
Solve the equation by graphing
You can rewrite the equation as
[tex]x^3+65=0[/tex]step 2
Using a graphin calculator as Desmos
x=-4.021
The solution is x=-4.021
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Consider the following data set where “x” is a positive integer: {x+2, x+4, x-4, x-3, x+6} Which of the following statements are true? Select all that apply.A. The mode is x-4B. The median is x+2C. The mean is x+1D. None of above
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Before start analyzing the mode, median and mean of the data set, we must organize it from lowest to highest:
{x+2, x+4, x-4, x-3, x+6}
↓
{x-4, x-3, x+2, x+4, x+6}
ModeThe mode is the most frequently repeated data. Since every data appears just one time, then this set has not mode.
MedianThe median is the data that is in the center. We find it just by counting the same numbers from left to right and from right to left:
The median is x+2
MeanThe mean is given by the addition of all the data, and the division by the number of data.
there are 5 values, then we should divide their sum by 5:
[tex]\begin{gathered} \frac{(x-4)+(x-3)+(x+2)+(x+4)+(x+6)}{5} \\ =\frac{x-4+x-3+x+2+x+4+x+6}{5} \\ =\frac{5x+5}{5}=x+1 \end{gathered}[/tex]The mean is x+1
ANSWERS: B and Cwhat does 1,580÷25=I know the answer, I need to show how I got it.
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5/12×6/34 pls help me
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The given numerical expression can be simplified as a fraction as 5/68 .
The given expression is 5/12 × 6/34
This is a multiplication of fractions.
therefore here we will multiply the numerators and divide it by the product of the denominators.
5/12 × 6/34
or , (5×6) ÷ (12×34)
or, 30 ÷ 408
or, 5 / 68
therefore the required expression is 5 / 68
Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.
Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers. It seems like a fixed amount of money.
A variable is a symbol without a known value. One constant, one variable, or a collection of variables and constants multiplied or divided can make up a term. The coefficient in an equation is a number that is further multiplied by a variable.
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find the volume of a right rectangular prism with the following measurements by multiplying The edge lengths. length 3/4 width 1/2 heigth 2/3
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Explanation
The volume of a rectangular prism is given by:
[tex]\text{Volume}=\text{ length}\cdot width\cdot height[/tex]then,Let
length= 3/4
width=1/2
heigth=2/3
Now, replace,
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{Volume}=(\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{2}{3}) \\ \text{Volume}=\frac{3\cdot1\cdot2}{4\cdot2\cdot3}=\frac{1}{4} \\ \text{Volume}=\frac{1}{4}\text{cubic units} \end{gathered}[/tex]I hope this helps you
Which of the following is a simplified version of 11 + 4(x + 3) = 10? A 4x + 4 = 10 B В 4x + 23 = 10 15x + 3 = 10 15x + 45 = 10
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11 + 4(x + 3) = 10
Apply distributive property:
11+ 4(x)+4(3) = 10
11+ 4x+12 = 10
Combine like terms:
4x+11+12 = 10
4x +23 = 10
Determine if the expression s3+s2+s5/4 is a polynomial or not. If it is a polynomial state the type and degree of the polynomial
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Given the algebraic expression
[tex]s^3+s^2+s^{\frac{5}{4}}[/tex]For the algebraic expression to be classified as a polynomial, all expressions must have a non-negative integer exponent.
From the given expression, we can see that the last term doesn't obey this rule (an exponent that is in fraction term).
Hence, the expression given is not a polynomial.
A survey of 130 freshmen business students at a local university produced the results listed below. How many students took only psychology?
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We could draw the following Venn's diagram to solve this problem.
So, after drawing this diagram, we notice that the number of students that took only psychology were 9.
A chemist is using 328 milliliters of a solution of acid and water. If 13.7% of the solution is acid how many milliliters of acid are there? Round to nearest tenth
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Hello
Let's find 13.7% of 328
[tex]\begin{gathered} \frac{13.7}{100}=\frac{x}{328} \\ x=\frac{13.7\times328}{100} \\ x=44.94 \end{gathered}[/tex]From the calculation above, 44.94mL of acid is present in the solution
Based on sample data, newborn males have weights with a mean of 3242.4 g and a standard deviation of 844.4 g. Newborn females have weights with a mean of 3095.9 g and a standard deviation of 508.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
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The formula for calculating z score is expressed as
z = (x - μ)/s
where
x is the sample mean
μ is the mean
s is the sample standard deviation
Considering the newborn males,
x = 1700
μ = 3242.4
s = 844.4
Thus,
z = (1700 - 3242.4)/844.4
z = - 1.83
Considering the newborn females,
x = 1700
μ = 3095.9
s = 508.6
Thus,
z = (1700 - 3095.9)/508.6
z = - 2.74
The most extreme value is the z score that is furthest from zero. It is z = - 2.74. Thus, the female who weighs 1700 g is more extreme relatively
Since the z score for the male is z = - 1.83 and the z score for the female is z = - 2.74, the female has the weight that is more extreme.
After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)
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Since Mike drove at 65 mph for 3 hours, we have that he traveled:
[tex]3\cdot65=195\text{ miles}[/tex]for Sandra, we have the following:
[tex]3\cdot70=210\text{ miles}[/tex]notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:
[tex]x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}[/tex]therefore, Sandra and Mike are approximately 287 miles apart after 3 hours
g(x) = 2x + 3, find g(a + 1). *
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ANSWER:
g(a+1) = 2a + 5
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]g(x)=2x+3[/tex]Replacing, when x is a + 1:
[tex]\begin{gathered} g(a+1)=2\cdot(a+1)+3 \\ g(a+1)=2a+2+3 \\ g(a+1)=2a+5 \end{gathered}[/tex]Calculator 5 ft С A window in the shape of a parallelogram has the dimensions given What is the area of this window?A.20 ftB.24 ftC.28 ftD.40 ft
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Area of a parallelogram = b x h
The table below shows the value for the function y=f(x)If g(x)=1/2 which of the following are solutions to g(x) select all that applyA (-3,5.5)B(-1,-2)C(0,4)D (5,-8)
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So we have a table of values that associate x values with a function f(x). The pairs (x,y) are solutions to the equation y=f(x) and they are:
[tex]\begin{gathered} (-3,5) \\ (-1,-4) \\ (0,2) \\ (5,-8) \\ (6,3) \end{gathered}[/tex]If we define a new function g(x)=(1/2)*f(x) its solutions will be those of f(x) but with their y values divided by 2. Then the solutions to g(x) are:
[tex]\begin{gathered} (-3,\frac{5}{2})=(-3,2.5) \\ (-1,-\frac{4}{2})=(-1,-2) \\ (0,\frac{2}{2})=(0,1) \\ (5,-\frac{8}{2})=(5,-4) \\ (6,\frac{3}{2})=(6,1.5) \end{gathered}[/tex]Then the only option with a solution to g(x) is the second option (-1,-2).
what value of x makes this equation true?[tex]12x - 15 = 6 - 3x[/tex]
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The value of x that makes the equation true is;
[tex]x\text{ = }\frac{7}{5}[/tex]Here, we want to get the value of x that makes the equation true
All have to do here is to solve the equation for x
We have this as follows;
[tex]\begin{gathered} 12x-15\text{ = 6-3x} \\ 12x\text{ + 3x = 6 + 15} \\ 15x\text{ = 21} \\ x\text{ = }\frac{21}{15} \\ \\ \text{ x = }\frac{7}{5} \end{gathered}[/tex]What effect does changing the function f(x)=3sin(x)+1to the function g(x)=3sin(x4)+2 have on the graph of f(x)?
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Step 1
The parent function f(x) is given as;
[tex]f(x)=3\sin (x)+1[/tex]If we transform the function by adding 1 to it we will have;
[tex]\begin{gathered} f(x)=3\sin (x)+1+1 \\ f(x)=3\sin (x)+2 \end{gathered}[/tex]We have the following graph;
which means when you add 1 to the to get f(x)=3sin(x)+2, the function is shifted up by 1 unit.
Step 2
If the function is further transformed to;
[tex]f(x)=3\sin (\frac{x}{4})+1[/tex]we will have the graph below;
This means that the graph stretches horizontally by a factor of 4.
Therefore the changes f(x) passes through to g(x) are;
[tex]\begin{gathered} f(x)=2\sin (\frac{x}{4})+1_{}--(A\text{ horizontal stretch by a factor of 4)} \\ g(x)=2\sin (\frac{x}{4})+2---(A\text{ shift up by 1 unit)} \end{gathered}[/tex]Answer; The graph is stretched horizontally by a factor of 4 and shifted up by 1 unit.
Ahmad is putting 11 colored light bulbs into a string of lights. There are 5 green light bulbs, 4 yellow light bulbs, and 2 red light bulbs. How many distinct ordersof light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
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So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:
[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:
[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]So, Ahmad has 6,930 distinct orders