The result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
The function is
f(p) = [tex]p^2[/tex] + 3p + 1
The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.
The values of p = -2
Substitute the value of p in the function and find the solution
f(p) = [tex]p^2[/tex] + 3p + 1
f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1
f(-2) = 4 - 6 + 1
f(-2) = -1
Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
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Find the derivatives of the following using the different rules.1. f(x) = -67x
To derive f(x) = -67x, we can use the Power Rule.
[tex]x^n\Rightarrow nx^{n-1}[/tex]In the given term, our n = 1 since x¹ = x. So, following the power rule, we will multiply the exponent 1 to the constant term -67, then subtract 1 from the exponent 1, hence x¹ will become x⁰.
[tex]-67x^1\Rightarrow1(-67)(x^{1-1})[/tex]Then, simplify.
[tex]-67x^0\Rightarrow-67(1)=-67[/tex]Therefore, the first derivative of f(x) = -67x is -67.
[tex]f^{\prime}(x)=-67[/tex]Based on the degree of the polynomial f(x) given below, what is the maximum number of turning points the graph of f(x)
can have?
f(x) = -3+x²-3x - 3x³ + 2x² + 4x4
The maximum number of turning points based on the degree of the polynomial is 2.
What is the turning point?A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.A turning point is a point in the graph where the graph changes from increasing to decreasing or decreasing to increasing.Turning point = n-1, where n is the degree of the polynomial.
The highest order of the polynomial is 3.n = 3Turning point = 3 - 1 = 2Therefore, the maximum number of turning points based on the degree of the polynomial is 2.
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Need help with my math yall please??
The value of the expression after simplification is found as -3.
What is termed as simplification?Simplify simply way of making something easier to understand. Simply or simplification in mathematics refers to reducing an expression/fraction/problem to a simpler form. It simplifies the problem by calculating and solving it. We can —Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This helps make the expression simple to understand and solve.For the given expression;
5x + 8 = 2x - 1
Subtract 8 from both side.
5x + 8 - 8 = 2x - 1 - 8
Simplify
5x = 2x - 9
Subtract both side by 2x.
5x - 2x = 2x - 9 - 2x
3x = -9
Divide both side by 3.
3x/3 = -9/3
x = -3
Thus, the value of the expression is found as -3.
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3 2 — · — = _____ 8 5 2 9· — = _____ 3 7 8 — · — = _____ 8 7 x — · y = _____ y a b —— · — = _____ 2b c m n2 —- · —— = _____ 3n mGive the product in simplest form: 1 2 · 2— = _____ 2Give the product in simplest form: 1 2 — · 3 = _____ 4 Give the product in simplest form: 1 1 1— · 1— = _____ 2 2 Give the product in simplest form: 1 2 3— · 2— = _____ 4 3
Given:
[tex]\frac{3}{8}\cdot\frac{2}{5}[/tex]Required:
We need to multiply the given rational numbers.
Explanation:
Cancel out the common terms.
[tex]\frac{3}{8}\cdot\frac{2}{5}=\frac{3}{4}\cdot\frac{1}{5}[/tex][tex]Use\text{ }\frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d}.[/tex][tex]\frac{3}{8}\cdot\frac{2}{5}=\frac{3}{20}[/tex]Consider the number.
[tex]\frac{7}{8}\cdot\frac{8}{7}=\frac{1}{1}\cdot\frac{1}{1}[/tex]Cancel out the common multiples
[tex]9\cdot\frac{2}{3}[/tex][tex]9\cdot\frac{2}{3}=3\cdot2=6[/tex]Consider the number
[tex]\frac{7}{8}\cdot\frac{8}{7}[/tex]Cancel out the common multiples.
[tex]\frac{7}{8}\cdot\frac{8}{7}=\frac{1}{1}\cdot\frac{1}{1}[/tex][tex]\frac{7}{8}\cdot\frac{8}{7}=1[/tex]Consider the number
[tex]\frac{x}{y}\cdot y=x[/tex][tex]\frac{a}{2b}\cdot\frac{b}{c}=\frac{a}{2}\cdot\frac{1}{c}=\frac{a}{2c}[/tex][tex]\frac{m}{3n}\cdot\frac{n^2}{m}=\frac{1}{3}\cdot\frac{n}{m}=\frac{n}{3m}[/tex]Final answer:
[tex]\frac{3}{8}\cdot\frac{2}{5}=\frac{3}{20}[/tex][tex]9\cdot\frac{2}{3}=6[/tex][tex]\frac{7}{8}\cdot\frac{8}{7}=1[/tex][tex]\frac{x}{y}\cdot y=x[/tex][tex]\frac{a}{2b}\cdot\frac{b}{c}=\frac{a}{2c}[/tex][tex]\frac{m}{3n}\cdot\frac{n^2}{m}=\frac{n}{3m}[/tex]f(x)=-17x+2 and g(x)=x^2+1 find f(-7) + g(-7)
Answer:
171
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f\mleft(x\mright)=-17x+2 \\ g\mleft(x\mright)=x^2+1 \end{gathered}[/tex]To find the value of f(-7) + g(-7), substitute -7 for x in both functions:
[tex]\begin{gathered} f\mleft(-7\mright)=-17(-7)+2=121 \\ g\mleft(-7\mright)=(-7)^2+1=50 \\ \implies f\mleft(-7\mright)+g\mleft(-7\mright) \\ =121+50 \\ =171 \end{gathered}[/tex][tex]5x + 17 = 82[/tex]simplify as much as possible
To answer this question, we can follow the next steps:
1. Subtract 17 to both sides of the equation (we apply here the subtraction property of equality):
[tex]5x+17-17=82-17\Rightarrow5x+0=65\Rightarrow5x=65[/tex]2. To isolate the variable, x, in the equation, we need to divide by 5 to both sides of the equation, as follows:
[tex]\frac{5x}{5}=\frac{65}{5}\Rightarrow\frac{5}{5}=1\Rightarrow x=\frac{65}{5}\Rightarrow x=13[/tex]We can check this result if we substitute this last value into the original equation:
[tex]5x+17=82\Rightarrow5(13)+17=82\Rightarrow65+17=82\Rightarrow82=82[/tex]The result is always TRUE.
Therefore, the value for the unknown value of x is x = 13.
There are 120 teachers. Select a sample of 40 teachers by using the systematic sampling technique.
Given:
Total number of teachers = 120
To select a number of teachers = 40
Required:
To find a sample of 40 teachers by using the systematic sampling technique.
Explanation:
The probability formula is given as:
[tex]\begin{gathered} P=\frac{number\text{ of favourable outcomes}}{Total\text{ number of outcomes}} \\ P=\frac{40}{120} \\ P=\frac{1}{3} \end{gathered}[/tex]Final Answer:
[tex]undefined[/tex]Geometric mean of36 and 21
The Geometric Mean is:
[tex]6\sqrt[]{21}[/tex]Explanation:Given 36 and 21, the Geometric Mean is given as:
[tex]\begin{gathered} m=\sqrt[]{36\times21} \\ =\sqrt[]{6^2\times21} \\ =6\sqrt[]{21} \end{gathered}[/tex]Eliza had $14 and Emma had $64 more than Eliza how much did Emma have?
Given
Eliza had $14
Emma had $64 more than Eliza
Find
how much did Emma have
Explanation
as we have given
Eliza has $14
so , Emma = $64 + $14 = $78
Final Answer
Therefore , the Emma had $78
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2)? Responses The graph of g(x) is the graph of f(x) translated 2 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units right. The graph of g(x) is the graph of f(x) translated 2 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units down. The graph of g(x) is the graph of f(x) translated 2 units up. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units up. The graph of g(x) is the graph of f(x) translated 2 units left.
The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2) so option (D) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
If a function f(x) is transformed by funciton g(x) as shown,
g(x) = f(x+a)
For a>0, then the graph of f(x) shifts left by "a" unit, while if a<0, then the graph of f(x) shifts right side by "a"units.
As per the given function,
g(x) = f(x + 2)
Since 2 > 0 therefore the function will shift 2 units left.
Hence "The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2)".
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The Leaning Tower of Pisa
was completed in 1372 and
makes an 86* angle with
the ground. The tower is
about 57 meters tall, measured
vertically from the ground
to its highest point. If you
were to climb to the top and
then accidently drop your
keys, where would you
start looking for them?
How far from the base of.
the tower would they land?
The distance where the keys would drop from the base is 3.5m
Calculation far from the base of tower?Height of the tower = 57m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
The distance from where the keys drop to the base of the tower can be calculated using
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 57m
Cos θ = x / hyp
Cos 86 = x / 57
X = 57 × cos 86
X = 57× 0.06976
X = 3.97 = 4m
The keys would fall from the tower's base at a distance of about 4 meters.
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Find the exact values of the six trigonometric functions of the real number t
In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.
Then use the trigonometric identity to solve for tangent.
We therefore have the following ratios for sin, cos, and tan.
[tex]\begin{gathered} \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=\frac{\sin t}{\cos t}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8} \\ \\ \text{Therefore,} \\ \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=-\frac{15}{8} \end{gathered}[/tex]Solving for the reciprocal of sin, cos, and tan we have
[tex]\begin{gathered} \csc t=\Big(\sin t\Big)^{-1}=\Big(\frac{15}{17}\Big)^{-1}=\frac{17}{15} \\ \sec t=\Big(\cos t\Big)^{-1}=\Big(-\frac{8}{17}\Big)^{-1}=-\frac{17}{8} \\ \cot t=\Big(\tan t\Big)^{-1}=\Big(-\frac{15}{8}\Big)^{-1}=-\frac{8}{15} \\ \\ \text{Therefore,} \\ \csc t=\frac{17}{15} \\ \sec t=-\frac{17}{8} \\ \cot t=-\frac{8}{15} \end{gathered}[/tex]Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured and the scientists realize that the gas is leaking over time in a linear way. Eight minutes since the experiment started the gas had a mass of 302.4 grams. Seventeen minutes since the experiment started the gas had a mass of 226.8 gramsLet x be the number of minutes that have passed since the experiment started and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time.a) This lines slope-intercept equation is [ ] b) 39 minutes after the experiment started, there would be [ ] grams of gas left. c) if a linear model continues to be accurate, [ ] minutes since the experiment started all gas in the container will be gone.
Here, we want to model an experiment linearlly
From the question, we have it that;
The coordinates are written as;
(number of minutes, mass of gas)
So, what we have to do know is to set up the two given points
These are the points;
(8,302.4) and (17,226.8)
Now, using these two points, we can model the equation
We start by getting the slope of the line that passes through these two points
To do this, we shall use the slope equation
We have this as;
[tex]\begin{gathered} \text{slope m = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (8,302.4)} \\ (x_2,y_2)\text{ = (17,226.8)} \\ \text{substituting these values;} \\ m\text{ = }\frac{226.8-302.4}{17-8}\text{ = }\frac{-75.6}{9}\text{ = -8.4} \end{gathered}[/tex]The general equation representing a linear model is ;
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ is slope} \\ b\text{ is y-intercept} \\ y\text{ = -8.4x + b} \end{gathered}[/tex]To get the y-intercept so as to write the complete equation, we use any of the two points and substitute its coordinates
Let us substitute the coordinates of the first point
[tex]\begin{gathered} 302.4\text{ = -8.4(8) + b} \\ 302.4\text{ = -67.2 + b} \\ b\text{ = 67.2 + 302.4} \\ b\text{ = 369.6 } \end{gathered}[/tex]a) Thus, we have the complete linear model as;
[tex]y\text{ = -8.4x + 369.6}[/tex]b) To get this, we simply substitute the value of x given into the linear model
[tex]\begin{gathered} y\text{ = -8.4(39) + 369.6} \\ y\text{ = -327.6 + 369.6} \\ y\text{ = 42} \end{gathered}[/tex]39 minutes after the experiment started, there would be 42 grams
c) If all the gas is gone, then the value of y will br zero at this point
To get the corresponding x-value which is the time, we have it that;
[tex]\begin{gathered} 0\text{ = -8.4x +369.6} \\ 8.4x=\text{ 369.6} \\ x\text{ = }\frac{369.6}{8.4} \\ x\text{ = 44} \end{gathered}[/tex]In 44 minutes, all the gas in the container will be gone
Choose an equation that models the verbal scenario. The cost of a phone call is 7 cents to connect and an additional 6 cents per minute (m).
"The cost of a phone call is 7 cents to connect and an additional 6 cents per minute (m)"
If "C" indicates the total cost of a phone call and "m" corresponds to the number of minutes the phone call lasted.
The phone call costs 7 cents to connect, this means that regardless of the duration of the call, you will always pay this fee. This value corresponds to the y-intercept of the equation.
Then, the phone call costs 6 cents per minute, you can express this as "6m"
The total cost of the call can be calculated by adding the cost per minute and the fixed cost:
[tex]C=6m+7[/tex]A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different options are available at this store?
If a gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. The number of different options that are available at this store is 1344.
How to find the different options?Using this formula to determine the number of different options
Number of different options available = Number of shapes of boxes × Number of wrapping paper × Number of different bowl
Let plug in the formula
Number of different options available = 8 × 14 × 12
Number of different options available = 1,344
Therefore we can conclude that 1,344 different options are available.
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hello,Can you please help me with question # 25 in the picture?Thank you
To find the sum of an arithmetic sequence up to the nth term, we use the sum formula, which is
[tex]S_n=n(\frac{a_1+a_n}{2})[/tex]where a1 represents the first term, and an the nth term.
The general term of our sequence is
[tex]a_n=3n+2[/tex]We want to sum up to the 16th term. Evaluanting n = 16 and n = 1 on this expression, we get the terms to plug in our formula
[tex]\begin{gathered} a_1=3(1)+2=3+2=5 \\ a_{16}=3(16)+2=48+2=50 \end{gathered}[/tex]Then, the sum is equal to
[tex]\sum_{i\mathop{=}1}^{16}(3i+2)=16(\frac{50+5}{2})=8\cdot55=440[/tex]The result of this sum is 440.
Find the y-coordinate of point P that lies 1/3 along segment CD, closer to C, where C (6, -5) and D (-3, 4).
SOLUTION:
The given ratio is:
[tex]1:3[/tex]• The given points are ,C(6, -5) and D (-3, 4).
Using the section formula, the coordinate of P is:
[tex]\begin{gathered} P=(\frac{1(-3)+3(6)}{1+3},\frac{1(4)+3(-5)}{1+3}) \\ P=(\frac{-3+18}{4},\frac{4-15}{4}) \\ P=(\frac{15}{4},\frac{-11}{4}) \end{gathered}[/tex]Therefore the coordiantes of P
[tex]P=(\frac{15}{4},\frac{-11}{4})[/tex]Newton's law of cooling is T = A * e ^ (- d * t) + C where is the temperature of the object at time and C is the constant temperature of the surrounding mediumSuppose that the room temperature is 71^ + and the temperature of a cup of tea 160when it is placed on the table. How long will it take for the tea to cool to 120 degrees for k = 0.0595943 Round your answer to two decimal places.
Solution
Given
[tex]\begin{gathered} T=Ae^{-kt}+C\text{ --------\lparen1\rparen} \\ \\ C=71 \\ \\ A=160-71 \\ \\ T=120 \\ \\ k=0.0595943 \end{gathered}[/tex]To find the time, we nee to substitute the C, A, T, and k in (1) and then determine (t
[tex]\begin{gathered} 120=(160-71)e^{-0.0595943t}+71 \\ \\ \Rightarrow\frac{120-71}{160-71}=e^{-0.0595943t} \\ \\ \Rightarrow\frac{49}{89}=e^{-0.0595943t} \\ \\ \Rightarrow-0.0595943t=\ln(\frac{49}{89}) \\ \\ \Rightarrow t=\frac{1}{-0.0595943}\ln(\frac{49}{89})=10.01456\text{ s} \end{gathered}[/tex][tex]t=\frac{10.01465}{60}\text{ mins}=0.17\text{ mins}[/tex]Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers
Explanation
Let's remember some properties ofthe fractions ans exponents,
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (ab)^n=a^nb^n \\ (a^n)^m=a^{m\cdot n} \end{gathered}[/tex]so
Step 1
[tex]\lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2[/tex]reduce by using the properties
[tex]\begin{gathered} \lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2 \\ \lbrack\frac{4q}{3^{-1}m^3p^2}\rbrack^2 \\ \lbrack\frac{3^1\cdot4q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{12q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{144q^2}{m^{3\cdot2}p^{2\cdot2}}\rbrack^{} \\ \lbrack\frac{144q^2}{m^6p^4}\rbrack^{} \end{gathered}[/tex]therefore, the answer is
[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]I hope this helps you
A $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent
SOLUTION
From the question, we want to find the value in dollars of the account after 2 years.
We will usethe formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]Hence the answer is 43,548.47 to the nearest cent
There are 3 consecutive even integers that have a sum of 6. What is the value of the least integer?
We can express this question as follows:
[tex]n+(n+2)+(n+4)=6[/tex]Now, we can sum the like terms (n's) and the integers in the previous expression. Then, we have:
[tex](n+n+n)+(2+4)=6=3n+6\Rightarrow3n+6=6[/tex]Then, to solve the equation for n, we need to subtract 6 to both sides of the equation, and then divide by 3 to both sides too:
[tex]3n+6-6=6-6\Rightarrow3n=0\Rightarrow n=\frac{3}{3}n=\frac{0}{3}\Rightarrow n=0_{}[/tex]Then, we have that the three consecutive even integers are:
[tex]0+2+4=6[/tex]Therefore, the least integer is 0.
Multiply the expressions.
-0.6y(4.5 - 2.8y) =
answer 1
-2.86
-2.7
1.68
3.9
--------- y² +
answer 2
-2.86
-2.7
1.68
3.9
Answer:
1.68y²+ 2.7y is the answer
hope it helps
if you halved a recipe that calls for 5 c. chicken broth how much broth would you use
If halved a recipe that calls for 5 c chicken broth, then you would end up using 2.5 c chicken broth (that is two and half c of chicken broth).
Classwork Area of Algebra Tiles 1 An If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units. 1 The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called? ?
The other side of a tile can be called as width of hte tile
A play court on the school playground is shaped like a square joined by a semicircle. The perimeteraround the entire play court is 182.8 ft., and 62.8 ft. of the total perimeter comes from the semicircle.aWhat is the radius of the semicircle? Use 3.14 for atb.The school wants to cover the play court with sports court flooring. Using 3.14 for, how manysquare feet of flooring does the school need to purchase to cover the play court?
The total perimeter of the court is 182.8 ft, of this, 62.8ft represents the perimeter of the semicircle.
a)
The perimeter of the semicircle is calculated as the circumference of half the circle:
[tex]P=r(\pi+2)[/tex]Now write it for r
[tex]\begin{gathered} \frac{P}{r}=\pi \\ r=\frac{P}{\pi} \end{gathered}[/tex]Knowing that P=62.8 and for pi we have to use 3.14
[tex]\begin{gathered} r=\frac{62.8}{3.14} \\ r=20ft \end{gathered}[/tex]The radius of the semicircle is r=20 ft
b.
To solve this exercise you have to calculate the area of the whole figure.
The figure can be decomposed in a rectangle and a semicircle, calculate the area of both figures and add them to have the total area of the ground.
Semicircle
The area of the semicircle (SC) can be calculated as
[tex]A_{SC}=\frac{\pi r^2}{2}[/tex]We already know that our semicircla has a radius of 10ft so its area is:
[tex]A_{SC}=\frac{3.14\cdot20^2}{2}=628ft^2[/tex]Rectangle
To calculate the area of the rectangle (R) you have to calculate its lenght first.
We know that the total perimeter of the court is 182.8ft, from this 62.8ft corresponds to the semicircle, and the rest corresponds to the rectangle, so that:
[tex]\begin{gathered} P_T=P_R+P_{SC} \\ P_R=P_T-P_{SC} \\ P_R=182.8-62.8=120ft \end{gathered}[/tex]The perimeter of the rectangle can be calculated as
[tex]P_R=2w+2l[/tex]The width of the rectangle has the same length as the diameter of the circle.
So it is
[tex]w=2r=2\cdot20=40ft[/tex]Now we can calculate the length of the rectangle
[tex]\begin{gathered} P_R=2w+2l \\ P_R-2w=2l \\ l=\frac{P_R-2w}{2} \end{gathered}[/tex]For P=120ft and w=40ft
[tex]\begin{gathered} l=\frac{120-2\cdot40}{2} \\ l=20ft \end{gathered}[/tex]Now calculate the area of the rectangle
[tex]\begin{gathered} A_R=w\cdot l \\ A_R=40\cdot20 \\ A_R=800ft^2 \end{gathered}[/tex]Finally add the areas to determine the total area of the court
[tex]\begin{gathered} A_T=A_{SC}+A_R=628ft^2+800ft^2 \\ A_T=1428ft^2 \end{gathered}[/tex]GEOMETRY Draw the next two figures in the pattern shown below. OOO
Given , the pattern
O , OO , .....
so, the first term is 1 circle
The second is 2 circles
So, the next two figures are:
OOO , OOOO
The Hughes family and the Gonzalez family each used their sprinklers last summer. The Hughes family's sprinkler was used for 15 hours. The Gonzalez family's sprinkler was used for 35 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Answer:
Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour
Step-by-step explanation:
Let us use the following variables to denote the output rates for each sprinkler.
Let H = water output rate for the Hughes family
Let G = water output rate for the Gonzalez family
(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)
The general equation for the volume of water outputted, V, in time h hours at a rate of r per hour is
V = r x h
Given r
Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H
Water Output for Gonzalez family at rate G for 35 hours = 35 G
The total of both outputs = 1475
That gives us one equation
15H + 35G = 1475 [1]
We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate
H + G = 65 [2]
Let's write down these two equations and solve for H and GThese figures are similar. Thearea of one is given. Find thearea of the other.area=32 in?9 in12 in[ ? Jina
To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inchesIdentify the vertex, axis of symmetry, and if the graph has a maximum or minimum. Then write the function for the graph shown
Answer:
Step-by-step explanation:
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The value of the composite function is: (f o g)(2) = 33.
How to Find the Value of a Composite Function?To evaluate a composite function, take the following steps:
Step 1: Find the value of the inner function by substituting the value of x into the equation of the functionStep 2: Use the value of the output of the inner function as the input for the outer function and simplify to get the value of the composite function.Given the following:
f(x) = x² - 3x + 5
g(x) = -2x
Therefore,
(f o g)(2) = f(g(2))
Find the value of the inner function g(2):
g(2) = -2(2)
g(2) = -4
Find f(g(2)) by substituting x = -4 into the function f(x) = x² - 3x + 5:
(f o g)(2) = f(g(2)) = (-4)² - 3(-4) + 5
= 16 + 12 + 5
(f o g)(2) = 33
Learn more about composite functions on:
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