Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?
Answers
Area = base x height
A = 8 x 6 = 48 m²
Related Questions
[tex] \frac{x - 2}{x + 3} + \frac{10x}{x {}^{2 } - 9}[/tex]simplify the sum. state any restrictions on the variables.
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We have
[tex]\frac{x-2}{x+3}+\frac{10x}{x{}^2-9}[/tex]first, we need to factorize the next term
[tex]x^2-9=(x+3)(x-3)[/tex]so we have
[tex]\frac{x-2}{x+3}+\frac{10x}{(x+3)(x-3)}[/tex]Remember in order to sum a fraction the denominator must be the same
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]then we solve the multiplications (x-2)(x-3)
[tex]\frac{x^2-3x-2x+6+10x}{(x+3)(x-3)}=\frac{x^2+5x+6}{(x+3)(x-3)}[/tex]then we can factorize the numerator
[tex]x^2+5x+6=(x+3)(x+2)[/tex]so the simplification will be
[tex]\frac{x^2+5x+6}{(x+3)(x-3)}=\frac{(x+3)(x+2)}{(x+3)(x-3)}=\frac{(x+2)}{(x-3)}[/tex]the final result is
[tex]\frac{(x+2)}{(x-3)}[/tex]Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
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1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]The picture below shows a pole and its shadow:
What is the height of the pole?
121 centimeters
220 centimeters
225 centimeters
231 centimeters
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The height of the pole according to the attached image and parameters given is; 220 cm.
What is the height of the pole as required in the task content?It follows from the task content that the height of the pole is to be determined from the parameters given.
From observation, the triangle formed by the situation is a right triangle.
Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².
Therefore, we have;
221² = 21² + p²
p² = 48,841 - 21²
p² = 48,400
p = √48,400
p = 220.
On this note, the height of the pole is; 220 cm.
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If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m
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One square has area 289 square meters, and the other has area
[tex]8m\times8m=64m^2[/tex]Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have
[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]Please help solve thank you
Answers
a) 2711/7576
b) 43
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Explanation:
a) 2711 are e-bikes and there are 3277+2711+1588 = 7576 total bikes. Divide the values to get 2711/7576 . This fraction cannot be reduced because the GCF of 2711 and 7576 is 1.
---------
b) There are 3277 bikes with fat tires out of 7576 total. Use a calculator to get 3277/7576 = 0.43255 approximately. This converts to 43.255% and then rounds to 43%
The percent sign is already typed in, so you just need to type in the whole number 43 for this box.
use the graph to find the following A) find the slope of the lineB) is the line increasing or decreasingC) estimate the vertical intercept(x y)=
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The Solution.
To find the slope of the line from the given graph:
First, we shall pick two coordinates in the graph, that is
[tex](0,2),(2,-1)[/tex]This implies that
[tex]\begin{gathered} (x_1=0,y_1=2)\text{ and} \\ (x_2=2,y_2=-1) \end{gathered}[/tex]By formula, the slope is given as below:
[tex]\text{ slope=}\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the values in the above formula, we get
[tex]\begin{gathered} \text{ Slope=}\frac{-1-2}{2-0} \\ \\ \text{ Slope =}\frac{-3}{2} \end{gathered}[/tex]So, the slope of the line is -3/2
b. From the graph, and from the slope being a negative value, it is clear that the line graph is Decreasing.
c. To estimate the vertical intercept is to find the y-intercept of the line.
Clearly from the graph, we can see that the vertical intercept is (0,2), that is, the point where the line cut the y-axis.
Therefore, the vertical intercept is (0,2).
The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.6, 8, 9, 6, 5,Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
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For this type of problem we use the following formula:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x_i-\mu)^2}{N},} \\ \\ \end{gathered}[/tex]where μ is the population mean, xi is each value from the population, and N is the size of the population.
First, we compute the population mean in order to do that we use the following formula:
[tex]\mu=\frac{\Sigma x_i}{N}\text{.}[/tex]Substituting each value of x_i in the above formula we get:
[tex]\mu=\frac{6+8+9+6+5}{5}=\frac{34}{5}=6.8.[/tex]Now, we compute the difference of each x_i with the mean:
[tex]\begin{gathered} 6-6.8=-0.8, \\ 8-6.8=1.2, \\ 9-6.8=2.2, \\ 6-6.8=-0.8, \\ 5-6.8=-1.8. \end{gathered}[/tex]Squaring each result we get:
[tex]\begin{gathered} (-0.8)^2=0.64, \\ (1.2)^2=1.44, \\ (2.2)^2=4.84, \\ (-0.8)^2=0.64, \\ (-1.8)^2=3.24. \end{gathered}[/tex]Now, we add the above results:
[tex]0.64+1.44+4.84+0.64+3.24=10.8.[/tex]Dividing by N=5 we get:
[tex]\frac{10.8}{5}=2.16.[/tex]Finally, taking the square root of 2.16 we obtain the standard deviation,
[tex]\sigma=\sqrt[]{2.16}\approx1.47.[/tex]Answer:
[tex]\sigma=1.47.[/tex]Evaluate: sin-¹(1)
A) 0
B) pi/3
C)pi/2
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Answer:
The correct answer is C. Pi/2
Step-by-step explanation:
I got it wrong on edgen, and it told me the correct answer was C.
I'm having a problem with this logarithmic equation I will include a photo
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For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,
[tex]\begin{gathered} x-8=0 \\ x-8+8=0+8 \\ x=8 \\ \text{Vertical asymptotes: x = 8} \end{gathered}[/tex]The domain of the function can be found below
[tex]\begin{gathered} x-8>0 \\ solve\text{ the inequality to obtain the domain} \\ x>8 \\ solve\text{ for x to obtain the domain: x>8 or interval form :(8, }\infty\text{)} \end{gathered}[/tex]y = 2x - 4 Find the solution/root/zero.
Answers
The solution of the linear equation y = 2 · x - 4 is x = 2.
How to find the solution of a linear equationLinear equations are first order polynomials. In this problem we need to solve for x in a linear equation, this can be done by means of algebra properties. The complete procedure is shown below.
Step 1 - We find the find the following expression:
y = 2 · x - 4
Step 2 - We make y equal to zero and we use the symmetric property for equalities:
2 · x - 4 = 0
Step 3 - By compatibility with addition, existence of additive inverse, modulative, associative and commutative properties
2 · x = 4
Step 4 - By compatibility with multiplication, existence of multiplicative inverse and modulative, associative and commutative properties we get the following result:
x = 2
The solution of the linear equation is x = 2.
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Write the standard form of the equation and the general form of the equation of the circlewith radius r and center (h.k). Then graph the circle.r= 10; (h,k) = (8,6)The standard form of the equation of this circle isThe general form of the equation of this circle is(Simplify your answer.)Graph the circle.-20 -18Click toenlargegraph
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To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be
[tex](x-h)^2+(y-k)^2=r^2[/tex]In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be
[tex](x-8)^2+(y-6)^2=10^2=100[/tex]The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that
[tex](a-b)^2=a^2-2a\cdot b+b^2[/tex]So, applying this to the standard equation we get
[tex](x-8)^2=x^2-16x+64[/tex][tex](y-6)^2=y^2-12y+36[/tex]So our equation becomes
[tex]x^2-16x+64+y^2-12y+36=100[/tex]Operating on the left side, we have
[tex]x^2-16x+y^2-12y+100=100[/tex]By subtracting 100 on both sides, we get
[tex]x^2-16x+y^2-12y=0[/tex]which the general form of the equation of the given circle.
Using a graphing tool, we have that the circle's graph would be
im doing math and im wondering when do i switch the inequality?
Answers
Question:
Solve the following inequality:
[tex]12x+6<17[/tex]Solution:
Consider the following inequality
[tex]12x+6<17[/tex]solving for 12x, we get:
[tex]12x<17-6[/tex]this is equivalent to:
[tex]12x<11[/tex]solving for x, we get:
[tex]x<\frac{11}{12}[/tex]so that, the correct answer is:
[tex]x<\frac{11}{12}[/tex]What is the probability that a data value in a normal distribution is between a Z score of -1.52 and Z score of -.34
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We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34
[tex]P(-1.52First, we need to find out the probability corresponding to the given two Z-scoresFrom the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643
From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669
So, the probability is
[tex]\begin{gathered} P(-1.52Therefore, the probability that a data value in a normal distribution is between a Z score of -1.52 and a Z score of -0.34 is 30.3%Option A is the correct answer.
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answers
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
To kknow more about the even number
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Please help 100 points
Answers
Answer:
y = - 6x² - 12x + 2======================
GivenVertex of parabola = (- 1,8),Point on the graph = (0, 2).To findThe equation of the parabola in standard form.SolutionWe can represent the quadratic equation in vertex or standard forms.
Vertex form:
y = a(x - h)² + k, where (h, k) is the vertex, a- coefficientStandard form:
y = ax² + bx + c, where a and b are coefficients and c- constantUse the vertex form with given coordinates of the vertex:
y = a(x - (-1))² + 8 ⇒y = a(x + 1)² + 8Use the other point to find the value of a:
2 = a(0 + 1)² + 82 = a + 8a = - 6The equation is:
y = - 6(x + 1)² + 8Convert it to standard form:
y = - 6x² - 12x - 6 + 8y = - 6x² - 12x + 2Answer:
[tex]y=-6x^2-12x+2[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex.
Given:
Vertex = (-1, 8)Point on the curve = (0, 2)Substitute the given values into the vertex formula and solve for a:
[tex]\implies 2=a(0-(-1))^2+8[/tex]
[tex]\implies 2=a(1)^2+8[/tex]
[tex]\implies 2=a+8[/tex]
[tex]\implies a=-6[/tex]
Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:
[tex]\implies y=-6(x-(-1))^2+8[/tex]
[tex]\implies y=-6(x+1)^2+8[/tex]
[tex]\implies y=-6(x^2+2x+1)+8[/tex]
[tex]\implies y=-6x^2-12x-6+8[/tex]
[tex]\implies y=-6x^2-12x+2[/tex]
Therefore, the quadratic function in standard form whose graph has the given characteristics is:
[tex]y=\boxed{-6x^2-12x+2}[/tex]
3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
Answers
we have the expression
[tex]3a^2-3a-36[/tex]step 1
Factor 3
[tex]3(a^2-a-12)[/tex]step 2
equate to zero
[tex]3(a^2-a-12)=0[/tex]step 3
Solve
[tex](a^2-a-12)=0[/tex][tex]\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}[/tex]Rewrite as perfect squares
[tex](a-\frac{1}{2})^2=\frac{49}{4}[/tex]take the square root on both sides
[tex]\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}[/tex]the values of a are
a=4 and a=-3
therefore
[tex]3(a^2-a-12)=3(a-4)(a+3)[/tex]Can you help me please and thank you very much
Answers
Answer:
∠ FAE = 120°
Step-by-step explanation:
4x and 2x are a linear pair and sum to 180° , that is
4x + 2x = 180
6x = 180 ( divide both sides by 6 )
x = 30
then
∠ FAE = 4x = 4 × 30 = 120°
A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.
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We know the formula d=rt where d is distance, r is rate and t is time
Emmet:
d = 6 yd/s * t
Ayana:
d = 9 yd/s * t
We give Emmet 30 less yards to run
Emmet:
d - 30 = 6 yd/s * t
d = 6t + 30
Setting the equations equal to each other
9 * t = 6t + 30
Subtract 6t from each side
9t-6t = 30
3t = 30
Divide by 3
3t/3 = 30/3
t = 10 seconds
It will take 10 seconds for Ayana to catch up
Ayana:
d = 9 yd/s * t
d = 8 * 10 = 90 yds
through: (-5,4) perpendicular to x=5
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First let's calculate the slope of the straight line
For slopes that are perpendicular to each other we can use the following formula
[tex]m1m2=-1[/tex]Where
m1 = original slope
m2 = perpendicular slope
[tex]\begin{gathered} m2=-\frac{1}{m1} \\ m2=-\frac{1}{5} \end{gathered}[/tex]Now for the intersection
[tex]\begin{gathered} b=y-mx \\ b=4-(\frac{-1}{5})\cdot(-5) \\ b=4-1 \\ b=3 \end{gathered}[/tex]The equation of the line that passes through the point (-5,4) with a slope of -1/5 is
[tex]y=-\frac{1}{5}x+3[/tex]What's the volume of a cube with a side length of 3 inches?
Answers
ANSWER
27 in³
EXPLANATION
The volume of a cube is the cube of its side length, L,
[tex]V=L^3[/tex]So, if a cube has a side length of 3 inches, then its volume is,
[tex]V=3^3in^3=27\text{ }in^3[/tex]Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.
Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.X=60 degrees
Answers
Given:
An angle is x= 60 degrees.
Required:
Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.
Explanation:
First, draw a line then construct an angle of 60 degrees.
Now take a point B on the line that is making an angle of 60 degrees cut the arc from point B with the same measure of arc A.
Now cut the arcs from point A that join the line l and from C that joins m as with the same arc. Draw a line with the intersecting arc.
Thus the angle
[tex]\theta[/tex]will be an interior angle of measures 60 degrees.
Final Answer:
The figure is attached in the explanation part.
- A chemist mixes 2,362 milliliters of a solution. The solution must be divided equally among 8 beakers. How much solution should be poured into each beaker?
Answers
Answer:
295.25mm
Explanation:
If the chemist mixes 2362mm of a solution and needs to divide it equally into 8 breakers, to determine how much solution should be poured into each breaker, we have to divide 2362mm divide 8;
[tex]\frac{2362}{8}=295.25\operatorname{mm}[/tex]In the diagram below, BS and ER intersect as show. Determine the measure of
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Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14
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An exponential function which is represented by the table above is: f(x) = 4(1/2)^x
What is an exponential function?An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.From the table above, we would calculate the value of a and b:
At x = 0 and y = 4; the value of a (initial value) is 4.
Rate of change, b = Δy/Δx
Rate of change, b = 1/2
Substituting the parameters into the formula, we have;
f(x) = abˣ
f(x) = 4(1/2)^x
Check:
f(x) = 4 × (1/2)^x f(x) = 4 * ( 1/2 )^x
f(x) = 4 × (1/2)² f(x) = 4 × (1/2)⁻²
f(x) = 4 × 1/4 f(x) = 4 × 4
f(x) = 1 f(x) = 16
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How do I understand Standard Form of a Line? I don't know how to do it.
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There are several forms in which one can write the equation of a line. Have in mind that TWO variables should be included in the equation. These two variables are: x and y.
If you type the equation in a form that looks like:
A x + B y = C
where the A, B, and C are actual numbers (like for example: 3 x - 2 y = 5)
This is the standard form of a line. to recognize it notice that bith variables x an y appear in separate terms on the LEFT of the equal sign., and a pure number (no variables) appears on the right of the equal sign.
Another form of writing the equation of a line is in the so called "solpe-intercept" form. This form looks like:
y = m x + b
Notice that in this case the variable ÿ" appears isolated on the left , and on the right of the equal sign you get a term with the variable x, and another constant (pure number) term (b). Like for example in the case of:
y = 3 x
please help me with this problem this question asks for the angle measure and if the lines are tangent
Answers
step 1
we have that
44=(1/2)[180-arc} ------> by exterior angle
solve for arc
88=180-arc
arc=180-88
arc=92 degrees
give me a minute to draw a figure with letters to better understand the problem
we have that
x+?=180 degrees -------> by form a linear pair (supplemenatry angles)
x=arc=92 degrees ------> by central angle
so
?=180-92
?=88 degrees
therefore
the missing angle is 88 degreesQUESTION 241 POINTFor a rectangular solid with length 14 feet, height 17 feet, and width 6 feet, find the a. volume and b. surface area.Provide your answer below:volume =cubic feet, surface areasquare feetFEE
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The volume and surface area of a rectangular prism are given by the formulas below
[tex]\begin{gathered} V=l*b*h \\ A=2(lb+bh+hl) \\ l\rightarrow\text{ length} \\ w\rightarrow width \\ h\rightarrow\text{ height} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} l=14,w=6,h=17 \\ \Rightarrow V=14*6*17=1428 \\ and \\ A=2(14*6+6*17+17*14)=848 \end{gathered}[/tex]Thus, the answers are: Surface area=848ft^2, and Volume=1428ft^3
Solve the system. Is the answer (3,0) or (0, -1) or no solution or infinitely many solutions?
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Given:
[tex]\begin{gathered} \frac{1}{3}x+y=1\ldots..(1) \\ 2x+6y=6\ldots\text{.}(2) \end{gathered}[/tex]Solve the system of equations.
Equation (2) can be simplified as,
[tex]\begin{gathered} 2x+6y=6 \\ \text{Divide by 6 on both sides} \\ \frac{2x}{6}+\frac{6y}{6}=\frac{6}{6} \\ \frac{1}{3}x+y=1\text{ which represents the equation (1)} \end{gathered}[/tex]Moreover, the slope and y-intercept of both the equation of lines are the same.
It shows that the lines are coincident.
The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.
Converting between scientific notation and standard form in a real-world situation
Answers
Answer:
[tex]\begin{gathered} a)9.54\times10^6\text{square miles} \\ b)0.0061\sec onds_{} \end{gathered}[/tex]Explanations:
a) The scientific notation is generally expressed as;
[tex]A\times10^n[/tex]A is any real numbers between 1 and 10
n is an integer
Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;
[tex]9,540,000=9.54\times10^6mi^2[/tex]From the scientific notation, A = 9.54 and n = 6
b) Given the scientific notation as shown:
[tex]6.1\times10^{-3}\text{seconds}[/tex]Writing in standard form means writing in the normal way we write numbers/decimals. Hence;
[tex]6.1\times10^{-3}=0.0061\text{seconds}[/tex]How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50 foot radius? Round to the nearest whole number if needed
Answers
Given:
The radius of the circular garden is 50 feet.
First, find the circumference of the circle.
[tex]\begin{gathered} C=2\pi\times r \\ C=2\pi(50) \\ C=100\times3.14 \\ C=314 \end{gathered}[/tex]As we know that 6 inches equal 1/2 feet.
[tex]\frac{314}{\frac{1}{2}}=314\times2=628[/tex]Answer: There are 628 flowers will be needed for 314 feet circular garden.