The equation given is a quadratic equation that has roots -1 and 5.
Roots of Quadratic EquationTo solve this problem, we have to find the roots of the quadratic equation and we can simply multiply through and then calculate the roots.
[tex](x+1)(x-5) = x^2 -5x + x - 5\\f(n) = x^2 -4x - 5[/tex]
Let's solve this quadratic equation above.
Using factorization method, we can find the factors of the quadratic equation and simplify.
[tex]x^2 - 4x -5 = 0\\(x+1)(x-5) = 0\\x + 1 = 0\\or \\x - 5 = 0\\x = -1 or x = 5[/tex]
The roots to the equation (x + 1)(x - 5) = 0 are - 1 and 5.
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Four hundred yards of fence is to be used to endose a rectangular area next to a straight river. The river bank acts as one side of the rectangle, and the fence is used to make the other three sides ofthe rectangle. Suppose the width w in yards of the rectangle is along the river bank.(a) Express the height of the rectangle in terms of w.b) Express the area of the rectangle in terms of w.
400 yards of fence = total fencing
400 = 2 widths + 2 heights
Since one side (width) is along the river, and the river bank acts as one side of the rectangle, the fence will be used in 3 sides:
400 = w+2h
Solving for h:
400-w=2h
(400-w)/2 = h
h= (400-w)/2 (a)
h= 200-1/2w (simplified)
To express the area:
Area of a rectangle : height x width
Since h = 200-1/2w
A = (200-1/2w) w
A = 200w-1/2w^2 (b)
A) graph the function: f(x) = -2^xB) domain of the function?C) range of the function?D) Equation of the asymptote?E) y-intercept of the graph?
We are given the following function:
[tex]y=-2^x[/tex]Part A. We are asked to draw the graph of the function. This is an exponential function with a negative sign, this means that the graph is reflected across the x-axis. Therefore, the graph is:
Part B. The domain of a function is the values that the fuction can take as an input. Since the function is an exponential function, it can take any value of "x" therefore, the domain is all the real numbers, we write this as follows:
[tex]D=(-\infty,\infty)[/tex]Part B. The range of a function is the values that the function outputs, The range of an exponential function are the values that are greater than zero, but since the given function is reflected across the x-axis, this means that the rage is the negative real numbers, therefore, the range is:
[tex]R=(-\infty,0)[/tex]Part D. For an exponential function of the form:
[tex]y=a(b^x)[/tex]The asymptote is x-axis, since zero is never an output of the function. Therefore the equation of the asymptote is:
[tex]y=0[/tex]Part E. The y-intercept is the value of the function when "x = 0", therefore, substituting in the function we get:
[tex]f(0)=-2^0[/tex]Solving the operations:
[tex]f(0)=-1[/tex]Therefore, the y-intercept is -1
Which of the following numbers is a square number? Check all that apply.A. 62B. 64C. 100D. 116
the answer
a perfect square is a number that when two exact same number multiply each other, it produce
example 2 * 2 = 4
4 is a square number and the square root is 2
[tex]\begin{gathered} \text{square root of } \\ a.62=\sqrt{62}=7.87 \\ b.64=\sqrt{64}=8 \\ c.100=\sqrt{100}=10 \\ d.116=\sqrt{116}=10.77 \end{gathered}[/tex]the answer to your question is 64 and 100 which is option B and C
Which of the following represents the difference quotient for f of x is equal to 4 over x question mark
The difference quotient for the given function is:
[tex]-\frac{4}{x*(x + h)}[/tex]
How to get the difference quotient?For the function f(x), we define the difference quotient as:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
In this case, the function is f(x) = 4/x, replacing that in the general difference quotient:
[tex]\frac{4/(x + h) - 4/x}{h}[/tex]
Now we can simplify this to get:
[tex]\frac{4/(x + h) - 4/x}{h} = 4*\frac{1/(x + h) - 1/x}{h} \\\\4*\frac{1/(x + h) - 1/x}{h} = 4*(\frac{1/(x + h)}{h} - \frac{1/x}{h})[/tex]
[tex]4*(\frac{1/(x + h)}{h} - \frac{1/x}{h}) = 4*(\frac{1}{(x + h)*h} - \frac{1}{x*h}) = 4*\frac{x - x - h}{x*h*(x + h)} = -\frac{4}{x*(x + h)}[/tex]
So the correct option is the last one.
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The distance between two cities on a map is 4.1 centimeters. The map uses a scale in which 1 centimeter represents 18 kilometers. What is the actual distance between these two cities in kilometers?
The actual distance between the two cities in kilometers is 73.8 kilometers.
Given:
The distance between two cities on a map = 4.1 centimeters
The Scale used by the map is, 1 centimeter is equivalent to 18 kilometers.
To find the actual distance between the two cities in kilometers,
We know, 1 centimeter = 18 kilometers.
For converting the distance in centimeters to kilometers we multiply the value in centimeters by the value of 1 centimeter i.e.18 kilometers.
So, 4.1 centimeter = (4.1 × 18) kilometers
= 73.8 kilometers
Therefore, the actual distance between the two cities calculated in kilometers is 73.8 kilometers.
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pnereThe radius, R, of a sphere is 5.8 m. Calculate the sphere's volume, V.Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume of a sphere is given by the following formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where r is the radius of the sphere r=5.8m.
Replace this value and solve for V:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot(5.8m)^3 \\ V=\frac{4}{3}\cdot3.14\cdot195.112m^3 \\ V=\frac{2450.61m^3}{3} \\ V=816.9m^3 \end{gathered}[/tex]The volume of the sphere is 816.9 cubic meters.
Find the missing sides
The missing side and angle of the similar polygons are as follows:
∠H = 90°FI = 5.4IH = 4.8BC = 7.7What are similar polygons?Similar polygons are two polygons with the same shape, but not the same size.
Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.
Therefore, polygon ABCD is similar to polygon FGHI. This means the corresponding angles are congruent and the corresponding sides are proportional.
Therefore,
∠C is corresponding angle to ∠H. This means they are both congruent.
Hence,
∠H = 90 degrees
Let's find FI,
10 / 6 = 9 / FI
cross multiply
FI = 54 / 10
FI = 5.4
Let's find IH
10 / 6 = 8 / IH
cross multiply
IH = 48 / 10
IH = 4.8
Let's find BC
10 / 6 = BC / 4.6
cross multiply
BC = 46 / 6
BC = 7.66666666667
BC = 7.7
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Which equation has the same value as X 2/3(6x+12)=-24
The equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .
In the question ,
the equation 2/3(6x+12)=-24 is given
on solving for x ,we get
4x+8 = -24
4x = -24-8
4x = -32
x = -8 .
Solving option(a)
4x+8 = -24
4x = -24-8
4x = -32
x = -8
Solving for option(b)
9x+18 = -24
9x = -24-18
9x = -42
x = -42/9
solving for option(c)
4x = -16
x = -4
solving for option(d)
(18x+36)/2 = -24
18x + 36 = -48
18x = -48-36
18x = -84
x = -84/18
solving for option(e)
4x = -32
x = -32/4
x = -8
we can see that only option (a) and option(e) , given the value of x as -8 .
Therefore , the equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .
The given question is incomplete , the complete question is
Which equation has the same value as X 2/3(6x+12)=-24 ?
Select two options
(a) 4x+8 = -24
(b) 9x+18 = -24
(c) 4x = -16
(d) (18x+36)/2 = -24
(e) 4x = -32
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8.12 Midpoint formula: find the endpoint EUW
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The midpoint of PQ is M(4, 0). One endpoint is P(6, 0). Find the coordinates of the other
endpoint Q.
Write the coordinates as decimals or integers.
‹=OD
Work
The coordinates of the other endpoint Q.=(2,0)
How to calculate the coordinates of the other endpoint Q ?
Given:
Midpoint = PQ = M(4,0)
One endpoint = P = [tex](x_1,y_1)[/tex] = (6,0)
Other endpoint Q= [tex](x_2,y_2)[/tex]
We know that,
[tex]\text{Midpoint PQ}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\=(\frac{6+x_2}{2} ,\frac{0+y_2}{2} )=(4,0)\\\\= > \frac{6+x_2}{2} =4\\\\= > 6+x_2= 8\\\\= > x_2=2[/tex]
[tex]\text{Similarly},\\\\\frac{0+y_2}{2} =0\\\\= > y_2=0[/tex]
So, the Other endpoint Q=(2,0)
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I really need help pls I’m in need of help
Let:
A be the number of pairs of Jeans Amina has.
I be the number of pairs of Jeans Idris has.
T be the total of pairs of Jeans.
Then,
A = 2
I = 3
Then, the equation that represents the total of pairs of jeans is:
[tex]T=A+I[/tex]Substituting the values we can find T:
[tex]\begin{gathered} T=2+3 \\ T=5 \end{gathered}[/tex]Answer:
The equation is: T = A + I.
And the solution is T = 5.
Please help will give Brainliest!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucketw of popcorn and the other axis to represent the number of drinks.
Explain your graph.
Answer:
(Score for Question 2: ___ of 5 points)
Graph the absolute value function.
f(x)=|1/3 x+2|-4
Answer:
(Score for Question 3: ___ of 4 points)
(a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
The required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have been given that the price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
The total amount of spend is $45
As per the given condition, the required inequality would be as
4x + 2y ≥ 45
The situation's representation is in the attached graph with labels for the intercepts.
Here y-axis represents the number of drinks, and the x-axis represents the number of buckets of popcorn.
Thus, the required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.
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What is a number that when you divide it by 2 and subtract 3.8 from the quotient, you get 7?
Let the number x.
Then the number divided by 2 gives
[tex]\frac{x}{2}[/tex]Subtract 3.8 from the quotient gives
[tex]\frac{x}{2}-3.8[/tex]Hence,
[tex]\frac{x}{2}-3.8=7[/tex][tex]\begin{gathered} \frac{x}{2}-3.8=7 \\ \frac{x}{2}=7+3.8=10.8 \\ \Rightarrow x=2\times10.8=21.6 \end{gathered}[/tex]x = 21.6
The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
From the graph, the range of the function in the graph is; 0 ≤ M ≤ 6.5
What is the range of the graph Function?
The range of a function is the set of all possible output values for which the function still exists.
Now, from the graph, we can see that it is a linear graph that starts on the vertical axis with a coordinate of approximately (0, 1) which denotes 1 kg when the volume is 0 liters.
Now, we see that the line of the graph stops at the coordinate (7.5, 6.5) which denotes 6.5 kg when the volume is 7.5 liters.
Therefore the maximum mass is 6.5 kg while the minimum is 0 kg. Thus,;
Range; (0 ≤ M ≤ 6.5)
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36. Hiking You hiked 8.3 miles in Denali
National Park which is 3 miles farther than
you hiked yesterday. How far did you hike
yesterday?
Answer:
You hiked 5.3 miles yesterday
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=5/2x–1y=7/2x–3
System of equations:
[tex]y=\frac{5}{2}x-1[/tex][tex]y=\frac{7}{2}x-3[/tex]Using a graphing calculator we can get the graph:
As the point in which both functions meet is (2, 4), then this is the solution.
Answer: (2, 4)
Jacob bought a book that cost $11.95 and magazines that cost $4.95 each. Isabella bought a book that cost $15.79 and magazines that cost $3.99 each. Jacob spent the same amount or less money than Isabella. Write and solve an inequality to find m, the number of magazines for which Jacob spent less than or the same amount as Isabella.
Answer:
16.90≤19.78
Step-by-step explanation:
g (x)=5x-5,find g (-6)
Answer: -35
Step-by-step explanation:
set the every x in the equation to (-6)
g(-6) = 5(-6)-5
g(-6) = -30-5
g(-6) = -35
(03.06) 5.)Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2OPTIONS: A.) y-6 = 1/2(x+3)B.) y = 1/2x - 6C.) y+3 = 1/2(x-6)D.) y-2y = 12I NEED THIS DONE ASAP!
Answer the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2
A linear equation can have the form
y = mx + b
The slope is m
The point-slope form is
(y- y1) = m(x -x1) (1)
the point (x1, y1) = (6, -3)
______________
Replacing in (1) the slope and the point (x1, y1)
(y- y1) = m(x -x1)
(y- (-3)) = 1/2(x -6)
y+3 = 1/2(x-6)
__________________
So, checking the options the correct answer is C
A.) y-6 = 1/2(x+3)
B.) y = 1/2x - 6
C.) y+3 = 1/2(x-6)
D.) y-2y = 12
An investment offers a total return of 17 percent over the coming year. Powell Arms thinks the total real return on this investment will be only 12 percent. What does Powell believe the inflation rate will be over the next year?
Powell believe that the inflation rate will be 4.46% over the next year .
In the question ,
it is given that
total return offered by the investment((nominal rate) = 17% = 0.17
return according to Powell Arms(real rate) = 12% = 0.12
let the inflation rate be x.
The inflation rate over the next year can be calculated using the formula .
(1+Real rate ) = (1+nominal rate )/ (1+ inflation rate )
Substituting the values , we get
(1+0.12) = (1+0.17)/(1+x)
1.12 = 1.17/(1+x)
1+x = 1.17/1.12
1 + x = 1.0446
x = 1.0466-1
x = 0.0446
x = 4.46%
Therefore , Powell believe that the inflation rate will be 4.46% over the next year .
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Find the constant of proportionality from a graph
Answer: 2
Step-by-step explanation:
The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), [tex]\frac{4-0}{2-0}=2[/tex].
Determining SimilarityAre the following triangles similar?YesNoExplain which similarity condition you used andjustify completely
Given data:
The given figure of the triangles.
In triangle STH and triangle GFH.
[tex]\begin{gathered} \angle T=\angle G \\ \angle THS=\angle GHF(vertically\text{ opposite)} \\ \end{gathered}[/tex]Thus, yes the triangles are similar by angle-angle (AA) property.
3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are each sisters ages
Answer: Jenny = 6 | Kim = 7 | (Unknown Sister because no name) = 44
Step-by-step explanation:
Jenny = 6 years (that we already know)
6 x 2 = 12 - 5 = 7 years for Kim
7 + 6 = 13
To find the unknown age of the last sister, we will subtract 57 - 13 = 44
So the last sister is 44.
(I am very sorry if this is wrong, I am only in Middle School).
Solve the system by substitution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)3x − 2y = 545x + 10y = −30(x, y) =
Solution:
Given:
[tex]\begin{gathered} 3x-2y=54 \\ 5x+10y=-30 \end{gathered}[/tex]Using the graphical method,
The solution is the point of intersection of the two lines.
Therefore, the solution is;
[tex](x,y)=(12,-9)[/tex]Help me pls it would be nice thank youuuuu
(3z + 2) (6-z) = 0 is there more then one solution to this if so can you tell me and use commas?
Answer:
Yes, [tex]z=-\frac{2}{3}, 6[/tex]
Step-by-step explanation:
Using the zero-product property,
[tex]3z+2=0, 6-z=0 \\ \\ \implies z=-\frac{2}{3}, 6[/tex]
Given the right triangle ABC with altitude BD drawn to the hypotenuse AC. If AC=6 and DC=4, what is the length of BC in simplest radical form ?
This problem is an application of the Geometric mean theorem. It says that
[tex]\frac{6}{x}=\frac{x}{4}[/tex]Comment: In other words, it says that the length of BC (x) is the geometric mean between the lengths of AC and DC.
Then,
[tex]x^2=6\cdot4=24[/tex][tex]x=\sqrt[]{24}=2\cdot\sqrt[]{6}[/tex]................................................................................................................................................................
Let's talk a little about the simplest radical form of a square root
[tex]\sqrt[]{a}[/tex]The first step to finding it is to write the number within the root as a product of prime powers, such product is called its integer factorization. Let's do that for 24:
Then, the integer factorization of 24 is
[tex]24=2^3\cdot3[/tex]Thus,
[tex]\sqrt[]{24}=\sqrt[]{2^3\cdot3}[/tex]The idea now is to take out of the root all we can. The rule is that we can only take out powers of 2 (for our root is a square root). In the expression
[tex]2^3\cdot3[/tex]There is only one power of 2, within 2^3. We can write it as
[tex]2^2\cdot2\cdot3[/tex]How are we going to take out it? We are going to take out the base of the power, which is 2 in this case. Then,
[tex]\sqrt[]{24}=2\cdot\sqrt[]{2\cdot3}=2\cdot\sqrt[]{6}[/tex]In simple terms, the simplest radical form of a root is what results after taking out the root all that can be taken out.
Find the length of side QS. Round to the nearest tenth.Q39Р16°R28°S
QS = 20.7
Explanation:To get length of side QS, we will consider triangle SQR (right angle triangle)
opposite (the side opposite the angle 28°) = QS
adjacent = base = 39
We apply tangent ratio:
tan28 = opposite/adjacent
tan28 = QS/39
QS = 39 × tan28
QS = 39 × 0.5317
QS = 20.7363
To the nearest tenth, QS = 20.7
5x - 29.4 + 1/2x when x equals -11/5
The answer is -83/2
Decimal Form: -41.5
Mixed Number Form: -41 1/2
Given any triangle ABC labeled as shown, the law of sines states: B B AN b sino sin 4 sin B А. sin 4 sin B В. sino sin 4 sin B C. sino a sin A sino sin B D.
Answer: According to the law of sines, we have the following:
Therefore, according to this, the answer is Option (B).
Find the length of the missing hypoden as a right triangle if the two legs have lengths five and 12.
To find the hypotenuse we going to use the Pythagorean theorem
[tex]c^2=a^2+b^2[/tex]being c the hypotenuse and a and b the other two sides
Replacing
[tex]c^2=5^2+12^2[/tex]Solving
[tex]\begin{gathered} c^2=25+144 \\ c^2=169 \\ c=\sqrt{169} \\ c=13 \end{gathered}[/tex]Answer: hypotenuse = 13