The component form of the vector that translates the top triangle to the bottom triangle is (3, -5). This is further explained below.
What is a vector?Generally, a number with both direction and magnitude, especially when used to map out where one point in space is in relation to another.
In conclusion, The vector that converts the top triangle to the bottom triangle has the following component form: (3, -5).
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Let f(x)=147+2e−0.6x.
What is f(3)?
The value of f(3) is 147.3306
How to evaluate the function?The function is given as:
[tex]f(x)=147+2e^{-0.6x[/tex]
Substitute 3 for x
[tex]f(3)=147+2e^{-0.6*3[/tex]
Evaluate the product
[tex]f(3)=147+2e^{-1.8[/tex]
Evaluate the exponent
f(3)=147 + 2* 0.1653
Evaluate the sum
f(3) = 147.3306
Hence, the value of f(3) is 147.3306
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Find the range of the function y=-x^2-3x when the domain is {-5, 0, 2}
The range of the function y = -x² - 3x when the domain is {-5,0,2} is:
{-10, 0}.
What is the range of a function?The range of a function is the set that contains the output values for the given domain of the function.
In this problem, the domain is:
{-5,0,2}.
Hence the output values are:
-(-5)² - 3(-5) = -25 + 15 = -10.-(0)² - 3(0) = 0.-(2)² - 3(2) = -4 + -6 = -10.Hence the range is:
{-10, 0}.
-10 repeats, but goes only once on the range.
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Use a calculator to find the mean of the data. {211, 226, 186, 221, 181, 228, 207, 215, 203, 203, 204, 196, 226, 212, 212, 201, 219, 191, 191, 185, 193, 231}
The mean of the given data is 206.5.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."It is the total (sum) of all the values in a set of data, such as numbers or measurements, divided by the number of values in the list. Add up all of the values in the set to find the mean. Then divide the total by the number of possible values.To find the mean of the given data:
Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542
Number of values = 22
Mean = 4,542 ÷ 22 = 206.5
Therefore, the mean of the given data is 206.5.
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Answer:
Step-by-step explanation:
Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
72.5 in2
75.5 in2
83 in2
96 in2
Answer:
83in²
Step-by-step explanation:
This can also be expressed as;
Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF
For ∆ABF;
Area of ∆ABO=∆AOF
Area of ∆ABF=2×Area of ∆ABO
Area of ∆ABO=1/2×Length×height
=1×4×7/2=28/2=14in
But area of ∆ABF=2×Area of ∆ABO
Area=2×14in=28in.
Area of rectangle;
Area=length×breadth
Area=5in×8in=40in.
Area of ∆DEF=2×Area of ∆EFG
Area=1/2× base× height
Area=1×2.5×6/2
Area=15/2=7.5in.
But area of ∆EFG=2×7.5in
=15in.
Area of polygon=28in+40in+15in=83in
If a random variable is characterized by (infinitely) uncountable values within any interval, it is known as ________ variable
Answer:
Step-by-step explanation:
i doont know
Evaluate each of the following
1: -21 ÷ 7
In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.
Divide 21 ÷ 7
we get = 3
Mark it as negative number = -3
Hope this helps :)
Given: y varies directly as x squared and inversely as z cubed. If y = 12 when x = 4 and z = 2, find x when y = 1.728 and z = 5.
Select one:
a. x=6
b. x=18
c. x=27
d. x=36
Answer:
a
Step-by-step explanation:
given y varies directly as x² and inversely as z³ then the equation relating them is
y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 4 and z = 2 , then
12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )
96 = 16k ( divide both sides by 16 )
6 = k
y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation
when y = 1.728 and z = 5 , then
1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )
216 = 6x² ( divide both sides by 6 )
36 = x² ( take square root of both sides )
[tex]\sqrt{36}[/tex] = x , that is
x = 6
Please help
Rewrite in index notation and then differentiate. Answer in the same form as the question.
[tex]y=-5x^2 \sqrt{x}[/tex]
I think that [tex]y=-5x^2(x)^\frac{1}{2}[/tex]
is the first part rewriteing in index notation if u could tell me if I am right then differentiate just show each step as I know how to differentiate I just for some reason can get this question right.
Answer:
I hope I've finally done justice to it.
Step-by-step explanation:
[tex]y=-5x^2 \sqrt{x}[/tex]
[tex]y=-5x^2(x)^\frac{1}{2}[/tex]
[tex]y=-5( {x}^{2 + \frac{1}{2} }) = - 5 {x}^{ \frac{5}{2} } [/tex]
[tex] \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } [/tex]
[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } [/tex]
[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } [/tex]
can someone please help me(20 points will give brainliest!!!)
Answer:
a. 1080
b. 405
Step-by-step explanation:
Function evaluation is often conveniently done using a calculator. Many calculators know about the order of operations, so can be used without fear of an incorrect evaluation.
a)Put the value where the variable is and do the arithmetic.
f(x) = 40(3^x)
f(3) = 40(3^3) = 40(27) = 1080
b)g(x) = 5(3^(x+1))
g(3) = 5(3^(3+1)) = 5(3^4) = 5(81) = 405
Which expression is equivalent to 3square root x^5y?
Answer: Choice B
Work Shown:
[tex]\sqrt[3]{\text{x}^5\text{y}}\\\\(\text{x}^5\text{y})^{\frac{1}{3}}\\\\(\text{x}^5)^{\frac{1}{3}}*(\text{y})^{\frac{1}{3}}\\\\\text{x}^{\frac{5}{3}}\text{y}^{\frac{1}{3}}\\\\[/tex]
What are the solutions of the equation x4 6x2 5 = 0? use u substitution to solve.
The value of the x from the given equation is a +i and -i and +5i and -5i.
According to the statement
we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]
and we have to find the value of x by the u substitution.
So,
The given equation is
[tex]x^4 + 6x^2 +5 =0[/tex]
Put [tex]x^2 = u[/tex]
By substitution method
Then the equation become
[tex]u^2 +6u +5 = 0[/tex]
And solve the equation then
[tex]u^2+ u +5u +5 = 0[/tex]
Then
u(u +1) + 5(u +1) = 0
(u+5) (u +1) = 0
Then
the value of u is -1 and -5 then
The value of x is
[tex]x = \sqrt{u}[/tex]
x = √-5 And √-1
Then the value of x is +i and -i and +5i and -5i.
So, The value of the x from the given equation is a +i and -i and +5i and -5i.
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Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
Answer:
a) 52
b)115
Step-by-step explanation:
(Sequences and Summations) How would you solve this? Please give an explanation rather than just answering the question.
Step-by-step explanation:
To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.
Use the above formula by replace a and d then you'll get the answer. Hope this helps.
This table defines function f:
Answer:
Neither
Step-by-step explanation:
This function isn't even, because
[tex]f(x) = f( - x)[/tex]
Basically this mean for every x opposites the y value should be the same.
Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.
This function isn't odd because
[tex]f( - x) = - f(x)[/tex]
Basically, this means our y values should be reflected about the orgin,
here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.
So The answer is neither
Need help with my work please
Study island math pls helppp
I will love you if you answer
Answer:
Since <ABC ~= <DBE and <BAC ~= <BDE, the triangle s are similar by angle-angle.
Alan is arranging 3 different stuffed toys in a row on a shelf. create a sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e).
The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
How to create the sample space?The given parameters are
Stuffed toys, n = 3
Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).
The number of arrangement is calculated as;
Ways = nPr
Substitute the known values in the above equation
Ways = 3Pr
Apply the permutation formula
Ways = 3!/0!
0! =1
So, we have
Ways = 3!/1
This gives
Ways = 3!
Expand
Ways = 3 * 2 * 1
Evaluate
Ways = 6
This means that the sample size is 6
Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
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using graphing, what is the approximate solution of this equation?
3x[tex]3xx^{2} -6x-4=\frac{2}{x+3}+1[/tex]
Answer:
D. x ≈ 2.60
Step-by-step explanation:
The equation we have graphed is the one shown in the attachment. It is slightly different from the one in this problem statement.
Graphical solutionIt is often convenient to find a graphical solution to an equation by writing it in the form ...
f(x) = 0
Then the solutions are the x-intercepts of the graph, points that most graphing calculators can readily identify.
We have done this here by defining ...
[tex]y_1=3x^2-6x-4\\\\y_2=-\dfrac{2}{x+3}+1[/tex]
The graph is of y₁ -y₂. X-values where y₁-y₂ = 0 are solutions to the original equation, y₁ = y₂.
This equation is seen to have three solutions, approximately ...
x = {-3.05, -0.55, 2.60}
Of these, only x ≈ 2.60 is listed among the answer choices.
__
Additional comment
The value of y₁ -y₂ expressed in standard form is ...
[tex]3x^2-6x-4+\dfrac{2}{x+3}-1=0\\\\\dfrac{(x+3)(3x^2-6x-5)+2}{x+3}=0\\\\\dfrac{3x^3+3x^2-23x-13}{x+3}=0\\\\3x^3+3x^2-23x-13=0\quad(x\ne -3)[/tex]
The irrational solutions to this cubic can be found "exactly" by any of several applicable formulas. Numerical solutions are almost trivial to find with appropriate technology.
x ≈ {−3.04857564747, −0.547524627423, 2.5961002749}.
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
Two spheres have volumes of 87 cm³ and 647 cm³. If the surface area of the smaller sphere is 167 cm², what is the
surface area of the larger sphere?
64 cm²
96 cm²
128 cm²
256 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
How to determine the surface area of the sphere by the use of direct variation formulas
In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:
V/A = k · r (1)
Where:
r - Radiusk - Proportionality constantThen, we can derive the following relationship between the two spheres by eliminating the proportionality constant:
V/(A · r) = V'/(A' · R) (2)
Where:
r - Radius of the smaller sphere.R - Radius of the larger sphere.First, we need to determine the radii of the spheres:
Larger radius
R = ∛(3 · V' / 4π)
R = ∛(3 · 647 / 4π)
R ≈ 5.365 cm
Smaller sphere
r = ∛(3 · V / 4π)
r = ∛(3 · 87 / 4π)
r ≈ 2.749 cm
Lastly, we find the surface area of the larger sphere:
A · r · V' = A' · R · V
A' = (A · r · V') / (R · V)
A' = (167 · 2.749 · 647) / (5.365 · 87)
A' = 636.365 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
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Differentiation of x raised to the power of x
Answer:
[tex] {x}^{x} (1 + log(x)) [/tex]
I hope this helps you.
Write an equation that represents the line.
Use exact numbers.
First point (1,2)
Second point is (4,4)
Answer: equation y= 3/2x+ 4/3
How many solutions does this system of equations have? a. no solution b. 1 solution c. 2 solutions d. 3 solutions
This system of equations have infinite solution.
how many solution does this equation have?If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
Given that,
The system is 2x + y = 1 and 4x + 2y = 2. It is graphed below.
Solutions to a system are the intersection points. Since these two lines are the same line they intersect everywhere. There are infinitely many solutions.
2x+y = 1 ...........(1)
4x+2y = 2 .......(2)
Then from equation (2) dividing by 2 on both side
2x+y = 1
since both lines are same. They overlap to each other.it means the equation have many solution.
Hence,This system of equations have infinite solution.
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The above question is not complete.
How many solutions does this system of equations have?
(a) none
(b) exactly two
(c) infinitely many
(d) exactly one
Graph of a system of linear equations. Equation 1 is 2x plus y equals 1.. Equation 2 is 4x plus 2y equals 2. The graphs are the same line.
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.
Translate the phrase into a variable expression. Use the letter d to name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
the number of dollars Paul owes minus 18...
Answer here
Answer:
d - 18
Step-by-step explanation:
The question said to use d as the variable. We do not know the number of dollars Paul owes. So we put d for that amount.
Then "minus" means to subtract 18.
Writing the expression is all that is being asked for. Translating the words into algebra. We aren't solving anything. Not even writing an entire equation, just an expression, so it has no equals sign.
let h(x)=-1/3x+2. Find -4h(9)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]
we need to find -4 h(9) :
[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]
[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]
[tex]\qquad❖ \: \sf \:4[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
Solid rock is an unlevered firm with an ebit of $10 million and an unlevered cost of capital of 12 percent. if the tax rate is 40 percent, what is the value of the firm?
The value of the firm is $50 million
How to determine the value of the firm?The given parameters are:
EBIT = $10 million
Tax Rate, Tc = 40%
Unlevered cost of capital, RU = 12%
The value of the firm is calculated as:
Value = EBIT*(1 - Tc)/Ru
This gives
Value = 10 million *(1 - 40%)/12%
Evaluate the expression
Value = 50 million
Hence, the value of the firm is $50 million
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At the movie theatre, child admission is $6.80 and adult admission is $9.90. On Thursday, twice as many adult tickets as child tickets were sold, for a total sales
of $984.20. How many child tickets were sold that day?
Number of child tickets:0
Answer:
37 child tickets / 74 adult tickets
Step-by-step explanation:
I randomly picked a number and increased or decreased whether the solution was too high or low (guess and check)
The number of child tickets sold that day is 37.
We have,
Let's assume the number of child tickets sold is "C" and the number of adult tickets sold is "A."
The cost of a child ticket: $6.80
The cost of an adult ticket: $9.90
The total sales for the day: $984.20
The number of adult tickets sold is twice the number of child tickets sold:
A = 2C
To find the number of child tickets sold, set up an equation based on the total sales:
6.80C + 9.90A = 984.20
Substituting the value of A from equation 4:
6.80C + 9.90(2C) = 984.20
Simplifying the equation:
6.80C + 19.80C = 984.20
26.60C = 984.20
C = 984.20 / 26.60
C ≈ 37
Therefore,
37 child tickets were sold that day.
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HELP ME THIS IS DUE IN 2 HOURS
The volume of the composite figure is 3532.5 cubic inches
How to determine the volume of the composite figure?From the given figure, we have the following dimensions:
Height, h = 15 inchesRadius of small cylinder, r = 5 inchesRadius of large cylinder, R = 10 inchesThe volume of a cylinder is
V = πr^2h
So, the volume of the composite figure is
V = πR^2h - πr^2h
Substitute the known values in the above equation
V = 3.14 * 10^2 * 15 - 3.14 * 5^2 * 15
Evaluate the product
V = 3532.5
Hence, the volume of the composite figure is 3532.5 cubic inches
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What is the slope of the line that passes through
the points (2,
-4) and (5, 2)? Write your
answer in simplest form.
Answer:
2
Step-by-step explanation:
slope : ( The amount y increases , when x is increased by 1 )
slope : { y2 - y1 / x2 - x1 }
slope : y2 = 2
y1 = -4
x2 = 5
x1 = 2
You must minus the values in the formula to find the slope line that passes through the points:
slope : { y2 - y1 / x2 - x1 }
slope : (2) - (-4) / (5) - (2)
=> 2 + 3 / 3
=> 6/3
=> 2
Text explanation:
Difference between both y-coordinates. = 6
Difference between both x-coordinates. = 3
Divide the difference between y and x. =
y/x =2
Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Hope this helps! Sorry it took so long! ⸜(。˃ ᵕ ˂ )⸝ xx
The slope of the line that passes through the points (2, -4) and (5, 2) is 2.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,
Slope = (y₂-y₁)/(x₂-x₁) = [2 - (-4)] / (5 - 2)= 6/3 = 2
Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.
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which is equivalent to (-2x^3y^5)^2
Answer:
[tex]4x^{6} y^{10}[/tex] A.
The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
The length of rectangle is 25 feet and the width of rectangle is 135 feet.
According to the question,
The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)
=5x+10.
Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,
P = 2(l + b)
In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.
2(length + width) = 320
Length+ width=160
x+5x+10=160
6x=150
x=25
Length = 25 feet
width = 5(25+2)=135 feet.
Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..
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