Answer:
C) (12, 16)----------------
Use midpoint equation to find each coordinate:
x = (8 + 16)/2x = 12and
y = (25 + 7)/2y = 16So the midpoint is (12, 16).
The point (–1, 0.5) lies on the graph of
f –1(x) = 2x. Based on this information, which point lies on the graph of f(x) = log2x?
The point which would lie on the graph of f(x) = log2x is; (1, 0.301).
Which point would lie on the graph of f(x) = log2x?Since it follows from the task content that the given point (–1, 0.5) lies on the graph of f –1(x) = 2x.
The subsequent graph of f(x) = log2x would result from taking logarithms in which case, we have the graph passing through points determined as follows;
f(x) = log2^x
f(x) = x log2
Hence, when x = 1;
f(1) = 1log 2
Hence, we have point; (1, 0.301).
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Which of the following is a true proportion of the figure based on the triangle
proportionality theorem?
Based on the triangle proportionality theorem, the true proportion is h/j=k/i
How to solve for the true proportionIn the diagram that we have here, we have TU to be parallel to QR.
We have following
ST is equal to h, TQ is equal to j, SU is equal to k and UR is equal to i.
This can then be used to form the equation
ST/TQ = SU/UR
When we h/j = k/i
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Linda is training to be an assistant at the local animal shelter. To become an assistant she needs to complete 48 h of training. Linda keeps a graph of the number of hours of training left to be completed. What is the rate of change of the number of hours remaining with respect to the number of days? Remember to include units.
The equation between the number of days remaining and number of hours is given as y= -5x+50.
How to illustrate the equation?Let y be the number of days remaining and x be the no.of hours.
From the graph the slope of the line is given by m.
m=(y2 - y1)/(x2 - x1)
m=(30 - 40)/(4 - 2)
m= -10/2 = -5.
The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.
Therefore the equation between the no.of days remaining and no.of hours is given by
y=mx +c.
y=-5x+c
Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,
50= -5(0)+c
c=50.
Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.
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Beginning with the graph of f(x) x2, what transformations are needed to form g(x) = 3(x + 2)2 - 1?
O The graph of g(x) is narrower than f(x) and S shifted to the right 2 units and down 1 unit.
O The
graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
• The graph of g(x) is wider than f(x) and is shifted to the right 2 units and down 1 unit.
Answer: The graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.
Step-by-step explanation:
See attached image.
The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.
What are graph transformations ?By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.
According to the given question given a graph f(x) = x² and g(x) is 3(x+2)² - 1.
Let us break transformations of g(x) one by one.
g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.
Now, g(x) = 3(x+2)² implies the graph is shifted towards left by 2 units as x + 2 = 0 is x = -2.
Now, g(x) = 3(x+2)² - 1 implies that the whole graph has been shifted 1 units down along the y axis.
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find the value of x
a) 2:5=8:x
Step-by-step explanation:
solution:
given,
or, 2:5 = 8:x
or, 2/5 = 8/x [ changing into fraction form ]
or, 2x = 40 [ doing cross-multiplication ]
or, x = 20 [ dividing both sides with 2]
Two sides of a triangle have lengths 18m and 23m. Describe the possible length of the thired side
The possible length of the third side will be values that are less than 41 and greater than 5
Triangular theoremFor three sides to be the sides of a triangle, the sum of any two sides of the triangle must be greater than the third.
Given the two sides of a triangle have lengths 18m and 23m, the sum of the sides is given as:
sum = 18 + 23
Sum = 41
Let the third side be x, such that;
x + 18 >23
23 + x > 18
x > 23 - 18
x > 5
Similarly
x > -5
Hence the possible length of the third side will be values that are less than 41 and greater than 5
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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/5 for pink, 1/25 for blue, 1/10 for yellow, and 1/15 for black. What is the probability of pulling a blue or yellow card,
The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50
How to determine the probability of pulling a blue or yellow card, written as a reduced fraction?From the question, we have the following probabilities:
P(Pink) = 1/5
P(Blue) = 1/25
P(Yellow) = 1/10
P(Black) = 1/15
The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:
P(Blue or yellow card) = P(Blue card) + P(Yellow card)
Substitute the known values in the above equation
P(Blue or yellow card) = 1/25 + 1/10
Express 1/25 as 2/50 and 1/10 as 5/10
P(Blue or yellow card) = 2/50 + 5/50
Take the LCM
P(Blue or yellow card) = (2+ 5)/50
Evaluate the sum
P(Blue or yellow card) = 7/50
Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50
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−6 + 3 = −21 pls can uhelp me with this
Answer:
No Solution
Step-by-step explanation:
1) Simplify -6 - 3 to -3.
-3 = -21
2) Since -3 = -21 is false, there is no solution.
No solution
A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles. Round your answer to the nearest whole number (percent).
The percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%
How to determine the percentage?The given parameters are:
Mean = 169200
Standard deviation = 19400
x = 188600
Calculate the z value using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z = \frac{188600 - 169200}{19400}[/tex]
Evaluate
z = 1
Using the Empirical Rule, we have:
P(x > 188600) = P(z > 1.5)
From z table of probability, we have:
P(x > 188600) = 0.93319
Express as percentage
P(x > 188600) = 93.319%
Approximate
P(x > 188600) = 93%
Hence, the percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%
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Q1. A man wants to paint his house in 3 colors. If he can choose 3 colors out of 6 colors, how many
different color settings can he make?
(A) 216 (B) 20 (C) 18 (D) 120
Calculate the distance between the points C = (0,-2) and L= (-4, 1) in the coordinate plane. Give an exact answer. (not a decimal approximation)
Answer: 5
Step-by-step explanation:
[tex]\sqrt{(-4-0)^2 + (1-(-2))^2}=5[/tex]
A government buys `x`fighter planes at `z` dollars each, and `y` tons of wheat at w dollars each. It spends a total of `B`dollars, where `B=xz+yw`. Write an equation whose solution is the given quantity:
2. The price of a ton of wheat, given that a fighter plane costs 100,000 times as much as a ton of wheat, and that the government bought 20 fighter planes and 15,000 tons of wheat for a total cost of $90 million.
The equation whose solution is the given quantity is 90,000,000 = 2,000,000w + 15,000w where w = $44.67
EquationB = xz + yw
Where,
B = Total cost = 90x = number of fighter plane = 20y = tons of wheat = 15,000w = cost of each tons of wheatz = cost of fighter planez = 100,000wB = xz + yw
90,000,000 = (20 × 100,000w) + (15,000 × w)
90,000,000 = 2,000,000w + 15,000w
90,000,000 = 2,015,000w
w = 90,000,000 / 2,015,000
= 44.6650124069478
Approximately,
w = $44.67
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2) (x+3)
2) Correct the error:
There is an error in the students' work shown below:
Question: Simplify (x-3)(x-7)
Solution: (x-3)(x-7)
x-x-3(x)-7(x) - 21
x²-10x-21
What is the error? Explain how to solve the problem.
The expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
Simplifying factorsQuadratic equations are equations that has a leading degree of 2. The standard quadratic equation is given as;
f(x) = ax^2+bx+c
Given the product of the expression below;
f(x) = (x-3)(x-7)
Expand
f(x) = x(x) - 7x - 3x -3(-7)
f(x) = x^2 - 7x - 3x + 21
f(x) = x^2 - 10x + 21
Hence the expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
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Can anyone help me with this question?:)
Answer:
ΔABC ≅ ΔEDF
Step-by-step explanation:
Triangle ABC is congruent to triangle EDF because they're the same size.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \sf\triangle ABC \cong \triangle DEF[/tex]
For checking congruency, we need to follow a proper order when choosing the triangle. because each triangle name is unique in itself.
So, According to Triangle ABC, we need to find the triangle with first two letters That resembles AB, that is :
AB = DEand next should be :
BC = EF[tex] \qquad \large \sf {Conclusion} : [/tex]
so, now we got the sense for naming, therefore the answer will be :
[tex] \sf\triangle ABC \cong \triangle DEF[/tex]
A couple deposits $20,000 into an account earning 5% annual interest for 30 years. Calculate the future value of the investment if the interest is compounded monthly. Round your answer to the nearest cent.
The future value of the investment if the interest is compounded monthly is $89,354.89.
What is the future value of the investment?Given that;
Principal P = $20,000Annual interest rate r = 5% = 5/100 = 0.05Time t = 30 yearsCompound monthly = 12Future value = A = ?Using the compound interest formula;
A = P( 1 + r/n )^(nt)
We plug in our values.
A = 20000( 1 + 0.05/12 )^(12 × 30)
A = 20000( 1 + 0.0041666666666667)^(360)
A = 20000( 1.0041666666666667)^(360)
A = 20000( 4.46774965 )
A = 89354.89
Therefore, the future value of the investment if the interest is compounded monthly is $89,354.89.
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A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. A total of 10 cars were rented which can hold 66 people altogether. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.
The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;
x + y = 10
x + y = 105x + 7y = 66
Simultaneous equationSmall car = 5 peopleLarge car = 7 peopleTotal cars = 10Total number of people = 66Let
Number of small cars rented = x
Number of large cars rented = y
x + y = 10
x + y = 105x + 7y = 66
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The function f(x)=−4x4+3x3−2x2−x+5 is/has A. order 2 rotational symmetry about the origin
B. neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin
C. even
D. odd
The answer choice which describes the function is; Choice B; neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.
What is rotational symmetry?Rotational symmetry, otherwise termed radial symmetry, is the characteristic of a shape when it looks the same after some rotation by a partial turn. On this note, since the function represents a quartic graph, it follows that the function has neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.
Therefore, the function f(x) = −4x⁴ + 3x³ − 2x² − x + 5 is neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.
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the function f(t) = 5 cos(pi/4*t) + 11 represents the tide in dark sea. it has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. the sea repeats this cycle every 8 hours. after six hours, how high is the tide?
The height of the tide after eight hours is 16 feet.
How to illustrate the function?From the information given, the function is given as 5cos (π/4)t + 11.
In this case, the time is given as eight hours. This will be:
f(8) = 5 × cos (π/4) × 8 + 11
f(8) = 5 × cos(2π) + 11
= (5 × 0.999) + 11
= 16 feet
The height is 16 feet.
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QUICK I need help on what the answer is and an explanation would be much appreciated too thank you
The nonreal solutions to the polynomial equation are: (2 + i√11, 2 - i√11).
How to determine the nonreal solutions?By critically observing the graph given, we can logically deduce that the real solutions of the polynomial are -1 and 4. This ultimately implies that, the given polynomial expression can be evaluated as follows:
(x + 1)(x - 4) = x² - 3x - 4.
x⁴ - 7x³ + 23x² - 29x - 60 = x² - 3x - 4.
Also, the nonreal solutions can be determined by dividing the polynomial expression by the real solutions as follows:
Nonreal solutions = (x⁴ - 7x³ + 23x² - 29x - 60)/(x² - 3x - 4)
Nonreal solutions = (2 + i√11, 2 - i√11).
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PLEASE HELP! And thank you so much! I will mark you brainliest. I just need an urgent response! Thank you for your time
Answer:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
Step-by-step explanation:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
Replacing y with x + 20 in the first equation ->
x + x + 20 = 80
2x + 20 = 80
2x = 60
x = 30
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
Find DE
3x - 28
3x - 30
D
G
E
F
33
Answer:
11
Step-by-step explanation:
(3x-28) + (3x-30) + x = 33
7x - 58 = 33
7x = 91
x = 13
DE = 3x - 28 = 3*13 - 28 = 11
Molly wants to buy a dress that costs $20. She has a coupon for 40% off, and there is a 10% sales tax. how much will she pay all together
1. after using the coupon what is the sale price of the dress Show Your Work
2.how much is th 10% tax on the sale price Explain how you found your answer
Answer:
$13.50
Step-by-step explanation:
If I am taking off 40%, that means that the dress now cost 60% of the original cost. .6 x 20 is 12.
You could also calculate the 20% off and subtract that from the original cost. .4 x 20 =8. Now 20 - 8 is also 12.
Now, we have to calculate the tax. 10% of 12 is .1 x 12 or $1.20. We add the tax to the 12 to get 13.50.
Thomas took 3h to paint a room. Brian could paint the same room in 6h. How long would it take for both of them to finish painting the same room together?
please help !! no algebra please
Answer:
2 hours
Step-by-step explanation:
If Thomas can paint 1/3 = 2/6 of the room in a hour and Brian can paint 1/6 of the room in an hour. Which means in an hour they can collectively paint 3/6 = 1/2 of the room. Now you need to find how long it would take then to paint 2/2 of the room. Knowing that 1/2+1/2 = 2/2, it would take them 2 hours to paint the room together
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.
Given the system of inequalities:
3y > 2x + 12
3y - 2x > 12 (1)
2x + y < -5 (2)
Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached
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What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
Answer:
A
Step-by-step explanation:
Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.
Let's see what we have so far:
The base of the triangle is 3.8
The angle at the bottom is 90
The angle at the top is 36
We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.
This gives you adjacent = opposite / tan(angle)
adjacent = 3.8 / tan(36)
adjacent = 5.2m
Drag a statement or reason to each blank in the table to complete the proof that <1 is congruent to <7.
Step-by-step explanation:
<1 congruent to <5.
<5 congruent to <7.
<1 congruent to <7.
Answer:
don't know but i need thee points
Step-by-step explanation:
A matrix A has x rows and x+5 columns. B has y rows and 11−y columns. Both AB and BA exist. Find x and y.
Answer:
x = 3
y = 8
Step-by-step explanation:
A matrix product exists if and only if the number of columns in the left matrix is equal to the number of rows in the right matrix.
SetupFor AB to exist, we must have ...
columns of A = rows of B
x +5 = y
For BA to exist, we must have ...
columns of B = rows of A
11 -y = x
SolutionUsing the second equation to substitute for x in the first equation, we have ...
(11 -y) +5 = y
16 = 2y
8 = y
Then the value of x is ...
11 -8 = x = 3
The values of x and y are ...
x = 3y = 8__
Additional comment
The dimensions are A = 3×8; B = 8×3.
A linear function always increases
-true
-false
Answer: False
Step-by-step explanation:
If the function has a negative slope, then it will decrease.
The equation T^2= A^3 shows the relationship between a planets orbital period, T, and the planets mean distance from the sun, A, in astronomical units, AU. if the orbital period of planet Y is twice the orbital period of planet x, by what factor is the mean distance increased?
The mean distance increased by a factor of 2^(²/₃)
How to find the factor of increase?
The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is;
T² = A³.
Let the orbital period of planet X = T(X).
Let the orbital period of planet Y = T(Y).
Let the mean distance of planet X from the sun = A(X).
Let the mean distance of planet Y = A(Y).
Thus;
A(Y) = 2A(X)
Therefore;
[T(Y)]² = [A(Y)]³ = [2A(X)]^3
However, [T(X)]² = [A(X)]³
Thus;
[T(Y)]² = 2³[T(X)]² * [T(Y)]²/[T(X)]² = 2³T(Y)/T(X) = 2^(³/₂)
That's for orbital period but the mean distance will increase by 2^(²/₃)
Thus we conclude that, the mean distance increased by a factor of 2^(²/₃)
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Answer:
2 Superscript three-halves
Step-by-step explanation:
Edge
PLEASE HELP!!!!
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
Answer:
(a) 100 meters
Step-by-step explanation:
You want the width at the base of a cooling tower whose walls are modeled by the equation (x/20)² -((y-110)/48)² = 1.
BaseThe width at the base will be the difference in the values of x when y=0.
(x/20)² -((0 -110)/48)² = 1
(x/20)² = 1 +3025/576
x = ±20/24√3601 ≈ ±50.01
The width will be 50.01 -(-50.01) ≈ 100 meters.
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