To determine the width of the statue:
[tex]\begin{gathered} L+W=28\ldots\ldots..(1) \\ L+H=26\ldots\ldots\ldots(11) \\ W+H=22\ldots\ldots..(111) \end{gathered}[/tex]A local park has a length (L), width (W), and height (H) (all in feet)
Solve equation 1 and 2 simultaneously,
[tex]\begin{gathered} L+W=28 \\ L+H=26 \\ \text{Subtract equation (1) - (11)} \\ W-H=2\ldots\ldots\ldots(IV) \end{gathered}[/tex]Solve equation 3 & 4 simultaneously, make W the subject of formular
[tex]\begin{gathered} W+H=22 \\ W-H=2 \\ \text{Add the two equation} \\ 2W=24 \\ \text{divide both side by 2} \\ \frac{2W}{2}=\frac{24}{2} \\ W=12 \end{gathered}[/tex]Therefore the value of width of the statue = 12 feet
the length of a rectangle is 2 inches more than the width. The area is 24 square inches. Find the dimensions
Given:
length(l) = width(w) + 2
[tex]\text{Area}=24[/tex][tex]l\times w=24[/tex][tex](w+2)w=24[/tex][tex]w^2+2w-24=0[/tex][tex](w+6)(w-4)=0[/tex][tex]w=4\text{ or -6}[/tex]Negative not possible.
[tex]\text{width(w)}=4\text{ inches}[/tex][tex]\text{length(l)}=w+2[/tex][tex]\text{length of the rectangle=4+2}[/tex][tex]\text{length of the rectangle=}6\operatorname{cm}[/tex]Hello can you please help me with problem number 12
Turn the 48in to ft
[tex]\begin{gathered} 1ft=12in \\ \\ 48in\times\frac{1ft}{12in}=4ft \end{gathered}[/tex]Then, 48 inches is equal to 4ft.
Comparing the given quatities you get that:
48inches > (greater than) 3ftExpress the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).
Answer:
y = 5u², u=x-6
Explanation:
Given the function:
[tex]y=5(x-6)^2[/tex]We want to express f(x) as a composition of two functions.
Let u = x-6
[tex]\implies y=5u^2[/tex]Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)
[tex]\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}[/tex]the sum of two numbers is 24 . one number is 3 times the other number . find the two numbers
We are given that the sum of two numbers is 24. If "x" and "y" are the two numbers then we have that:
[tex]x+y=24[/tex]We are also given that one number is three times the other, this is expressed as:
[tex]x=3y[/tex]Now, we substitute the value of "x" from the second equation in the first equation:
[tex]3y+y=24[/tex]Now, we add like terms:
[tex]4y=24[/tex]Now, we divide both sides by 4:
[tex]y=\frac{24}{4}=6[/tex]Therefore, the first number is 6. Now, we substitute the value of "y" in the second equation:
[tex]\begin{gathered} x=3(6) \\ x=18 \end{gathered}[/tex]Therefore, the other number is 18.
Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10min for calls. Find the model of the total cost of company a's plan. using m for minutes.
Based on the monthly fee charged by Company A and the charges per minute for calls, the model for the total cost of Company A's plan is Total cost = 20 + 0.05m.
How to find the model?The model to find the total cost of Company A's plan will incorporate the monthly fee paid as well as the amount paid for each minute of calls.
The model for the cost is therefore:
Total cost = Fixed monthly fee + (Variable fee per minute x Number of minutes)
Fixed monthly fee = $20
Variable fee per minute = $0.05
Number of minutes = m
The model for the total cost of Company A's plan is:
Total cost = 20 + 0.05m
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The required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
As of the given data, Company A has a monthly fee of $20 and charges $.05/min for calls. An equation that represents the total cost of Company a's plan is to be determined.
Here,
Let x be the total cost of the company and m be the number of minutes on a call.
According to the question,
Total charges per minute on call = 0.5m
And a monthly fee = $20
So the total cost of company a is given by the arithmetic sum of the sub-charges,
X = 20 + 0.5m
Thus, the required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
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Which statement is the converse of the conditional statement:
If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
• If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
O If point 8 is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
O if point B
does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
Point B is the midpoint if it divides line segment AC into two congruent segmentsIf point B is not the midpoint, then point B does not divide the line segment AC into two congruent segments, which is the statement opposite to the one that has been made.
Which statement is the converse of the conditional statement ?
A point that separates a segment into two congruent segments is the segment's midpoint.The segment is bisected by a point (or segment, ray, or line) that separates it into two congruent segments.Trisecting is the process of dividing a segment into three congruent segments using two points (segments, rays, or lines). A perpendicular bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway. The x-coordinate of the midpoint M of the line segment AB is, as we can see from the formula, equal to the arithmetic mean of the x-coordinates of the segment's two endpoints.The midpoint's y-coordinate is also equal to the mean of the endpoints' y-coordinates. Even a unique postulate just for midpoints exists.Midpoint of a Segment Hypothesis.Any line segment will only have one midpoint, neither more nor less. Any line segment with equal measure is referred to as a congruent line segment.Congruent line segments, for instance, refer to the sides of an equilateral triangle since they all have the same length. Line segments that are congruent have the same length.There is a point in a line segment that will divide it into two congruent line segments.The middle is where you are now. A segment bisector runs through the middle of a line segment and divides it into two congruent portions.A segment bisector that intersects the segment at a right angle is called a perpendicular bisector.AB B C A C D E By applying algebraic techniques to solve the midpoint formula for one endpoint, the endpoint formula can be discovered.After performing the necessary algebra, (xa,ya)=((2xmxb),(2ymyb)) (x a, y a) = ((2 x m x b), (2 y m y b)) is the formula for the Endpoint A A of line AB A B.To learn more about mid point refer
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One of the legs of a right triangle measures 13 cm and the other leg measures
2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest
tenth.
Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
with regard to promoting standards of excellence, lafasto and larson (2001) identified three rs that help improve performance: require results, review results, and ______.
With regard to promoting standards of excellence, Lafasto and Larson (2001) identified three Rs that help improve performance:
require results, review results, and Reward Results.What did the Larson and LaFasto 1989 study capture?
The LaFasto and Larson Model investigated team effectiveness. It is founded on the premise that, while individuals might be highly competent and talented, teams solve the most challenging issues.
It doesn't matter how skilled an individual is if they can't operate as part of a team.
They studied the traits of 75 highly successful teams. They discovered that high standards of excellence were a critical component in team performance.
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Domain and range from the graph of a quadratic function
Given the graph of the quadratic function with vertex (-4,-3) as shown below:
The domain of the function is a set of input values. The range of a quadratic function continues in either direction along the x-axis, as shown by the arrows in the above plot. The range is the set of output values. In other words, it is the possible values of y in a quadratic function.
Thus, the domain of the function is:
[tex](-\infty,\text{ }\infty)[/tex]The range of the function is :
[tex]\lbrack-3,\text{ }\infty)[/tex]e22. Which expressions have values less than 1 whenx = 47 Select all that apply.(32)xo3x4
To know the expression that is less than 1 when x=4
we will need to check each expression
As for the first one;
[tex](\frac{3}{x^2})^0[/tex]anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1
Hence it is not less than 1
For the second expression;
[tex]\frac{x^0}{3^2}=\frac{4^0}{9}=\frac{1}{9}[/tex]The value is less than 1
For the third expression;
[tex]\frac{1}{6^{-x}}[/tex]substituting x=4 in the above expression
[tex]\frac{1}{6^{-4}}[/tex]The above is the same as;
[tex]undefined[/tex]What is the y-intercept of 4x + 8y = 12?
i have questions on a math problem. i can send when the chats open
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
Two figures are similar. The smaller figure has dimensions that are 3:4 the size of the largerfigure. If the area of the larger figure is 100 square units, what is the area of the smallerfigure?
Answer:
56.25
Explanation:
We are told that the side lengths of the smaller figure are 3/4 the length of the larger figure.
[tex]S_{small}=\frac{3}{4}\times S_{large}[/tex]Now since the area is proportional to the equal of the side lengths, we have
[tex]A_{small}=S_{small}^2^[/tex][tex]A_{small}=(\frac{3}{4})^2\times S_{large}^2[/tex][tex]=A_{small}=(\frac{3}{4})^2\times A_{large}^2[/tex]The last is true since A_large = S^2_large.
Now we are told that A_large = 100 square units; therefore,
[tex]A_{small}=(\frac{3}{4})^2\times100[/tex][tex]\Rightarrow A_{small}=\frac{9}{16}\times100[/tex]which we evaluate to get
[tex]A_{small}=\frac{9}{16}\times100=56.25[/tex][tex]\boxed{A_{small}=56.25.}[/tex]Hence, the area of the smaller figure is 56.25.
although the actual amount varies by the season and time of the day the average volume of water that flows over the false each second is 2.9 x 10 to the 5th power gallons how much water flows over the falls in an hour write the result in scientific notation hint 1 hour equals 3600 second
We were told that volume of water that flows over the fall each second is 2.9 x 10^5 gallons.
Recall, 1 hour = 3600 seconds
If 1 second = 2.9 x 10^5 gallons, then
3600 seconds = 3600 x 2.9 x 10^5
= 1.044 x 10^9 gallons
Thus, 1.044 x 10^9 gallons of water will flow over the falls in an hour.
Which postulate or theorem proves that ∆ABC and ∆EDC are congruent?
O AAS Congruence Theorem
O HL Congruence Theorem
O SAS Congruence Postulate
O SSS Congruence Postulate B
write the function below in slope. Show ALL the steps and type the answer.
This is a simple question to solve. First, let's take a look at a slope-intercept form equation as follows:
Once we know how a slope-intercept form looks like all we need to do is to simplify our equation to find that as follows:
And that is our slope-intercept form:
The distance d (in inches) that a ladybug travels over time t(in seconds) is given by the function d (1) = t^3 - 2t + 2. Findthe average speed of the ladybug from t1 = 1 second tot2 = 3 seconds.inches/second
The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]Therefore, the correct answer is 11 inches/second.
Simplify the expression (3^1/4)^2 to demonstrate the power of a power property. Show any intermittentstepsthat demonstratehow you arrived at the simplified answer.
(3^1/4)²
= (3^1/4) x (3^1/4)
=(3)^1/4 + 1/4
=(3)^1/2
Which can also be expressed as
= √3
²
At what rate (%) of simple intrest will $5,000 amount to $6,050 in 3 years?
Rate of interest for
A = $5000
THEN apply formula
A-P= P•R•T/100
T = 3 years
Then
6050 - 5000= 1050 =
1050= P•R•T/100
Now find R
R= (1050•100)/(P•T) = (105000)/(5000•3) = 7
Then ANSWER IS
ANUAL RATE(%) = 7%
Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?
SOLUTION
From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side
So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So
[tex]\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}[/tex]So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.
The answer is option C
Translate each sentence into an equation. Then find each number.
The sum of six, and a number divided by two is 0.
the possible answers are:
y/2-6=0;y=12
2y+6=0;y=-3
y/2+6=0;y=12
y/2+6=0;y=-12
The sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
The given sentence is "The sum of six and a number is divided by two is 0"
Consider the number as y
A number is divided by two = y/2
The sum of 6 and a number divided by two = y/2 + 6
The sum of six and a number is divided by two is 0
y/2 + 6 = 0
We have to solve the equation
Move the 6 to the right hand side of the equation
y/2 = -6
Move the 2 to the right hand side of the equation
y = -6×2
Multiply the numbers
y = -12
Hence, the sum of six and a number divided by two is zero is translating into an equation is y/2+6 = 0, and the number is y = -12
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value of a machine10(thousands of dollars)01 2 3 4 5 6 7 8 9 10Age of Machine(years)Which equation best represents the relationship between x, the age of the machine in years, and y, thevalue of the machine in dollars over this 10-year period?F.y = -0.002x + 2,500G.y = -500x + 8,000H.y = 500x + 8,000J.y = 0.002x + 2,500
To find the right answer, first, we find the slope.
Let's use the slope formula, and the points (0,8) and (8,4).
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]m=\frac{4-8}{8-0}=\frac{-4}{8}=-\frac{1}{2}=-0.5[/tex]However, the Value is express in thousands of dollars, which means the slope is -500.
Observe that G is the only equation with the correct slope.
Therefore, G is the right answer.Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
I need help with a math assignment. i linked it below
Since Edson take t minutes in each exercise set
Since he does 6 push-ups sets
Then he will take time = 6 x t = 6t minutes
Since he does 3 pull-ups sets
Then he will take time = 3 x t = 3t minutes
Since he does 4 sit-ups sets
Then he will take time = 4 x t = 4t minutes
To find the total time add the 3 times above
Total time = 6t + 3t + 4t
Total time = 13t minutes
The time it takes Edison to exercise is 13t minutes
A small toy rocket is launched from a 32-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−2t2+0t+32 . How long will it take the rocket to hit the ground?t=______(Separate answers by a comma. Write answers as integers or reduced fractions.)
Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula
[tex]h=-2t^2+0t+32[/tex]Required: To find out how long will it take the rocket to hit the ground.
Explanation: When the rocket touches the ground its height will be zero i.e.,
[tex]\begin{gathered} -2t^2+0t+32=0 \\ 2t^2=32 \\ t^2=16 \end{gathered}[/tex]Which gives
[tex]t=\pm4[/tex]Neglecting the negative value of t since time cannot be negative. We have
[tex]t=4\text{ seconds}[/tex]Final Answer: Time, t=4 seconds.
Use the commutative property of multiplication to write an equivalent expression to 69xuse the distributive property to write an equivalent expression to 8(c+5) that has no grouping symbols.
Answer
69x = 69 × x = x × 69
8 (c + 5)
= 8c + 40
Explanation
The commutative property of multiplication for two numbers a and b, is given as
a × b = b × a = ab
69x = 69 × x = x × 69 = 69x
Question 2
The distributive property for openingh brackets involving three numbers a, b and c is given as
a (b + c)
= ab + ac
So, for this question
8 (c + 5)
= 8c + 40
Hope this Helps!!!
Gabe made a scale drawing of a neighborhood park. The scale of the drawing was 1 millimeter : 6 meters. If the actual length of the volleyball court is 18 meters, how long is the volleyball court in the drawing?
If f(x) = ln [ sin2(2x)(e-2x+1) ] , then f’(x) is
I want to solve ?
Here we will write our function in regular form using an identity.
[tex]log(ab)=loga+logb[/tex][tex]log(a/b)=loga-logb[/tex]Therefore, the rule of our function [tex]f(x)[/tex] will be as follows.
[tex]f(x)=ln(sin^2(2x))+ln(e^{-2x}+1)[/tex]The derivative of the natural logarithm [tex]ln(x)[/tex] function is of the following form.
[tex](ln(x))'=\frac{x'}{x}[/tex]It is found by dividing the derivative of the function in [tex]lnx[/tex] by the function in [tex]lnx[/tex].
For example:
[tex](ln(5x))'=\frac{(5x)'}{5x} =\frac{5}{5x} =\frac{1}{x}[/tex]According to this information, let's take the derivative of our function.
[tex]f'(x)=\frac{2sin(4x)}{sin^2(2x)} +\frac{-\frac{2}{e^{2x}} }{e^{-2x}+1}[/tex][tex]f'(x)=4cot(2x)-\frac{2}{1+e^{2x}}[/tex]Rules:[tex]((sin2x)²)'=2.2sin(2x)cos(2x)=2sin(4x)[/tex][tex](e^x)'=x'.e^x[/tex]For f(x)=x^2 and g(x)=x^2+9, find the following composite functions and state the domain of each.
(a) f.g (b) g.f (c) f.f (d) g.g
The composite functions in this problem are given as follows:
a) (f ∘ g)(x) = x^4 + 18x² + 81.
b) (g ∘ f)(x) = x^4 + 9.
c) (f ∘ f)(x) = x^4.
d) (g ∘ g)(x) = x^4 + 18x² + 90.
All these functions have a domain of all real values.
Composite functionsFor composite functions, the outer function is applied as the input to the inner function.
In the context of this problem, the functions are given as follows:
f(x) = x².g(x) = x² + 9.For item a, the composite function is given as follows:
(f ∘ g)(x) = f(x² + 9) = (x² + 9)² = x^4 + 18x² + 81.
For item b, the composite function is given as follows:
(g ∘ f)(x) = g(x²) = (x²)² + 9 = x^4 + 9.
For item c, the composite function is given as follows:
(f ∘ f)(x) = f(x²) = (x²)² = x^4.
For item d, the composite function is given as follows:
(g ∘ g)(x) = g(x² + 9) = (x² + 9)² + 9 = x^4 + 18x² + 90.
None of these functions have any restriction on the domain such as fractions or even roots, hence all of them have all real values as the domain.
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Graph the exponential function.f(x)=4(5/4)^xPlot five points on the graph of the function,
We are required to graph the exponential function:
[tex]f(x)=4(\frac{5}{4})^x[/tex]First, we determine the five points which we plot on the graph.
[tex]\begin{gathered} \text{When x=-1, }f(-1)=4(\frac{5}{4})^{-1}=3.2\text{ }\implies(-1,3.2) \\ \text{When x=0, }f(0)=4(\frac{5}{4})^0=4\text{ }\implies(0,4) \\ \text{When x=1, }f(1)=4(\frac{5}{4})^1=5\implies(1,5) \\ \text{When x=2, }f(2)=4(\frac{5}{4})^2=6.25\implies(2,6.25) \\ \text{When x=3, }f(3)=4(\frac{5}{4})^3=7.8125\text{ }\implies(3,7.8125) \end{gathered}[/tex]Next, we plot the points on the graph.
This is the graph of the given exponential function.