Answer: It is not possible for f(x) = 5(2^x) to equal to 200.
Step-by-step explanation: I put it in a calculator. When x = 5.321, the output is approximately 199.871380105. But when x = 5.322, the output is about 200.009968414. This means that the output of exactly 200 is impossible.
ƒ(x) = x²+x+6
g(x) = 3x +5
Find: f(g(x)) c
The value of f(g(x)) is f(g(x)) = 9x² + 33x + 36.
What are composite functions and how are they defined?
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Mathematically, Let g: A→B and h: B→C denote two functions, then the composition of g and h denoted by hog: A→C given by hog(x) = h(g(x)) for all x ∈ A.
Given, f(x) = x² + x + 6 and g(x) = 3x + 5
Thus, following the above literature,
f(g(x)) = fog(x) = (3x + 5)² + (3x + 5) + 6 = 9x² + 33x + 36
Therefore, the required value of f(g(x)) is f(g(x)) = 9x² + 33x + 36.
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Mrs. Shaughnessy’s science class and Mr. Ruth’s social studies class are going on two separate field trips. They have the same budget for their trips. Mrs. Shaughnessy’s class has 30 students, and they are taking a bus to a planetarium. Mr. Ruth’s class of 20 students is taking the subway to a museum. Admission to the planetarium is 12 the cost of admission to the museum, as shown in the table. What is the cost of admission per student to the museum?
The cost of admission per student is given as 10 dollars to the museum
How to solve for the costWe have the following details that we would have to solve this problem with.
The number of people in this Mrs Shaughnessy’s class is 30 students
The number of persons in Mr Ruth's class is 20 students
The admission that is made to the planetarium is given as 12
we would have this equation
30 * 1/2x + 3 x 30
= 15x + 90
For the next equation we would have
20 x x + 2 x 20
= 20x + 40
We have to make the two equations to be equal
15x + 90 = 20x + 40
take the like terms
15x - 20x = 40 - 90
-5x = -50
divide through by -5 to get the value of x
x = -50 / -5
x = 10
Therefore the cost of admission per student would be 10 dollars
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Simplify the linear expression by combining like terms. 2x + 8y - 7x - y
Please hurry!!!
Answer:
-5x + 7y
Step-by-step explanation:
2x - 7x = -5x
8y - y = 7y
Robert pays for his family to go to the arcade he pays an interest fee for his food and additional amount per game that his family plays as shown in the graph use the graph to answer 5-7
Answer:
5) ¾, The slope is ¾ since the cost increases by 3 dollars for every 4 games Robert and his family play.
6) 12, The y-intercept is 12 since Robert had to pay an entrance fee of 12 dollars in order to enter the arcade.
7) y=¾x+12
Someone please help me
Using relations in a right triangle, it is found that:
1. Angelica's mistake is stating that we can find the length of AB, as we can only find the simplified length with the ratio, not the actual length.
2. Graziella mistake is stating that since we don't know the sides we cannot find the ratios.
3. The measures are as follows: sin(A) = 3/5, cos(A) = 4/5.
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
Sine: opposite side/hypotenuse.Cosine: adjacent side/hypotenuse.Tangent: opposite side/adjacent side.In this problem, we have that the tangent of angle A is of 3/4, hence the lengths are given as follows:
AC = 4.BC = 3.Applying the Pythagorean Theorem, the hypotenuse AB is given as follows:
x² = 3² + 4²
x² = 9 + 16
x² = 25
x = 5.
Then the sine and the cosine of A are given as follows:
sin(A) = 3/5.cos(A) = 4/5.This is a procedure in which we can find the smallest possible length of the hypotenuse, not the actual length, which is Angelica's mistake.
Even without knowing the actual length, we could find the ratios for the sine and for the cosine, which is Graziela's mistake.
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On Monday Harold picked up six donuts and two large coffees for the office staff. He paid $5.80. On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02. What is the cost of one donut? What is the cost of one large coffee?
Cost of tjhe donut: D
Cost of the large coffee: C
On Monday Harold picked up six donuts and two large coffees for the office staff, he paid $5.80:
[tex]6D+2C=5.80[/tex]On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02:
[tex]4D+5C=7.02[/tex]Use the next system of linear equations to find the value of D and C:
[tex]\begin{gathered} 6D+2C=5.80 \\ 4D+5C=7.02 \end{gathered}[/tex]1. Solve D in the first equation:
[tex]\begin{gathered} \text{Subtract 2C in both sides of the equation:} \\ 6D+2C-2C=5.80-2C \\ 6D=5.80-2C \\ \\ \text{Divide both sides of the equation into 6:} \\ \frac{6}{6}D=\frac{5.80}{6}-\frac{2}{6}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}C \end{gathered}[/tex]2. Substitute the D in the second equation by the equation you get in step 1:
[tex]4(\frac{5.80}{6}-\frac{1}{3}C)+5C=7.02[/tex]3. Solve C:
[tex]\begin{gathered} \frac{23.2}{6}-\frac{4}{3}C+5C=7.02 \\ \\ \frac{-4C+15C}{3}=7.02-\frac{23.2}{6} \\ \\ \frac{11}{3}C=\frac{42.12-23.2}{6} \\ \\ \frac{11}{3}C=\frac{18.92}{6} \\ \\ C=\frac{3}{11}\cdot\frac{18.92}{6} \\ \\ C=\frac{56.76}{66} \\ \\ C=0.86 \end{gathered}[/tex]4. Use the value of C=0.86 to find D;
[tex]\begin{gathered} D=\frac{5.80}{6}-\frac{1}{3}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}(0.86) \\ \\ D=\frac{5.80}{6}-\frac{0.86}{3} \\ \\ D=\frac{17.4-5.16}{18} \\ \\ D=\frac{12.24}{18} \\ \\ D=0.68 \end{gathered}[/tex]The solution fot the system is:
[tex]\begin{gathered} C=0.86 \\ D=0.68 \end{gathered}[/tex]The cost of one dount is $0.68The cost of one large coffee is $0.86evaluate the function when x=3 h(x) = -x + 5
Answer:
2
Step-by-step explanation:
substitute x = 3 into h(x)
h(3) = - 3 + 5 = 2
The sides of ABC are a, b, and c. If the lengths of a = 7 and b = 10, what are the
possible lengths of c?
A) 3
B) 3
C) 3
D) 7
27.405 x 18 using algorithm
The value of the expression using algorithm is 493.29 .
An algorithm is a finite sequence of exact instructions used to solve a class of particular problems or carry out a calculation in mathematics and computer science.
For performing calculations and processing data, algorithms are employed as specifications. Advanced algorithms can do automated deductions (also known as automated reasoning) and employ logical and mathematical checks to reroute the execution of the code along several paths (referred to as automated decision-making).A well-defined formal language and a finite amount of time and space are both capable of being used to represent an algorithm for computing a function. In accordance with the instructions, a calculation is to be performed that, once completed, goes through a finite number of precisely defined subsequent phases, producing "output", and finally concludes at a specific ending state. Starting with an initial state and starting input—which may be empty—the computation can be performed.The given expression is 27.405 x 18
This can be computed using algorithm of multiplication to get the result 493.29 .
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Which expression has a value of -10 when p=25 and q = 10? OA) 3√p-q+5 OB) 3√√p-q)+5 OC) (3√ √p)-q+5 OD) 3√√p(q+5)
Answer:
Answer B
Step-by-step explanation:
B is:
[tex]3 (\sqrt{25} - 10) + 5 \\ 3(5 - 10) + 5 \\ 3 ( - 5) + 5 \\ - 15 + 5 = - 10[/tex]
For each ordered pair, determine whether it is a solution to y=3x-6
-4,18
5,24
7,-45
-8,-30
The point (-8,-30) is ordered pair which is the correct solution to y=3x-6.
What is ordered pair?The position of a point on the coordinate plane with respect to the origin is represented by an ordered pair in coordinate geometry. Two parallel intersecting lines, with one line being the x-axis and the other being the vertical, form a coordinate plane (y-axis).
The origin is the place where the two axes meet. An ordered pair (x, y), where x is known as the x-coordinate and y is known as the y-coordinate, is used to represent each point on the coordinate plane.
To find the solution of the y = 3x - 6 we will simply use the trial and error method to find if the given the ordered pair are correct or incorrect.
(-4,18)
y = 3x - 6
18 = 3(-4) - 6
18 = -12 - 6
18 = -18
Incorrect solution
(5,24)
y = 3x - 6
24 = 3(5) - 6
24= 15 - 6
24= 9
Incorrect solution
(7,-45)
y = 3x - 6
-45 = 3(7) - 6
-45 = 21 - 6
-45 = 15
Incorrect solution
(-8,-30)
y = 3x - 6
-30 = 3(-8) - 6
-30 = -24 - 6
-30 = -30
Correct solution
Thus, The point (-8,-30) is ordered pair which is the correct solution to y=3x-6.
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An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the front of the garage?
The graph shows a five-edged polygon. The five edges are on (minus 5.5, 0), (minus 5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).
Answer:
37.26 units
Step-by-step explanation:
You want to know the perimeter of the pentagon defined by the points (-5.5, 0), (-5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).
GraphThe attached graph shows the points and the distances between them. The perimeter is the sum of those distances.
7 +6.13 +6.13 +7 + 11 = 37.26
The perimeter of the polygon is about 37.26 units.
__
Additional comment
The length of the slant edges can be found using the distance formula.
d = √((x2 -x1)² +(y2 -y1)²) = √((0 -5.5)² +(9.7 -7)²) = √(30.25 +7.29)
= √37.54 ≈ 6.12699
The lengths of the horizontal and vertical edges can be found by differencing the x- and y-coordinates of the points, respectively. (The distance formula can be used, as well.)
Keandra is taking a trip to visit her extended family and makes a stop somewhere during her trip. The distance between Cincinnati, where Keandra started, and Dayton, where Keandra made the stop is 54 miles. The distance between Dayton and Toledo, where Keandra’s family lives is 150.2 miles. How far did Keandra travel on her trip? Round to the correct number of significant figures.
Keandra travelled a total distance of 204.2 miles on her trip
Distance between Cincinnati and Dayton = 54 miles
Distance between Dayton and Toledo = 150.2 miles
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language (e.g. "two counties over"). For instance: - My office and house are 3 kilometres apart.
Total distance travelled by Keandra from Cincinnati to Toledo = Distance between Cincinnati and Dayton + Distance between Dayton and Toledo
= 54 + 150.2
= 204.2 miles
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Given ƒ(x) = −x − 1, find ƒ(0).
The value of f(0) is '-1'.
Let's see the step-by-step solution:
Step 1:
For f = -x -1
substitute the x with 0
So, f(0) = -0-1
Step 2:
Simplifying it: -0-1: -1
Thus, the value of f(0)= -1
Delvin is practicing free throw shots. After a jump, Delvin releases the basketball from a height of 8 feet (ft) above the ground. When the ball is 2 ft horizontally from Delvin, it is 11 ft in the air. The ball then passes through the basket, which is 10 ft above the ground and 15 ft horizontally from Delvin. What is the maximum height that the basketball reaches in its path? You can assume that the ball travels in a parabolic arc, as shown in the figure.
The maximum height that the basketball reaches in its path is 8.48ft
What is Parabola?A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Then the path of the ball may be modeled by the parabola
y = (-16x^2/0.434v^2)+1.15x+8
Let x = 15
y = 10
Then, Substituting the value of x and y
10 = (-16(15)^2/0.434v^2)+1.15(15)+8
10 = (-16(225)/0.434v^2)+17.25+8
10 = (-3600/0.434v^2) + 25.25
Subtracting 25.25 both side we get
-15.25 = (-3600/0.434v^2)
Multiplying v^2 both side we get
-15.25v^2 = -3600/0.434
-15.25v^2 = -8294.93
Dividing -15.25 both side we get
v^2 = -8294.93/-15.25
v^2 = 543.93
v = [tex]\sqrt{543.93}[/tex]
v = 23.32ft/sec
To find the maximum height we use
max = -b/2a
Lets find out a and be by
y = (-16x^2/0.434(23.32)^2)+1.15x+8
y = 0.06779 + 1.15x + 8
where, a = 0.06779 and b = 1.15
Substituting the value
max = -1.15/2(0.06779)
max = 8.48 ft
Hence, The maximum height that the basketball reaches in its path is 8.48ft
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Angela is building a fence for a circular playground, with a radius of 7 feet. How much fence will Angela need for the playground?
Given:
Circular playground with radius=7 feet
To find:
Fence for the playground
Solution:
To find the fence required for the circular playground, we will have to find the circumference of the ground.
Circumference =2πR ( where R is the radius of the circle)
= 2*3.14*7
= 44 feet
Therefore, the fence required is 44 feet.
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How long can someone shower to use only 10 gallons of water?
Answer:
4 minutes
Step-by-step explanation:
A standard showerhead uses 2.5 gallons a minute, or 25 gallons for 10 minutes, therefore 10/2.5 = 4.
An international company has 15,900 employees in one country. If this represents 34,6% of the company's employees, how many employees does it have in total?
Using percentage, we calculated that the total number of employees in the company equals 45954.
How do we express Percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
Given,
34.6% of the employees in the company equals 15,900
Let the total number of employees in the company = x
According to the given question,
34.6 / 100 × x = 15,900
⇒ x = 15900 × 1000 / 346
⇒ x = 45954
∴ Total employees in the company equals 45954.
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Simplify. (5x² + 2x - 5) (3x² + 3x + 1)
Answer: 15[tex]x^{4}[/tex]+21[tex]x^{3}[/tex]-4[tex]x^{2}[/tex]-13[tex]x[/tex]-5
Step-by-step explanation:
(5x² + 2x - 5) (3x² + 3x + 1) times the two brackets together.
15[tex]x^{4}[/tex] + 15[tex]x^{3}[/tex]+ 5[tex]x^{2}[/tex]+6[tex]x^{3[/tex]+6[tex]x^{2}[/tex]+2[tex]x[/tex]-15[tex]x^{2}[/tex]-15[tex]x[/tex]-5 simplified =
15[tex]x^{4}[/tex]+21[tex]x^{3}[/tex]-4[tex]x^{2}[/tex]-13[tex]x[/tex]-5
in a certain english class, one fourth of the number of girls is equal to one sixth of the total number of students. what is the ratio of the number of boys to the number of girls in the class?
Answer:
1
Step-by-step explanation:
Comment
This is a very interesting question.
The first statement says
1/3 girls = 1/6 of the total Multiply both sides by 3
3(1/3) girls = 3(1/6) total
girls = 1/2 of the total
The boys must be 1/2 as well because all the students who are not girls must be boys.
Ratio (boys / girls) = 1/2 // 1/2 = 1
The ratio is 1
Determine whether each graph represents a function explain
The correct statement regarding whether each graph represents a function is given as follows:
a. Represents a function, as each input is mapped to only one output.
b. Does not represent a function, as there are inputs mapped to two outputs.
When does a graph represents a function?A graph will represent a function if the graph contains no vertically aligned points, that is, each value of x is mapped to only one value of y.
Vertically aligned points mean that a value of the input x is mapped to multiple values of the output y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
In the context of this problem, we have that:
In the discrete graph a, each value of x, x = 1, x = 2, x = 3, x = 4 and x = 5, is mapped to only one value of y, hence the graph is a function.In the continuous graph b, there are values of x mapped to two values of y, hence it is not a function.On the continuous graph, a vertical line is drawn and shown at the end of the answer, representing visually when does a graph does not represent a function, as the vertical line crosses the function at multiple points.
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Tom says he is comparing banks to see what interest rates they offer on savings accounts. Explain how Tom should use the information he gets to decide which bank to open a savings account with.
Tom should choose the bank that gives the highest interest rate on savings accounts
What is interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.
A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields. In this case, the one that gives the best rate is the best option to choose.
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Answer:
Tom should choose the bank that offers the highest interest rate on savings accounts. Since the principal and time would be the same for each bank, the higher the interest rate, the more money Tom would earn.
Step-by-step explanation:
this was the sample answer on edge. I hate edge
Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
3.4
8.0
11.4
13.11
Answer:
d. 11.4, 3.4
Explanation:
Given
Required
Determine the zeros
The best way to solve this is to apply the graphical method.
First, we plot the graph of:
See attachment
Next, we write out all values of x when the line crosses the y-axis.
From the attached graph, the points are (approximately):
Option (d) is the closest to the above values.
Hence, the zeros are: -1.4 and 3.4
active attachment
Answer:
13.11
Step-by-step explanation:
[tex]\frac{x}{5\frac{7}{10} }[/tex] = 2 [tex]\frac{3}{10}[/tex] ( multiply both sides by 5 [tex]\frac{7}{10}[/tex] to clear the fraction
x = 5 [tex]\frac{7}{10}[/tex] × 2 [tex]\frac{3}{10}[/tex] = 5.7 × 2.3 = 13.11
use a table, an equation, and a graph to represent:sue swims 1.5 laps per minute
Represent the situation by using a function. If Sue swims 1.5 laps per minute, the equation that represents this situation is
[tex]y=1.5x[/tex]Where y is the number of laps and x is the time in minutes
With this equation you can make a table
Finally, make the graph
Can anyone give me a hand?
Answer:
Step-by-step explanation:
I tried to put my hand through the computer but it didn't work! Lol
Anyways,
m<WZY= 70 degrees
35+35= 70
Answer:
70
Step-by-step explanation:
Angle WZX = 35
As ZX is a bisector, it cuts it down the middle and splits it in half. This means that angle WZX is half of the original angle, WZY.
35 * 2 = 70.
A shape has only three angles, and only one of those angles measures 90 degrees. What is the name of the shape?
Answer:
A right Triangle
Step-by-step explanation:
A right triangle has 3 angles and one of those angles measures 90 degrees.
Can someone let me know if I’m right?
Answer:
d
Step-by-step explanation:
using the tangent ratio in the right triangle
tan61° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.8}[/tex] ( multiply both sides by 3.8 )
3.8 × tan61° = x , then
x ≈ 6.9 cm ( to the nearest tenth )
A movie theatre currently has 49 empty seats. 3
people enter every minute to fill those seats. The
scenario is modeled by the arithmetic sequence
= 46 − 3( − 1)
The number of empty seats based on the arithmetic sequence in 6 minutes is 28.
How to illustrate the information?It should be noted that an expression simply means the function that's given to show the relationship between the variables.
From the information, the movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence:
= 46 − 3m.
In this case m = number or minutes.
The empty seats in 6 minutes will be:
= 46 - 3m
= 46 - 3(6)
= 46 - 18
= 28
There are 28 empty seats.
The complete question is written below.
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A movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence
= 46 − 3m. Find the numberof empty seats in 6 minutes.
In a group of 40
people, 22 of them
have brown hair.
What percent of
them don't have
brown hair?
Answer:
Step-by-step explanation:
Hi:
First determine those without brown hair:
40-22=18 don't have brown hair.
18/40 don't have brown hair:
Divide by 2
9/20
Multiply by 5 to get percent
45/100= 45 percent don't have brown hair
A parasail is $\frac{3}{100}$
mile above the water. After 5 minutes, the parasail is $\frac{1}{50}$
mile above the water. Find the change in height of the parasail.
The change is height is
mile.
The change in height of the parasail = 1/100.
What is height?Height of defined as the measurement that is taken for an object which starts from its base to the topmost point. This is usually measured in meters.
From the question,
The height of the parasail above the water level= 3/100
The height of the parasail above the water level after 5 minutes= 1/50
The change in height of the parasail is determined by finding the difference between the two heights.
That is, = 3/100 - 1/50
= 0.03- 0.02 = 0.01
When changed to fraction is = 1/100
Therefore, the change in height after 5 minutes is = 1/100
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