Answer:
The range of the relation is {1, 0, -1}.
Step-by-step explanation:
The range of a relation will be all the y-values in the ordered pairs.
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.
A formula for converting degrees Fahrenheit (F) to degrees Celsius(C) is given by the formula C = 5/9(F -32). Solve the formula for F in terms of C.
Answer:
F=(9C/5)+32
Step-by-step explanation:
In the image
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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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
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
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
If f(n) = n 2 - n, then f(-4) is _____.
first f(-4)=-4(2)-(-4)
=-8+4
=-4
answer :-4
F(x)=7x-4 and f(x)=17 find x
Answer:
x = 3
Step-by-step explanation:
We are given an equation in function notation and asked to solve for x. We can do this by isolating the variable.
Solving for x
First, substitute 17 into the equation for f(x).
17 = 7x - 4Now, we can isolate the x-variable by adding 4 to both sides.
21 = 7xThen, divide both sides by 7.
3 = xThis means when f(x) = 17, x = 3.
Checking the Answer
Now that we have solved for x, we can check the answer we got. Plug 3 into the original equation for x and see if the equation remains true.
17 = 7(3) - 417 = 17Since 17 = 17 is a true statement, the answer x = 3 must be correct.
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
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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B is between A and C. C is the midpoint of BD. D is between C and E.
AB=6x+5, BC=3x+1, DE=7x+3, AE =12x+31 Find AD.
C is the midpoint of BD, Therefore, BC = CD
Now, AD = AB + BC + CD = (6x +5) + (3x + 1) + (3x + 1) = 12x + 7 .... eqn 1
Also, AD = AE - DE = (12x + 31) - (7x + 3) = 5x + 28 ....... eqn 2
From Eqn 1 and Eqn 2,
12x + 7 = 5x + 28
⇒ 12x - 5x = 28 - 7
⇒ 7x = 21
⇒ x = 21/7
⇒ x = 3
So, AD = 12x + 7 = 12(3) + 7 = 36+7
⇒ AD = 43 units
What is a Line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length. Half-open line segments contain exactly one of the endpoints, while closed-line segments have both of the endpoints. Open line segments do not contain either of the endpoints. A line drawn above the symbols for the two endpoints is frequently used in geometry to indicate a line segment.The sides of a triangle or a square are examples of line segments. A line segment is either an edge (of that polygon or polyhedron) if its endpoints are nearby vertices, or a diagonal more broadly when both of its end points are vertices of a polygon or polyhedron. A line segment is referred to as a chord when both of its endpoints are located on a curve, like a circle (of that curve).To learn more about the Line segment, refer to:
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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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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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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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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 $0.86A 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.
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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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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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.
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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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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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.)
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
Kylie gets an email
account for 7
months. She puts in
$681 in her email
account and she
earns 55% each year
How much interest
will
she earn?
Kylie gets an interest of $214.48.
What do you mean by interest?
In the fields of finance and economics, interest is the payment of a sum over and above the principle amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. Interest is not the same as a charge that the borrower could pay to the lender or another entity. Additionally, it differs from a dividend, which is a payment made to shareholders from a company's profit or reserve, but not at a set rate predetermined in advance, but rather on a pro rata basis as a portion of the rewards received by risk-taking business owners when revenue earned exceeds all costs. In contrast to profit, which is obtained by the owner of an asset, investment, or business, interest is paid to the lender.
Interest earned by Kylie = (55x7)/(100x12) x 681
= 218.48
Hence, Kylie gets an interest of $218.48.
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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 )
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]
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.
25x = 3 (1 + 8x) + 2
x=7
x = 5
x=2
x = 11
In the given equation 25x = 3 (1 + 8x) + 2, the value of x is found to be x = 5 by solving the equation.
What exactly is an equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.What are the three kinds of equations?Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given equation is :
25x = 3 (1 + 8x) + 2
On solving the equation for x we get,
25x = 3 + 24x + 2
25x - 24x = 5
x = 5
Therefore, the value of x in the given equation 25x = 3 (1 + 8x) + 2 is found to be x = 5.
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15. A copying service charges a uniform rate for the first one hundred copies or less and a fee
for each additional copy. Nancy Taylor paid $7.00 to make 200 copies and Rosie Barbi paid
$9.20 to make 310 copies.
c. What is the cost of the first one hundred copies?
d. What is the cost of each additional copy?
The cost of the first hundred copies is $5
The cost of each additional copy is $0.02
What are the costs?The first step is to form a system of equation using the information that is provided in the question:
100a + [(200 - 100)b] = 7
100a + 100b = 7 equation 1
100a + [(310 - 100)b] = 9.20
100a + 210b = 9.2 equation 2
Where:
a = cost of each of the first hundred copiesb = cost of the additional copiesThe two equations formed above would be solved using the elimination method.
Subtract equation 1 from equation 2
110b = 2.2
Divide both sides of the equation by 110: b = 2.2 / 110
b = 0.02
Substitute for b in equation 1:
100a + 100(0.02) = 7
100a + 2 = 7
Combine similar terms: 100a = 7 - 2
Add similar terms: 100a = 5
Divide both sides of the equation by 100 : a = 5 / 100
a = 0.05
Cost of the first hundred copies = $0.05 x 100 = $5
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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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