The function graphed represents the amount of water in a container, in gallons, x minutes after a drain is opened.
What is the meaning of each key feature of the graph?
Drag the answer into the box to match each item.
Answers
The y-intercept: The number of gallons in the container before the drain is open
Hope this helps!!
Let
x-------> the time in minutes
y-----> the function that represent the amount of water in gallons
Step 1
Find the x-intercept
we know that
The x-intercept is the value of x when the value of the function is equal to zero
In this problem (see the graph)
For [tex]y=0[/tex]
the value of x is [tex]15\ min[/tex]
so
the x-intercept is the point [tex](15,0)[/tex]
that means
The number of minutes it takes for the container to empty is [tex]15\ min[/tex]
Step 2
Find the y-intercept
we know that
The y-intercept is the value of the function y when the value of x is equal to zero
In this problem (see the graph)
For [tex]x=0[/tex]
the value of the function y is [tex]120\ gal[/tex]
so
the y-intercept is the point [tex](0,120)[/tex]
that means
The number of gallons in the container before the drain is open is [tex]120\ gal[/tex]
therefore
the answer in the attached figure
Related Questions
What are 3 consecutive integers who's sum is 396?
Answers
x+x+1+x+2 = 396.
Combine like terms. All the x's will add together to become 3x, while the ones without will be 1+2 = 3.
3x+3 = 396.
We need to start getting the x by itself. We must subtract 3 from both sides. This is how it should end up:
3x = 393.
Then, we will finally get x by itself by dividing 3 by both sides.
x = 131. The answer is x = 131.
Which of the following is not a pair of similar polygons?
Answers
Answer: The answer is the last figure, figure (D). Attached the image.
Step-by-step explanation: We are given four pairs of polygons and we are to select the pair in which the two polygons are not similar.
In the first pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2}{\frac{2}{3}}=\dfrac{4}{\frac{4}{3}}=3.[/tex]
So, the polygons are similar.
In the second pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2.82}{1.41}=\dfrac{2.24}{1.12}=\dfrac{3}{1.5}=2.[/tex]
So, the polygons are similar.
In the third pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{1.41}{1.41}=\dfrac{1.12}{1.12}=\dfrac{1.5}{1.5}=1.[/tex]
So, the polygons are similar.
In the fourth pair of polygons, we have
[tex]\dfrac{12}{\frac{4}{3}}=12\times\dfrac{3}{4}=9,[/tex]
and
[tex]\dfrac{4}{\frac{2}{3}}=4\times\dfrac{3}{2}=6\neq 9.[/tex]
So, the polygons are not similar in this case.
Thus, the last figure, attached herewith, is the correct option.
All of the figures are pair of similar polygons
What are similar shapes?Similar shapes have the same shape but may differ in size.
Their corresponding angles are equal, and their corresponding sides are in proportion.
This property allows for resizing through a constant scale factor while maintaining identical angles.
We can test of the polygons are similar by checking the ratio of their corresponding sides are equal.
Fig 1 = 2/2/3 = 3
4/4/3 = 3
therefore the pair of polygons in fig1 are similar.
fig 2 = 3/1.5 = 2
2.82/1.41 = 2
therefore fig2 is a pair of similar polygons.
Therefore, all of the figures are pair of similar polygons
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Morgan drove from los angeles, at an elevation of 330 feet, to death valley, at an elevation of -282 feet. what is the difference in elevation between los angeles and death valley?
Answers
Answer:
The answer is D because if you made a number line you would contrast them and there you get 612.
Step-by-step explanation:
Your Welcome;)
what is the average rate of change from x = 0 to x=4
A. 0
B. 1
C. 4
D. 8
Answers
How are the two angles below related? *Drawing not to scale*
A) Supplementary
B) Adjacent
C) Complimentary
D) Vertical
Answers
answer
A) Supplementary
Answer:
Supplementary is correct!
Step-by-step explanation:
ΔMNP is an isosceles triangle with MN ≈NP. If ∠ M = 3x + 1 and ∠ N = x - 11. What is the measure of ∠P?
Answers
How many parallelograms are there?
Answers
what is the slope i need the answer now please help
Answers
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line
An investment is currently worth 2.125 × 10^4 dollars . Ten years ago, the investment was worth 1.25 × 10^3 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago?
Answers
The investment today is 17 times greater than it was ten years ago.
To find out how many times greater the value of the investment is today compared to ten years ago, you can divide the current value by the value ten years ago.
So, let's do the calculation:
Current value = 2.125 × 10^4 dollars
Value ten years ago = 1.25 × 10^3 dollars
[tex]\( \text{Times Greater} = \frac{\text{Current Value}}{\text{Value Ten Years Ago}} \)[/tex]
Substitute the values:
[tex]\( \text{Times Greater} = \frac{2.125 \times 10^4}{1.25 \times 10^3} \)[/tex]
To divide these numbers, subtract the exponents:
[tex]\( 10^4 \div 10^3 = 10^{4-3} = 10^1 = 10 \)[/tex]
So,
[tex]\( \text{Times Greater} = \frac{2.125}{1.25} \times 10 = 1.7 \times 10 = 17 \)[/tex]
Therefore, the value of the investment today is 17 times greater than the value of the investment ten years ago.
Prove that if a transversal is perpendicular to one of the two parallel lines, it it parallel to the other line
Answers
If a transversal is perpendicular to one of the two parallel lines, it is parallel to the other line.
Given:
Parallel lines: AB and CD
Transversal: EF
EF is perpendicular to AB
To prove: EF is parallel to CD
Since EF is perpendicular to AB, ∠AFE = 90°.
Since AB and CD are parallel, corresponding angles are equal: ∠AFE = ∠CFE.
Now, ∠CFE = 90° (since ∠AFE = 90°).
This means EF is perpendicular to CD.
By the converse of the perpendicular transversal theorem, EF is parallel to CD.
Explain in detail why the degree of the polynomial below is not 6. 3x^2+6xy-10x^5+y^6-10x^3y^5
Answers
p(x,y) = 3x² + 6xy - 10x⁵ + y⁶ - 10x³y⁵
To determine the degree of the polynomial, let us determine the degrees of the monomials.
3x² has degree 2,
6xy has degree 1+1 = 2,
10x⁵ has degree 5,
y⁶ has degree 6,
10x³y⁵ has degree 3+5 = 8
Answer:
The degree of the polynomial is not 6, but 8.
Explanation:
The degree of the polynomial is 8 because that is the highest degree of the terms in the polynomial.
HELP SCIENCE! BRAINLIEST
What evidence supports the law of conservation of energy?
Light energy is converted to chemical energy during photosynthesis.
Oxygen is made from the breakdown of carbon dioxide during photosynthesis.
Energy is absorbed by chlorophyll during photosynthesis.
The sun gives off light energy that is absorbed by plants.
Answers
hope this helps
q-r=r solve for r
Please can someone explain this to me
Answers
Flip
r = Q - r
Add r to both sides
2r = Q
Divide both sides by 2
r = Q/2
Have an awesome day! :)
To solve the equation q-r=r for r, add r to both sides to isolate the variable r. Then, divide both sides by the coefficient of r to find the value of r.
Explanation:To solve the equation q-r=r for r, we want to isolate the variable r on one side of the equation. To do this, we can add r to both sides of the equation:
q - r + r = r + r
This simplifies to:
q = 2r
Next, we can divide both sides of the equation by 2 to solve for r:
q/2 = r
Therefore, the solution is r = q/2.
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How many tangents to the circle can be constructed through point P?
Answers
Assuming it looks like this, here's your answer. For future reference of course.
Answer:
Two tangents.
Step-by-step explanation:
A circle is given and we have to draw the tangents on the circle from an external point P. By the definition we can draw only two tangents on a circle from an external point P and no tangent can be drawn form a point within the circle.
Therefore answer is two.
For a data set, the mean is 3.17 and the range is 1.4. The data set is transformed by adding 0.5 to each data value. What are the mean and range of the new data set?
a. mean: 3.67; range: 1.9
b. mean: 3.67; range: 1.4
c. mean: 3.17; range: 1.9
d. mean: 3.17; range: 1.4
Answers
Adding 0.5 to each value in the data set increases the mean to 3.67 while the range remains at 1.4. Hence, the correct answer is option b.
When a constant is added to each data value in a data set, the mean of the data set increases by that constant, while the range remains unchanged. In this case, adding 0.5 to each data value will increase the mean by 0.5 but the range will stay the same.
Given the original mean: 3.17 and original range: 1.4:
New mean = 3.17 + 0.5 = 3.67
New range = 1.4
Therefore, the correct answer is option b: mean: 3.67; range: 1.4.
The graph illustrates a reflection of . What is the line of reflection?
A.
x-axis
B.
y-axis
C.
y=x
D.
y=2x
Answers
Answer:
A. x-axis
Step-by-step explanation:
It is a mirror image. The doesn't change.
The figure J'K'M' is just reflected over the x-axis.
So it is reflection about the x-axis.
Therefore, answer is A. x-axis
Hope this will helpful.
Thank you.
) Tell whether the sequence is Arithmetic, Geometric, or Neither. -5, 95, 195, 295, 395, …
Answers
What does h(40)=1820 mean it terms of problem?!!! HELPP
Answers
Answer:
D is the correct option.
Step-by-step explanation:
In the given table, the first column is for "hours of training" and the second column is for "Monthly pay".
Now, we have to state the meaning of the term h(40)=1820.
In coordinate system we can write this as (40,1820).
Since, the first column represents "hours of training" and second column is for "Monthly pay". Hence, we can say that for 40 hours of training the monthly payment is $1820.
In other words, if the training attended by the worker is 40 hours, h/she would pay $1820.
Therefore, D is the correct option.
Answer: D
Step-by-step explanation:
A P E X
x= r-h/y
solve for h and r
Answers
Let's first solve for h :)
Add h/y to both sides.
h/y + x = r
So, r = h/y + x
Now, let's solve for h.
x = r-h/y
Subtract r from both sides.
-r + x = -h/y
Multiply both sides by y.
y(-r + x) = y(-h/y)
Simplify.
-ry + xy = -h
Divide both sides by -1.
ry - xy = h
So, h = ry - xy
~Hope I helped!~
To solve for h, rearrange the equation to h = r - xy, and to solve for r, rearrange it to r = xy + h. This process involves basic algebraic manipulation to isolate each variable on one side of the equation.
Explanation:The original equation given is x = r - h/y. To solve for h, we need to get h by itself on one side of the equation. First, we can rearrange the equation to isolate h:
Multiply both sides by y to get rid of the fraction: xy = r - h.Move all terms containing h to one side and the rest to the opposite side: h = r - xy.To solve for r, we take the original equation and solve for r explicitly:
First, isolate the term containing r: r = xy + h.Now we have both variables solved in terms of x, y, and each other.
The sum of two numbers is 64 . the larger number is 18 more than the smaller number. what are the numbers?
Answers
Final answer:
To solve the problem, we use a system of equations: x + y = 64 and y = x + 18. The smaller number is found to be x = 23, and the larger number is y = 41.
Explanation:
To find the two numbers where their sum is 64 and the larger number is 18 more than the smaller number, we can set up a system of equations. Let x represent the smaller number and y represent the larger number. We have the following equations:
x + y = 64
y = x + 18
We can substitute the second equation into the first one to solve for x:
x + (x + 18) = 64
2x + 18 = 64
2x = 64 - 18
2x = 46
x = 23
Therefore, the smaller number is 23, and the larger number is:
y = x + 18
y = 23 + 18
y = 41
Hence, the two numbers are 23 and 41.
What are four different ways of representing functions? how can you tell if a relationship is a function?
Answers
Functions can be represented verbally, algebraically, graphically, and numerically. A relationship is a function when for every input, there is exactly one output which is described by the vertical line test. Graphs for different types of functions vary in shape.
Explanation:Functions can be represented in four various ways: verbally, algebraically, graphically, and numerically. For instance, verbal representation uses words to describe the function. Algebraically, we express the function via an equation. Graphically, we visually represent the function through graphs. Numerically, we represent the function using a table.
A relationship is a function if for every input, there is exactly one output. In a graph, this corresponds to an instance where a vertical line drawn anywhere on the graph would intersect it at only one point. This is also known as the vertical line test.
Examples of different types of functions graphically could include (a) a linear graph, showing a straight line, (b) a quadratic graph, parabolic in shape, (c) an inverse graph, where y decreases as x increases, and (d) an exponential graph, where the rate of growth is proportional to the function's current value.
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Glaciers store about 75% of the world's freshwater.
Question 1 options:
True
False
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 2
Question 2 (1 point) Question 2 Saved
Atlantic Canada, located on the eastern edge of North America, has a climate that is influenced by prevailing westerly winds.
Question 2 options:
True
False
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 3
Question 3 (1 point) Question 3 Saved
An ecoregion is defined as a large area of land or water that contains a geographically distinct assemblage of natural communities.
Question 3 options:
True
False
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 4
Question 4 (3 points) Question 4 Saved
What caused virtually all of Canada and some of the northern US to be once covered by thick glacial ice almost 15,000 years ago?
Question 4 options:
Changes in the earth's climate caused the ice sheets to grow.
Changes in the orbit of the earth caused the ice sheets to spread across Canada.
The ice sheets were widespread because they were prevalent all around the world.
There is no apparent reason why the glacial ice was present.
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Question 5 (3 points) Question 5 Saved
The impacts of El Niño upon climate in temperate latitudes show up most clearly during which season?
Question 5 options:
Summer
Winter
Fall
Spring
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 5
Question 6 (3 points) Question 6 Saved
Approximately what portion of North America is covered by forests?
Question 6 options:
1/4
1/3
1/2
3/5
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Question 7 (3 points) Question 7 Saved
These winds are found in the middle latitudes between 30 and 60 degrees latitude.
Question 7 options:
Polar Easterlies
Trade Winds
Roaring Forties
Prevailing Westerlies
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 6
Question 8 (3 points) Question 8 Saved
Which of the following factors helped make inland transportation and commerce possible in the United States?
Question 8 options:
The vast mineral deposits
Extremely fertile soils
The intricate river systems
Ample water from the snowmelts
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Question 9 (3 points) Question 9 Saved
Which of the following is not a resource the Appalachian Mountain range is well known for providing?
Question 9 options:
silver
coal
petroleum
iron
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Question 10 (3 points) Question 10 Unsaved
Canada's strong regionalism is mainly attributable to which of the following?
Question 10 options:
The collapse of the cod fishing industry
Large differences in natural resource distribution throughout the country
Continuous large natural resource discoveries
The logging industries adaptation of a more sustainable model
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 8
Question 11 (3 points) Question 11 Unsaved
Approximately what percentage of energy in the U.S. is provided by renewable energy resources?
Question 11 options:
5%
9%
15%
25%
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2.03 Quiz: Physical Characteristics and Systems of North America Quiz Pool 9
Question 12 (3 points) Question 12 Unsaved
According to this world map of potential renewable energy, what form of renewable energy has the greatest potential in North America?
Graphic titled World Potential Renewable Energy with four world maps in cluster with each titled wind energy, biomasse, hydroelectricity, and solar energy. Circles represent the amount of equipment in tons are placed over each continent. Biomass has largest circles followed by hydroelectric, solar, and wind. The biomass circle on North America is largest, the hydroelectricity circle is a little smaller, and the solar and wind circles are smaller but about the same size.
Question 12 options:
wind
biomass
hydroelectricity
solar
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Answers
All I know is that Number One is TRUE.
Hope this is helpful :)
Triangle lmn is similar to triangle nop. both are right triangles. which statements about the two triangles must be true? choose all answers that are correct.
a. sides ln and np have the same slope.
b. sides ln and np are congruent.
c. triangle lmn and nop are congruent.
d. sides lm and mn are proportional to sides no and op.
Answers
The slopes might be the same
All right triangles are congruent,
The corresponding parts or congruent triangles are congruent
"sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
"Congruent" means the same
Two triangles are said to be congruent if they both have same length and same angles.
"Similar" means the area and sides will be proportional, it means when we divide or multiply with a number we get the measure of the other.
If triangle lmn is similar to triangle nop. both are right triangles.
Then we need to check which options will be correct and holds.
a. sides ln and np have the same slope it is correct because the triangle will have same slopes
b. It must not be true "sides ln and np are congruent" because as they are congruent the sides should be same.
c. triangle lmn and nop are congruent, is not true because there measures are different.
d. As the triangles are similar " sides lm and mn are proportional to sides no and op." must be true, because of proportionality.
Hence "sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
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c) Solve the equation you wrote in part b to find how many hours you would have to work to pay for the first year of video streaming service. Show your work and round your answer to the nearest tenth.
Answers
Every Month $68 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18
Total For Year$68 $86 $104 $122 $140 $158 $176 $194 $212 $230 $248 $266
TRUE OR FALSE
"All 4 sides are equal in a rhombus but not in a parallelogram"?
Answers
_____________________________________________
NOTE: A "square" is also a rhombus AND a parallelogram ; and a "square" has 4 equal sides. Furthermore, a "rhombus" is also a parallelogram ; and a rhombus has 4 equal sides.
_____________________________________________
The container that holds the water for the football team is 7/10 full. after pouring out 6 gallons of water, it is 1/2 full. how many gallons can the container hold?
Answers
7/10 = 7/10 & 1/2 = 5/10
7/10 - 6 gallons = 5/10
7/10 - 5/10 = 6 gallons
2/10 = 6 gallons
multiply each side by 5
10/10 = 30 gallons
container can hold 30 gallons
The total capacity of the container is 30 gallons in volume.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is that the container that holds the water for the football team is 7/10 full. After pouring out 6 gallons of water, it is 1/2 full.
Assume that the container total capacity is [x] gallons. Then, according to the question -
7x/10 - 6 = x/2
7x/10 - x/2 = 6
x(0.7 - 0.5) = 6
0.2x = 6
x = 6/0.2
x = 6/(1/5)
x = 30 gallons
Therefore, the total capacity of the container is 30 gallons in volume.
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I shuffle a standard deck with 52 cards and randomly draw the ace of hearts, then put it to one side. what is the probability that the next card i draw is either an ace or a heart?
Answers
The perimeter of this shape is 82 cm. what is the length of side d? cm
Answers
Paulo has $145 in his savings account. he earns $36 a week mowing lawns. if paulo saves all of his earnings, after how many weeks will he have $433 saved?
Answers
Answer:
8 week
Step-by-step explanation:
= $ 433 − $ 145 = $ 288
= $ 36 for 1 week
$ 288 for x weeks
x = 288 divide 36
x = 8 weeks
Triangle XYZ is shown on the coordinate plane below:
Triangle XYZ on the coordinate plane with ordered pairs at X 3, negative 1, at Y 4, negative 4, at Z 1, negative 2
If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'?
Answers
(3, -1)
(4, -4)
(1, -2)
The triangle created is the first file attached.
When reflected off of the line y = 1, it is one higher y than reflecting off the y axis. So, the coordinates are (1,-4) (3, 3) (4, 6)
The ordered pair of [tex]X'[/tex] is [tex](3,3)[/tex]
Explanation
According to the below diagram, the co ordinates of [tex]\triangle XYZ[/tex] are: [tex]X(3, -1), Y(4,-4)[/tex] and [tex]Z(1,-2)[/tex]
The triangle [tex]XYZ[/tex] is reflected across the line [tex]y=1[/tex] to create triangle [tex]X'Y'Z'[/tex]
Distance of the point [tex]X[/tex] from the line [tex]y=1[/tex] is 2 units.
So, the point [tex]X'[/tex] will be also 2 units above the line [tex]y=1[/tex]. As the triangle is reflected across a horizontal line, so the [tex]x[/tex] co-ordinate of the point will remain same.
[tex]y[/tex] co-ordinate of the point [tex]X'[/tex] will be: [tex]y=1+2 =3[/tex]
So, the ordered pair of [tex]X'[/tex] is [tex](3,3)[/tex]