The equation y = −3x + 7 represents the amount of water y left in a 7-gallon tub after x minutes. What is the slope of the line? What does the slope mean in this context?
Answers
Hope this helps!!
The slope means in this context, the draining of water is 3 gallons per minute. Then the slope of the line will be negative 3.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
y = −3x + 7, represents the amount of water y left in a 7-gallon tub after x minutes.
Then the slope of the line will be negative 3.
The slope means in this context, the draining of water is 3 gallons per minute.
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Related Questions
Write and solve an equation.
A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?
Answers
Answer:
13.25
Step-by-step explanation:
1. you have to subract the cost of the drink:
94.25-1.50=92.75
2.you have to divide to get the individual cost of pizzas by doing
92.75÷7=13.25
so therefore your answer is 13.25 per pizza
I need help with this question please. Fyi, this is just apart of a homework practice
Answers
Okay, here we have this:
Considering the provided equation, we are going to find all the roots, so we obtain the following:
\(\begin{gathered} x^4-2x^3+x^2-8x-12=0 \\ \mleft(x+1\mright)\mleft(x-3\mright)\mleft(x^2+4\mright)=0 \\ x+1=0\quad \mathrm{or}\quad \: x-3=0\quad \mathrm{or}\quad \: x^2+4=0 \\ x=-1\quad \mathrm{or}\quad \: x=3\quad \mathrm{or}\quad \: x^2=-4 \\ x=-1\quad \mathrm{or}\quad \: x=3\quad \mathrm{or}\quad \: x=\sqrt[]{-4} \\ x=-1,\: x=3,\: x=2i,\: x=-2i \end{gathered}\)Finally we obtain that the correct answer is the second option.
- left his house and drove to the store. He stopped and went inside. From he drove in the same direction until he got to the bank. He stopped and went the bank. Then he drove home. The graph below shows the number of blocks com home Connor is a minutes after he left his house, until he got back home.Connor left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Connor is a minutes after he left his house, until he got back home.
Answers
The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.
What is graph?Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.
It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.
The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.
Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.
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Which statement best describes a strategy for estimating the perimeter of the figure below if the grid squares have
side lengths 1 cm?
Add the lengths of the horizontal and vertical segments, and then subtract 5 because the diagonal side is 4 units
wide and 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then subtract 3 because the diagonal side is 4 units
wide but only 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then add 3 because the diagonal side is 4 units wide
but only 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide
and 2 units tall.
Answers
The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;
Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall
What is an estimate of an amount?An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.
Please find attached a diagram of the possible figure created with MS Word
The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;
Base length = 5 units
Height = 4 units
The figure has a diagonal side which is 4 units wide and 2 units tall.
The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5
The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall
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What is the meaning of "\(F=\left \{ (x,y):\varphi (x,y,p) \right \}\)"?
![What is the meaning of "[tex]F=\left \{ (x,y):\varphi (x,y,p) \right \}[/tex]"?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/qPezzQZ7dJhdA0YcETQG5fBdyZW4BfQR.png)
Answers
The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.
The expression "F = {(x, y) : φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function φ, which takes the variables x, y, and p as inputs.
To fully understand the meaning of F, we need to delve into the function φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.
For instance, let's consider a specific example where vraphi(x, y, p) is defined φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.
It is important to note that the specific meaning and implications of F heavily rely on the nature of the function φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.
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Find an equation in point-slope form for the line having the slope of m=4 and containing the point (5,4).
The equation in point-slope form is ___.
Answers
Answer:
y - 4 = 4(x - 5)
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of 4 and passes through the point (5,4).
We want to write this equation in point-slope form.
Point-slope form is given as \(y-y_1=m(x-x_1)\), where m is the slope, and \((x_1,y_1)\) is a point.
SolvingSince we are given the slope and the point, we can immediately plug them into the formula.
Let's start with the slope; we can replace m in \(y-y_1=m(x-x_1)\) with 4.
\(y-y_1=4(x-x_1)\)
We can now plug 5 for \(x_1\) and 4 for \(y_1\).
y - 4 = 4(x - 5)
Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
Answers
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
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5.
Raul has a recipe for Spanish Crepes that yields 20 crepes, but he needs to make 75 crepes
for his party. What must Raul do?
O A increase the yield percentage
OB find a different food to make
OC scale up his recipe
OD scale down his recipe
Answers
Answer:
Step-by-step explanation:
You would scale up the recipe to make a greater portion to accomodate for 75 crepes.
Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answers
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
3x^2-17x=56. What is x?
Answers
Answer:
\(x=-\frac{7}{3} \\x=8\)
Step-by-step explanation:
\(3x^2-17x=56\)
\(3x^2-17x-56=0\\\)
\(3x^2+7x-24x-56=0\)
\(x(3x+7)-8(3x+7)=0\)
\((3x+7)(x-8)=0\)
\(x=-\frac{7}{3} \\x=8\)
Hope this is helpful.
HELP PLEASE Which equation shows a proportional relationship between x and y?
y = 4x
y=−3x−2
y = 3x + 1
y = 9
Answers
Answer:
y = 3x + 1 I think........
What is
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Answers
Answer:
Can you elaborate more on the question?
Solve 2-3 cos x=5+3 cosx for 0° ≤ 180°
Answers
The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.
1. Start with the given equation: 2-3cos(x) = 5+3cos(x).
2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.
3. Combine like terms: 2-6cos(x) = 5.
4. Subtract 2 from both sides: -6cos(x) = 3.
5. Divide both sides by -6: cos(x) = -1/2.
6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.
7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.
8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.
9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.
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The two-way table represents data from a survey asking schoolchildren whether they are attending a summer camp, taking swimming lessons, or both.
A 4-column table with 3 rows. The first column has no label with entries swimming lessons, no swimming lessons, total. The second column is labeled camp with entries 42, 18, 60. The third column is labeled no camp with entries 32, 4, 36. The fourth column is labeled total with entries 74, 22, 96.
Which is the joint relative frequency for school children who plan to attend camp and have swimming lessons? Round the answer to the nearest percent.
4%
19%
33%
44%
Answers
The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.
The correct option to the given question is option d.
We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.
To find the joint relative frequency, we use the formula as follows:
Joint relative frequency = frequency of interest / total frequency
Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96
(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)
Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375
Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).
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If x= -4, find the value of x²-5+6.
Answers
Answer:
x^2_5+6
=-4^2-5+6
=+16-5+6
=+11+6
=17
Step-by-step explanation:
then the answer is 17
I hope it helps you c:
Step-by-step explanation:
If x= -4, find the value of x²-5x+6=(-4)²-5×-4+6
=16+20+6=42
8. The probability that Ava gets promoted is 7/10. Find the odds in favor of Ava getting promoted.
Answers
Please help meee!!!!!!!
Answers
Answer:
1) two spaces are being added per figure. 2)203
Step-by-step explanation:
Answer:
1. Two tiles add per figure, one on each side.
2. The hundredth figure would have 201, because if you want to find the answer to any figure you multiply by two and add one
Step-by-step explanation:
three people are asked to throw a fair die. what is the probability that all ofthem get the same number? [10 pts]
Answers
The probability that all of them get the same number would be 1/36. Or probability that they will have a chance of get the same number after 36 throws. And the probability concept that use here is theoretical probability.
How to calculate?Theoretical probability It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. The chance that any one die matches another is 1 out of 6.Amount of people whom asked to throw are 3 people.Then everybody will get the some chance to get the same number.And then the probability works out this way:Total out comes in three dice = ( 6 × 6 × 6 = 216 ).
Probability of getting same number = 6 × 1/6 × 1/6 × 1/6
= 6 × 1/6 × 1 × 1/6 × 6
= 6/6 × 1/36
= 1 × 1/36
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Find f(4) when f(x)= x^2 + 5x +2
Answers
In order to find f evaluated at 4, we need to replace the number 4 into the place of x, that is,
\(f(4)=(4)^2+5(4)+2\)which gives
\(f(4)=16+20+2\)Therefore, the answer is:
\(f(4)=38\)Felix needs to determine whether x + 3 is a factor of f(x)=−2x4−8x3−2x−63. How can Felix use the factor theorem to determine whether x + 3 is a factor of f(x)? Drag a value, expression, or phrase into each box to correctly complete the statements. Felix evaluates{ } Response area and determines its value to be{ } Response area. Felix concludes that x + 3{ } Response area a factor of f(x)=−2x4−8x3−2x−63.
Answers
Answer:
1st Slot: f(-3)
2nd Slot: -3
3rd Slot: is not
Step-by-step explanation:
Using the Remainder Theorem, we plug in the root of x + 3 (which is x = -3) and see the remainder.
If the remainder = 0, it is a factor
If the remainder ≠ 0, it is NOT a factor
f(-3) = -2(-3)⁴ - 8(-3)³ - 2(-3) - 63
f(-3) = -3
So, x + 3 is NOT a factor.
We then have our 3 answers.
Which expression is equivalent to the expression 1/2 to the power of 3
A 3x 1/2
B 1/2 + 1/2 + 1/2
C 1/2 x 1/2 x 1/2
D 3 + 1/2
Answers
Answer:
C
Step-by-step explanation:
\(\dfrac12^3=\dfrac12 \times\dfrac12 \times\dfrac12\)
Answer:
C 1/2 x 1/2 x 1/2
Step-by-step explanation:
(1/2)³ = 1/2 x 1/2 x 1/2
Hope it helps.
pls answer this!!!
worth 30 points
find the circumference of a circle with d=97cm diameter
round to 3 significant figures
Answers
The circular is around 305 cm in circumeference.
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle.
Substituting d = 97 cm and using the value of π to be 3.14159, we get:
C = πd
C = 3.14159 × 97 cm
C ≈ 304.731 cm
Rounding this to 3 significant figures, we get:
C ≈ 305 cm
Therefore, the circumference of the circle is approximately 305 cm.
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A plane goes from a standstill to 350 mi/hr in about 45 sec. What is the plane's acceleration?
Answers
Answer:
The acceleration is 466.7m/s^2
Step-by-step explanation:
Given
\(u = 0m/s\) -- Initial Velocity
It is 0 because the plane starts from a standstill
\(v = 350mi/h\) -- final velocity
\(t = 45s\) -- time
Required
Determine the acceleration
This is calculated using Newton's first equation of motion
\(v = u + at\)
Convert time to hour
\(t = 45s\)
\(t = \frac{45}{60}hr\)
\(t = 0.75hr\)
Substitute values for v, u and t
\(350 = 0 + a*0.75\)
\(350 = 0.75a\)
Divide both sides by 0.75
\(\frac{350}{0.75} = a\)
\(466.67 = a\)
\(a=466.67m/s^2\)
Hence, the acceleration is 466.7m/s^2
in a convergent geometric series the sum to infinity is 18 and the sum of the first four terms is 130÷9 calculate the common ratio
Answers
The common ratio is approximately -0.6.
Step by step explanationLet the first term in the geometric series be "a" and the common ratio be "r". Then, the formula for the sum to infinity of a geometric series is:
S = a / (1 - r)
And the formula for the sum of the first n terms of a geometric series is:
Sn = a * (1 - r^n) / (1 - r)
So, using the information given:
18 = a / (1 - r)
And:
130/9 = a * (1 - r^4) / (1 - r)
Solving for "r" using these two equations:
18 = a / (1 - r) ==> a = 18 * (1 - r)
130/9 = a * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r) * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r^4)
Dividing both sides by 18:
7/5 = (1 - r^4)
So:
r^4 = 1 - 7/5 = -2/5
Taking the fourth root of both sides:
r = (-2/5)^(1/4)
So, the common ratio is approximately -0.6.
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Solve by graphing. tan(30x - 90°) = -x³
Answers
The solution to the equation is 0.07, 0.17, 0.27, 0.38........
How to determine the solution to the trigonometry equation?The trigonometry equation is given as:
tan(30x - 90°) = -x³
We start by splitting the trigonometry equation as follows, by creating two different equations
y = tan(30x - 90°)
y = -x³
Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³
From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:
x = 0.07, 0.17, 0.27, 0.38........
Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .
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Write a real world problem where the Unit rate is 6 miles per hr
Answers
Emma is going somewhere for vacation. Emma has been traveling for 6 hours and in those 6 hours, she has travelled 36 miles. How many miles did she travel in one hour?
if 8% = 2400, then 100% =
Answers
The required 100% of the value is 30000.
What are percentages?the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Let the parent value be x,
According to the question,
8% of x = 2400
x = 2400 / 8%
x = 2400 / 0.08
x = 30000
Thus, the required 100% of the value is 30000.
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if the system of equations y=b/6x-3 and y=2/3x-3 has infinitely many solutions, what is the value of b?
Answers
Answer:
b = 4
Step-by-step explanation:
4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
Answers
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
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3 1/2 inches so what is the area of this circle?
Answers
Answer:
19.6 in²
Step-by-step explanation:
area of circle = π r²
= π (3 1/2)²
= π (5/2)²
= π 25/4
= 22/7 x 25/4
= 275/14
=19.6 in²