Answers
Given:
Find-:
Rate is the depth of the pool water increasing
Explanation-:
The rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two points is:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ \\ (x_2,y_2)=(4,2) \end{gathered}[/tex]So, the rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{4-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]So, 1/2 ft per hour
Related Questions
A bag contains 5 red marbles and 3 blue marbles. A marble is selected at random and not replaced into the bag. Another marble is then selected from the bag. How would you describe these two events?
Answers
Marble Events
there are 5 + 3 = 8 marbles
If one marble is selected then there are now
8 - 1 = 7 marbles
Then answer is
The two events are Dependent
Event B is dependent on Event A
what is 3 x 10 to the 4 in standard notation
Answers
Bill has these expenditures for his utilities: December,
$234.45; January, $281.23; February, $284.33. What is his
average monthly expense for utilities?
Answers
The average monthly expenses for Bill's utilities is $266.67.
It is given in the question that:-
Expenditure in December by Bill = $ 234.45
Expenditure in January by Bill = $ 281.23
Expenditure in February by Bill = $ 284.33
We have to find the average monthly expenses for Bill's utilities.
We know that,
Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3
Hence, using the data given in the question, we can write,
Average monthly expense for utilities = (234.45 + 281.23 + 284.33)/3
Average monthly expense for utilities = 800.01/3 = $266.67
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Type the correct answer in the box. Consider functions f and g: f(x) = (x+1)^3g(x)= x^1/3 +1Evaluate the function composition. (fog)(–64) =
Answers
The composition
[tex](f\circ g)(x)[/tex]Means that you have to evaluate x in g(x) first, and then evaluate that result in f(x)
In other words:
[tex](f\circ g)(x)=f(g(x))[/tex]Let's use this for this question:
[tex]\begin{gathered} f(x)=(x+1)^3 \\ g(x)=\sqrt[3]{x}+1 \\ \\ (f\circ g)(-64)=f(g(-64)) \\ \rightarrow g(-64)=-3 \\ \rightarrow f(-3)=-8 \\ \\ \text{Thereby} \\ (f\circ g)(-64)=-8 \end{gathered}[/tex]10 × 1/3
make sure the answer is a fraction and that u explain
Answers
multiply the top and bottom ----> 10*1 and 1*3
10/3 would be your answer
Jenna organizes the food in her pantry. She organizes 4 cereal boxes, 6 cans, t pieces of fruit, and 2 bags of rice. How many food items does Jenna organize?
Answers
Solution:
The number of food items is given by the following expression:
4 cereal boxes + 6 cans+ t pieces of fruit+ 2 bags of rice
that is, she organizes
4+6+t+2 meals
this is equivalent to
(4+6+2)+t
this is equivalent to say
12 + t meals.
So that the correct answer is:
12 + t
a rectangle width is 3 1/2 inches and the lenght is 4 3/4 inches. What is the area of the rectangle?
Answers
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of the rectangle = [tex]4 \frac{3}{4}[/tex] inches
= 19 / 4 inches
The width of the rectangle = [tex]3 \frac{1}{2}[/tex] inches
= 7 / 2 inches.
Since, We know that;
The area of the rectangle = Length x Width
Substitute all the values , we get;
The area of the rectangle = Length x Width
The area of the rectangle = 19 / 4 x 7 / 2
= 133 / 8 inches²
= [tex]16 \frac{5}{8}[/tex] inches²
Therefore,
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
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Graph the line y = 5x - 1, then name the slope and y-intercept by looking at the graph. What is m= and what is b= and how do I graph this what are the points ?
Answers
Answer:
Step-by-step explanation:
Slope-intercept form: y = mx + b
The 'm' in this formula means slope. The 'b' means the y-intercept.
y = 5x - 1
m = 5.
b = -1.
Now that we have identified the slope and the y-intercept, we can graph the equation.
When graphing these kinds of equations, always start at the y-intercept.
The y-intercept is -1, so we start from there and move up 5 and right 1 repeatedly.
Remember, slope = rise/run. We rise 5, and we run 1.
5 can also be represented as a fraction: [tex]\frac{5}{1}[/tex]
Let me know if you have any questions.
Which expression is undefined? (9-9) A 2 -3) )B. O C. )D. 0
Answers
Answer:
Option B
Step-by-step explanation:
Undefined expression:
An undefined expression is a division by 0, or a fraction in which the denominator is 0.
In this question, the undefined expression is given by option B.
7. An antique dealer has a fund of $1,160 for investments. She spends 50%of the fund on a 1911 rocking chair. She then sells the chair for $710, all ofwhich she returns to the fund.a) What was the percent gain on the investment?b) What percent of the original value of the fund is the new value of the fund?
Answers
Given:
Total amount dealer has is $1160.
Spend 50% of the fund to buy a 1911 rocking chair and sells it for $710.
[tex]Fund\text{ she spends on chair=}1160\times\frac{50}{100}[/tex][tex]Fund\text{ she spends on chair= \$580}[/tex]a)
[tex]\text{Fund gain on selling the chair= 710-580}[/tex][tex]\text{Fund gain on selling the chair= \$}130[/tex][tex]\text{Percent gain on the investment=}\frac{130}{580}\times100[/tex][tex]\text{Percent gain on the investment=}22.41\text{ \%}[/tex]b)
[tex]\text{New value of the fund=1160+130}[/tex][tex]\text{New value of the fund= \$}1290[/tex][tex]\text{Percentage of original to the new value = }\frac{1290}{1160}\times100[/tex][tex]\text{Percentage of original to the new value =111.21 \%}[/tex]111.21% of the original value of the fund is the new value of the fund.
Dave and his friends went out to celebrate his birthday at Chill's in buda. their meal cost $86 and they left a 15% tip how much was the total bill including tip?
Answers
The meal cost is $86
its 15% is:
$86 x 0.15 = $12.9
then the tip was $12.9. Then, the total bill would be:
$86 + $12.9 = $98.9
that is the total bill was $98.9
The area of this figure 20 in. is square inches. 28 in. 30 in. 7 in. 25 in.
Answers
The shape can be broken into two separate rectangles of the forms below.
Bothe shapes give a rectangle, therefore the area of the shape is
Area of Shape = Area of rectangle A + Area of rectangle B
Since Area of rectangle = LENGTH X BREADTH, we then have below
[tex]\begin{gathered} \text{Area of shape = (28 x 7)}+(25\times30) \\ =196+750 \\ =946\text{ square inches} \end{gathered}[/tex]In conclusion, the answer is 946 square inches
Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Answers
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
Let f(x)= 1/x-2 and g(x)=5/x+2Find the following functions. Simplify your answers.F(g(x))=g(f(x))=
Answers
Given:
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{x\text{ - 2}} \\ g(x)\text{ = }\frac{5}{x}\text{ + 2} \end{gathered}[/tex]To find:
a) f(g(x)) b) g(f(x))
[tex]\begin{gathered} a)\text{ f\lparen g\lparen x\rparen\rparen: we will substitue x in f\lparen x\rparen with g\lparen x\rparen} \\ f(g(x))\text{ = }\frac{1}{(\frac{5}{x}+2)-2} \\ \\ f(g(x))\text{ = }\frac{1}{(\frac{5+2x}{x})-2} \\ \\ f(g(x))\text{ = }\frac{1}{(\frac{5+2x-2x}{x})}\text{ = }\frac{1}{\frac{5}{x}} \\ \\ f(g(x))\text{ = }\frac{x}{5} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ g\lparen f\lparen x\rparen\rparen: we will substitue x in g\lparen x\rparen with f\lparen x\rparen} \\ g(f(x))\text{ = }\frac{5}{\frac{1}{x-2}}+2 \\ \\ g(f(x))\text{ = }\frac{5(x\text{ -2\rparen}}{1}+2 \\ \\ g(f(x))\text{ = }5(x\text{ -2\rparen}+2\text{ = 5x - 10 + 2} \\ \\ g(f(x))\text{ = 5x - 8} \end{gathered}[/tex]what is the answer and how do i solve it?
Answers
EXPLANATION
Since we have the expression:
[tex]\frac{x}{x^2+x-6}-\frac{2}{x+3}[/tex]First, we need to find the least common multiplier as follows:
Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)
Ajust fractions based on the LCM:
[tex]=\frac{x}{\left(x-2\right)\left(x+3\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]\mathrm{Apply\: the\: fraction\: rule}\colon\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]=\frac{x-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]Expand\text{ x-2(x-2)}[/tex][tex]=\frac{-x+4}{\left(x-2\right)\left(x+3\right)}[/tex]The final expression is as follows:
[tex]=\frac{-x+4}{(x-2)(x+3)}[/tex]
What is 5 5/7 divided by 1 3/5 divided by 4 2/3 in simplest form?
Answers
The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].
What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.
Given that: (55/7)/(13/5)/(42/3)
First to simplify:
[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]
So, expression becomes,
[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]
Now to simplify this expression.
Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]
Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]
Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.
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It's in the photo, it's a bit to hard to type out.
Answers
Perpendicular lines have slopes that are negative reciprocals.
If two perpendicular lines have slopes m1 and m2, then we have the following equation:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, we can analyze each pair.
a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.
b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.
c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.
d) In this case, the slopes are negative reciprocals:
[tex]-\frac{1}{m_2}=-\frac{1}{-\frac{3}{2}}=\frac{1}{\frac{3}{2}}=\frac{2}{3}=m_1[/tex]Then, this lines are perpendicular.
Answer: Option d.
For each expression build a rectangle using all of tiles,....
Answers
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]the ratio of red candies to Blue candies is 5:4 in the bag if there are 20 blue candies in the bag how many rare candies are there
Answers
The ratio of Red candies to Blue candies is 5:4 in the bag.
In a competition of 837 people, Jenny scored at the 77th percentile.
In what place did she finish?
Answers
Answer:
Jenny scored 644th place.
Step-by-step explanation:
To find out what place she finished, you need to write it out first like this:
77% of 837.
Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.
The term "of" means multiplication.
So, in turn, we have the equation:
0.77 x 837 = 644.49
And, if you round it, your answer would be:
Jenny scored 644th place.
Answer:
See below
Step-by-step explanation:
77th percentile means she scored better than 77 per cent of the test takers...
So Jenny's place was .23 * 837 = ~ 193 rd Out of 837 people
Find the length of the arc. Use 3.14 for it.270°8 cm
Answers
The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
Point B is on line segment AC. Given BC = 10 and AB = 5, determine the lengthAC.Answer: AC= Anyone know how to solve these???
Answers
3
1) Let's sketch that, to better understand this:
2) Considering the Segment Addition Postulate, we can write that:
DF = DE + EF Plug into that the given values
9 = 6 + EF
9-6 = 6-6 + EF
3 = EF
EF =3
3) Hence, the line segment EF is 3 units long
There are 4 options on the dessert menu at a restaurant. Bill and Laura like all of the choices equallyeach choose a dessert at random from the menu. What is the probability that Bill will choose apple pLaura will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessalyour answer to the nearest thousandth.0 0.938O 0.063O 0.25O 0.083
Answers
Solution
If we have 4 options and we want to find that Bill select one option and then Laura a different second option is:
1/2 * 1/2= 1/4= 0.25
Then the best answer is:
0.25
Please help with this practice question
Answers
Explanation below:
Find an equation of the line described. Write the equation in slope-intercept form.With slope of -2 through (0,4)the equation of the line is y=0
Answers
y = -2x + 4
Explanations:The equation of the line having a slope m, and passing through the point (x₁, y₁) is given as:
y - y₁ = m (x - x₁)
From the description given:
The line passes through the point (0, 4)
That is, x₁ = 0, y₁ = 4
The slope of the line, m = -2
Substitute x₁ = 0, y₁ = 4, and m = -2 into the equation y - y₁ = m (x - x₁)
y - 4 = -2 (x - 0)
y - 4 = -2(x)
y - 4 = -2x
y = -2x + 4
Help in writing an equation. I believe that it is supposed to be a linear equation
Answers
Since the information required us that the equation has to start in zero we can think of functions like the root of x but also we have to add a value of 1/3. In other words one equation with those characteristics is
[tex]y=\sqrt{x}+\frac{1}{3}[/tex]can you help me please
Answers
What is the area of a rectangle with vertices
(-1, -4), (-1, 6), (3, 6), and (3, -4)?
* 16 square units
24 square units
O 36 square units
40 square units
Answers
The most appropriate choice for distance formula will be given by Area of rectangle is 40 sq units
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Here,
Let A = (-1 , -4), B = (-1, 6), C = (3, 6) and D = (3, -4)
Length of AB =
[tex]\sqrt{((-1)-(-1))^2 + (-4-6)^2}\\\sqrt{100}\\10 units[/tex]
Length of BC =
[tex]\sqrt{((-1)-3)^2 + (6-6)^2}\\\sqrt{16}\\4 units[/tex]
Length of rectangle = 10 units
Breadth of rectangle = 4 units
Area of rectangle = [tex]10 \times 4[/tex] = 40 sq units
Fourth option is correct
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PLS HELP ASAP
Clara and Toby are telemarketers.
Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls.
If they continue at those rates, who will reach more people in 40 phone calls?
Use the drop-down menu to show your answer.
Answers
Find the surface area of a glazed donut with an outer diameter of 7 cm and an inner diameter of 3 cm. The donut is 2 cm tall
Answers
Solution:
If the outer diameter is 7, then the outer radius is b=7/2.
On the other hand, if the inner diameter is 3, then the inner radius is a= 3/2.
Now, the surface area of a torus (glazed donut) with inner radius a and outer radius b is given by
[tex]SA=\pi^2\mleft(b+a\mright)\mleft(b-a\mright)\text{ =}\pi^2(b^2-a^2)[/tex]Then, applying the data of the problem to the above equation, we can conclude that the surface area of the given glazed donut would be:
[tex]SA=\pi^2(b^2-a^2)=\pi^2((\frac{7}{2})^2-(\frac{3}{2})^2)=98.69[/tex]so that, the correct answer is:
[tex]SA=98.69\approx98.7[/tex]