Answer: The x-axis is tangent to the curve when the value of y is equal to 0. So, to find the possible values of d when the x-axis is tangent to the curve, we need to solve the equation:
x^3/3 + 7x^2/2 + 10x + d = 0
To solve this equation, we need to use a method such as the cubic formula or a numerical method such as Newton-Raphson. However, it is not possible to determine a general solution for d without additional information, such as the value of x at which the tangency occurs. The possible values of d will depend on the specific value of x that satisfies the equation.
Step-by-step explanation:
find the x value of the point of intersection
The value of x at the point of intersection is given as follows:
x = -1.
How to obtain the value of x?
We must test for both definitions of the second function, and find which solution is in the correct range.
For the first definition, the solution is given as follows:
2x + 1 = x
2x - x = -1
x = -1.
-1 is less than 1, hence x = -1 is one solution to the system of equations.
For the second definition, the solution is given as follows:
2x + 1 = -x + 2
3x = 1.
x = 1/3.
Which is less than one, while the function is defined for values greater than 1, hence it is an extraneous solution.
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Derek buys 5 small bottles of mango juice from the grocery store. He plans on drinking 1/2 of a bottle every morning when he has breakfast. How many days will the mango juice last for?
Answer:
Derek's mango juice will last for 10 days.
Step-by-step explanation:
Derek buys 5 small bottles of mango juice, so he has 5 bottles in total.
He plans to drink half the contents of each bottle every morning, which means he will drink 1/2 * 1 bottle = 1/2 bottle of mango juice every day.
Since Derek drinks 1/2 bottle of mango juice every day, the 5 bottles of mango juice will last for 5 bottles / (1/2 bottle per day) = 10 days.
So, the answer is that the 5 bottles of mango juice will last for 10 days.
Hi there, here's your answer:
Given Derek buys 5 small bottles of Mango Juice
Also given that Derek drinks half a bottle every morning.
So taking the number of days to be 'x'
We get an equation [tex]\frac{1}{2} x = 5[/tex]
Upon cross multiplication, we get 1 × x = 5 × 2 = 10 days.
Therefore, the mango juice will last for 10 days.
Hope it helps! Please mark as Brainliest!
A figure has a perimeter of 12 units. Which describes the perimeter of the figure after a dilation with a scale factor of 4?
The perimeter of the figure after a dilation with a scale factor of 4 is
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
Given;
The perimeter= 12units
Scale factor=4
Now,
Dilation with the given scale factor;
= 12*1/4
=12/4
=3
Therefore, dilation by the given scale factor will be 3.
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Please help this those.
The values of x and y are 30 and 80
The value of x is 63The slope of GH is 0How to determine the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The parallel line and the transversal
The value of y is calculated as
y + 25 = 105 ---- alternate angle theorem
So, we have
y = 80
For x, we have
3x - 15 + 105 = 180 --- coresponding angle
So, we have
3x = 90
Divide
x = 30
How to determine the value of xHere, we make use of
2x + 54 = 180 --- sum of alternate interior angles
So, we have
2x = 126
Divide
x = 63
The slope of line GHThis is calculated as
Slope = (y2 - y1)/(x2 - x1)
So, we have
Slope = (6 - 6)/(5 - 2)
Slope = 0
Hence, the slope is 0
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a. Draw a tree diagram for the results from tossing a fair two-sided coin (H, T) four times
b. How many stages are there in the tree diagram?
c. List all the possible outcomes (the sample space).
d. How many outcomes are there in the sample space?
▪ You must show ALL of your work in order to receive full credit.
Answer:
Step-by-step explanation:
a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:
(1)
/ \
(H) (T)
/ \ / \
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
b) There are four stages in the tree diagram.
c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTTT
d) There are 2^4 = 16 outcomes in the sample space.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1)
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4)
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1).
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4).
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.
Area of composite shapes, There is a pair of parallel sides in the following shape.
What is the area of the shape?
The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².
What does mathematicians mean by area?Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.
The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.
So, 1/2 * ( 9+5) * 3
= 1/2 * 14 * 3
= 1/2 * 42
= 21 cm²
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A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 quarts of vegetable broth. What is the unit rate in quarts per pound?.
10 pounds of barley should be used by the cook to mix in with the 35 quarts of the vegetable broth.
lets say we know that there is a mix of 2 pounds of barley into 7 quarts of vegetable broth, so we can say that,
2:7 is the ratio used for the mix
similarly we can say,
let the pounds of barley into 35 quarts of vegetable broth used be x
x:35 because its given that there are 35 quarts used in the vegetable soup so we need to find the value of 'x'
then, 2/7=x/35, that is pounds/quarts
then, x= 2/7 × 5
then, x = 2×5
therefore we know that x = 10
so we can say that there are 10 pounds of barley used in the mix by the cook along with the 35 quarts of vegetable broth.
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What is the area of the parallelogram shown?
yd²
The area of the parallelogram that is shown above would be = 9 yd².
What is a parallelogram?A parallelogram is defined as the quadrilateral that has four sides whose sides are also parallel to each other.
The formula that can be used to calculate the area of the parallelogram = base × height ( diagonal)
The base = 4½ yd
height = 2 yd (diagonal)
Area = 4½× 2 = 9yd².
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Calculate the Volume of the log
Answer:(A=πr2).
Step-by-step explanation:The cubic feet, or volume, of a cylindrical log is given by the volume of a cylinder V=πhr2. A log with radius of 2 feet and height of 10 feet would have a volume of about 125.66 cubic feet (or ft3). The volume can also be thought of as the area of the base times height with the base area being the area of a circle (A=πr2).
pls help me
i need to pass my geo class
Answer:
XY = 18
Step-by-step explanation:
In this picture, XD = DW, and YE = EZ, so we are able to use the midline theorem. From the midline theorem, we can easily determine that (XY + WZ)/2 = DE. From this, we can plug in: (XY + [tex]\frac{4}{3}[/tex]XY) = 2 * 21. So, simplifying that equation gets: [tex]\frac{7}{3}[/tex]XY = 42. So, XY = [tex]42 * \frac{3}{7} = 18[/tex].
(if i'm going to be honest, i'm sure your geometry teacher covered this in class. just make sure to pay attention next time.)
Answer:
XY = 18 ft.
Step-by-step explanation:
Solve the system using the substitution method. For the system that does not have one unique solution, also state the number of solutions and
whether the system is inconsistent or the equations are dependent. Express numbers as integers or simplified fractions.
y=2x+7
4x+3y=-19
Answer:
(-4, -1)
Step-by-step explanation:
The system has one solution
What is the solution to the equation?
√x + 2 = 1
O A. 1
OB. 4
O C. 1 and 4
OD. no solution
Answer:
The solution of the equation is B. 4
Step-by-step explanation:
√x + 2 = x
√x = x - 2
(√x)² = (x-2)²
x = (x-2) (x-2)
x = x² - 4x + 4
x moves to the right
0 = x² - 4x - x + 4
0 = x² - 5x + 4
0 = (x-1) and (x-4)
x-1 = 0 x-4 = 0
x = 1 (not) x = 4
So, the solution to the equation is B. 4
Simplify fully 8c^4d^5+2c^3d^3
The expression when simplified is 2c^3d^3(4cd^2 + 1)
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
8c^4d^5+2c^3d^3
Factor out 2 from the expression
So, we have the following representation
2(4c^4d^5 + c^3d^3)
Factor out c^3d^3 from the expression
So, we have the following representation
2c^3d^3(4cd^2 + 1)
Hence, the expression is 2c^3d^3(4cd^2 + 1)
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PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Step 1: Understanding the Problem
The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.
Step 2: Writing the Equation
We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:
f(x) = 240 - 0.15x
This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.
Step 3: Interpreting the Equation
The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).
Step 4: Conclusion
So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).
Solve c =3/7(wm+a) for m
Answer:
Step-by-step explanation:
To solve the equation c = 3/7(wm + a) for m, we can isolate m on one side of the equation.
Here's the step-by-step process:
Distribute the 3/7:
c = 3/7 * wm + 3/7 * a
Subtract 3/7 * a from both sides:
c - 3/7 * a = 3/7 * wm
Divide both sides by 3/7 * w:
(c - 3/7 * a) / (3/7 * w) = m
And that's it! m is the value you're looking for. Just remember to use the values of c, w, and a that you have in your specific problem when you evaluate the expression.
[tex]m=\frac{7 c-a}{3w}.[/tex]
Step-by-step explanation:1. Write the expression.[tex]c=\frac{3}{7} (wm+a)[/tex]
2. Divide by [tex]\frac{3}{7}[/tex] on both sides of the equation.Remember that dividing by a fraction is the same as multiplying by its multiplicative reciprocate. Hence, we may multiply by [tex]\frac{7}{3}[/tex] on both sides and it'd have the same efect as dividing by [tex]\frac{3}{7}[/tex].
[tex]\frac{7}{3} c=\frac{3}{7} (wm+a)*\frac{7}{3}[/tex]
The two fractions on the right side cancel each other out and we're left with:
[tex]\frac{7}{3} c=(wm+a)[/tex]
3. Remove the parenthesis.[tex]\frac{7}{3} c=wm+a[/tex]
4. Subtract "a" on both sides of the equation.[tex]\frac{7}{3} c-a=wm+a-a\\ \\\frac{7}{3} c-a=wm[/tex]
5. Divide by "w" on both sides of the equation.[tex]\frac{\frac{7}{3} c-a}{w} =\frac{wm}{w} \\ \\\frac{7 c-a}{3w} =m[/tex]
6. Conclude.[tex]m=\frac{7 c-a}{3w}.[/tex]
-------------------------------------------------------------------------------------------------------
(Extra step) 7. Verification.If you want to verify whether the answer is correct or not, you may take the original equation and plug the calculated value of "m" in the place of said variable. Then, if the equation returns the same value after simplifying completely, the solution is correct!
This step is show on the attached image.
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
4 is subtracted from the product of 5 and a number.
I need answer
The mathematical Expression is 5x- 4.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given:
We have the unknown variable x.
4 is subtracted from the product of 5 and a number.
Now, Translating the word problem (sentence) into an algebraic expression, we get
= 5x - 4
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Jennifer plans to drive from Spokane, Washington to Missoula, Montana, to visit her aunt. On the map Jennifer is using, each inch represents 20 miles. If the distance on the map from Spokane to Missoula is 5% inches, how far is it in actual miles?
Actual distance from Spokane to Missoula = 100 miles
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Given,
On map one inch represents 20 miles
Distance between Spokane to Missoula on map = 5 inches
Actual distance = 5 × 20 = 100 miles
Hence, 100 miles is the actual distance from Spokane to Missoula.
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NEED HELP ASAP PLEASE! The table below represents a linear function. What is the slope of the graph of this function?
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
A: 2
B: -1/2
C: 1/2
D: -2
The slope of the graph of this function is 1/2, the correct option is C.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We are given that;
The x input and y output of function.
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
Now
m=y2-y1/x2-x1
m= 2-1/5-3
m=1/2
Also, m=-1+2/-1+3
m=1/2
Therefore, the slope of the function will be 1/2
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Solve 2y-k=b+5 for y
Answer:
y=b+5+k/2
Step-by-step explanation:
2y-k=b+5
2y=b+5+k
2y/2=b+5+k/2
y=b+5+k/2
Answer:
y = b+ 5 + k/2.
Step-by-step explanation:
2y - k = b + 5
the subject for y
[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]
What are the coordinates of D'when the quadrilateral is reflected across the line Y - X?
The coordinates of D' will be at (x, - y) when reflected along the line Y-X.
What are transformations?Mathematical transformations can be used to move two-dimensional figures along a plane or coordinate system.
Dilation, To construct the image, the preimage is scaled up or down.
The image is a preimage that has been turned around or a reflection.
Rotation, To produce the final image, the preimage is rotated about a specified point.
Translation, The picture is relocated a set distance from the preimage while also being translated.
Given, A quadrilateral ABCD and one is the vertex D(x, y).
Now, The reflection of the quadrilateral ABCD is reflected across the Y-X.
We know a reflection along Y-X changes (x, y) to (x, -y).
Therefore, The vertex D' will have coordinates (x, - y).
Q. What are the coordinates of D'when the quadrilateral ABCDis reflected across the line Y - X, Given, preimage D(x, y).
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If the California Current moves at 0.25 cm/s, how fast is that in knots?
Answer:
0.4850 knots.
Step-by-step explanation:
To convert the speed of the California Current from centimeters per second to knots, we can use the conversion factor of 1 knot = 0.514444444 cm/s.
So, 0.25 cm/s * 1 knot / 0.514444444 cm/s = 0.4850 knots.
Therefore, the California Current moves at a speed of approximately 0.4850 knots.
Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.
If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.
What is Function?
In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.
They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.
If x and y vary inversely, we can write their relationship as:
x * y = k
where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:
10 * 8 = k
k = 80
Therefore, the function that models the inverse variation is:
x * y = 80
or
y = 80/x
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Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times. Here are the mpg values from the experiment:
37.2 21.0 17.4 24.9 27.0 36.9 38.8 35.3 32.3 23.9
19.0 26.1 25.8 41.4 34.4 32.5 25.3 26.5 28.2 22.1
Suppose that the standard deviation of the population of mpg readings of this vehicle is known to be σ=6.5mpg
a) What is σx¯, the standard deviation of x¯ (x Bar)?
b) Based on a 95% confidence level, what is the margin of error for the mean estimate?
c) Given the margin of error computed in part (b), give a 95% confidence interval for μμ, the mean highway mpg for this vehicle. The vehicle sticker information for the vehicle states a highway average of 27 mpg. Are the results of this experiment consistent with the vehicle sticker?
a) The standard deviation of 1.45 mpg.
b)The margin of error for the mean estimate 3.03 mpg
c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is 27 mpg.
a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.
b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.
c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.
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verify the identity by converting the left side into sines and cosines:
cotx-tanx = secx(cscx - 2sinx)
Answer: To verify the identity, we need to convert both sides into sines and cosines and see if they are equal.
Starting with the left side:
cotx = 1/tanx
So,
cotx - tanx = 1/tanx - tanx
Using the identity tan^2x = sec^2x - 1, we get
cotx - tanx = (sec^2x - 1) / tanx
Expanding the right side using the definition of cscx and sinx, we get:
cotx - tanx = secx(1/sinx - 2sinx)
So,
cotx - tanx = secx(cscx - 2sinx)
Since both sides are equal, we can conclude that the identity is verified.
Step-by-step explanation:
Selina claims single having one exemption. Her state tax deduction is 21% of her federal tax contribution. Calculate the amount of state tax selina owes if her gross pay for two weeks is $840. The following federal tax table is for biweekly earnings of a single person. A. $16. 17 b. $16. 80 c. $32. 34 d. $33. 60 please select the best answer from the choices provided a b c d.
The amount of federal state tax Selina owes if her gross pay for two weeks is $840 is $14.11, which is closest to option A: $16.17. so the best answer is A as it is the closest.
To calculate Selina's federal tax contribution, we first need to determine her taxable income. From her gross pay of $840, we can subtract the biweekly standard deduction for a single person, which is $191.15 (based on the federal tax table provided). This gives us a taxable income of $648.85.
Using the federal tax table for biweekly earnings of a single person, we can see that the federal tax on this amount is $67.25.
Selina's state tax deduction is 21% of her federal tax contribution, which is 0.21 x $67.25 = $14.11.
Therefore, the amount of state tax Selina owes is $14.11, which is closest to option A: $16.17. However, none of the given options match the calculated amount exactly, so the best answer is A as it is the closest.
To know more about federal state tax:
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Find the value of b if the graph of y = 0.3x + b goes through the point.
N(5,d)
If 10,000 catfish can be accommodated by a pond with an area of 30 square meters, how large a pond is needed if the number of catfish is 20,000?
Answer:
60
Step-by-step explanation:
10,000 * 2 = 20,000, so multiply 30 by 2:
30 * 2 = 60
Answer:
A 60 square meter pond is needed to accommodate 20,000 catfish.
Step-by-step explanation:
We know that 30 square meters is needed per 10,000 catfish.
How large a pond is needed for 20,000 catfish?
We can create an equation like this
[tex]\frac{30}{10000} =\frac{x}{20000}[/tex]
let [tex]x[/tex] represent the number of square meters needed for 20,000 catfish
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]30*20000=x*10000[/tex]
Evaluate [tex]30*20000[/tex]
[tex]600000=10000x[/tex]
Divide both sides by [tex]10000[/tex].
[tex]60=x[/tex]
Jonathan is a single taxpayer. His taxable income before deductions was $63,110. He was able to reduce his taxable income by $10,312 when he filled out Schedule A and Schedule 1.
a. How much did he save in tax by using Schedule A?
In a linear equation. , $12,215 did he save in tax by using Schedule A .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given,
Taxable income with out deductions = $63,110
total deductions = $10,312
the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is
tax = $12,215
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PLEASE HELP I NEED THIS RN
x = 415.
Step-by-step explanation:1. Identify the information provided in the statement.Check attached image 1.
2. Find a value to solve the equation.So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.
Check attached image 2.
3. Write the equation.We know that the sum of angles DBE and CBE equal 90°. Hence:
[tex]DBE+CBE=90[/tex]
In terms of variable "x", this is:
[tex](0.1x-22)+(0.3x-54)=90[/tex]
4. Solve the parenthesis.[tex]0.1x-22+0.3x-54=90[/tex]
5. Operate with like terms.[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]
6. Add "76" on both sides of the equation.[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]
7. Divide by "0.4" on both sides of the equation.[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]
8. Verify.To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!
[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]
9. Conclude.x = 415.
A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.
A more accurate value would be 13.8271643518519
Round it however you need to.
======================================================
Explanation:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Let's see how many seconds there are in a day.
[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]
I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".
There are exactly 86,400 seconds in 1 day.
This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.
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1 drop = 0.003 cubic inches approximately
x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.
0.003x = 3584
x = 3584/0.003
x = 1,194,666.66666667 approximately
Round up to the nearest whole number to get 1,194,667
The sink starts to overflow when we have 1,194,667 drops of water in it.
Divide this over 86,400 mentioned earlier.
(1,194,667)/(86,400) = 13.8271643518519 approximately.
Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827
