Answer:
327
Step-by-step explanation:
To calculate how much Francisca and Elizabeth will raise together, we need to know how many laps or miles they walked. Unfortunately, the problem doesn't provide us with that information.
However, we can calculate how much each girl will raise individually.
Francisca will walk for 3 hours which is equal to 6 half-hours. She raises $25.50 every half-hour so she will raise:
$25.50 x 6 = $153
Elizabeth will walk for 3 hours which is equal to 12 quarter-hours. She raises $14.50 every quarter-hour so she will raise:
$14.50 x 12 = $174
Therefore, Francisca and Elizabeth will raise a total of:
$153 + $174 = $327
FIRST TO ANSWER GETS BRAINLESS AND NEEDS EXPLANATION
Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answer:
D is correctStep-by-step explanation:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (d)Answer:
ye D is correctStep-by-step explanation:
To combine the terms 12a + 26b - 4b - 16a, you first simplify the like terms. Add the coefficients of a terms and add the coefficients of b terms separately. You get 12a - 16a + 26b - 4b which results in -4a + 22b. Therefore, the correct answer is (c) -4a + 22b.
What is the equation of the line shown in this graph?
PLEASEEE help
Answer:
Y=1
Step-by-step explanation:
Please help me with this question
The surface area of the prism is 112 in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as;
SA = 2B +pH
where h is the height and B is the base area and p is the perimeter of the base
The perimeter of the base = 2(l+b)
= 2(3+4) = 2×7 =14 in
The area of the base = l× b
= 4× 3 = 12 in²
height = 7
Therefore the surface area = 2 × 12 + 14 × 7
= 14+98
= 112 in²
therefore the surface area of the prism is 112 in²
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On Friday, three friends shared how much they read during the week
Barbara read the first 100 pages from a 320-page in the last 4 days
Judy read the first 54 pages from a 260-page book in the last 3 days.
Nancy read the first 160 pages from a 480-page book in the last 5 days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
Answer:
Step-by-step explanation:
Barbara read the first 100 pages from a 320-page in the last four days
Judy read the first 54 pages of a 260-page book in the previous three days.
Nancy read the first 160 pages from a 480-page book in the previous five days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
The number of international Netflix subscriptions (in millions) can be approximated by the function N(x)=24.9(1.736)^x, where x is the number of years after 2012. (Source: Statista.com) a. How many million international Netflix subscriptions were there in the year 2012? blank1 - Numeric Answer 24.9 You are correct million (Do not round answer.) b. Estimate the number of Netflix subscriptions in the year 2020.
According to the given function.
There were approximately 24.9 million international Netflix subscriptions in the year 2012.
There were approximately 167.7 million international Netflix subscriptions in the year 2020,
We have,
a.
Since the function N(x) gives the number of international Netflix subscriptions x years after 2012, to find the number of Netflix subscriptions in the year 2012,
We need to set x = 0.
So,
N(0) = 24.9(1.736)^0
= 24.9 million
b.
To estimate the number of Netflix subscriptions in the year 2020, we need to set x = 8 (since 2020 is 8 years after 2012).
N(8) = 24.9(1.736)^8
= 167.7 million
Thus,
According to the given function.
There were approximately 24.9 million international Netflix subscriptions in the year 2012.
There were approximately 167.7 million international Netflix subscriptions in the year 2020,
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Halle tres números enteros pares consecutivos que satisfacen el Teorema de Pitágoras
The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.
We have,
The Pythagorean Theorem in a right-angled triangle,
a² + b² = c²
To find three consecutive even integers that satisfy this theorem, we can start by assuming that one of the even integers is x.
Then, the next two consecutive even integers would be x+2 and x+4.
We can then use the Pythagorean Theorem to set up an equation and solve for x:
x² + (x+2)² = (x+4)²
Expanding and simplifying:
x² + x² + 4x + 4 = x² + 8x + 16
Simplifying further:
x² - 4x - 12 = 0
Now we can use the quadratic formula to solve for x:
x = [4 ± √(4² - 4(1)(-12))] / (2 x 1)
x = [4 ± √64] / 2
x = [4 ± 8] / 2
x = 6 or x = -2
Since we are looking for three consecutive even integers, we can discard the negative solution and choose x = 6.
This gives us the three consecutive even integers: 6, 8, and 10, which satisfy the Pythagorean Theorem:
6² + 8 = 10²
36 + 64 = 100
100 = 100
Thus,
The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.
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The complete question.
Find three consecutive even integers that satisfy the Pythagorean Theorem.
Jamal has 44 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 192 square meters. List each set of possible dimensions (length and width) of the field
The two sets of possible dimensions for the rectangular plot of land are:
11 m x 22 m
8 m x 28 m
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be A
Now , the length of the rectangle be L
Let the width of the rectangle be W
Let's assume that the length of the rectangular plot of land is L meters and the width is W meters. Since Jamal has only 44 meters of fencing available, the perimeter of the enclosure will be 44 meters:
Perimeter = 2L + W = 44
W = 44 - 2L
The area of the rectangular plot of land is given as 192 square meters
Area = L x W = L x (44 - 2L) = 192
2L² - 44L + 192 = 0
Solving for L using the quadratic formula, we get:
L = (44 ± √(44² - 4 x 2 x 192)) / (2 x 2)
L = (44 ± √(1600)) / 4
L = (44 ± 40) / 4
So, the possible values of L are 11 and 8
If L = 11, then W = 44 - 2L = 22, and the dimensions of the rectangular plot of land are 11 m x 22 m
If L = 8, then W = 44 - 2L = 28, and the dimensions of the rectangular plot of land are 8 m x 28 m
Hence , the two sets of possible dimensions for the rectangular plot of land are 11 m x 22 m and 8 m x 28 m
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Two similar octagons have areas of 4 ft2 and 16 ft2. Find their similarity ratio.
1:4
1:2
1:16
1:8
Answer: 1:4
Step-by-step explanation:
In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4
1. Sketch a graph of a system generated by a linear equation and a quadratic equation that has no solution. Explain how the possibility occurs.
2. Sketch a graph of a system generated by a linear equation and a quadratic equation that has exactly one solution. Explain how the possibility occurs.
3. Sketch a graph of a system generated by a linear equation and a quadratic equation that has exactly two solutions. Explain how the possibility occurs. (You do not need to write any equations.
Just provide a simple sketch and explanation please, no equations are necessary.
Answer:
Sure give me a sec
Step-by-step explanation:
1) A system of equations has no solution if the graphs of the equations do not intersect. 2) A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. 3) A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points.
Systems with no solution
A system of equations has no solution if the graphs of the equations do not intersect. This can happen if the graphs are parallel, or if one graph is completely contained within the other graph.
For example, the graph of a linear equation is a line, and the graph of a quadratic equation is a parabola. If the line and the parabola are parallel, then they will never intersect, and the system will have no solution.
Another way for a system to have no solution is if one graph is completely contained within the other graph. For example, the graph of the equation y = x is completely contained within the graph of the equation y = [tex]x^2[/tex]. This means that there are no points that satisfy both equations, and the system will have no solution.
Systems with exactly one solution
A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. This can happen if the graphs are intersecting lines, or if the graphs are intersecting parabolas.
For example, the graph of the equations y = x and y = [tex]x^2[/tex] intersect at exactly one point, which is the point (0,0). This is because the two graphs intersect when x = 0, and there is no other point where they intersect.
Systems with exactly two solutions
A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points. This can happen if the graphs are intersecting parabolas that have different slopes.
For example, the graph of the equations y = [tex]x^2[/tex] and y = 2[tex]x^2[/tex] intersect at exactly two points, which are the points (0,0) and (1,1). This is because the two graphs intersect when x = 0 and when x = 1, and there are no other points where they intersect.
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Please explain the answer and why for this question
Answer:
Figure A is greater.
Step-by-step explanation:
Figure A has 60 cubic units in volume, if you do length x width x height you get 60. And for figure B the volume is 40 because of again l x w x h.
Evaluate:
2-(16-14)² + (6-14)³ +8
Answer:
-506
Step-by-step explanation:
Answer:
-506
Step-by-step explanation:
2 - ([tex]2^{2}[/tex]) + [tex](-8)^{3}[/tex] + 8
2 - 4 -512 + 8
-2 - 512 + 8
-514 + 8
-506
Helping in the name of Jesus.
Will give Brainliest for right answer and extra points!!!!
New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma negative 200
Answer:
The amount of money the painter earns, in dollars, depends on the number of rooms he paints.
For each room painted, the painter charges $25. Therefore, the amount of money earned, y, is given by the equation:
y = 25x + 100
where x is the number of rooms painted and 100 is the cost of supplies.
To graph this equation, we can plot a point on the y-axis where x=0 (the fixed cost of supplies) at (0, 100), and then use the slope of 25 to find additional points. For example, when x=1, y=125; when x=2, y=150; and so on.
With this information, we can eliminate options (b) and (d) because they both show negative slopes, which would mean the painter loses money as he paints more rooms.
Option (c) shows a positive slope, but the line goes through the point (0,100) and (4,200), which means the painter earns $200 after painting 4 rooms, but this contradicts the given information that the painter charges $25 per room. Therefore, option (c) is also incorrect.
Option (a) correctly shows the slope of 25 and goes through the point (0, 100), and the line reaches the x-axis when x=4, indicating that the painter earns $0 after painting 4 rooms. This matches the given information that the painter charges $25 per room. Therefore, the correct answer is option (a).
Therefore, the graph that shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints is:
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0
Answer:
The correct answer is a C. coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.
The painter pays $100 for supplies, so he will only earn money for the rooms he paints after he has recouped that cost. The first room he paints will earn him $25, the second will earn him $50, and so on. After he has painted 4 rooms, he will have earned $200.
The graph of this relationship would be a line that starts at the point (0, 100) and goes up to the point (4, 200).
Step-by-step explanation:
z varies directly as x^2. When z = 96 when x = 4, find z when x = 3
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"z" varies directly with }x^2}{z = k(x^2)}\hspace{5em}\textit{we also know that} \begin{cases} z=96\\ x=4 \end{cases} \\\\\\ 96=k(4^2)\implies \cfrac{96}{4^2}=k\implies 6=k\hspace{8em}\boxed{z=6x^2} \\\\\\ \textit{when x = 3, what's "z"?}\qquad z=6(3^2)\implies z=54[/tex]
Help its due today and I'm stuck on this question
Convert 75 gram per cm 3 to pounds per cubic inch (round to nearest tenth) [ 1 pound = 0.4536 kg] [ 1 cm = 0.3937 in] [ 1 kg = 1000g] (Show your work)
2.07 pounds/in 3
1.7 pounds/in 3
2.7 pounds/in 3
3.2 pounds/in 3
Answer:
It’s 2.07 pounds/in 3
Step-by-step explanation:
1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces
this data shows the amount of rainfall in mm that fell on an island during a 12-day period in June
a. work out the range of the rainfall and comment on this value as a measure of the spread of the data
The calculated range of the amount of rainfall in mm is 20.5 mm
Working out the range of the rainfallFrom the question, we have the following parameters that can be used in our computation:
Data values in mm
0.0, 12.2, 2.1, 0.0, 20.5, 5.5 and 1.0
The range of the rainfall is the difference between the least and the highest amount of rainfalls
Using the above as a guide, we have the following:
Range = 20.5 - 0.00
Evaluate
Range = 20.5
Hence, the range of rainfall is 20.5 mm
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Calculate the arc length of the
sector.
147°
7 mm
Give your answer correct to 1
decimal place.
Answer:
Arc length = (147/360) x (2π x 7)
Arc length = (0.40833) x (2 x 3.14159 x 7)
Arc length = 0.40833 x 43.9823
Arc length = 17.9955
What is the sum of the interior angle
measures of a regular hexagon? Show
or explain how you can use the sum
of the interior angles of a triangle to
determine the answer.
Answer:
The sum of the interior angle measures of a regular hexagon is 720°.
Step-by-step explanation:
To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:
Sum of interior angles = (n - 2) × 180°
In the case of a hexagon, n = 6. So, we can plug this value into the formula:
Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:
Sum of interior angles of hexagon = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
Please answer the question
Answer:
The height of the desk is 8 cubic inches.
Hope this helps!
Step-by-step explanation:
The formula for the volume of a rectangular prism is Width × Length × Height or Base × Height.
Because the Base is already given ( 400 in² ), that means the height of the desk can be found by dividing 3200 by 400.
3200 ÷ 400 = 8
The height of the desk will be 8 cubic inches.
The parallelogram is reflected across the line y = x. Which of the following are coordinates of a vertex of the image?
D'(1, 3)
B'(-3, -4)
A'(1, -5)
C'(-1, -2)
The coordinates of a vertex of the image of D are (3, 1)
Which are coordinates of a vertex of the image?From the question, we have the following parameters that can be used in our computation:
The coordinates of point D is
D = (1, 3)
The transformation rule is given as
y = x
Mathematically, this is represented as
(x, y) = (y, x)
Substitute the known values in the above equation, so, we have the following representation
D' = (3, 1)
Hence, the image of point D is D' = (3, 1)
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Your goal is to create a college fund for your child. Suppose you find a fund that the fees an APR of 4% . How much should you deposit monthly to accumulate $80,000 in 17 years?
Please answer this Calculus webwork question about differential equations:
Answer:
1.
[tex]p(t) = 2000({2}^{ \frac{t}{4} }) [/tex]
2.
[tex]p(8) = 2000( {2}^{ \frac{8}{4} } ) = 2000( {2}^{2} ) = 2000(4) = 8000[/tex]
3. p'(t) = 2,000(1/4)(2^(t/4))(ln 2)
= (500 ln 2)(2^(t/4))
p'(t) = 2,000 ln 2 cells/hour
= about 1,386 cells/hour
What are the values of a and B
Answer:
a = 48
b = 28
Step-by-step explanation:
b = 0.5 × 56
b = 28
52 = 0.5 × (56 + a)
104 = 56 + a
a = 48
If is invested $9000 in an account earning 7.5% interest compounded continuously, determine how long it will take the money to triple. Round up to the nearest year.
The time to take the money to triple is, 15.2 years
We have to given that;
It is invested $9000 in an account earning 7.5% interest compounded continuously.
Hence, We can formulate;
27,000 = 9000 (1 + 7.5/100)ⁿ
3 = (1 + 0.075)ⁿ
3 = (1.075)ⁿ
log 3 = n log (1.075)
0.477 = n x 0.0314
n = 0.477 / 0.0314
n = 15.2 years
Thus, The time to take the money to triple is, 15.2 years
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Please help answer this question!!!
The solution is the area of triangle ABC is 9.56 square units .
Given:
The objective is to find the area of triangle ABC
Explanation:
The general formula to find the area of a triangle is,
A = 1/2 *b*h
To find the area of triangle ABC:
The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.
DC = √ 9 - 6.25
=1.65
On plugging the given values in equation
Thus, the height of triangle ABC is 2.5
So the base of the triangle CB = 6 + 1.65 = 7.65.
Now, substitute the obtained values in equation
area = 1/2 * 7.65 * 2.5
= 9.56
Hence, the area of triangle ABC is 9.56 square units .
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Use the form |x – b | ≤ c or |x – b | ≥ c to write an absolute value
inequality that has the solution set x ≤ –9 or x ≥ –5.
The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is
|x + 7| ≤ 2
We have,
To write an absolute value inequality with a solution set x ≤ –9 or x ≥ –5, we first need to find the midpoint of the two given values:
Midpoint of –9 and –5
= (-9 + (-5)) / 2
= -7
We can now use the midpoint and one of the given values to write the absolute value inequality.
Since the solution set includes both values, we need to use the form
|x – b | ≤ c.
We can choose to use either value, let's use x ≤ –9:
|x – (-7)| ≤ |-9 – (-7)|
|x + 7| ≤ 2
Therefore,
The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is
|x + 7| ≤ 2
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A composite figure is composed of a semicircle whose radius measures 5 inches added to a square whose side measures 10 inches.
A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.
How to calculate the probability of a selected point in the composite figure?To calculate the probability of a selected point, the formula for probability should be chosen. That is;
Probably = possible outcome/sample space
Possible outcome is the area of the semicircle = πr²/2
where r = 5 in
Area of semicircle = 3.14×5×5/2
=78.5/2 = 39.25 in²
The sample space = area of semicircle+area of square.
But Area of the square;
= length×width
= 10×10 = 100in²
sample space = 100+39.25 =139.25
Probability = 39.25/139.25 = 0.28
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∫1/^2+4+25 by partial of integration
The integral of 1/(2+4x²+25x²) using partial integration is (1/2) arctan(10x) + C, where C is the constant of integration.
To solve this integral, we will use the technique of partial integration. This technique is also known as integration by parts and is used to find the integral of a product of two functions. The formula for integration by parts is as follows:
∫u dv = uv - ∫v du
where u and v are functions, and du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.
Let's apply this formula to our integral:
∫1/(2+4x²+25x²) dx
We need to choose two functions, u and dv, such that when we differentiate u, we get a simpler function, and when we integrate dv, we get a simpler function. In this case, we can choose:
u = 1, and dv = 1/(2+4x²+25x²) dx
Now, let's find du/dx and v:
du/dx = 0 (since u is a constant)
To find v, we need to integrate dv. We can use the substitution method to evaluate the integral:
Let u = 5x
du/dx = 5
dv = 1/(2+4x²+25x²) dx
Substituting u and dv:
v = ∫ dv/dx du = ∫1/(2+4u²) du
v = (1/2) arctan(2u)
v = (1/2) arctan(2(5x))
v = (1/2) arctan(10x)
Now, we can apply the formula for integration by parts:
∫1/(2+4x²+25x²) dx = uv - ∫vdu
∫1/(2+4x²+25x²) dx = (1) x (1/2) arctan(10x) - ∫(1/2) arctan(10x) x 0 dx
∫1/(2+4x²+25x²) dx = (1/2) arctan(10x) + C
where C is the constant of integration.
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A recent market survey indicated that 37% of the citizens in town would support a new coffee shop. The survey has a margin of error of
1.7%, and the population of the town is 36,170. Based on the survey, which statement about the number of people who would support for
a new coffee shop is true?
Based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.
The margin of error is a measure of the uncertainty in the survey results. It is based on the sample size and the level of confidence desired. In this case, the margin of error is 1.7%.
This means that the actual percentage of citizens in the town who would support a new coffee shop could be as much as 1.7% higher or lower than the survey result of 37%.
To calculate the range of possible values for the percentage of citizens who would support a new coffee shop, we add and subtract the margin of error from the survey result:
37% + 1.7% = 38.7%
37% - 1.7% = 35.3%
Therefore, based on the survey, we can say that between 35.3% and 38.7% of the citizens in the town would support a new coffee shop.
To determine the number of people who would support a new coffee shop, we need to multiply the percentage by the population of the town:
35.3% of 36,170 = 12,776
38.7% of 36,170 = 14,000
Therefore, based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.
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Someone help me with this!!!!.... Given f(x)=x^2−3x−4
and g(x)=|x+3|−2, which value is a solution to the equation f(x)=g(x) ?
A
−4
B
−3
C
−1
D
4
Answer:
C -1
Step-by-step explanation:
in such a case the simplest way is to simply try the 4 numbers and see :
x² - 3x - 4 = |x + 3| - 2
x² - 3x - 2 = |x + 3|
A x = -4
(-4)² - 3×-4 - 2 = |-4 + 3|
16 + 12 - 2 = 1
26 = 1
wrong.
B x = -3
(-3)² - 3×-3 - 2 = |-3 + 3|
9 + 9 - 2 = 0
16 = 0
wrong.
C x = -1
(-1)² - 3×-1 - 2 = |-1 + 3|
1 + 3 - 2 = 2
2 = 2
correct.
D x = 4
4² - 3×4 - 2 = |4 + 3|
16 - 12 - 2 = 7
2 = 7
wrong.
18 divided by 5.5
PLEASE ANSWER FULL INSTRUCTIONS
Answer:
Step-by-step explanation:
To divide 18 by 5.5, we can use long division method as follows:
_________
5.5 | 18.0000
-16.5
------
1.5
We first divide 5.5 into the first digit of 18, which is 1. This gives us 0 as the whole number part of the quotient. We then multiply 0 by 5.5 to get 0, and subtract it from 1, which gives us 1.
We then bring down the next digit 0 and get 10. We then divide 5.5 into 15, which gives us 2 as the whole number part of the quotient. We then multiply 2 by 5.5 to get 11, and subtract it from 15, which gives us 4.
We then bring down the next digit 0 and get 40. We then divide 5.5 into 40, which gives us 7 as the whole number part of the quotient. We then multiply 7 by 5.5 to get 38.5, and subtract it from 40, which gives us 1.5.
Since there are no more digits to bring down and the remainder is less than the divisor 5.5, we can stop here. Therefore, the result of 18 divided by 5.5 is approximately 3.27, which we get from the quotient of 0.327 rounded to two decimal places.
So 18 divided by 5.5 is approximately 3.27 or 3.27 to two decimal places.
Answer:
3.27 to 2dp
Step-by-step explanation:
18÷5.5
18/1×11/2