It looks like you're asking to solve for the coefficients [tex]a,b,c[/tex] such that
[tex]2x^2 - 5 = a(x+2)^2 - b(x+1) + c[/tex]
Expanding the right side gives
[tex]2x^2 - 5 = ax^2 + 4ax + 4a - bx - b + c[/tex]
[tex]2x^2 - 5 = ax^2 + (4a - b)x + (4a - b + c)[/tex]
The coefficients on both sides must be equal, so
[tex]\begin{cases}a = 2 \\ 4a-b = 0 \\ 4a - b + c = -5\end{cases}[/tex]
Solving the system yields [tex]\boxed{a=2 \implies b = 8 \implies c = -5}[/tex].
Which of the following is the graph of y= e^x + 1?
Answer + Step-by-step explanation:
y= e^x + 1
+ 1 will shift the graph up 1In the natural exponential function, eˣ = e power x, we employ e. In the eˣ function, the tangent line's slope to any point on the graph is equal to that point's y-coordinate. The sequence we employ to calculate the value of e is (1 + 1/n)Learn more about Natural Exponential Functions here: https://brainly.com/question/1979778
Determine the number of zeros of the polynomial function. f(x) = x^3 + 7x^2 + 2
Answer:
3
Step-by-step explanation:
The fundamental theorem of algebra tells you the number of zeros is equal to the degree of the polynomial.
__
applicationThe given degree-3 polynomial has 3 zeros.
__
Additional comment
Descarte's rule of signs tells you the absence of sign changes among the coefficients means that there are no positive real roots. Changing the sign of the one odd-degree term gives one sign change, so there is one negative real root. The other two zeros are complex.
one negative real zero, and two complex zeros
A graph confirms that the only real zero is negative and irrational, about -7.04.
Math Topic: Sum, Difference, and Product of two functions
Help with this!
The expression are; [tex](h - g) (x) = 3x^{3} -x^{2}[/tex], [tex](h + g) (x) = 3x^{3} +x^{2}[/tex] , [tex](h.g) (-1) = -3[/tex].
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given function;
g(x) = [tex]x^{2}[/tex]
h(x) = [tex]3x^{3}[/tex]
The expression;
[tex](h - g) (x) = 3x^{3} -x^{2}[/tex]
[tex](h + g) (x) = 3x^{3} +x^{2}[/tex]
[tex](h.g) (-1) = x^{2} .3x^{3} \\\\(h.g) (-1) = 3x^5\\\\(h.g) (-1) = 3(-1)^5\\\\(h.g) (-1) = -3[/tex]
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Item 2
A container holds 54.6 gallons of liquid. The container leaks 8.4 gallons per hour.
How many hours will it take for the container to empty?
Enter your answer as a decimal in the box.
Answer:
54.6 ÷ 8.4 = 6.5 hours
6 hours, 30 minutes:)
The formula M = 5/8 K gives the approximate distance in miles as a function of kilometers. Use the inverse to express 25 miles in kilometers.
The table below shows the participation in the town soccer league during its first five seasons.
Town Recreational Soccer League Participation
Number of participants
88
95
100
108
115
Year
1
2
23
3
4
fo
5
Which is the equation of the trend line that can be generated by using the data from years 1 and 5?
Oy-6.75x-688.25
Oy-6.75x-1.75
O y-6.75x+81.25
Oy-6.75x+148.75
Using a calculator, the equation of the trend line that can be generated by using the data from years 1 and 5 is:
y = 6.75x + 81.25.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points, in the format (x,y), are given as follows:
(1,88), (2,95), (3,100), (4,108), (5,115).
Hence, using a calculator, the regression line is:
y = 6.75x + 81.25.
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8 cm
6 cm
2 cm
Find the surface area of the rectangular prism.
Surface Area = [?]cm²
Answer:
152cm²
Step-by-step explanation:
math and stuff and things
curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm
The area of wafer required to make the ice cream cone 68.75 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
Given:
r= 2cm, l=9 cm
Surface area,
=πr(l +r)
=3.14*2(9 + 2)
= 6.25*11
=68.75 cm²
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The line whose equation is y=4x+2 has a y-intercept with coordinates
Answer: 2xy
Step-by-step explanation: 2xy is the answer bra
Given 2 (x+3) - 4x = x
Prove = 2
Complete the proof. Provide reasons for 1-6 below.
step-by-step explanation:
#1: simplify both sides of the equation.
2(x+3)−4x=x
(2)(x)+(2)(3)+−4x=x
2x+6+−4x=x
(2x+−4x)+(6)=x
−2x+6=x
−2x+6=x
***
#2: subtract x from both sides.
−2x+6−x=x−x
−3x+6=0
***
#3: subtract 6 from both sides.
−3x+6−6=0−6
−3x=−6
***
step 4: divide both sides by -3.
−3x/-3 = -6/-3
solution x = 2
ƒ(x) = x² - x - 1
What is the average rate of change of f over
the interval -1 ≤ x ≤ 1?
Answer: -1
Step-by-step explanation:
[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]
Please someone help me with steps!
Answer:
96
Step-by-step explanation:
The formula for average = [tex]\frac{Sum \hspace{0.15cm} of\hspace{0.15cm} Items}{No.\hspace{0.15cm} of \hspace{0.15cm} Items}[/tex]
After taking 3 tests, the average is 88.
∴ 88 = Sum of Items / 3
Sum of Items = 88 x 3
= 264
This means Lenny's total score after 3 tests is 264.
We now have to calculate how many marks needs to be added to 264 so that after four tests, the average is 90.
Now the number of items (tests) = 4, and average = 90.
Let the marks required in 4th test = [tex]x[/tex]
∴ [tex]\frac{264 + x}{4} = 90[/tex]
264 + [tex]x[/tex] = 360
[tex]x[/tex] = 360 - 264
= 96
Which function is represented by this graph? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through (negative 6, 10), (0, 4), (4, 0) to (7, negative 3), and then it rises through (10, 0). A. f(x) = |x + 7| − 3 B. f(x) = |x − 7| − 3 C. f(x) = |x + 3| − 7 D. f(x) = |x − 3| − 7
The line that represents the graph satisfying all condition is f(x) = |x − 7| − 3.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the points are given.
We have to find which equation satisfies all the points.
f(x) = |x − 7| − 3
put x= -6
y= 13-3 = 10
Similarly by putting all the values the only condition that satisfies is
f(x) = |x − 7| − 3
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The driving distance from Seattle to Portland is 175 miles. Your car gets 25 miles per gallon. If gasoline is $2.80 per gallon, how much will the round trip from Seattle to Portland and back cost in dollars?
Answer:
$980
Step-by-step explanation:
Given the cost of gasoline = $2.80/mile
Total Distance = 175miles x 2 (Back and forth)
= 350 miles
Total Cost = Cost of gasoline x Total Distance =
= $2.80 x 350
= $980
The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The driving distance from Seattle to Portland is 175 miles.
Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Now,
Since, The driving distance from Seattle to Portland is 175 miles.
Hence, The total distance from Seattle to Portland and back = 175 + 175
= 350 miles
And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Hence, The cost of gallon = 350/25 x $2.50
= 100 x $2.50
= $250
Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
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Q5
The following are data from an independent measures experiment comparing
two treatment conditions:
Treatment 1
n=8
M = 8
SS=104
Treatment
n=8
M = 14
SS = 120
a. Do these data indicate a significant difference between the two
treatments?
b. Compute r2 and interpret the size of the treatment effect.
Answer:
A 2kg block is moved a long a level floor by a horizontal force of 20N if the coefficient of sliding friction is 0.4
what is the acceleration of the blove
if the length of a side of a square is x CM its perimeter is
Square perimeter =4x cm.
The complete length that a square's edge encompasses is referred to as its perimeter. Any enclosed geometric shape's perimeter may be computed by measuring the space around it.
By calculating the total of all the sides of a square, the perimeter may be determined. The perimeter of a square will be stated as,
The perimeter of square = s + s + s + s
⇒Perimeter of square = 4s, where "s" is the side length of the square.
This is because all edges of a square are equal and each edge measures "s" units.
Calculating the perimeter of a square:Mathematically, the formula for calculating a square's perimeter is: Square perimeter, (P) = 4 Side
⇒P= 4x cm
It is concluded that the solution is 4x cm.
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X^2=50 where x is a real number
The value of x in the given expression x² = 50 is 5√2
Data obtained from the questionx² = 50Value of x =?How to determine the value of xx² = 50
Thake the square root of both sides
x = √50
Recall
√50 = √(25 × 2) = 5√2
Thus,
x = √50
x = 5√2
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Solve the equation -8 = -3 - 6 cube root x^2
a. 0.76, -0.76
b. 4.98
c. 3.87
d. 1.53, -1.53
Answer:
0.76
Step-by-step explanation:
-8+3=-6x^(2/3)
-5=-6 x^(2/3)
-5/-6=x^(2/3)
(2/3)√{5/6}=x
0.76=x
x=0.76
Consider the matrix [tex]A_{4x4}, det(A) = -2[/tex]
Show that the following is true or false:
[tex]det(adj(2A^{-1}) =-2^{9}[/tex]
We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible choices, one of which is correct. Let X=X=X, equal the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:
n = 4, p = 1/5 = 0.2.
The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096[/tex]
0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
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A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. The following display shows what their favorite color patterns were.
The counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. What is the
missing value in the table?
NEN
OA. 12
OB. 10
O C. 11
D. 13
Color Pattern
Blue on gray
Green
Pink polka dots
Purple
Red and orange
stripes
Yellow
Frequency
6
7
8
7
3
The missing value in the table is 12 , Option A is the correct answer.
What is a Graph ?A graph is a mathematical representation of the data available , It makes the study of the data over a wide period easier.
It is given in the question that there are 40 students and the frequency they select for each pattern is mentioned as number , which can be seen in the image attached with the answer.
It has been asked to determine the missing value in the frequency table corresponding to the pink Polka dots
The other number in the frequency table is 4, 6 ,8 ,7, 3
Total students are 40
Therefore the value corresponding to the pink polka dot is given by
40 - ( 4+6+7+8 +3)
= 12
Therefore The missing value in the table is 12 , Option A is the correct answer.
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Triangle A B C is shown as the path of a ferry. Side A B is 3.5 miles long. The ferry turns 75 degrees to side B C. Side B C is 6 miles long. Side C A has an unknown length d.
A ferry transports passengers to three different ports. From port A, the ferry travels east 3.5 miles to port B. The ship then turns 75° south and travels for 6 miles to reach port C. What is the distance d from port C to port A? Approximate to the nearest tenth of a mile.
miles
The length of C from A is 3.5 miles if AB=3.5 miles and BC is 6 miles .
Given The length of triangle ABC AB=3.5 miles , BC=6miles and AC=d
We have to find the value of d
First of all we have to draw a perpendicular from point A on side BC .
It forms two triangles ABE and AEC if E is the point where perpendicular stands on BC.
In triangle BEA
AE=[tex]\sqrt{3.5^{2} -3^{2} }[/tex]
=[tex]\sqrt{12.25-9}[/tex]
=[tex]\sqrt{3.25}[/tex]
=1.8
Now in triangle AEC
AC=[tex]\sqrt{1.8^{2} +3^{2} }[/tex]
=[tex]\sqrt{3.24+9}[/tex]
=[tex]\sqrt{12.24}[/tex]
=[tex]\sqrt{12.24}[/tex]
=3.49 MILES
By rounding off to the nearest tenth we will get 3.4 miles
Hence the value of d is 3.4 miles.
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Answer:its 7.7
Step-by-step explanation: i did it on edge
definition of Identity property, Association property and communicative property please answer!
Answer:
09
Step-by-step explanation:
07
2 ft
4.5 ft
6 ft
A) 38 cubic feet
B) 54 cubic feet
C)
66 cubic feet
D) 125 cubic feet
What is the volume?
Answer:
B
Step-by-step explanation:We know Volume = (a*b*c)
Answer:
B) 54 cubic feet
Step-by-step explanation:
3
O Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of π.
4cm
4cm
4cm
The diagram is not drawn to scale.
Answer:
12pi cm
Step-by-step explanation:
The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.
Thus, the Perimeter of the full shape can be written as an equation:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.
Parts of a circle
Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).
Let's call the diameters of each of our curves "[tex]d_{big}[/tex]" "[tex]d_1[/tex]" "[tex]d_2[/tex]" "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.
Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.
So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]
Substituting back into the main equation above:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]
Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]
Substituting and simplifying (in terms of pi):
[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]
Additional Understanding
Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]
[tex]P_{overall}=\pi d_{big}[/tex]
Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.
So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.
The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.
can someone help me
Answer:
See Pictures
Step-by-step explanation:
Which information could he have used to determine this?
O GLH = ILM
O m KLM = 5m ILMO
O m GLI = 2m GLH
O m GLI = 1/2m GLH + 1/2m HLI
Answer:
m∠GLI = 2m∠GLH
Step-by-step explanation:
Angle GLI (red) is made of angles GLH (purple) and HLI (green).
m∠GLI = m∠GLH + m∠HLI
First option: ∠GLH ≅ ∠ILM (Angle GLH is congruent to angle ILM.)
This doesn't tell us anything about the relationship between angles GLI, GLH and HLI. So it can't be used.
Second option: m∠KLM = 5m∠ILM (Measure of angle KLM is 5 times the measure of angle ILM.)
This also cannot be used, because it doesn't include angles GLI, GLH or HLI.
Third option: m∠GLI = 2m∠GLH (Measure of angle GLI is two times the measure of angle GLH.)
Now this option is more interesting. It includes two angles of three that we are interested in.
If angle GLI is two times angle GLH, then that means that angle GLH is congruent to angle HLI!
Let's prove this with equations.
1) m∠GLI = m∠GLH + m∠HLI (from picture)
2) m∠GLI = 2m∠GLH (from third option)
Substitute m∠GLI in first equation with m∠GLI in second.
m∠GLI = m∠GLH + m∠HLI
2m∠GLH = m∠GLH + m∠HLI
m∠GLH = m∠HLI
So this proves that the angles GLH and HLI have the same measure, therefore ray LH is bisector of GLI.
Fourth option: m∠GLI = 1/2m∠GLH + 1/2m∠HLI
There are all angles we are interested in, but there is a mistake. We can see in the picture that angle GLI is made of angle GLH and HLI and not of half of them. This just is not true. The correct equation would be m∠GLI = m∠GLH + m∠HLI.
Please solve these questions with an explanation
Answer:
Step-by-step explanation:
If the sides of a square measure 9sqrt3 units, then find the length of the fishbowl.
The length of the diagonal of the square is 22.05 units
How to find the diagonal of a square?A square have all its sides equal to each other.
Therefore, using Pythagoras theorem,
c² = a² + b²
c² = (9√3)² + (9√3)²
c² = 81 × 3 + 81 × 3
c² = 243 + 243
c² = 486
square root both sides
c = √486
c = 22.045407685
c = 22.05 units
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A new element with atomic number 116 was discovered in 2000. In 2012 it was named livermorium, Lv. Although Lv is radioactive and short-lived, its chemical properties and reactivity should follow periodic trends.
a. Determine the electron configuration for the valence electrons of Lv in the ground state. (2 pts)
Answer:
7s²7p⁴
Step-by-step explanation:
Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.
Let's check
116 is the atomic noElectronic configuration
1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶4f¹⁴6s²5d¹⁰6p⁶7s²5f¹⁴6d¹⁰7p⁴Valence electrons
7s²7p⁴