ANSWERS
1. Domain: all real values
2. Zeros: 0 (with multiplicity 2) and 3
3. Not periodic. Symmetric about the point (1, 2)
4. Positive for x < 3; negative for x > 3
5. f → ∞ as x → -∞; f → -∞ as x → ∞
6. none
EXPLANATION
1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.
2. To find the zeros of the function, we have to solve,
[tex]-x^3+3x^2=0[/tex]First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,
[tex]\begin{gathered} -x^2\left(\frac{-x^3}{-x^2}+\frac{3x^2}{-x^2}\right)=0 \\ \\ -x^2(x^{3-2}-3x^{2-2})=0 \end{gathered}[/tex]So, we have,
[tex]-x^2(x-3)=0[/tex]In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.
Hence, the zeros are 0 and 3. 0 has multiplicity 2.
3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).
4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,
[tex]with\text{ }x=-1:\text{ }y=-(-1)^3+3(-1)^2=-(-1)+3\cdot1=1+3=4[/tex]For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.
Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.
Hence, is the function is positive for x < 3 and negative for x > 3.
5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.
Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.
6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.
Write the equation in slope intercept form:2x+y=2
Answer:
y = - 2x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + y = 2 ( subtract 2x from both sides )
y = - 2x + 2 ← in slope- intercept form
1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer.
NEED HELP ASAP WILL GIVE BRAINLIST TO BEST AWNSER
Answer:
3.456 × 10^11
Step-by-step explanation:
= 3.456 × 10^11
scientific notation
= 3.456e11
scientific e notation
= 345.6 × 10^9
engineering notation
billion; prefix giga- (G)
= 3.456 × 10^11
standard form
11
Order of Magnitude
for scientific and standard forms
= 345600000000
(real number)
= three hundred forty-five billion six hundred million
word form
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given a circle with a diameter of eight what is the circumference?
Answer:
D
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( d is the diameter ) , then
C = π × 8 = 8π
Answer: C=2pir or diameter(pi)
Step-by-step explanation:
The diameter of a circle stretches from one side to the other, the Radius (r) goes from the center to the side meaning it is twice the diameter.
To solve this just half the diameter and insert it into the first equation or just plug it in for diameter.
The answer is
D. 8pi
y = 2x - 4 what is the slope
Remember that the slope-intercept equation of the line is:
[tex]y=mx+b[/tex]where 'm' is the slope and b is the y-intercept.
In this case, we have the following:
[tex]y=2x-4[/tex]therefore,, the slope is m = 2
Find the measure of angle b
Answer: B=30
Step-by-step explanation:
because of corresponding angles
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If the diameter of a circle is 20 , what is the area ?
the diameter of a circle is 20
The radius of circle is the half of the diameter of the circle :
Radius = Diamter/2
In the given question , we have Diameter = 20
So,
Radius = 20/2
Radius = 10
The expression for the radius 'r' of the circle is express as :
[tex]\text{ Area of Circle =}\Pi(radius)^2[/tex]Substitute the value of Radius r = 10 in the expression of the area of circle:
[tex]\begin{gathered} \text{ Area of Circle =}\Pi(radius)^2 \\ \text{ Area of Circle =}\Pi(10)^2 \\ \text{ Area of Circle =}3.14\times10\times10 \\ \text{ Area of Circle =}3.14\times100 \\ \text{ Area of Circle =}314 \end{gathered}[/tex]Area of the circle is 314
Answer : 314 unit square.
Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
Find the slope answer fast
Answer:
y=65/100x+2.5
Step-by-step explanation:
Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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O is the center of the regular decagon below. Find its perimeter. Round to the nearest
tenth if necessary.
16
Answer:
Step-by-step explanation:
The perimeter of the given polygon rounded to the nearest tenth is; 24.7
What is the perimeter of the Polygon?
The given polygon as we can see has 10 sides.
Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.
Thus, the other two angles will be; (180 - 36)/2 = 72° each
Using sine rule, we can find the length of a side of the polygon as;
x/sin 36 = 4/sin 72
x = (4 * sin 36)/sin 72
x = 2.472
Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7
matthew is thinking about applying for a credit card with a low interest rate. the loan application asks how much he owes on his mortgage and on his existing credit cards matthew used his calculator to figure out these two numbers and they are 2.4e5 and 1.25e4. how much money does matthew owe?(a) $232,500(b) $240,000(c) $252,500(d) $265,000
so:
[tex]240000+12500=252000[/tex]Answer:
(c) $252,500
the temperature at sunrise is 48°F . each hour the temperature rises 6°F write an equation that models the temperature y in degrees Fahrenheit after x hours. what is the graph of the equation.
EXPLANATION
Let's see the facts:
Temperature at sunrise = 48 °F
Rate = 6°F/h
The equation is given by the following expression:
Let's call "x" to the number of hours elapsed
y = 48 + 6x
The graph is given by the following representation:
Which rule explains why these triangles are congruent?
Answer:
SAS Congruence Rule
A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.
Answer: SAS (side side angle postulate.)
Step-by-step explanation:
can be used to prove triangles congruent.
sides and the corresponding angle of the other, then the triangles are congruent.
Can someone please answer this!
Considering the situation described, it is found that:
a) The numeric values of the piecewise function are as follows:
W(30) = $300.W(40) = $400.W(47) = $505.W(52) = $580.b) The new piece-wise function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38.c) The new piece-wise function is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the rule is one for times up to 40 hours, and another for times greater than 40 hours, hence the numeric values are given as follows:
W(30) = 10 x 30 = $300.W(40) = 10 x 40 = $400.W(47) = 15 x (47 - 40) + 400 = $505.W(52) = 15 x (52 - 40) + 400 = $580.For item b, the new reference is of 38 hours, hence the function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38. (the earnings for the first 38 hours are of 38 x 10 = $380).For item c, the new hourly wage is of 12 hours, hence the rule is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. (pay and half = 12 x 1.5 = 18, wage for the first 40 hours of 40 x 12 = 480).More can be learned about piecewise functions at brainly.com/question/19358926
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I haven’t came across one of these questions so not sure how to solve
m∠F = 140º
1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:
[tex]\begin{gathered} S_i=180(n-2) \\ S_i=180(4-2) \\ S_i=180(2) \\ S_i=360 \end{gathered}[/tex]Note that "n" refers to the number of sides:
Notice also that angle H is a right angle since this is not an Isosceles Trapezoid
So we can write out the following
9x +14x +4x + 90 = 360º
27x = 360 -90
27x = 270
x =10
Alternatively, angles between parallel lines are supplementary
2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:
m∠F = 14x
m∠F = 140º
6. The quadratic functions f(x) =-x+2x+6 and g(x)= x’ +2x are shown graphed below. The positivesolution to f(x)=g(x) is closest to which of the following?Y(1) x=6.5(3) x=1.7(2) x = 3.7(4) x=0.5
Notice that the intersection between both functions on the positive values of x is near the line x=2. From the provided options, the closest to that value is 1.7
Then, the positive solution to f(x)=g(x) is closest to:
[tex]x=1.7[/tex]4. 3. The price of a computer is $699.00. The sales tax rate is 8%. What is the 10 points
sales tax on this computer in dollars and cents?
Mark only one oval.
0000
$55.92
$754.92
$5,592.00
$5.59
Answer:
$754.92
Step-by-step explanation:
699.00 plus 8% of 699.00 is 754.92
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2.
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
The equation of the line in standard form is -1/2x + y = 1 or y = 1/2x + 1 in slope-intercept form.
(note: none of the option given is correct).
What is the Equation of a Line?In standard form, the equation of a line can be expressed as Ax + By = C, where x and y are coordinate of a point on the line, A, B, and C are integers.
This equation can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope.
Given:
Slope (m) = 1/2Point (x, y) = (4, 3)Substitute m = 1/2, x = 4, and y = 3 into y = mx + b to find b:
3 = 1/2(4) + b
3 = 2 + b
3 - 2 = b
1 = b
b = 1
Write the equation by substituting b = 1 and m = 1/2 into y = mx + b:
y = 1/2x + 1
Rewrite in standard form
- 1/2x + y = 1
Thus, none of the options is correct, The equation is: y = 1/2x + 1 in slope-intercept form or - 1/2x + y = 1 in standard form.
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Negative t divide by four equal’s negative three pie?
Answer:
Step-by-step explanation:
yes it does
Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
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Isaiah's school is having a spring carnival. When Isaiah carries a bin of water balloons outside for the balloon toss, he trips and breaks 12 balloons. He counts the remaining water balloons, and there are 14 left. Which equation can you use to find the number of water balloons w in the bin before Isaiah trips?
Solve this equation for w to find the number of water balloons in the bin. Water balloons
Equation: w - 12 = 14
Answer: 26
Step-by-step explanation:
Lost 12, left with 14.
Let W be water balloons before the trip.
w - 12 = 14
14 + 12 = 26
Proof:
26 - 12 = 14
The sizes of two matrices A and B are given. Find the sizes of the product AB and BA, whenever these products exist.A=3*2, B=2*3
Let's begin by identifying key information given to us:
A is a 3 x 2 matrix
B is a 2 x 3 matrix
AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix
Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist
Determine the distance between the points (−4, −7) and (−8, −13).
Answer:
2[tex]\sqrt{23}[/tex]
Step-by-step explanation:
The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.
To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:
[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:
x1 = -4, y1 = -7 (coordinates of the first point)
x2 = -8, y2 = -13 (coordinates of the second point)
Now, we substitute these values into the distance formula:
[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.
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Find the slope between these two points:
(3, 0), (-11, -15)
Answer:
3/4 or 0.75
Step-by-step explanation:
aMathWhich of the following shows the solution and graph to the inequality2x + 1 s 15?
Answer:
[tex]\text{ Option }\Rightarrow\text{ D}[/tex]Explanation: We need to find the answer to the inequality
[tex]2x+1\leq15[/tex]Solution:
[tex]\begin{gathered} 2x+1\leq15 \\ 2x\leq15-1 \\ \therefore\Rightarrow \\ 2x\leq14\rightarrow2x\leq\frac{14}{2} \\ x\leq7 \end{gathered}[/tex]Graph:
The solution as found through solving inequality and demonstrated in the graph is
[tex]\text{ is Option D}[/tex]What is the value of x?
40
20
12
At
P60°
8x-4
a
b
Answer:
8x - 4 = 60 (alternate angles, parallel lines a and b)
8x = 64
x = 8
1x + 2y = 7 and y = -2x + 3
Answer:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
Solve the system of equations:
1x + 2y = 7
y = –2x + 3
Substitute y = –2x + 3 for y in the first equation:
1x + 2y = 7
1x + 2(–2x + 3) = 7
Substract 6 from both sides:
–3x + 6 = 7
–3x + 6 – 6 = 7 – 6
–3x = 1
Divide:
–3x/–3 = 1/–3
x = –1/3
Substitute –1/3 for x in the second equation:
y = –2x + 3
y = –2(–1/3) + 3
y = 11/3
Solution:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
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what 15/60 as a decimal?
Answer:
0.25 (1/4 as a fraction)
Step-by-step explanation:
what 15/60 as a decimal?
Fraction is a division, 15/60 is the same as 15 : 60so
15 : 60 =
0.25 (1/4 as a fraction)
Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
The property demonstrated by:
a(b+c)=(a.b)+(a.c)
Is the Distributive property
Which property is demonstrated below?Here we have the next expression:
a*(b + c) = (a*b) + (a*c)
So we have the product between a and the sum of b and c, is equal to the sum between the products of a and b, and a and c, so we "distributed" the product.
This property is called the "Distributive property".
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Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of d days that have passed. A. Write an equation for the situation.B. Find the a amount of money he began with.C. How much money does Marty have after 9 days?
Given:
Amount Marty spent per day = $3
Number of days = 14
Remaining amount = $68
Since the amount left depends on the number