Answer:
Step-by-step explanation:
(x^3 + 2x − 3)(x^4 − 3x^2 + x)
Multiply each value of 2nd bracket with 1st bracket:
=x^4(x^3 + 2x − 3) - 3x^2(x^3 + 2x − 3) +x(x^3 + 2x − 3)
=x^7+2x^5-3x^4-3x^5-6x^3+9x^2+x^4+2x^2-3x
Now combine the terms with same power:
=x^7-x^5-2x^4-6x^3+11x^2-3x
You can also take the common from the expression:
x(x^6-x^4-2x^3-6x^2+11x-3)....
The product of (x^3 + 2x − 3)(x^4 − 3x^2 + x) is x(x^6-x^4-2x^3-6x^2+11x-3)....
5(2x-3) in distributive property
Answer:
The answer is (5*2x) - (5*3)
Step-by-step explanation:
You just have to multiply the coefficient by the individual numbers and variables inside the parentheses. :)
the algebraic expression for "the quotient of 51 and x" is?
Answer:
51/x
The first number/ variable always goes on top
which set represents the domain of function shown? {(-3,6),(0,2),(4,7),(11,15)}
Answer:
{-3,0,4,11}
Step-by-step explanation:
{(-3,6),(0,2),(4,7),(11,15)}
The domain is the input values, or x coordinates
{-3,0,4,11}
Subtract
(6x^2 + 5) - (4x-3)
[tex](6x^2+5)-(4x-3)=6x^2+5-4x+3=6x^2-4x+8[/tex]
ANSWER B
I took the test and that was the correct answer
The graph of f(x) = |x| is transformed to g(x) = [X + 11-7. On which interval is the function decreasing?
Answer:
The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Step-by-step explanation:
* Lets explain how to solve it
- Decreasing function means a function with a graph that moves
downward as it is followed from left to right.
- For example, any line with a negative slope is decreasing function
- Lets look to the attached graph to understand the meaning of the
decreasing function
∵ f(x) = IxI ⇒ green graph
∵ g(x) = Ix + 1I - 7 ⇒ purple graph
- From the graph f(x) translated 1 unit to the left and 7 units down to
form g(x)
- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}
- The range of f(x) is {y : y ≥ 0}
- The range of g(x) is {y : y ≥ -7}
# For f(x)
- The slope of the green line from (-∞ , 0) is negative
- The slope of the green line from (0 , ∞) is positive
# For g(x)
- The slope of the purple line from (-∞ , -1) is negative
- The slope of the purple line from (-1 , ∞) is positive
∵ The line with negative slope represent decreasing function
∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
The function g(x) = |x+11|-7 is a transformed absolute value function, which is decreasing on the interval (-infinity, -11) due to the horizontal shift to the left by 11 units.
The question is asking about the transformation of the absolute function f(x) = |x| into a new function g(x). The function provided, g(x) = |x+11|-7, is a transformed version of f(x) where the graph has been shifted horizontally and vertically. To determine on which interval g(x) is decreasing, we need to consider the properties of the absolute value function and its transformations.
The graph of the standard absolute value function, f(x) = |x|, is shaped like a 'V', increasing for x > 0 and decreasing for x < 0. When we introduce a horizontal shift to the function (such as adding 11 to x), this shifts the vertex of the 'V' horizontally. For g(x), the graph is shifted to the left by 11 units due to the '+11' inside the absolute value. Therefore, the function will be decreasing on the interval (-infinity, -11) since the function will decrease to the left of the vertex (which is now located at x = -11). The vertical shift (subtracting 7) simply moves the graph down but does not affect the intervals of increasing or decreasing behavior.
The system of equations y=-1/2x+4 and y = 2x – 1 is shown on the graph below. According to the graph, what is the solution to this system of equations?
A. (2, 3)
B. (3, 2)
C. (–1, 4)
D. (4, –1)
Answer: You can use a graphing calculator in the future
(2,3)
A
Answer: A(2,3)
Step-by-step explanation:
To solve the system of equations;
y=-1/2x+4 and y = 2x – 1
y=-1/2x+4 ----------(1)
y = 2x – 1 -----------(2)
Lets substitute equation 2 in equation 1
2x - 1 = -1/2x+4
Collect like term
(We move the x variables from the right -hand side of the equation to the right-hand side of the equation to the right-hand-side of the equation and then move the constants to the right-hand side of the equation)
2x + 1/2x = 4 + 1
5x/2 = 5
To get the value of x, we will multiply both-side of the equation by 2/5
5x/2 × 2/5 = 5 × 2/5
(On the left-hand side of the equation, the 5/2 will cancel out the 2/5 leaving us with x and on the right-hand side of the equation 5 will cancel out 5 leaving us with 2)
x = 2
Substitute x =2 in equation (2)
y = 2x - 1
y = 2(2) - 1
y = 4 -1
y =3
The solution to the system of the equations is x=2 and y=3
Therefore the answer is A(2,3)
.
In which quadrants do solutions for the inequal
the inequality
[tex]y \leqslant \frac{2}{3}x - 4[/tex]
exist.
A.I, III, and IV
B.I, II, and III
C.I and IV
D.All four quadrants
Answer:
A.I, III, and IVStep-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
If m > 0, then the function is increased
If m < 0, then the function is decreased
We have
[tex]m=\dfrac{2}{3}>0[/tex] - the function is increased
[tex]b=-4[/tex] - the y-intercept is -4 → (0, -4)
Therefore the line passes through III, IV and I quadrant.
========================================
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
========================================
We have [tex]y\leq\dfrac{2}{3}x-4[/tex] → ≤ - shaded region below the line.
Therefore the inequal the inequality exist in I, III and IV quadrant.
Look at the picture.
The inequality exists in quadrants A.I, III, and IV.
The answer is option A
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the line
slope(m)=tan∅=y axis/x axis.
If m > 0, then the function is increased
If m < 0, then the function is decreased
=function is increased
=y-intercept is -4 = (0, -4)
Therefor the line passes through III, IV and I quadrant.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
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In ∆ABC, m<A = 72 and m<B = 83. What is the measure of <C?
Answer:
25 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees therefore:
m < C = 180 - 72 - 83
= 180 - 155
= 25 degrees.
Answer:
25
Step-by-step explanation:
Theorem:
The sum of the measures of the interior angles of a triangle is 180 degrees.
The theorem is can be written as the equation below.
m<A + m<B + m<C = 180
We know the measures of angles A and B, so we substitute the values for those measures, and we solve for the measure of angle C.
72 + 83 + m<C = 180
Add like terms on the left side.
155 + m<C = 180
Subtract 155 from both sides.
m<C = 25
Answer: m<C = 25
How would you find f(-3)?
Answer:
f(-3) = 12
Step-by-step explanation:
-3 < 2; 9 + 3 = 12 [(-3)² - -3 (double negative)]; DO NOT change -3 to 3.
I hope this helps, and as always, I am joyous to assist anyone at any time.
Simplify 4(x - 3) - 2x + 9.
Answer:
2x-3
Step-by-step explanation:
4(x - 3) - 2x + 9
Distribute the 4
4x -12 -2x+9
Combine like terms
4x-2x -12+9
2x -3
given the two Fibonacci numbers below, which number would follow? F(14) = 377 and F(15) = 610
Answer:
987.
Step-by-step explanation:
The terms in a Fibonacci series are obtained form the sum of the previous 2 terms. So the next number F(16) = 377 + 610 = 987.
APEX ANSWER: 987
Step-by-step explanation:
377 + 610 = 987
Mischa wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form. What is the value of c in her equation?
Answer:
-7
Step-by-step explanation:
Mischa's equation is -x² + 4x - 7 = 0
The standard form is ax² + bx + c = 0
c is the constant term in the quadratic equation.
If we compare terms, we find that c = -7.
Could you guys please help me with number 1
Answer:
Option B 6 30 am
Step-by-step explanation:
step 1
Sum all the times
(45+5+10+30+15)=115 minutes
Convert minutes to hours
we know that
60 minutes = 1 hour
so
115 minutes=60+55= 1 hour 55 minutes
Subtract 1 hour 55 minutes from 8 25 am
(8 25 am)-(1 hour 55 minutes)=(8 25 am-1 hour)-(55 minutes)
=7 25 am-55 minutes
=7 25 am-(25+30) minutes
=(725 am-25 minutes)-(30 minutes)
7 00 am-30 minutes
=6 30 am
The length of a rectangle is three times its width. The perimeter is 160 cm. What is the number of square centimeters in the area of the rectangle?
Answer:
1200 cm²
Step-by-step explanation:
width = x cm
length = 3x cm
perimeter = 160 cm
2(x + 3x) = 160
4x = 160/2
4x = 80
x = 80/4
x = 20 cm - width
length = 3x = 3 · 20 = 60 cm
Area = length · width = 60 · 20 = 1200 cm²
The rectangle's width is 20 cm and its length is 60 cm. Thus, the area of the rectangle is 1200 square centimeters.
Explanation:We are given that the length of a rectangle is three times its width. Let's denote the width as 'w'. Consequently, the length would be '3w'.
The perimeter of a rectangle is given by the formula: 2*(length + width). Given that the perimeter is 160 cm, we can substitute our variables into the formula: 2*(w + 3w) = 160. This simplifies to 8w = 160. Therefore, the width (w) equals 20 cm, and the length is 60 cm (3w).
The area of a rectangle is calculated by multiplying its length and width. Hence, the area of our rectangle is: 60 cm * 20 cm = 1200 square centimeters.
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Angles 4 and 5 form what type of angles?
complementary angles
supplementary angles
vertical angles
obtuse angles
Answer:
the answer will be verticle angles
Step-by-step explanation:
∠4 and ∠5 form vertical angles.
What is vertical angles?When two lines intersect each other, then non-adjacent opposite angles are called vertical angles.
Vertical angles are always equal in measurement.
If line AB and CD intersect each other at point O, ∠AOC and ∠BOD are vertical angles, similarly, ∠AOD and ∠BOC are also vertical angles.
Here lines 1 and 2 intersect each other.
So ∠4 and ∠5 are formed which are non-adjacent and opposite also.
Therefore ∠4 and ∠5 form vertical angles.
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The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 4.5 years after a model is introduced?
Answer:
20875
Step-by-step explanation:
Given:
y = 5500 ln (9t + 4
y is number of mowers sold
t is years after a particular model is introduced
f(t)= 9t+4
How many mowers will be sold 4.5 years after a model is introduced?
t=4.5
putting t=4.5 in given function we get,
y= 5500ln(9(4.5) +4)
= 20875.19
20875 mowers will be sold 4.5 years after a model is introduced!
QUESTION 3
In the set of ordered pairs {(4, 7), (4, -3), (-5, -9)}, the range is:
{(4, 7), (4, -3), (-5, -9)}
{(7, 4), (-3, 4), (-9, -5)}
{-5, 4}
{-9, -3, 7
The function consists of three points, as shown in the graph below. Determine the range of the function.
graph of three points, (negative 4, negative 2), (2, 1), and (4, 1)
{-4, 2, 4}
{-2, 1}
{-2, 0, 1}
none of these
QUESTION 5
Select the table that represents the following graph.
line through the points (negative 4, 4), (negative 2, 2), (1, negative 1), (3, negative 3), and extends beyond in both directions
x y
-3 2
-1 1
0 -1
2 -3
x y
-4 3
-2 2
1 -2
3 -4
x y
-2 3
0 1
2 -3
4 -5
x y
-4 4
-2 2
1 -1
3 -3
QUESTION 6
Select the table that represents the function. f (x) = x^2 -4x
x y
-1 5
1 -3
2 -4
5 5
x y
-3 -3
-1 0
1 1
2 3
x y
-4 1
-3 2
0 3
2 4
x y
0 -5
1 -3
3 1
4 3
QUESTION 7
Which graph is represented by the following table?
x f(x)
-2 0
0 -4
1 -3
3 5
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (5, 1) and (negative 5, 1)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (4, 4) and (negative 4, 4)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (2, 0) and (negative 2, 0)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (2, 4) and (negative 2, 4)
QUESTION 8
Collette’s Superstore is having a sale on desk lamps. The following graph shows the number of desk lamps left in the store t minutes after opening. How many minutes after opening will the store only have 40 desk lamps remaining?
Graph with t in minutes on the x axis and number of desk lamps remaining on the y axis. Graph shows line hitting points (0, 120), (5, 110), (10, 100), (15, 90), (20, 80), (25, 70), and (30, 60)
30 minutes
35 minutes
40 minutes
45 minutes
3 points
Answer:
see explanation
Step-by-step explanation:
The range is the set of y- values of the ordered pairs without repeats.
3
given
(4, 7), (4, - 3), (- 5, - 9)
Then the values of y are 7, - 3, - 9
hence range is { - 9, - 3, 7 }
For
(- 4, - 2), (2, 1), (4, 1)
Then the values of y are - 2, 1, 1
Hence range is { - 2, 1 }
A car wash had to make their soap last 8 days .If they only have one-seventh of a gallon of soap ，how many should they use each day so it lasts 8 days ？
Answer:
1/56 gallon
Step-by-step explanation:
The car wash has 1/7 gallons of soap and they can use 1/8th of it each day. So, you would set up [tex]\frac{1}{7}[/tex] x [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{56}[/tex].
I need help!!!!
Which represents the inverse of the function f(x)=4x?
Answer:
[tex]h(x)=\frac{1}{4}x[/tex].
Step-by-step explanation:
The inverse is basically you just swapping x and y. People want to solve it for y to make it a function of x.
[tex]y=4x[/tex]
Swap x and y:
[tex]x=4y[/tex]
Now solve for y by dividing y on both sides:
[tex]\frac{x}{4}=y[/tex]
[tex]\frac{1}{4}x=y[/tex]
[tex]y=\frac{1}{4}x[/tex].
Find the length of KB¯¯¯¯¯¯¯¯+AK¯¯¯¯¯¯¯¯.
A. 28
B. 33
C. 21
D. 35
Intersecting chord rule:
DK x KB = AK x CK
12 x 4x+1 = 14 x 3+3x
Simplify:
48x +12 = 42x +42
Subtract 12 from each side:
48x = 42x + 30
Subtract 42x from each side:
6x = 30
Divide both sides by 6:
x = 5
Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21
Now add KB and AK:
21 + 14 = 35
The answer is D. 35
The required length of KB(21) + AK(14) is 35. Option D is correct.
The figure is given,
where AK = 14. DK = 12, KB = 4x+1 and KC =3+3x.
KB + AK to be determined.
The ratio can be defined as the relativeness of the fraction of one quantity towards others.
Here,
The ratio of AK: DK = KB:KC
[tex]14/12= 4x+1/3+3x\\14*(3+3x) = 12*(4x+1)\\2+42x = 48x+12\\42-12=48x-42x\\6x= 30\\x = 5[/tex]
Now,
= KA + KB
= 14 + 4x+1
= 14+ 4(5)+1
= 35
Thus, the required length of KB + AK is 35.
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What is the perimeter of AYXZ?
3.5 in.
5.3 in.
6.4 in.
7.8 in.
Answer: The perimeter of ΔYXZ6.4
Answer:6.4
Step-by-step explanation:
What is the quotient of -13/8 divided by -1/4
Answer:
0.40625
Step-by-step explanation:
Answer:
The answer is 13/2
Step-by-step explanation:
What is the slope of the line represented by the equation y = x – 3? –3 3
Answer:
None of then, the slope is 1
Step-by-step explanation:
We have to use the general equation for lines, that is:
[tex]y=mx+b[/tex]
where 'm' is the slope (by comparison)
So, we only need to compare your equation ([tex]y=x-3[/tex]) with the general one.
We can see that m=1, b=-3
So our slope turns out to be equals to 1
Find the area of the image.
See the attached picture:
(-6,5)
(-3,3)
(0,1)
what are the intercepts
Answer:
(0, 1)Step-by-step explanation:
y-intercept: (0, y)
x-intercept: (x, 0)
Therefore the y-intercept is only (0, 1).
Are the triangles similar? if so, what postulate or theorem proves their similarity?
A. yes, by SSS Similarity Theorem
B. yes, by SAS Similarity Theorem
C. yes, by AA Similarity Theorem
D. no the triangles are not similar
Answer: A. yes, by SSS Similarity Theorem
Step-by-step explanation:
From the given picture, it can be seen that we have all the sides of bothe the triangles.
SSS Similarity Theorem says that if the ratio of lengths of the corresponding sides of two triangles are then the triangles must be similar.
From the given picture , the ratio of the sides is given by :-
[tex]\dfrac{10}{35}=\dfrac{2}{7}\\\\\dfrac{12}{42}=\dfrac{2}{7}\\\\\dfrac{11}{36.5}=\dfrac{2}{7}[/tex]
Thus, the ratio of lengths of the corresponding sides of two triangles are equal.
Hence, the triangles must be similar by SSS similarity theorem.
Which ordered pair is a solution of this equation x-7y=-3
Answer:
-3,0
Step-by-step explanation:
this is the answer hope u like it
PLEASE HURRY
WILL GIVE BRAINLIEST
You need to catch two different buses to get to the shops Bus 1 is due to leave at 2 o'clock and arrive at 2.30. You have a half hour wail between getting off the first bus and getting on the second bus.
Bus 2 is due to arrive at the shops at 3.15.
(a) What time is bus 2 scheduled to leave? Bus 2 leaves 15 minutes early
(b) What time does it leave? () What time does it anive?
Bus 1 is 15 minutes late.
(c) What time does it arrive?
Answer:
rxch.ace_
Step-by-step explanation:
Final answer:
Bus 2 is scheduled to leave at 3:00 pm, but if it leaves 15 minutes early, it departs at 2:45 pm and arrives at the shops at 3:00 pm. If Bus 1 is 15 minutes late, it arrives at 2:45 pm, the same time Bus 2 leaves, preventing the transfer.
Explanation:
To solve the question regarding bus schedules and arrival times, let's break down each part of the problem step by step.
Part (a): Scheduled Departure Time of Bus 2
Bus 1 arrives at the first stop at 2:30 pm. There is a half-hour wait, so the earliest you can board Bus 2 is at 3:00 pm. Since Bus 2 arrives at the shops at 3:15 pm, and it leaves 15 minutes before its scheduled arrival time, Bus 2 is scheduled to leave at 3:00 pm.
Part (b): Bus 2 Leaves Early
Bus 2 is supposed to leave 15 minutes early. If its scheduled departure was 3:00 pm, it actually leaves at 2:45 pm. Since it leaves 15 minutes early and the travel time remains unchanged, Bus 2 would still arrive at 3:00 pm at the shops.
Part (c): Bus 1 is Late
Bus 1 is 15 minutes late. Instead of leaving at 2:00 pm, it leaves at 2:15 pm and arrives at the first stop at 2:45 pm. Since Bus 2 leaves at 2:45 pm, you would not be able to transfer from Bus 1 to Bus 2 since their arrival and departure times coincide.
Which expression is equivalent to (7+4i) +(8+I)?
Answer: B) 15 + 5i
Step-by-step explanation:
(7 + 4i) + (8 + i)
Add like terms: (7 + 8) + (4i + i)
Simplify: 15 + 5i.