Answers
The correct answer is the first option: y=(2x-1)(2x-3)(2x+5)
Because: if you give values to the variable "x" and graphic each point calculated, you will obtain the graph above. For example:
If x=-3/2:
y=(2x-1)(2x-3)(2x+5)
y=(2(-3/2)-1)(2(-3/2)-3)(2(-3/2)+5)
y=48 (As you can see in the graph)
If x=0:
y=(2x-1)(2x-3)(2x+5)
y=(2(1)-1)(2(1)-3)(2(1)+5)
y=15 (It is shown in the graph)
If x=1:
y=(2x-1)(2x-3)(2x+5)
y=(2(1)-1)(2(1)-3)(2(1)+5)
y=-7 (As you can see the graph attached)
Related Questions
Find the simplified form of the expression. Give your answer in scientific notation.
(9 x 10 5)(6 x 10 -7)
A. 5.4 x 10 -34
B. 1.5 x 10 -1
C. 5.4 x 10 -1
D. 1.5 x 10 -34
Answers
Now we get: [tex](9*10^5)(6*10^{-7})=9*6*10^5*10^{-7}[/tex] by associativity of multiplication.
This is equal to: [tex]54*10^{5+(-7)}=54*10^{-2}[/tex] by the property we stated above, for a=10. Scientific notation requires that the coeeficient in fron tof the power of 10 is between 1-10 and thus since 54=10*5.4, we have that the expression is equal to: 5.4*10*[tex]10^{-2}[/tex]=[tex]5.4*10^{-1}[/tex]. Hence the correct answer is C
Calculate the principal amount which earns $500 simple interest over 3 Years at a rate of 8% p.a round to the nearest cent
Answers
so, to find one year
500 ÷ 3 = $166.67
Interest for one year is $166.67
Interest rate for one year is 8%
8% = 166.67
1% = $20.83
100% = $2083.33
Principal amount is $2083.33
Final answer:
To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.
Explanation:
Calculating the Principal Amount from Simple Interest
To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal × 0.24.
To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.
Graph this function f(x)=x^2-4x-5
Answers
Answer:
Step 1: a = 1, b = -4
Step 2: x = 2, f(2) = -9
Step 4: (5,0) and (-1,0)
Step 6: f(0) = -5
On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)
About 65 out of 300 students prefer walking instead of riding the bus to school. About what percent of the students prefer walking?
Answers
To find the percentage of students who prefer walking, divide the number of students who prefer walking by the total number of students and multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.
Explanation:To find the percentage of students who prefer walking, you divide the number of students who prefer walking by the total number of students and then multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.
So, you divide 65 by 300 and multiply by 100 to get the percentage.
Percentage of students who prefer walking = (65/300) * 100 = 21.67%
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what are the approximate solutions of 2x^2-x+10=0? f) -2,2.5 g) -1.97,2.47 h)-2.5,2 i) no solution. help me please. :*
Answers
(-b +/- sqrt(b^2 - 4ac))/2a,
where
a = 2
b = -1
c = 10
Solve:
(1 +/- sqrt(1 + 4*2*10))/4
(1 +/- 9)/4
The two solutions are
10/4 = 2.5
(1-9)/4 = -2. The correct answer is f.
Picture included!
What is the slope of the line shown in the graph?
A.) -1
B.) -2
C.) 1/2
D.) 2
Answers
:D
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 3~) % (c,d) &&(~ 1 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-3}{1-0}\implies \cfrac{-2}{1}\implies -2[/tex]
witch property is used to simplify 3 C + 9 + 4 C equals 3 C + 4 C + 9
Answers
A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange
Answers
P(pink) = 7/28
P(orange) = 17/28
P(pink or orange) = P(pink) + P(orange)
P(pink or orange) = 7/28 + 17/28
P(pink or orange) = 24/28
P(pink or orange) = 6/7 or 0.857143 or 85.7%
What must be the value of x so that lines c and d are parallel lines cut by transversal p?
12
18
81
99
Answers
since "y" and 3x+45 are both linear angles, then y + (3x + 45) = 180.
but wait a second!! "y" is a corresponding angle to 81°, so y = 81° then, therefore,
[tex]\bf y+(3x+45)=180\implies 81+(3x+45)=180 \\\\\\ 126+3x=180 \implies 3x=54\implies x=\cfrac{54}{3}\implies x=18[/tex]
and that can only happen, if c || d.
The value of x so that lines c and d are parallel lines cut by transversal p is 18.
What is a Transversal line?Transversal lines are lines that passes intersects the two lines on a plane in two different points.
Given are two parallel lines c and d.
p is the transversal line passing through c and d.
The angle at the exterior side of angle 81° is 180° - 81° = 99°
When two parallel lines are intersected by a transversal line, then the angles formed at the corresponding corners of the transversal with each of the parallel line is called corresponding angles.
(3x + 45)° and 99° are corresponding angles.
Corresponding angles are always equal.
(3x + 45)° = 99°
3x = 99 - 45
3x = 54
x = 54 / 3
x = 18
Hence the value of x is 18.
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A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
How would this graph look??
Answers
Final answer:
A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.
Explanation:
The graph of the sine function with the given properties will have the following characteristics:
The amplitude is 4, which means the function will oscillate 4 units above and below the midline.
The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.
The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.
The y-intercept is (0, 1), which means the function starts at the midline.
Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.
Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.
In this budget, how much money is going toward optional expenses?
Answers
Answer:
$70
Step-by-step explanation:
Let's define the expenses first
Fixed expenses are those expenses that remain constant in all months like mortage payments, rents etc
Flexible expenses also called variable expense are expenses that are used for comfortable living like car maintenance o groceries.
Discretionary expenses are the expenses spent on non essential items like movie tickets, outings etc.
Savings are the expenses that are stored for future plans.
Hence, from the given pie chart the money going for optional expenses is $70 ..
What is the initial value of the function represented by this graph? A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5. 0 1 2 5 Question 7(Multiple Choice Worth 5 points)
Answers
Answer:
The initial value of the graph is 2. Third option is correct.
Step-by-step explanation:
It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
The line is passing through the points (0,2) and (7,5).
The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.
Slope of line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]
The equation of line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept. So the equation of given line is
[tex]y=\frac{3}{7}x+2[/tex]
At initial condition the value of x is 0. So, put x=0.
[tex]y=\frac{3}{7}(0)+2=2[/tex]
Therefore the initial value of the graph is 2. Option 3 is correct.
Answer:
Option 3 rd is correct
Initial value = 2
Step-by-step explanation:
A equation of line is given by:
[tex]y =mx+b[/tex] ....[1]
where
m is the slope of the line and b is the y-intercept or the initial value
As per the statement:
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
It is also given that:
A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)
Calculate slope:
using formula:
[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given ordered pairs we have;
[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]
y-intercept states that the graph which cut y-axis.
Substitute x =0 and solve for x:
we have given with the ordered pair (0, 2)
⇒y-intercept(b) = 2
Substitute the given values of m and b in [1]
[tex]y = \frac{3}{7}x+2[/tex]
The equation of straight line joins the ordered pair (0, 2) with the ordered pair (7, 5) is:
[tex]y = \frac{3}{7}x+2[/tex]
The initial value of the function represented by the given graph as shown below is: 2
What is the simplest form of (8x2)3?
Answers
[tex] = 8^3 \times (x^2)^3 [/tex]
[tex] = 512x^{2 \times 3} [/tex]
[tex] = 512x^6 [/tex]
please help attachment on please don't skip any parts
will get brainliest
Answers
helppppppppppppppppppppppp
Answers
10.3 units
Explanation:
Triangle ABC is a right-angled triangle. This means that we can apply special trig functions.
We are given that:
angle B = 25 degrees and AB = 4 units
Therefore:
cos(B) = adjacent / hypotenuse
cos(25) = 4 / BC
BC = 4.414 units
tan(B) = opposite / adjacent
tan(25) = AC / 4
AC = 1.865
Finally, we can get the perimeter as follows:
perimeter = AB + BC + AC
perimeter = 4 + 4.414 + 1.865
perimeter = 10.279 which is approximately 10.3 units
Hope this helps :)
Side c = 4
Angle B = 25°
Step #1: Find angle C by subtracting the other 2 angles from 180°.
C = 180° - A° - B°
C = 180° - 90° - 25°
C = 65°
Step #2: Use the Law of Sines to find side a.
a / sin(A) = c / sin(C)
a / sin(90°) = 4 / sin(65°)
a = (sin(90°) x 4) / sin(65°)
a = 4.414
Step #3: Use the Law of Sines to find side b.
b / sin(B) = c / sin(C)
b / sin(25°) = 4 / sin(65°)
b = (sin(25°) x 4) / sin(65°)
b = 1.865
So you have the sides
c = 4
b = 1.865
a = 4.414
The perimeter is all the sides added up
P = 4 + 1.865 + 4.414
P = 10.279
That can be rounded to 10.3 units
Hope this helps!
A sandbox has a volume of 648 cubic feet. what is the volume, in cubic yards, of the sandbox?
Answers
1 cubic yards equals to--------------> 27 cubic feet
then
I apply a rule of three
if 1 cubic yards ------------------- 27 ft³
X----------------------------------> 648 ft³
X=648/27=24 cubic yards
the answer is 24 cubic yards
2x + 3y = 18 3x -4y > 16. Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer. 2x + 3y = 18 3x -4y > 16 Slope-Intercept Form: Slope-Intercept Form: Domain: Domain: Range: Range: Slope: Slope: Y-intercept: Y-intercept:
Answers
2x + 3y = 18
3x -4y > 16
Part A)
2x + 3y = 18 -------> 3y=[18-2x]---------> y=6-(2/3)x (Slope-Intercept Form)
using a graph tool
see the attached figure
the domain is the interval (-∞,∞)--------> ( all real numbers)
Domain of a function f (x) is the set of all the values of x for which the function is defined
the range is the interval (-∞,∞)--------> ( all real numbers)
Range of the function f(x) is the set of all the values that f(x) takes
Slope-Intercept Form------------> y=6-(2/3)x---------> [y=mx+b]
where
m------> is the slope------------> m=-2/3
Slope=-2/3
Y-intercept is the point for y=0
y=6-(2/3)x-------------> 0=6-(2/3)x--------> x=9
Y-intercept is the point (9,0)
Part B)
3x -4y > 16----------> -4y > 16-3x-----> y < -4+(3/4)x (Slope-Intercept Form)
using a graph tool
see the attached figure
the domain is the interval (-∞,∞)--------> ( all real numbers)
Domain of a function f (x) is the set of all the values for which the function is defined
the range is the interval (-∞,∞)--------> ( all real numbers)
Range of the function f(x) is the set of all the values that f(x) takes
Slope-Intercept Form------------> y = -4+(3/4)x---------> [y=mx+b]
where
m------> is the slope------------> m=3/4
Slope=3/4
Y-intercept is the point for y=0
y = -4+(3/4)x------------->0= -4+(3/4)x-----> 4=(3/4)x----> 16/3 = x----> x=16/3
Y-intercept is the point (5.33,0)
Which TWO transformations could show that triangle A and triangle B are similar triangles?
Answers
..
...
it's translation and Dilation
helppppppppppppppppppppppppppppppppppppppppppppp
Answers
You must respect the properties of the roots.
Group the terms correctly.
Answer
option 2
See attached graph.
The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.
Answers
Answer:
y = 0.0027*x^2 + 0.0111*x + 2.8574
Step-by-step explanation:
Using Excel the procedure is:
First, insert x and y values in a table format, as can be seen in the figure
Then, select data
Next, go to insert tab and inside charts options select scatter plot without any lines
Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option
Look at the following number sequence. 3, 11, 19, 27, . . . Based on the pattern, what are the next two terms? 31, 40 43, 51 35, 43 216, 1728
Answers
Find measure B ???????
Answers
Put this information into an equation and solve for x:
(7x+27)°+(9x-7)°=180°
7x+27°+9x-7°=180°
16x+20°=180°
16x=160°
x=10°
Angle B is (7x+27)°, so just substitute x:
B = 7(10)+27
B = 70+27
B = 97°
90 + 90 + (7x + 27) + (9x - 7) = 360
Simplify and solve.
180 + 16x + 20 = 360
16x + 20 = 180
16x = 160
x = 10
Now plug this in for x in the two "algebra" angle measures.
Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?
Answers
650(2000) = 800x + 800(650)
x = 975 ft
Give an indirect proof of the following statement
If x^2 + x = 4, then x ≠ 2.
Please help :)
Answers
By assuming that x = 2 and substituting this into the original equation x^2 + x = 4, we arrive at a contradiction because 4 + 2 ≠ 4. Thus, we conclude through indirect proof that x cannot equal 2.
To give an indirect proof of the statement If x2 + x = 4, then x ≠ 2, we start by assuming the opposite of what we want to prove, which is that x = 2. Our goal is to show that this assumption leads to a contradiction.
Assume that x = 2. Substituting 2 for x in the original equation gives us (2)2 + 2 = 4 + 2 = 6, which is clearly not equal to 4. This contradicts the original equation x2 + x = 4. Since our assumption that x = 2 leads to a false statement, it follows that x cannot be 2, thereby proving the original statement by contradiction.
The method of assuming the negation and arriving at a contradiction shows that the original statement must be true according to the logical principle of indirect proof. Hence, if x2 + x = 4, then indeed x ≠ 2.
Suppose you find a rock and measure that 12.5% of the original uranium-235 still remains it, while the other 87.5% has decayed into lead-207. about how old is the rock?
Answers
713x10^6 years x 3 half-lives = 2139x10^6 years= 2.139 billion years.
How old is the rock?
The answer is: 2.139 billion years
A pack of cinnamon-scented pencils sells for $5.00. What is the sales tax rate if the total cost of the pencils is $5.20?
Answers
520-500 = 20
20÷500 =.04
.04 ×100= 4%
Final answer:
The sales tax rate is 4%.
Explanation:
To calculate the sales tax rate for the cinnamon-scented pencils, you first need to determine the amount of sales tax paid and then relate that to the original price of the pencils.
The total cost is given as $5.20, and the original price is $5.00.
The difference between these two amounts is the sales tax paid.
Subtract the original price from the total cost to find the sales tax amount:
$5.20 - $5.00 = $0.20.
Next, to find the sales tax rate, divide the sales tax amount by the original price and multiply by 100 to get a percentage:
Sales Tax Rate = ($0.20 / $5.00) x 100 = 4%
Therefore, the sales tax rate is 4%.
Which of these sequence is an arithmetic sequence??
Answers
Answer:
a and c
Step-by-step explanation:
Which statement about this product is true?
0.44 ×(−5 3/4)
It is equal to 0 because 0.44 rounded to the nearest whole number is 0, and 0 times any number is 0.
It is equal to −5 3/4 because 4/4 is equal to 1, and 1 times any number equals that number.
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
It is less than −5 3/4 because multiplying by a number less than 1 gives a smaller number.
Answers
Answer:
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
Step-by-step explanation:
i guessed it and it was right so ye.
find the arithmetic mean an of an-1 = 3.9 and an+1 = 7.1
a. 11
b. 5.5
c. 3.7
d. 1.6
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
We are asked to find arithmetic mean of two terms given.
For finding arithmetic mean, we add up the values and divide the sum by the number of values.
Here we have given two numbers , below
[tex]a_{n-1}=3.9[/tex]
[tex]a_{n+1}=7.1[/tex]
So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]
So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]
So, arithmetic mean for given two numbers are 5.5 : Answer (b)
Hope it will help :)
b. 5.5
Step-by-step explanation:FOR LEARNING ONLY.. not necessary to read, but I hope it helps!
you start with:
[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]
arithmetic questions like this are like finding an average.
so you add the values while dividing by the total of values there are.
in this case:
[tex]\frac{7.1+3.9}{2}[/tex]
which is simplified to:
[tex]\frac{11}{2}[/tex]
then decimal:
[tex]5.5[/tex]
You enter 5 tickets into a raffle, in which a total of 65 tickets are entered. the announcer chooses two tickets from the pool of raffle tickets. what is the probability that you win both prizes from the raffle? write your answer as a fraction in simplest form.