Answer:
The product of [tex]3x-9[/tex] and [tex]6x^2-2x+5[/tex] is [tex]18x^3 -60x^2 + 33x - 45[/tex]No, they are not equalStep-by-step explanation:
a. Given
[tex]3x-9[/tex] and [tex]6x^2-2x+5[/tex]
Required
Product
The solution is as follows
First, put both expression in different brackets
[tex](3x-9)(6x^2-2x+5)[/tex]
Expand [tex](6x^2-2x+5)[/tex] bracket by [tex](3x-9)[/tex]
To do that. we first multiply [tex](6x^2-2x+5)[/tex] by 3x then by -9. This is done as follows
[tex]3x (6x^2-2x+5) - 9(6x^2-2x+5)[/tex]
Now, we proceed to opening the bracket
[tex](3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)[/tex]
[tex](18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)[/tex]
Open both brackets
[tex]18x^3 -6x^2+ 15x -54x^2 + 18x -45[/tex]
Collect like terms
[tex]18x^3 -6x^2 -54x^2 + 15x + 18x -45[/tex]
[tex]18x^3 -60x^2 + 33x - 45[/tex]
Hence, the product of [tex]3x-9[/tex] and [tex]6x^2-2x+5[/tex] is [tex]18x^3 -60x^2 + 33x - 45[/tex]
b. Given
[tex]3x-9[/tex] and [tex]6x^2-2x+5[/tex][tex]9x-3[/tex] and [tex]6x^2-2x+5[/tex]Required
Are their products equal?
To check if they are equal or not, we find the product of both and compare the solutions
We've already solved for [tex]3x-9[/tex] and [tex]6x^2-2x+5[/tex] in the (a) part of this exercise, so we move to the product of [tex]9x-3[/tex] and [tex]6x^2-2x+5[/tex]
The solution is as follows
First, put both expression in different brackets
[tex](9x-3)(6x^2-2x+5)[/tex]
Expand [tex](6x^2-2x+5)[/tex] bracket by [tex](9x-3)[/tex]
To do that. we first multiply [tex](6x^2-2x+5)[/tex] by 9x then by -3. This is done as follows
[tex]9x (6x^2-2x+5) - 3(6x^2-2x+5)[/tex]
Now, we proceed to opening the bracket
[tex](9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)[/tex]
[tex](54x^3 - 18x^2+ 45x) - (18x^2 - 6x +15)[/tex]
Open both brackets
[tex]54x^3 - 18x^2+ 45x -18x^2 + 6x -15[/tex]
Collect like terms
[tex]54x^3 - 18x^2 -18x^2 + 45x + 6x -15[/tex]
[tex]54x^3 - 36x^2 + 51x -15[/tex]
Now, we compare both answers
Is
[tex]18x^3 -60x^2 + 33x - 45[/tex]
equal to
[tex]54x^3 - 36x^2 + 51x -15[/tex]
No, they're not.
Reason is that, for both expressions to be equal, we must have the same expression after expanding both of them
Identify the graph of g(x) = –x2 + 9x – 20 from the choices below.
The graph of the quadratic function g(x) = -x^2 + 9x - 20 will be a downward opening parabola with vertex at (4.5, 0.25), x-intercepts at (4, 0) and (5, 0), and a y-intercept at (0, -20). To graph it, label the axes as 'f(x)' and 'x' and scale them to include these critical points.
Explanation:The student wants to identify the graph of the quadratic function g(x) = –x2 + 9x – 20. To do this, first note that the standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants.
In this case, a = -1 (which makes the parabola open downward), b = 9, and c = -20.
The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b/(2a).
For g(x), this gives h = -9/(2 * -1) = 4.5.
We can then find the value of k by substituting h back into g(x), which gives us k = -4.52 + 9(4.5) - 20.
Therefore, k = 0.25.
The vertex of the parabola is at (4.5, 0.25), and because a is negative, the parabola opens downward. The x-intercepts (or roots) of the parabola can be found by factoring the quadratic equation or using the quadratic formula. In this case, the x-intercepts are (4, 0) and (5, 0). Lastly, the y-intercept occurs when x = 0, which for g(x) is -20.
To label the graph, we'd use 'f(x)' for the vertical axis and 'x' for the horizontal axis. The scale of the axes depends on the maximum and minimum x and y values of the graph, which in this instance would include at least the vertex, x-intercepts, and y-intercept.
The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.
51,54,57,60,63,66,69,72,75,78,81,84
Which statement about the temperatures in Orlando must be true?
A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.
Answer:
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
The box ranges from 66 to 75... meaning that most of the days were in those temperatures.
The lines mean that there were only a few days that were in those temperatures.
You're welcome if I'm correct.
The correct answer is about 50% of the days in January had average temperatures between 66 and 75 degrees.
What is the box and whisker plot?A Box and Whisker Plot (also known as a Box Plot) is a visual representation of data distribution through quartiles.
The maximum and minimum value of the function is plotted at the ends of a box and whisker plot.The box in the middle displays the interquartile range, which means that about 50% of values when the data is arranged in ascending or descending order.In the graph given in the question we can clearly see that the interquartile range of the data is lying between the temperatures 66° to 75°, which means that 50% of days in January had the temperature between 66 to 75 degrees.
Hence, Option(c) is correct for the given question.
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4x-2 >-18
what is the answer?!
Hope this will help u....
Need help!!!!!!
This is so confusing
Answer:
Omar
Step-by-step explanation:
to find the base, which i am to assume they want to find the triangle base based on the formula they are using,
you should multiply base * height, then divide by 2, since it is a triangle, you not solving for a rectangle.
dividing by 2 and multiplying by 1/2 is the same thing!
so,
1/2 (7* 24) is the right answer to finding the base!
Kari looked at he direct base of 7*28, however, that shape is actually a rectangle... so Kari is wrong because he multiplied that dimension by 1/2, which is the formula for a triangle.
Omar is correct because he chose the dimensions of a triangle, and properly used the triangle formula!
i hope this helped you out!
stay safe!
:)
if 3300 equals 4.5 percent what is the price of 100%
Answer:
73333.333
Step-by-step explanation:
100/4.5= 22.222
3300*22.222= 73333.333
Vicky works in retail. Her annual gross salary is $24,000. From this, she must pay 15% income tax. In addition, she must repay a loan at a rate of $120 per month. The loan amount is taken out of her post-tax pay (i.e. after the tax has been calculated). What is Vicky's take home pay per month?
Answer:
Vicky's take home pay per month will be $1,580
Step-by-step explanation:
Given that her salary per annual i.e salary for the year = $24,000
Therefore salary per month would be $24,000/12 = $2,000.
From this, she must pay 15% income tax.
i.e 15% of salary
15/100 * 2000
= 0.15*2000
= $300.
Salary after paying tax = $2,000 - $300= $1,700.
Since, she must repay a loan at a rate of $120 per month we will reduct the loan from her salary,
$1,700 - $120 = $1,580
Vicky's take home pay per month will be $1,580
Answer: Vicky's take home pay per month is $1,580
Step-by-step explanation: If Vicky's annual gross salary (salary before any deductions) is given as 24000, then her monthly gross salary is derived as;
Salary Per month = 24000/12
Salary per month = 2000
She must pay 15 percent income tax and this derived as follows;
Income tax = 2000 x 0.15
Income tax = 300
Therefore her salary after tax deduction is derived as follows;
Salary after tax = 2000 - 300
Salary after tax = 1700
However, she must repay a loan (after tax deduction) at a rate of 120 per month, which is now derived as follows;
Salary after loan repayment = 1700 - 120
Salary after loan repayment = 1580
Therefore the calculations show that her take home pay after all adjustments comes down to $1,580 per month.
Find X (image attached)
Line NP is a tangent line, so angle N is 90 degrees.
Use the Pythagorean theorem to solve for x.
X = sqrt( 10^2 - 6^2)
X = sqrt(100-36)
X = sqrt(64)
X = 8
What is the perimeter of the rhombus below?
Answer:
16
Step-by-step explanation:
the perimeter of the given rhombus is 8√5.
To find the perimeter of a rhombus, we need to calculate the sum of the lengths of all four sides.
Given the coordinates of the points touching the graph: (-5,-3), (-1,-1), (3,-3), and (-1,-5), we can calculate the distances between these points to find the lengths of the sides.
Let's calculate the lengths of the sides:
1. Side 1: Distance between (-5,-3) and (-1,-1)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - (-5))^2 + (-1 - (-3))^2]
Length = √[4^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
2. Side 2: Distance between (-1,-1) and (3,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(3 - (-1))^2 + (-3 - (-1))^2]
Length = √[4^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
3. Side 3: Distance between (3,-3) and (-1,-5)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - 3)^2 + (-5 - (-3))^2]
Length = √[(-4)^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
4. Side 4: Distance between (-1,-5) and (-5,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-5 - (-1))^2 + (-3 - (-5))^2]
Length = √[(-4)^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
Now, we can calculate the perimeter by adding the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 2√5 + 2√5 + 2√5 + 2√5
Perimeter = 8√5
Therefore, the perimeter of the given rhombus is 8√5.
Please help me idk what the answer is?!??
Answer:
w ≤ 13
Step-by-step explanation:
-2(w-4) ≥ -18
Divide both sides by -2:
w-4 ≤ -18/-2
Don't forget to turn the inequality around, because we divided by a negative number!! We had greater than, now we have less than.
w-4 ≤ 9
Add 4 to both sides:
w ≤ 13
What is the circumference of the circle? Use 3.14 for pi
r = 6.4 cm
20 096 cm
40 192 cm
200 96 cm
401 92 cm
Answer:
its
40 192 cm
Step-by-step explanation:
Answer:
40.192cm
Step-by-step explanation:
the circumference of a circle = ?
radius = 6.4cm
recall that,
circumference of a circle = 2πr
circumference of a circle = 2 x 3.14 x 6.4cm
circumference of a circle = 40.192cm
therefore the circumference of a circle whose radius is 6.4cm is evaluated to be equals to 40.192cm.
the answer to your question is option B 40.192cm
A shop owner bought some T-shirts and purses.
Each T-shirt cost $8 and each purse cost $5
She bought a total of 28 T-shirts and purses.
She spent $161 altogether.
How many T-shirts did she buy? [3 marks]
Answer:
20 t shirt
Step-by-step explanation:
1.
What is the mean for the following scores: 2, 5, 4, 1, 8?
A. 3
B. 4
c. 5
20
Answer to your question is:
B. 4
Explanation:
2 + 5 + 4 + 1 + 8 = 20
20 ÷ 5 = 4
The mean is found out by adding the scores given and dividing the total by the number of scores.
In the given question the mean of the scores is 4.
The mean is calculated to get an average about something that is given.
Here
n= number of scores= 5
Sum of scores = ∑x= 2+5+4+1+8= 20
Mean = x bar= ∑x/n= 20/5= 4
For different distributions mean may or may not be the middle value.
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If a-b = 4 and ab = 60, what is the value of a + b?
Answer:
a + b = 16 or -16.
Step-by-step explanation:
a - b = 4
ab = 60 so a = 60/b
Substituting for a in the first equation:
60/b - b = 4
60 - b^2 = 4b
b^2 + 4b - 60 = 0
(b + 10)b - 6) = 0
b = 6, -10.
Therefore, from the first equation:
When b = -10 . a + 10 =4 giving a = -6 or
When b = 6, a - 6 = 4 giving a = 10.
So when a = -6, b = -10 and
when a = 10, b = 6.
So a + b is either 16 or -16.
Amir and Marvin continue until they each flip a coin
200 times. How do you expect Amir's results and
Marvin's results to compare? How will their results
compare with expected results based on theoretical
probability?
We are told that each person flips a coin 200 times. We know that a coin has two options when heads or tails fall, therefore, the results between Amir and Marvin are compared with the number of heads and the number of tails that each one obtained.
The theoretical probability says that out of 200 times a coin is flipped by having 50% heads or tails come out, 100 must be heads and 100 must be tails, theoretically obviously speaking.
Therefore with these values it would be the comparison.
Answer:
3456
Step-by-step explanation:
convert 20 miles to km
Answer:
32.1869
Step-by-step explanation:
multiply 20 by 1.609
multiplying miles by 1.609 will give you the answer
Answer:
20 miles =32.1869
Step-by-step explanation:
For an approximate result multiply the length value by 1.609.
If y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, what is the area of the object?
The information given, y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, is not enough to calculate the area of an object unless its shape is known. If it's a rectangular prism, the volume can be calculated. But without further information, we cannot provide a specific area calculation.
Explanation:The type of area an object will have depends on its shape. For example, the area of a rectangle is given by width times height (w * h). Similarly, the volume of a rectangular prism would be length times width times height (l * w * h). However, the given dimensions in the question (y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches) are not enough to determine the shape of the object. We need additional information on how these dimensions are related to the shape of the object before we can calculate the area.
If for instance, this object is a rectangular prism, then we could calculate its volume. That volume would be y (depth) * z (width) * h (height). In this case with the provided values, the volume would be 11 inches * 14 inches * 7 inches = 1078 cubic inches.
Without more information on the object’s shape, we can’t make assumptions and provide a definitive calculation of the area.
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What is the sum of the zeros of the equation (m-4) (3m-2)=0 ? Enter your answer as a fraction.
Answer:
4 2/3
Step-by-step explanation:
(m-4) (3m-2)=0
Use the zero product property to find the zeros
m-4 = 0 3m-2 =0
m =4 3m =2
m = 2/3
We want the sum of the zero's
4+ 2/3
4 2/3
From the quadratic equation (m-4) (3m-2)=0, we find the zeros of this equation are m=4 and m=2/3. The sum of the zeros is 4 + 2/3 = 4 2/3 or 14/3.
Explanation:The subject of the question is related to the zeros of a quadratic equation. A zero of a function is also referred to as a root or solution of the equation, which is the value of m that makes the function equal to zero. This equation has the form of (m-4) (3m-2)=0. It has two zeros: m=4 from (m-4)=0 and m=2/3 from (3m-2)=0.
Since the question asks for the sum of the zeros, we need to add these two solutions together: 4 + 2/3 = 4 2/3 or 14/3, which is our final answer.
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A transit train from Boston to New York and a passenger train from New York to Boston departed at the same time, at 3:00 PM. The distance between New York station and Boston station is 280 miles. The speed of the transit train was 80 miles per hour. The speed of the passenger train was 60 miles per hour.
Chapter Reference
At what time will the trains pass each other?
The transit and passenger trains will pass each other at 5:00 PM, considering their combined speed and the distance between New York and Boston.
The question involves using relative speed to determine the time at which two trains traveling towards each other will meet. The transit train travels from Boston to New York at a speed of 80 mph, and the passenger train travels from New York to Boston at a speed of 60 mph. Since both trains start at the same time and move towards each other, their combined speed is the sum of their individual speeds, which is 80 mph + 60 mph = 140 mph. To find the time taken for the trains to meet, we divide the total distance by their combined speed.
The distance between New York and Boston is 280 miles. Therefore, the time taken to meet is calculated by dividing the distance by the combined speed, which is 280 miles / 140 mph = 2 hours. Given that they departed at 3:00 PM, they will pass each other at 3:00 PM + 2 hours = 5:00 PM.
The coordinates of trapezoid ABCD are A (-6,3) B (-3,6) C (9,6) and D (-5,-8). Find the coordinates of trapezoid A’ B’ C’ D’ after the translation whose rule is T 3,4.
Answer:
A' (-3,7)
B' (0,10)
C' (12,10)
D' (-2,-4)
Step-by-step explanation:
A' (-6+3 , 3+4) = (-3,7)
B' (-3+3 , 6+4) = (0,10)
C' (9+3 , 6+4) = (12,10)
D' (-5+3 , -8+4) = (-2,-4)
What area is 20 and perimeter 18
Answer:
Width 4 Length 5
Step-by-step explanation:
4+4+5+5=18
4*5=20
Answer:if your talking about a square or rectangle then two sides would 5 and the other two four
Step-by-step explanation:area equals base times height
Base=5
Height=4
5*4=20 which is area
5+5+4+4=18 which is perimeter
Six more than the product of 24 and Vidya’s age
If we use v for Vidya's age, then the expression (24v)+6
Hellpppppppppppppppp
Answer:
The sum of the interior angles of this polygon is (180°)(9 - 2) = 7(180°) = 1,260°.
This graph shows a car moving at a
constant speed. For example, in 8 hours
the car travels 400 miles.
Which equation shows the line on the
graph?
A y = 2x
B y = 50x
C y = 400x
Answer:
B
Step-by-step explanation:
If you set x to hours and y to the amount of miles, you can multiply the hours to the numbers and equal out your miles. So, if 8 hours is multiplied to 50, it equals out the 400 miles.
What is the answer to this question
Answer:
A
Step-by-step explanation:
Given the exponential function
f(t) = 228[tex](0.975)^{t}[/tex] ← where t is time in years
Substitute t = 20 into f(t), that is
f(20) = 228 × [tex](0.975)^{20}[/tex] = 228 × 0.60268.... ≈ 137 → A
In account is gaining value at a rate of 4.9% per year that account held $150 and it's first year how much will be in the account after 10 years
Answer:
$242
Step-by-step explanation:
You will need to use the compound interest formula for this.
[tex]P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
Your equation will look like this:
[tex]150(1+\frac{.049}{1} )^{10}[/tex] = $242
Your answer is: $242
Similar triangles are two triangles with equal ____ angles.
a. vertical
b. corresponding
angles.
c. horizontal
d. elliptical
Similar triangles are defined as two triangles having equal B. corresponding angles, shown by the congruence of vertical angles, alternate interior angles, and the application of the AAA theorem.
Similar triangles are two triangles with equal corresponding angles. According to the question, in the figure, two triangles named triangle ABC and triangle FCE are observed to be similar because they have three sets of congruent angles - vertical angles (Angle ACB \\<=\ Angle FCE), alternate interior angles (Angle CAB \\<=\ Angle CFE), and another set of alternate interior angles (Angle CBA \\<=\ Angle CEF).
This is summed up by the AAA (Angle Angle Angle) theorem which states that two triangles are similar if all their corresponding angles are congruent. An example will be two right triangles which are equal when the hypotenuse and an acute angle of one are equal, respectively, to the hypotenuse and an acute angle of the other. These principles help us understand the similarity of triangles in geometry.
The two-way table displays the hair color of the sophomore (So), junior (Jr), and senior (Sr) classes at West Coast High School, represented by percents in the table. A 5-column table has 3 rows. The first column has entries Blonde, brown, total. The second column is labeled Sophomore with entries 10, 10, 20. The third column is labeled Junior with entries 30, 20, 50. The fourth column is labeled Senior with entries 20, 10, 30. The fifth column is labeled Total with entries 60, 40, 100. Let E be the event that the student is blond, and let F be the event that the student is a junior. Are events E and F independent? P(E|F) = % P(E) = % Events E and F are
Answer:
P(E|F)=60% P(E)=60% Events E and F are independent
Step-by-step explanation:
I took it and got it right
The events E (being blond) and F (being a junior) are not independent because P(E|F) = 30% does not equal P(E) = 60%.
Explanation:To determine whether the events E (being blond) and F (being a junior) are independent, we compare the probability of E given F, denoted as P(E|F), to the probability of E. If P(E|F) is equal to P(E), the two events are independent. Using the table, we first calculate P(E|F). Since 30% of juniors are blond, we have P(E|F) = 30%. Next, we determine P(E) by looking at the total percentage of students who are blond, which is 60%. Now, we compare P(E|F) with P(E).
If the events were independent, the probability of a student being blond should not change based on whether they are a junior. However, since P(E|F) = 30% which is different from P(E) = 60%, events E and F are not independent.
please solve this question
Given:
Number of mice and frequency
Mean = 7
To find:
The value of x.
Solution:
Number of mice = X
Frequency = Y
XY = Multiply X and Y values.
X Y XY
5 4 20
6 13 78
7 16 112
8 x 8x
9 6 54
Sum of Y = 4 + 13 + 16 + x + 6
= 39 + x
Sum of XY = 20 + 78 + 112 + 8x + 54
= 8x + 264
Mean formula:
[tex]$Mean = \frac{\Sigma XY }{\Sigma Y}[/tex]
[tex]$7=\frac{8x+264}{39+x}[/tex]
Do cross multiplication.
[tex]7(39+x)=(8x+264)[/tex]
[tex]273+7x=8x+264[/tex]
Subtract 264 from both sides, we get
[tex]9+7x=8x[/tex]
Subtract 7x from both sides, we get
[tex]9=x[/tex]
The value of x is 9.
Solve the equation log(x−7)=2
Answer:
x=107
Step-by-step explanation:
6.
(08.01)
The graph shows two lines, M and N.
A coordinate plane is shown with two lines graphs. Line M has a slope of 1 and passes through the y axis at negative 2. Line N has a slope of 1 and passes through the y axis at negative 2.
How many solutions are there for the pair of equations for lines M and N? Explain your answer. (5 points)
Answer:
infinite solutions, they overlap infinetely and go on infinitely, therefore they have infinite points of intersection.
Step-by-step explanation:
BRAINLIET PLZ
The number of solutions for the coincident lines is infinity many solutions.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A coordinate plane is shown with two lines graphs.
Line M has a slope of 1 and passes through the y axis at negative 2.
Line N has a slope of 1 and passes through the y axis at negative 2.
It means that both lines are one over the other which is coincident.
Then the number of solutions for the coincident lines is infinity many solutions.
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