Answer:
a. [tex]18x^3 -60x^2 + 33x - 45[/tex]
b. No
Step-by-step explanation:
Given:
(3x-9) and [tex]6x^2-2x+5[/tex]
=> the production of them is:
[tex](3x-9)(6x^2-2x+5)[/tex] , we will use distributive law to solve this 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] [tex]= (3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)\\\\= (18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)[/tex]
Then Open both brackets
= [tex]18x^3 -6x^2+ 15x -54x^2 + 18x -45[/tex]
After that, we group the same terms
= [tex]18x^3 -(6x^2 +54x^2)+ (15x + 18x) -45[/tex]
= [tex]18x^3 -60x^2 + 33x - 45[/tex]
(b) Is the product of (3x-9) and [tex]6x^2-2x+5[/tex] equal to the product of (9x-3) and [tex]6x^2-2x+5[/tex]
No, let find the product of (9x-3) and [tex]6x^2-2x+5[/tex] , we will use distributive law to solve this as the above example.
= (9x-3)[tex](6x^2-2x+5)[/tex]
= [tex]9x (6x^2-2x+5) - 3(6x^2-2x+5)[/tex]
=[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]
After that, we open the bracket to find the same terms
= [tex]54x^3 - 18x^2+ 45x -18x^2 + 6x -15[/tex]
= [tex]54x^3 - 18x^2 -18x^2 + 45x + 6x -15[/tex]
= [tex]54x^3 - 36x^2 + 51x -15[/tex]
As you can see [tex]54x^3 - 36x^2 + 51x -15[/tex] ≠[tex]18x^3 -60x^2 + 33x - 45[/tex]
Hope it will find you well.
Debra plans to invest $2,250 for 10 years. She can invest in a savings account that pays 4% simple intrest or a savings account that pays 4% intrest compounded annually. How much more money will she have at the end of 10 years if she chooses the account with compound interest?
Answer:
[tex]\$180.55[/tex]
Step-by-step explanation:
step 1
Simple interest
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04[/tex]
substitute in the formula above
[tex]A=2,250(1+0.04*10)[/tex]
[tex]A=2,250(1.4)[/tex]
[tex]A=\$3,150[/tex]
step 2
Interest compounded annually
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=2,250(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=2,250(1.04)^{10}[/tex]
[tex]A=\$3,330.55[/tex]
step 3
Find the differences between the two final amounts
[tex]A=\$3,330.55-\$3,150=\$180.55[/tex]
11. Find the next 4 numbers in the pattern. 21, 24, 19, 22, 17, 20,
Answer:
The answer is 23???....?
Answer:
16,19,15,18
Step-by-step explanation:
rule=+3,-4
(will give brainlesit if correct )
The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 96 miles due north of the warehouse.
A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?
156
192
216
252
Answer:
its 176, the warehouse is 88 miles from the airport and the factory
Step-by-step explanation:
In which month was the peak, the largest deposit, made?
A January. B June. July. D August
Answer: It was made in B June
Step-by-step explanation: The following transactions occurred in June through August 2020. June 1 After much thought, Natalie sells a mixer to Curtis on credit, terms n/30, for $1,150 (cost of mixer $620). 30 Curtis calls Natalie. He is unable to pay the amount outstanding for another month, so he signs a one-month, 8.35% note receivable. July 31 Curtis calls
Answer:
C. July
Step-by-step explanation:
It's the tallest one in the plot.
I hope this helped. B)
0.4x=18=-13 what is x?
Answer:
x = 77.5
Step-by-step explanation:
Assuming that you meant:
0.4x+18 = -13
Subtract 18 on both sides:
0.4x = -31
Multiple by 5/2 on both sides
x = 77.5
Support me by marking my answer as brainiest
Find the Surface area AND Volume of the figure. Round to the nearest hundredths.
Answer:
SA= 902.88 yd²
V = 1386.24 yd³
Step-by-step explanation:
Surface area
Since the bases are right triangles, you need to find the base of the triangle. Use Pythagorean theorem as you are given the hypotenuse and one leg.
19² = 15.2² + b²
361 = 231.04 + b²
Subtract 231.04 from both sides
b² = 129.96
Root that
b = 11.4
Now that you have the base, find the areas of the triangles and rectangles.
Triangles - (15.2*11.4)1/2 (2)
15.2*11.4 = 173.28
Rectangles - (15.2)(16) = 243.2
(16)(11.4) = 182.4
(16)(19) = 304
Add them all together and the SA equals 902.88 yd²
Volume
V = Bh
V = 1/2(15.2)(11.4)(16)
V = 1/2 (2772.48)
V = 1386.24 yd³
Can you get this question answered please
B to the zero power over B to the second power
Answer:
b^-2 or 1/b^2
Step-by-step explanation:
b^0
--------
b^2
We know when we divide powers of the same base, we subtract
b^(0-2)
b^-2
If we are not allowed negative exponents then
1/b^2
What is the slope if the line graphed below? Type answer as fraction. Rise divided by run or whole number if can be reduce.
Answer:
3/5
Step-by-step explanation:
3 up and 5 over from point to point
Answer:
3/5
Rise=3
Run=5
Step-by-step explanation:
For this question it makes it easy because they have provided you with Lines labeled Rise and Run. All you need to do now is Count the rise and run.
For Rise over run if you go up as a rise it's a positive number...But if you go down its a Negative number same with Run.... If it runs to the right its positive and if it runs to the left its negative.
For Rise it goes up...1,2,3 Spaces so Rise is 3
For run it moves to the Right 1,2,3,4,5 spaces so Run is 5
3/5 cant be reduce so it stays as a fraction.
Find the zeroes of the function g(x).
g(x) = (x + 9)(x + 6)
Answer:
[tex]x = -9, x = -6[/tex]
Step-by-step explanation:
Step 1: Find the zeroes
(x + 9)
[tex]x + 9 - 9 = 0 - 9[/tex]
[tex]x = -9[/tex]
(x + 6)
[tex]x + 6 - 6 = 0 - 6[/tex]
[tex]x = -6[/tex]
Answer: [tex]x = -9, x = -6[/tex]
The length of a rectangle is four times the width. The
perimeter of the rectangle is 40 inches. What is the area of
the rectangle (in square inches)?
Answer:
Step-by-step explanation:
let the width=x
length=4x
P=2(l+w)=2(4x+x)=10x
10x=40
x=40/10=4
width=4 in
length=4×4=16 in
area=16×4=64 square inches.
The required area of the given rectangle is given as 64 inch².
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
As mentioned in the question,
The length of a rectangle is four times the width.
l = 4w
Now,
The perimeter of the rectangle is 40 inches.
2 [l + w] = 40
2 [4w + w] = 40
5w = 20
w = 4 inches
Length,
l = 4(4) = 16 inches
Area of rectangle = l × w
= 16 × 4 = 64 inch²
Thus, the required area of the given rectangle is given as 64 inch².
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Find the solution(s) to the system of equations. y= x^2 -2x -3 y= x -3
Answer:
two solutions : (0,-3) , (3,0)
Step-by-step explanation:
hello :
y= x² -2x -3 ...(*)
y= x -3....(**)
x²-2x-3 = x -3
x²-3x=0
x(x-3) = 0
x=0 or x-3=0
x=0 or x=3
but : y=x-3
1) x=0 y=0-3=-3
2) x=3 y=3-3=0
two solutions : (0,-3) , (3,0)
HELPPPppp MEEEEEEeeee
How to write 0.985 in expanded form in decimals
The expanded form of 0.985 is 0.9 + 0.08 + 0.005.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Example: 1.2 is the decimal number, where 1 is the whole part and 0.2 is the fractional part.
Given:
The decimal number 0.985.
To find the expanded form of 0.985:
First, convert the number to fractional form.
0.985 = 985/1000
= 900/1000 + 80/1000 + 5/1000
= 0.9 + 0.08 + 0.005
0.985 = 0.9 + 0.08 + 0.005
Therefore, 0.9 + 0.08 + 0.005 is the expanded form of 0.985.
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At a New Car Dealership a particular model comes in 4 trims levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
Answer:
60 different versions
Step-by-step explanation:
4 times 5 times 3 is 60.
The number of different versions of this car model that can be created from these options is 60.
Number of different versions:Using this formula
Number of different versions=Trims levels×Different colors×Different Interior
Where:
Trims levels=4
Different colors=5
Different Interior=3
Let plug in the formula
Number of different versions=4×5×3
Number of different versions=60
Inconclusion the number of different versions of this car model that can be created from these options is 60.
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What is the slope of the line through
(2,−2)(2,-2)
(2,−2)
left parenthesis, 2, comma, minus, 2, right parenthesis
and
(9,3)(9,3)
(9,3)
left parenthesis, 9, comma, 3, right parenthesis
?
Answer:
Slope is 5/7
Step-by-step explanation:
the slope of a line is given by;
m = (y-y1)/(x-x2)
Where;
y represents the coordinate of point 1 on the Y-axis
x represents the coordinate of point 1 on the X-axis
y1 represents the coordinate of point 2 on the Y-axis
x1 represents the coordinate of point 2 on the X-axis
Points on a line are written as the ordered pair (x, y)
We are given point 1 (2, -2) and it corresponds to (x, y)
Point 2 (9, 3) and it corresponds to (x1, y1)
Therefore the slope,
m = (-2-3)/(2-9)
m = -5/-7
m = 5/7
Therefore, the slope of the line through (2,−2) and (9, 3) is 5/7
Determine the magnitude of the sum of the two vectors: 2.5i+1.8j; -6i-0.7j
Answer:
Answer for this question would be: A, 3.67
Answer:
A. 3.67
Step-by-step explanation:
1. Add the two vectors (2.5,1.8)+(-6,-.7)=(-3.5,1.1)
2. Find the magnitude using square root of a^2+b^2
sqrt(-3.5)^2+(1.1^2)=sqrt(12.25+1.21)=sqrt(13)=3.67
Find the measure of Arc QRM
Answer:
200°
Step-by-step explanation:
The angle subtended at the centre is equal to the measure of the intercepted arc, thus
arc MQ = 85° + 75° = 160°
The measure of the circle is 360°, thus
arc QRM = 360° - 160° = 200°
Please help me out with this homework question
A pack of 4 chocolate bars costs £1.20
What is the price per unit?
Answer:
30 cents
Step-by-step explanation:
Since 4 bars cost 1.20 pounds, divide 1.20 by 4
You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to have flowers on them?
what is shows in the picture:
2 with thank you's then one with flowers that says thank you than on with a dragon fly that says thank you for you kindness
this is the question: You would expect ___cards to have flowers on them.
Out of 20 there are 5 cards which have flowers on them.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have total 20 thank-you cards.
Now, we choose four cards.
Out of 4 cards 2 with thank you then one with flowers that says thank you than on with a dragon fly
So, We choose pair of 4 cards 5 times.
Then, we get total cards with flower
= 1 x 5
= 5
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I'LL GIVE BRAINLIEST, NEED HELP.
Create a proportion that can be used to solve the following scenario. Solve your proportion and show your work.
As the Space Station orbits around the Earth, it travels about 75 miles in 15 seconds. At that speed, how far would it travel in 12 minutes?
Answer:
3600 miles
Step-by-step explanation:
75mi/15 seconds is our proportion
there are 60 seconds in 1 minute. 60/15 = 4
there are 12 minutes. 12X 4 = 48
we need to multiply 75 mi by 48 to find our distance
75 X 48 = 3600
4. Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How
much change will Mrs. Sloan receive if she gives the cashier $20.00
F. $14.45
G. $12.55
H. $5.55
J. $7.45
Hi, What is 678 divided by -4 times 56xs then added 7h.
Answer:-9492xs+7h
Step-by-step explanation:if you do 678 divided by -4 it would be -169.5 then multiply that by 56 witch would be -9492 then times s would be -9492xs then that added to 7h would be -9492xs+7h and your final answer
Pleaseeeee helppppppppp
Answer:
1)
b= -7
m=1
2)
b= 4
m=0
3)
b=3
m=-2
Step-by-step explanation:
Answer:
1 . m=1 b =7
2.m=0 b = 4
3. m= -2 b = 3
your welcome mark branliest if possible thanks
the salesman claims that the new machine can produce more items in an 8-hour workday than the old machine is the salesmans claim true
Answer:
No
Step-by-step explanation:
the salesman's claim is false because the new machine only makes 20 items an hour and the old one makes 25. So in 8 hours the new machine will only make 160 items and the old one will make 200
Which expression represents 22 more than the difference between 95 and 63
A. (22+95)
B. 22+(95+63)
C. (95-63)+22
Answer:
C
Step-by-step explanation:
Difference: 95 - 63
22 more: (95 - 63) + 22
Answer:
C. (95-63)+22
Step-by-step explanation:
difference means subtraction
95-63
more than means add after
(95-63) +22
Avery received $80 in cash for mowing lawns. She did the following with the $80. Put 20% of the $80 into a bank account. Spent 1/4 of the $80. Kept the rest of the $80 in cash. How much of the $80 did Avery keep as cash?
Answer:
$48
Step-by-step explanation:
To start off, we know that Avery put 20% of the $80 in her bank account. We can figure out how much 20% of 80 is by multiplying 80 by 20% and then subtracting that number from 80. Remember to switch 20% to its decimal form (20% -> .2).
Step 1) 80 x .2 = 16
Step 2) 80 - 16 = 64
Next, we have to figure out how much 1/4 of the remaining $64 would be. We just simply divide 64 by 4 to figure out how much Avery spent.
Step 3) 64 / 4 = 16
Lastly, since we know Avery spent 16 dollars, we can subtract the 16 from 64 to get our final answer.
Step 4) 64 - 16 = 48
Avery kept $44 of the $80 as cash after putting 20% into a bank account and spending 1/4 of it.
Avery received $80 in cash for mowing lawns. Let's calculate how much she kept after her transactions. First, she put 20% of the $80 into her bank account. Calculating 20% of $80 involves multiplying $80 by 0.20, resulting in $16. Next, Avery spent 1/4 of the $80, which equals $20, as $80 divided by 4 gives $20. To find the amount Avery kept as cash, we subtract the amounts she put in her bank and spent from the original $80.
$80 - $16 - $20 = $44
Therefore, Avery kept $44 of the $80 as cash.
Find which term in the geometric sequence 1, 3, 9, 27, ... is the first to exceed 7,000.
hint (use a table)
Answer:
10th term
Step-by-step explanation:
3ⁿ⁻¹ > 7000
log₃ 7000 = 8.05
n - 1 > 8
n > 9
10th term
check: 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683
The graph shows a linear relationship between the
height and years of a plant's growth. Find the rate of
change. Select all that apply.
The rate of change of a linear function is always the
same.
Height (in)
The rate of change of a linear function increases as
the input increases.
The rate of change from 2 years to 4 years on the
graph is 1.5 inches per year.
L! The rate of change from 0 years to 6 years on the
graph is 1.5 inches per year.
8
Time (yrs)
Answer:
a, c, d
Step-by-step explanation:
Answer:
The rate of change from 2 years to 4 years on the graph is 1.5 inches per year & The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
Step-by-step explanation: