Answer:
f(x) = x⁴ - 8x³ + 25x² - 72x + 144
Step-by-step explanation:
f(x) = (x-4)²(x+3i)(x-3i)
= (x²-8x+16)(x²+9)
= x⁴ - 8x³ + 25x² - 72x + 144
A linear function contains the points (-3, -7) and (6,-4). Which of the following points does it also include?
A.(-9,3)
B.(3,-6)
C.(12,2)
D.(9,-3)
The given points defines a line from which the linear function can be
determined and the included point on the line can be found.
The point also included on the line is D. [tex]\underline {(9, \, -3)}[/tex]
Reasons:
The given points on the linear function are; (-3, -7), (6, -4)
The slope of the line is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, we get;
[tex]Slope, \, m =\dfrac{-4-(-7)}{6-(-3)} = \dfrac{1}{3}[/tex]
The equation of the function is therefore;
[tex]y - (-4) = \dfrac{1}{3} \cdot (x - 6)[/tex]
[tex]y = \dfrac{x}{3} - 6[/tex]
Graphing the above equation on the calculator gives the points;
(-9, -9), (3, -5), (12, -2), and (9, -3)
Therefore;
The point also included on the line is D. [tex]\underline {(9, \, -3)}[/tex]
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What is the slope of this line?
-2/3
2/3
3/2
I don’t know
Answer: 2/3
Step-by-step explanation:
For an arithmetic sequence, a35=57. If the common difference is 5. Find a1 and the sum of the first 61 terms.
[tex]\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\[/tex]
.
[tex]\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276[/tex]
.
[tex]\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}[/tex]
Identify the set of ordered pairs that represents y as a function of x.
{(0, 0), (1, 1), (2, 3), (3, 3)}
{(0, 0), (0, 1), (2, 3), (3, 4)}
{(1,0), (2, 0), (3, 3), (3, 4)}
2,0)3
{(-1,0), (1, 0), (3, 0), (3, 4)}
Please help asap
possible answers: 1, -1, - 1/7, -2
Answer:
B it's -1 and the reason why I know is because trust me
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3^2 - 2^3}{3\times5-4^2}}[/tex]
[tex]\mathsf{= \dfrac{9 - 8}{3\times5-4^2}}[/tex]
[tex]\mathsf{= \mathtsf{\dfrac{1}{3\times5-4^2}}}[/tex]
[tex]\mathsf{= \dfrac{1}{15 - 4^2}}[/tex]
[tex]\mathsf{= \dfrac{1}{15 - 16}}[/tex]
[tex]\mathsf{= \dfrac{1}{-1}}[/tex]
[tex]\mathsf{\rightarrow 1\div -1}[/tex]
[tex]\mathsf{= -1}[/tex]
[tex]\huge\boxed{\star\text{Therefore, your answer is: \boxed{\mathsf{Option\ B. -1} \ }}\star}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
please help me thank you
Answer:
Here's how I'd do it
Step-by-step explanation:
What are the partial products of 8.6 x 9.2
Answer:
79.12
Step-by-step explanation:
1st number has 1 decimal places.
2nd number has 1 decimal places.
So 2 decimal places will apper in the final answer.
× 80 6 sum
90 7200 540 7740
2 160 12 172
sum 7360 552 7912
Remember the decimal places!
Final answer: 79.12
A map has a scale of 1:5000 cm, On the map a rectangle plot of land measures 30.5 cm and 23.5 cm.
what is the actual perimeter of the plot of land in meters?
please explain and answer the question correctly ☺ thank you.
Answer:
5,400 meters
Step-by-step explanation:
Perimeter of a rectangle = 2(l+w)
2(30.5+23.5) = 54
54 · 5,000 = 540,000 cm
540,000 cm = 5,400 m
I hope this helps!
simplify 2(3)(3)-2(3)(3)
Answer:
the answer is 0
Step-by-step explanation:
which expressions are equivalent to 4^-2 times 7^-2
Step-by-step explanation:
[tex] = {4}^{ - 2} \times {7}^{ - 2} [/tex]
[tex] = {(4 \times 7)}^{ - 2} [/tex]
[tex] = {28}^{ - 2} [/tex]
[tex] = \frac{1}{ {28}^{2} } [/tex]
n = 8
measurements: 4, 3, 6, 7, 5, 5, 4, 6
Calculate the mean.
Answer:
5
Step-by-step explanation:
mean=4+3+6+7+5+5+4+6/8mean=40/8mean =5Anna put 2500 in the bank and left it for 2 years. At the end of the 2 years she found that she had 2700. What is the annual rate percent paid by the bank
Answer:
rate percent paid by the bank
=2700-2500
=200
HELP PLEASE!
what are the solutions of the equation (x-2)^2=3x+6
Answer:
B. x -2
Step-by-step explanation:
The factors of (x -2)^2 are (x -2), twice.
The factors of -3x +6 are -3 and (x -2):
-3x +6 = -3(x -2)
The expression that is a factor of both is ...
x -2
i need help on this if anyone doesn't mind also very bad camera
Answer:
F:20%
Step-by-step explanation:
Hope it helps
What’s the slope of the black line
Answer:
Slope= - 1/2
Step-by-step explanation:
Help, plz! Math. TYSM IF U DO!
Answer: 1/16
Step-by-step explanation: ur right:)
Please help me!!! I will try to give brainliest!!
Answer:
_4 to 4 from the number line
what property is (-9+2) x 0=0
Answer:
ZERO MULTIPLICATION PROPERTY
Step-by-step explanation:
Anything multiplied by 0 is 0
a factory made 39 jars of creamy peanut butter and 61 jars of chunky peanut butter. what percentage of the jars of peanut butter were creamy?
Answer:
39+61= 100 total peanut butter jars
39 out of 100 is 39%
Step-by-step explanation:
Therefore 39% of the peanut butter jars were creamy.
Rewrite the fraction in the sentence below as a percentage.
The 15 overseas investors own 23/25 of the business.
Answer:
92%
Step-by-step explanation:
(a) Pei has x dollars, when she passed her exam, her dad doubled her money and mum gave another $10. Altogether she got $100. i) Write a mathematical equation for this.
Answer:
a: (x2)+10 = 100
Step-by-step explanation:
and if you need an answer, x = 45
What is 8 82% expressed as a fraction? 8 8 100 7. 80 7 40 8 8. 25. look at pic. plx
Answer:
7/80
so basically;
convert 3/4 to a decimal = 0.75
8.75% and convert to fraction = 7/80.
9514 1404 393
Answer:
(b) 7/80
Step-by-step explanation:
As a decimal
8 3/4% = 0.0875 = 875/10000 = (125×7)/(125×80) = 7/80
__
As a fraction
8 3/4% = (8 3/4)/100 = (35/4)/100 = 35/400 = 7/80
_____
Additional comment
The symbol % is fully equivalent to the division /100. That is why we can replace (8 3/4)% with (8 3/4)/100.
WRITE AN EQUATION IN SLOPE INTERCEPT FORM FOR THE PERPENDICULAR TO Y=2X-3 Y=2X-3 PASSES THOUGH THE POINT (-3,-3)
Step-by-step explanation:
The slope of the line [tex]y = 2x - 3[/tex] is 2, which means that a line perpendicular to this will have a slope equal to its negative reciprocal or [tex]m = -\frac{1}{2}.[/tex] So we can write the slope-intercept form of the line's equation as
[tex]y = -\frac{1}{2}x + b[/tex]
To find the value of b, we use the value of the given point (-3, 3):
[tex]\Rightarrow 3 = -\frac{1}{2}(-3) + b[/tex]
Solving for b, we get
[tex]b = \frac{3}{2}[/tex]
Therefore, the slope-intercept form of the equation for the perpendicular line is
[tex]y = -\frac{1}{2}x + \frac{3}{2}[/tex]
Explain solving Slope
ratio of vertical change between 2 points
Find its base and height
Area of parallelogram = 96 square miles
Base = x + 5
Height = x - 5
[tex]x + 5 \times x - 5 = 96 \\ 2x - 0 = 96 \\ x = \frac{96}{2} \\ x = 48[/tex]
Height = 48 - 5 = 43
Base = 48 + 5 = 53
4. If f(x) = x2, g(x) = 5x, and h(x) = x +4, find each value.
Find h[f(4)].
Step-by-step explanation:
f(x) = x²
g(x) = 5x
h(x) = x + 4
= h[f(4)]
= x + 4
= f(4) + 4
= (4)² + 2
= 16 + 2
= 18
h[f(4)] = 18
Alex spends 40 minutes on his paper route every day. If he earns $6 a day from his paper route, how much does he get paid per hour?
Answer:
$9
Step-by-step explanation:
There are 60 minutes in an hour, and you have to multiply 40 by 1.5. Doing this, you would also have to multiply $6 by 1.5, getting $9 per hour.
Parallelogram has a base of 9 and height of two thirds what is the area
Answer:
Area or parallelogram = base * height
Area = 9 units * 2/3 units
Area = 9/1 * 2/3 square units
Area = 18/3 square units
Area = 6 square units
Answer: area = 6 square units
At Handy Hardware Shop's annual spring-cleaning sale, every ratchet set in the shop gets marked down. Austin purchased 2 ratchet sets during the sale: one for himself and one to give to his dad on Father's Day. Each ratchet set cost $8 less than its full price. He paid a total of $56. What is the cost of each ratchet set at full price?
Answer:
answer is 36
Step-by-step explanation:
The cost of each ratchet set at full price was $36.
Given that in a sale a ratchet set cost $8 less than its full price. Austin paid a total of $56.
We to find the cost of each ratchet set at full price,
Let's denote the cost of each ratchet set at full price as "x" dollars.
According to the information given, each ratchet set was marked down by $8, so their sale price would be (x - $8) dollars each.
Austin purchased 2 ratchet sets, so the total cost of his purchase would be:
2 (x - $8) = $56
Now we can solve for "x":
2 (x - $8) = $56
2x - $16 = $56
2x = $56 + $16
2x = $72
x = $72 / 2
x = $36
So, the cost of each ratchet set at full price was $36.
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Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
O x + y = 29, 5x + 2y = 100
O x + y = 100, 5x + 2y = 29
O 5x + y = 29, 2y + x = 100
O 2x + y = 100, 5y + x = 29
h
Answer:
x + y = 29, 5x + 2y = 100 is the answer
Step-by-step explanation:
it IS the answer so the next person, DON'T TRY TO TAKE IT DOWN!!!!!!!
