Answer:
a = – 8
Step-by-step explanation:
From the question:
When P(x) = 2x³ – ax² + 4x – 4 is divided by x – 1, it gives a reminder of 10.
To obtain the value of a, we shall equate x – 1 to 0 as illustrated below:
x – 1 = 0
x = 0 + 1
x = 1
Next, we shall substitute the value of x into 2x³ – ax² + 4x – 4 and equating it to 10 as illustrated below:
2x³ – ax² + 4x – 4 = 10
x = 1
2(1)³ – a(1)² + 4(1) – 4 = 10
2 – a + 4 – 4 = 10
2 – a = 10
Collect like terms
– a = 10 – 2
– a = 8
Divide through by –1
a = – 8
Therefore, the value of a is –8.
PLEASE HELP:
On a number line, suppose point E has a coordinate of 5, and EG=4. What are the possible coordinates of point G?
The possible coordinates for G are ___
(Type integers or decimals. Use a comma to separate answers as needed.)
Answer:
G = 1, 9.
Step-by-step explanation:
There are two cases to this problem: G is either to the left or right of E. If G is to the left of E, then G = 5 - 4 = 1 and if G is to the right of E, then G = 5 + 4 = 9. Therefore, our answer is G = 1, 9.
please help me as soon as you can please
Answer:
f(x) = 5 * ( 8/5) ^x
Step-by-step explanation:
f(x) = a b^x
Let x = 0
5 = a * b^0
5 = a*1
a = 5
Let x = 1
8 = 5 * b^1
Divide each side by 5
8/5 = b
f(x) = 5 * ( 8/5) ^x
Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6
Answer:
y = - [tex]\frac{1}{16}[/tex](x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-1)^2+(y+2)^2^}[/tex] = | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = - [tex]\frac{1}{16}[/tex] (x - 1)² + 2
if the area of the rectangle is 120, what is the area of triangle cpd
Answer:
Step-by-step explanation:
area of rectangle=120
find area of CPD
area=1/2 (area of the rectangle)
area = 1/2×120=60
The area of triangle CPD IS 30 square units.
If the area of the rectangle is 120, then the area of triangle CPD is 30.
The area of a rectangle is given by the formula:
Area = length × width
In this case, the length of the rectangle is 120/width.
The area of a triangle is given by the formula:
Area = (1/2) × base × height
The base of triangle CPD is the width of the rectangle, and the height of triangle CPD is half the length of the rectangle.
Therefore, the area of triangle CPD is:
(1/2) × width × (120/width) = 30
So the answer is 30.
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The solutions to \[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[tex]The solutions to\[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[/tex]
Answer:
5/8
Step-by-step explanation:
(10 +/- √100-104)/4
(10 +/- 2i)/4
5/4 +/- 1/2i
5/4 * 1/2 = 5/8
PLEASE FOR THE LOVE OF FOOD ANSWER MY QUESTION!
Given that a quadrilateral PQRS is a parallelogram, PQ and RS are opposite sides, PQ = 7x + 16, RS = 5x +28, and QR = 67 which of the following statements are correct? More than one answer may be correct.
Answer:
PQ = 58
Perimeter = 250
Opposite sides are congruent
Step-by-step explanation:
PQ = 58:
Because PQRS is a parallelogram, PQ equals RS.
1. Set up the equation and solve
7x + 16 = 5x + 28
2x = 12
x = 6
2. Plug in x into PQ
7(6) + 16 = 58
Perimeter = 250:
PQ = RS and QR = SP
1. Add the sides
58 + 58 + 67 + 67 = 250
Opposite sides are congruent:
definition of a parallelogram
A 12 section game wheel has a 25% probability that the pointer will land on green. What is the likelihood that the pointer will land on green
Answer:
I’m not entirely sure what the question is asking but...
The spinner has a 1/4 chance of landing on green
with this, being a 12 section game wheel, it means that 3 of the sections are green.
3x is a ____ of 3x^2 - 6x^3.
Answer:
[tex]\boxed{factor}[/tex]
Step-by-step explanation:
Hey there!
3x * x = 3x^2
3x * 2x = 6x^3
So 3x is a factor of 3x^2 - 6x^3.
Hope this helps :)
1/3(12-6x)=4-2x I need help pls
Answer:
no solution
Step-by-step explanation:
1/3(12-6x)=4-2x
4-1.3x=4-2x
4=4-0.7x
0=0.7x
ns
Determine the intercepts of the line.
y - 4= 7(x – 6)
x-intercept:
y-intercept:
i hope this helppppsss
what do you think would happen to a person if mortor neuron from the grey matter of spinal cord is removed?
Step-by-step explanation:
Introduction
Until World War II, a serious spinal cord injury (SCI) usually meant certain death. Anyone who survived such injury relied on a wheelchair for mobility in a world with few accommodations and faced an ongoing struggle to survive secondary complications such as breathing problems, blood clots, kidney failure, and pressure sores. By the middle of the twentieth century, new antibiotics and novel approaches to preventing and treating bed sores and urinary tract infections revolutionized care after spinal cord injury. This greatly expanded life expectancy and required new strategies to maintain the health of people living with chronic paralysis. New standards of care for treating spinal cord injuries were established: reposition the spine, fix the bones in place to prevent further damage, and rehabilitate disabilities with exercise.
Today, improved emergency care for people with spinal cord injuries, antibiotics to treat infections, and aggressive rehabilitation can minimize damage to the nervous system and restore function to varying degrees. Advances in research are giving doctors and people living with SCI hope that spinal cord injuries will eventually be repairable. With new surgical techniques and developments in spinal nerve regeneration, cell replacement, neuroprotection, and neurorehabilitation, the future for spinal cord injury survivors looks brighter than ever.
Find the length of AC
А
12°
C
B
44
Answer:
9.35
Step-by-step explanation:
Using basic trigonometric ratios,
tan X° = opposite/adjacent
but,X° = 12°
opposite = AC.
adjacent = 44
tan X° = AC/44
AC = tan(12°) × 44
AC = 9.35
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
Astrid needs 280 tons of wood to build ships that can accommodate 2100 sailors
Step-by-step explanation:
Here, in this question, we want to know the amount of wood needed by Astrid to accommodate 2100 sailors.
From the question, we can see that 40 tons are needed to build a ship that can accommodate 300 sailors.
Now, we want to make a calculation for the amount of wood needed for 2100 sailors.
Let’s have it this way;
40 tons = 300 sailors
x tons = 2100 sailors
So mathematically,
x * 300 = 2100 * 40
x = (2100 * 40)/300
x = 280 tons of wood
We can see that 280 tons of wood are needed to build ships that can accommodate 2100 sailors
Answer:
280 tons of wood
Step-by-step explanation:
Khan
I NEED HELP PLEASE FIRST PERSON TO GET ANSWER RIGHT GETS 5 STARS !
Answer:9/5
Step-by-step explanation:
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
15.6 ft²
Step-by-step explanation:
Given:
Radius (r) of circle = 5.7 ft
m<CBD = 55°
Required: Area of the shaded sector
SOLUTION:
Area of shaded sector = θ/360*πr²
Where,
θ = 55°
π = 3.14
r = 5.7 ft
Plug in your values
[tex] Area = \frac{55}{360}*3.14*5.7^2 [/tex]
[tex] Area = \frac{55}{360}*3.14*32.49 [/tex]
[tex] Area = 15.59 [/tex]
Area of shaded sector to nearest tenth = 15.6 ft²
Answer:
unij.,hsakj hdku ugkzsssssssjbfskjgfbskufjbghjbgfhjbghbfkjhbfsdf mdftedtmtedemedeedttfgtubjcufttttttttgxdcgfvcdhfvvvvvdyuyuyuyfyfyfftftftftftyytftfftftffttyfjvhghfhgfghfgfghfhgfghfhgfghfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfhf
Step-by-step explanation:
u suck balls
Using a sample of 60 undergraduates, Dr. Hotchkins discovers a negative correlation between stress and emotional well-being. While looking at a scatterplot of the data, Dr. Hotchkins realizes there are 4 outliers in the data, all for individuals with extremely high scores on stress and extremely high scores on well-being. What is the effect of these outliers on the correlation
Answer and explanation:
A negative correlation means a relationship between two variables whereby each variable affects the other such that an increase in one variable means a decrease in the other and vice versa. This is the situation with the correlation graph/scatter plot of Dr. Hotchkins: An increase in stress would cause a decrease in emotional well being and vice versa
An Outlier is a data point on the scatter plot that does not fall into the pattern of the correlation graph. From the above, 4 points are outliers: extremely high points on stress and emotional well being. These points would affect (increase or decrease) the correlation coefficient depending on where they fall in the pattern. In this case there are 4 outliers out of 60 data points and we know that the more outliers there are the more effect they have on the correlation coefficient and vice versa(also depending on where the outlier is on the scatter plot)
In the figure shown, what is the measure of angle x? (5 points) 115 degrees 130 degrees 145 degrees 150 degrees
Answer:
x=115
Step-by-step explanation:
180 - (115) =65(triangle)
65 + x = 180(on a line)
x=180-65
x = 115
Answer:
115 degrees
Step-by-step explanation:
the person above me is right, but there is an easier way.
Just add 50 and 65 degrees and boom you have your answer.
PLEASE HELP!!! What is factoring? Why is it useful to try to factor out the GCF first when factoring? Explain the relationship between factoring and multiplying polynomials. Give an example to help explain. Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6 . What are the key features needed to graph a polynomial function? Explain how to find these key features to sketch a rough graph of a polynomial function. Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.
Answer:
What is factoring?Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.
Why is it useful to try to factor out the GCF first when factoring?Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .
Explain the relationship between factoring and multiplying polynomials. Give an example to help explainFactoring take away the multiplication, to factorize a polynomial it means take apart what is multiplied. the best example is a²+b²+2ab ( multiplied)
factorize :(a+b)(a+b) take apart what is multiplied
Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6x²-25 =(x+5)(x-5)
3x²-12x-15 = 3(x²-4x-5) GCF=3
3(x-5)(x+1)
x³+2x²+3x+6 (x+2) common factor
(x+2)(x²+3)
What are the key features needed to graph a polynomial function?the key features are the vertex, axis of symmetry, x and y intercept
Explain how to find these key features to sketch a rough graph of a polynomial functionparabola : y=ax²+bx+c
ex: 3x²-12x-15
find vertex (h,k)
h=-b/2a =-(-12)/2(3)=2
k=f(h)=f(2)=3(2)²-12(2)-15
k=12-24-15=-27
vertex=(2,-27)
x intercept is when the graph =0 (y=0)
y intercept when x=0 then y= the constant c and where the graph cross the y axis
axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.
Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.
example from real life:
A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it the length is 4 feet than the width , and the height is 4
solve:
length=W+4
height=1/3 w
V=length* width* height
240=(w+4)(w)(4)
351= 4w²+16w
4w²+16w-240=0
take 4 as common factor
4(w²+4w-60)
now factorize:
4(w-6)(w+10)=0
A factory costs $280,000. You forecast that it will produce cash inflows of $80,000 in year 1, $140,000 in year 2, and $220,000 in year 3. The discount rate is 12%. What is the value of the factory?
Answer:
=$339,627.36
Step-by-step explanation:
PV = FV/(1+R)^n
where
PV = Present Value
FV = Future Value
R = Rate
n = number of periods
PV
Year 1=$80,000
Year 2=$140,000
Year 3=$220,000
r=12%=0.12
Year 1:
PV=80,000 / (1+0.12)^1
=80,000 / 1.12
=$71,428.57
Year 2:
PV=140,000 / (1+0.12)^2
=140,000 / (1.12)^2
=140,000 / 1.2544
=$111,607.14
Year 3:
PV=220,000 / (1+0.12)^3
=220,000 / (1.12)^3
=220,000 / 1.404928
=$156,591.65
Value of the factory= 71,428.57 + 111,607.14 + 156,591.65
=$339,627.36
Find the marked angle P
Answer:
the answer is (d) 57°
Step-by-step explanation:
since it's a straight angle it equals to 180°
you divide 180° from 123°
Which of the following sets represents a function? {(1, 2), (3, 2), (5, 7)} {(3, 5), (-1, 7), (3, 9)} {(1, 2), (1, 4), (1, 6)}
Answer:
{(1, 2), (3, 2), (5, 7)}
Step-by-step explanation:
A function has a one to one correspondence
Each x can go to only 1 y value
{(1, 2), (3, 2), (5, 7)} function
{(3, 5), (-1, 7), (3, 9)} 3 goes to more than 1 y value
{(1, 2), (1, 4), (1, 6)} 1 goes to more than 1 y value
Answer:
[tex]\huge \boxed{ \{(1, 2), (3, 2), (5, 7)\} }[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex]\{(1, 2), (3, 2), (5, 7)\} \ \sf represents \ a \ function.[/tex]
[tex]\{(3, 5), (-1, 7), (3, 9)\} \ \sf does \ not \ represent \ a \ function.[/tex]
[tex]\{(1, 2), (1, 4), (1, 6)\} \ \sf does \ not \ represent \ a \ function.[/tex]
The sum of the cubes of 3 numbers which are in the ratio 1:2:3 is 7776. Find the numbers
the numbers - [tex]x,2x,3x[/tex]
[tex]x^3+(2x)^3+(3x)^3=7776\\x^3+8x^3+27x^3=7776\\36x^3=7776\\x^3=216\\x=6\\2x=12\\3x=18[/tex]
6,12,18
The amount of juice in a container is
normally distributed with a mean of
70 ounces and a standard deviation of
0.5 ounce. What is the probability that a
randomly selected container has more
than 70.5 ounces of juice?
Answer:
0.15866
Step-by-step explanation:
To solve for the above question, we use z score formula
z = (x - μ) / σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
x is the raw score = 70.5
μ is the population mean = 70
σ is the population standard deviation = 0.5
z = 70.5 - 70/ 0.5
z= 0.5/0.5
z = 1
We used the z score table to find the probability of z = 1
P( x = z) = P(x = 70.5)
= P( z = 1) = 0.84134
Hence, the probability that a randomly selected container has more than 70.5 ounces of juice is calculated as
P(x>70.5) = 1 - P(x =70.5)
P(x>70.5) = 1 - 0.84134 = 0.15866
Therefore, the probability that a randomly selected container has more than 70.5 ounces of juice is 0.15866.
Please help, 50 points! :)
PDF attached below
Answer:
See below
Step-by-step explanation:
Attachment 1 : (a) Remember that it mentions x is the years since 1900. That would mean that the table is a bit different. To create this " new table " simply subtract 1900 from the years provided, and substitute.
To create this equation we will need a regression calculator. The equation will be as follows.
y = 0.125873x - 7.11916 ( note that you can double check this equation be substituting points from the table in the attachment )
(b) 2025 - 1900 = 126 years,
y = 0.125873(125) - 7.11916 = $ 8.614965
Minimum Wage : $ 8.614965
Attachment 2 : The rest of the problems can be solved similarly...
(a) Quadratic Regression Equation : - 0.49311x² + 23.2798x + 996.029
(b) - 0.49311(20)² + 23.2798(20) + 996.029 = 1264.381 mg/cm³
Attachment 3 : (a) Exponential Regression : 9.08292(1.09965)ˣ
(b) 9.08292(1.09965)⁶⁰ = [tex]2713.27743\dots[/tex] ( About 2713 recommendations )
what's 700.00divided by 120
Answer:
[tex]\Large \boxed{\frac{35}{6} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{700}{120}[/tex]
Reduce and simplify the fraction to lowest terms.
[tex]\displaystyle \frac{20(35)}{20(6)}[/tex]
[tex]\displaystyle \frac{35}{6}[/tex]
Jasmine is having friends over to watch a football game. She has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. How much time does Jasmine spend preparing snacks?
Answer:
1 Hour and 30 Minutes
OR
1 1/2 Hours
Step-by-step explanation:
Convert 2 1/2 hours to minutes.
That is 150
Multiply 2/5 with 150.
Subtract that from 150.
It gives 120 minutes.
Convert that back to Hours.
You get 1 Hour and 30 Minutes or 1 1/2 Hours.
A fraction is a way to describe a part of a whole. The time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
What is a Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
Given that Jasmine has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. Therefore, the time spent on preparing snacks is,
Time spent on preparing for snacks = 2 1/2 - 2/5
= 5/2 - 2/5
= 2.5 - 0.4
= 2.1 hours
= 2 1/10
Hence, the time that is spent by Jasmine to prepare for snacks is 2.1 hours or 2 1/10 hours.
Learn more about Fraction:
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please this is urgent
Answer:
i can only do the question no 1, 5 ,6, 7
hope it'll help you and my answers are correct
:)
Two Fair six-sided dice are rolled and the face values are added. What is the probability of obtaining an even number less than 7?
Answer:
The probability is 1/4
Step-by-step explanation:
In this question, we are interested in calculating the probability of obtaining even numbers which are less than 7, when two fair six-sided dice are rolled.
Now, mathematically the probability will be;
number of even numbers less than 7/total number of outcomes
Firstly, the total number of outcomes is 36. Now to get the number of even numbers less than 7, we need to construct tables that could show our sample space.
Please check attachment for this.
Now from the constructed table, we can find the number of even numbers less than 7.
By counting, we can see that the we have 9 even numbers which are less than 7
Thus, the probability of selecting an even number which is less than 7 is;
9/36 = 1/4
PLEASE HELP
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity.
Answer:
h,k,i,m,g,l
Step-by-step explanation:
I did all the work and i(x) limt should = -.25 and k(x) =0 but it said it was wrong. f(x) and j(x) cant be used, so my guess is to switch i(x) and k(x)
The answer is given in the image below.
Do all functions have limits?One of the fundamental standards of calculus is limits (limits of a function); it offers the fee of a function at a particular factor called limit. Limits are used to calculate the exact vital of the function. Not all functions include limits. A few functions no longer have any restrictions as the variable has a tendency to infinity.
What are examples of nonfunctions?The equations y = ± x and x 2 + y 2 = 9 are examples of non-function due to the fact there is at least one -price with or greater -values.
Learn more about Limits here: https://brainly.com/question/251701
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Find the measure Of PR
Answer:
18
Step-by-step explanation:
The formula for this is a x b = c x d where a is SR, b is FR, c is QR and d is PR. This will give us the equation 9(16) = 8(5x + 8); 144 = 40x + 64; 80 = 40x; x = 2. Now, plug this into PR which will be 5(2)+8 = 18. This is your answer.