Step-by-step explanation:
\underline{\textsf{Given:}}
Given:
\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx
3
+7x
2
+7x−15
\underline{\textsf{To find:}}
To find:
\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx
3
+7x
2
+7x−15
\underline{\textsf{Solution:}}
Solution:
\textsf{Factor theorem:}Factor theorem:
\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}
(x−a)isafactorP(x)⟺P(a)=0
\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x
3
+7x
2
+7x−15
\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0
\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)
\mathsf{When\;x=-3}Whenx=−3
\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)
3
+7(−3)
2
+7(−3)−15
\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15
\mathsf{P(-3)=63-63}P(−3)=63−63
\mathsf{P(-3)=0}P(−3)=0
\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor
\mathsf{When\;x=-5}Whenx=−5
\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)
3
+7(−5)
2
+7(−5)−15
\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15
\mathsf{P(-5)=175-175}P(−5)=175−175
\mathsf{P(-5)=0}P(−5)=0
\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor
\underline{\textsf{Answer:}}
Answer:
\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x
3
+7x
2
+7x−15=(x−1)(x+3)(x+5)
\underline{\textsf{Find more:}}
Find more:
Which expression is equivalent to 5(x + 7)?
Answer:
5x+35
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
5th Grade Science Very Easy plz help me :3 NO LINKS
What makes a balloon electrically charged?
Adding more air to the balloon
Placing the balloon against a wall
Rubbing the balloon against your hair
Running water over the balloon
Answer:
rubbing it against your hair it causes friction and with friction comes energy
Which table of values represents possible solutions to
the equation y = 0.7x - 4.3?
х
49
у
30
X y
49 40
19 19
-11-12
-31-16
19 19
-11-12
-31 -26
B
Х
у
30
49
19 9
-11-12
-31 -26
Х
у
49 40
19 19
-11 -2.
-31 -16
D
Step-by-step explanation:
it will be c as shown in the photo
PLZ answer correctly! Brainliest!
Answer:
[tex]A=\left(-1\dfrac{5}{5}\right)=(-2)\\\\B=\left(-\dfrac{4}{5}\right)\\\\C=\left(\dfrac{3}{5}\right)[/tex]
Step-by-step explanation:
Look at the picture.
[tex]\dfrac{2}{10}=\dfrac{1}{5}[/tex]
what is c3 - 1 when c = 4
Determine if the sequence is geometric . If it is , find the common ratio , the explicit formula and the recursive formula .
1. -40 , 20 , -100 , 500
2. 4 , 20 , 100 , 500
3. 4 , 24 , 144, 864
5. 3 , -12 , 48 , -192
Step-by-step explanation:
if it is a geometric sequence, then
sn = sn-1 × r
with r being the common ratio.
1.
s2 = s1 × r
20 = -40 × r
r = 20/-40 = -1/2
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
-100 = 20 × -1/2 = -10
this is wrong, so, it is not geometric.
2.
s2 = s1 × r
20 = 4 × r
r = 20/4 = 5
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
100 = 20 × 5 = 100
s4 = s3 × r
500 = 100 × 5 = 500
this is all correct, so, it is geometric.
sn = sn-1 × 5
sn = s1 × 5^(n-1) = 4 × 5^(n-1)
3.
s2 = s1 × r
24 = 4 × r
r = 24/4 = 6
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
144 = 24 × 6 = 144
s4 = s3 × r
864 = 144 × 6 = 864
this is all correct, so, it is geometric.
sn = sn-1 × 6
sn = s1 × 6^(n-1) = 4 × 6^(n-1)
5.
s2 = s1 × r
-12 = 3 × r
r = -12/3 = -4
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
48 = -12 × -4 = 48
s4 = s3 × r
-192 = 48 × -4 = -192
this is all correct, so, it is geometric.
sn = sn-1 × -4
sn = s1 × (-4)^(n-1) = 3 × (-4)^(n-1)
How ur wants to get a car loan with 4% simple interest rate. If the car costs $25,000, how much would Howie need to pay back at the end of one year, including the interest?
The amount Howie need to pay back at the end of one year, including the interest is $26,000
Given:
Interest rate = 4%
Cost of car = $25,000
Time = 1 year
Amount of interest = Principal × Rate × Time
= 25,000 × 4% × 1
= 25,000 × 0.04 × 1
= $1,000
Amount to be paid = Amount of interest + Cost of car
= 1,000 + 25,000
= $26,000
Therefore, the amount Howie need to pay back at the end of one year, including the interest is $26,000
Learn more about interest rate:
https://brainly.com/question/1115815
The amount that Howie would need to pay back at the end of one year, including the interest for a car loan of $25,000 is $26,000.
What is simple interest?Simple interest is a finance charge that does not compound. It is calculated on the principal portion of a loan only.
The formula for computing simple interest is Principal x APR x Number of years.
Data and Calculations:Car loan = $25,000
Simple interest rate = 4%
Period of loan = 1 year
Principal + Interest for 1 year = $26,000 ($25,000 x 4% x 1).
Thus, the amount that Howie would need to pay back at the end of one year, including the interest for a car loan of $25,000 is $26,000.
Learn more about simple interests at https://brainly.com/question/25793394
Use the slope formula to determine the slope of the line containing the two points (4,-8) and (-1,-2)
the slope is 6/-5
subtracting the y values gives you -2-(-8)=6
subtracting the x values gives you -1-4= -5
Given:-
Two points (4,-8) and (-1,-2) .To find :-
The slope of the line through these points .Solution :-
As we know that the slope is ,
[tex]\longrightarrow\sf Slope = y_2-y_1/x_2-x_1[/tex]
Substitute the values ,
[tex]\longrightarrow[/tex] Slope = -8 -(-2) / 4 -(-1)
[tex]\longrightarrow[/tex] Slope = -8 +2/4 + 1
[tex]\longrightarrow[/tex] Slope = 6/5
Hence the slope of the line is 6/5 .
Tessa feeds her dog,Roscoe 3 3/4 cups of dog food per day.if she buys a bag of food that contains 165 cups, how many days will the bag last?
HELP PLEASE!! WILL GIVE BRAINLIEST TO CORRECT QNSWER.
Use the quadratic formula to find the solution to the quadratic equation given below.
x²-x+¼=0
Solve the linear system using elimination.
46) -2x+4y=-2
6x - y=28
Answer:
x = 5, y = 2
Step-by-step explanation:
just trust me, I used a calculator
An 80 ounce bottle of apple juice contains 32 ounces of water and 64 ounce bottle of orange juice has 48 ounces of water which juice has a greater percent of water?
round 3,817,453 to the nearest 100
Answer:
The nearest hundredth would be 3,817,500
Step-by-step explanation:
The hundreds place is the four and the five behind it rounds the number to a up to a 5
A bag contains three green marbels and eight white marbels. suppose in marble is randomly selected. what are the odds in favor of picking a white marble?
A. 8 to 3
B. 8 to 11
C. 3 to 8
D. 3 to 11
Answer:
A. 8 to 3
Step-by-step explanation:
since its in favor, the amnt of white marbles goes first.
HELP!!
Name the property below
(2+7) +3= 2+(7+3)
A. associative
B. Commutative
2^x+2=4. yall i got this problem and i dont rlly understand how to do it. Hope yall can help me:)))))))))))))))
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Ok, so we start off with [tex]2^x+2=4[/tex]
Then, we subtract 2 from both sides so that becomes: [tex]2^x+2-2=4-2[/tex]
After that, we simplify to get: [tex]2^x=2[/tex]
Finally, the solution becomes: [tex]x=1[/tex]
Answer:
x=1
Step-by-step explanation:
2^x=4-2
2^x=2
2^x=2^1
x=1
If f(x) = 4x2 + 2x + 7, find the value of f(-5).
=
A. -103
B. -83
C. 97
D. 117
Writing
Tammy bought some books. She spent a total of $45 after a discount of S6 off of her total purchase. Each book cost $3. How many books did she buy?
(a) Write an equation that could be used to answer the question above.
First, choose the appropriate form. Then, fill in the blanks with the
numbers 45, 6, and 3. Let b represent the number of books.
X
5
o 16+ = 0
(b) Solve the equation in part (a) to find the number of books.
b = 0
Answer:
b=17
Step-by-step explanation:
b=(45+6)/3
b=51/3
b=17
she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.
Does 28/4 have a remainder
Remainder=0
Quotient=7
Thanks!!
find the mean of 100
Answer:
100.
Step-by-step explanation:
100 + 0 = 100
100 ÷ 1 = 100
Using the formula F = 9/5 C + 32, convert 25° Celsius (C) to
degrees Fahrenheit (F).
A.) 57°
B.) 77°
C.) 257°
D.) 269.5
Answer:77°
Step-by-step explanation:
Since we are trying to convert Celsius to Fahrenheit, we just need to replace C in the equation with the value of 25°.
[tex]F=\frac{9}{5}C+32[/tex]
[tex]F=\frac{9}{5}25+32[/tex]
[tex]F=45+32[/tex]
[tex]F=77[/tex]
The answer is 77°
The sum of a number times 7 and 15 is at least -19
Answer:
x(7+15) [tex]\leq[/tex] -19
Step-by-step explanation:
Okie help help math math math math
Answer: 33
Step-by-step explanation: In the problem, you are given the figure with the following:
2x+3 and 3x+12
Method: Lets set this into an equation. Remember that straight lines add up to 180°.
2x+3+3x+12=180° Combine like terms.
5x+15=180°
5x=165°
x=33°
You can always plug in 33° in the expression that was set to make sure it does give you 180°.
Hope this helps.
Answer:
33
Step-by-step explanation:
Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.75 miles she bikes. If Emily bikes 24 miles, how much will her mother donate?
Answer:
4 dollars and 80 cents
Step-by-step explanation:
24 times 20 is 480 but its money so u would say $4.80.
the price of a stock rose from a yearly low of $9.68 to $18.61. what was the stock percent increase from its low price that year?
please help me, thankyou
Answer:
From the time Ms. Cruz purchased a stock till closing time that day, the value of the stock changed by -27.2 points. During that time, the stock value
changed at a steady rate of -6.4 points per hour.
Find the slope of the line that goes through the points (-4,4) and (4,6)
Answer:
1/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-4)/(4-(-4))
m=2/(4+4)
m=2/8
m=1/4
Find the slope of the line that passes through the given points. (4, - 3) and (9. - 7) Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The slope is (Type an integer or a simplified fraction.) O B. The slope is undefined.
Answer:
-4/5
Step-by-step explanation:
Answer: A. -4/5
Step-by-step explanation:
Slope Formula: y2 - y1 / x2 - x1
-7 - (-3) = -4
9 - 4 = 5
slope = -4/5
Correct me if I am incorrect.
An online survey asked a sample of high school students their favorite type of music, and the results were tabulated above. Find the probability that a person chosen at random did not choose pop music, given that the student is a sophomore or a junior.
Answer:
87/103
Step-by-step explanation:
I been on this for days and no one can give me a right answer
Answer:
2x²=6x-5= x=3+i/2
-x²-10x=34= x = -(5+3i)
Step-by-step explanation: 2x²=6x-5 and -x²-10x=34 are the answers
Nolan flipped his lucky coin 13 times and got 8 heads. Nolan used these numbers to estimate the probability of getting a head with his lucky coin. What is the estimated probability of Nolan flipping a head with his lucky coin
Answer:
8/13 = 0.615
Step-by-step explanation:
Nolan is only using these numbers, not actual probabilities, to formulate his results. Therefore, only using these numbers, there is an 8/13 chance of Nolan flipping a head with his lucky coin, as he flipped heads 8/13 times.
Answer:
13 time /8 head
= 8/ 13
= 0.615
