Help would be much appreciated! :)
Answer:
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4} = x^2 + 5x - 4 + \frac{3x - 8}{x^2 + 5x - 4}[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
ExpandingAlgebra II
Polynomial Division
Long DivisionSynthetic DivisionStep-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4}[/tex]
Step 2: Long Division
See attachment.
Multiply quotient a and divisor, then subtract from dividend: [tex]\displaystyle x^2(x^2 + 5x - 4) = x^4 + 5x^3 - 4x^2 \leftarrow \text{red 1}[/tex]Multiply quotient b and divisor, then subtract from new dividend: [tex]\displaystyle 5x(x^2 + 5x - 4) = 5x^3 + 25x^2 - 20x \leftarrow \text{red 2}[/tex]Multiply quotient c and divisor, then subtract from new dividend: [tex]\displaystyle 4(x^2 + 5x - 4) = 4x^2 + 20x - 16 \leftarrow \text{red 3}[/tex]Write remainder: [tex]\displaystyle \frac{r(x)}{b(x)} = \frac{3x - 8}{x^2 + 5x - 4}[/tex]Please excuse the bad handwriting.
Suppose that Juan can choose to get home from work by car or bus.
When he chooses to get home by car, he arrives home after 7 p.m. 14 percent of the time.
When he chooses to get home by bus, he arrives home after 7 p.m. 62 percent of the time.
Because the bus is cheaper, he uses the bus 83 percent of the time.
What is the approximate probability that Juan chose to get home from work by bus, given that he arrived home after 7 p.m.?
Using conditional probability, it is found that there is a 0.9556 = 95.56% probability that Juan chose to get home from work by bus, given that he arrived home after 7 p.m.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Arrived home after 7 p.m.Event B: Got home by bus.The percentages associated with arriving home after 7 p.m. are:
14% of 17%(by car).62% of 83%(by bus).Hence:
[tex]P(A) = 0.14(0.17) + 0.62(0.83) = 0.5384[/tex]
The probability of both arriving home after 7 p.m. and using bus is:
[tex]P(A \cap B) = 0.62(0.83)[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.62(0.83)}{0.5384} = 0.9556[/tex]
0.9556 = 95.56% probability that Juan chose to get home from work by bus, given that he arrived home after 7 p.m.
You can learn more about conditional probability at https://brainly.com/question/14398287
Some people use this rule to work out
how many hours' sleep each night
young children need.
tract the child's age in years from 30,
ten divide the result by 2
Sanjay is 8 years old.
Use the rule to work out how many
hours' sleep he needs.
Jaycee and Tyler are selling candy bars for a school fundraiser. Rylee sold 84 candy bars and raised 210$. If Jaycee raised 70$ how many candy bars did he sell?
Answer:
28 bars because 84/3 = 28
Step-by-step explanation:
Four friends went to dinner. They each ordered a meal and decided to split the final bill evenly between them. They left a tip of $12. The final cost of the meal and tip was $74.00. what was the price each person paid for their meal before tip?
AGAIN BE SERIOUS THIS IS DUE TOMORROW
3 2/9 x -1 5/7 make an improper fraction, multiply, then make it a simplified mixed number.
Answer:
-145/63
Step-by-step explanation:
Easy way to do decimal multiplication.
Answer:
first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Step-by-step explanation:
Natalie walked 35 mile in 12 hour. How fast did she walk, in miles per hour?
a. 3/10 mile per hour
b. 5/6 mile per hour
c. 1 1/5 miles per hour
d. 2 miles per hour
Answer:
almost 3 mph so I'm guessing (d) is the answer
Step-by-step explanation:
35 ÷ 12 = 2.9 miles per hour
pls help asap! i will mark brainliest!
Answer:
19 or 17
Step-by-step explanation:
I need help...........
Answer:
D. 62 1/4 inches
Step-by-step explanation:
Convert 3 1/2 to 3 2/4 so the denominator is 4. Then add that to 58 3/4 inches and you get 62 1/4.
Hope this helps!
Explain how to apply the substitution property of equality to the equation
a
+
42
=
b
if
a
=
−
16
and
b
=
26
.
Answer: Substitute the values given. The equation is a + 42 = b. Since a = -16 and b = 26, the equation will become -16 + 42 = 26. This equation holds true so it is correct.
Would appreciate brainliest <3
A rectangle has an area of 888 square centimeters.
Which of the following could be the rectangle's length and width?
Answer:
i think 222 for eatch side
Step-by-step explanation:
Work out the mean for the data set below:
3.4, 5.2, 4.7, 3.5, 0.5
Give your answer as a decimal.
Answer:
3.4 + 5.2 + 4.7 + 3.5 + 0.5
= 17.3
There are a total of 5 numbers
17.3 / 5
= 3.46
What is the measurement of this angle?
Answer:
54°
Step-by-step explanation:
All the angle measures of a triangle must add up to equal 180°. So,
59°+67°+x°=180°
x=54°
7/9 - 2/8 x 49 in simplest form
Answer:
7/9 - 2/8 x 49
First, according to BODMAS we will solve multiplication7/9 - 2/8 x 49 = 7/9 - 49/4= -61/12Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
When playing a game of capture the flag how would a player best position themselves from being tagged and placed in the jail?
On their own team's side of the center line
On their opponent's side of the field, nearest the flags
Near the center line so they can move back and forth between the two sides
Near the back corner of the opponents flag area
Answer:
Near the center line so they can move back and forth between the two sides
Step-by-step explanation:
Cristian comió un 3/8 de pizza y Adriana comió 1/4 de la misma pizza. ¿Quién comió mas?
What is the greatest common factor of 15, 35, and 10?
Answer: The GCF of 10, 15, and 35 is 5.
Would appreciate brainliest <3
Answer:
5.
Step-by-step explanation:
First, we write them in prime factor form, then pick out the common factors.
15 = 3*5
35 = 5*7
10 = 2*5
So the GCF is 5.
what is the common denominator 4/15 and 1/3? Need answers ASAP
Answer:
15
Step-by-step explanation:
To find the common denominator we look for the LCM
15: 15,30,45,60
3: 3,6,9,12,15
Our LCM is 15
Meaning our LCD is 15
Brainliest please :)
What is an equation of the line that passes through the points (6,-3) and (-6,-5)
Answer:
y = 6x - 4
Step-by-step explanation:
I drew a graph slope formula is (y2 - y1)/(x2 - x1) and if the line passes through a point that is not zero (in this case it does) we add or subtract that as the y-intercept. we recently passed this so I know it.
Slope-intercept form: (y = mx + b) y = 6x - 4
Standard form: (Ax + By = C) -6x + y = -4
Point-slope form: (y - y1 = m (x - x1)) (let's use the point (6, -3)) y + 3 = 6 (x - 6)
Tell me if I'm wrong :)
Answer:
Step-by-step explanation:
Bu using the formula of Two-Points form:
[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2}-x_{1} }[/tex]
Substitute the points in the above equation:
y+3/-5+3=x-6/-6-6
y+3/-2=x-6/-12
-12(y+3)=-2(x-6)
-12y-24=-2x+6
2x-12y-24-6=0
2x-12y-30=0
Or
x-6y-15=0
If you need to ask any question,let me know.
Alexa is y years old. Nate is 22 years old, and Alexa is one-half Nate's age Which equation shows an equality between two different ways of expressing Nate's age? OA) 22 = 2y OB) 22 = 2 + y OC) 22==y - 22 OD 22 = y2
Answer:
A. is the correct answer
Step-by-step explanation:
Stay safe.
Please help me with this!! - Solve: 5 - 2x < 7
A) x < -1
B) x > -1
C) x < -12
D) x > -12
Answer:
B
Step-by-step explanation:
A jar contains 6 red marbles numbered 1 to 6 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event.
Answer:
Step-by-step explanation:
a)
p
(
red marbles
)
=
6
6
+
8
p
(
red marble
)
=
3
7
b)
p
(
o
d
d
n
u
m
b
e
r
s
)
=
3
+
4
6
+
8
p
(
o
d
d
n
u
m
b
e
r
s
)
=
1
2
c)
p
(
red marbles or odd numbers
)
=
p
(
red marbles
)
+
p
(
odd numbers
)
−
p
(
red marbles and odd numbers
)
p
(
red marbles or odd numbers
)
=
6
14
+
7
14
−
3
14
p
(
red marbles or odd numbers
)
=
10
14
d)
p
(
Blue marbles or even number
)
=
p
(
Blue marbles
)
+
p
(
even numbers
)
−
p
(
blue marbles and even numbers
)
p
(
Blue marbles
)
=
8
14
p
(
even numbers
)
=
7
14
p
(
Blue marbles or even number
)
=
8
14
+
7
14
−
4
14
p
(
Blue marbles or even number
)
=
11
14
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What is Probability in Math? - Definition & Overview
from
Chapter 24 / Lesson 7
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The formula of probability is possible choices over the total number of options. Discover the definition of probability and get an overview of its calculation and application in math.
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4. What are deductions?
A.)the amount of money added to the gross pay for commission-based sales
B.)the amount of money included with tips
C.)the amount of money subtracted from the gross pay earned for things like taxes, medical benefits, and retirement benefits
D.)incentives employees earn for the amount sold
Answer:
C.) the amount of money subtracted from the gross pay earned for things like taxes, medical benefits, and retirement benefits
Step-by-step explanation:
Answer:
the answer is C.) the amount of money subtracted from the gross pay earned for things like taxes, medical benefits, and retirement benefits
Which expression shows the distance on the number line between −7 and 16?
∣∣−7+16∣∣
∣∣−7−16∣∣
∣∣−16−(−7)∣∣
∣∣7−16∣∣
Answer:
c
Step-by-step explanation:
Hope this helps
Brainliest pls
Have a great day!
Which of the following is the difference of two squares

4g-16h
16a^2-4y^2
2x^2-4y^2
25m^3+100n^2
Answer:
2nd option
Step-by-step explanation:
A difference of squares has the general form
a² - b²
where the terms on either side of the subtraction ( the difference ) are both perfect squares.
The only one fitting this description is
16a² - 4y²
= (4a)² - (2y)² ← difference of squares
0.125 ultiply by 1000
Answer:
125 is answer .........:)
what is the answer because i need help with it
Josh will take 10 test in 5 weeks at school how many test will he have taken after 7 weeks
Answer:14
Step-by-step explanation:
He takes 2 a week so 2 times 7 is 14
Which expression is equivalent to 1/2(4x+8)? Answer choices: A. x + 4 B. 2x+4 C. 2x+8 D. 4x+4. Please provide explanation as well!
each of the 17 gorillas at the nature preserve eats 45 pounds a food a day. write an expression that models the amount of food all of the gorillas eat in a day. then evaluate the expression to find how much food they eat
Answer:17x 45=765 pounds
Step-by-step explanation:
All you have to do is multiply.
If each gorilla eats 45 pounds then you multiply amount of gorilla by pounds of food , in this case 17x 45