The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))
How to carry out Polynomial Long Division?
We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.
4x² + 3x - 8
-------------------------
3x - 1 | 12x³ + 5x² - 27x + 13
- 12x³ - 4x²
-----------------------------
9x² - 27x
- 9x² - 3x
-----------------------------
-24x + 13
- -2x + 8
-----------------------------
5
-----------------------------
Expressing the solution of the polynomial division in the given quotient and remainder form gives us; 4x² + 3x - 8 + (5/(3x - 1))
Read more about Polynomial Long division at; https://brainly.com/question/25289437
#SPJ1
three times the sum of a number and seven is greater than five times the number less thirteen in a equation
3) -7y + 9 = 3y + 49
Answer:
y = -4
Step-by-step explanation:
first add 7y to both sides
9 = 10y + 49
second subtract 49 from both sides
-40 = 10y
flip it
10y = -40
now divide both sides by 10
y = -4
that is your answer
Answer: 7y+9=3y+49
We move all terms to the left:
-7y+9-(3y+49)=0
We get rid of parentheses
-7y-3y-49+9=0
We add all the numbers together, and all the variables
-10y-40=0
We move all terms containing y to the left, all other terms to the right
-10y=40
y=40/-10
y=-4
Select whether the model is an angle of elevation or an angle of dep270 ITCMathBits.comB
Explanation:
The term angle of depression is defined as the angle from the horizontal line downward to an object. An observer's line of sight would be below the horizontal.
For angle of elevation, an observer's line of sight would be above the horizontal.
According to the diagram shown; The diagram with angle 27degrees models angle of depression while that of angle 25 degrees models an angle of elevation.
ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved.
The probability that three parents are involved" in making decisions about their underage child’s healthcare treatment is 0.7787.
What is probability?It should be noted that probability simply means the likelihood that something will happen.
In this case, ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions.
The probability of the involvement of the three parents will be:
= P(involvement)³
= (92%)³
= 0.92 × 0.92 × 0.92
= 0.7787
Learn more about probability on:
brainly.com/question/25870256
#SPJ1
Ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved. Find the probability that three parents are involved" in making decisions about their underage child’s healthcare treatment,
Solve the compound inequality.
- 3x≤ - 9 or 5x-18 ≥ 12
Answer:341623456245
Step-by-step explanation:78325687345
Kyle invests $600 which earns 3% annual simple interest for 5 years Use A(t)=P (1+rt) to determine how much money he will have after 5 years. Interpret the rate of change in this situation
The amount of money that Kyle will have after 5 years is $690.
How to calculate the interest?From the information, Kyle invests $600 which earns 3% annual simple interest for 5 years.
The formula for the amount is given as:
A(t)=P (1+rt)
where P = principal = $600
R = rate = 3%
T = time = 5 years
This will be:
A(t)=P (1+rt)
A = 600 [ 1 + (3% × 5)]
A = 600 (1 + 0.15)
A = 600(1.15)
A = 690
The amount is $690.
Learn more about money on:
brainly.com/question/24373500
#SPJ1
Choose the answer that best completes the sentence.
-2 - √3i is a known root not a possible root, option 4 will be the correct answer.
What are real and imaginary roots ?
A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.
In other words real roots can be represented in a number line where as imaginary roots can not.
Here, the given root is -2 + √3i :
It is known that the complex roots comes in pairs that is in form a ±ib, where, a is real part of imaginary root and b is imaginary part.
Therefore, the other root will be -2 - √3i.
So, -2 - √3i is a known root not a possible root, option 4 will be the correct answer.
To learn more about the complex roots visit:
https://brainly.com/question/18303711
#SPJ1
Use the equality to find the ratio a : b . a/5=b/7
during december the average daily temperature in a town is -1.7.the average daily temperature in the same town is 3.2 lower in january what is the average daily temperature in january?
Answer:
the average daily temperature in January is -4.9
Make a table of ordered pairs for the equation.
y=-1/3x+1
show steps and pic of the quiz graph pls!
The ordered pairs (-3, 2), (0, 1), (3, 0), and (6, -1) for the equation y = -1/3x+1 which satisfies the equation.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation:
y = -1/3x+1
When substituting the value x = -3, then get the value of y = 2
When substituting the value x = -0, then get the value of y = 1
When substituting the value x = 3, then get the value of y = 0
When substituting the value x = 6, then get the value of y = -1
The table of ordered pairs for the given equation y = -1/3x + 1.
x y
-3 2
0 1
3 0
6 -1
The required graph has been attached below which represents the given equation.
Therefore, the ordered pairs (-3, 2), (0, 1), (3, 0), and (6, -1) for the equation y = -1/3x+1 which satisfies the equation.
Learn more about the graph here:
brainly.com/question/16608196
#SPJ1
Find the equation of the line that passes through (-3,1) and is parallel to
y
=
4
−
3
x
.
Leave your answer in the form
y
=
m
x
+
c
Answer:
y=3x-5
Step-by-step explanation:
parallel lines have the same slope
the probability that a fair die falls on 6 is 1/6. however, if that fair die is one of two dice, and you know that the sum of the two dice is 12, then the probability that the fair die fell on 6 is ?
Answer:36
Step-by-step explanation:
1/6 is 6
so we need to find 6/6 which would be 6×6=36
Question 5(Multiple Choice Worth 1 points)
(01.05 LC)
What is the converse of the following statement?
"If the shoes are clean, then the shoes are new."
O If the shoes are not clean, then the shoes are not new.
O If the shoes are clean, then the shoes are not new.
O if the shoes are not new then the shoes are not clean.
O If the shoes are new, then the shoes are clean.
The converse of the statement on shoes being clean and new is If the shoes are new, then the shoes are clean.
How to write a converse statement?When converting a statement that involves two clauses to a converse statement, you should exchange the position of the two clauses to make a converse statement.
This means that if you had a statement as (if a then b) the converse statement is (if b than a). The statement, "If the shoes are clean, then the shoes are new" would then be "If the shoes are new, then the shoes are clean."
Find out more on converse statements at https://brainly.com/question/28396750
#SPJ1
what is (x squared -4x+3)-(3x squared -3x -5)
Is the equation a true statement when x = 3? In other words, is 3 a solution to theequation?7x – 5 = 23 + 10A. Yes, 3 is a solution.B. No, 3 is not a solution.
SOLUTION:
Case: Simple equation
Given:
7x – 5 = 23 + 10
Required:
Is the equation a true statement when x = 3?
Method:
Step 1: Rewrite the equation
7x – 5 = 23 + 10
Step 2: Plug the value x= 3 into the equation
7x – 5 = 23 + 10
7(3) - 5 = 33
21 - 5 = 33
16 is not equal to 33
Final answer:
B. No, 3 is not a solution.
In the figure below, points D, E, and F are the midpoints of the sides of ABC. suppose DF =34, AC =48, and BC =78. find the following lengths.
For any given Triangle ABC, its medial triangle is constructed by finding the midpoints of its three sides (Segments AB, BC, and AC) and constructing segments to join these midpoints.
An important property of the medial triangle is that it divides the original triangle into four smaller, congruent triangles that are each similar to the original triangle.
With this in mind we now that the four triangles are congruent. Then:
[tex]CF=DE[/tex]but we know that CF is half of BC, then:
[tex]DE=\frac{78}{2}=39[/tex]From the figure we also notice that:
[tex]\begin{gathered} BE=DF \\ BE=34 \end{gathered}[/tex]Ans that AB is twice BE, then
[tex]AB=68[/tex]Summing up we have:
[tex]\begin{gathered} DE=39 \\ AB=68 \\ BE=34 \end{gathered}[/tex]Jason is in the business of manufacturing phones. He must pay a daily fixed cost of $500 to rent the building and equipment, and also pays a cost of $150 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Total cost of phone in a day $650
What is Algebra ?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Total cost of rent in a day = $500
Total cost of per phone = $150
The equation which represents values in term of c:
150p + 500 = C
The total cost he had in a day :
= 150 + 500
= $650
Hence, the total cost throughout the day is $650
To learn more about Algebra click on the link
https://brainly.com/question/22399890
#SPJ9
Your hotel has been reviewed on yelp 10 times you received the following ratings 4,5,5,3,5,4,2,3 what is your overall rating
The overall rating is 31 and the average rating is 3.8.
What is average?A large number of data points are reduced into a single value using averages. It is a visual depiction of all the data set's available numbers. The average is derived by adding up all the data values and dividing them by the total number of data points.
The word "average" is used in many different contexts in daily life. The average is computed and a single value is used to represent the values for quantities with fluctuating values.
Overall rating = 4+5+5+3+5+4+2+3
Overall rating = 31
Average rating = Overall rating/ Total number of ratings
= 31/8
= 3.8
To learn more about the average, visit :
https://brainly.com/question/24057012
#SPJ13
ANSWER QUICK I WILL GIVE BRAINLIEST
Solve 3x + 2 = 5.
A) x = 1
B) x = 2
C) x = 3
D) x = 4
Answer:
x = 1
Step-by-step explanation:
3x + 2 = 5
3x + 2 - 2 = 5 - 2
3x = 3
3x/3 = 3/3
x = 1
Hope this helps! :)
Answer:
I think it's A, hope this helps
If you wanted to take a simple random sample for a study on screen time in elementary school students in your town, which describes the sample you would ask?
twenty students from one elementary class in your town
twenty students from each elementary school in your town
twenty students that are friends from an elementary school in your town
twenty students that are friends from each elementary school in your town
The option that describes the sample you would ask is A. twenty students from one elementary class in your town.
What is a simple random sampling?It should be noted that a simple random sampling simply means a form of sampling whereby everybody has an equal chance of being selected.
In this case, it should be noted that the person wanted to take a simple random sample for a study on screen time in elementary school students in the town. Therefore, twenty students can be chosen to illustrate this.
Learn more about sample on:
brainly.com/question/24466382
#SPJ1
6. There are 45 cans of mixed nuts. Each
can has 338 nuts. Below is Mary's work
to find the total number of nuts.
The total number of nuts is 15210 and the missing number is 5
Number of cans of mixed nuts = 45 cans
Number of nuts in each can = 338 nuts
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.
Finding the total number of nuts we get:
Total number of nuts = Number of cans*Number of nuts in each can
[tex]338\\*45\\= 1690\\+ 13520\\= 15210[/tex]
So, the missing number is 5
Learn more about multiplication:
https://brainly.com/question/5992872
#SPJ9
James and Lucas are eating a pizza. James ate 2/3 of the pizza and Lucas ate 1⁄4 of pizza. Who ate more pizza and by how much?
Answer: James ate more pizza by 5/12 parts.
Step-by-step explanation:
To solve let us takes the lcm of the denominators 3 and 4
which is 12.
James ate 2/3 * 4/4 = 8/12 parts
Lucas ate 1/4*3/3= 3/12 parts
now, we can see 8/12>3/12
Therefore, James ate more pizza by 8/12-3/12= 5/12 parts.
-16 = -8x solve for x simplify your answer as much as possible
Answer:
x = 2
Step-by-step explanation:
-16 = -8x
divide both sides by -8:
-16/-8 = -8x/-8
x = 2
Answer:
x=2
Step-by-step explanation:
[tex]x = \frac{ - 16}{ - 8} [/tex]
[tex]x = 2[/tex]
What is d to the power of 6 and d to the power of 0 equal together?
The value of d to the power of 6 and d to the power of 0 equal together is d^6.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
The information given regarding the power is illustrated thus:
d^6 + d^0
In this case, the addition of the power will be 6 + 0 = 6. Therefore, the value is d^6.
Learn more about exponents on:
brainly.com/question/13669161
#SPJ1
Determine the values of x in the equation x2 = 81.
A. x = −9
B. x = ±9
C. x = ±40.5
D. x = 40.5
Answer:
The Answer Is C X = 40.5
Step-by-step explanation: Half of 81 = 40.5 and 40.5 x 2 = 81 (x only multiplies 40.5 by 2 which equals 81)
Which postulate could we use to prove that the angles
Answer:
PWP (Part Whole Postulate)
Step-by-step explanation:
Supplementary angles add up to 180 degrees. The part whole postulate states that two angles make up a whole.
Answer:
Supplement postulate
Step-by-step explanation:
Supplement Postulate:
If two angles form a linear pair, then they are supplementary.
In 1992, a postage stamp cost $0.25. In 2004, a postage stamp cost $0.37. What is the average rate of change in postage cents per year?
Answer: 0.01 (One cent per year)
Step-by-step explanation:
We need to find the price the stamp increased per year.
The difference in years is 12.
2004 - 1992 = 12
The difference in price is 0.12.
0.37 - 0.25 = 0.12
So to find price increase per year we do the following:
$0.12/12 = 0.01
$0.01 is one cent per year.
Line a is parallel to line b. If the
measure of 2 is 78°, what is the
measure of 5?
78=21
34
65
78
→ а
b someone actually help
Answer:
102 degrees
Step-by-step explanation:
m<6 = 78,
m<5 = 102
:]
Given m||n, find the value of x.
Answer:
kt
49
O
xº
Submit Answer
x° = 49°
What are alternate angles?Alternate interior angles are formed when two parallel lines are cut by a transversal and the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal. These angles are equal.
Pairs of alternate angles around the transversal are equal to each other. Angles can either be alternate interior or exterior angles. Sum of the angles formed on the same side of the transversal of the two parallel lines is equal to 180°.
Given , ∠t = 49°,
Therefore angles x° will also 49° because alternate angles are equal when two parallel lines are cut by a transversal.
To know more about alternate angles, refer
https://brainly.com/question/28353669
#SPJ13
The ground temperature at an airport is 11 °C. The temperature decreases by 7 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
The temperature outside a plane flying at an altitude of 5 kilometers is
°C.
Under the linear assumption of temperature and altitude, the temperature outside the plane is - 24 °C.
What is the temperature outside a plane flying at a given altitude?
In this problem we must determine the temperature outside the plane on the assumption that the temperature decreases linearly with the altitude:
T(z) = T' + (ΔT / Δz) · z
Where:
T' - Temperate at ground level, in degrees Celsius.Δz - Level change, in kilometers.ΔT - Temperature change, in degrees Celsius.If we know that T' = 11, Δz = 1 and ΔT = - 7, then the temperature at an altitude of 5 kilometers is:
T(5) = 11 + (- 7 / 1) · 5
T(5) = 11 - 35
T(5) = - 24
The temperature outside the plane is - 24 °C.
To learn more on temperatures: https://brainly.com/question/15267055
#SPJ1