Answer:
x = 4 is the only real zeroStep-by-step explanation:
Find the zero's of f(x)
2x³ - 12x² + 20x - 16 = 0x³ - 6x² + 10x - 8 = 0x³ - 4x² - 2x² + 8x + 2x - 8 = 0x²(x - 4) - 2x(x - 4) + 2(x - 4) = 0(x - 4)(x² - 2x + 2) = 0(x - 4)(x² - 2x + 1 + 1) = 0(x - 4)[(x - 1)² + 1] = 0x - 4 = 0 ⇒ x = 4, we already know this(x - 1)² + 1 = 0 ⇒ (x - 1)² = - 1, no real solution as the square is never negativeAnswer:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
Step-by-step explanation:
Given polynomial:
[tex]f(x)= 2x^3-12x^2+20x-16[/tex]
According to the Factor Theorem, if f(4) = 0 then (x - 4) is a factor of the given polynomial.
[tex]\implies f(x)=(x-4)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-4ax^2-4bx-4c[/tex]
[tex]\implies f(x)=ax^3+(b-4a)x^2+(c-4b)x-4c[/tex]
Compare coefficients with the given polynomial:
[tex]\implies a=2[/tex]
[tex]\implies -4c=-16 \implies c=4[/tex]
[tex]\implies (b-4a)=-12 \implies b-8=-12 \implies b=-4[/tex]
Substitute the found values of a, b and c:
[tex]\implies f(x)=(x-4)(2x^2-4x+4)[/tex]
To find the zeros of f(x), set the function to zero and solve for x:
[tex]\implies (x-4)(2x^2-4x+4)=0[/tex]
[tex]\textsf{Therefore},\: (x - 4) = 0\: \textsf{ and }\: (2x^2-4x+4)=0[/tex]
[tex]\textsf{To solve}\: (2x^2-4x+4)=0\: \textsf{ use the quadratic formula}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(2)(4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{-16}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16 \cdot -1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16}\sqrt{-1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm 4i}{4}[/tex]
[tex]\implies x=1 \pm i[/tex]
Therefore, the zeros of the function are:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
I NEED HELP FAST
I will mark brainliest whoever gets it right
its b i know
Step-by-step explanation:
Please help me I really need it
Answer: 170
Step-by-step explanation: Like I answered before: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.
Answer:
<CDA = 170⁰
Step-by-step explanation:
<A + <D = 180⁰ { Adjacent Angles of an parallelogram are supplementary}
10⁰ + <D = 180⁰
<D = 180⁰ - 10⁰ = 170⁰
<D = x⁰ = 170⁰ = <CDA
If the point with coordinate
(k,7) lies on the equation 2x−y=5 determine the value of k
Answer:
k = 6
Step-by-step explanation:
since (k, 7 ) lies on the line then it satisfies the equation.
substitute the coordinates of the point into the equation and solve for k
2k - 7 = 5 ( add 7 to both sides )
2k = 12 ( divide both sides by 2 )
k = 6
Answer:
k = 6
Step-by-step explanation:
The point (k, 7) lies on the line with the equation 2x - y = 5
Substitute the coordinates of the point in the equation2(k) - 7 = 52k = 12k = 6At a restaurant, 8 plates are accidentally broken each day for a week (7 days). What number represents the change in the number of plates the restaurant has?
You want to paint the four walls in your
bedroom. Each wall is 9
feet tall by 12 feet
wide. What is the total
area
whats 2+7
a. 14
b. 19
c.88383838837
Answer:
9
Step-by-step explanation:
Was this a joke or something
whats 50% of 1/2 of a mile
Answer:
0.25 or 1/4
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
Half of half a mile is one quarter mile: (1/2)(1/2) = 1/4
1. the height of a right triangular prism is inches. each side of the triangular base measures 10 inches, and the height of the base is inches. the triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube. what is the surface area of the solid formed?
The surface area of the solid formed by the triangular prism and cube will be 598.33 square inches.
What is a prism?A prism is a closed solid that has two parallel bases connected by a rectangle surface.
The height of a right triangular prism is 11/6 inches.
Each side of the triangular base measures 10 inches, and the height of the base is 26/3 inches.
The triangular prism is placed at top of a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
Then the surface area of the prism will be
[tex]\rm Surface \ area = 5 \times (10 \times 10) + 0.5 \times 10 \times \dfrac{26}{3} + 3 \times 10 \times \dfrac{11}{6}\\\\\\Surface \ area = 598.33\ in^2[/tex]
More about the prism link is given below.
https://brainly.com/question/12649592
2q^2+5+2q+–3+10+–5q
how do I do this?
Answer:
First you add up all the numbers and then the unknowns.
Step-by-step explanation:
2q^2+12-2q-5q
2q^2+12-3q
2q^2-3q+12
Write the proportion. do not include units in the answer.
60feet is to 100feet as 12feet is to 20feet.
Answer:
(60/100) = (12/20)
Step-by-step explanation:
What is the measure of \angle R∠Rangle, R?
Answer:
106⁰
Step-by-step explanation:
As in cyclic quadrilateral sum of opposite angles is equal to 180⁰
Please help me this is hard and its due today!
Answer: A, C and E.
Step-by-step explanation: They all equal to 5.
A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number greater than 10?
Write your answer as a fraction in the simplest form.
Answer:
Here;
Step-by-step explanation:
The numbers greater than 10 are 11 and 12 on the dice meaning we've got 2 options out of 12.
So, 2/12 gives 1/6 in its simplest form
Apply properties of operations to show why 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n)
Applying the properties of operations; it follows that; 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n).
Properties of OperationsThere are four (4) basic properties of real numbers which apply to addition and multiplication: namely; commutative, associative, distributive and identity.
Hence, by the cumutative property of multiplication and associative property of addition, it follows that;
4× -1.5 = -21(2/7)3.5n + 4(5 1/4n) = -21(7/6n)Hence, it follows that the expressions are equivalent.
Read more on properties of operations;
https://brainly.com/question/16136176
4. Sebastian's lemonade recipe uses 4 cups
of water and 1 cup of lemon concentrate.
What is the percentage of the lemonade
recipe that is lemon concentrate,
Exercise Sophia pays a $19.99 membership fee for an online music store. a. If she also buys two songs from a new album at a price of $0.99 each, what is the total cost? b. If Sophia purchases 푛 songs for $0.99 each, write an expression for the total cost. c. Sophia’s friend has saved $118 but is not sure how many songs she can afford if she buys the membership and some songs. Use the expression in part (b) to write an equation that can be used to determine how many songs Sophia’s friend can buy. d. Using the equation written in part (c), can Sophia’s friend buy 101, 100, or 99 songs? Relevant Vocabulary VARIABLE (DESCRIPTION): A variable is a symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number). EQUATION: An equation is a statement of equality between two expressions. NUMBER SENTENCE: A number sentence is a statement of equality between two numerical expressions. SOLUTION: A solution to an equation with one variable is a number that, when substituted for the variable in both expressions, makes the equation a true number sentence.
.
What's the answer for all of them??
Answer:
first, how much were her songs? It's two songs each, and their separate prize was 0.99:
total prize was 2*0.99=1.98
this gets added to the membership prize:
19.99+1.98=21.97
you can also calculate this by rounding all the numbers (20+1+1) and substracting the amount you rounded (three times one cent) - the result would be the same.
B 19.99+.99n
C okay so it says Sophia's friend has saved $118 so she already knows she has $118 and then the next step is to figure out about Part B so she does not know how many songs you can afford to buy so the expression in Part B whatever the expression is if you figured out the answer to Part B and there's a number what you want to do what you would want to divide that number into 118 to see how how many equal groups you can make and you don't want to go overboard 18 so what you would want to do it if you would want to do if you figure out the number to expression be in the boring part B they don't want to take that and keep making a go go to that until you reach 118 and then you would get your total
D N=99 songs
The Molina family's pancake recipe uses 2 teaspoons of baking powder for every 1 3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
Answer: 7
Step-by-step explanation:
the ratio of boys to girls in mrs.cunnginghams class is 2 to 3. there are 18 girls in the class. what is the total number of students in mrs.cunninhams class
Answer:
The total number of students that are in Ms. Cunningham's class is 30 students
Step-by-step explanation:
the number of boys are represented by X
18 divided by 3 is 6
2 times 6 is 12.
12 plus 18 is 30.
Total number of students = 12 + 18 = 30
A map uses a scale of centimeter 0.5 = 75 kilometers. The actual distances between various cities are are at 40 kilometers
An auditorium has rows of seats with a seats in each row Kayla
knows there are at least 70 seats but fewer than 156 seats in the
auditorium. How many rows of seats can there be in the auditorium
Use Exercises 1-a to answer the question
1. Explain how you would find the least possible number of rowe
in the auditorium
2. How would you find all the possible numbers of rows, without
having to check if & is a factor of every number between
70 and 1507
3. Name all the possible numbers of rows in the auditorium,
Step-by-step explanation:
Note: there is a typo, 'a' should be '8'The number of seats in each row is 8 and the total number of seats is between 70 and 150.
Let x be the number of rows, then we have the inequality:
70 ≤ 8x < 156Divide all sides by 8 to get:
70/8 ≤ x < 156/89 ≤ x ≤ 19 (taking closest integers)So the number of rows is between 9 and 19 both inclusive.
All possible number of rows
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19Answer:
1. 9 rows
2. see below
3. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Step-by-step explanation:
Please note that I believe there are typing errors in the question and that the given information should be:
8 seats in each rowAt least 70 seatsLess than 150 seatsQuestion 1
To determine the least possible number of rows in the auditorium, divide the least number of seats by the number of seats in a row:
⇒ 70 ÷ 8 = 8.75
As the answer is a decimal, round it up to the nearest whole number.
Therefore, the least possible number of rows in the auditorium is 9 rows.
Question 2
Find the greatest number of rows by dividing the greatest number of seats by the number of seats in a row:
⇒ 150 ÷ 8 = 18.75
As there should be fewer than 150 seats we cannot round the number up (as this would make there be more than 150 seats), so instead must round it down to 18.
Therefore, the greatest number of rows in the auditorium is 18 rows.
Question 3
As we have found the least number of rows in question 1 and the greatest number of rows in question 2, all we need to do is list all the numbers between (and including) these numbers.
Therefore, all the possible numbers of rows in the auditorium are:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Answer:
please see photo for detailed analysis
Can someone help me with this pls
Correct solution:
⇒ 8 ÷ 1/8⇒ 8 x 8⇒ 64for f(x)=4x+2, what value of x makes f(x)=-14
Hey there,
f(x) = 4x + 2
what value of x makes f(x) = -14?
Answer :x = -4 ✅
Explanations:f(x) = 4x + 2
>> We want f(x) to be equal to -14:
4x + 2 = -14
>> Substract 2 from both sides :
4x + 2 - 2 = -14 - 2
4x = -16
>> Divide both sides by 4:
4x/4 = -16/4
x = -4
✅
Have a good day ;)
Answer:
x = -4
Step-by-step explanation:
Given:
f(x) = 4x + 2If the value of f(x) is -14,
⇒ 4x + 2 = -14 [f(x) = 4x - 2 and -14]
To simplify the equation, we need to isolate the variable completely. Start out by subtracting 2 both sides. This will isolate "x" and the cooeficient of x.
⇒ 4x = -14 - 2⇒ 4x = -16Then, divide 4 both sides to isolate the cooeficient of x on one side and a constant on the other side. The constant will be the value of x.
⇒ 4x/4 = -16/4⇒ x = -4Thus, -4 is the value of x that makes f(x) equivalent to -14
Use the point-slope form of a line to write the equation of
a line that has a slope of 2 and passes through the point
(4,3). Write the equation in slope-intercept form.
Answer:
y=2x-5
Step-by-step explanation:
Hi there!
We are given that a line has a slope of 2, and passes through the point (4,3)
We want to use point-slope form to find this equation of the line, yet we want to write this in slope-intercept form
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
As we are already given the slope and a point, we can substitute these values into the formula to find the line.
First, substitute 2 as m in the equation:
[tex]y-y_1=2(x-x_1)[/tex]
Now substitute 4 as [tex]x_1[/tex] and 3 as [tex]y_1[/tex]
[tex]y-3=2(x-4)[/tex]
This is the equation of the line in point-slope form.
Now we need to write it in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
We can actually get to slope-intercept form from point-slope form.
First, distribute 2 to both x and -4 on the right side
y-3=2x-8
Now add 3 to both sides
y=2x-5
Hope this helps!
question number 4 please help
Answer:
The correct answe is H , if yu sub the x value in each of the equations yu should get y
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex]
m = the slopeb = the y-intercept (the value of y when x=0)To find the slope of a line (m):
Find the coordinates of two points that fall on the linePlug them into the following formula:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the pointsTo find the y-intercept of a line (b):
Plug the slope into [tex]y=mx+b[/tex]Plug in one of the pointsSolve for bSolving the Question
We're given a set of coordinates for this linear relation.
First, solve for the slope.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
⇒ Plug in any two points that fall on the line (in this case we used (-2,-7) and (2,1)):
[tex]m=\dfrac{1-(-7)}{2-(-2)}\\\\m=\dfrac{1+7}{2+2}\\\\m=\dfrac{8}{4}\\\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
Now, let's solve for the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in any of the given points:
[tex]1=2(2)+b\\1=4+b\\b=-3[/tex]
Therefore, the y-intercept of the line is 3. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x-3[/tex]
Answer[tex]y=2x-3[/tex]
Find the missing angle
Step-by-step explanation:
a + 156° = 180° ( supplementary angle )
a = 180° - 156°
a = 24°
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answer:
third side: 2√14
using pythagoras theorem:
a² + b² = c²
t² + 5² = 9²t² + 25 = 81t² = 81 - 25t² = 56t = √56t = 2√14Answer:
The unknown side of this triangle is √56 or 2√14
Step-by-step explanation:
Let the unknown side of this right angled triangle be x , so by using Pythagoras theorem we can find out the third side .
=> P² + B² = H²
=> P² = H² - B²
=> P² = 9² - 5²
=> P² = 81 - 25
=> P² = 56
=> P = √56 or 2√14
Kate has a coin collection. She keeps 7 in a box, which is only 5% of her entire collection. What is the total number of coins in Kate’s coin collection?
Answer:
140
Step-by-step explanation:
5%/100 = 7/?
7 times 100 = 700
700 divided by 5 = 140 coins
At an assembly 7 out of the first 10 students who entered the gym were carrying a backpack. Based on this information, if 70 students were at the assembly, how many students could be expected to be carrying a backpack?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answer:
Step-by-step explanation:
49
i need help can someone help
Answer:
Step-by-step explanation:
The distributive property is for example 3(2*4) the outside number multiplies everything inside the parenthesis. For the communitive, its like opposites, but they give the same answer, for example 4*5, 5*4. And for associative is like the distributive property, but not at the same time, for example, (a*b)*c = a*(b*c) it has the numbers, but pluged in in another type of way
Hope this helps!