Answer:
p(x) = (x - 5)(x + 1)(x + 4)
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringAlgebra II
Factoring Cubes: [tex]\displaystyle (a \pm b)(ax^2 \mp bx + c)[/tex]Long DivisionSynthetic DivisionStep-by-step explanation:
*Note:
Please excuse my bad handwriting :)
Step 1: Define
Identify
p(x) = x³ - 21x - 20
Linear factor (x - 5)
Step 2: Factor
Option 1: Factoring cubes formula
Factor [Factoring Cubes]: p(x) = (x - 5)(x² + 5x + 4)Factor: p(x) = (x - 5)(x + 4)(x + 1)
Option 2: Long Division
See Attachment
Option 3: Synthetic Division
See Attachment #2
What is the expected value?
Answer:
2.1
Step-by-step explanation:
The expected value of a probability is given by the formula:
E(x) = Σxp(x)
Therefore from the table showing the winnings of a game, the expected value of the probability distribution is:
E(x) = Σxp(x) = (0 * 0.5) + (2 * 0.2) + (4 * 0.15) + (6 * 0.1) + (10 * 0.05)
E(x) = 0 + 0.4 + 0.6 + 0.6 + 0.5 = 2.1
Hence we can conclude that the expected value of the winnings of the game is 2.1.
Find f(-3) if f(x) = x2 .
Type a numerical answer in the space provided. Do not type spaces in your answer.
Answer:
f(-3) = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-3) = (-3)²Exponents: f(-3) = 9NEED some HElp please
Explain why the amount of money in the account at the end of the first year is given by the formula with n as the exponent:
P = P∨0 (1 + r/n)^n
Answer:
Is this answer correct.Does the anwer help you
(4,-5) with slope of 2
that's a point slope form so
y +5 = 2(x -4)
form a polynomial whose factors are (x+1) , (x+2) and (x-3)
Answer:
x³-7x-6
Step-by-step explanation:
Find the products of the factors
(x+1)(x+2)(x-3)
x²+3x+2(x-3)
x³+3x²+2x-3x²-9x-6
x³-7x-6
PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
=============================================================
Explanation:
1/2 = 4/8 after multiplying top and bottom by 8
So the mixed number 7 1/2 is the same as 7 4/8
We can convert to an improper fraction like so
7 4/8
7 + 4/8
7*(8/8) + 4/8
56/8 + 4/8
(56+4)/8
60/8
Notice how dividing 60 over 8 leads to 7 remainder 4. Think of it like having 60 cookies and you want to share them amongst 8 friends. Each friend gets 7 whole cookies (7*8 = 56 taken so far) and then we have 60-56 = 4 left over as the remainder.
Through similar steps, you should find that the mixed number 1 7/8 converts to the improper fraction 15/8.
-----------------------------
To rephrase the problem with improper fractions would be to say:
"The electrician needs to buy 60/8 feet of wire. There are 15/8 feet of wire in each spool. How many spools should the electrician buy?"
Let x be the answer to that question.
We multiply the number of spools (x) by the amount of feet of wire per spool (15/8) to get the expression (15/8)x
Set this equal to the target 60/8 and solve for x
(15/8)x = 60/8
15x = 60 .... multiply both sides by 8 to clear out the fractions
x = 60/15
x = 4
The electrician needs to buy exactly 4 spools
-----------------------------
A different approach could have us convert each mixed number into decimal form
7 1/2 = 7 + 1/2 = 7 + 0.5 = 7.5
1 7/8 = 1 + 7/8 = 1 + 0.875 = 1.875
So the electrician needs to buy 7.5 ft total and each spool has 1.875 ft of wire.
Using the same idea as before, we would then have,
1.875x = 7.5
x = (7.5)/(1.875)
x = 4
1. write it on a piece of paper
[tex]\\ \sf\longmapsto 1\dfrac{1}{2}+2\dfrac{3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{2}+\dfrac{11}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6+11}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{4}[/tex]
2:-
[tex]\\ \sf\longmapsto 4\dfrac{3}{7}+6\dfrac{1}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{31}{7}+\dfrac{31}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{155+225}{35}[/tex]
[tex]\\ \sf\longmapsto \dfrac{380}{35}[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
3:-
[tex]\\ \sf\longmapsto 4\dfrac{2}{5}+5\dfrac{2}{6}[/tex]
[tex]\\ \sf\longmapsto \dfrac{22}{5}+\dfrac{32}{6}[/tex]
[tex]\\ \sf\longmapsto \dfrac{132+160}{30}[/tex]
[tex]\\ \sf\longmapsto \dfrac{292}{30}[/tex]
4:-
[tex]\\ \sf\longmapsto 3\dfrac{7}{7}+3\dfrac{1}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{28}{7}+\dfrac{10}{3}[/tex]
[tex]\\ \sf\longmapsto 4+\dfrac{10}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{12+10}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{22}{3}[/tex]
[tex] \bf \large \longrightarrow \: \: 1 \frac{1}{2} \: + \: 2 \frac{3}{4} \: = \: \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{3}{2} \: + \: \frac{11}{4} \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{6 \: + \:11 }{4} \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{17}{4} \\ [/tex]
2.[tex]\bf \large \longrightarrow \: \: 4 \frac{3}{7} \: + \: 6 \frac{1}{5} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{31}{7} \: + \: \frac{31}{5} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{155 \: + \: 217}{35} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{372}{35} \\ [/tex]
3.[tex]\bf \large \longrightarrow \: \: 4 \frac{2}{5} \: + \: 5 \frac{2}{6} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{22}{5} \: + \: \frac{32}{6} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{132 \: + \: 160}{30} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{292}{30} \\ [/tex]
4.[tex]\bf \large \longrightarrow \: \: 3 \frac{7}{7} \: + \: 3 \frac{1}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{28}{7} \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \cancel\frac{28 ^{4} }{7 \: ^{1} } \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{4}{1} \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{12 \: + \: 10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{22}{3} \\ [/tex]
What is the correct answer to this multiple choice question? Please help!
Answer:
[tex]\sqrt[3]{4}[/tex]
Step-by-step explanation:
To solve this we need to take the square root of both sides with a certain degree.
[tex]4^6 = a^{18}[/tex]
We can take the root of both sides with a degree of 18.
[tex]\sqrt[18]{4^6} = \sqrt[18]{a^{18}} \\(4^6)^{\frac{1}{18} } = a\\a = 4^{\frac{6}{18} } = 4^{\frac{1}{3} } = \sqrt[3]{4}[/tex]
It's helpful to understand that when a number has its square root taken with some degree n. The square root can be represented as just the value raised to the (1/n) power.
It's also helpful to understand that when you raise something to the power of another power, you can simply multiply the powers together. For instance (2^3)^5 = 2^15
Write the function for the graph.
Answer:
B)
Step-by-step explanation:
exponential function given by:
[tex] \displaystyle f(x )= a \cdot{b}^{x} [/tex]
where:
a is the y-interceptb can be any numbersince the function crosses y-axis at (0,4) point
[tex]a = 4[/tex]to find a we can consider (1,8) point it tells us when x is 1 then y is 8 thus:
[tex] \displaystyle 8= 4 \cdot{b}^{1} [/tex]
[tex] \displaystyle 8= 4 \cdot{b}^{} [/tex]
divide both sides by 4:
[tex] \displaystyle \boxed{b = 2}[/tex]
altogether substitute:
[tex] \displaystyle f(x)= 4 \cdot{2}^{x} [/tex]
hence our answer is B)
Two friends go to a Mexican restaurant for lunch. One friend orders 1 soft taco and
3 burritos and his bill was $8.75. The other friend's bill was $10.00 and he ordered 4
soft tacos and 2 burritos. What is the cost of a taco and what is the cost of a
burrito?
The cost of a taco is:
The cost of a burrito is:
Answer:
cost of a taco: $1.25
cost of a burrito: $2.50
Step-by-step explanation:
Let the cost of a taco be $t and the cost of a burrito be $b.
t +3b= 8.75 -----(1)
4t +2b= 10
Divide both sides by 2:
2t +b= 5
Making b the subject of formula:
b= 5 -2t -----(2)
Substitute (2) into (1):
t +3(5 -2t)= 8.75
Expand:
t +3(5) +3(-2t)= 8.75
t +15 -6t= 8.75
t -6t= 8.75 -15
-5t= -6.25
t= -6.25 ÷(-5)
t= 1.25
Substitute t= 1.25 into (2):
b= 5 -2(1.25)
b= 5 -2.5
b= 2.50
Thus, the cost of a taco is $1.25 and the cost of a burrito is $2.50.
Elias made a polyhedron with 9 edges and 5 faces. Which solid could he have made?
The polyhedron that Elias could have made is a TRIANGULAR BASED PRISM.
Triangular based prism are as described below:
A triangular-based prism is known to consists of 9 edges and 5 faces as shown in the diagram below.
It is a three-sided prism and also a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sidesThe edges are made up of lines and these lines are the ones that intersect to form facesLearn more here: https://brainly.com/question/16682058
Answer: c
Step-by-step explanation:
Answer ASAP Please!
cos(13°) correct to four decimal places is:
A:0.2311
B:0.2312
C:0.9734
D:0.9735
E:0.9744
Answer:
E:0.9744
Step-by-step explanation:
Answer: E) 0.9744
Explanation:
This is something you'll need a calculator for. As far as I know, there isn't a clean formula that will allow you to compute this by hand, and get something like sqrt(3)/2. There is a way to find the decimal value by hand, but it will require knowledge of Taylor polynomials and it will take a very long while to compute the value. So again, it's better to use a calculator. When using a calculator, make sure it's in degree mode. You can check by computing cos(60) and you should get 0.5
integers
[tex]18 \div ( - 9) = [/tex]
[tex] - 10 \div 2 = [/tex]
[tex] - 2 + ( - 6) = [/tex]
[tex] - 8 - 4 = [/tex]
[tex]( - 2 \times - 12) \div (18 \div - 9 = [/tex]
[tex](120 - 30) \div ( - 42 - 3) = [/tex]
[tex]1000 \div (125 \times - 2) = [/tex]
[tex](5 - 30) \div ( 8 - 3) = [/tex]
[tex]12 \div (4 - 8) = [/tex]
please mark this answer as brainlist
Which shows two triangles that are congruent by ASA?
Answer:
A and D
Step-by-step explanation:
The two triangles that are congruent by ASA is discussed below.
What is Congruency?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. "Congruent" refers to things that are precisely the same size and shape.
Angle-Side-Angle refers to the ASA Congruence rule.
According to this rule, two triangles are said to be congruent if any two of their respective angles and the side that is included between them are equal to the corresponding angles and the included side of the other triangle.
For example, there are ABC and DEF in which ∠ B = ∠ E, ∠ C = ∠ F, and BC = EF
Then, the triangle that Δ ABC ≅ Δ DEF by ASA congruence rule.
Learn more about Congruency here:
https://brainly.com/question/7888063
#SPJ5
The lengths of the diameters of two concentric circles are 6 and 8. What is the distance between the circles?
Answer: 1 unit
Explanation:
The diameters are 6 and 8, which cut in half to 3 and 4 respectively.
The difference in these radii values is 4-3 = 1.
This is the distance from one circle's edge to the other circle's edge, such that we're on the same line that goes through the center of the circles. This is the gap width or ring width so to speak.
The numbers 8,x,9 and 36 are in proportion.Find x
If you can give the proportion then it would be better.
I am asuming
8:x::9:36
Then 8:x::1:4
So x = 32
Answered by Gauthmath must click thanks and mark brainliest
Answer:
x = 32
Step-by-step explanation:
[tex]\frac{8}{x}[/tex] = [tex]\frac{9}{36}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )
x = 8 × 4 = 32
3
Select the correct answer.
The angle of depression between the top of a 100-foot cliff and a ship approaching the shore is 37°.
cliff top
37°
100
feet
37°
ship
d
What is the approximate distance, d, between the bottom of the cliff and the ship?
ОА
166.2 feet
OB. 60.2 feet
ОС.
75.4 feet
OD.
132.7 feet
Reset
Next
Answer:
132.7 feet.
Step-by-step explanation:
tan 37 = height of cliff / distance of the ship
= 100/d
d = 100/tan37
= 132.7 feet.
write x²-y² in factorize form.
write (p+p) ²in expanded form.
Answer:
(x-y)^2
p^2+p^2
Step-by-step explanation:
^2 means square
Answer:
see explanation
Step-by-step explanation:
x² - y² ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - y²
= (x - y)(x + y)
------------------------------
(p + p)²
= (2p)²
= 2p × 2p
= 4p²
If 12 out of 30 fruits are oranges, how many oranges fruits will there be per 100 fruits total?
Answer:
40 oranges are there in 100 fruites.
Please help: 6m - m = 5/6(6m - 10)
Will mark brainliest!!
Answer:
No solution.
Step-by-step explanation:
[tex]6m-m=\frac{5}{6}(6m-10)\\5m=5m-\frac{25}{3}\\0\neq -\frac{25}{3}[/tex]
Therefore, there is no solution.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The median of the lower half of the data set is the _____________.
A. Third quartile
B. First quartile
C. Fourth quartile
D. Second quartile
Answer:
B. First quartile
Step-by-step explanation:
The first quartile is the first 25% of a line graph, and the median of the lower half of a data set would be the median of the median, which means it would split the graph at 25%
Joylin is writing an equation to model the proportional relationship between y, the total cost in dollars of downloading videos from a website, and x, the number of videos downloaded. She knows that the total cost to download 3 videos was $12. Her work to find the equation is shown below.
Joylin’s Work
Step 1
k = StartFraction 3 over 12 EndFraction = 0.25
Step 2
y = 0.25 x
Where did Joylin make her first error?
Answer:
Step-by-step explanation:
Jocelyn was attempting to find out how much she will be charged per download. She has the fraction upside down. To find the amount of money per download, the fraction should be $12/3downloads to get $4/1download. That is the slope of the equation, the rate of change or, for us, the fact that your cost will go up $4 for every single video you download. The equation would then be
y = 4x
The way she has it, we are paying only a quarter for a download. If that be the case, for 3 downloads we would only be paying .75, but it says we pay $12, so we know something is wrong right there.
Answer:
The answer is A
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST!!!!
Answer:
wqhg
Step-by-step explanation:
its situated in u.s, in quahog , rhode island
Find the value of x-8 when x=16.
Answer:
8
Step-by-step explanation:
x=16
x(16)-8=8
The football team loses 5 yards on first down.
a. Write an integer to represent this situation.
Answer:
-5
Step-by-step explanation:
since it is a lose, it is represented by a negative sign.
if you have 500 dollars and spend 20 every week then what would be the slope explain
Answer:
y=-20m+500
Step-by-step explanation:
i need help anybody ?
Answer and Step-by-step explanation:
Simply use the Pythagorean Theorem to solve.
The Pythagorean Theorem is used to solve for a side in right triangles.
[tex]A^{2} +B^{2}= C^{2}[/tex]
Plug the sides values into the equation.
[tex]A^{2} + 13^2 = 20^2\\\\A^2 + 169 = 400\\\\A^2 = 231\\\\A = 15.1987[/tex]<- This is the answer.
#teamtrees #PAW (Plant And Water)
HELP PLEASE BRAIN FOR CORRRECT
Answer:
1/6
Step-by-step explanation:
you divide y by x
y ÷ x
each column when you you divide y by x the answer is 1/6
13 Water is pulled up from a well in a bucket on a rope. The rope winds on a cylindrical drum 15 cm in diameter. It takes 28 turns of the drum to pull the bucket up from the bottom of the well. How deep is the well? (Use the value 2 for m.)
x.(9x-1).(x+2)-x(3x-1).(3x+1)
Answer:
Sorry if i'm wrong.
=6x² + 16x - 2