Answer:
[tex]P(x)=x^3+12x^2+45x+50[/tex]
Step-by-step explanation:
Roots of a polynomial
If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula
[tex]P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)[/tex]
Where a is an arbitrary constant.
We are given the following roots:
-5 multiplicity 2 (-5 twice)
-2 multiplicity 1
Thus, the polynomial is:
[tex]P(x)=a(x-(-5))(x-(-5))(x-(-2))[/tex]
[tex]P(x)=a(x+5)(x+5)(x+2)[/tex]
We are not given any clue about the value of a, so we choose a=1. Multiplying:
[tex]P(x)=(x^2+5x+5x+25)(x+2)=(x^2+10x+25)(x+2)[/tex]
[tex]P(x)=x^3+2x^2+10x^2+20x+25x+50[/tex]
Simplifying:
[tex]\mathbf{P(x)=x^3+12x^2+45x+50}[/tex]
For the triangles described, which of the following statements must be true? In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°. (1 point) ∠Q≅∠F ∠R≅∠F DE¯¯¯¯¯¯¯¯≅PQ¯¯¯¯¯¯¯¯ ∠E≅∠Q
Answer:
∠Q≅∠F
Step-by-step explanation:
Two triangles are said to be congruent if all the three sides of the triangles are equal and all the three angles are equal.
Given that: In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°.
Hence we can say that ΔDEF is congruent to ΔPQR. According to the side-angle-side (SAS) triangle congruence theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Therefore:
DF = PQ, DE = PR, EF = RQ, ∠D = ∠P, ∠E = ∠R and ∠F = ∠Q
A trucker drove 300 miles in 5 hours, took a rest for an hour, then drove another 400 miles is 6.6 hours. What is the truckers average speed in miles per hour?
Answer:
25x = - 1820
x = -72.8
The truck drove 72.8 miles at 45mph and 100-72.8 = 27.2 miles at 20mph
Step-by-step explanation:
Order the numbers from greatest to least value.
1.444.
29|13
0.875
47|45
Answer:
0.875, 47/45, 1.444, 29/13
Step-by-step explanation:
0.875 is the least then 47/45 is 1.0444 as a decimal then 1.444 then 29/13 is 2.23 as a decimal hope that helps
Easy question 20 POINTS
Answer: 11 over 9 power by 2
Step-by-step explanation:
A 0.8-liter bottle of Mexican wine costs 90 pesos. At that price, how much would a half-gallon jug of the same wine cost in dollars?
A half-gallon jug of the same wine would cost $10.82
How much would a half-gallon jug of the same wine cost in dollars?The given parameter is:
0.8-liter bottle = 90 pesos
As a general rule of conversion
1 liter = 0.26 gallon
This means that:
0.8 liter = 0.8 * 0.26 gallon
Evaluate
0.8 liter = 0.208 gallon
Substitute 0.8 liter = 0.208 gallon in 0.8-liter bottle = 90 pesos
0.208 gallon = 90 pesos
Divide both sides by 0.208
1 gallon = 432.69 pesos
Divide both sides by 2
0.5 gallon = 216.35 pesos
1 peso = 0.050 United States Dollar
So, we have:
0.5 gallon = 216.35 * $0.05
Evaluate
0.5 gallon = $10.82
Hence, a half-gallon jug of the same wine would cost $10.82
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2/3 times what equals 1
Answer:
2/3 times 3/2 equals 1.
Step-by-step explanation:
I've done it
A box of juice has 5 cups of pineapple juice and 2 cups of orange juice. Write the ratio of cups of pineapple juice to the number of cups of orange juice. WRITE THE RATIO IN THREE DIFFERENT WAYS. *
I am very stuck on theis question. What is 4 times 4,000
Answer:
16000
Step-by-step explanation:
4*4 is 16 4*0 is 0 4*0
Answer:16000
Step-by-step explanation: basic calculator math
I'm big-brained lol :) have fun besties ace the quizzes!!
Eva made sand art bottles to sell at her school's craft fair. First, she bought 4 kilograms of sand in different colors. Then, she filled as many 100-gram bottles as she could. How many sand art bottles did Eva make?
Answer: Eva made 40 sand art bottles
Step-by-step explanation:
1 kilogram =1000 grams
she bought 4000 grams
4000/100 =40
she filled 40 bottles
asap
pleeaseeeeeeeeeeeeeeeeeeeeeee
Answer:
Your answer is 89760!!!
hope this helps!!!
Answer:
89760
Step-by-step explanation:
17*5280=89760
Simplify the following square roots:
[tex]\sqrt{32}[/tex]
[tex]\sqrt{28}[/tex]
[tex]\sqrt{12}[/tex]
Answer:
Sqrt32 = 4[tex]\sqrt{2}[/tex], Sqrt28 = 2[tex]\sqrt{7}[/tex], Sqrt12 = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Square root of 32:
First we find the prime factors of the number by making a factor tree.
32 splits into 8 and 4.
8 splits into 4 and 2
4 splits into 2 and 2
4 splits into 2 and 2
This becomes the square root of [tex]2^{2}[/tex] x [tex]2^{2}[/tex] x 2. It will simplify to:
4[tex]\sqrt{2}[/tex]
Square root of 28:
The prime factors of this number are:
2, and 2
This simplifies to 2[tex]\sqrt{7}[/tex]
Square root of 12:
The prime factors of this are:
3, 2, 2
This simplifies to:
2[tex]\sqrt{3}[/tex]
Answer:
They can not be simplified because they are not perfect squares.
-16 + the quotient of a number and 2 is 35
Answer:
Step-by-step explanation:
A school bought $548 in basketball equipment and uniforms costing $29.50 each. The total cost was $2,023. Write an equation you can use to find the number of uniforms the school purchased.
(a) what would the variable (x) represent in this problem?
(1) the cost of the uniforms
(2) the number of basketballs purchased
(3) The number of uniforms purchased
(b) what is the total cost of the equipment and uniforms? |____________| (no symbols)
(c) write an equation to represent this problem. use x as your variable. |___________|
Answer:
Step-by-step explanation:
Draw the dilation of ABCD with center D and scale factor. Label the dilation (JKL.
Camden accepted a new job at a company with a contract guaranteeing annual raises. Camden's salary after working for nn years can be determined using the equation S=2000n+55000.S=2000n+55000. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
2000
Step-by-step explanation:
Given the equation :
S=2000n+55000
Comparing the equation given to the standard linear equation formula :
y = mx + c
Where ; c = intercept ; m = slope ; y = dependent variable and x = independent variable
From The comparison, the slope of the equation given = 2000.
According to the context, the slope means that Camden salary will increase by 2000 each year.
Mookie, Gandalf, and O’Malley are selling tickets to a play. Gandalf sold five less than three times the number of tickets Mookie sold. O’Malley sold one more than seven times the number of tickets Mookie sold. The number of tickets O’Malley sold is four more than twice the number of tickets that Mookie and Gandalf sold together. How many tickets did they sell in total?
9514 1404 393
Answer:
73
Step-by-step explanation:
Let m, g, o represent the numbers sold by Mookie, Gandalf, and O'Malley, respectively. Then the relations between these values are ...
g = 3m -5
o = 7m +1
o = 4 +2(m +g)
Equating expressions for o, we have ...
7m +1 = 4 +2(m +g)
Substituting for g, we have ...
7m +1 = 4 +2(m +(3m -5))
7m +1 = 8m -6
7 = m . . . . . . . . add 6-7m
g = 3·7 -5 = 16
o = 7·7 +1 = 50
The number sold in total is ...
m + g + o = 7 +16 +50 = 73
They sold 73 tickets in total.
The coefficient of determination of a set of data points is 0.93 and the slope of the regression line is -5.26. Determine the linear correlation coefficient of the data.
Answer:
- 0.964
Step-by-step explanation:
Given that Coefficient of determination (R^2) = 0.93
Slope of regression line = - 5.26
The linear correlation Coefficient =?
The Coefficient of determination (R^2) is used to obtain the proportion of explained variance of the regression line. It is the square of the linear correlation Coefficient (R).
Hence. To obtain the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2
Therefore,
R = √R^2
R = √0.93
R = 0.9643650
R = 0.964
However, since the value of the slope is negative, this depicts a negative relationship between the variables, hence R will also be negative ;
Therefore, R = - 0.964
The linear correlation coefficient of the data is: -0.96
Recall:
Coefficient of determination = R²R represents the linear correlation coefficient.A negative slope of regression line suggests relationship between variables will be negative, hence linear correlation coefficient will be negative.Thus, given:
Coefficient of determination of a set of data points = 0.93
Slope of the regression line = -5.26
Therefore:
R² = 0.93
R = √0.93
R = 0.96
Since the slope the regression line is negative, R will be negative in this case.
Therefore, the linear correlation coefficient of the data is: -0.96Learn more about linear correlation coefficient on:
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it's really easy Pleaseplease answer this I'm desperate please ill give brainliest to the first right answer
Answer:
It should be 12 i dont know ,,I learned it in class but my teacher told me that there are different types of this math so I don’t know if this is the one I learned
Step-by-step explanation:
GUYS PLEASE HELP ME OUT WITH THIS ONE QUESTION.
Answer: A&R is X-3 R&E are 5 B&C are parallel
Step-by-step explanation:
Please help please i’m begging you
Answer:
C. -4 = 16x
Step-by-step explanation:
That is the graph i got when I typed -4 = 16x.
Brainliest Please!!!
- Hermionia
Ms. Baetz will receive a 25 % discount off her cellphone bill . Her monthly cell phone plan charges a flat monthly fee $30.00 plus $0.10 per minute . If m.s baetz talks on her call phone for 200 minutes during the first moth of cell phone service , what will be the amount of her first cell phone bill ?
A. 50.00
B. 37.50
C. 42.50
D. 25.00
Answer:
$50
Step-by-step explanation:
A rectangle has a length of 12 inches and a width of 8 inches. Lexi draws a scale
copy of the rectangle using a scale factor of.What are the dimensions of the
scalle copy?
The dimensions of the scale copy of the rectangle are given by 8 inches and 16/3 inches respectively.
What is a rectangle?
A rectangle is a closed geometric figure with opposite sides parallel and equal to each other. In a rectangle, all the angles are equal and right to each other. The diagonals of a rectangle bisect each other.
Calculating the dimensions of the scale copy
Given length and width of a rectangle are 12 inches and 8 inches respectively
Lexi draws a scale copy of this rectangle using scale factor ⅔.
The new dimensions of the scale copy of the rectangle are given below:
Length Of the scale copy of rectangle = 12 × (⅔) = 8 inches
Width Of the scale copy of rectangle = 8 × (⅔) = 16/3 inches
Hence, the dimensions of the scale copy of the rectangle are 8 inches and 16/2 inches respectively.
To learn more about the rectangle, visit the link given below:
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I need help please solve for x given that TSU ~ FSG
Answer: X = 4
Step-by-step explanation:
TS/FS = SU/SG
3x-2/5 = 6/3
3(3x-2) = 6* 5
9x - 6 = 30
9x -6 + 6 = 30 + 6
9x = 36
x = 36/ 9
x = 4
Answer:
[tex]x = \frac{9}{6}[/tex]
Step-by-step explanation:
The first step is figuring out what the scale factor is
since [tex]2 \overline{\rm US} = \overline{\rm GS}[/tex] we know the scale factor is two
The second step is setting up the equation then solving the equation
[tex]2(3x -5) = 5[/tex]
[tex]6x - 4 = 5[/tex]
[tex]6x = 9[/tex]
[tex]x = \frac{9}{6}[/tex]
It takes Sara 1/2 day to make a birdhouse. How much of the birdhouse will be built after 2/5 day?
Answer:
80%
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIST PLEASE
Answer:
C)
Step-by-step explanation:
The number of playes can only be 8, 9, 10 ,11 , 12
7.6375 to 3 significant figures
Answer: 7.64
Step-by-step explanation:
It's rounded off.
When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.
NO LINKS! Please help me with these problems. Part 2
Answer:
For question 6 :
> Vertical stretch by 4 ( Multiply y co-ordinates by a)
> Horizontal compress by 2 ( Multiply x co-ordinates by 1/a)
For question 7 :
> Horizontal compress by 3 (Multiply x co-ordinates by 1/a)
> Graph moved down 4.
I hope this is what you looking for.
Answer:
6. Stretched horizontally by a factor of 1/2 and stretched vertically by a factor of 4.
7. Stretched horizontally by a factor of 1/3 and translated 4 units down.
Step-by-step explanation:
Transformations
[tex]\textsf{For $a > 0$}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Question 6Parent function:
[tex]f(x)=\sqrt{x}[/tex]
Stretched horizontally by a factor of 1/2:
Multiply the x-variable by 2:
[tex]\implies f(2x)=\sqrt{2x}[/tex]
Stretched vertically by a factor of 4:
Multiply the function by 4:
[tex]\implies4f(2x)=4\sqrt{2x}[/tex]
Question 7Parent function:
[tex]f(x)=\lfloor x \rfloor[/tex]
Stretched horizontally by a factor of 1/3:
Multiply the x-variable by 3:
[tex]\implies f(3x)=\lfloor 3x \rfloor[/tex]
Translated 4 units down:
Subtract 4 from the function:
[tex]\implies f(3x)-4=\lfloor 3x \rfloor-4[/tex]
Of 50 employees of a store located in downtown Boston, 18 people take the subway to work, 12 take the bus, and 7 people take both the subway and the bus. How many employees
Complete question :
Of 50 employees of a store located in downtown Boston, 18 people take the subway to work, 12 take the bus, and 7 people take both the subway and the bus. How many employees (a) Take the subway or the bus to work? employees (b) Take only the bus to work? employees (c) Take either the bus or the subway to work (but not both)? employees (d) Get to work by some other means? employees
Answer:
23 ; 5 ; 16 ; 13
Step-by-step explanation:
Given that:
Subway (s) = 18
Bus (b) = 12
Subway and bus = 7
a) Take the subway or the bus to work?
Number of subway + number of bus - (subway and bus)
18 + 12 - 7 = 23
(b) Take only the bus to work?
Number of bus - (subway and bus)
12 - 7 = 5 employees
(c) Take either the bus or the subway to work (but not both)?
Number of bus - (subway and bus) + Number of bus - (subway and bus)
(12 - 7) + (18 - 7) = 5 + 11 = 16 employees
(d) Get to work by some other means?
Total employees - (subway + bus + subway and bus)
50 - (18 + 12 + 7)
50 - 37
= 13 employees
Graph these equations:
y = -2x + 5
y = -2x + 6
Answer:
the answers are
Step-by-step explanation:
for the +5
slope -2
y intercept (0,5)
for the +6
slope is -2
y-intercept (0,6)
if this helped give brainlyest
How do I compare decimal numbers
Answer: You do the same thing that you do for whole numbers but with a decimal
Step-by-step explanation: 3.76 > 2.09 because of the first number