Using the factor theorem, it is found that the polynomial is:
[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]
Given by the first option
---------------------------
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] using the factor theorem it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
---------------------------
In this question:
[tex]x_1 = 2[/tex][tex]x_2 = \sqrt{3}[/tex][tex]x_3 = -\sqrt{3}[/tex]By the options, leading coefficient [tex]a = 1[/tex]Thus:
[tex]f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})[/tex]
[tex]f(x) = (x - 2)(x^2 - 3)[/tex]
[tex]f(x) = x^3 -2x^2 - 3x + 6[/tex]
Which is the polynomial.
A similar problem is given that: https://brainly.com/question/4786502
In parallelogram ABCD, m∠B = 105°.
What is the value of x. (Round your answer to the nearest tenth, if necessary.)
Answer:
x=52.5
Step-by-step explanation:
Since ABCD is a parallelogram, B= ADC. So angle ADC is 105. Next since ED=AD, angle EAD=angle AED=x and ADE=75. So 2x+75=180, 2x=105, x=105/2
In parallelogram ABCD, m∠B = 105° then the value of x = 52.5
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since ED ≈ AD,
∆AED is an isosceles triangle where ∠EAD and ∠AED has the same angle measurement
Now, ∠B = 105°, since ABCD is a parallelogram,
∠B = ∠D
∠ADC = 105°
∠ADE = 180°-105° = 75°
Now, ∠EAD + ∠AED+ ∠ADE = 180°
∠AED+∠AED+∠ADE = 180°
x+x+75°=180°
2x=180+75°
2x = 105°
x = 52.5°
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BRAINLIEST, 5 STARS AND THANKS IF ANSWERED CORRECTLY.
A quadratic equation with a negative discriminant has a graph that..
A. touches the x-axis but does not cross it
B. opens downward and crosses the x-axis twice
C. crosses the x-axis twice.
D. never crosses the x-axis.
Answer:
never crosses the x-axis.
Step-by-step explanation:
A quadratic equation with a negative discriminant has a graph that - never crosses the x-axis.
Answer:
The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis. The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point. To be clearer, it can be seen in the attached image.
Step-by-step explanation:
Answer D
Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame, in inches?
Answer:
41 inches
Step-by-step explanation:
Let the point at the top of the door on the left be x
Wx + xH = 45
Let the point at the top of the door on the right be c
Yc + cZ = 37
We know the door is
xH + plus the width of the tile
The width of the tile is Yc
xH + Yc
On the right door
cZ + the height of the tile
cZ + Wx
Add the two doors together
xH + Yc + cZ + Wx = 2 times the height of the door
Rewriting
xH + Wx + Yc + cZ = 2 times the height of the door
45+ 37 = 2 times the door height
82 = 2 times the door height
Divide by 2
41 = door height
I need help with 6 and 7
Answer:
Step-by-step explanation:
6):
Take the small right triangle with the sides 25 and 7.
☆ The Pythagorian theorem ☆
Let x be the third side.
● 25^2 = x^2 + 7^2
Substract 7^2 from both sides
● 25^2 -7^2 = x^2 +7^2 -7^2
● x^2 = 25^2 -7^2
● x^2 = 576
● x = 24 inches
The third that we find is the half of the side of the square.
Multiply it by 2 and get the side of the square.
● 24 × 2 = 48 inches
The perimeter of the square is the side times 4.
● P = 48 × 4
● P = 192 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
7):
Both triangles are righr and they have a khown angle.
Start with the small one and calculte the third angle.
The sum of a triangle angles is 180°
Let B be the third angle.
● B = 180-(90+51) = 39°
That's equal to the second angle of the second's triangle.
So it's an AA similarity.
So:
● x/24 = 7/15
● x = (7/15)×24
● x = 11.2
What is the constant term for 4x-2y+3
Answer:
Step-by-step explanation:
3 is the constant term.
Constant term is the term without any variables
Answer:
3
Step-by-step explanation:
The constant number is the number that has no variable and just a number.
Triangles ABC and XYZ are similar. Find side x.
Answer:
x=6
Step-by-step explanation:
side AB is proportional to side XY
side AC is proportional to side XZ
Since we know side AB and side XY are proportional to each other, if we divide side AB by side XY, we can find the size difference...
12 / 4 = 3
The smaller triangle is 3 times smaller than the bigger triangle so we can find side XZ by dividing side AC by 3...
18 / 3 = 6
x = 6
The measure of the length of x is 9 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≈".
Given triangles ABC ≈ XYZ
for similar triangles, corresponding sides are proportionately equal and corresponding angles are congruent,
so AB/XY = AC/XZ = BC/YZ
substitute the values
12/4 = 18/x = 9/YZ
12/4 = 18/x
x= 9 units
Hence the value of x is 9 units.
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Solve for the value of p.
p =
Answer:
p = 4
Step-by-step explanation:
[tex](8p + 4) \degree + 54 \degree = 90 \degree \\ (complementary \: \angle s)\\ (8p + 4+54) \degree = 90 \degree \\ (8p + 58) \degree = 90 \degree \\ 8p + 58 = 90 \\ 8p = 90 - 58 \\ 8p = 32 \\ p = \frac{32}{8} \\ p = 4[/tex]
Answer:
p = 4
Step-by-step explanation:
8p+4+90+54=180
180-90-54=36
36-4=32
32/8=4
p=4
to check the answer
90+54+(8×4)+4=180⁰
Does anyone know this?
Answer:
f(-4) = 92
Step-by-step explanation:
f(x) = 3x^2 - 10x + 4
f(-4) = 3(-4)^2 - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Alonso overdrew his bank account and his account balance showed -$50. He spent an
additional $37 going out to the movies with friends. Write an expression and draw a line
number to determine Alfonso's current bank account balance.
Answer:
-$87
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
last option
Step-by-step explanation:
Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
Helpppp pleaseeeeee!!!
Answer: yes.
Step-by-step explanation:
Answer: Yes
The roll of the dice is a random process that Jon has no control over (this is assuming the dice is fair of course). Whoever is selected first is not selected again, so the probability for the second selection will increase as there is a smaller pool of people to pick from.
darious buys a bottle of chemical solution that contains 70% alcohol. the bottle contains 500 ml of solution. how many ml of alcohol r in the solution
Answer:
350 ml of alcohol
Step-by-step explanation:
70% = 70/100 = 0.7
70% of 500 ml is:
500*0.7 = 350 ml
there are:
350 ml of alcohol
if polynomial ax3 + 3x2 - 3 and 2x3 - 5x + a leaves the same remainder when each is devided by x - 4 find the valuse of a
Answer:
a = 1
Step-by-step explanation:
Given that both ax³ + 3x² - 3 and 2x³ - 5x + a have the same remainder when divided by x - 4.
x - 4 = 0
x = 4
When ax³ + 3x² - 3 is divided by x - 4, the remainder is gotten by substituting x = 4:
a(4)³+3(4)²-3 = 64a + 48 - 3 = 64a + 45
The remainder is 64a³ + 45
For 2x³ - 5x + a we find the remainder by substituting x = 4:
2(4)³ - 5(4) + a = 128 - 20 + a = 108 + a
Since they both have the same remainder, therefore:
64a + 45 = 108 + a
64a - a = 108 - 45
63a = 63
a = 1
Adding the fractions
3/14+2/21+1/6
Answer:
[tex]\frac{10}{21}[/tex]
Step-by-step explanation:
The LCM of 14, 21 and 6 is 42
We require to change the fractions to fractions with a denominator of 42
[tex]\frac{3(3)}{14(3)}[/tex] + [tex]\frac{2(2)}{21(2)}[/tex] + [tex]\frac{1(7)}{6(7)}[/tex]
= [tex]\frac{9}{42}[/tex] + [tex]\frac{4}{42}[/tex] + [tex]\frac{7}{42}[/tex] ← add the numerators, leaving the denominator
= [tex]\frac{9+4+7}{42}[/tex]
= [tex]\frac{20}{42}[/tex] ← divide both values by 2
= [tex]\frac{10}{21}[/tex] ← in simplest form
If p varies directly with T and p =105 when T=400.Find p when T =500
Answer:
p = 131.25Step-by-step explanation:
The variation p varies directly with T is written as
p = kT
where k is the constant of proportionality
To find p when T =500 we must first find the formula for the variation
That's
when p = 105 and T = 400
105 = 400k
Divide both sides by 400
[tex]k = \frac{21}{80} [/tex]So the formula for the variation is
[tex]p = \frac{21}{80} T[/tex]when
T = 500
Substitute it into the above formula
That's
[tex]p = \frac{21}{80} \times 500[/tex]
Simplify
The final answer is
p = 131.25Hope this helps you
The dosage for a certain drug calls for 20mg per kg per day and is divided into two doses(1every 12 hours) if a person weighs 197 pounds how much of the drug should be given each dose
Answer:
893.42
Step-by-step explanation:
1kg=2.205pounds
so 20mg is for 2.205pounds
therefore for 197pounds will be 1784.84mg
but the dose is once every 12hrs meaning twice a day so divide 1784.84/2 to get the pounds
Solve 2(x - 5) = 48 - 4(x + 1)
Answer:
x = 9
Step-by-step explanation:
first remove the brackets
2x - 5 = 48 - 4x + 1
then take numbers to the opposite sides
2x + 4x = 48 + 5 + 1
I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4
now solve
2x + 4x= 6x
48+5+1= 54
6x = 54
now solve for x
divide both sides by 6x
x = 9
A typical television newscast has three cameras. The center camera directly faces the news anchor’s desk. The other two cameras are both angled 45 degrees away from the center camera. Suppose each camera has a filed if 60 degrees. What is the total angle covered by three cameras? Explain your reasoning.
The width of a rectangle measures (6.8d-4.2)(6.8d−4.2) centimeters, and its length measures (9.2d+8.7)(9.2d+8.7) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.
Step-by-step explanation:
The perimeter ([tex]p[/tex]) of a rectangle, measured in centimeters, is represented by this formula:
[tex]p = 2\cdot (w+l)[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are width and length, measured in centimeters.
If [tex]w = 6.8\cdot d-4.2[/tex] and [tex]l = 9.2\cdot d+8.7[/tex], the expression that represents the perimeter is:
[tex]p = 2\cdot (16\cdot d +4.5)[/tex]
[tex]p = 32\cdot d + 9[/tex]
The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.
4. A prism has an area of cross-section of 89 cm². The volume of the prism is
4895 cm?. Find the height of the prism.
Answer:
55 cm
Step-by-step explanation:
height = 4895/89 = 55 cm
Kia was 200 m north of the Liebrary when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes cost round-trip
Answer:
His speed is 2 m/s
His velocity is 0 m/s
Step-by-step explanation:
I'll assume the question is
Kia was 200 m north of the Library when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes hist round-trip.
Kia's distance from the Library is 200 m
the round-trip took him 200 s
The total distance for the round trip = 200 x 2 = 400 m
His displacement for the round trip = 0 m (since he returns to his original position)
His speed = distance/time = 400/200 = 2 m/s
His velocity = displacement/time = 0/200 = 0 m/s
A study found that the expected annual income in a certain area is $17,255. Which of the following statistical measurements most likely led to this conclusion? Mean, range, median or mode?
Answer:
Mean
Step-by-step explanation:
mean is the average of numbers put together and divided by the total amount of numbers, when finding the average annual income using the mean would be most effective
Complete the ordered pairs below so they satisfy the equation.
y = - 7x + 8
Answer:
x=8/7-y/7
Step-by-step explanation:
Solve equation show all steps what 2x-3x+5=18
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]2x-3x+5=18[/tex]
Step 1: Simplify both sides of the equation.
[tex]2x-3x+5=18\\2x + -3x + 5 = 18[/tex]
[tex]( 2x + -3x ) + ( 5) = 18[/tex] (Combine Like Terms)
[tex]-x + 5 = 18\\-x + 5 = 18[/tex]
Step 2: Subtract 5 from both sides.
[tex]-x + 5 - 5 = 18 - 5 \\-x = 13[/tex]
Step 3: Divide both sides by -1.
[tex]\frac{-x}{-1} = \frac{13}{-1} \\x = -13[/tex]
Answer : [tex]\boxed {x = -13}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
[tex] \boxed{ \bold{ \mathsf{ \purple{x = - 13}}}}[/tex]Step-by-step explanation:
[tex] \mathsf{2x - 3x + 5 = 18}[/tex]
Collect like terms
[tex] \mathsf{ - x + 5 = 18}[/tex]
Move constant to R.H.S and change it's sign
[tex] \mathsf{ - x = 18 - 5} [/tex]
Calculate the difference
[tex] - x = 13[/tex]
Change the signs on both sides of the equation
[tex] \mathsf{x = - 13}[/tex]
---------------------------------------------------------------
[tex] \blue{ \mathsf{verification}}[/tex]
[tex] \mathsf{LHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RHS}[/tex]
[tex] \mathsf{2x - 3x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18}[/tex]
[tex] \mathsf{ = 2 \times ( - 13) - 3 \times ( - 13) + 5}[/tex]
[tex] \mathsf{ - 26 + 39 + 5}[/tex]
[tex] \mathsf{ = 13 + 5}[/tex]
[tex] = 18[/tex]
Thus, LHS = RHS
hope I helped!
Best regards!
Question
0
Which angle between 90 and 270 has the same sine value as 60°?
Which angle between –180° and 0 has the same cosine value as 290°?
degrees
Answer:
(i) 120°
Step-by-step explanation:
(i)
sine 90 = 1
sine 120 = 0.87 (rounded up to two decimal places)
sine 150 = 0.5
sine 180 = 0
sine 210 = -0.5
sine 240 = -0.87 (rounded up to two decimal places)
sine 270 = -1
sine 60 = 0.87 (rounded up to two decimal places)
So the angle x such that 90° < x < 270° that has the same sine value as 60° is 120°
What is the value of d to the nearest tenth?
Answer:
d=13.8
Step-by-step explanation:
secant-secant theorem: (a+b)b=(c+d)d
(14+20)14=(16+d)16
34*14=256+16d
476=256+16d
220=16d
d=13.75
Answer:
[tex]\frac{14}{16}=\frac{20}{d}[/tex]
[tex]14d=16\cdot \:20[/tex]
Multiply 16 × 20
[tex]14=320[/tex]
Now, Divide both sides by 14
[tex]\frac{14d}{14}=\frac{320}{14}[/tex]
[tex]d=22.9[/tex]
OAmalOHopeO
Distribute 10 (3x + 8x2).
Answer:
30x+160
simple all you had to do is 10*3x and 8x2=16 and 10*16 and you will get 30x+160
Step-by-step explanation:
Answer:
30x + 80x^2
Step-by-step explanation:
10 (3x + 8x^2)
10 * 3x + 10 * 8x^2
30x + 80x^2
30 in.
20 in.
36 in.
Find the area of the trapezoid shown above.
[?] square inches
Answer:
660 in^2
Step-by-step explanation:
The formula to calculate area of trapezoid : (a+b)/2*h (a: base, b: base, h: height)
(30+36)/2*20 = 660 in^2
the base of a rectangle is three times as long as the height. of the perimeter is 64, what is the area of the rectangle
Answer: 192
Step-by-step explanation:
Use algebra
x + 3x + x + 3x = 64 (perimeter)
Combine Like Terms
8x = 64
x = 8
8 + 24 + 8 + 24 = 64
24/8 = 3
The interest of the sum of money at the end of 10 years is one third of the sum. Find the rate of interest
Answer:
3.33%
Step-by-step explanation:
Intrest = P. A. *Intrest Rate * Time
(1/3)*P. A. = P. A. *Intrest Rate * 10
Intrest Rate = 1/30)=3.33%