Answer:
The first and third polynomials have roots in x = 3 and x = -i. (A, C)
Step-by-step explanation:
The quickest form to determine if [tex]x = 3[/tex] and [tex]x = -i[/tex] are roots consist in evaluating each polynomial and proving that result is zero.
A. [tex]f(x) = x^{3}-3\cdot x^{2}+x-3[/tex]
x = 3
[tex]f(3) = 3^{3}-3\cdot (3)^{2}+3-3[/tex]
[tex]f(3) = 27-27+3-3[/tex]
[tex]f(3) = 0[/tex]
x = -i
[tex]f(-i) = (-i)^{3}-3\cdot (-i)^{2}-i-3[/tex]
[tex]f(-i) = i + 3-i-3[/tex]
[tex]f(-i) = 0[/tex]
B. [tex]f(x) = x^{5}+9\cdot x^{4}+28\cdot x^{3} + 36\cdot x^{2}+27\cdot x +27[/tex]
x = 3
[tex]f(3) = 3^{5}+9\cdot (3)^{4}+28\cdot (3)^{3}+36\cdot (3)^{2}+27\cdot (3)+27[/tex]
[tex]f(3) = 2109[/tex]
x = -i
[tex]f(-i) = (-i)^{5}+9\cdot (-i)^{4}+28\cdot (-i)^{3}+36\cdot (-i)^{2}+27\cdot (-i)+27[/tex]
[tex]f(-i) = -i+9 -28\cdot i +36-27\cdot i +27[/tex]
[tex]f(-i) = -56\cdot i +64[/tex]
[tex]f(-i) = 64 -56\cdot i[/tex]
C. [tex]f(x) = x^{5}-9\cdot x^{4}+28\cdot x^{3} - 36\cdot x^{2}+27\cdot x -27[/tex]
x = 3
[tex]f(3) = (3)^{5}-9\cdot (3)^{4}+28\cdot (3)^{3}-36\cdot (3)^{2}+27\cdot (3)-27[/tex]
[tex]f(3) = 0[/tex]
x = -i
[tex]f(-i) = (-i)^{5}-9\cdot (-i)^{4}+28\cdot (-i)^{3}-36\cdot (-i)^{2}+27\cdot (-i)-27[/tex]
[tex]f(-i) = -i - 9+28\cdot i+36-27\cdot i-27[/tex]
[tex]f(-i) = 0[/tex]
D. [tex]f(x) = x^{3}+3\cdot x^{2}+x+3[/tex]
x = 3
[tex]f(3) = (3)^{3}+3\cdot (3)^{2}+(3)+3[/tex]
[tex]f(3) = 60[/tex]
x = -i
[tex]f(-i) = (-i)^{3}+3\cdot (-i)^{2}+(-i)+3[/tex]
[tex]f(-i) = -i+3-i+3[/tex]
[tex]f(-i) = 6-i\,2[/tex]
The first and third polynomials have roots in x = 3 and x = -i. (A, C)
complete the square to solve
f(x)=x^2-6x+5
A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?
Answer:
The two stadiums are approximately 3115.1 meters away from each other
Step-by-step explanation:
Since we can construct two right angle triangles between the blimp and the two stadiums as shown in the attached image, then the distance "x" between the two can be find as the difference between the right triangle legs that extend on the ground.
In order to find the size of such legs, one can use the tangent function of the given depression angles as shown below:
[tex]tan(75.2^o)=\frac{1100}{a} \\a=\frac{1100}{tan(75.2^o)}\\a\approx 290.6\,\,meters[/tex]
and for the other one:
[tex]tan(17.9^o)=\frac{1100}{b} \\b=\frac{1100}{tan(17.9^o)}\\b\approx 3405.7\,\,meters[/tex]
The the distance between the stadiums is the difference:
b - a = 3405.7 - 290.6 meters = 3115.1 meters
If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2,
find the values of
1) a-b
2) 2a-b
need help will give you a good rating us
Answer:
[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
[tex]2x^2-8x=-7[/tex]
[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]
[tex]2x^2-8x+7=-7+7[/tex]
[tex]2x^2-8x+7=0[/tex]
[tex]ax^2 +bx+c=0[/tex]
[tex]\sf Apply \ quadratic \ formula.[/tex]
[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]
[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]
[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]
[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 236(1.06) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 6%; $448.00 million B. 16%; $474.88 million C. 16%; $250.16 million D. 6%; $422.64 million
Answer:
A. 6%, $448 million
Step-by-step explanation:
a) The base of the exponential term is 1.06, so the projected annual growth is 1.06 -1 = .06 = 6%
__
b) Filling in 11 for t, we find the projected worth to be ...
w = 236(1.06^11) ≈ $448 . . . million
Cory remembers that his ATV had 4 gallons of gasoline in the tank on Monday. After driving a total of 40 miles during
the week, he has 2 gallons of gas remaining. Find the slope of the graph representing this situation.
Answer:
-1/20
Step-by-step explanation:
For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.
To find slope the formula is (y2-y1)/(x2-x1)
So in this case it is 2-4/40-0
-2/40
This reduces to -1/20
In which direction must the graph of Ax) = x be shifted to produce the graph of g(x) = f(x) - 4?
ОА. up
OB. down
O c. left and down
OD. right and up
Answer: B. down
Step-by-step explanation:
Translation rules:
For a function h(x):
h(x+c) is a left-shift by c units.h(x-c) is a right-shift by c units.h(x)+c is a up-shift by c units.h(x)-c is a down-shift by c units.Here, the graph of f(x) becomes the graph of g(x) =f(x)-4 which is similar to "h(x)-c".
That means , f(x) is shifted 4 units down to become g(x).
So, correct option : B. down
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
Answer:
is it 2
Step-by-step explanation:
Is 7 a solution of 5x - 3 = 12?
Answer:
no
Step-by-step explanation:
5x - 3 = 12
5x=12+3
x=15/5=3
x=3
substitute x with 7 to find if it is a solution :
5(7)-3=12
35-3 ≠12 ( so no 7 is not a solution)
Please help me answer this question. -15 - g/3 = -5.
What is g?
Answer:
g = -30
Step-by-step explanation:
-15 - g/3 = -5
Add 15 to each side
-15+15 - g/3 = -5+15
-g/3=10
Multiply by -3 to each side
-g/3 * -3 = 10*-3
g = -30
Answer:
g= -30
Step-by-step explanation:
after writing down the problem, multiply both sides of the equation by 3 to get -45-g= =15. then subtract 15 from both sides to get g=-30, which is your answer. hope this helps!
Solve for x. 3x-91>-87 AND 17x-16>18
Answer & Step-by-step explanation:
For this problem, we have two inequalities to solve for x.
3x - 91 > -87
17x - 16 > 18
Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.
3x - 91 > -87
Add 91 on both sides.
3x > 4
The solution for the first inequality is 3x > 4
Now let's do the second inequality.
17x - 16 > 18
Add 16 on both sides.
17x > 34
Divide by 17 on both sides.
x > 2
The soultion for the second inequality is x > 2
Answer:
The answer is x>2
Step-by-step explanation:
A 2-gallon bottle of fabric softener costs $30.24. What is the price per pint?
Answer:
$1.89
Step-by-step explanation:
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 8 pints
2 gallons = 16 pints
Divide the cost of the fabric softener by 16 to find the price per pint.
$30.24/16 = $1.89
The fabric softener costs $1.89 per pint.
Answer:
$1.89
Step-by-step explanation:
one gallon= 8 pints
two gallons= 16 pints
Therefore, we divide 16 from $30.24
30.24/16= $1.89
Hopefully this answer helps!
I need help ASAP!!
Can someone explain this? And answer it? I am so confused!!
Answer:
Step-by-step explanation: hope this helps
Mummy shade has three children one is Ade, the one second is sumbo. WHAT IS THE NAME OF THE THIRD ONE
just to think wisely about it.
Answer:
Shade
Step-by-step explanation:
she's called Mummy shade, so I think her other child's name is shade
Answer:
Shade
Step-by-step explanation:Her name is Mummy shade
1. 3x + 6y = 3 and 7x + 3y = 7
ons for bo
Answer:
(1,0)
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
Multiply the second equation by -2
-2( 7x + 3y = 7)
-14x -6y = -14
Add this to the first equation to eliminate y
3x + 6y = 3
-14x -6y = -14
--------------------
-11 x = -11
Divide by -11
x = 1
Now find y
3x + 6y = 3
3 +6y = 3
Subtract 3 from each side
6y = 0
y =0
Answer:
x = 1
y = 0
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
=> 3y = 7 - 7x
=> y = -7/3x + 7/3
3x + 6(-7/3x + 7/3) = 3
=> 3x - 14x + 14 = 3
=> -11x = -11
=> -x = -11/11
=> -x = -1
=> x = 1
So, 3(1) + 6y = 3
=> 3 + 6y = 3
=> 6y = 0
=> y = 0/6
=> y = 0
So, x = 1
y = 0
ANSWER QUICKLY PLZZZZZZ
ANSWER QUESTION B
Answer:
16
Step-by-step explanation:
We know that: 5 + ? = 10.5
we now need to solve for ? , by using the inverse method
10.5 x 2 = 21
21 - 5 = 16
Now to double check the answer, we substitute the ? with the answer
so, 5 + 16 = 21
21/2 = 10.5 so it is clearly correct
I HOPE THIS HELPED :)
Latanya buys 5 yard of blue fabric and 8 yards of green fabric. the blue fabric cost $2 dollars more than the green fabric.she pays a total of $ 62. what would be the combined cost of 1 yard of blue fabric and one yard of green fabric?
Answer: $10
Step-by-step explanation:
let x = the price of green fabric, then x+2 = blue fabric price
8x+5(x+2)=62
8x+5x+10=62
13x+10=62
13x=52
x=4
price of green fabric=$4
price of blue fabric=$6
4+6=$10
Can someone help me solve parts (a) and (c) please? Thank you!
a) 4x +6
Add up all the sides to calculate perimeter
Answer:
a) 6x + 6
b) 15 x 24
c) see explanation
Step-by-step explanation:
a) 2x + x + 3 + 2x + x + 3 = 6x + 6
b) 6x + 6 = 78
6x = 72
x = 12
2(12) = 24
(12) + 3 = 15
15 x 24
c) 2x(x + 3) = 2x² + 6x
2(12)² + 6(12) = 288 + 72 = 360
15 x 24 is also 360
Georgina has $5.60 in quarters and dimes. If Georgina has 14 more dimes than quarters, how many quarters does she have?
[I don't want the answer i just want someone to show me how the problem is set up because its confusing me...Thanks]
Answer:
She has 12 quarters.
Step-by-step explanation:
You have two unknowns, the number of quarters and the number of dimes. You need one equation per unknown, so you need two equations. One equation deals with the number of coins. The other equation deals with the values of the coins.
The first step is to choose variables. We can go with x and y, but I prefer to choose q and d, so I remember more easily what they represent.
Let q = number of quarters.
Let d = number of dimes.
Let's deal with the numbers of coins first.
"Georgina has 14 more dimes than quarters"
She has q number of quarters, but the number of dimes is 14 more than the number of quarters. d is 14 more than q. Our first equation is
d = q + 14
Now we deal with the values of the coins.
We don't know yet the actual numbers of dimes and quarters, so we use d and q to represent those numbers.
One dime is worth $0.10; d number of dimes is worth 0.1d.
A quarter is worth $0.25; q number of quarters is worth 0.25q.
The total value of the dimes and quarters is the sum of the values of the two sets of coins:
0.1d + 0.25q
We are told "Georgina has $5.60 in quarters and dimes."
This gives us our second equation.
0.1d + 0.25q = 5.6
Now we have a set of two equations in two variables:
d = q + 14
0.1d + 0.25q = 5.6
There are several methods for solving a system of equations. Since the first equation is already solved for a variable, d, we can use the substitution method.
We rewrite the second equation, but we substitute q + 14 for d in the second equation.
Second equation:
0.1d + 0.25q = 5.6
Substitute q + 14 for d:
0.1(q + 14) + 0.25q = 5.6
Distribute on the left side:
0.1q + 1.4 + 0.25q = 5.6
Combine like terms on the left side:
0.35q + 1.4 = 5.6
Subtract 1.4 from both sides:
0.35q = 4.2
Divide both sides by 0.35:
q = 12
There are 12 quarters.
(You are asked only the number of quarters, so you can stop here. I will continue to find also the number of dimes for 2 reasons. 1) You see how it's done, so it will help with other problems. 2) By finding the numbers of dimes and quarters, then we can check if our solution is correct, which I will do below at the end.)
Now we use the first equation, d = q + 14. We substitute 12 for q and solve for d.
d = q + 14
d = 12 + 14
d = 26
There are 26 dimes.
Check:
We check the numbers of coins:
26 - 12 = 14 The number of dimes is indeed 14 more than the number of quarters.
We check the values of the coins:
0.1(26) + 0.25(12) = 2.6 + 3 = 5.6 The value of the coins is indeed $5.60.
Our answer is correct.
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 10.5 cm
B. 3.4 cm
C. 8.5 cm
D. 12 cm
Answer:
12 cm is the right answer pls mark me brainliest
The height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles is 12 cm.
What is Area of Triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
What is Heron's formula?Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:
Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given:
Three sides are: 15cm, 25 cm and 2 cm
Now, Using Heron's formula
semi-perimeter= (25+ 20 + 15)/2
s= 30 cm
Now,
Area of triangle
=√s(s-a)(s-b)(s-c)
=√30* 5 * 10* 15
=√5*2*3*5*2*5*3*5
=5*5*2*3
=150 cm²
Again, area of triangle= 1/2* b* h
150= 1/2* 25* x
12cm= x
Learn more about Area of Triangle here:
https://brainly.com/question/9817285
#SPJ2
-5x-10=10 solve for x
Answer:
x = -4
Step-by-step explanation:
-5x-10=10
Add 10 to each side
-5x-10+10=10+10
-5x = 20
Divide each side by -5
-5x/-5 = 20/-5
x = -4
Answer: x= -4
Step-by-step explanation:
[tex]-5x-10=10[/tex]
add 10 on both sides
[tex]-5x=20[/tex]
divide -5 on both sides
[tex]20/-5=-4[/tex]
[tex]x=-4[/tex]
Which of the following is an irrational number?
5 / 4
√5 / 7
1/ 8
3 / 5
Answer: [tex]\sqrt{5} /7[/tex]
Step-by-step explanation:
5/4 is not an irrational number because it is already in a fraction the same as 1/8 and 3/5.
The square root of 5 is not rational because it cannot be converted to a fraction or in other words is not a perfect square.
Answer:√5 / 7
Step-by-step explanation:
on a map, the distance between jacksonville FL and tallahasse FL is about 5 inches. According to the scale, 1 inch represents 25 miles. About how far apart are these two cities?
Help the question is there
Answer:
y = 7 when x = -5
Step-by-step explanation:
First go to x = -5
Then go up to where you meet the green line
The y value is 7
y = 7 when x = -5
what is the value of a in the functions equation?
Answer:
y= -2x^2 + 12x -14
Step-by-step explanation:
when I put the points into a graphing calculator this is what I got so I think the answer is -2
Answer:
Step-by-step explanation:
It is -2
Number17) Find length of CD.
Answer:
2.4
Step-by-step explanation:
similar triangles
Therefore
4/CD = 5/3
CD= 12/5
Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
A. 7[tex]\sqrt{2}[/tex]
B. [tex]\frac{7\sqrt{3} }{2}[/tex]
C. [tex]7\sqrt{3}[/tex]
D. [tex]\frac{7\sqrt{2} }{2}[/tex]
Answer:
7 sqrt(2)/2 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = x/7
7 sin 45 =x
7 sqrt(2)/2 =x
Answer:
[tex]\large \boxed{\mathrm{D. \ \displaystyle \frac{7\sqrt{2} }{2 }}}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve the problem.
[tex]sin \theta = opp/hyp[/tex]
The opposite side to the angle 45 degrees is x and the hypotenuse of the triangle is 7.
[tex]sin 45 = x/7[/tex]
Multiply both sides of the equation by 7.
[tex]7 sin 45 = x[/tex]
Simplify the value.
[tex]\displaystyle \frac{7\sqrt{2} }{2 }=x[/tex]
Describe the relationship between quartiles and percentiles. ▼ are special cases of ▼ ▼ Upper Q 2 Upper Q 3 Upper Q 1 is the 25th percentile, ▼ Upper Q 2 Upper Q 1 Upper Q 3 is the 50th percentile, and ▼ Upper Q 2 Upper Q 3 Upper Q 1 is the 75th percentile.
Answer:
Q1 is the 25th percentile
Step-by-step explanation:
Quartiles are known to be one-fourth of an entity, that is, 1/4th with the whole evaluating to 1. The numerator cannot exceed four, as the division compares an item in an entity to the whole of the entity or sample.
Percentiles represents a whole entity as a 100 with the symbol "%" which denote its use.
The first quartile is 25th percentile, the second is the 50th percentile, the third is the 75th percentile while the fourth quartile which is 4/4 is the 100th percentile mark.
Will Give Brainliest, answer ASAP x=
y=
z=
Opposite angles are identical.
11y = 55
Y = 55/11
Y = 5
3z-4 = 110
Add 4 to both sides
3z= 114
Z = 114/3
Z = 38
180 -110 = 70
55 + x = 70
X = 70-55
X =15
X = 15, y = 5, z = 38
Answer:x=15, y=5, z=38
Step-by-step explanation: you know that opposite angles are the same. y=5
add 4 to both sides. and you get the value for x y z.
