solve the polynomial equation:
x^3-7x^2-x+7=0
show your steps please
Answer:
x = {-1, 1, 7}Step-by-step explanation:
Solving for x
x^3 - 7x^2 - x + 7 = 0(x^3 - x) - (7x^2 - 7) = 0x(x^2 - 1) - 7(x^2 - 1) = 0(x - 7)(x^2 - 1) = 0(x - 7) (x + 1) (x - 1) = 0x - 7 = 0 ⇒ x = 7x + 1 = 0 ⇒ x = -1x - 1 = 0 ⇒ x = 1The solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
The given polynomial is [tex]x^3 - 7x^2 - x + 7 = 0[/tex]
We can observe that the polynomial has a common factor of (x - 1).
By dividing the polynomial by (x - 1), we can simplify the equation:
[tex](x - 1)(x^2 - 6x - 7) = 0[/tex]
Now we have factored the polynomial equation as a product of two factors, [tex](x - 1)[/tex] and [tex](x^2 - 6x - 7).[/tex]
To find the solutions, we set each factor equal to zero and solve for x.
Setting [tex](x - 1) = 0[/tex], we get [tex]x = 1.[/tex]
Now, let's solve the quadratic factor [tex](x^2 - 6x - 7) = 0[/tex]
Using factoring or the quadratic formula, we find the roots of the quadratic equation:
[tex]x^2 - 6x - 7 = 0[/tex]
[tex](x - 7)(x + 1) = 0[/tex]
Setting each factor equal to zero:
[tex]x=7[/tex] and [tex]x=-1[/tex]
Therefore, the solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
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PLSS HELPP
What is the value of x in this equation?
4x − 2(2x − 2) = 2(2x − 4)
what is six less than 9
Answer:
3
Step-by-step explanation:
9-6=3
rewrite the function and isolate Y
solve the inequality 2(4+2x) is less than or equal to 5x+5
a. x is Less than or equal to -2
b. x is greater than or equal to -2
c. x is less than or equal to 3
d. x is greater than or equal to 3
Answer:
the answer is d, anything lower than 3 would make the solution incorrect
Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The difference of half the number of oranges and half the number of apples is 4.
An equation created to find the number of apples Javier has in the basket will have
Number of oranges is (2a + 2)
Half the number of oranges is 1/2(2a + 2)
Half the number of apples is 1/2a
The difference between half the number of oranges and half the number of apples equals 4 looks like this:
1/2(2a + 2) - 1/2a = 4
Now solve.
1/2(2a + 2) - 1/2a = 4 (multiply 1/2 by what's inside the parenthesis)
1a + 1 - 1/2a = 4
1a + 1 -1 - 1/2a = 4 - 1
1a - 1/2a = 3
1/2a = 3
1/2a ÷ 1/2 = 3 ÷ 1/2
a = 6
He has 6 apples.
Substitute 6 into the equation for the number of oranges.
2a + 2
2(6) + 2 = 14
He has 14 oranges.
Check your work.
The difference between half the number of oranges (7) and half the number of apples (3) does indeed equal 4.
Therefore, the equation has one solution.
Answer:
it is one solutionStep-by-step explanation:
I have a six sided cube what is the experimental probability of rolling a six
The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?
360π
720π
21,600π
43,200π
Answer:
i think c 21600pi
Step-by-step explanation:
Answer:
C. 21600π
Step-by-step explanation:
A rectangle is twice as long as it is wide. If it has an area of 84.5 square inches, what are its dimensions?
Enter them below, separated by a comma.
Answer:
The rectangle is 18 square inches
Step-by-step explanation:
A rectangle has Length that is twice its Width.
The Width = 3.
What is the area of the rectangle?
First, we know that L, the length, is 6 (twice as long as its width).
Remember that the area of a rectangle is Length times Width:
A = L W
and so
A = 6 × 3 = 18
The rectangle is 18 square inches
The equation 2(4x + 1) = 4(2x + 5) has no solutions. Which of the following best explains why?
Answer:
See below
Step-by-step explanation:
[tex]2(4x + 1) = 4(2x + 5)[/tex]
[tex]8x + 2 =8x + 20[/tex]
[tex]\nexists x \in \mathbb{R} \text{ That makes the equality true}[/tex]
The equation has no solution because no matter what the value we plug for [tex]x[/tex] in the equation, it will not be true and will lead to a contradiction. This is the meaning of not having a solution.
Find the width of a rectangular wall if the perimeter is 148 feet and the width is two more than seven times the length.
Answer:
Step-by-step explanation:
Perimeter of a rectangular wall P = 2L+2W
L is the length of the wall
W is the width
Given
P = 148feet
If the width is two more than seven times the length, this is represented as
W = 7L+2
Substitute W = 7L+2 into the formula above
P = 2L + 2(7L+2)
P = 2L +14L+4
P == 16L+4
148 = 16L+4
16L = 148-4
16L = 144
L = 144/16
L = 9
To get the width
W = 7L+2
W = 7(9)+2
W = 63+2
W = 65feet
Hence the width of the rectangular wall is 65feet
Use the information given to answer the question
An artist prints T shirts to sell at a fair for $14 each
• The artist has some initial T shirts ready to sell and works for h hours more, printing a constant number of T-shirts every
hour
• The expression 14(12h + 30) represents the amount, in dollars, the artist will earn selling all the T-shirts.
Part A
How many T shirts did the artist have initially?
-5m - 2m = 21 what is m
Answer:
m=-3
Step-by-step explanation:
Answer:
m = -3
Step-by-step explanation:
Simplify -5m - 2m to -7m
-7m = 21
Divide both sides by -7
m = 21/-7
Simplify 21/-7 to -3
m = -3
Hope this helps!
-Jerc
Write an equation for the line graphed.
A) y = 2
B) y = 2x
C) y = -2x
D) y = 2x + 1
Answer:
the answer is "d" because the x region is negative 2 and the y region is a positive1
MARKING BRAINLY PLEASE JUST HELPPP
Planet Earth has a mass of 5.9726 × 10 24 kilograms. And although 70% of the Earth's surface is made of water, the water's mass is only 5 × 10 -4 percent of the Earth's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
Answer:
i don't it is correct or not........
Step-by-step explanation:
The Mass of Earth = 5.9742 × 1024 kilograms == == The Earth is (As of May 2000) is thought to be approximately 5.972 sextillion (5,972,000,000,000,000,000,000) metric tons.
A metric ton is a thousand kilograms, or 2,204.62 pounds.
Approximately 6,000,000,000,000,000,000,000,000 (6x1024) kilograms.
Answer:
Mass on water on earth is 29.5×10^20 kg approximately.
Step-by-step explanation:
Mass of earth= 5.9726 × 10^ 24 kg
water's mass is only 5 × 10 -4 percent of the Earth's total mass.
so mass of water = 5.9726×10^24 kg×5×10^-4=29.8603×10^20kg approximately
wolverine and cyclops ordered large pizzas for dinner. Wolverine ate 1-3/8 pizzas and cyclops ate 1/12 of a pizza. which of the following statements is true
Answer:
What statements are you talking about
Step-by-step explanation:
Psychology 101: Is it normal for school age people to have crushes on their teachers or professors?
Answer:
it is normal, but not right to act upon
In a quadratic equation a^2+ bx + c = 0, why is it that the value of a cannot be equal to zero?
Answer:
Someone please help me because i have this question on my test someone please help us
Step-by-step explanation:
How is dividing and multiplying with an area model similar and How is it different?
Answer:
In multiplication the numbers you multiply are called factors; the answer is called the product. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.
2.) Bill sells cleaning products on commission. He earns 40% commission on his sales. If
he has sales of $983, how much commission does he earn?
Answer:
$393.20
Step-by-step explanation:
There are two easy ways to solve this:
1) Use a setup and cross multiply.
First, set up your problem.
$ x = 40%
$983 100%
$983 is the total amount, so it is equal to 100%. We're trying to find 40% of it, so we can label the amount as $x. Remember, each side has to be in the same type of measurements (i.e. dollars, percentages, inches, etc.).
Then, cross multiply. You should end up with:
100x = 39,320
Then, simplify.
x = 393.2
x = $393.20
2) Convert the percentage to a decimal and multiply.
First, convert the percentage you're looking for into a decimal:
40% × 100 = 0.4
Then, multiply the decimal with the total sales amount:
$983 × 0.4 = 393.2
= $393.20
40% × 100 = 0.4
$983 × 0.4 = $393.20
Bill earns $393.20 commission total.
what is the area of the figure?
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
you can split it into two parts. One with 4 x 3 = 12 and the other with 2 x 6 = 12. then add them together and you get 24.
Three times a number decreased by 5 equals 10. Write the equation and find the number.
Answer:
3x - 5 = 10
Step-by-step explanation:
Question 11 of 17
What division equation does the model show ?
Jessica, Kareem, and Lamar served a total of 64 orders Monday at the school cafeteria. Jessica served 8 fewer orders than Lamar. Kareem served 2 times as
many orders as Lamar. How many orders did they each serve?
Answer:
Jessica: 10 orders
Lamar: 18 orders
Kareem: 36 orders
Step-by-step explanation:
Let's first designate each person with a letter.
The number of orders served by Jessica can be designated as [tex]J[/tex]
The number of orders served by Kareem can be designated as [tex]K[/tex]
The number of orders served by Lamar can be designated as [tex]L[/tex]
We know that they all served a total of 64 orders. This can be expressed as the sum of their orders equaling 64.
[tex]J+K+L=64[/tex]
We also know that Jessica served 8 fewer orders than Lamar. This can be expressed as the number of orders served by Jessica, [tex]J[/tex], being equal to Lamar's orders [tex]L[/tex] minus 8.
[tex]J = L-8[/tex]
Fianlly, we know that Kareem served twice as many orders as Lamar. This can be expressed as the number of order's served by Kareem, [tex]K[/tex], being 2 times Lamar's orders [tex]L[/tex].
[tex]K = 2L[/tex]
With these 2 equalities, we can substitute [tex]J[/tex] and [tex]K[/tex] in our original equation,
[tex]J+K+L=64[/tex]
with their values expressed as a subtraction or multiplication of [tex]L[/tex].
[tex]J[/tex] will be substituted with [tex]L-8[/tex], and [tex]K[/tex] will be substituted with [tex]2L[/tex].
[tex]J+K+L=64[/tex]
With substitutions:
[tex](L-8) + 2L + L = 64[/tex]
We can simplify this by combining the L-terms:
[tex]L + 2L + L -8 = 64\\4L - 8 = 64[/tex]
Next, we'll add 8 to both sides.
[tex]4L = 72[/tex]
Divide both sides by 4:
[tex]L = 18[/tex]
Thus, Lamar served 18 orders.
Using our expressions, we can find how many orders the others served.
Jessica:
[tex]J = L-8\\J = 18 -8\\J = 10[/tex]
Jessica served 10 orders.
Kareem:
[tex]K = 2L\\K = 2*18\\K = 36[/tex]
Kareem served 36 orders.
Simplify: (x3 y-2)12 (x-5y)-12
A) xy
B) x12xy
C) yx
D) y12xy
Answer: b
Step-by-step explanation:
3 questions on percentage ❤️
Answer:
Question 1: 131.25 Question 2: 83.33 Question 3. 133.33
Step-by-step explanation:
1. 131.25% x 150
2. Trial and error
3. 60 ÷ 45%
What is the fraction in simplest form?
14/16
7/8
28/32
7/16
7/9
Answer:
7/8
Step-by-step explanation:
Someone please help me.
Answer:
C
Step-by-step explanation:
Prime factors: 2, 3, 3
factorizar por el motodo de aspas
[tex]12x^2 = 3x + 2[/tex]
Answer:
Step-by-step explanation:
12x²-3x=2
[tex]x^2-\frac{1}{4}x=\frac{1}{6}\\x^2-\frac{1}{4}x+\frac{1}{64}=\frac{1}{6}+\frac{1}{64}\\(x-\frac{1}{8})^2=\frac{ 32+3 }{192}=\frac{35}{192}\\\\(x-\frac{1}{8} )^2-(\sqrt{\frac{35}{192} } )^2=0\\(x-\frac{1}{8} +\sqrt{\frac{35}{192} } )(x-\frac{1}{8} -\sqrt{\frac{35}{192} } )=0[/tex]
what’s 4 2/3 divided by 3 1/2 ?
Answer:
the answer to this problemis 1 1/3