Here we are given with a equation:
[tex] {x}^{3} = - 2197[/tex]
And we have to solve it with appropriate steps.
So, let's start solving.
Add 2197 to both sides of the equation,
[tex] {x}^{3} + 2197 = - 2197 + 2197[/tex]
[tex] {x}^{ 3} + 2197 = 0[/tex]
Now, using the identity:
a³ + b³ = (a + b)(a² - ab + b²)Let's proceed further.
x³ is the cube of x and 2197 is the cube of 13
[tex](x) {}^{3} + (13) {}^{3} = 0[/tex]
[tex](x + 13)( {x}^{2} - x \times 13 + {13}^{2} ) = 0[/tex]
[tex](x + 13)( {x}^{2} - 13x + 13) = 0[/tex]
Now,
x + 13 = 0x² - 13x + 13 = 0So, x = -13
And, for the second let's use the discriminate formula,
➝ D = b² - 4ac
➝ D = (-13)² - 4(1)(13)
➝ D = 169 - 52
➝ D = 117
Now, using the D. formula,
[tex]x = \dfrac{ - b \pm \sqrt{ D} }{2a} [/tex]
[tex]x = \dfrac{13 \pm \sqrt{117} }{2} [/tex]
[tex]x = \dfrac{13 \pm 3 \sqrt{13} }{2} [/tex]
So the roots of the equation are:
[tex]{ \boxed{ \bf{x = - 1 ,\: \frac{13 + 3 \sqrt{13} }{2} and \: \frac{13 - 3 \sqrt{13} }{2} }}}[/tex]
And we are done !!
#CarryOnLearning
━━━━━━━━━━━━━━━━━━━━
given f(7)=4, f'(7)=10, g(7)=-1, g'(7)=8, find the values of the following: 1. (fg)'(7) = 2. (f/g)'(7) =
By the product rule,
[tex](fg)'=f'g+fg'[/tex]
so that
[tex](fg)'(7)=f'(7)g(7)+f(7)g'(7)=10\cdot(-1)+4\cdot8=22[/tex]
By the quotient rule,
[tex]\left(\dfrac fg\right)'=\dfrac{f'g-fg'}{g^2}[/tex]
so that
[tex]\left(\dfrac fg\right)'(7)=\dfrac{f'(7)g(7)-f(7)g'(7)}{g(7)^2}=\dfrac{10\cdot(-1)-4\cdot8}{(-1)^2}=-42[/tex]
PLS HELP!! ITS URGENT!!! SHOW YOUR WORK PLEASE
Answer:
x = 6, y = 8
Step-by-step explanation:
First, we need to find the scale factor from the smaller polygon to the larger polygon. To do this, we can calculate 18 / 12 which is 1.5. Therefore, we can write the following equations:
x · 1.5 = 9 → x = 6
y · 1.5 = 12 → y = 8
pls help math 15 points
3 x's at 1
4 x's at 1 1/4
3 x's at 1 1/2
1 x at 1 3/4
No x's at 2.
Now, let's combine all the recipes with 1 1/4
5/4 * 4 = 20 / 4 = 5 teaspoons
Which of the following steps should be completed first when simplifying ?
Answer:C
Step-by-step explanation:
how do you multiply a fraction with a mixed number
Answer: Covert the mixed number to an improper fraction for them to be too simple fractions and multiply them.
Step-by-step explanation:
By multiply fraction by a mixed fraction you will have to rewrite the mixed number as an improper fraction.
For example ,
1 1/2 is a mixed fraction. If you convert it to improper fraction, you will get 3/2 then you multiply.
S = 4LW + 2WH; S = 168, L = 8, W = 4
H=
Answer:
h=5
Step-by-step explanation:
which property is illustrated?
3. (8 + 0) = 3.8
Michael spent $18 at a local farmers’ market. Apples cost $2 each and peppers cost $3 each. Select the equation that represents the scenario. O) p = 2a + 3a + 18 O) 2a + 3a = 18p O) 2p + 3a = 18 O) 2a + 3p = 18
Answer:
its B, C and E
Step-by-step explanation:
on edge
Answer:
2a + 3p = 18
Step-by-step explanation:
The total has to equal 18 so then you have $2 and $3. Apples cost $2 so the 2 should have an a for Apples. The peppers cost $3 so the 3 should have a p for peppers. So the equation would be 2a + 3p = 18.
HELP What is the perimeter of this rectangle?
Answer:
7×2=14 (for the long side)5×2=10 (for the short sides) the you add up the two answers 14+10=24
10. The weight of an object on a particular scale is 125.2 lbs. The measured weight
may vary from the actual weight by at most 0.4 lbs. What is the range of actual
weights of the object?
A. 124 8 2 x 2 125.6
B. 124.8 2 x 125.6
C. 124 8 5 x 125.6
D. XS 124.8 or x 21256
Given :
The weight of an object on a particular scale is 125.2 lbs.
The actual weight by at most 0.4 lbs.
To Find :
The range of actual weights of the object.
Solution :
It is given that uncertainty in weight is 0.4 lbs.
So, minimum weight can be( 125.2 -0.4 ) = 124.8 lbs.
Maximum weight is given by ( 125.2 + 0.4 ) = 125.6 lbs.
Therefore, the range of actual weights of the object is between :
124.8 x 125.6 .
Hence, this is the required solution.
by ignoring your real intersets when choosing a career,you risk spending your work life feeling bored, and dissatisfied.
A. intrigued
B. content
C. elated
D. frustrasted
Answer: D because it would mess with your feelings
I would put the answer as D.
Enter an algebraic expression to model the given context. Give your answer in simplest form.
The price s of a pair of shoes plus 6% sales tax.
The algebraic expression is
(s)+(s×0.06)=t
t is the total
s is the shoes
Is this correct? Please let me know
Answer:
Step-by-step explanation:
i think yes
i’m not sure if this is right??
Answer:
I think its right
Step-by-step explanation:
thats what I got too
how would i simplify this?
find the domain of the function, picture included
Answer:
[4,∞)
Step-by-step explanation:
x≥4
[4,∞)
11-3(a-2)=27 HELP PLZ
Answer:
a==3.3 a=-3 1/3 a=-10/3
all of those are different possible answers
Step-by-step explanation:
Brian can type 1 and one-third pages every 20 minutes. How many pages can he type in 2.5 hours? 7.5 pages 10 pages 22.5 pages 200 pages
Answer:
10 pages
Step-by-step explanation:
1 and 1/3 pages multiplies by 7.5 brings us to the answer of ten pages
20 minutes goes into 2 and 1/2 hours 7.5 times
10 pages i did this on edge
2020 hope this helps
your welcome =)
Austin removed 16 fish from his pond over a period of 2 days. He removed the same number of fish each day. What was the change in the number of fish in the pond each day?
Answer:
-8
Step-by-step explanation:
if he took out the same number of fish each day then it would be 8 a day resulting in a decrese of 8 fish a day.
132891 round the nerast hundred
MAYBE THIS IS EASY BUT I STILL DOMT GET IT :c
Answer:
What's the question???
Answer:
Cool can you give me brainliest
Step-by-step explanation:
21 +3+ (3 x 9) * 9+5
Answer:
272
Step-by-step explanation:
Do you need this?
Answer:
272
Step-by-step explanation:
what is 70-30+12 then divided by 20
Answer:
2.6
Step-by-step explanation:
First you subtract and get 40 and then you add the 12 which gets 52 and then you divide it by 20 and get your 2.6
Answer:
Step-by-step explanation:
40.6 hope it helps
Determine the range and injective of the function.
j(x) = -x - 1
Answer and Step-by-step explanation:
Solution:
Range:
Let f(x) = -x-1
Here a=0 and b= -1, x=-b/a
Put the values, we get
X= - (-1)/0 = infinity
Hence the range of the function f(x) = (-∞, ∞)
Injective:
A function is said to be injective if f(x1) = f(x2), gives x1=x2
Let f(x1) = -x1-1
f(x2) = -x2-1
f(x1) = f(x2)
Solve the equation algebraically. x^2-7x-1/7=0
Answer:
[tex]x1=\frac{49+\sqrt{2429}}{14} \\x2=\frac{49-\sqrt{2429}}{14} \\[/tex]
Step-by-step explanation:
[tex]x^2-7x-\frac{1}{7} =0\\7x^2-49x-1=0\\D=b^2-4ac=(-49)^2-4*7*(-1)=2429\\x1=\frac{49+\sqrt{2429} }{14} \\x2=\frac{49-\sqrt{2429} }{14} \\[/tex]
Find the missing length, X.
Find the missing length
X= [ ] in
33 in corresponds with the 11 in side
33 in / 11 in = 3
The scale factor is 3
24 in / 3 = 8 in
x = 8 in
Answer:
Step-by-step explanation:
In similar triangles, corresponding sides will be in same ratio.
[tex]\frac{33}{11}=\frac{24}{x}[/tex]
Cross multiply,
33*x = 24 * 11
[tex]x=\frac{24 *11}{33}\\\\x=\frac{24*1}{3}\\\\x = 8 in[/tex]
Write an equation for the line that is parallel to y=-4x+2 and goes through (0,7)
Answer: y=-4x+7
Step-by-step explanation:
To find a parallel line, we know that the slope must be the same because parallel lines NEVER touch or cross. All we have to do is use the given point to find the y-intercept.
y=-4x+b
7=-4(0)+b [multiply]
b=7
Now, we know that the final equation is y=-4x+7.
Answer:
The answer is
y = - 4x + 7Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is y = - 4x + 2
Comparing with the general equation above
Slope / m = - 4
Since the lines are parallel their slope are also the same
Slope of parallel line = - 4
So the equation of the line using point (0,7) and slope - 4 is
[tex]y - 7 = - 4(x - 0) \\ y - 7 = - 4x[/tex]
We have the final answer as
y = - 4x + 7Hope this helps you
Estimate the difference.
689.2 - 263 = ?
To estimate the difference, first round each number to the nearest hundred.
PLZ HELP ME I AM STUCK ON THIS QUESTION :(
Answer:430.2
Step-by-step explanation:
Find two consecutive integers whose product is 12.
Answer:
3 and 4
Step-by-step explanation:
Look at the factors of 12 and list them out
1 and 12
2 and 6
3 and 4
Find the 2 numbers that are consecutive
3 and 4
What is the scale factor from Figure 1 to Figure 2?