Answers
Answer:
4
Step-by-step explanation:
An equilateral triangle has 3 equal sides.
So
4(x-1) = x +8
4x-4=x+8
3x=12
x=4
Same result obtained when comparing the other pairs of equations.
Explanation:
Since it is an equilateral Triangle their sides are the same.
Thus, 4(x - 1) = x + 8 = 2x + 4
But we can take 2 sides to work with:
To solve for x:
4(x - 1) = x + 8
4x - 4 = x + 8
4x - x = 8 + 4
3x = 12
x = 12/3
x = 4
Therefore, x = 4 and the equation involving x is 4(x - 1) = x + 8
Related Questions
check my answers please?
Answers
Answer:
5
Step-by-step explanation:
Since, Left Hand Limit and Right Hand Limit at x = 2 are approximately equal to 5 at the point of discontinuity (x = 2), the limit of f(x) as x approaches 2 is 5.
Carly solved a quadratic equation by completing the square, but her work has errors. Identify the first error in Carly's work.
Answers
Answer:
D. She added the wrong value to both sides of the equation to complete the square.
Step-by-step explanation:
Got it right on plato
The first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given equation is x(x+4)=117.
Here, x²+4x=117
Now, b/2 =4/2 =2
So, add 2² to both the sides of an equation, we get
x²+4x+2²=117+2²
⇒ x²+4x+4=117+4
⇒ (x+2)²=121
⇒ x+2=±√121
⇒ x+2=±11
⇒ x=±11-2
⇒ x=11-2=9 and x=-11-2=-13
The solution for the given a quadratic equation is x=9 and x=-13. Therefore, the first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².
To learn more about the solution of quadratic equation visit:
https://brainly.com/question/18305483.
#SPJ2
"Brad is trying to determine the Cp of a process. The USL is 10, the LSL is 2, and the standard deviation is 1. What is the Cp"
Answers
Answer:
1.33
Step-by-step explanation:
Given that:
Upper specification limit ( USL ) = 10
Lower specification limit ( LSL ) = 2
the standard deviation σ = 1
What is the Cp"
The Cp is the process capability ratio which can be expressed by the formula:
[tex]C_P = \dfrac{USL -LSL}{6 \times \sigma}[/tex]
[tex]C_P = \dfrac{10 -2}{6 \times 1}[/tex]
[tex]C_P = \dfrac{8}{6}[/tex]
[tex]C_P = \dfrac{4}{3}[/tex]
[tex]C_P =1.33[/tex]
True or false: If you re-word what an author says in your own work, you do not have to provide a citation. * 1 point True False
Answers
Answer:
False
Step-by-step explanation:
In an essay, you have to cite every source you use because
a) the teacher needs to KNOW you didn't copy
b) the teacher needs to know if you got your info from a reliable source
c) the teacher needs to see your ability to use info from a source to put into your essay
This may be different for books, but citation is always a rule of thumb for essays in school, so don't forget unless you want points to be taken off of your score.
Which is the measure of the reference angle for 227 degrees ?
a.35 degrees
B.23 degrees
C.47 degrees
D43 degrees
Answers
Answer:
C. 47°
Step-by-step explanation:
The angle between the terminal ray of 227° and the nearest x-axis (the negative x-axis) is ...
227° -180° = 47°
The reference angle is 47°.
_____
In mathematical terms the reference angle is the minimum of the angle modulo 180° and the supplement of that angle.
227° modulo 180° = 47°
180° -47° = 133° . . . . supplement of 47°
min(47°, 133°) = 47° . . . the reference angle
3 days converted to seconds
Answers
hope this helps :)
Answer:259,200 seconds
Step-by-step explanation:
24 hours in one day
1 hour= 60 minutes
1 minute =60seconds
60x60=3,600
3,600x24=86,400 seconds
86,400x3(days)=259,200 seconds
Match the vocabvulary
Answers
Answer: The answers are in the steps I numbered it as a question from 1 to 12 hopes it helps.Read it carefully.
Step-by-step explanation:
(1) Answer is RATIONAL NUMBERS.
(2) Answer is Fraction
(3) Answer is Terminating decimal
(4) Answer is Decimal
(5) Answer is Integer
(6) Answer is Repeating Decimal
(7) Answer is Perfect Square
(8) Answer is CLASSIFY
(9) Answer is Real Numbers
(10) Answer is Percent
(11) Answer Whole numbers
(12) Answer is Irrational numbers
the time difference between London and New York is -5 hours. The time difference New York and San Francisco is -3 hours. If it is 11:32 in London, what is the time in San Francisco
Answers
Answer:
found this on the web. hopefully it helps
f(x)= -3x+7 what is f(-20)?
Answers
Answer:
67
Step-by-step explanation:
Evaluate 7 - 3 x where x = -20:
7 - 3 x = -3 (-20) + 7
Hint: | Multiply -3 and -20 together.
-3 (-20) = 60:
60 + 7
Hint: | Evaluate 60 + 7.
60 + 7 = 67:
Answer: 67
Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 + 1 f(x) = sigma^infinity_n = 0 (-1)^n x^2n+1 6^n Determine the interval of convergence. (Enter your answer using interval notation.)
Answers
Looks like your function is
[tex]f(x)=\dfrac x{6x^2+1}[/tex]
Rewrite it as
[tex]f(x)=\dfrac x{1-(-6x^2)}[/tex]
Recall that for [tex]|x|<1[/tex], we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
If we replace [tex]x[/tex] with [tex]-6x^2[/tex], we get
[tex]f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}[/tex]
By the ratio test, the series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2<1[/tex]
Solving for [tex]x[/tex] gives the interval of convergence,
[tex]|x|^2<\dfrac16\implies|x|<\dfrac1{\sqrt6}\implies -\dfrac1{\sqrt 6}<x<\dfrac1{\sqrt 6}[/tex]
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.
The interval of the convergence is (-1/√6 < x < 1/√6). We can confirm that the interval is open by checking for convergence at the endpoints.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The given function is
[tex]\rm f(x) = \dfrac{x}{6x^2 + 1} \\\\or \\\\f(x) = \dfrac{x}{1 - (-6x^2)}[/tex]
For |x| < 1, we have
[tex]\rm \dfrac{1}{1-x} = \Sigma_{n=0}^{\infty} \ x^n[/tex]
If x is replaced with -6x², then we have
[tex]\rm f(x)= \Sigma_{n=0}^{\infty} (-6x^2 )^n = \Sigma_{n=0}^{\infty} (-6)^n x^{2n+1}[/tex]
Then by the ratio test, the series converges if
[tex]\displaystyle \lim_{n \to \infty} \left| \dfrac{(-6)^{n+1}x^{2(n+1)+1}}{(-6)^{n}x^{2n+1}} \right|=6|x^{2}| \displaystyle \lim_{n \to \infty }1=6|x^{2}| < 1[/tex]
Solving for x, the interval of convergence will be
[tex]|x^2| < \dfrac{1}{6} \\\\|x| < \dfrac{1}{\sqrt6} \\\\-\dfrac{1}{\sqrt6} < x < \dfrac{1}{\sqrt6}[/tex]
We can confirm that the interval is open by checking for convergence at the endpoints.
More about the function link is given below.
https://brainly.com/question/5245372
PLEASE HELP! A) 6,135º C B) 6,681º C C) 502º C D) 47º C
Answers
Answer:
[tex]\huge \boxed{\mathrm{47\° C}}[/tex]
Step-by-step explanation:
The velocity is given as 358 meters per second.
358 = 20√(273 + t)
Solve for t.
Divide both sides by 20.
17.9 = √(273 + t)
Square both sides.
320.41 = 273 + t
Subtract 273 from both sides.
47.41 = t
Round to nearest degree.
t = 47°C
warehouse A has 200 tons of coal and sells 15 tons every day. warehouse B has 80 tons and buys 25 everyday in how many days does a=b
Answers
Hey there! I'm happy to help!
Let's represent the number of days with x.
WAREHOUSE A
200-15x
WAREHOUSE B
80+25x
We want to find how many days it will take for the two warehouses to have the same amount of coal. Let's put these expressions into an equation to show that they are equal and see what x is.
200-15x=80+25x
We subtract 25x from both sides.
200-40x=80
We subtract 200 from both sides.
-40x=-120
We divide both sides by -40
x=3
Therefore, warehouse A and warehouse B will have the same amount of coal after 3 days.
Have a wonderful day! :D
Please help. I’ll mark you as brainliest if correct!
Answers
Answer:
-2°F
Step-by-step explanation:
So on Sunday night, the temperature was -10°F.
And by Monday morning, the temperature has increased by 8°F.
In other words, to find the temperature on Monday morning, we just have to add 8 to -10. Therefore:
[tex](-10)+(8)=-2[/tex]
The temperature on Monday morning is -2°F
Answer:
-2 degrees F.
If you have -10, you have to add positive 10 just to get to 0.
when 1760 is divided into 14 equal parts the remainder is 10. what is a correct way to write the quotient
Answers
Answer:
125 10/14
Step-by-step explanation:
1,760/14 = 125 r10
- 125 x 14 + 10 = 1,760
You turn the remainder into a fraction using whatever number you divided the main number by. In this case that would be 14.
f(x)=g(x)? What is the solution
Answers
Answer:
The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
;)
sarah set up a lemonade stand and sold each glass for $1.25. write an algebraic expression to represent sarah's profit.
Answers
Answer:
Y=1.25M
Step-by-step explanation:
Y represents the total amount of money being earn
1.25 is how much 1 lemonade drink cost
M represents the number of lemonade that was sold
The amount of lemonade sold time's How much each lemonade drink cost shall give you the total amount of money earn.
The sum of two of the angles of a heptagon is 200ᵒ. If the remaining angles are equal, find the value of each of the remaining angles.
Answers
Answer: 140°
Step-by-step explanation:
Heptagon is a seven-sided polygon. So heptagon has 7 angles.
As known the sum of the angles in poligon is
N=180°*(n-2)
So N(7)=180°*(7-2)=900°
if the sum of 2 angles are 200° then the sum of residual 5 angles is
900°-200°=700°
The remaining 5 angles are equal so each of them is
∠α=700°:5=140°
A vendor bought a supply of ice cream bars at three for 20 cents. He ate one and sold the remainder at 10 cents each. If he made $200.00, how many bars did he buy?
Answers
201 bars
Step-by-step explanation:Let the number of bars bought be x.
Cost of three bars is 20 cents.
Therefore, 1 bar will cost [tex]\frac{20}{3}[/tex] cents.
He ate one of the bars...
Therefore, remaining bars will be x - 1
... He sold the remainder at 10 cents each i.e
1 bar = 10 cents
(x - 1) bars = 10( x - 1) cents
...He made $200.00 from selling the remaining bars.
10( x - 1) cents = $200.00 ---------------(i)
Convert from dollars to cents
$1 = 10 cents
$200 = 200 x 10 cents = 2000 cents
From equation (i)
10(x - 1)cents = 2000 cents
=> 10( x - 1) = 2000 [divide both sides by 10]
=> x - 1 = 200
=> x = 200 + 1
=> x = 201
Therefore, he bought 201 bars of ice cream.
Match each verbal description to its corresponding expressio.
Verbal Description
Expression
the cube of the difference of 5 times x and
7 divided by the sum of 7 times x and 1
7 times the difference of 5 times x and 7 and
the sum of x and 1
the sum of 5 times the cube of x, 1, and
7 times x, divided by 5
the difference of 5 times the cube of x and
7 divided by 7 times the sum of x and 1
553 +75 + 1
558 +19
(51 – 7)3
78 +1
(51 - 7
715 + 1)
The+1) 7(51 – 7)(8 + 1)
Answers
Answer:
Step-by-step explanation:
The solutions to the answers are given below :
1) option c
2) option f
3) option b
4) option d
[tex]a)\frac{5x -7}{7(x+1)} \\\\\\b) 7(5x-7) (x+ 1 )\\\\\[/tex]
[tex]c)\frac{5x^3 + 7x +1}{5}[/tex]
[tex]d) \frac{5x-1 }{7(x+1)}[/tex]
An Expression is a mathematical term consisting of variables, connected using some operators.
Example : 2x + 3
where x is the coefficient of 2 and both the terms are joined using the addition operator.
The verbal description of the corresponding expression is:
1) The cube of the difference of 5 times x and divided by the sum of 7 times x and 1
ans.[tex]\frac{5x - 7}{7(x+1)}[/tex]
2) 7 times the difference of 5 times 6 and 7 and the sum of x and 1.
ans. [tex]7( 5x - 7 )( x+1)[/tex]
3) The sum of 5 times the cube of x , 1 and 7 times x , divided by 5 .
ans. [tex]\frac{5x^3 = 7x +1}{5}[/tex]
4) The difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1.
ans [tex]\frac{5x -7}{7(x+ 1)}[/tex].
Learn more about expression here :
https://brainly.com/question/28170201
#SPJ2
add or subtract
7 + 3 + (-7)
Answers
Answer: 3
Step-by-step explanation: you add 7+3 which is 10 - 7 =3
Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).
Answers
Answer: the real solution: x = - 2
Find the attached file for the remaining solution
Step-by-step explanation:
The equation given is:
x3 - 5x2 + 28 = 0
Let assume that -2 is one of the root of the equation. Substitute -2 for x
(-2)^3 - 5(-2)^2 + 28
-8 - 20 + 28 = 0
Therefore, -2 is one of the root of the equation since the equation tend to zero.
If x = -2, then x+2 is one of the factors of the equation. Therefore, the real solution is x = -2
Please find the attached file for the remaining solution.
What are the attributes of the boundary line of this inequality? -3x − 2y < 6
Answers
Answer:
D. The line is dashed with a y-intercept at (0,-3) and slope of -.
Step-by-step explanation:
If you rearrange the inequality -3x-2y<6 to y=mx+b form you should get y>-3/2x-3
The slope would be mx or -3/2
The Y intercept would be b or -3
I hope this helps :)
The line with an inequality equation -3x - 2y < 6 when plotted on the graph, occupies a region with a dashed boundary line with the attributes, the slope m = -3/2, and the y-intercept c = -3.
What is an inequality equation of a line?An inequality equation for a line is the equation that is true for certain values of its variables. The inequality symbols are ' <, >, ≤, ≥ '.
How do graph an inequality?When inequality is graphed,
The region of values for which the inequality becomes true is shaded.If the inequality has < or > symbols, then the boundary of that region is represented with the dashed line. If the inequality has ≤ or ≥ symbols, then the boundary of that region is represented with the solid line (no breaks).Writing the given inequality in the slope-intercept form of a line:The inequality equation is re-arranged in the slope-intercept form to know the attributes of the line such as the slope of the line and the y-intercept of the line.
The given inequality is -3x - 2y < 6
Step 1: Rewriting the equation into the slope-intercept form:
-3x - 2y < 6
To change the sign, change the inequality symbol also.
⇒ 3x + 2y > 6
⇒ 2y > 6 - 3x
⇒ y > -3/2x - 3
Therefore, the obtained equation is in the slope-intercept form.
So, m = -3/2 and c = -3
Step 2: Graphing the inequality:
To graph the line, we need coordinates.
So, consider x = 0 inorder to get y-coordinate
On substituting,
-3(0) -2y = 6
y = -3
∴ (0, -3) is one of the coordinates of the line
Then, consider y = 0 inorder to get x-coordinate
On substituting,
-3x - 2(0) = 6
x = -2
∴ (-2, 0) is one of the coordinates of the line
These points are plotted in the graph and a line is drawn from these points.
Step 3: Observations from the graph:
Since the inequality is -3x -2y < 6 ( < ), the region above the line is shaded ( the values that satisfies the inequality). The line is represented as a dashed line that indicates the boundary for the inequality region.This means the line is excluded from the solution set of the given inequality.Therefore, the attributes of the boundary line (dashed line) are slope -3/2 and y-intercept -3.
Learn more about the graph of the inequalities here:
https://brainly.com/question/371134
#SPJ2
-3 yz; use y = 3, and 2 - 2
Answers
Step-by-step explanation:
-3(3)(2).
-3(6).
=-18.
name the property illustrated by each statement (8x+3)+12=(8x+3)+12
Answers
Answer:
Reflexive property
Step-by-step explanation:
The statement says that some number is equal to itself.
That's the reflexive property.
I need help with this
Answers
Answer:
x = 16
Step-by-step explanation:
Step 1: We know DF - DE = EF
9x - 39 - 47 = EF
Step 2: Simplify
9x - 86 = EF
Step 3: Set the equation equal to 3x + 10
9x - 86 = 3x + 10
6x = 96
x = 16
Therefore x is equal to 16
Answer:
58
Step-by-step explanation:
DE + EF = DF
47+ 3x+10 = 9x-39
Combine like terms
57 +3x = 9x-39
Subtract 3x from each side
57+3x-3x = 9x-3x-39
57 = 6x-39
Add 39 to each side
57+39 = 6x-39+39
96 = 6x
Divide by 6
96/6 = 6x/6
16 =x
We want the length of EF
EF = 3x+10
= 3*16 +10
= 48+10
= 58
Suppose a ball is thrown upward to a height of h0 meters. Each time the ballâ bounces, it rebounds to a fraction r of its previous height. Let hn be the height after the nth bounce and let Sn be the total distance the ball has traveled at the moment of the nth bounce. Complete parts a. and b below. h0 = 9, r = o.4Find the first four terms of the sequence (Se).
Answers
Answer:What if you were asking this question? How would you explain it to yourself?
Step-by-step explanation:
( 6m + 3 )( m - 2 ) A) 4m 2 - 2m - 20 B) 4m 2 - 20 C) 4m 2 + 18m + 20 D) 6m 2 - 9m - 6
Answers
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex](6m+3)(m-2)[/tex]
Use the distributive property and distribute:
[tex]=(6m+3)(m)+(6m+3)(-2)[/tex]
Distribute:
[tex]=(6m^2+3m)+(-12m-6)[/tex]
Combine like terms:
[tex]=6m^2+3m-12m-6\\=6m^2-9m-6[/tex]
The correct answer is D
Edit: Typo
Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to four decimal places.) [infinity] (−1)n + 1n 2n n = 1
Answers
Answer:
0.1875
Step-by-step explanation:
The well formatted expression for the series has been attached to this response.
Each term in the series is govern by the rule, Tₙ
Where
n = term position
Tₙ = [tex]\frac{(-1)^{n+1}n}{2^n}[/tex]
To get the first six terms, we substitute n = 1 through 6 into Tₙ as follows:
When n = 1, we have;
T₁ = [tex]\frac{(-1)^{1+1}(1)}{2^1} = \frac{1}{2}[/tex] = 0.50000
When n = 2, we have;
T₂ = [tex]\frac{(-1)^{2+1}(2)}{2^2} = \frac{-2}{4} = \frac{-1}{2}[/tex] = -0.50000
When n = 3, we have;
T₃ = [tex]\frac{(-1)^{3+1}(3)}{2^3} = \frac{3}{8}[/tex] = 0.37500
When n = 4, we have;
T₄ = [tex]\frac{(-1)^{4+1}(4)}{2^4} = \frac{-1}{4}[/tex] = -0.25000
When n = 5, we have;
T₅ = [tex]\frac{(-1)^{5+1}(5)}{2^5} = \frac{5}{32}[/tex] = 0.15625
When n = 6, we have;
T₆ = [tex]\frac{(-1)^{6+1}(6)}{2^6} = \frac{-6}{64} = \frac{-3}{32}[/tex] = -0.09375
Therefore, the approximate sum of the series using the sum of the first six terms is
=> T₁ + T₂ + T₃ + T₄ + T₅ + T₆
=> 0.50000 + -0.50000 + 0.37500 + -0.25000 + 0.15625 + -0.09375
=> 0.1875
Consider the function f(x) = log8 x. (a) What is the domain of f? (Enter your answer using interval notation.)
Answers
Answer:
The domain of f is equal to x = log8 x.
Step-by-step explanation:
Which statements are true about x? Select three options