Step-by-step explanation:
[tex] = {(3 \sqrt{ {x}^{2} } )}^{6} [/tex]
[tex] = {(3 {x}^{ \frac{2}{2} } )}^{6} [/tex]
[tex] = {(3x)}^{6} [/tex]
[tex] = {3}^{6} {x}^{6} [/tex]
[tex] = 729 {x}^{6} [/tex]
====================================
[tex]\large \sf \underline{Problem:}[/tex]
Which expression is equivalent to (3√x^2)^6
====================================
[tex]\large \sf \underline{Answer:}[/tex]
The answer is x⁴
====================================
[tex]\large \sf \underline{Explanation:}[/tex]
[tex]( \sqrt[3] {x}^{2} )⁶ \: {The \: cube \: root \: of \: x² \: is \: x^(2/3)} (x^(2/3))⁶ {Now, \: simply \: multiply \: 2/3 \: by \: 6 \: to \: get \: 4.}[/tex]
x⁴
[tex]( \sqrt[3] {x}^{2} )⁶ \: is \: equivalent \: to \: x⁴[/tex]
====================================
The first number in a pattern is 208. The pattern follows the rule subtract 18. What are the next three numbers? (3 points)
a
195, 183, 172
b
190, 183, 176
c
190, 181, 172
d
190, 172, 154
Answer:
d) 190,172,154
Step-by-step explanation:
208-18=190
190-18=172
172-18=154
find the volume of a rectangular prism with a length of 4 inches and a width of 7 inches and a height of 11 inches
Answer:308
Step-by-step explanation:Multiply 4*7*11
A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept, end behavior, symmetry, local and global extreme values, and intervals of increasing and decreasing to select the best choice of the polynomial function, f.
The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
How to determine the equation?From the graph, we have the following observations:
The graph has a turning point at x = 2The graph changes the factor of its direction at x = -5This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5
So, we have:
f(x) = a(x + 5)³(x - 2)²
The curve is inverted,
This means that a < 0
Assume a = -1.
Then, we have:
f(x) = -(x + 5)³(x - 2)²
Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
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Calculate the missing balances in Jane's check register.
Check # Date Transaction Deposit Withdrawal Balance
341 6/11 dress shop $71 99 $279 66
342 6/15 nail salon $41 50 $
6/20 graduation money $200 00 $
Day 6/11 = $6,920
Day 6/15 = $6,505
Day 6/20 = $6,305
Calculation of missing balancesDay 6/11 Jane deposited=$7,199She withdrew $279 to buy clothes
Therefore her final balance= $6,920
Day 6/15 from her balance, she made her nails in a nail salon for $41 5.Therefore, her balance is
= $6,920 - $415
= $6,505
Day 6/20 Jane withdrew her graduation money at the prize of $200Therefore her balance is
= $6,505 - $200
= $6,305
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A special-edition model of a smart watch is sold in gold, green, blue, or red. ernie's electronics sold 234 of these smart watches last week. they sold twice as many red watches as gold watches. they sold 3 times as many green watches as gold watches. they sold the same number of blue watches as green watches. how many green smart watches did the store sell last week?
The number of green watches that were sold is 78
How to determine the number of green watches?The given parameters are:
Total =234Red = 2 * GoldGreen = 3* GoldBlue = GreenThe number of watches can be represented as
Gold + Green + Blue + Red = 234
Substitute Blue = Green
Gold + Green + Green + Red = 234
Gold + 2 * Green + Red = 234
Substitute Red = 2 * Gold
Gold + 2 * Green + 2 * Gold = 234
Evaluate the like terms
2 * Green + 3 * Gold = 234
Make Gold the subject in Green = 3* Gold
Gold = Green/3
Substitute Gold = Green/3 in 2 * Green + 3 * Gold = 234
2 * Green + 3 * Green/3 = 234
Evaluate the product
2 * Green + Green = 234
Evaluate the sum
3 * Green = 234
Divide both sides by 3
Green = 78
Hence, The number of green watches that were sold is 78
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A Panel in a stained-glass window in the shape of a parallelogram has the dimensions shown. Find the area of the panel.
Answer: 20 sq ft
Step-by-step explanation: The base is AB = 5 ft because AB = CD. Recall that opposite sides in a parallelogram are congruent and parallel.
area of parallelogram = base * height = 5*4 = 20
note: the base is always perpendicular to the height
Jackie has a choice of 3 pairs of shoes, 3 pants, and 4 shirts that can make an outfit for today. Each pair of shoes has a different heel height, each pair of pants is made from a different fabric, and each shirt is a different color.
Jackie randomly picks some clothes.
What is the probability that she chooses an outfit consisting of the flat heel or spike heel shoes, the twill or the denim pants, and the white or black shirt?
Answer:
2/9
Step-by-step explanation:
i just took a test with this exact question, and the answer was 2/9
youre welcome future learners ;)
Please help me, I need an answer as soon as possible.
Answer:
[tex]\huge\boxed{\sf x = \pm \sqrt{7} }[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2-7[/tex]
We can also write it as:
[tex]y =x^2-7[/tex]
x-intercept is the point where y = 0
Put y = 0 in the above equation
[tex]0=x^2-7\\\\Add \ 7 \ to \ both\ sides\\\\7 = x^2\\\\Take \ sqrt \ on \ both \ sides\\\\\pm \sqrt{7} =x\\\\x = \pm \sqrt{7} \\\\\rule[225]{225}{2}[/tex]
PLEASE HELP ME I RELLY NEED IT
Answer:
[tex]KL=45.6[/tex]
Step-by-step explanation:
Property of a Rectangle: Opposite sides are equal.
This means:
[tex]KL = JM \text{ where JM = 45.6}[/tex]
[tex]KL = 45.6[/tex]
give answer in simplest form with working out pls
Answer:
5 x 5+3/5= 25+3/5=28/5÷8/3
28/5 x8/3= 224/15 =14.93
Which number sentence is represented by this model?
Answer:
Correct answer is B. -3 • 5 = - 15
how to solve x-3y=1 4x+5y=4 using elimination
Answer:
X=1, Y=0
Step-by-step explanation:
Solve for X and Y using a2 +b2 = c2
Type the missing number in this sequence:
6, 8, 11, 15, 20,____,33
Answer: 26
Step-by-step explanation: the pattern is +2, +3, +4, +5. +6, +7
6+2 = 8
8+3 = 11
11+4 = 15
15+5 = 20
20+6 = 26
26+7 = 33
Answer:
26
Step-by-step explanation:
In this, the addition of numbers is starting from 2 and continue. Such as 6+2=8,then 8+3=11. Similarly the addition of numbers is continuing
-x/8-11=-2 what is the answer because i have a tough time solving it
Answer:
[tex]x=-72[/tex]
Step-by-step explanation:
[tex]-\frac{x}{8}-11=-2\\ -\frac{x}{8}=9\\ -x=72\\x=-72[/tex]
I need help on this please
Answer:
Volume of a cone = (1/3) πr³
r = radius = d/2 = 2/2 = 1 ft
Volume = (1/3) * π * 1³
volume = 1.04 cubic ft
Please help! Im a bit confused, offering 25 points! This mix and match!
Addition:
Increased by, greater than, more than, sum
Subtraction:
Decreased by, decrease, less than, difference
Multiplication:
Times, equal groups, __ times as many, product
Division:
Quotient, divided by, goes into, split equally
What is f(4) for the function f(x) = 5x + 3?
What should I write for this?
Answer:
a. Solve the System of Equations. Show your work
The left windshield wiper on a Chevrolet Traverse cleans an area of 500.3in ^2.when in motion it has a cleaning pattern that arcs 98 degree . What is the length of the windshield wiper? Approximate the length to the nearest inch.
The length of the windshield wiper to the nearest inch is 24 inches
How to calculate the area of a sectorThe formula for calculating the area of a sector is given as:
A = r²β/2
r is the length of the wiper
β is the subtended angle
Given the following
A = 500.3 square in
β = 98 degrees = 98pi/180 = 49pi/90
Substitute
500.3 = r²49pi/180
500.3 = 153.86r²/180
153.86r² = 90054
r² = 585.298
r = 24.19
Hence the length of the windshield wiper to the nearest inch is 24 inches
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Please help help …….. pls
…..
Answer:
1) 1/2or 50%
2) 38/50 or 76%
3) 38/60 or 63%
4) not sure tbh
Step-by-step explanation:
Question 1 (Multiple Choice Worth 1 points)
(03.01 MC)
Solve 7/3+2V9 and explain whether the answer is rational or irrational.
O The answer 9/12 is rational because the sum of a rational number and irrational number is a rational number.
The answer 9/12 is irrational because the sum of a rational number and irrational number is an irrational number.
The answer 773 +6 is rational because the sum of a rational number and irrational number is a rational number.
The answer 713+6 is irrational because the sum of a rational number and irrational number is an irrational number.
Answer:
The answer 7|3+6 is irrational because the sum of a rational number and irrational number is an irrational number.
ANSWER ASAP PLS
Which of the following equations have exactly one solution?
Choose all answers that apply:
2x 31 = 2x - 31
2x 31=-2x-31
2x+31= 2x - 31
2x-2=2x-31
The equation that has exactly one solution will be 2x + 31 = - 2x - 31. Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear equations are given.
Check whether the equation is linear or not.
1. 2x + 31 = 2x - 31, this is not a linear equation.
2. 2x + 31 = - 2x - 31, this is a linear equation.
Then the solution of the linear equation will be
4x = - 62
x = - 15.5
3. 2x + 31 = 2x - 31, this is not a linear equation.
4. 2x - 2 = 2x - 31, this is not a linear equation.
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Write 14 16 in lowest terms.
By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.
How to simplify a rational number
Rational numbers are real numbers of the form n/m, where n, m ∈ [tex]\mathbb{Z}[/tex] and n ≠ 0. Rational numbers are in lowest terms whether they cannot be reduced. A rational number is simplified by applying the following property:
[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex] (1)
Where c is the common multiplier.
Now we proceed to simplify the given rational number, whose common multiplier is 2:
[tex]\frac{14}{16} = \frac{7}{8}[/tex]
By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.
RemarkThe statement is poorly formatted: Write 14/16 in lowest terms.
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Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work.
The area is 812ft
Answer:
about 98 dollars to cover the whole room in carpet
Step-by-step explanation:
The Carpet costs $8.30 per square foot, so 812 ÷ 8.30 = 97 with remainder. Therefore 98 as a rounded total ✅
4. Find (f◦g)(x) and (g◦f)(x) and the domain of each.
f(x)=x+3, g(x)=
Answers:
[tex](f \circ g)(x) = 2x^2-5x\\\\(g \circ f)(x) = 2x^2+7x\\\\[/tex]
The domain is "all real numbers" which you could type in (-infinity, infinity) or [tex](-\infty, \infty)[/tex] when doing interval notation. This applies to both.
=========================================================
Explanation:
See the attached image for the steps of each.
The domain is the set of all real numbers because each result is a polynomial. We don't have to worry about dividing by zero, taking a square root of a negative number etc. There are no restrictions on x. Any real number can replace x to get some real number result for y. This applies to both composite functions.
what is an event in which the outcome does impact the probability of the next event?
Answer:
Dependent Event
Step-by-step explanation:
Dependent Events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
Place the correct coefficients
x²y³ +
in the difference.
xy² +
y
The difference between the two polynomials is 11x²3y³ - 4xy².
What is the Difference between the Polynomials?The difference between two polynomials is the result you get by subtracting one from the other.
Thus:
= (4x²2y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)
= 4x²2y³ + 2xy² – 2y + 7x²y³ - 6xy² + 2y
= 11x²3y³ - 4xy²
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PLEASE HELP ME WITH THIS QUESTION!!!
9x²+3x-1=0
D=b²-4ac
= 3²-4×9×-1
=9+36
=45
x1= (-b+VD)/2a
= (-3+V45)/2×9
= (-3+3V5)/18
=(-1+V5)/6
x2=(-b-VD)/2a
=(-3-3V5)/18
=(-1-V5)/6
Does anybody understand this? QSRT is a Rectangle and SQR=55
Answer:
90°; 55°; 35°; 110°; 70°
Step-by-step explanation:
A rectangle has corner angles that are 90°. When the corner angle is divided into two parts, the total of the parts is 90°.
Each of the triangles is isosceles. The figure is symmetrical about its center.
An exterior angle to a triangle is equal to the sum of the remote interior angles.
__
∠SRT = 90° . . . . a corner angle
∠STR = 55° . . . . symmetrical to the given angle
∠QRS = 180° -55° -90° = 35° . . . . sum of angles in ΔQRS is 180°
∠QPT = 2×55° = 110° . . . . exterior angle to ΔQPS; ∠QSP =∠SQP
∠TPR = 180° -110° = 70° . . . . forms a linear pair with ∠QPT
_____
There are numerous ways to figure any or all of these angles. They come down to the fundamentals: angles in a triangle total 180°; angles that form a line total 180°; corner angles of a rectangle are 90°. Base angles of an isosceles triangle are congruent.
The exterior angle rule derives from the sum of angles in a triangle and on a line both being 180°.
PLEASE HELP WILL GIVE BRAINLEST! Which trigonometric function does the graph below represent?
Answer:
Answer In this Picture.