Answer:
(-7/9)^4 = 2401/6561
Step-by-step explanation:
The rules of exponents apply.
(a^b)/(a^c) = a^(b-c) . . . . . quotient rule
(a^b)^c = a^(bc) . . . . . . . . power rule
__
value of a/bThe first rule of exponents shown above helps us find the value of a/b.
[tex]\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2[/tex]
value of (a/b)^2The second rule of exponents shown above tells us how to find the square.
[tex]\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}[/tex]
_____
Additional comment
Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.
Which equations and/or functions represent the graphed line? Select three options.
A coordinate plane with a line passing through the points, (negative 4, 0), (negative 2, 1), (0, 2), and (2, 3).
The equations of the graphed line and function can be written as:
f(x) = 1/2x + 2
y - 3 = 1/2(x - 2)
y - 1 = 0.5(x + 2)
What is the Equation of a Graphed Line?Equation of a graphed line can be expressed in:
Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or
Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.
Find the slope (m) of the line:
Slope (m) = change in y / change in x = 1/2 = 0.5
y-intercept (b) = 2
To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:
f(x) = 1/2x + 2.
Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):
y - 3 = 1/2(x - 2)
Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):
y - 1 = 0.5(x - (-2))
y - 1 = 0.5(x + 2)
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HELP ASAP
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
V = 3053.63 mm^3
Step-by-step explanation:
radius : 9mm
V = 4/3 * pi * r^3
V = 4/3 * (3.1415926535898...) * 9^3
V = 3053.63 mm^3
To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether they would receive the coupon until after the final sale. The website claimed that one in five customers received the coupon. Six customers each made purchases from the website. Let X = the number of customers that received the 50% off coupon.
To increase sales, an online clothing store began giving a 50% off coupon to random customers Six customers each made purchases from the website the binomial random variable and mean and standard deviation of X is mathematically given as
[tex]X ~ Bin(n = 6, p = 0.2)[/tex]
x= 0.9798
What is a binomial random variable?
Generally, the equation for is mathematically given as
P(coupon) = 1/5
P(coupon)= 0.2
the binomial distribution
[tex]X ~ Bin(n = 6, p = 0.2)[/tex]
Therefore, The mean and standard deviation of X
[tex]пВ = np \\np= 6* 0.2 = 1.2\\[/tex]
[tex]x=\sqrt{ np(1 - p)} \\ x=\sqrt{ 6 * 0.2 + (1 -0.2)} \\[/tex]
x= 0.9798
In conclusion, mean and standard deviation of X
x= 0.9798
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Question 3 of 10
Theresa has a credit card that uses the average daily balance method. For the
first 12 days of one of her billing cycles, her balance was $350, and for the
last 19 days of the billing cycle, her balance was $520. If her credit card's APR
is 14%, which of these expressions could be used to calculate the amount
Theresa was charged in interest for the billing cycle?
The amount that Theresa was charged in interest for the billing cycle is $5.30
How to calculate the interest?By using the average daily balance, the amount will be:
= (350 × 12) + (520 × 19) / (12 + 19)
= (4200 + 9880)/31
= 454.19
Therefore, the interest will be:
= (454 × 0.14)/12
= $5.30
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Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2
Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]
[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]
PLS HELP ASAP !!!!!!!!!!
Answer:
Alice
Step-by-step explanation:
14$ the amount he had - X the amount he lost (the unknown) is what is described by Alice
According to this factor tree, which of the following statements is true?
Answer:
option c
Step-by-step explanation:
a) NOT TRUE
A composite number is a positive integer that can be formed by multiplying two smaller positive integers.
3 and 7 are not composite numbers because each of them can only be divided by one and itself
b) NOT TRUE
2 is also a prime number so 3 and 7 are not the only numbers
c) TRUE
All the number listed are prime numbers hence why they are all at the bottom of the tree (only have 1 and itself as factors)
d) NOT TRUE
21 is not a prime number. The number 21 is divisible by 1, 3, 7, 21. For a number to be classified as a prime number, it should have exactly two factors. Since 21 has more than two factors, i.e. 1, 3, 7, 21, it is not a prime number.
If A = (-2, -4) and B = (-8, 4), what is the length of AB?
A.) 14 units
B.) 10 units
C.) 16 units
D.) 12 units
Please helpppp!
Answer:
10
Step-by-step explanation:
Using the distance formula,
[tex] \sqrt{ {( - 2 - ( - 8))}^{2} + { (- 4 - 4)}^{2} } = 10[/tex]
Sara sells aloe vera plants and barrel cacti at the local street fair. Each aloe vera plant is $3 and each barrel cactus is $2.
On Monday she sold a total of 12 plants for $31. How many of each type of plant did Sara sell?
x:# aloe vera y : # barrel cacti
Round 4/15 to the nearest thousandth
Answer:
0.267
Step-by-step explanation:
4/15 as a decimal is 0.26 repeating so rounded to the nearest thousandth would be 0.267
Sally learnt how to fix boxes using nails from her father. 4 nails are needed to set up a box. Sally bought 692 nails and had 200 nails left after setting up some boxes. How many boxes did Sally set up?
Answer:
Step-by-step explanation:
Answer: 123 boxes
Step-by-step explanation:
Find how many nails she used.
692-200=492
she used 492 nails
we know that 4 nails are needed to set up a box
so we divide.
492/4=123
Sally set up 123 boxes
4(x − 3) + 5x − x² for x = 2
Answer:
2
Step-by-step explanation:
Start by simplifying the expression:
[tex]4(x-3)+5x-x^2[/tex]
Use distribution:
[tex]4x-4(3)+5x-x^2\\4x-12+5x-x^2[/tex]
Add like terms:
[tex]9x-12-x^2[/tex]
Now, substitute the given value of x into the expression:
[tex]9(2)-12-2^2\\18-12-4\\6-4\\2[/tex]
Answer:
2
Step-by-step explanation:
Given: 4(x − 3) + 5x − x²
x = 2Substitute 2 for the value of x in the expression and simplify:
➜ 4(2 − 3) + 5(2) − (2)²
➜ 4(−1) + 10 − 4
➜ -4 + 10 - 4
➜ 2
Therefore, the value of the expression when x equals 2 is 2.
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5• (4 • x ) simplified
Step-by-step explanation:
= 5 • ( 4• x )
= 5 ( 4x )
= 20x
[tex]...[/tex]
Not sure how to do this
Answer:
[tex]\underline{\boxed{\sf{2(x - 11)(x + 11)}}}[/tex]
Step-by-step explanation:
[tex]\sf{2x^2 - 242}[/tex]
Common factor :
[tex]\sf{2x^2 - 242}[/tex]
[tex]\sf{2(x^2 - 121)}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Use the sum-product pattern :
[tex]\sf{2(x^2-121)}[/tex]
[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Common factor from the two pairs :
[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]
[tex]\sf{2(x(x+11) -11(x + 11))}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Rewrite in factored form :
[tex]\sf{2(x(x+11)- 11(x + 11))}[/tex]
[tex]\sf{2(x - 11)(x + 11)}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Solution :
[tex]\sf{2(x - 11)(x + 11)}[/tex]
Mrs cunningham wants to use rubber tiles to cover the floor of an indoor playground
what is the unit cost per ruber tile
Answer:
the unit cost per rubber tile is $$$$$$$$$$$$$6
Step-by-step explanation:
..
Type the correct answer in the box.
✔
b
b
In the figure, a square is inside another bigger square.
If a=4 units and b=3 units, the length of the diagonal of the outside square rounded to the nearest tenth is
Inside square rounded to the nearest tenth is
units.
units and the length of the diagonal of the
Answer:
5.7 and 4.2
Step-by-step explanation:
Outside diagonal = √a² + a² = √4² + 4² = 4√2
= 5.7
Inside diagonal = √b² + b² = √3² + 3² = 3√2
= 4.2
Use the euclidean algorithm to find integers $x$ and $y$ such that $164x + 37y = 1,$ with the smallest possible positive value of $x$. state your answer as a list with $x$ first and $y$ second, separated by a comma.
Well, let's use the Euclidean algorithm:
164 = 4×37 + 16
37 = 2×16 + 5
16 = 3×5 + 1
Then working backwards,
1 = 16 - 3×5
1 = 16 - 3×(37 - 2×16) = 7×16 - 3×37
1 = 7×(164 - 4×37) - 3×37 = 7×164 - 31×37
so that x = 7 and y = -31.
kelly has read 5/6 of a book helen has read 9/12 of the same book who read more of the book?
Answer:
Kelly has read more of the book
what does it want me to put to 6 decimal places
They want you to solve the iterative process to a point where the value of x is greater than or equal to 6 decimal places.
What is an iterative process?An iterative process is a mathematical approach that employs an initial value to build a series of improving estimated solutions for a problem, where the nth-term estimation is generated from the prior ones.
You're required to put the value of x₁ = -1 into the equation:
[tex]\mathbf{x_{n+1}= \dfrac{(x_n)^3-1}{4}}[/tex]
where, [tex]x_1 = -1[/tex]So;
[tex]\mathbf{x_{2}= \dfrac{(-1)^3-1}{4}}[/tex]
[tex]\mathbf{x_{2}=-0.5}[/tex]
[tex]\mathbf{x_{3}= \dfrac{(-0.5)^3-1}{4}}[/tex]
[tex]\mathbf{x_{3}=-0.28125}[/tex]
[tex]\mathbf{x_{4}=\dfrac{(-0.28125)^3-1}{4}}[/tex]
[tex]\mathbf{x_{4}=-0.2555618286}[/tex]
x₄ ≅ -0.255562 ( to 6 decimal places)
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3500 people attended a baseball game. 1330 of the people attending supported the home team, while 2170 supported the visiting team. what percentage of people attending supported the home team?
Answer:
38% is your answer boss. hope that helps :)
The percentage of people who supported the home team is 38 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total number of people attending the baseball game = 3500 people
The number of people supporting the home team = 1300 people
The number of people supporting the visiting team is = 2170
Now , the equation will be
The percentage of people supporting the home team is = number of people supporting the home team / total number of people attending the baseball game
Now , the equation will be
The percentage of people supporting the home team is A = ( 1300 / 3500 ) x 100
The percentage of people supporting the home team is A = 0.38 x 100
The percentage of people supporting the home team is A = 38 %
Therefore , the value of A is 38 %
Hence , The percentage of people who supported the home team is 38 %
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help meeee i need 100
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
[tex]x = 2, y = -1[/tex]
Step-by-step explanation:
We can add the 2 equations together to solve for y.
[tex](-3x + 5y) + (3x + 7y) = (-11) + (-1)\\-3x + 3x + 5y + 7y = -11 -1\\12y = -12\\y = -1[/tex]
Now we can solve for x by substituting y in one of the original equations.
[tex]3x + 7y = -1\\3x + 7(-1) = -1\\3x - 7 = -1\\3x = 6\\x = 2[/tex]
Those are the answers
- Kan Academy Advanced
Find the volume.
Area = 16.4 cm²
8.1 cm
cm³
Answer:
132.84 is the answer as volume is area times length
Order the numbers from least to greatest. 0.35, 3/5 , 38%
Least # _________ U, _________ I, _________ N Greatest #
Answer:
.35 < 38% < 3/5
Step-by-step explanation:
.35 is the same as 35 percent which is less than 38, and 3/5 when divides is .60 turned into percent is 60 percent
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the pairs of polynomials to their products. (xy + 9y + 2) and (xy – 3) x2y2 + 3x2y – 7xy – 27x – 18 (2xy + x + y) and (3xy2 – y) 6x2y3 – 2xy2 + 3x2y2 – xy + 3xy3 – y2 (x – y) and (x + 3y) x3y + 3x2 + 3x2y2 + 7xy – 6 (xy + 3x + 2) and (xy – 9) x2 – 9y2 (x2 + 3xy – 2) and (xy + 3) (x + 3y) and (x – 3y)
The products of the polynomials are:
(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²(x - y) * (x + 3y) = x² + 2xy + 3y²(xy + 3x + 2) * (xy – 9) = x²y² - 7xy + 3x²y - 27x - 18(x² + 3xy - 2) * (xy + 3) = x³y + 3x² + 3x²y² + 7xy - 6(x + 3y) * (x – 3y) = x² - 9y²How to evaluate the products?To do this, we multiply each pair of polynomial as follows:
Pair 1: (xy + 9y + 2) and (xy – 3)
(xy + 9y + 2) * (xy - 3)
Expand
(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6
Evaluate the like terms
(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6
Pair 2: (2xy + x + y) and (3xy² - y)
(2xy + x + y) * (3xy² - y)
Expand
(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²
Pair 3: (x – y) and (x + 3y)
(x - y) * (x + 3y)
Expand
(x - y) * (x + 3y) = x² + 3xy - yx + 3y²
Evaluate the like terms
(x - y) * (x + 3y) = x² + 2xy + 3y²
Pair 4: (xy + 3x + 2) and (xy – 9)
(xy + 3x + 2) * (xy – 9)
Expand
(xy + 3x + 2) * (xy – 9) = x²y² - 9xy + 3x²y - 27x + 2xy - 18
Evaluate the like terms
(xy + 3x + 2) * (xy – 9) = x²y² - 7xy + 3x²y - 27x - 18
Pair 5: (x² + 3xy - 2) and (xy + 3)
(x² + 3xy - 2) * (xy + 3)
Expand
(x² + 3xy - 2) * (xy + 3) = x³y + 3x² + 3x²y² + 9xy - 2xy - 6
Evaluate the like terms
(x² + 3xy - 2) * (xy + 3) = x³y + 3x² + 3x²y² + 7xy - 6
Pair 6: (x + 3y) and (x – 3y)
(x + 3y) * (x – 3y)
Apply the difference of two squares
(x + 3y) * (x – 3y) = x² - 9y²
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what’s the answer to this
Answer:
Step-by-step explanation:
(2,1) and (4,2) are on the line.
slope
[tex]=\frac{2-1}{4-2} =\frac{1}{2} \\[/tex]
eq. of line is
[tex]y-1=\frac{1}{2} (x-2)\\2y-2=x-2\\2y=x\\or \\x-2y=0\\[/tex]
in slope intercept form
[tex]y=\frac{1}{2} x[/tex]
13. (a) In any triangle ABC, if C = 300,b= 4, a = 2 find A and B. [3] (b) If a = b = c and a,b,c are in G.P., show that x,y,z are in H.P. [2]
please, solve them
Step-by-step explanation:
oksosjaoqkqeand
[tex]66 \sqrt[3x9 \frac{ \sqrt[xx. \sqrt[36 \sqrt[3136(2 > kaki \: kwl{]{?} ]{?} ]{?} }{?} ]{?} [/tex]
What is the value of x in the figure?
X
40⁰
OA. 40°
OB. 70°
OC. 80°
OD. 120°
OE. 150°
70⁰
Answer:
E 150
Step-by-step explanation:
The coordinates of the mid - point of the line AB is (-1, -5).
What is mid - point?A midpoint is a point that divides a given line into two equal parts.
Given is that AB has endpoints at A(4, -8) and B(-6, -2). It is asked to find the coordinates of the midpoint of AB.
We can write the coordinates of the midpoint of AB as -
{x} = (x₁ + x₂)/2
{x} = (4 - 6)/2
{x} = - 2/2
{x} = -1
{y} = (y₁ + y₂)/2
{y} = (-8 - 2)/2
{y} = - 10/2
{y} = - 5
Therefore, the coordinates of the mid - point of the line AB is (-1, -5).
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Find the greatest common factor of 15x2y³ and -18x³yz.
Answer:
GCF=3[tex]x^{2}y[/tex]
Step-by-step explanation:
First, take a look at the numbers.
GCF of 15 and -18 = 3
Then, look at the variables.
GCF of (x^2)(y^3) and (x^3)(y)(z) = (x^2)(y)
Lastly, combine the two expressions
GCF = 3(x^2)(y)
Answer: 3(x^2)(y)
Hope this helps!
geometry problem please help!
Answer:
x = 3
Step-by-step explanation:
the midsegment XW is half the sum of the parallel bases , that is
7x + 10 = [tex]\frac{1}{2}[/tex] (46 + 16 ) = [tex]\frac{1}{2}[/tex] × 62 = 31 ( subtract 10 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3