Find the correct missing value: y⁹ (x^²y = ³ ) ⁰ 12 X =
Answer:
-3
Step-by-step explanation:
Given equation:
[tex]\implies (x^4y^{-3})^n=\dfrac{y^9}{x^{12}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}:[/tex]
[tex]\implies (x^4y^{-3})^n=x^{-12}y^9[/tex]
Rewrite -12 as (4 × -3) and 9 as (-3 × -3):
[tex]\implies (x^4y^{-3})^n=x^{(4 \times -3)}y^{(-3 \times -3)}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c[/tex]:
[tex]\implies (x^4y^{-3})^n=(x^4)^{-3}(y^{-3})^{-3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^c b^c=(ab)^c[/tex]
[tex]\implies (x^4y^{-3})^n=(x^4y^{-3})^{-3}[/tex]
Therefore, the missing value is -3
Part B
What is the area of the target that earns at least 30 points on a throw?
Select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
The area of the target which earns 30 points on a throw.
Solution:[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]
[tex]4+3[/tex]
[tex]=7[/tex]
Let's solve
We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.
[tex]a={7}^{2}[/tex]
[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]
Hence, the area of the target which earns 30 points on a throw is 49π square inches.
Answer= Option B
Find the midpoint of the line segment. (Giving 25 points please hurry)
Answer:
(-4,-3)
Step-by-step explanation:
Answer:
(-4, -3)
Step-by-step explanation:
well, the only points possible are 3 points, a first, 2nd, and 3rd point. And the 2nd point is the mid-point.
Suppose that g(x) = f(x-4). Which statement best compares the grap
g(x) with the graph of f(x)?
The transformation of a function may involve any change. The graph of g(x) is the graph of f(x) shifted 4 units to the right.
How does the transformation of a function happen?The transformation of a function may involve any change.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
As per the transformation of the function, if the function g(x) = f(x-4), then the graph of g(x) will be 4 units in the right of f(x).
Hence, the graph of g(x) is the graph of f(x) shifted 4 units to the right.
Learn more about Transforming functions:
https://brainly.com/question/17006186
#SPJ1
using technology find the solution for the following system of equations
y = -2x + 6
y=3x-4
Answer:
(1.333, 0) and (3, 0)
Step-by-step explanation:
Use desmos to input your equations then click on the solutions (zeroes)
If the length of a rectangle is 6 more than twice the width and the total perimeter is 84cm, what is the rectangle's length?
Step-by-step explanation:
length = 2×width + 6
84 = 2×length + 2×width
now using the first in the second equation :
84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width
84 = 6×width + 12
72 = 6×width
width = 12 cm
length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm
Mo buys a house for £120 000
He sells the house for £150 000
Work out the percentage profit that Mo makes.
Answer:
25%Step-by-step explanation:
The profit = 150 000 - 120 000 = 30 000
………………………………………………………
The profit percentage is :
[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]
How to find the sum of these terms. 1. 5x,12x,9x
2. -5x,19x,-7x
Answer:
just solve normally as if theres no x,
1. 26x
2. -7x
A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120 . What is the theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots?
Using the hypergeometric distribution, it is found that there is a 0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters are given as follows:
N = 130, k = 40, n = 10.
The theoretical probability of 5 students from your school being selected is P(X = 5), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,120,10,40) = \frac{C_{40,5}C_{80,5}}{C_{120,10}} = 0.1363[/tex]
0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant spots.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
#SPJ1
which coordinate is on the graph of the equation 4x-3y=8
Answer:
Coordinates (0, -8/3)
A
What is the formula for margin of error?
ZON'S
O ME=
√s
O ME=
O ME=
Ο ΜΕ
=
Z NS
7
Z S
Z•S
7
Answer:
[tex]\displaystyle ME=\frac{z\cdot s}{\sqrt{n}}[/tex]
Step-by-step explanation:
[tex]z[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] represents the sample size.
PLEASE HELP!!! Use the vertical line to test to determine if the relation whose graph is provided is a function
Answer:
This graph does not represent a function.
Step-by-step explanation:
The vertical line test describes how, in order to be a function, there must be only one output for every input. Remember, the input of a function is the "x" value and the output is the "y" value.
Because of the circular nature, this graph does not represent a function. As you can see, there are "x" values which could correspond with mutliple "y" values. For example, when x = 2, there are two "y" values: y = -1 and y = -5.
[tex]\huge\fbox\green{question}[/tex]
#Combine the members of the following sets to from new sets.Show the members in diagrams
a)A={Mine,Shine,Hari} and B={Ram,Sita,Dolma}
b)M={3,6,9,12>and N={5,10,15,20}
c)A={Mari,Rahlm,Bishnu}and B={Bishnu, Kishan,Dorge}
d)C={4,8,12,16,20} and F={8,16,24,32}
Refer to the attachment
In the diagram, triangle SOP~ triangle GNQ, fine the value of x and explain
Answer: 33
Step-by-step explanation:
Because corresponding sides of similar triangles are in proportion, [tex]\frac{x}{22}=\frac{39}{26} \longrightarrow x=\boxed{33}[/tex]
What might the area of the rectangle be?
Answer:
Not enough information to determine the area.
Step-by-step explanation:
What is the area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches
long? Round the answer to the nearest tenth.
2,331.0 in.²
1,554.0 in.²
1,165.5 in.²
194.3 in.²
The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²
How to calculate the area of a regular hexagon
The formula is given thus;
Area of hexagon = (1/2) × a × P
where a = the length of the apothem
P = perimeter of the hexagon
Given a = 18. 5 inches
Note that Perimeter, p = 6a with 'a' as side
p = 6 × 21 = 126 inches
Substitute values into the formula
Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²
Thus, the area of the regular hexagon is 1, 165. 5 In²
Learn more about the area of a hexagon here:
https://brainly.com/question/15424654
#SPJ1
The bases of the prism below are right triangles. If the prism's height measures 8 units and its volume is 60 units³, solve for x.
Answer:
3
Step-by-step explanation:
Volume of prism = 0.5 times height times length times width
60 = (0.5)(8)(5)(x)
120 = 8(5)(x)
120 = 40x
x = 3
Let me know if its right
Length of another side of base x = 3 unit
What is prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have square, rectangular, pentagonal and other polygon shapes but not the circular shape.
Height of the prism = 8units
Length of one side of base = 5 units
Length of another side of Base = x
Base is a right angle
Base Area = 5x/2
Volume of prism = 60 unit³
Volume of Prism = Base Area × Height
60 = (5x/2) × 8
60/8 = 5x/2
x = 120/40
x = 3 unit.
Hence, x = 3 unit which is length of another side of base.
Learn more about prism here:
https://brainly.com/question/29722724
#SPJ2
When h is one-half and j is one-third, g is 4. if g varies jointly with h and j, what is the value of g when h is 2 and j is 3? 4 6 24 144
Answer:
D) 144Giveng varies jointly with h and jg = 4 when h = 1/2, j = 1/3To findValue of g when h = 2 and j = 3Joint variation:g = khj, where k- coefficient
Use given values of h and j, and find the value of k:
4 = k*(1/2)(1/3)4 = (1/6)kk = 4*6k = 24The equation is now:
g = 24hjFind the value of g when h is 2 and j is 3:
g = 24*2*3 = 144Correct choice is D
Answer:
D. 144
Step-by-step explanation:
Given the graph of the function below, which of the following is the graph of it's inverse?
The inverse of the graph is (b)
How to determine the inverse?To determine the inverse of the graph, we have to swap the x and the y axes.
This means that we plot the y coordinates on the x coordinates and vice versa.
The interpretation of this on the given curve is that:
The vertical curve becomes an horizontal curve (as seen in graph b)
Hence, the inverse of the graph is (b)
Read more about inverse functions at:
https://brainly.com/question/3603397
#SPJ1
The function f(x) is shown on the graph. If f(x) = 0, what is x,?
Answer:
-2, 1 or 3 only
Step-by-step explanation:
just did it
Pls help asap !!! Show all work and I’ll give brainliest
Implementing the LSA from your other question
https://brainly.com/question/27870363?
LSA=3360ft²One can can paint 400ft²
Total cans
3360/4008.4cans9cans you need
The value of a car decreases by 7.2% each year.
When bought the car cost £6200.
Work out how much the car will be worth after one year.
The car will be worth after one year is £ 5753.6.
What is exponential function?An exponential function is defined by the formula f(x) = [tex]a^{x}[/tex], where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = [tex]a^{x}[/tex]
Where a > 0 and a is not equal to 1.
x is any real number.
Given
Car cost when bought A = £ 6200
Value of a car decreases by 7.2% each year.
n = 1
r = 7.2% or 0.072
The car will be worth after one year
[tex]y= A (1-r)^{n}[/tex]
⇒ [tex]y =6200(1-0.072)^{1}[/tex]
⇒ [tex]y = 6200(0.928)[/tex]
⇒ y = £ 5753.6
Hence, the car will be worth after one year is £ 5753.6.
Learn more about exponential function here
https://brainly.com/question/11487261
#SPJ2
Use the following triangles to determine the trig ratios below simplify all fractions rationalize and simplify all radicals and convert all decimals answers to fractions
Find the amplitude of this function.
Answer:
2.5
Step-by-step explanation:
The amplitude of a function is the amount by which the graph of the function travels above and below its midline.
The distance from the highest most point to the lowest point vertically is 5, meaning that the midpoint is 2.5 units from either end.
what is the median of this data set
Answer:
8
Step-by-step explanation:
The median is the number right in the middle. Eight is in the middle of the number line making it the median.
There are square tiles arranged in a pattern. the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. how many are in the original pattern?
An equation is formed of two equal expressions. The number of rows in the original pattern will be 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of rows be represented by x. Now, the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. Therefore, we can write,
(Number of Tiles before) + 1 tile = (Number of Tiles afterward)
5x + 1 = 3(x+3)
5x + 1 = 3x + 9
5x - 3x = 9 - 1
2x = 8
x = 4
Hence, the number of rows in the original pattern will be 4.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
Convert 7.5% to a fraction in lowest terms.
75/100
7 5/10
3/4
7 1/2
Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calculations to find the length of AC.
What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.
12.0 units
12.4 units
15.0 units
15.4 units
Answer:
15 units
Step-by-step explanation:
15.0
Modeling an Equation
Use the algebra tiles to model the equation
2x + 4 = 3x + (−1). Then complete the sentences.
To model 2x + 4, you need:
positive x-tiles to represent 2x.
positive unit tiles to represent 4.
To model 3x + (−1) you’ll need:
3
x-tiles to represent 3x.
1
unit tile to represent –1.
Yes all your used tiles are correct.
Let's solve the equation too
2x+4=3x+(-1)2x+4=3x-14+1=3x-2xx=5The value of variable x in the equation 2x+4=3x+(-1) is 5.
What is equation?Equation is a relationship between two or more variables that are expressed in equal to form. Equation of twwo variable looks like ax+y=c. It cab be linear equation, quadratic equation and cubic equation. linear equation has a straight line curve.
How to solve equation?We have been given equation 2x4=3x+(-1) and we have to solve the equation. Our equation has only one variable, so we have to solve for that variable only.
2x+4=3x+(-1)
2x+4=3x-1
5=x
Hence the value of x in the equation 2x+4=x+(-1) is 5.
Learn more about equation at https://brainly.com/question/2972832
#SPJ2
H
Which line is parallel to line r?
Oline p
O line q
O line s
Oline t
Answer:
Line s
Step-by-step explanation:
They are the same distance apart, so this makes them parallel.
By the definition of parallel lines, the line r is parallel to line s.
What is Coordinate System?Arrangement of reference lines or curves used to identify the location of points in space is called as Coordinate System.
We have to find the line which is parallel to line r.
Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
They are always parallel and are at equidistant from each other.
Parallel lines are non-intersecting lines.
We can also say Parallel lines meet at infinity.
As we observe the figure line s is parallel to line r and it is equidistant from r.
Hence, line s is parallel to line r.
To learn more on Coordinate system click:
https://brainly.com/question/4726772
#SPJ5