The simplified answer for the given equation is: Theta = π/2, 7π/6, 11π/6, 5π/2, 19π/6, 23π/6.
To solve the equation 2 sin 2 Theta - sin Theta-1 = 0 in the interval 0 ≤ Theta ≤ 2pi, we can use the substitution u = sin Theta, which gives us the quadratic equation:
2u^2 - u - 1 = 0
We can solve this using the quadratic formula:
u = (-(-1) ± √((-1)^2 - 4(2)(-1))) / (2(2))
u = (1 ± √9) / 4
u = (1 ± 3) / 4
So we have two solutions for u:
u = 1 and u = -1/2
Substituting back to solve for Theta, we have:
sin Theta = 1
Theta = π/2 + 2nπ (where n is an integer)
and
sin Theta = -1/2
Theta = 7π/6 + 2nπ or 11π/6 + 2nπ (where n is an integer)
Therefore, the solutions in the interval 0 ≤ Theta ≤ 2pi are:
Theta = π/2, 7π/6, 11π/6 (when n = 0)
Theta = 5π/2, 19π/6, 23π/6 (when n = 1)
So the simplified answer is:
Theta = π/2, 7π/6, 11π/6, 5π/2, 19π/6, 23π/6.
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Need help with this pls and thanks
Answer:
J
Step-by-step explanation:
Short to the point way compare it by Up to Down
4/9
Answer:
G
Step-by-step explanation:
a proportional relationship is defined by
y = ax
that means, if x = 0, then also y = 0.
let's look at the slope (the constant of change) :
y coordinate change / x coordinate change
when going from 1 point to another in the line.
we see e.g. for (4, 9) and (5, 12)
x changes by +1 (from 4 to 5).
y changes by +3 (from 9 to 12).
the slope is +3/+1 = 3.
but the slope cannot be the "constant of proportionality" ("a" above), because starting e.g. from (2, 3) to get to x = 0 would mean
x has to change by -2 (= -2×1).
and then y has to change by -6 (= -2×3) to keep the same slope "alive".
and so, for x = 0, we would get y = -3. but not 0.
the only equation with slope 3 (the factor of x, yes) is in G.
therefore, G is the right answer.
we can also check, when using x = 4, x = 5 and x = 2, we get the given y-values (9, 12, 3) from y = 3x - 3.
so, it is correct.
Which point is the reflection of (- 3 2 over the y-axis?
The reflection of (-3, 2) over the y-axis is (-3, -2).
The reflection of a point (x, y) over the y-axis is (x, -y).
Therefore, the reflection of (-3, 2) over the y-axis is (-3, -2).
To calculate the reflection of (-3, 2) over the y-axis, we first use the formula (x, -y).
In this case, x = -3 and y = 2, so the reflection of (-3, 2) over the y-axis is (-3, -2).
We can also calculate the reflection of (-3, 2) over the y-axis using the distance formula.
The distance formula is d = √(x2-x1)2 + (y2-y1)2
In this case, x1 = -3, x2 = 0, y1 = 2, and y2 = 0.
Therefore, the distance d = √(02-(-3)2 + (02-2)2 = √(9 + 4) = √13
The reflection of (-3, 2) over the y-axis is (-3, -2). This can be verified using the distance formula.
d = √(x2-x1)2 + (y2-y1)2 = √(-3-0)2 + (-2-0)2 = √(9+4) = √13
The distance d is equal to the distance between (-3, 2) and (-3, -2). Hence, the reflection of (-3, 2) over the y-axis is (-3, -2).
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A piece of wood is 1212 feet long, and a nail is 33 inches long. The piece of wood is how many times as long as the nail?.
The piece of wood is as long as 48 nails. It is the quotient of the length of wood by the length of nail. In calculation, they should have the same unit length, that is inch.
How to convert feet into inches?One foot is equal to 12 inches.
Mathematically, it is expressed as
1 ft = 12 in
A piece of wood is 12 feet long. The nail has the length of 3 inches. Find the number of the nails so it equals the length of the piece of wood!
The length of piece of wood in inches would be
12 feet = 12 × 12 inches
12 feet = 144 inches
The number of nails needed so that the length would be as long as a piece of wood is
= length of wood / length of nail
= 144 inches / 3 inches
= 48 nails
Hence, a piece of wood is equal to 48 nails.
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How do you find the missing coordinate using the midpoint formula?
The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:
Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.
To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.
For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:
Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )
(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )
So, by solving above equation we can get the missing coordinate
(x₂, y₂) = (5,7)
In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.
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Hideki buys 2 sweaters for $18 each. He can use one of the following coupons :
Coupon 1: Buy one, get one 40% off
Coupon 2: 25% off entire purchase
Which coupon should Hideki use to get a better deal?
Hideki should use coupon 2 to get a better deal.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Hideki buys 2 sweaters for $18 each.
Coupon 1: Buy one, get one 40% off
Here, 40% of 18
= 40/100 ×18
= 0.4×18
= $7.2
So, cost of entire purchase 2(18)-7.2
= 36-7.2
= $28.8
Coupon 2: 25% off entire purchase
25% of 2(18)
= 25/100 ×36
= 0.25×36
= $9
Now, 36-9 =$27
Therefore, Hideki should use coupon 2 to get a better deal.
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if Mr.Kimble gets 12.6 gallons of gas for each of his 15 trips to the gas station over the summer, how much money did he spend altogether on gas?
Mr.Kimble spent an amount of $636.17 altogether on gas.
What is the idea price of Gas per gallon today?Today, the US Retail Gas Price is at a current level of 3.366, up from 3.331 last week and down from 3.381 one year ago. Hence, the amount of $3.366 will be used in our computation.
Data
He used 12.6 gallons of gas for each of his 15 trips.
The total amount of money spent altogether on gas if the price is $3.366, is computed as follows:
= ($3.366 * 12.6 gallons) * 15 trips
= $42.4116 * 15 trips
= $636.17400
= $636.17.
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What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph?
A. f(x + 3)
B. f(x − 3)
C. f(x) + 3
D. f(x) − 3
The answer is Option D) f(x)-3
what is the logarithmic function?In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.
Given here: f(x)=log2x
Now in the attached graph we clearly see that f(x)-3 is the graph that looks identical to the one given in the graph.
Hence, option D is the correct answer.
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Please help thankyou:)
The total volume of the object is 40 in³
What is the volume of a solid object?The volume of a solid object encompasses the space and capacity that the object can occupy. Here, we have two shapes that make up the solid object, a cylinder, and a sphere. A cylinder is an object that resembles a tube and has two circular sides with the same radius linked by a flat round surface.
The volume of the cylinder is calculated by using the formula:
V = πr²h
where; π = 3V = 3 * 2² * 3 ..... (since radius r = d/2 = 4/2 = 2)
V = 3 * 4 * 3
V = 36 in³
The volume of the sphere = 4/3 πr³
V = 4/3 * 3 * 1³
V = 4 in³
The total volume of the object = volume of the cylinder + volume of the sphere
The total volume of the object = 36 in³ + 4 in³
The total volume of the object = 40 in³
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Camila and her children went into a grocery tore and where they ell apple for $0. 50 each and mange for $0. 75 each. Camila ha $7. 75 to pend and mut buy no le than 11 apple and mango altogether. IfCamila decided to buy Rapple. Determine the maximum number of mango that he could buy. If there are no poible olution, hmit an empty amont
The maximum number of mangos that she could buy = 9
Let x represents the number of apples and y represents the number of mangos.
Given that:
the cost of each apple = $0.50
and the cost of each mango = $0.75
Camila has $7. 75 to spend.
This means, the total cost of apples and mangos together must be less than or equal to 7.75
So, we get an inequality,
0.50x + 0.75y ≤ 7.75
And she must buy no less than 11 apples and mangos altogether.
x + y ≥ 11
consider a system of equations.
0.50x + 0.75y = 7.75
x + y = 11
If we solve this system of equations we get x = 2 and y = 9
So, she can buy at most 9 mangos.
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√x = √3x
What is the solution to the equation above?
Answer:
[tex]x=0,\;x=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{x}=\sqrt{3}x[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]
[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]
[tex]\implies x=3x^2[/tex]
Subtract x from both sides:
[tex]\implies x-x=3x^2-x[/tex]
[tex]\implies 0=3x^2-x[/tex]
[tex]\implies 3x^2-x=0[/tex]
Factor out the common term x:
[tex]\implies x(3x-1)=0[/tex]
Apply the zero-product property:
[tex]\implies x=0[/tex]
[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]
Answer:
[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]
Step-by-step explanation:
The equation given is,
→ √x = √3x
Now the value of x will be,
→ √x = √3x
→ x = (√3x)²
→ x = 3x²
→ 3x² = x
→ 3x² - x = 0
→ (3x - 1)(x) = 0
→ 3x - 1 = 0 || → x = 0
→ 3x = 0 + 1 || → [ x = 0 ]
→ 3x = 1 ||
→ [ x = 1/3 ] ||
These are the values of x.
Mrs. Wright is planning her best friend's baby shower. She calculates that the food will cost $9 per guest, and she has already spent $43 on decorations.
Based on the questions, 13 guests are attending her best friend’s baby shower.
How did we get 13 guests as a result?Firstly, we need to write down the numbers that are already stated in the question.
The food will cost around $9 per guests. She spent $43 on decoration for the event. Then, she can afford to spend $160 for the event.43 + 9 × х = 160
Secondly, move the x to continue counting.
9x = 160 – 43
Thirdly, calculate the numbers above.
9x = 117
Then, move the X to get the answer.
X = [tex]\frac{117}{9}[/tex]
Lastly, try to finish the division.
X = 13
In conclusion, the result shows that 13 guests attend Mrs. Wright’s best friend's baby shower.
The above question is about the algebraic word problem.
A word problem is a math question written in a short story scenario. Usually, it is a simple short story that is easy to understand.
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What is the mirror image of point 2 3 under origin?
The mirrors image of points (2, 3) under the origin is (-2, -3)
What is a mirror image?
A mirror image is a reflected duplicate of a seemingly identical item that is turned the other way in the plane perpendicular to the mirror surface. It manifests as an optical effect as a result of reflection off of materials like a mirror or water.
Here,
We have to find the mirror image of points (2, 3) under the origin.
We concluded that the mirror image of a point(2,3) is (-2,-3).
The coordinates of the origin are denoted by (0, 0). It means that at origin, x=0 and y=0.
Hence, the mirrors image of points (2, 3) under the origin is (-2, -3)
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Show two
different ways to find the answer to the problem below.
Dog and cat food are sold in 20-pound bags. There are 14 bags of dog food and 12 bags of cat food on the store shelves. How many pounds of dog and cat food are on the shelves?
Answer: There are 520 pounds of dog and cat food
Step-by-step explanation:
1. 14+12= 26
2. 26x20=520
What is substitution reaction explain with two examples?
The reaction in which one (or more) hydrogen atoms of a hydrocarbon are replaced by some other atoms (like chlorine), is called a substitution reaction.
Substitution reaction is a type of chemical reaction in which an atom, ion, or group of atoms or ions in a molecule is replaced by another atom, ion, or group.
The examples of substitution reactions are as follows:
1. Reaction of copper with zinc sulphate gives zinc with copper sulphate by replacing the zinc with copper.
[tex]Cu + ZnSO_{4}[/tex] → [tex]CuSO_{4} + Zn[/tex]
2. Reaction of magnesium with copper sulphate gives magnesium sulphate with copper by replacing copper with magnesium.
[tex]Mg + CuS0_{4}[/tex] → [tex]MgSO_{4} + Cu[/tex]
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Which graph represents the equation y equals one half times x plus 2? graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1 graph of a line passing through the points negative 2 comma 0 and 0 comma 1 graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2 graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph is the third one: graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2.
A graph is what?News grapher using a function with inputs and outputs to depict a function. A function is a connection between two variables in which the input determines the output. In a graph, the y-axis shows the output, while the x-axis shows the input.
An unweighted, undirected graph with no graph loops or numerous edges is referred to as a simple graph (also known as a strict graph; Tutte 1998, p. 2; West 2000, p.
The line that connects the coordinates (x, y) = (-2, -3) and (y = 1/2x + 2) on this graph expresses the equation y = 1/2x + 2. (0, -2). When we enter those coordinates into the equation, we get the points on the graph, y = 1/2(-2) + 2 = -3 and y = 1/2(0) + 2 = 2.
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What does it mean that stocks and bonds are relatively liquid? a. They are easier to buy and sell than other forms of investment. b. They tend to go up and down in value. c. The amount of income they can bring changes frequently. d. There are more of them to choose from than other forms of investment. Please select the best answer from the choices provided Group of answer choices A B C D
The correct option a. They are easier to buy and sell than other forms of investment, describes the relatively liquid.
Define the term relatively liquid bonds?A type of debt fund known as "liquid funds" mostly invests in higher financing instruments with 91-day maturities.
Liquid money are allocated to bank deposits, t - bills, bills of exchange, and other assets.Compared to other investment options, they are simpler to buy and sell. When an asset is described as liquid, it simply indicates that it can be quickly changed into cash. Because there will always be a buyer and a seller willing to exchange money for the stock or bond, liquid bonds and stocks are simpler to sell and buy.Thus,
Liquid assets are those that are challenging to buy, sell, or convert into cash.
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Juan has $24 to spend at the bookstore. If books cost $6 each how many books cam he buy?
4Answer:
Step-by-step explanation:
24 divided by 4 = 6
HELP NOW PLS (100 POINTS)
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
Part A: Find f(2) and g(2). Show your work. (2 points)
Part B: Find f divided by g of 2. Show your work. (2 points)
Part C: What is the domain of f divided by g of x? (2 points)
Answer:
A) f(2) = 120, g(2) = 4.
B) f'(x) = 5x + 20
C) R - {-2}.
Step-by-step explanation:
A) Just apply given value and resolve:
[tex]f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4[/tex]
B) g(2) is 4, so just divide f(x) by 4:
[tex] \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20[/tex]
C)
[tex] \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} [/tex]
Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.
1. The value of F(2) = 120 and g(2) = 4.
2. The division is 5(x+4)
3. The domain is real number except -2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
1. F(2)= 20(2)+ 80= 40+ 80= 120
and, g(2)= 2 + 2 = 4
2. The division is
= F(x) / g(2)
= (20x + 80)/ (2+2)
= 20 (x+4) / 4
= 5 (x+4)
3. The domain of F(x) / g(x) is all real number except -2.
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What is standard exponential form?
The Standard Exponential form is defined as the way of expressing a very large or very small number .
What is Standard Exponential form ?
The standard Exponential for is defined as a the representation of large numbers or small numbers. The exponents are used to represent such numbers in standard form.
The Steps to write a large number in exponential form are :
Consider the number 48600000000 ;
(i) Count the number of the trailing zeros in the given number.
(ii) Use the beginning of number to write digits from left till the last non-zero digit followed by a 10 raised to power equal to number of trailing zeros.
(iii) Place the decimal point after the first digit from the left side and add the number of decimal places created to the power of 10.
For example, in 48600000000 we place a decimal point after 4, then two decimal places will be created in the number 4.86 .
So, we will add 2 to the existing power of 10 , that was 8 as there were 8 trailing zeros, but now they become 10.
Therefore, the standard exponential form of the number 48600000000 is [tex]4.86 \times 10^{10}[/tex].
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A zip code for eagar, Arizona is 85925. Which digit is in the "hundreds" place?
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
Answer:
(d) The IQR is the best measure of variability, and it equals 18.5.
Step-by-step explanation:
You want to know the best measure of variability for the data in the given stem-and-leaf plot.
0 | 51 | 0, 3, 72 | 4, 6, 83 | 24 |5 | 8StatisticsThe attachment shows the values of interest are ...
Range = 58 -5 = 53
IQR = 30 -11.5 = 18.5
Measure of variabilityYou can see from the shape of the stem-and-leaf plot that the mean and median are near 24, and most of the data is clustered in that neighborhood. The outlier at 58 skews the distribution to the right.
Since the data has an outlier, we choose the IQR as a better measure of the variability than the range is.
The IQR is the best measure of variability, and it equals 18.5.
__
Additional comment
Neither the IQR nor the range is 45. The range is definitely not 18.5. This means the answer choice we have selected is the only true statement about the data set. (It will often be the case that the only answer that is a true statement is the correct answer.)
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Three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle. Find the measure of the angle .
Answer:
3x of 180=8x of 90
Use this equation
What is the slope of Y 10x?
you need to rent a video camera for your school project. Murphy’s camera charges a $30 rental fee plus $35 per day. Allied rental charger is at $45 rental fee plus $30 per day. Which company should you choose?
Answer:
Step-by-step explanation:
Murphys camera
30+35 = $65 - Murphys is cheaper
45+30= $75
Find the measurement of V.
On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines
what are perpendicular lines?A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.
1) For this case, we have to define perpendicular lines:
Angle y = angle H
10x-27 - 2x + 29
x = 32
they are perpendicular
2) they are perpendicular
3) they are intersecting lines
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Find the values of a and b such that
X^2 + 2x - 7 = (x + a)^2 + b
The values of a and b are 1 and -8 respectively.
What are the values of a and b?[tex]x^{2} + 2x- 7 = (x+a)^{2}+b[/tex]
Let us consider the Right Hand Side of the given equation.
[tex](x+a)^{2}+b = x^{2} +2ax+a^{2} +b\\[/tex]
So,
[tex]x^{2} + 2x- 7 = x^{2}+2ax+a^{2}+b\\\\= x^{2}+2x(1)+1^{2}-8\\\\= (x+1)^{2} -8\\\\[/tex]
Here, a = 1 and b = -8
What is an equation?Equation is also known as a statement of equivalence between two expressions with variable and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them. likewise see equation system. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.To learn more about equation, refer:
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What is 0 to the 0 exponent and why?
0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
The value of 0 to the 0 exponents is undefined or indeterminate. The reason for this is that the mathematical definition of exponentiation states that any number to the power of 0 is equal to 1, except for 0, which is undefined. However, when we try to apply this rule to 0 to the power of 0, it creates a paradox.
If we assume that 0 to the 0 exponents is 1, then any number raised to the power of 0 would be equal to 1, which is not true. For example, 2 to the power of 0 is not equal to 1, but 2, so this assumption doesn't hold true.
On the other hand, if we assume that 0 to the 0 exponents is 0, then any number multiplied by 0 would be 0, which is not true either. For example, 2 multiplied by 0 is not equal to 2.
Therefore, 0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
It's important to note that in some fields of mathematics such as limit, the value of 0 to the 0 exponent is defined as 1, but this is limited to the context of limit and not in general math.
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What is the exponential form for 8x8x8x8 taking base as 2?
The exponential form of 8x8x8x8 is 2^(4*3) = 2^12.
What is an example of inequality math?
Answer: 5x − 4 > 2x + 3
Step-by-step explanation:
The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.
Please help! Please! Thank you! :) 30+ points
Answer:
x=6 z=73
Step-by-step explanation:
9x+53=6x+71
3x+53=71
3x=18
x=6
9(6)+53
54+53
107
107+z=180
z=73