Write [tex](2a)^3[/tex] without exponents.
HELP ASAP PLEASE QUESTION IS
4x + 2(x – 3) = 4x + 2x – 11 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points)
Final answer:
The given equation has no solution, as simplifying both sides leads to the false statement -6 = -11. The number of solutions is zero, and the Distributive Property was used to solve the equation.
Explanation:
To solve the equation 4x + 2(x – 3) = 4x + 2x – 11, follow these steps:
Expand the left side of the equation: 4x + 2x - 6.
Combine like terms: 6x - 6.
Since the left and right side both have 4x, we can cancel out 4x from both sides, leaving 2x - 6 = 2x - 11.
Subtract 2x from both sides to get -6 = -11, which is a contradiction.
There is no solution to this equation because we arrived at a false statement. Therefore, the number of solutions is zero.
Part B: The property I used to solve this equation is the Distributive Property when expanding 2(x - 3).
Two dice are rolled. Are the events, “rolling doubles” and “rolling an even sum”, mutually exclusive? Justify your response.
There are 8 students lined up at the classroom door. What is the probability that Laura and Kimiko will end up next to each other if the students arrange themselves blindfolded?
If 3 consecutive integers sum to 63, the largest of the 3 = ?
This problem states that the sum of 3 consecutive integers is 63 and it asks us to find the largest integer.
Three consecutive integers can be represented as followed.
X → first integer
X + 1 → second integer
X + 2 → third integer
Since the sum of our three consecutive integers is 24, we can write an equation.
X + X + 1 + X + 2 = 63
We can simplify our equation on the left and it will read...
3x + 3 = 63 -3 -33x = 60 ÷3 ÷3 ← divide both sides by 3X = 20Largest integer = X + 220 + 2 = 22Largest integer = 22If i want to be a real boy whats the equation?
Answer: 15²=225
225-(7.5²•3.14)=48.375 or to the nearest form 48.38.
Step-by-step explanation: In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".
Approximately 31,000 citizens of a country died in automobile accidents in 2015 express this toll in deaths per hour
Answer:
4 deaths per hour
Step-by-step explanation:
We have been given that approximately 31,000 citizens of the country died in automobile accident in 2015.
Since we know that 1 year = 365 days,
1 day = 24 hours
In one year there are total hours = 365 × 24 = 8,760 hours
Death per hour = [tex]\frac{31000}{8760}[/tex] = 3.5388 ≈ 4
Therefore, the toll in deaths per hour is approximately 4 in 2015.
On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30
c. what is the actual area of the room?
A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3. The irrational conjugates theorem states that which of the following must also be a root of the function?
Answer:
Step-by-step explanation:
option b
Given a polynomial with rational coefficients, if √3 is a root, its irrational conjugate -√3 must also be a root due to the Irrational Conjugates Theorem, ensuring that the polynomial maintains rational coefficients.
Explanation:The subject of this question is a polynomial function with rational coefficients, which is encountered in mathematics, particularly in algebra. When a polynomial has rational coefficients and one of its roots is an irrational number, such as the square root of 3 (√3), the Irrational Conjugates Theorem states that its conjugate, in this case, the negative square root of 3 (-√3), must also be a root of the polynomial. Therefore, the polynomial function in question must include both √3 and -√3 as roots to have rational coefficients.
Given that the function already has -2 as a root, we know that (x + 2) is a factor of the polynomial. Additionally, because √3 is a root, the factors (x - √3) and (x + √3) will also be part of the polynomial. To find the roots of a quadratic equation or higher-order polynomials, one can set the function equal to zero and solve for x, either by factoring, applying the quadratic formula, or other algebraic methods.
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Simplify 1/x-10 divided by 9x/x^2-9x-10
Answer:(x+1)/9x
Step-by-step explanation: Hope this helps
use any method to solve the equation. If necessary, round to the nearest hundredth. 11x^2=8
Answer:
x = + 0.85 , -0.85
Step-by-step explanation:
Given : 11x² = 8.
To find : use any method to solve the equation. If necessary, round to the nearest hundredth.
Solution : We have given that : 11x² = 8.
First we divide both sides by 11,
x² = [tex]\frac{8}{11}[/tex].
Now taking square root both sides .
x = [tex]\sqrt{\frac{8}{11}}[/tex].
x =± 0.8528.
Therefore, x = + 0.85 , -0.85
The probability that a flipped coin will show heads on four consecutive flips is
Which phrases can be used to represent the inequality mr024-1.jpg? Check all that apply. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and the sum of a number and 1.5 is at minimum 21. The sum of 1.5 and the product of 6.5 and a number is at least 21. The product of 6.5 and a number, when increased by 1.5, is at most 21.
Answer:
b and c
Step-by-step explanation:
2020 edge assignment
Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
What is the area of the region completely bounded by the curve y=-x^2+x+6?
To find the area of the region completely bounded by the curve y=-x^2+x+6, you can integrate the equation with respect to x and evaluate it between the x-values where the curve intersects the x-axis. By solving the quadratic equation -x^2+x+6=0, you can determine the x-values. Then, evaluate the definite integral between these x-values to find the area.
Explanation:The area of the region completely bounded by the curve y=-x^2+x+6 can be found by integrating the equation with respect to x and evaluating it between the appropriate bounds. The integral of the given equation is ∫(-x^2+x+6) dx. To find the area, we need to find the definite integral between the x-values where the curve intersects the x-axis. First, set the equation equal to zero and solve for x:
-x^2+x+6=0
This quadratic equation can be factored as: (x-2)(x+3). Therefore, the curve intersects the x-axis at x=2 and x=-3.
By evaluating the definite integral between x=-3 and x=2, we can find the area of the region:
Area = ∫-32 (-x^2+x+6) dx
Integrating this equation will give you the area of the region bounded by the curve y=-x^2+x+6.
Lou has 3 over 4 of an hour to do his math homework, play video games and help with dinner. If he splits his time equally between the three activities, how much time will he spend on each?
_____ of an hour
3/4 divided by 3
3/4 *1/3 = 3/12 = 1/4
John translated parallelogram ABCD using the rule (x,y)→(x+3, y−2). If angle A is 110° and angle B is 70°, what is the degree measurement of angle A'?
Answer:
The correct answer is B. 110.
using the formula C=2TTr, find the circumference of a circle with a diameter of 28 in. round your answer to the nearest inch
A. 56in
B. 28 in
C. 44in
D.88in
radius = diameter/2
so 28/2=14
using 3.14 for PI
2*3.14*14 = 87.92 = 88 inches
The variable is Z is inversely proportional to X. When X is 6, Z has the value 0.5. What is the value of Z when X = 10
A fence is to be installed around a rectangular field. the field's perimeter is 204204 feet. find the dimensions of the field if the length of the field is 8 feet more than the width.
The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Here, we have,
given that,
A fence is to be installed around a rectangular field.
the field's perimeter is 204204 feet.
now, we have,
204204 - 16 = 204188
we get,
204188 / 4 = 51,047
so, we get,
width = 51,047
length = 51,055
Hence, The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
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How to find where the tangent line is horizontal?
Final answer:
To determine where the tangent line to a function is horizontal, find the derivative of the function, set it equal to zero, and solve for 'x'. This value of 'x' is where the slope is zero, indicating a horizontal tangent line.
Explanation:
How to Find Where the Tangent Line is Horizontal
To find where the tangent line to a curve is horizontal, you need to determine where the slope of the tangent (which is the derivative of the function) is zero. This involves calculating the derivative of the given function and solving for the value of 'x' where this derivative equals zero.
For example, if we have a function y = 4x - x², we first find its derivative: dy/dx = 4 - 2x. Setting this derivative equal to zero gives us 4 - 2x = 0. Solving for x gives us x = 2. This is the value of x where the tangent line is horizontal.
If we are given a graph, like in a velocity-time graph, a horizontal tangent indicates a moment where the velocity is zero, signifying a change in direction of the particle. At such points, we can see that the slope of the tangent line is zero, meaning it is a horizontal tangent.
Jordan is cutting a 2 meter by 1 1/4 meter piece of rectangular paper into two pieces along its diagonal. what is the area of each of the pieces?
area = 1/2 * b * h=
1/2 * 2 * 1 1/4 = 1 1/4 square meters each
Answer: area = 1/2 * b * h=
1/2 * 2 * 1 1/4 = 1 1/4 square meters each
Find x and the measures of the indicated parts.
BC and AC
What's 9080 each number in expanded notation
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $25 . The total cost to rent 2 chairs and 6 tables is $40 . What is the cost to rent each chair and each table?
The cost to rent each chair is $5, and the cost to rent each table is also $5.
Explanation:This problem can be solved using the method of substitution in solving systems of linear equations. We can set up two equations based on the information given: 5C + 3T = 25 and 2C + 6T = 40 where C represents the rental cost of each chair and T represents the rental cost of each table.
When we simplify the second equation, we get C + 3T = 20. We can then substitute this into the first equation, which gives us 5(C + 3T) = £25. Solving these equations gives us the cost to rent each chair (C) as $5 and each table (T) as $5.
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The circumference of a circle is 19πinches. find the radius.c=2πr
At a store, 2 gallons of milk cost $6. Which is the value of the ratio of dollars to gallons of milk?
Answer:
3:1 or 3/1
Step-by-step explanation:
We have the next information:
Gallons of Milk Cost
2 ⇒ $6
dividing both quantities by two, we get the price for a single gallon of milk:
Gallons of Milk Cost
1 ⇒ $3
We are asked for the ratio of dollars to gallons of milk (the order is important since dollars go first than gallons) so we will have the following:
dollars:gallons or dollars/gallons
and since $3 dollars pay for 1 gallon of milk, the ratio is:
3:1 or 3/1
A jar of 57 coins contains only dimes and quarters. The value of all the coins in the jar is $10.05. How many dimes are in the jar?
The dimes are 28 dimes
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
total coins = 57
So,
D + Q = 57
D= 57 - Q....(1)
0.10D + 0.25 Q = 10.05
Using (1), we get
0.10(57 - Q) + 0.25Q= 10.05
5.7 - 0.10Q + 0.25Q = 10.05
0.15Q = 4.35
Q= 29
So, dimes = 57- 29= 28 dimes
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How do you do this problem?
What is a rule for the total cost of the tickets ? Give the rule in words and as a algebraic expression