Answer:
Restrictions: x ≠ 0, 3
The value of x is equal to 5.
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Expanding/FactoringDomain
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \frac{2}{x - 3} = \frac{5}{x}[/tex]
Step 2: Examine
Since we have an x - 3 and x in the denominator, we must make sure the denominator cannot equal 0, or that would get us an undefined answer. Therefore, our restrictions are that x ≠ 0, 3.
Step 3: Solve for x
[Multiplication Property of Equality] Cross-multiply:Since 5 is not equal to 0 or 3, it can be our solution.
∴ we have found the value of x from the given rational function.
---
Topic: Algebra I
How many solutions does the system of equations have 4x+2y=-8 2x+y=4 explain your answer
Answer:
x=-y/2
Step-by-step explanation:
1. The value of a variable that makes an equation true.
2. In chemistry, a solution is a homogeneous mixture composed of only one phase
What is equivalent to 10/24
Answer:5/12
Step-by-step explanation:
If you cut 10 ( the numerator) in half you get 5 and if you cut 24(the denominator) in half you get 12
Answer:
15/36Step-by-step explanation:
1536 is equivalent to 10/24 because 15 x 24 = 36 x 10 = 360. 2048 is equivalent to 1024 because 20 x 24 = 48 x 10 = 480.
Anyone know this.
What is the negation of the following statement?
A triangle cannot contain two obtuse angles.
A. A triangle can contain two obtuse angles.
B. A triangle does not contain two obtuse angles.
Answer:
it's B
Step-by-step explanation:
a triangle cannot two obtuse angles
A traingle does not contain two obtuse angles. Option B is correct.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
Here,
A triangle cannot contain two obtuse angles.
A triangle cannot have the two obtuse angle, becaue for a triangle sum of the iternal angle must not exceeds 180°
Thus, A traingle does not contain two obtuse angles. Option B is correct.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
Due to financial difficulties the owner of 4 skateboard stores is going to close 2 of his stores. Based on the money earned at each store, which two stores should remain open?
A) Ben's Boards and Skateaway
B) Skateaway and Great Skates
C) Skateaway and Discount Sports
D) Discount Sports and Ben's Boards
Answer:
B
Step-by-step explanation:
Because, according to the graph, they are making the most sells.
What is angle A? 313 degrees 133 degrees 143 degrees 147 degrees
133 is the Answer bc that is a supplementary angle and supplementary angles always sum up to 180 hope this helps please mark brainliest
Step-by-step explanation:
If three workers paint a house in 12 hours how long will it take 5 painters to paint the same house
Answer:
60 hours
Step-by-step explanation:
you multiply 5×12 and then you get 60
What is 2/2 simplified
Answer:1
Step-by-step explanation:just divide numerator by denominator
Which of the following accurately describes the square root of 10?
1. It is rational
2. it is an integer.
3.It is a whole number.
4. It is irrational.
Answer:
4
Step-by-step explanation:
√10 is a irrational number
Final answer:
The square root of 10 is an irrational number because it is a non-terminating, non-repeating decimal that cannot be expressed as a simple fraction. It lies between the integers 3 and 4 on the number line.
Explanation:
The square root of 10 is an example of an irrational number. Unlike integers and whole numbers, which are exact and do not have an ending decimal or fraction, and unlike rational numbers which can be written as a ratio of two integers (like 1/2 or 3/4), an irrational number cannot be expressed as a simple fraction.
The square root of 10 cannot be precisely written as a fraction because it is a non-terminating, non-repeating decimal. In other words, if we were to write out the decimal form of the square root of 10, it would have an infinite number of digits after the decimal point without any repeating pattern.
For a real-world example, consider that knowing whether a number is rational or irrational can influence how we represent that number in various contexts, such as in engineering or architecture, where precision is paramount.
Solve for x 2x+6>20 please help
Answer:
x>7
Step-by-step explanation:
2x+6>20
2x>20-6
2x>14
x>14/2
x>7
Find the area of the following geometric figure.
Find the area of a triangle with base of 6 m and altitude of 4 m.
Area =
m2
The quotient of a number and -5, decreased by 9, is 2
Hello there n ÷ 5 - 9 = 2!
Here's how i solved it:
The quotient of a number and -5, decreased by 9, is 2
"is 2" means the result is 2, so we can have one side of the equation set up to look like this: = 2.
The quotient of a number and -5, decreased by 9, is 2
This looks like: n ÷ 5
The quotient of a number and -5, decreased by 9, is 2
We are taking 9 away from the previous expression, so n ÷ 5 - 9
Putting it all together, we have: n ÷ 5 - 9 = 2
The algebraic mathematical problem is to solve the equation x/-5 - 9 = 2. Simplifying this equation through a series of algebraic steps gives the result x=-55.
Explanation:The subject of your question is algebra, a branch of mathematics. You are looking for a number which, when divided by -5 and then decreased by 9, equals 2. The equation that represents this problem is x/-5 - 9 = 2.
To solve for x, we would first get rid of the -9 from the left side of the equation. We do this by adding 9 to both sides of the equation. We then have x/-5 = 2 + 9, which simplifies to x/-5 = 11.
Next, we isolate x by multiplying both sides of the equation by -5. We now get x= -5*11, which gives x = -55. Thus, the number x that satisfies this equation is -55.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ3
(1 point)
10. A sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g. Construct a 95% confidence interval estimate of the mean weight of all the coins.
a) 7.6675g
b) 8.0518g
c) 8.0447g
d) 8.0329g
Answer:
Step-by-step explanation:
i think its b or c
The confidence interval of the mean weight of all the coins is 8.0518g. The correct option is B.
What is a confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.
Given that a sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g.
The confidence interval is calculated by the formula:-
CI = X ± z (S / √n)
CI = 8.0710 ± [ (1.96 x 0.0411) / √20 ]
CI = 8.0710 - 0.018
CI = 8.053 g
To know more about confidence intervals follow
https://brainly.com/question/15712887
#SPJ5
Which expression is not a polynomial?
x-1
4+p
5x² - x
8x - z3
The given question have mistake.
Question:
Which expression is not a polynomial?
(1) x – 1
(2) 4 + p
(3) [tex]5x^2-\sqrt x[/tex]
(4) [tex]8x-z^3[/tex]
Answer:
[tex]5x^2-\sqrt x[/tex] : Not a polynomial
Solution:
Definition of polynomial:
A polynomial can have constants, variables and exponents.
Constants = 2, 5
Variables = x, y, z
Exponents = [tex]x^2[/tex]
Not a polynomial:
Roots, fractions in power, negative powers and dividing by a variable are not polynomials.
Given expressions:
(1) x – 1 : Polynomial
(2) 4 + p : Polynomial
(3) [tex]5x^2-\sqrt x[/tex] : Not a polynomial
(4) [tex]8x-z^3[/tex] : Polynomial
Hence in the given expressions [tex]5x^2-\sqrt x[/tex] is not a polynomial.
What is an example of a situation that you might not be able to use an equation with a single unknown to understand?
Answer:
An example of a situation that you might not be able to use an equation with a single unknown is
[tex]x = \ln{e^x}[/tex]
Step-by-step explanation:
An example of a situation that you might not be able to use an equation with a single unknown is
[tex]x = \ln{e^x}[/tex]
The identity on both sides which results in 1 = 1 and thus the equation is not usable.
A situation where an equation with a single unknown cannot be effectively used is when you need to explore or solve multiple variables or dimensions, like best represented by physics-related problems. The number of unknowns should not exceed the number of equations for correct problem-solving. Equations with a single unknown may not always suffice, especially for problems involving various dimensions or variables.
Explanation:An example of a situation where you may not be able to use an equation with a single unknown to understand is a problem that involves multiple elements or dimensions needing exploration. For instance, in physics, if you're calculating an object's motion, you may need to take into account various forces acting on it, its initial velocity, its acceleration, and the time. No single equation with just one unknown can solve this problem; you would need multiple equations to represent each of these dimensions.
Remember that the number of unknowns should not be larger than the number of equations. Otherwise, the problem can't be solved. Therefore, the complexity of your problem can sometimes make it impossible to use an equation with a single unknown. Physics is often an area where this is true, due largely to the dimensional consistency of equations.
Nevertheless, equations with a single unknown can often be combined together or manipulated to solve specific problem-solving strategies. Overall, while an equation with a single unknown is a powerful tool, it may not always be sufficient to understand every situation, especially those involving multiple dimensions or variables.
Learn more about Single Unknown Equations here:https://brainly.com/question/30855865
#SPJ11
What are the dimensions of a rectangular wall that can be constructed with 400 feet of brick that will maximize the area enclosed by that brick
Answer:
The dimensions of the wall are 100 ft x 100 ft
Step-by-step explanation:
we know that
The perimeter of a rectangular wall is
[tex]P=2(x+y)[/tex]
where
x is the length
y is the width
we have
[tex]P=400\ ft[/tex]
so
[tex]400=2(x+y)[/tex]
simplify
[tex]200=x+y[/tex]
[tex]y=200-x[/tex] ----> equation A
The area of a rectangular wall is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-x)\\A=-x^2+200x[/tex]
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
Convert the quadratic equation in vertex form
[tex]A=-x^2+200x[/tex]
Factor -1
[tex]A=-(x^2-200x)[/tex]
Complete the square
[tex]A=-(x^2-200x+100^2)+100^2[/tex]
[tex]A=-(x^2-200x+10,000)+10,000[/tex]
Rewrite as perfect squares
[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form
The vertex is the point (100,10,000)
The x-coordinate of the vertex represent the length of the wall for a maximum area
so
[tex]x=100\ ft[/tex]
Find the value of y
equation A
[tex]y=200-(100)=100\ ft[/tex]
therefore
The dimensions of the wall are 100 ft x 100 ft
To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.
Explanation:To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,
which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.
The angle of depression from the top of a cruise ship to the top of a sailboat is 22. Sitting above water, the cruise ship is 236 feet tall while the sailboat is 27 feet tall. Find the distance between the cruise ship and the sailboat.
Answer:
The distance between the cruise ship and the sail boat is 517 feet.
Step-by-step explanation:
The cruise ship is 236 feet tall, and the sailboat is 236 tall; this means the distance between the top of the cruise ship and the top of the sail boat is
236 feet - 27 feet = 209 feet.
We also know that the angel of depression from the top of the cruise ship to the bottom of the cruise ship is 22°. This forms a right triangle as shown in the figure attached.
Now from trigonometry we get:
[tex]tan \: \theta = \dfrac{209}{d}[/tex]
[tex]d= \dfrac{209}{tan\:\theta }[/tex]
[tex]\boxed{d=517ft}[/tex]
The distance between the cruise ship and the sailboat is 517 feet.
Final answer:
To calculate the horizontal distance between the cruise ship and the sailboat, we subtract the sailboat's height from the cruise ship's height to get 209 feet, use the angle of depression and tangent function, and find that the distance between them is approximately 517.57 feet.
Explanation:
To find the distance between the cruise ship and the sailboat, we need to apply trigonometry. First, we determine the difference in height between the two, which is the cruise ship's height above the water subtracted by the sailboat's height. This will be 236 feet - 27 feet = 209 feet. Since the angle of depression from the cruise ship to the sailboat is 22 degrees, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.
The opposite side, in this case, is the difference in height (209 feet), and the adjacent side is the horizontal distance between the ships, which we're trying to find. Thus:
tangent(22 degrees) = opposite/adjacent
adjacent = opposite/tangent(22 degrees)
= 209 feet / tangent(22 degrees)
Now we calculate the tangent of 22 degrees and then divide 209 feet by this amount to find the distance between the two vessels.
Using a calculator, tangent(22 degrees) ≈ 0.4040, so:
adjacent ≈ 209 feet / 0.4040 ≈ 517.57 feet
Therefore, the horizontal distance between the cruise ship and the sailboat is approximately 517.57 feet.
Add and write the fraction or mixed number in its simplest form 2/5+1/4+7/10=
Answer:
1 7/20 mixed= 27/20
Step-by-step explanation:
Chandra's heart beats 1860 times during 15 min of running. While resting, Chandra records her heart beating 36 times in 30 seconds what is the difference between Chandra's heart rate while running vs. resting?
A. 56 beats/min
B. 52 beats/min
C. 1912 beats/min
D. 1788 beats/min
Answer:
B. 52 beats/min
Step-by-step explanation:
while resting her heart beats : 36×2 = 72 beats/min
while running her heart beats : 1 860÷15 = 124 beats/min
difference = 124-72 = 52 beats/min
:)
Answer:
B. 52 beats/min
Step-by-step explanation:
To find the answer you have to find the bpm of each time that Chandra recorded her heart rate. So when she recorded her heart rate when running, you simply divide 1850 by 15, and you should get 123.333 (repeating) I am assuming by the answers that we are rounding, so we are going to round that answer up. Next to find her heart rate while resting, you take her heart rate in 30 seconds, which is 36, and multiply it by 2, because it was her heart rate in half of the time that we are measuring it in. So when you multiply 36 by 2 you should get 72. The next step is to subtract 124 from 72. You answer is 52.
Solve the quadratic equation for x. What is one of the roots?
2x2 + 9x − 5 = 0
A) −
1
2
B) −
1
5
C)
1
2
D)
1
5
Final answer:
To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.
Explanation:
To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.
Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.
Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:
x1 = (-9 + 11) / 4 = 2 / 4 = 0.5 or 1/2x2 = (-9 - 11) / 4 = -20 / 4 = -5Thus, one of the roots of the equation is 1/2, which corresponds to option C.
20. Coin Collecting The value of Gerald's coins is the
value of his brother's coins. Gerald's coins are worth $14.
What is the value of his brother's coins? Write and solve
an equation.
Answer:
$14
Step-by-step explanation:
if Gerald's coins have the same value as his brothers, then that means they have exactly the same amount
If there are 46 scores in a set of data, in which position will the lower quartile lie
Answer:
Position 12.
Step-by-step explanation:
It will be n the center of the bottom 23 numbers ( when the data is arranged in ascending order).
That is in position 12.
Write the inequality shown in the graph below:
Referring to the figure, evaluate the expression shown.
a. (-3) b. 7 c. -3 d. 3
Answer:
d
step-by-step explanation:
How fast should the ant walk to go around the rectangle in 4 minutes?
The ant should walk__ inches per minute.
Question:
How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches
Answer:
The ant should walk 14 inches per minute
Solution:
Given that,
Dimensions of rectangle are 12 inches and 16 inches
Find the perimeter of rectangle
Perimeter = 2(length + width)
Perimeter = 2(12 + 16)
Perimeter = 2(28) = 56
Thus perimeter of rectangle is 56 inches
Time taken = 4 minutes
We have to find the speed at which ant covers 56 inches in 4 minutes
The speed is given by formula:
[tex]speed = \frac{distance}{time}[/tex]
[tex]speed = \frac{56}{4} = 14[/tex]
Thus the ant should walk 14 inches per minute
(-4-3n).-8
Need help
What is the value of x in the proportion (x-1)/5=(4x+3)/35
Answer:
x = 10/3
Step-by-step explanation:
(x - 1)/5*35 = (4x + 3)/35*35
7(x - 1) = 4x + 3
7x - 7 - 4x + 7 = 4x + 3 - 4x + 7
3x/3 = 10/3
x = 10/3
In the diagram above which two red lines are parallel.!?
Answer:L F and K G
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The answer is not A because:
lines gk and kg are the same line
The answer is not B because:
lines il and gk are perpendicular if they were to touch
The answer is not C because:
line fl and il are perpendicular
The answer IS D because:
lines fl and gk are parallel because they will never touch
[tex]5 \times 5[/tex]
Step-by-step explanation:
[tex]5 \times 5= 25[/tex]
solve each inequality, graph the solution on the number line, and write the solution in interval notation
3x− 2 > 4 or 5x− 3 ≤ 7
Answer:
[tex](-\infty,+\infty)[/tex]
Step-by-step explanation:
The given inequality is 3x-2>4 or [tex]5x-3\leq 7[/tex]
We group similar terms to obtain: 3x>4+2 or [tex]5x\le7+3[/tex]
Simplify to get:
3x>6 or [tex]5x\le10[/tex]
x>2 or [tex]x\le 2[/tex]
This implies that the solution set is all real numbers.
The solution in interval notation is [tex](-\infty,+\infty)[/tex]
Can someone help me plzzzz!
8.2is the answer
Step-by-step explanation:
|CB|+8