The statement that is true about equations and expressions is that an example of an equation is because it shows that two expressions are equal.
While an example of an expression is because it is a mathematical phrase represented by numbers, a variable, and an operation.
An equation is a mathematical statement where two expressions are equal. It's important to note that an equation has an equals sign, so the left side of the equation is equal to the right side of the equation.
Expressions are combinations of numbers, symbols, and operators that represent a value. A symbol or letter that represents a value is a variable. It's important to note that an expression does not have an equals sign, so the value of the expression is not defined.Why is an example of an equation true?An equation can be written in the form x = y. The equals sign indicates that x and y are equal. This means that two expressions, x and y, are equal. Therefore, an equation shows that two expressions are equal.
An example of an equation is 3x + 4 = 10. This equation is an example of an equation because it shows that two expressions, 3x + 4 and 10, are equal. The left side of the equation (3x + 4) equals the right side of the equation (10). Therefore, this statement is true: "An example of an equation is because it shows that two expressions are equal."
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How to solve it and what the answer
Answer:
34.56 in
Step-by-step explanation:
2.4*2.4*6=34.56
Ms. Kent measures the perimeter of a common shape. One of the sides is 7 centimeters, and the perimeter is
21 centimeters. If all of the sides are the same length, what shape does Ms. Kent measure? Explain.
Answer:
Step-by-step explanation:
If the perimeter of a shape is 21 centimeters and one side is 7 centimeters, then we can find the total number of sides by dividing the perimeter by the length of one side:
Number of sides = Perimeter / Length of one side
Number of sides = 21 cm / 7 cm
Number of sides = 3
This means that the shape has 3 sides, which makes it a triangle.
Since all sides of the triangle have the same length, we can call it an equilateral triangle. In an equilateral triangle, all sides have the same length, and all angles are 60 degrees.
pls answer!!!
worth 60 points <33
Answer:
a. 4
b. -2
c. 0,5
Step-by-step explanation:
1. 4
2.2
3.0,5
IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS
Find the coordinate of the midpoint segment for(7, 0), (3, 4)
a.2,5
b.5,2
c.7,4
d.2, 5
I NEED HELP ON THIS ASAP!
Answer:
(-2,4) is quadrant 2, (8,4) is quadrant 1, (6,-2) is quadrant 4
Step-by-step explanation:
On three of the first four math tests, Daniel earned the following scores: 84, 92 and 88. If Daniel’s
average for all four tests is 87.5, what score did Daniel earn on his fourth test?
Answer: 86
Step-by-step explanation:
let x be the unknown
(84+92+88+ x)
----------------------- = 87.5
4
then cross multiply
(84+92+88+ x )= 87.5 times 4
84+ 92+ 88 + x= 350
add the left side
264+ x=350
subtract 264 from both sides
264 - 264 + x= 350 - 264
therefore x= 86.
What is the volume of this sphere? responses 8π cm³ 8 pi, cm³ 16π cm³ 16 pi, cm³ 27π cm³ 27 pi, cm³ 36π cm³
The volume of a sphere with a radius of 3cm is 113.04 cm³, which is approximately equal to 36π cm³. So, the correct option is D).
The formula for calculating the volume of a sphere, V = 4/3πr³, is used to find the amount of space enclosed by a sphere with a given radius. In this case, the sphere has a radius of 3cm. By substituting this value into the formula, we can solve for the volume of the sphere.
V = 4/3πr³
V = 4/3 × 3.14 × 3³ = 113.04 cm³
= approximately 36π cm³
The result is 113.04 cm³, which is approximately equal to 36π cm³. This calculation is important in many applications, such as engineering, physics, and mathematics. The correct answer is D).
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_____The given question is incomplete, the complete question is given below:
What is the volume of sphere r = 3cm? responses A 8π cm³ 8 pi, cm³ B 16π cm³ 16 pi, cm³ C 27π cm³ 27 pi, cm³ D 36π cm³
What is the theoretical probability of selecting a vowel from the word orange?
A. 10%
B. 75%
C. 20%
D. 50%
Answer:50%
Step-by-step explanation: Since there are 6 letters in orange, and there are 3 vowels in the word (o,a,e), that would mean there is a 3/6 chance (50%) of selecting a vowel.
20 POINTS.
Solve 4x+2 = 12 for x using the change of base formula
−1. 442114
−0. 207519
2. 55789
3. 79248
Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.
The given equation is 4x+2 = 12.
To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:
4x+2-2 = 12-2
4x = 10
Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.
Rewrite equation:
x = log base 4 of 10
Use the change of base formula, we can present this as:
x = [tex]log base 10 of 10 / log base 10 of 4[/tex]
Simplifying:
x = 1.442114
Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.
In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.
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Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?
A.{x | x R, x < 5}
B.{x | x R, x > 5}
C.{x | x R, x ≤ 5}
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
What exactly is a set?
In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.
Now,
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.
In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.
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100 POINTS AND BRAINLIEST Please help solve at least 1 of these problems and show your work because I don’t know how to solve these
Step-by-step explanation:
Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.
a)
n = 6 : 2
n = 3
m = √(6²+3²)
m = √45
b)
x = 10 x 2 = 20
y = √(20²-10²)
y = √300
c)
a = √(5²+5²)
a = √50
the answers are in simple radical form as requested
If f(x) = x3, what is the equation of the graphed function?
A. y = f(x − 3) − 2
B. y = f(x + 3) – 2
C. y = f(x + 2) − 3
D. y = f(x − 2) + 3
Answer:
B. y = f(x + 3) – 2
Step-by-step explanation:
We need move point (0,0) to point (-3,-2).
(-3,-2)=(a,b)
y=f(x-a)+b
y=f(x-(-3))-2
y=f(x+3)-2
Answer:
f(x) = (x+3)^3
I think this is the right answer...
a faulty car odometer proceeds from digit $3$ to digit $5$, always skipping the digit $4$, regardless of position. for example, after traveling one mile the odometer changed from $000039$ to $000050$. if the odometer now reads $002005$, how many miles has the car actually traveled?
The car has actually travelled 1745 miles, even though the odometer reads 2005. This is because the odometer skips the digit 4, so the number of valid readings must be counted and subtracted from the odometer reading.
We can approach this problem by counting the number of valid readings on the odometer between 3000 and 5000. We can then subtract the number of invalid readings (i.e., readings that contain the digit 4) to determine the actual number of miles the car has travelled.
The valid readings between 3000 and 5000 are: 3001, 3002, 3003, 3005, 3006, 3007, 3008, 3009, 3010, ..., 4997, 4998, 4999, 5000.
There are a total of 2001 valid readings in this range.
However, we need to subtract the number of invalid readings, which are the readings that contain the digit 4. Since the odometer skips the digit 4, we can think of each valid reading as having four possible digits (0, 1, 2, or 5) for each of its four places. Therefore, the number of invalid readings is 4 x 4 x 4 x 4 = 256.
So the actual number of miles the car has travelled is 2001 - 256 = 1745.
Therefore, the car has actually travelled 1745 miles.
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10 Points
What is 9 < 3 x = 8
The equation has no solution that satisfies the inequality.
How to explain the InequalityThis equation doesn't have a unique solution because it's contradictory. It should be noted that to see why, we can simplify the equation by subtracting 9 from both sides:
3x = 18 - 9
which simplifies to:
3x = 9
Now we can solve for x by dividing both sides by 3:
x = 3
However, if we substitute x = 3 back into the original equation, we get:
9 < 3(3) = 9
This isn't true. Therefore, the equation has no solution that satisfies the inequality.
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help me with this please hurry
Answer: Its A
Ive took this test :3
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are: 10 are red, 8 are blue, 5 are green, and 2 are white
Based on the random sample results, how many of the 200 gumballs are red?
The proportion of red gumballs in the random sample is 0.4, meaning 40% of the 200 gumballs are red. To estimate the number of red gumballs in the entire population of 200 gumballs, we multiply the proportion of red gumballs by the total number of gumballs, 0.4 x 200 = 80.
What is proportion?Proportion in mathematics refers to the equality of two ratios. It asserts that two ratios are comparable. A ratio is a fractional comparison of two numbers or quantities, such as a/b or c/d.
To estimate how many of the 200 gumballs are red, we can use the proportion of red gumballs in the random sample and apply it to the entire population of 200 gumballs.
The proportion of red gumballs in the random sample is:
10/25 = 0.4
This means that 40% of the gumballs in the random sample are red.
To estimate the number of red gumballs in the entire population of 200 gumballs, we can multiply the proportion of red gumballs by the total number of gumballs:
0.4 x 200 = 80
Therefore, we can estimate that there are approximately 80 red gumballs in the machine.
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The radius of a circle is 18 cm. Find its area in terms of π
The school is located at (0, 0) on a coordinate plane. Mary lives 2 miles north of the school. Her classmate Roger lives 3 miles west of the school. What is the
distance between Mary's and Roger's houses? Round your answer to the nearest tenth of a mile.
Answer:
Step-by-step explanation:
that would be 5 miles bc 3+2 is 5
The distance between Mary's and Roger's houses is approximately 3.6 miles.
What are coordinates?
A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
We can use the Pythagorean theorem to find the distance between Mary's and Roger's houses since they form a right triangle with the school at the vertex:
Let A be the school (0, 0), B be Mary's house (0, 2), and C be Roger's house (-3, 0).
Then the length of AB is 2 miles and the length of AC is 3 miles.
The distance between Mary's and Roger's houses is the length of the hypotenuse BC.
Using the Pythagorean theorem, we have[tex]BC^2 = AB^2 + AC^2 = 2^2 + 3^2 = 13.[/tex]
Taking the square root of both sides, we get[tex]BC = \sqrt{(13)} = 3.6[/tex] miles.
Therefore, Between Mary and Roger's homes, there are roughly 3.6 miles.
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A student mows lawns on the weekends. It takes him 110 minutes to mow 2 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 10 hours to mow 12 lawns.
It will take him 11 hours to mow 12 lawns.
It will take him 17 hours to mow 12 lawns.
It will take him 48 hours to mow 12 lawns.
Answer:
It will take him 11 hours to mow 12 lawns
Step-by-step explanation:
110/2=55 (meaning it takes him 55 minutes to mow 1 lawn)
55x12=660 (meaning it takes him 660 minutes to mow 12 lawns)
660/60=11 (meaning it takes him 11 hours to mow 12 lawns)
Why 660/60? Because there is 60 minutes in 1 hour.
A vehicle purchased for $ 29800depreciates at a constant rate of 9% per year. Determine the approximate value of the vehicle 15 years after purchase.
Answer:
The value of the vehicle would be $7,242
Step-by-step explanation:
Given,
The original value of the vehicle, P = $29,800,
Rate of depreciation, r = 9% = 0.09
Time, t = 15 years,
Thus, the value of the car after 15 years,
[tex]A=P(1-r)^t[/tex]
[tex]=29800(1-0.09)^{15}[/tex]
[tex]=29800(0.91)^{15}[/tex]
[tex]=7241.64363066[/tex]
[tex]\thickapprox \bold{\$ 7,242}[/tex]
I don't understand this, can someone please help me?
Answer: You'll have to plug each function into a calculator and match the corresponding ones with each other.
for example Sin45° = B cos 45°
Step-by-step explanation:
Write a equation and solve.
A car moves 660 feet every 10 seconds. How far does it go if it moves for 10 sec, 20 sec, and 30 sec
Answer: 10sec 660 feet, 20sec = 1320 feet, 30 sec = 1980 feet.
Step-by-step explanation:
It states that a car moves 660 feet in 10sec.
10sec = 660 feet
20sec: 660+660=1320f
30sec: 660+660+660=1980f
Select the equivalent expression
Answer:
Step-by-step explanation:
Prove that 5^7 + 5^6 is divisible by 60
Answer:
I think it is not ?
Step-by-step explanation:
You get a remainder at the end when you solve it and that's the opposite of what divisible means
"(of a number) capable of being divided by another number without a remainder."
Answer:
Not divisible
Step-by-step explanation:
5^7 is 78125
5^6 is 15625
15625 + 78125 = 93750
93750/60 = 1562.5
Therefore it is not fully divisible by 60.
ABCD is rhombous wi4h M(<ADC)=135 find m(<BAD) and m(<ADC)
In the given figure of Rhombus, Angle ∠BAD is 0°. In summary: angle ∠ABC = 135°
angle ∠ADC = 135°
angle ∠BAD = 0°
What is rhombus?
A rhombus is a quadrilateral (four-sided) geometric shape with equal-length sides. Since it has two sets of opposite equal acute angles and opposite equal obtuse angles, it is also known as a diamond form. In other words, the opposite angles and the neighbouring sides of a rhombus are congruent. A rhombus has two equal-length diagonals that are right angles to one another. A rhombus's area is equal to the product of its diagonal lengths.
by the question.
In a rhombus, opposite angles are equal, so we know that:
angle ∠ABC = angle ∠ADC (opposite angles of rhombus)
angle ∠BCD = angle ∠BAD (opposite angles of rhombus)
We are given that angle ∠ADC is 135°. Therefore, angle ∠ABC is also 135°.
To find angle ∠BAD, we can use the fact that the angles of a quadrilateral sum to 360°. Since we know three of the angles (∠ABC, ∠BCD, and ∠ADC), we can find the fourth angle (∠BAD) by subtracting their sum from 360°:
∠BAD = 360° - (∠ABC + ∠BCD + ∠ADC)
= 360° - (135° + 90° + 135°)
= 360° - 360°
= 0°
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How do I prove that the sum of exterior angles of any polygon is equal to 360 degrees?
To prove that the sum of the exterior angles of any polygon is equal to 360 degrees, the Sum of interior angles = (n - 2) x 180 degrees.
we can use the following steps:
Draw any polygon and mark a point outside the polygon for each vertex.
Draw a line segment connecting each vertex to the point outside the polygon that corresponds to it, creating an exterior angle at each vertex.
Measure each exterior angle using a protractor and record the measurements.
Sum all the exterior angles together and observe the result.
We can see that the sum of all the exterior angles is always equal to 360 degrees, regardless of the number of sides or the shape of the polygon. This can be written as:
The sum of exterior angles = 360 degrees
To prove this algebraically, we can use the fact that the sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon. Each exterior angle is supplementary to the corresponding interior angle, so we can write:
The sum of exterior angles = Sum of interior angles (supplementary angles)
Substituting the formula for the sum of interior angles, we get:
Sum of exterior angles = (n - 2) x 180 degrees (supplementary angles)
= 180n - 360 degrees
= 360 degrees - 360 degrees + 180n
= 360 degrees - Sum of interior angles
= 360 degrees - (n - 2) x 180 degrees
= 360 degrees - 180n + 360 degrees
= 720 degrees - 180n
Since the sum of the exterior angles must be a positive value, we can take the absolute value and simplify:
|Sum of exterior angles| = |720 degrees - 180n|
= 180|4 - n|
Since n is always a positive integer greater than or equal to 3 (since a polygon must have at least three sides), we know that 4 - n is always a negative integer between -1 and -n+1. Therefore, |4 - n| is equal to n - 4. Substituting this into the equation above, we get:
|Sum of exterior angles| = 180|n - 4|
= 180(n - 4)
= 180n - 720 degrees
= 360 degrees - 360 degrees + 180n - 720 degrees
= 360 degrees - Sum of interior angles
Therefore, we have shown that the sum of the exterior angles of any polygon is equal to 360 degrees.
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Consider a chemical reaction, where “A” is one of the reactants.
Therefore, the reaction is first-order with respect to the concentration of "A".
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown values, and constants, which are known values. The goal in solving an equation is to find the values of the variables that satisfy the equation, that is, make it true. Equations can be linear or nonlinear, and they may involve one or more variables. Some common types of equations include polynomial equations, trigonometric equations, exponential equations, and logarithmic equations.
Here,
1. Table completion:
Time (s) [A] (M)
0 1.0
50 0.81
100 0.65
150 0.53
200 0.43
250 0.35
300 0.28
350 0.23
400 0.19
450 0.15
500 0.12
2. To determine the reaction order with respect to the concentration of "A", we need to manipulate the above equation for the different orders of the reaction and re-plot the tabulated numbers to determine the order.
For zero-order: [A]t = [A]o - kt
Taking the natural logarithm on both sides:
ln [A]t = ln [A]o - kt
This gives a straight line equation of the form y = mx + b, where y = ln[A]t, x = t, m = -k, and b = ln[A]o.
For first-order: ln [A]t = ln [A]o - kt
Taking the reciprocal on both sides:
1/[A]t = kt + 1/[A]o
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o.
For second-order: 1/[A]t = 1/[A]o + kt
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o. We can then plot the given data in Excel with the appropriate equation and check which equation gives us the best straight line fit. The slope of the line will give us the reaction order. Using Excel, we find that the first-order equation gives the best straight line fit with a slope of -0.0077.
3. To calculate the rate constant 'k', we can use the slope of the straight line fit obtained above.
From the equation ln [A]t = ln [A]o - kt, we have k = -slope.
Therefore, k = 0.0077 s⁻¹.
To estimate the half-life of "A", we can use the equation for the half-life of a first-order reaction:
t1/2 = ln 2/k
Substituting the value of k obtained above, we get:
t1/2 = ln 2/0.0077 s⁻¹
= 89.9 s
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what is the unit rate if the car traveled 300 km within 2.5 hrs
The unit rate of the given expression through which the relation is satisfied is 300km / 2.5 hrs = 120 km / hr
What about unit rate?
In mathematics, a unit rate is a ratio between two quantities in which one quantity is expressed in terms of one unit of measure. It is commonly used to compare the cost or value of two or more items. For example, if a store charges $4 for 2 pounds of bananas, then the unit rate is $2 per pound of bananas.
The general formula for calculating unit rate is:
Unit rate = Quantity of one item ÷ Cost or value of that item
This formula can be used to find the unit rate of any item or quantity, as long as the quantity and cost or value are known. Unit rate is a useful tool in mathematics, as it allows for easy comparison of different quantities or values, and helps to make complex calculations more straightforward.
According to the given information:
The unit rate = [tex]\frac{Distance}{Time}[/tex]
i.e , unit rate = 300/2.5 = 120
⇒ 120km/hr.
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Divide then show a model
g suppose an unknown radioactive substance produces 2800 counts per minute on a geiger counter at a certain time, and only 700 counts per minute 15 days later. assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance. the radioactive substance has a half-life of days.
The half-life of the radioactive substance is 7.5 days. This means that, after 7.5 days, half of the radioactive atoms will have decayed and the count per minute will be reduced by half
The half-life of a radioactive substance is the amount of time it takes for half of its radioactive atoms to decay. In this case, you are given the initial count per minute of 2800 and the count per minute after 15 days of 700. We can use this information to calculate the half-life of the radioactive substance. First, divide the initial count per minute (2800) by two. This gives us the count per minute that we need to find, which is 1400.
We then subtract the count per minute after 15 days (700) from the count per minute we need to find (1400). This gives us the difference in count per minute, which is 700. Now, we need to determine how much time it would take for the count per minute to decrease by 700. To do this, we divide the difference in count per minute (700) by the initial count per minute (2800). This gives us a decimal, which we then multiply by the number of days (15). The result is the half-life of the radioactive substance in days, which is 7.5 days.
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