The restrictions on the variables x and y be
x = 0 ⇒ 2/0 = ∞
y = 0 ⇒ 2/0 = ∞
What is meant by expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
How to divide the given expression (7x/4y³) ÷ (21x³/8y)?(7x/4y³) × (8y/21x³) = (2/3x² y³)
What are the restrictions on the variables?
Here, x = 0 ⇒ 2/0 = ∞
Similarly, y = 0 ⇒ 2/0 = ∞
So , x, y ≠ 0
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Suppose Angel is shooting baskets and makes 40% of the 15 shots. Does he get a prize? Explain your reasoning
Answer:
Well 40% of 15 is 6
Step-by-step explanation:
It depends on how many shots it takes to win a prize
In a class of 20 students, how many conversations must be had so that every student talks to every other students in the class?
Answer:
190
Step-by-step explanation:
Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people. Therefore, our answer is 190
a toy rocket is launched from a platform 6.3 meters above the ground in such a way that is a height, h (in meters) after t seconds is given by the equation h=-4.9t^2+43.4t+6.3. how long will it take for the rocket to hit the ground?
The toy rocket will take a time of 8.999 seconds to hit the ground.
How much time does the rocket take to hit the ground?
The height of the rocket (h), in meters, in terms of time (t), in seconds, is defined by a quadratic equation. In this question we must determine the time needed for the rocket to hit the ground, that is, a time t greater than zero such that the height is zero. Now we proceed to solve the polynomial:
- 4.9 · t² + 43.4 · t + 6.3 = 0
- 4.9 · (t² - 8.857 · t - 1.286) = 0
- 4.9 · (t - 8.999) · (t + 0.143) = 0
Only the first root offers a realistic value as time is a whole number. Hence, the toy rocket will take a time of 8.999 seconds to hit the ground.
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solve each equation(with explanation please)
-4+p=-7
x/10=-6
4-3(8n - 4) = -104
Answer:
1: P = -3
2: X = -60
3: N = 5
Step-by-step explanation:
Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.
Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60
Last one is a little tricky here's the equations I used to get the last one
-3 x 8n = -24x
New equation: 4-24x=-104
+4 + 4
___________________________
-24x = -100
___ ___
-24 -24
_
so the answer would be x = 5
Find the value of x to the nearest tenth. 228.4= πx
x = 73 is the value of x.
What exactly do we mean by a value?A value in mathematics is a number that indicates the result of a calculation or function.So, in the preceding example, you could tell your teacher that 5 x 6 equals 30 or that x + y equals 9 if x = 6 and y = 3.A value is another term for a variable or constant.To find the value of x:
Given: 228.4/x = πAfter we have entered the value of π, we will simplify the given equation to find the value of x.So,
228.4/x = π228.4/x = 3.14159228.4/3.14159 = xx = 72.702039Then rounding to the nearest tenths gives x = 73.
Therefore, x = 73 is the value of x.
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The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, which conclusion is accurate?
OA) The triangle is acute.
OB) The triangle is right.
OC) The triangle is obtuse.
OD) The triangle is isosceles.
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right. The correct option is B
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right.
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Find the seventh term of each geometric sequence. 1,-3,9, . . . . . . .
The seventh term of the given geometric progression is: 729.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Now,
Given GP: 1, -3, 9, .....
Here, a₁ = 1
a₂ = a₁ (r)
=> 3 = 1 (r)
=> r = 3
Thus, a₇ = a₁ (r⁷⁻¹) = 1 (3⁶) = 729.
Hence, The seventh term of the given geometric progression is: 729.
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1.
Solve each equation for the indicated variable.
a+m=n=p,
for a.
In linear equation, a = (n+p)/m is equation for the indicated variable.
What in mathematics is a linear equation?
A linear equation is an algebraic equation with the formula y=mx+b, . m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."In terms of algebra, writing "am" is the same as writing "a*m" or "a times m"
To undo the multiplication, we use division. We will divide both sides by m to get 'a' all by itself on the left side
So...
am = n+p
a*m = n+p
(a*m)/m = (n+p)/m .... divide both sides by m
a = (n+p)/m ... notice how the 'm's cancel out when we divide on the left side
a = (n+p)/m
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what is an example of a linear equation that is perpendicular to y = 5?
Answer:
Step-by-step explanation:
x=5
Calculate the distance between the following points: F(-9, -14) and G(1,-19)
The distance between points F and G is 15 units.
How to calculate distance between two points?The length of the line segment connecting two points on a plane is known as the distance between the points. The formula for distance between two points ([tex]x_{1}[/tex],[tex]x_{2}[/tex]) and ([tex]y_{1}[/tex],[tex]y_{2}[/tex]) is given by
distance between two points =[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]
The equation can be used to calculate the distance between any two locations on an x-y plane or coordinate plane.
The point F is (-9,14) and point G is (1,-19)
distance between F and G
=[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]
=[tex]\sqrt{(-9-1)^2+(-14-(-19))^2 } }[/tex]
=[tex]\sqrt{(-9-1)^2+(-14+19)^2 } }[/tex]
=[tex]\sqrt{(-10)^2+(5)^2 } }[/tex]
=[tex]\sqrt{100+25}[/tex]
=[tex]\sqrt{125}[/tex]
=15 units.
Distance between point F and G is 15 units.
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A man who is 6 feet tall is walking at a rate of 4 feet/second, directly away from a light that is located 10 feet above the ground.
How long is the man's shadow t seconds after he starts walking? The answer will be in terms of t.
Answer:
2.5t
Step-by-step explanation:
Let the man be
x
feet away from the street light, and his shadow length be
y
, Let the tip of the shadow be
l
feet away from the light such that
l
=
x
+
y
and we are given that
d
x
d
t
=
2
By similar triangles:
y
6
=
x
+
y
30
∴
30
y
=
6
(
x
+
y
)
∴
30
y
=
6
x
+
6
y
∴
30
y
−
6
y
=
6
x
∴
24
y
=
6
x
∴
y
=
1
4
x
Now,
l
=
x
+
y
⇒
l
=
x
+
1
4
x
∴
l
=
5
4
x
Differentiating wrt
x
gives;
d
l
d
x
=
5
4
And by the chain rule we have:
d
l
d
t
=
d
l
d
x
d
x
d
t
∴
d
l
d
t
=
5
4
×
2
∴
d
l
d
t
=
2.5
feet/sec
In 2006,500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded.
b. Find the slope of the line, and interpret its meaning.
The slope of the line is 150.
It is given the number of songs (in million) downloaded from the internet in 2006 and 2004.
We actually need to graph this data which will be a straight line. We try to find two points in this graph using the given data.
Represent the years as x coordinates and the number of songs as y coordinates. Also take 2006 as 6 only and 2004 as 4 only for convenience.
Now we get two points [tex](x_1,y_1)[/tex] = (4, 200) and [tex](x_2,y_2)[/tex] = (6, 500)
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150
Here the slope is positive, which means that the number of downloads are increasing with increase in years. The rate of change in number of downloaded songs from internet is 150 million in two years.
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Martina has 16 cars available to rent. let c be the number of cars she would have left after renting r of them. write an equation relating c to r. then use this equation to find the number of cars she would have left after renting 14 of them.
If Martina has 16 cars available to rent, and if c is the number of cars she would have left after renting r of them, then the equation relating c to r will be c = 16 - r, and the number of cars she would have been left with after renting 14 of them is calculated to be 2.
An algebraic expression is a type of expression consisting of both numerals and letters.
If Martina has a total of 16 cars available to rent, then the equation or algebraic expression relating c to r is,
c = total number of cars available to rent - r
c = 16 - r
After renting 14 of the total cars available, then the number of cars left can be calculated using this equation,
c = 16 - r
c = 16 - 14
c = 2
Thus, the number of cars she would have been left with is calculated to be 2.
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question in the picture
The salary after 6 years is $83,000.
The salary after tt years is 53,000 + 5000tt.
What is her total salary?The equation that can be used to determine Aisha's salary after a period of time can be represented by a linear equation. This is because that her salary increases by a constant rate each year.
A linear function represents a straight line when drawn on a coordinate plane. A linear function is a function that has a single variable raised to the power of 1. An example is y + 2. The variable y is raised to the power of 1. 2 is the constant term.
Total salary = beginning salary + (rate of increase x number of years)
Salary after 6 years: 53,000 + (5,000 x 6)
= 53,000 + 30,000 = $83,000
Salary after tt years: 53,000 + (5,000 x tt)
53,000 + 5000tt
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−4 5/9+8/9 pls help and hurry
exact form:
-11/3decimal form:
-3.6666mixed number form:
-3 2/3Answer:
-11/3
Step-by-step explanation:
Convert −4 5/9 to improper fraction -41/9 and do the math.
-41/9 + 8/9
-33/9
-11/3
Find two pairs of whole numbers with a geometric mean that is also a whole number. What condition must be met in order for a pair of numbers to produce a whole-number geometric mean?
2 and 18 are the two pairs of whole numbers with a geometric mean that is also a whole number.
The geometric mean is defined as the nth root of the product of n numbers, which means for a set of numbers x1, x2, ..., xn. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.
For example, we multiply them: 2 × 18 = 36
Then (as there are two numbers) take the square root: √36 = 6
Conditions: The square roots of the product of the pair of numbers must be whole-number. These two conditions must be met to have an exact geometric mean
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A coin is filmed using stop-motion animation so that it appears to move.
a. Describe the translation from A to B in function notation and in words.
The translation from A to B is described as-
In notation: From x = -3 to x = 0, the coin travels through y = (2/3)x + 1.In words: From A to B, the coin shifts three spaces to a right and then two spaces up.What is meant by translation?In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the exact size as that of the original shape, therefore the shapes are congruent.
Replace x with x - k whenever a shape is moved to the left by k units.Replace x with x + k whenever a shape is moved to the right by k units.Replace y with y + k whenever a shape is moved up by k units.Replace y with y - k whenever a shape is moved down by k units.Now, according to the question.
Consider the equation for the shifting from A to B as y = k x+b
The coordinates of the location A and B are-(see the diagram)
A(-3,-1) and B(0,1)
Thus, A, B into y = k x+b
Substitute the value of A in the equation;
-1 = -3k + b
b = 1
So, k = 2/ 3
Put value of k in 'y'.
Hence, AB ; y = (2/3)x + 1
Thus, the coin moves thought y = (2/3)x + 1 from x = -3 to x = 0.
In words; Shifting from A to B, the coin moves 3 spaces to the right after that moves 2 space up.
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Before signing a contract, you must review the terms and conditions of the contract. How many terms are there in the surface area formula below?
2(lw + wh + hl)
How many terms are there in the surface area formula below?2(lw + wh + hl) 3 terms.
What are the three terms ?
The total surface area of a cuboid= 2(lw + wh + hl)
Here, w= width, h= height, l= length
Thus, there are 3 terms in the surface area formula.
What is a total surface area?
There may be numerous flat surfaces throughout an entire object (such as a cube), each of which needs to be measured independently. The total surface area of an object is the sum of all the faces that make up the object.Keep in mind that the total surface area only accounts for the flat exterior of an object, treating it though it were two-dimensional.Even if there are many of them, these many flat surfaces join together to form the three-dimensional entity.Surface area and total surface area do not always represent the amount of space that an object occupies.To learn more about total surface area, refer:
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f(x) = -x + 4 and g(x) = x2 - 5, then g(f(3)) = ?
8 x 10^-3 is how many times greater than 4 x 10^-6
Answer:
.002 or
2x10^-3
Step-by-step explanation:
make sure the exponents match
8 x 10^-3 =
.008 × 10^-3
(.008 × 10^-6) ÷ (4 x 10^-6)
10^-6 cancels out
.008 ÷ 4 = .002
or
2x10^-3
Factor the equation.
Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Step-by-step explanation:
What is the value of x in the equation 6(x-4)=3 x ?
The value of x in equation is 8
To find the value of x, we will solve the given mathematical expression based on the sequence of signs and placement of bracket. Firstly bracket will be solved followed by subtraction or addition.
Rewriting the equation -
6(x - 4) = 3x
Performing multiplication on Left Hand Side of the equation to find the value of x
6x - 24 = 3x
Shifting 3x and 24 to other side of equation
6x - 3x = 24
Performing subtraction on Left Hand Side of the equation
3x = 24
Shifting 3 to other side of equation as denominator
x = 24 ÷ 3
Performing division on Right Hand Side of the equation
x = 8
Hence, the value of x is 8.
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PLEASE HELP PLEASE PLEASE PLEASE!! Please show work for brainliest!!! :)
What is the factored form of the expression over the complex numbers? 16x^2+9y^2
The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)
How to factorize expressions?We want to find the factored form of the expression 16x² + 9y² over the complex numbers.
We can rewrite the given expression 16x² + 9y² as perfect squares;
= (4x)² + (3y)²
Now, from using the difference of squares formula, we know that;
a² - b² = (a + b)(a - b)
Thus;
(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;
(4x + 3iy)(4x − 3iy)
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18. If ZW and ZV are supplementary angles and m2V = 49°, find m/W.
19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m23 = 56°, find m21.
Answer:
Step-by-step explanation:
18. Supplementary angles add up to 180°therefore
∠W+∠V=180°
∠W+49°=180°
∠W=180°-49°
∠W=131°
19.Complementary angles are angles that add up to 360°
∠2+∠3=90°
∠2+56°=90°
∠2=90°-56°
∠2=34°
Vertical angles are equal therefore this tells us that ∠1 and ∠2 are equal
∠1=∠2
∴∠1=34°
20. Angles which are in a linear pair add up to 180°(supplementary)
Mathematically what the statement is sayin is :
∠1+∠2=180°
and ∠1=5(∠2)-18°
therefore we can plug in ∠1=5(∠2)-18° in ∠1+∠2=180°
(5(∠2)-18°)+∠2=180°
5(∠2)+∠2=180°+18°
6(∠2)=192°
[tex]\frac{6 < 2}{6} =\frac{198}{6} \\ < 2=33[/tex]
∠1=5(33°)-18°
∠1=165°-18°
∠1=147°
26 divided by 5 1/5 Help!!
Find the 17 th term of each sequence. a₁₈ = 32, d=-4
36 is 17th term of sequence a₁₈ = 32, d=-4
Given the 18th term and the common difference, we subtract the common difference from the 18th term to determine the 17th term:
a₁₇ = a₁₈ - d
= 32 - (-4)
= 36
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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5) Diego had a pizza that was divided into 8 equal slices. He ate 3 of them. Hector has a pizza that
is the same size, but his is divided into 4 equal slices. He ate 3 slices of his pizza. Who ate more
pizza?
Find the geometric mean between pair of numbers.
√20 and √80
The geometric mean between pair of numbers √20 and √80 is 6.32
We know that for a sequence of numbers x1, x2,.., xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers √20 and √80
We need to find the geometric mean between pair of numbers, √20 and √80
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{\sqrt{20}\times \sqrt{80} }\\\\ \Pi=\sqrt{\sqrt{1600} }\\\\ \Pi=\sqrt{40}\\\\ \Pi=6.32[/tex]
Therefore, the geometric mean between pair of numbers √20 and √80 is 6.32
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Which set of points represents a function which is not one-to-one?
choice 1:
{(3, 2), (9, 6), (0, 7), (6, 5), (2, 0)}
Choice 2:
{(9,6), (4,3), (5, 4), (8, 0), (7, 9)}
Choice 3:
{(4,3), (8,5), (8, 7), (0, 2), (1, 6)}
Choice 4:
{(2, 6), (0, 2), (8, 9), (1, 1), (4, 6)}
Answer:
Choice 4
Step-by-step explanation:
A one to one function has every domain with only one range as their individual output. Choice 4 has the output 6 mentioned twice for both 2 and 4 so therefore it's not a one to one function because the range 6 has two outputs 2 and 4.
You bought a total of 6 pens and pencils for 4 . If each pen costs 1 and each pencil costs .50 , how many pens and pencils did you buy?
I bought 2 pens and 4 pencils from given amount.
Let us represent the number of pens and pencils as x and y respectively. Forming the equation as per the given information -
Equation representing total number of pens and pencils bought
x + y = 6 - Equation 1
Rearranging the equation 1 as per the variable x
x = 6 - y - Equation 2
Equation representing cost of bought pens and pencils
1x + 0.5y = 4 - Equation 3
Keep the value of x from Equation 2 in Equation 3
1 (6 - y) + 0.5y = 4
6 - y + 0.5y = 4
Rearranging the equation for positive sign on each side -
y - 0.5y = 6 - 4
Performing subtraction on Right Hand Side of the equation to find the value of y
0.5y = 2
Shifting 0.5 to Right Hand Side of the equation and performing division
y = 2 ÷ 0.5
y = 4
Calculating the value of x by keeping the value of y in Equation 2
x = 6 - 4
x = 2
Hence, I bought 2 pens and 4 pencils from given amount.
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