Answer:
3. n = 2
4. t = -13/4
Step-by-step explanation:
3)
. . . . (3a) Distribute (multiply) +5 into the expression (n-1)
. . . . . . . . [tex]n + 5n - 5 = 7[/tex]
. . . . (3b) Add like terms (terms with the same variable)
. . . . . . . . [tex]6n - 5 = 7[/tex]
. . . . (3c) Add 5 on both sides of the equation to "get rid" of the -5
. . . . . . . . [tex]6n -5 +5 = 7 +5[/tex]
. . . . . . . . [tex]6n = 12[/tex]
. . . . (3d) Divide both sides by 6 to isolate the variable
. . . . . . . . [tex]6n/6 = 12/6[/tex]
. . . . . . . . [tex]n = 2[/tex]
4)
. . . . (4a) Distribute (multiply) -2 into the expression (2t-1)
. . . . . . . . [tex]15 = -4t + 2[/tex]
. . . . (4b) Subtract 2 on both sides of the equation to "get rid" of the +2
. . . . . . . . [tex]15 -2 = -4t +2 -2[/tex]
. . . . . . . . [tex]13 = -4t[/tex]
. . . . (4c) Divide both sides by -4 to isolate the variable
. . . . . . . . [tex]13/-4 = -4t/-4[/tex]
. . . . . . . . [tex]-13/4 = t[/tex]
What is the relationship between the volumes of a rectangular prism and a rectangular pyramid whose length width and height are all equal?
The volume of the rectangular prism is 3 times the volume of the rectangular pyramid.
Consider a rectangular prism with length l, width w and height h.
The volume of the rectangular prism is:
volume of a rectangular prism = length * width * height
V1 = l * w * h
Consider a rectangular pyramid with rectangular base of length l1, width w1 and the height of pyramid is h1.
The volume of the rectangular pyramid is:
volume of a rectangular pyramid = 1/3 * base area * height
Here, base area = length * width
= l1 * w1
So, volume of a rectangular pyramid = 1/3 * base area * height
V2 = 1/3 * l1 * w1 * h1
We have been given a rectangular prism and a rectangular pyramid have equal length, width and height .
l1 = l, w1 = w and h1 = h
so, V2 = 1/3 * l * w * h
V2 = 1/3 * V1
V1 = 3 * V2
volume of a rectangular prism = 3 * volume of a rectangular pyramid
Therefore, the relationship between the volumes of a rectangular prism and a rectangular pyramid whose length width and height are all equal:
volume of rectangular prism = 3 * volume of a rectangular pyramid
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crestwood elementary school has an active four-square league, consisting of ten players, including justin and tim. each day at recess, the ten players split into two four-square games, each with five players in no relevant order. over the course of a semester, each possible match-up of five players occurs once. how many times did justin play in the same game as tim?
Justin and Tim have played the same game a total of 10 times.
There are 10 players in Crestwood Elementary's four-square league, including Justin and Tim. Over the course of a semester, each possible match-up of five players occurs once. This means that Justin and Tim have played the same game a total of 10 times.
To calculate this, we need to consider the different combinations of players that can make up a five-person game. There are a total of 10! (10 factorial) permutations of the 10 players, meaning that each possible game is made up of different players.
This includes the combination of Justin and Tim, which occurs 10 times. Therefore, Justin and Tim have played the same game 10 times during the semester.
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Answer: 1.5 and 20
Step-by-step explanation:
What is the greatest common monomial factor of 3x²-6x?
Answer:
The greatest common monomial factor of [tex]3x^2 - 6x[/tex] is 3x.
Step-by-step explanation:
To understand what the problem is asking us, let's define the terms.
⭐What does greatest common factor mean?
as factor means a term (x) that is a factor of a number or another term (y),the greatest common factor means the greatest number (x) that is a factor of a number/another term(y)⭐What does monomial mean?
as "mono" means 1,monomial means an expression or equation that consists of only 1 termThus, we need to find the greatest term that is a factor of [tex]3x^2 -6x[/tex]. This term must be a monomial.
First, divide both terms of the polynomial [tex]3x^2 -6x[/tex] by the largest term that is common between the terms.
[tex]3x[/tex] is the largest term.
[tex]3x[/tex] is also a monomial.
Therefore, [tex]3x[/tex] is the greatest common monomial factor.
⭐if this response helped you, please mark it the brainliest⭐
What is the mean in math?
A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe this measure of central tendency.
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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What is the solution to 2x² 8x X² 16?
Since the provided expression [tex]2x^{2} +8x-x^{2} +16[/tex] is quadratic, the solution of x are "-4" and "-4" .
What is a quadratic equation?Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
What are mathematical expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases.
Expression: [tex]2x^{2} +8x-x^{2} +16[/tex]
This means that you need to add the two x² terms and the two x terms, which gives you [tex]x^{2} +8x+16[/tex].
Next, you can simplify the equation by taking out a common factor of x from the consecutive two terms, which gives you [tex]x(x + 4) +4(x+4).[/tex]
Then the equation becomes [tex](x + 4)(x+4).[/tex] which on solving i.e [tex](x+4)=0[/tex]
you will get x= -4 and -4.
Therefore the solution to this equation is x = -4 or x = -4.
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A car moving at a constant speed passed a timing device at t = 0. After 9 seconds, the car has traveled 747 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
The linear function rule to model the distance d in feet of the car traveled after t seconds is d = 83t.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distance traveled after 9 seconds = 747 ft.
The function rule to model the distance d after t seconds.
d = 83t
When t = 9,
d = 83 x 9 = 747 ft
Thus,
The linear function is d = 83t.
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What is the 5th root called?
A root of degree 5 is called a fifth root.
A radicand, or nth root, in mathematics is a number r that, when raised to the power n, equals the number x: rn = x, where n is a positive integer, also known as the degree of the root. A root of degree 5 is called a fifth root.
The required number is the result of multiplying a fifth root by itself five times.
Due to the fact that two multiplied by itself five times is 32, 532 = 2
Seven multiplied by itself five times is 16807.
Hence 516807 Equals 7 since 7 x 7 x 7 x 7 = 16807.
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6 1/2+2/3+3/4 calcution with distribution
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
Distribution Property:According to the distributive property, multiplying the difference or aum of numbers will be equivalent to multiplying the individual parts of the difference or sum.
The expression that can explain the above rule is A ( B+ C) = AB + AC
Here we have
6(1/2 + 2/3+3/4)
By distribution property
=> 6(1/2 + 2/3+3/4)
= 6(1/2) + 6(2/3)+ 6(3/4)
= 3 + 2(2) + 3(3/2)
= 3 + 4 + 9/2
= 7 + 9/2
= (14+9)/2 [ add 7 and 9/2 by taking 2 as LCM ]
= 23/2
Therefore,
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
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Complete Question:
1. Find the value of this fraction computation: 6(1/2 + 2/3+3/4)
Use the diagram below to find the following measures. GN is the angle bisector of ∠MGO.
Answer:
∠MGN = 24°
∠NGO = 24°
Step-by-step explanation:
⭐What is an angle bisector?
An angle bisector is a line, segment, or ray that splits an angle in halfEach halve of the angle is equal to each otherThus, ∠MGN ≅ ∠NGO.
To solve for ∠MGN and ∠NGO, we need to:
Create an equation about their relationshipSolve for "x"Substitute "x" back into the equations to find the angle measures1. Create an equation about their relationship:
If ∠MGN ≅ ∠NGO, then...
[tex]5x-6 = 11x -42[/tex]
2. Solve for "x":
[tex]5x - 6 = 11x -42[/tex]
[tex]42 - 6 = 11x - 5x[/tex]
[tex]36 = 6x[/tex]
[tex]6 = x[/tex]
3. Substitute "x" back into the equations to find the angle measures:
[tex]< MGN = 5x - 6[/tex]
[tex]< MGN = 5(6) - 6[/tex]
[tex]< MGN = 30 - 6[/tex]
[tex]< MGN = 24[/tex]
❗❗❗At this point, you could write that ∠MGN and ∠NGO = 24°, as they are congruent, but you should still substitute "x" into ∠NGO to make sure "x" is correct.❗❗❗
[tex]< NGO = 11x - 42[/tex]
[tex]< NGO = 11(6) - 42[/tex]
[tex]< NGO = 66 - 42[/tex]
[tex]< NGO = 24[/tex]
∴ ∠MGN = 24°
∴ ∠NGO = 24°
Which is a quadratic equation in FACTORED FORM?
A
f(x)=2x2+5x−12f(x)=2x^2+5x-12f(x)=2x
2
+5x−12
B
f(x)=2x+5f(x)=2x+5f(x)=2x+5
C
f(x)=2(x+5)2−12f(x)=2(x+5)^2-12f(x)=2(x+5)
2
−12
D
f(x)=2(x+5)(x−12)f(x)=2(x+5)(x-12)f(x)=2(x+5)(x−12)
Answer:
D) f(x) = 2(x + 5)(x − 12)----------------------
Given options:
A) f(x) = 2x² + 5x − 12,
this is a standard form of quadratic function.B) f(x) = 2x + 5,
this is a linear function, not quadratic.C) f(x) = 2(x + 5)² − 12,
this is vertex form of a quadratic function.D) f(x) = 2(x + 5)(x − 12),
this is a factored form of a quadratic function.Given: 3x < -9. Choose the solution set. {x | x > -1/3} {x | x < -3} {x | x < 3} {x | x > -3}.
Answer:
D is the answer
Step-by-step explanation:
A 20-foot ladder is leaning against the side of a house so that the bottom of the ladder is 12 feet from the base of the house. Will the ladder reach a window that is 14.5 feet above the ground?
Yes, because the 16 feet ladder will reach to the window that is 14.5 feet above the ground.
What is Pythagoras theorem?Pythagoras' Theorem states that the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.
The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.
According to the question;
A 20-foot ladder is leaning against the side of a house.
Hypotenuse H= 20 feet
The bottom of the ladder is 12 feet from the base of the house.
Base B = 12 feet
And let P be the perpendicular.
Using Pythagoras theorem
H²= P² + B²
20² =12² +P²
P²= 400-144
P²= 256
Taking the square root.
P= 16 feet.
Since the height of the ladder is 16 feet, and we have to reach 14.5 feet above the ground.
16 > 14.5
That means, the ladder will reach to the window.
Hence, Yes, the 16 feet ladder will reach to the window.
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What is positive infinity called?
The Positive Infinity is called the Lemniscate.
Infinity:
Infinity is anything greater than infinity, infinity, or any natural number. Often represented by the infinity symbol {\displaystyle \infty }\infty. The most interesting point about infinity is – ∞ < x < ∞. This is a mathematical shorthand for negative infinity less than real and positive infinity greater than real. where 'x' represents a real number.
Positive Infinity:
Numbers approach negative infinity as they move left on the number line and positive infinity as they move right on the number line. Negative infinity is always less than any number and positive infinity is always greater than any number.
Positive Infinity: Differs from mathematical infinity in that:
A positive number divided by positive infinity yields positive 0.A negative number divided by positive infinity results in negative 0.0 multiplied by positive infinity yields NaN.NaN multiplied by positive infinity NaNPositive infinity divided by any negative number (except negative infinity) gives negative infinity.Positive infinity divided by any positive number (except positive infinity) yields positive infinity.Learn more about Positive Infinity:
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Urgent!! Help plsssss
Answer:
Step-by-step explanation:B
What are the factors of 6x² 5x 6?
The factors of 6x² 5x 6 are: 1, 2, 3, 5, 6, 10, 15, 30, x, 2x, 3x, 5x, 6x, 10x, 15x, 30x, x², 2x², 3x², 5x², 6x².
1. Find the common factors of 6x², 5x, and 6:
The common factors are 1, 2, 3, 5, and 6.
2. Find the factors of each individual term:
For 6x²: 1, 2, 3, 6, x, 2x, 3x, 6x, x², 2x², 3x², and 6x².
For 5x: 1, 5, x, and 5x.
For 6: 1 and 6.
3. Combine the factors from each term to get the full list of factors:
The full list of factors is: 1, 2, 3, 5, 6, 10, 15, 30, x, 2x, 3x, 5x, 6x, 10x, 15x, 30x, x², 2x², 3x², 5x², and 6x².
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What is the GCF of 28?
What is the image point (-4, 5) after a translation right 5 units and 2 units up?
The image of (-4, 5) after a translation right 5 units and 2 units up is (1, 7).
What is the image of the point?
The given point P is "reflected" in the mirror and appears on the other side of the line an equal distance it. Drag the point P to see this. The reflection of the point P over the line is by convention named P' (pronounced "P prime") and is called the "image" of point P.
Going right means the x value goes up. In this case, it went to the right 5 spaces. so, all you have to do is add 5 with -4 which is 1.
When going up on a graph, the y value goes up as well. Add 2 with 5 which is 7.
Therefore, the answer is (1, 7).
Hence , the image point (-4, 5) after a translation right 5 units and 2 units up is (1, 7).
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Solve for z [tex]2(5y+7x)^2=8\sqrt{3y-z[/tex]
The solution for z in the equation is z = 3y - 1/16(5y + 7x)⁴
How to determine the solution for z?From the question, we have the following parameters that can be used in our computation:
2(5y+7x)²=8√(3y-z)
Rewrite the equation
So, we have the following representation
2(5y + 7x)² = 8√(3y - z)
Take the square of both sides
This gives
4(5y + 7x)⁴ = 64(3y - z)
Divide both sides by 64
1/16(5y + 7x)⁴ = 3y - z
So, we have
z = 3y - 1/16(5y + 7x)⁴
Hence, the solution is z = 3y - 1/16(5y + 7x)⁴
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➡some one please help me please.
Answer:
Step 2
Step-by-step explanation:
3x-24=5x
he did -3x on each side but added 3x to 5x instead of subtracting
What is the statement of square?
Answer:
Step-by-step explanation:
Square's mission statement is simple. Square deliver “Economic Empowerment” to the thousands of business owners who use Square to manage their businesses.
2x+3y=0
x+2y=1
solving systems by substitution
Answer: x=-3, y=2
Step-by-step explanation: to solve using substitution, we need either x or y by itself in one equation. let's use x from the 2nd equation since it doesn't have a constant.
so the first equation stays the same at 2x+3y=0
for the second equation, rearrange to solve for x by moving the 2y to the right -> x=2y-1
then, we can plug in this x value to x in the first equation to get,
2(2y-1)+3y=0
then solve for y,
4y-2+3y=0
4y-3y=2
y=2
then to solve for x, plug in y in either of the initial equations. lets choose the second one.
so you'd have,
x+2(2)=1
x+4=1
x=-3
Find the domain for the rational function f of x equals quantity x plus 4 over quantity 3 times x minus 5.
1. negative infinity to negative five thirds and negative five thirds to infinity
2. negative infinity to five thirds and five thirds to infinity
3. (−[infinity], −4)( −4, [infinity]) (−[infinity], 4)(4, [infinity])
Answer:
2. negative infinity to five thirds and five thirds to infinity
Step-by-step explanation:
You want the domain of the rational function f(x) = (x +4)/(3x -5).
DomainThe domain is the set of input values for which the function is defined. A rational function is undefined when its denominator is zero. f(x) is undefined when ...
3x -5 = 0
x = 5/3
So, the value 5/3 must be excluded from the domain of f(x). The domain of f(x) is ...
-∞ < x < 5/3 ∪ 5/3 < x < ∞
Which expression results in a rational number
Answer:
B. (w)(y)
Step-by-step explanation:
(w)(y)
= 2 * √8 * 3 * √2
= 2 * √(2*2*2) * 3 *√2
= 2 * √2 * √2 * √2 * 3 * √2
= (2*3) * (√2 * √2) * (√2 * √2)
= 6 * 2 * 2
= 24
For what value of k are the roots of the quadratic equation 3x² 2kx 27/0 real and equal * 1 point K 7 K 9 K 11?
The value of k where the roots of the quadratic equation are real and equal is k = 9.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
3x + 6 = 9 is an equation.
We have,
3x² + 2kx + 27 = 0
This is in the form of ax² + bx + c.
a = 3
b = 2k
c = 27
Now,
The roots are real and equal.
D = 0
D = b² - 4ac
Now,
b² - 4ac = 0
(2k)² - 4 x 3 x 27 = 0
4k² - 324 = 0
4k² = 324
k² = 324/4
k² = 81
k = √81
k = ±9
Thus,
The value of k is 9 0r -9
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Find the distance from point $a\left(-1,\ 7\right)$ to the line $y=3x$. Round your answer to the nearest tenth. The distance is about units.
The distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is about 4.5 units, rounded to the nearest tenth.
The distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is equal to the length of the perpendicular line from point [tex]$a$[/tex] to the line[tex]$y=3x$[/tex]. The formula to find the distance from a point [tex]($x_1, y_1$)[/tex] to a line [tex]$ax+by+c=0$[/tex] is given by:
[tex]$$\frac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}.$$[/tex]
Substituting[tex]$$\frac{|ax_1+by_1+c|}[/tex] into the formula, we get:
[tex]$$\frac{|-3(-1)+1(7)+0|}{\sqrt{3^2+1^2}} = \frac{20}{\sqrt{10}}.$$[/tex]
Therefore, the distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is about 4.5 units, rounded to the nearest tenth
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Tyrese bought 35 tickets to use at a carnival. He used some of the tickets to ride the bumper cars and play some games. Now he has 28 tickets left. What is the percent of decrease in the number of tickets that he has?
The percent of decrease, in the number of tickets that he has, is 20%.
What is a percentage?The term "percentage" refers to any ratio or number that may be expressed as a fraction of 100. And the sign "%" is used to denote it.
Given, Tyrese bought 35 tickets to use at a carnival.
He used some of the tickets to ride the bumper cars and play some games. Now he has 28 tickets left.
That means,
he used 35 - 28 = 7 tickets.
To find the percentage of decrease:
Let m be the percentage of decrease.
Then,
7 = m x 35 / 100
m = 700 / 35
m = 20
Therefore, the percentage of decrease is 20%
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Rowan and 55 points playing a game Rowan’s mom earn three times as many points as a Rowan how many points does Rowan’s mom earn
If ΔABC ~ ΔDEF , find the value of x .
How do you determine the nature of the roots of a quadratic equation example?
The nature of the roots of a quadratic equation is described by the discriminant calculated by seeing the equation and comparing it with the standard equation which is given by -
[tex]ax^{2} + bx+c[/tex] , where a , b , c are real numbers .
The root of the equation is given by -
x= (-b )± [tex]\frac{\sqrt{b^{2} - 4ac}}{2a}[/tex]
Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .
This discriminant is the defining factor of the nature of the roots.
Now, here arise three cases-
(i) If (b^2 - 4ac) > 0, the roots are real and distinct .
(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.
(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.
Hence, it is the discriminant which determines the nature of roots.
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