Answer:
A. y = 8x
Step-by-step explanation:
y = 8x
From first term
32 = 8(4)
32=32
Correct
1*2 + 2*3 + 3*4 + . . . + n(n + 1) = [ (n)(n + 1)(n + 2) ] / 3 whenever n is a positive integer. What is the next term in the sequence for the equation on the left?
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+
What is mathematical induction ?To demonstrate that the mathematical proposition P(n) holds for all natural integers n = 1, 2, 3, 4,..., one uses the mathematical induction technique. It is frequently referred to as the induction principle in mathematics. We establish that P(1) holds in order to demonstrate a result P(n) using the mathematical induction technique. If P(1) is valid, we can assume that P(k) holds for some natural number k and use this assumption to demonstrate that P(k+1) is valid. The assertion P(n) applies to all natural numbers if and only if P(k+1) holds true.
Let
P(n): 1×2 + 2×3+3×4+........+n(n+1)=[tex]\frac{n(n+1)(n+2)}{3}[/tex]
Putting n =1 we get
P(1):1×2 =2
and
[tex]\frac{1(1+1)(1+2)}{3}=\frac{1(2)(3)}{3} =2[/tex]
Therefore P(1) is true.
Let P(K) is true
So,
P(k): 1×2 + 2×3+3×4+........+k(k+1)=[tex]\frac{k(k+1)(k+2)}{3}[/tex]
Now we have to show that P(k +1 )is also true.
P(k+1): 1×2 + 2×3+3×4+........+k(k+1)+(k+1)(k+2)=[tex]\frac{k(k+1)(k+2)}{3}+ (k+1)(k+2)[/tex]
= (k+1)(k+2)[[tex]\frac{k}{3}+1[/tex]]
=[tex]\frac{(k+1)(k+2)(k+3)}{3}[/tex]
P(k + 1) follows, and it is likewise true.
As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+.
To learn more about mathematical induction visit :
brainly.com/question/1333684
#SPJ9
Write down equation of lines l and m
ATTACHED IS THE SOLUTION
4x-3<-15 or 2x+4> 12
In given inequalities the value of x is x <-3 and x >4
What is inequalities ?Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.
Given that :4x-3<-15 or 2x+4> 12
4x -3 <-15
4x < -12
x <-3
2x + 4 > 12
2x > 8
x >4
x <-3 and x >4
In given inequalities the value of x is x <-3 and x >4
To learn more about inequalities visit :
brainly.com/question/28823603
#SPJ9
Tom says, "If you square a number the answer is always bigger". Show Tom is in correct using two different example.
answer
Answer:
Tom is correct.
Step-by-step explanation:
Squaring is equivalent to multiplying a number by itself, ie:
2 squared = 2x2 = 4
6 squared = 6x6 = 36
Find the slope of the line that passes through the pair of points.
(5, −1)
and
(−1, −7)
Answer:
The slope is 1.Step-by-step explanation:
Slope:
[tex]\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y2=(-7)
y1=(-1)
x2=(-1)
x1=5
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}}[/tex]
Solve.
[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}=\dfrac{-6}{-6}=\boxed{\sf{1}}}[/tex]
Therefore, the slope is 1, which is our answer.
I hope this helps, let me know if you have any questions.
In each figure, a is parallel to b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer. A line is reflected across line a, another line is reflected across line b to form a third line. a. Yes; it is one reflection after another with respect to the two parallel lines. b. No; it is a reflection followed by a translation. c. No; it is a reflection followed by a rotation. d. No; it is one reflection after another with respect to the two parallel lines. Please select the best answer from the choices provided A B C D
To determine whether the third figure is a translation image of the first figure, we say that; B: No; it is a reflection followed by a translation
How to Interpret Transformation of a figure?Transformation could be reflection, translation, rotation or even dilation.
Reflection can be thought of as the mirror image of a shape across a line.
Rotation is when one turns an object around a point
Translation is simply moving an object from one point to another without any change of dimension.
If we look at the given three figures in the attached image, we can see that the second image is the reflection or mirror image of the first figure.
After reflection, we can see that it is undergoes translation, which means it is moved apart from the first figure.
Thus, the third figure is a reflection of the first figure, and then it is translated.
Read more about Translation at; https://brainly.com/question/25055109
#SPJ1
Calculate the work done when a load of 50N is lifted through a distance of 6m.
The amount of work done when a load of 50 newton is lifted through a distance of 6m is 300 joules.
What is the amount of work done in lifting the load?Work done is simply the energy transfer that takes place when an object is either pushed or pulled over a distance by an external force.
It is expressed as;
Work done = force × distance
Given the data in the question;
Force applied = 50N = 50kgm/s²Distance covered = 6mWork done = ?To determine the work done, plug the given values into the above formula and solve W.
Work done = force × distance
Work done = 50kgm/s² × 6m
Work done = 50kgm²/s² × 6
Work done = 300kgm²/s²
Work done = 300J
Therefore, 300 joules is the work done in lifting the load.
Learn more about work done here: brainly.com/question/26115962
#SPJ1
The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's
A. adjacent side and hypotenuse.
B. adjacent side and opposite angle.
C. opposite side and hypotenuse.
D. opposite side and adjacent side.
The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's adjacent side and hypotenuse.
This is further explained below.
What is the cosine function?Generally, trigonometric functions are a set of real functions that link the ratios of the lengths of two sides of a right-angled triangle to an angle in the triangle.
They find widespread use in all fields of study that are in some way connected to geometry, including geodesy, solid mechanics, celestial mechanics, navigation, and a great many more.
In conclusion, The ratio of a triangle's adjacent side to its hypotenuse is used to determine the cosine function for a certain angle in the triangle.
Read more about the cosine function
https://brainly.com/question/17954123
#SPJ1
4 cups = ______ ounces
hint 1 cup = 8 ounces
Question 4 options:
2 oz
4 oz
12 oz
32 oz
1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bucket of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
Answer: Do you know the answer to this yet??
Step-by-step explanation:
The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
Given,
Kevin took $45 with him to spend on snack
and, The price for each bucket of popcorn was $4.
To plot the graph
Now, According to the question:
Sketch the graph that represents the situation and label the intercepts
Let,
x ------> the number of bags of popcorn
y -----> the number of drinks.
we know that
The price for each bag of popcorn was $4
The price of each drink was half the price of a bag of popcorn
So, The price of each drink was (1/2)$4 = $2
The total bags of popcorn multiplied by $4 plus the number of drinks multiplied by $2 must be equal $45
The equation that represent this situation is :
4x + 2y = 45 -----(1)
Now, Find the y - intercept form:
The y-intercept is the value of y when the value of x is equal to zero
For, x = 0 put the value of x in equation(1)
4(0) + 2y = 45
2y = 45
y = 22.5
The y-intercept is the point (0,22.5)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
For, y = 0 put the value of x in equation(1)
4x + 2(0) = 45
4x = 45
x = 11.25
The x-intercept is the point (11.25, 0)
That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero
Hence, The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)
Learn more about Graph at:
https://brainly.com/question/16957172
#SPJ1
A factory produces zips. Testing shows that for
every 6000 zips tested, approximately 0.01
are defective. Estimate the number of
defective zips in a batch of 6000.
A) 60
B) 600
C) 0.01
D) 6
This is a probability question! Urgent help please!
Answer:
A) 60 that's i know !!!
Step-by-step explanation:
A) 60
5. CONSTRUCT ARGUMENTS Isabel wrote the expression 6 + 3 x 5 - 6+8+2 and asked Tamara to evaluate it. When Tamara evaluated it, she got a value of 19. Isabel told Tamara that her value was incorrect and said that the value should have been 38.
Who is correct? Justify your argument.
Answer:
none is correct
Step-by-step explanation:
6+3×5-6+8+2
6+15-6+8+2
6+9+10
=25
The graph of the derivative of a function f crosses the x-axis 3 times. What does this tell you about the graph of f ?
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
Well whenever any function crosses the x-axis, it means that the y-value is equal to zero.
In this case when the derivative passes the x-axis it indicates the tangent line corresponding to that x-value has a slope of zero, which when plotted is a horizontal line.
This means that the graph f has 3 horizontal tangent lines.
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
i got 100%
Mary earns $12 per hour, plus 10% commission on all her sales. Mary worked 10 hours and her sales were $1500. How much money did Mary earn?
Here are two triangles.ABIs Triangle B a rotation of Triangle A? Explain your reasoning.HELP ASAPP
Answer
Triangle B is not a rotation of triangle A because on careful observation of this two triangles, one would see that they are mirror images of each other; reflections of each other.
A mental rotation of triangle A all through the 360° shows that at no point is it seeming exactly like triangle B.
This is why it is evident that triangle B is not a rotation of triangle A, rather, they are reflections of each other.
Hope this Helps!!!
which example are polynomials select each correct answer
Step-by-step explanation:
The bottom two expressions are polynomials.
For what values of x is the inequality (x-4)² > 0 true?
The values of x must be greater than 4 for the inequality (x-4)² > 0 to be true.
What values make an inequality true?A value that makes an inequality true is the solution to the inequality. There may be more than one way to solve an inequality.The solution set is the collection of all inequality solutions.Given inequality is (x - 4)² >0.
To solve the inequality, take square root on both sides
So, (x - 4) > 0
Adding 4 on both sides,
x > 4
The values of x must be greater than 4 for the inequality to be true.
To know more about inequalities visit:
https://brainly.com/question/15320842
#SPJ9
Find the distance between (5, 10) and (8, 10)?
Answer:
3 units
Step-by-step explanation:
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same each picture has a length of 8 inches,the wall has a length of 74 inches.if he wants to have 12 inches of horizontal wall space before the first picture and after the fourth picture how much space should he leave between pictures.help with this please
18 inches space should he leave between pictures of the wall with length 74 inches
What is Addition?Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.
Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same
Length of each picture is =8 inches
Length of the wall=74 inches
The horizontal wall space before the first picture and after the fourth picture = 12 inches
we are asked to find the space between pictures
12+12+8+8+8+8+x=74
x+56=74
x=18
the distance between the picture is 18 inches
to learn more about addition visit:
brainly.com/question/14092461
#SPJ1
How many ways can a three-person jury be selected from a pool of eleven people?
A three-person jury can be selected from a pool of eleven people in 165 ways.
What is meant by the term combination?A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the order of a selection is irrelevant. You can choose the items in any order in combinations. Permutations and combinations are often confused.We will employ the formula ⁿCₓ = n! / x! * (n - x)! to calculate combinations, where n is the total number of items and x represents the amount of items chosen at a time.For the given question;
The total number of person in the pool = 11.
The number of jury selected = 3.
Thus, the combination will be ⁿCₓ.
Where, n = 11 and x = 3.
¹¹C₃ = 11!/3!(11 - 3)!
Simplifying;
¹¹C₃ = 165
Thus, the number of ways in which three jury can be selected from 11 pool of members is 165.
To know more about the combination, here
https://brainly.com/question/295961
#SPJ10
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of 300 gigabytes. (Recall that giga means billion.)
Answer: My new music player has a capacity of 3 * 10^11 bytes.
Step-by-step explanation: giga=billion=10^9. 300 in scientific notation is 3*10^2. Since 3 is between 1 and 10. So 10^2 * 10^9=10^11.
Which equation shows a slope of -5 and a y-intercept of (0,1)?
Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. How many years was the loan period?
The loan that was borrowed by Georgina was for a period of 9 years.
How to calculate the value?From the information, Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. The Interest will be:
= $3,221.75 - $2,450
= $771.75
Therefore, the time taken for the loan will be expressed as:
Interest = PRT/100
where P = Principal
R = Rate
T = Time.
Interest = PRT/100
771.75 = (2450 × 3.5 × T) /100
Cross multiply
8575T = 77175
Time = 77175 / 8575
Time = 9
The time is 9 years.
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
Find each missing measure
Answer:
<U = 54
<T = 72
Step-by-step explanation:
Find the angle measures
The marks on the sides means the sides are the same length
That means the base angles have the same measurement
<S = <U = 54
The sum of the angles of a triangle equals 180
<S + <U + < T = 180
54 + 54 + < T =180
108 + < T =180
<T =180-108
<T = 72
Answer:
m<U = 54°
m<T = 72°
Step-by-step explanation:
According to the isosceles triangle theorem ( If two sides of a triangle are equal , then the angles opposite to these sides are also equal. ),
ST = UT
So,
m<S = m<U.
Given that,
m<S = 54°
So,
m<U = 54°
Also, we know that the sum of the interior angles of a triangle is added up to 180 degrees.
So,
m<S + m<U + m<T = 180°
54° + 54° + m<T = 180°
108° + m<T = 180°
m<T = 180° - 108°
m<T = 72°
Seven times the sum of a number and 9
is 5
Seven times the sum of a number and 9 is 5 then the number is -58/7 .
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
We have been given that
Seven times the sum of a number and 9 is 5
Let the number is n.
let's write "the sum of a number and 9"
n + 9 .
Then, "seven times" the sum can be written as:
7 (n + 9)
This "is 5" or "is equal to 5" and can be written as:
7 (n + 9) = 5
To solve, first expand the term in parenthesis on the left side of the equation by multiplying each term in the parenthesis by
(7×n) + (7×9) = 5
7n + 63 = 5
Next, subtract 63 from each side of the equation to isolate the n term while keeping the equation balanced:
7n + 63 - 63 = 5 - 63
7n = -58
Now, divide each side of the equation by 7 to solve for n while keeping the equation balanced:
7n / 7 = -58 / 7
n = -58/7
The number is −58/7.
Hence , the number is -58/7 when a number is seven times its sum and 9 is 5.
To learn more about Sum
https://brainly.com/question/25734188
#SPJ1
What is ab+ba?
and xz+zx
[tex]ab + ba[/tex]
Answers: 1) " 2ab ".
2) " 2xz ".
________________________
Step-by-step explanation:
ab + ba = ab + ab = 1ab + 1ab = (1+1)*ab = 2ab .
xz + zx = xz + xz = 1xz + 1xz = (1+1)*xz = 2xz.
________________________
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
Based on the definition of the functions, the value of x if f(x) = g(x) is 3
How to determine the value of x?The equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
It should be noted that the above equations are linear equations
From the question, we understand that the functions are equal
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
Graph the functionsSee attachment for the graph of the functions
Read more about functions at
https://brainly.com/question/2946572
#SPJ1
Only #15,17, and 19 please show work THANK YOU
The magnitude and direction of the vectors are
11. <0,4> :
Magnitude = 4
Direction = 90°
12. <-3,0>:
Magnitude = 3
Direction = 0°
13. <6,5>:
Magnitude = √(61)
Direction = 39.8°
14. <3,7>:
Magnitude = √58
Direction = 66.8°
15. <-2,1>:
Magnitude = √5
Direction = -26.57°
16. <-10,13>:
Magnitude = √(269)
Direction = -37.57°
17. <2,-5>:
Magnitude = √(29)
Direction = -68.2°
18. <8,-4>:
Magnitude = √(80)
Direction = -26.57°
19. <-4.-6>:
Magnitude = √(52)
Direction = 56.3°
20. <-1,9>:
Magnitude = √(82)
Direction = -83.66°
We are asked to find the magnitude and direction of the vectors given as <x, y>. We have the formulas for magnitude and direction of the vectors.
Magnitude = √(x²+y²)
and direction, θ = tan⁻¹(y/x)
11. The vector is <0,4>
Magnitude = √(0²+4²) = 4
Direction = tan⁻¹(4/0) = tan⁻¹∞ = 90°
12. The vector is <-3,0>.
Magnitude = √(-3²+0²) = 3
Direction = tan⁻¹(0/-3) = tan⁻¹0 = 0°
13.The vector is <6,5>
Magnitude = √(6²+5²) = √(61)
Direction = tan⁻¹(5/6) = 39.8°
14. The vector is <3,7>
Magnitude = √(3²+7²) = √58
Direction = tan⁻¹(7/3) = 66.8°
15.The vector is <-2,1>
Magnitude = √(-2²+1²) = √5
Direction = tan⁻¹(1/-2) = -26.57°
16.The vector is <-10,13>
Magnitude = √(13²+-10²) = √(269)
Direction = tan⁻¹(-10/13) = -37.57°
17.The vector is <2,-5>
Magnitude = √(2²+-5²) = √(29)
Direction = tan⁻¹(-5/2) = -68.2°
18.The vector is <8,-4>
Magnitude = √(8²+-4²) = √(80)
Direction = tan⁻¹(-4/8) = -26.57°
19.The vector is <-4.-6>
Magnitude = √(-4²+-6²) = √(52)
Direction = tan⁻¹(-6/-4) = 56.3°
20. The vector is <-1,9>
Magnitude = √(-1²+9²) = √(82)
Direction = tan⁻¹(9/-1) = -83.66°
Learn more about magnitude and direction at https://brainly.com/question/2142917
#SPJ1
Write brackets in this statement to make each statement correct
Answer:
a. 4 x (5 + 3) = 32
b. 3 + 4 x (5 + 6) = 47
c. (2 + 7) x (5 + 3) =72
Step-by-step explanation: