shade the portion of this figure that represents 14/4

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 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+.

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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°

18 inches space should he leave between pictures of the wall with length 74 inches

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

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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.

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.

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The amount of work done when a load of 50 newton is lifted through a distance of 6m is 300 joules.

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;

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.

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Answer:

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.

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)

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In given inequalities the value of x is x <-3 and x >4

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

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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:

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%

The values of x must be greater than 4 for the inequality (x-4)² > 0 to be true.

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.

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Answer:

3 units

Step-by-step explanation:

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.

Answer:

none is correct

Step-by-step explanation:

6+3×5-6+8+2

6+15-6+8+2

6+9+10

=25

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

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.

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The Solution:

GIven:

We are asked to graph the given inequalities.

Below is the graph of the inequalities:

Thus, the correct answer is [option 1]

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.

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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°

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Elsa used her money to make two purchases last year. The Total interest earned by the end of the year is 1200.

Given that,

Elsa used her money to make two purchases last year. She spent $7,000 on a certificate of deposit paying 3% interest annually and $9,000 on corporate bonds paying 11% interest annually.

We have to find the Total interest earned by the end of the year.

We know,

Total interest=adding the interest annually payment

Total interest=0.03×7000+0.11×9000

Total interest=1200

Therefore, The Total interest earned by the end of the year is 1200.

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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.

________________________

The loan that was borrowed by Georgina was for a period of 9 years.

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.

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Answer:

[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies x=\dfrac{-4 \pm \sqrt{4^2-4(2)(-3)}}{2(2)}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{16-8(-3)}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{16+24}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{40}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{4\cdot 10}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{4}\sqrt{10}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm 2\sqrt{10}}{4}[/tex]

[tex]\implies x=\dfrac{-2 \pm \sqrt{10}}{2}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]

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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.

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A three-person jury can be selected from a pool of eleven people in 165 ways.

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.

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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

Step-by-step explanation:

The bottom two expressions are polynomials.

ATTACHED IS THE SOLUTION