MATHEMATICS COLLEGE

. What would be the new coordinates if (-2,-4) is translated 5 units up and7 units to the left.

Answers

Answer 1

Answer:

Answer:

(-9, 1)

Step-by-step explanation:

translating UP is to increase on the y axis, so -4+5=1

translating to the LEFT is to subtract on the x axis so-2-7=-9

Answer 2

Answer: -9, 1 I think is the correct answer

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Solve the equation:

a+20=11

Answers

Answer:

Step-by-step explanation:

a +20=11

-20-20

a= -9

subtract 20 on each side, you get a=-9

The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 491. Find the first term of the progression and the common difference
2. Find the value of n

Answers

Answer:

For 1: The first term is 10 and the common difference is $(3)/(2)$

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

$a_n=a_1+(n-1)d$

where,

$a_1$ is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

$S_n=(n)/(2)[2a_1+(n-1)d]$

where,

$S_n$ is the sum of nth terms

For (1):

The 11th term of the progression:

$25=a_1+10d$ .......(1)

Sum of first 4 numbers:

$49=(4)/(2)[2a_1+3d$ ......(2)

Forming equations:

$98=8a_1+12d$

$25=a_1+10d$ ( × 8)

The equations become:

$98=8a_1+12d$

$200=8a_1+80d$

Solving above equations, we get:

$102=68d\n\nd=(102)/(68)=(3)/(2)$

Putting value in equation (1):

$25=a_1+10(3)/(2)\n\na_1=[25-15]=10$

Hence, the first term is 10 and the common difference is $(3)/(2)$

For 2:

The nth term is given as:

$49=10+(n-1)(3)/(2)$

Solving the above equation:

$39=(n-1)(3)/(2)\n\nn-1=26\n\nn=27$

Hence, the value of n is 27

Final answer:

The value of n when the nth term of the progression is 49 is 22.

Explanation:

The 11th term of the progression (a11) is 25.

The sum of the first 4 terms (S4) is 49.

The nth term (an) is 49.

Let's find the answers to your questions:

Find the first term of the progression (a1) and the common difference (d):

We know that the nth term of an AP can be expressed as:

an = a1 + (n - 1)d

Substituting the values:

a11 = a1 + (11 - 1)d

25 = a1 + 10d

Now, we need to find a1 and d. We'll also use the information that the sum of the first 4 terms (S4) is 49. In an AP, the sum of the first n terms (Sn) can be expressed as:

Sn = (n/2)[2a1 + (n - 1)d]

For S4:

49 = (4/2)[2a1 + (4 - 1)d]

49 = 2[2a1 + 3d]

Now, we have two equations:

25 = a1 + 10d

49 = 2[2a1 + 3d]

Let's solve this system of equations to find a1 and d.

1. First, rearrange the first equation to isolate a1:

a1 = 25 - 10d

Now, substitute this expression for a1 into the second equation:

49 = 2[2(25 - 10d) + 3d]

Simplify and solve for d:

49 = 2[50 - 20d + 3d]

49 = 2[50 - 17d]

49 = 100 - 34d

34d = 100 - 49

34d = 51

d = 51/34

d = 3/2

2. Now that we have the common difference (d), we can find a1 using the first equation:

a1 = 25 - 10d

a1 = 25 - 10(3/2)

a1 = 25 - 15/2

a1 = (50 - 15)/2

a1 = 35/2

a1 = 17.5

So, the first term of the progression (a1) is 17.5, and the common difference (d) is 3/2.

Find the value of n when the nth term of the progression is 49:

We know that an = 49, and we can use the formula for an in an AP:

an = a1 + (n - 1)d

Substitute the values:

49 = 17.5 + (n - 1)(3/2)

49 - 17.5 = (n - 1)(3/2)

31.5 = (n - 1)(3/2)

To isolate n, multiply both sides by (2/3):

(n - 1)(3/2) = 31.5 * (2/3)

(n - 1) = 21

Now, add 1 to both sides to find n:

n = 21 + 1

n = 22

So, the value of n when the nth term of the progression is 49 is 22.

Learn more about Arithmetic Progression here:

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the area of the triangle is 2/5 square foot the height is 6/5 ft. what is the length in feet of the base of the triangle?

Answers

$\bf \textit{area of a triangle}\n\nA=\cfrac{1}{2}bh~~\begin{cases}A=(2)/(5)\n\nh=(6)/(5)\end{cases}\implies \cfrac{2}{5}=\cfrac{1}{2}\left( b\cdot \cfrac{6}{5} \right)\implies \cfrac{2}{5}=\cfrac{6b}{10}\n\n\n\cfrac{20}{5}=6b\implies \cfrac{20}{30}=b\implies \cfrac{2}{3}=b$

I do have a time limit. I appreciate any helpIf YB = ZA find the value of X and the length of YB

Answers

Since ZA and YB are equal in length and the two lines are parallel to each other.

Also, we can see that YZ and AB are perpendicular to both ZA and YB, thus

YZ = AB

16x - 4 = 4 - 4x

16x + 4x = 4 + 4

20x = 8

x= 8/20 = 2/5

YB = ZA = 20x - 5 = 20(2/5) - 5 = 3

Thus, the value of x is 2/5 and length of YB is 3 units.

So, the correct answer is option A

Decrease 520 by 15% what Is the answer?

Answers

The number is 442 which is obtained after decreasing 520 by 15% the answer is 442.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number that is obtained after decreasing 520 by 15%

= (100 - 15)% of 520

= 85% of 520

= 0.85×520

= 442

Thus, the number is 442 which is obtained after decreasing 520 by 15% the answer is 442.

Learn more about the percentage here:

brainly.com/question/8011401

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Answer:

442

Step-by-step explanation: