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3 years ago

Find angle 1, if angle 2 = 56 and m LJKL = 145

Mathematics

1 answer:

Alexandra [31]3 years ago

3 0

Answer: NEED PICTURE TO ANSWER, we dont know if it a square or if its a rectangle, sry

Step-by-step explanation:

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The third term of an arithmetic sequence is equal to 9 and the sum of the first 8 term is 42. Find the first term and the common

zloy xaker [14]

Answer:

The first term is 14

The common difference is -2.5

Step-by-step explanation:

we know that

The rule to calculate the an term in an arithmetic sequence is

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

where

d is the common difference

a_1 is the first term

we have that

The third term of an arithmetic sequence is equal to 9

$a_3=9$

$n=3$

substitute

$9=a_1+d(3-1)$

$9=a_1+2d$ ----> equation A

The rule to find the sum of the the first n terms of the arithmetic sequence is equal to

$S=\frac{n}{2} [2a_1+(n-1)d]$

we have

The sum of the first 8 term is 42

$S=42$

$n=8$

substitute

$42=\frac{8}{2} [2a_1+(8-1)d]$

$42=4[2a_1+7d]$

$10.5=2a_1+7d$ ----> equation B

Solve the system of equations

$9=a_1+2d$ ----> equation A

$10.5=2a_1+7d$ ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is (14,-2.5)

see the attached figure

therefore

$a_1=14\\d=-2.5$

The first term is 14

The common difference is -2.5

8 0

3 years ago

What is the equation of the line that passes through the point (-4,-8)(−4,−8) and has a slope of 4

elena-s [515]

Answer:

y=4x+8

Step-by-step explanation:

8 0

3 years ago

Please help I’m in the middle of a testtt!

hichkok12 [17]

Answer:

first option

Step-by-step explanation:

5 0

3 years ago

Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44

ycow [4]

Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Step-by-step explanation:

Let's construct g(x) in baby steps.

Ok, we start with f(x) = x^2

The first thing we have is a horizontal translation of A units (where A is not known)

A vertical translation of N units to the right, is written as:

g(x) = f(x - N)

Then we have:

g(x) = (x - A)^2 = x^2 - 2*A*x + A^2

Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.

Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)

Then if we apply also a reflection over the x-axis, we have:

g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44

Then:

2*A = 16

A*A = 44.

The first equation says that A = 16/2 = 8

But 8^2 is not equal to 44.

Then we need another constant coefficient, which is related to a vertical translation.

If we have a relation y = f(x), a vertical translation of N units up, will be

y = f(x) + N.

Then:

g(x) = -f(x - A) + B

-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44

Now we have:

2*A = 16

-A^2 + B = - 44

From the first equation we have A = 8, now we replace it in the second equation and get:

-8^2 + B = -44

B = -44 + 64 = 20

Then we have:

The transformation is:

First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

8 0

3 years ago

Christopher walks 5km south then walks on a bearing of 036º until he is due east of his starting point. How far is he from his s

harina [27]

Christopher's distance from his starting point is 3.6 km

Since Christopher initially walks South 5 km and then walks on a bearing of of 036º until he is due east of his starting point, His distance South, his distance from his starting point and his distance from his 036º bearing, all form a right-angled triangle with opposite side to the angle 036º, as his distance from his starting point, x and the adjacent side to the angle 036º, as his distance 5 km south.

Since we have both the opposite and adjacent sides of a right-angled triangle,

From trigonometric ratios,

tanФ = opposite/adjacent

tanФ = x/5 km

Now Ф = 036º

So, tan36º = x/5km

x = 5 km(tan36º)

x = 5 km (0.7265)

x = 3.633 km

x ≅ 3.6 km to 1 decimal place.

So, Christopher's distance from his starting point is 3.6 km.

Learn more about bearing here:

brainly.com/question/11684993

5 0

3 years ago