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2 years ago

Point K is on line segment JL. Given JK=2x, KL=x+3, and JL=4x, determine the numerical length of KL

Mathematics

1 answer:

QveST [7]2 years ago

7 0

Answer:

Step-by-step explanation:

JK+KL=JL

2x + x + 3 = 4x

3x + 3 = 4x

-4x -4x

-x + 3 = 0

-3 -3

-x = -3

-x/-1 = -3/-1

x = 3

Plug in value of x to find KL:

JL = 4(3) = 12

it’s 6 because on the line it’s half; between JK and KL.

final answer:

KL = 6

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HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards

hodyreva [135]

Answer:

Each birthday card costs $2.2 ⇒ answer c

Step-by-step explanation:

* Lets explain how to solve the problem

- Package A contains 3 birthday cards and 2 thank-you notes

- It costs $9.60

- Package B contains 8 birthday cards and 6 thank-you notes

- It costs $26.60

- x represents the cost of birthday card and y represents the cost of

thank-you note

* Lets change these information to two equations

∵ x represents the cost of each birthday cards

∵ y represents the cost of each thank-you notes

∵ Bag A contains 3 birthday cards and 2 thank-you notes

∵ Bag A costs $9.60

∴ 3x + 2y = 9.60 ⇒ (1)

∵ Bag B contains 8 birthday cards and 6 thank-you notes

∵ Bag B costs $26.60

∴ 8x + 6y = 26.60 ⇒ (2)

* Lets solve this system of equations to find x and y

- Multiply equation (1) by -3 to eliminate y

∵ -3(3x) + -3(2y) = -3(9.60)

∴ -9x - 6y = -28.8 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -2.2

- Multiply both sides by -1

∴ x = 2.2

∵ x represents the cost of each birthday cards

∴ The cost of each birthday card is $2.2

* Each birthday card costs $2.2

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2 years ago

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tom and barb have only nickels and dimes. barb has 75 cents and Tom has 90 cents. both have the same number of coins and Tom has

Galina-37 [17]

They both he 9 coin barb has 3 nickels and 6 dimes

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2 years ago

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George still has 40 percent of his book to read. If George has read 180 pages, how many pages does he still have to read? How do

beks73 [17]

Answer: 72

Step-by-step explanation: so you do a line = line method the lines should look like they are fractions.

you do it for the both numbers the percent is always out of 100.

it should look like this

40% ?

--------- = -----------

100% 180

then you cross multiply 40 and 180 and than divide it by 100. your answer should be 72. you later replace the ? with 72

you know this because It is smaller than 180 and its bigger than the number 40.

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2 years ago

For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.

luda_lava [24]

Answer:

In the figure ∠ABO and ∠BCO have measures equal to 35°.

Step-by-step explanation:

<u><em>The complete question is</em></u>

For circle O, m CD=125° and m∠ABC = 55°

In the figure<____, (AOB, ABO, BOA) and <_____ (BCO, OBC,BOC) have measures equal to 35°

The picture in the attached figure

step 1

Find the measure of angle COB

we know that

$m\angle COB=arc\ CD$ ----> by central angle

we have

$arc\ CD=125^o$

therefore

$m\angle COB=125^o$

step 2

we know that

AB is a tangent to the circle O at point A

ABC and ABO are right triangles

In the right triangle ABC

Find the measure of angle BCA

Remember that

$m\angle BCA+m\angle\ ABC=90^o$ ---> by complementary angles in a right triangle

we have

$m\angle ABC=55^o$

substitute

$m\angle BCA+55^o=90^o$

$m\angle BCA=90^o-55^o=35^o\\$

step 3

In the triangle BCO

Find the measure of angle CBO

we know that

$m\angle CBO+m\angle COB+m\angle BCO=180^o$ ---> the sum of the interior angles in any triangle must be equal to 180 degrees

we have

$m\angle COB=125^o$

$m\angle BCO=m\angle BCA=35^o$ -----> have measure equal to 35 degrees

substitute

$m\angle CBO+125^o+35^o=180^o$

$m\angle CBO=180^o-160^o=20^o$

step 4

Find the measure of angle ABO

In the right triangle ABO

we know that

$m\angle ABC=m\angle CBO+m\angle ABO$ ----> by angle addition postulate

we have

$m\angle ABC=55^o$

$m\angle CBO=20^o$

substitute

$55^o=20^o+m\angle ABO$

$m\angle ABO=55^o-20^o=35^o$ ----> have measure equal to 35 degrees

therefore

In the figure ∠ABO and ∠BCO have measures equal to 35°.

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Which model represents the factors of 4x2 – 9?

GREYUIT [131]

The factors of 4 x² - 9 :
4 x² - 9 = ( 2 x - 3 ) · ( 2 x + 3 )
We have to use the formula for the difference of squares:
a² - b² = ( a - b ) · ( a + b )

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