All categories

3 years ago

Match the properties with steps to solving the following equation 1/2(8x-6)=x+9

Mathematics

1 answer:

dmitriy555 [2]3 years ago

5 0

Answer:

x = 4

Step-by-step explanation:

first, you need to distribute the 1/2 to (8x-6)

this makes the equation 4x - 3 = x + 9

subtract x from the right side to bring it to the left

so it's now 3x - 3 = 9

add 3 from the left to bring it to the right

so you have 3x = 12

now, just divide by 3

x = 4

You might be interested in

Which expressions are equivalent to 2 to the 11 power

STatiana [176]

$\text{Hey there!}$

$\text{Which expressions are equivalent to}\bf{ \ 2^{11}}?$

$\bf{2^{11} = 2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times2}$

$\bf{2\times2=4}\\\bf{2\times2=4}\\\bf{2\times2=4}\\\bf{2\times2=4}\\\bf{2\times2\times2 = 8}\\\bf{4\times4\times4\times4=16\times16=256}\\\bf{256\times8=2,048}\\\\\boxed{\boxed{\bf{Your\ answer: 2,048}}}\checkmark$

$\text{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst:)}$

6 0

3 years ago

A=1/2bh for b<img src="https://tex.z-dn.net/?f=a%3D1%2F2bh%20for%20b" id="TexFormula1" title="a=1/2bh for b" alt="a=1/2bh for b"

valkas [14]

Times both sides by 2
$2A=bh$
divide both sides b h
$\frac{2A}{h}=b$
$b=\frac{2A}{h}$

5 0

4 years ago

A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangl

AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

$m=\frac{8-5}{1+5}$

$m=\frac{3}{6}$

$m_A_B=\frac{1}{2}$

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

$m=\frac{2-8}{4-1}$

$m=\frac{-6}{3}$

$m_B_C=-2$

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

$m=\frac{-2-2}{-2-4}$

$m=\frac{-4}{-6}$

$m_C_D=\frac{2}{3}$

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

$m=\frac{-2-5}{-2+5}$

$m=\frac{-7}{3}$

$m_A_D=-\frac{7}{3}$

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

$m_A_B=\frac{1}{2}$

$m_C_D=\frac{2}{3}$

$m_A_B \neq m_C_D$

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0

3 years ago

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distrib

natali 33 [55]

Answer:

a) X is a discrete random variable.

b) 2% probability of choosing a unit with 10 rooms

c) 98% probability that a unit chosen at random is not a 10-room unit

d) 30% probability that a unit chosen at random has less than five rooms

e) 7% probability that a unit chosen at random has less than five rooms

Step-by-step explanation:

The distribution means that:

7% probability that a randomly chosen owner-occupied housing unit in a certain city has 3 rooms.

23% probability that a randomly chosen owner-occupied housing unit in a certain city has 4 rooms.

36% probability that a randomly chosen owner-occupied housing unit in a certain city has 5 rooms.

19% probability that a randomly chosen owner-occupied housing unit in a certain city has 6 rooms.

5% probability that a randomly chosen owner-occupied housing unit in a certain city has 7 rooms.

5% probability that a randomly chosen owner-occupied housing unit in a certain city has 8 rooms.

3% probability that a randomly chosen owner-occupied housing unit in a certain city has 9 rooms.

?% probability that a randomly chosen owner-occupied housing unit in a certain city has 10 rooms.

(a) Is X a discrete or continuous random variable?

X is the number of rooms in a randomly selected house. The number of rooms is a countable variable, that is, only assumes values like 1,2,3,4,... You cannot have 3.5 rooms, for example.

So X is a discrete random variable.

(b) What must be the probability of choosing a unit with 10 rooms?

The sum of all probabilities must be 100%(1 decimal). So

0.07 + 0.23 + 0.36 + 0.19 + 0.05 + 0.05 + 0.03 + ? = 1

0.98 + ? = 1

? = 0.02

2% probability of choosing a unit with 10 rooms

(c) What is the probability that a unit chosen at random is not a 10-room unit?

0.07 + 0.23 + 0.36 + 0.19 + 0.05 + 0.05 + 0.03 = 0.98

98% probability that a unit chosen at random is not a 10-room unit

(d) What is the probability that a unit chosen at random has less than five rooms?

7% probability it has 3 rooms

23% probability it has 4 rooms. So

7+23 = 30% probability that a unit chosen at random has less than five rooms

(e) What is the probability that a unit chosen at random has three rooms?

7% probability that a randomly chosen owner-occupied housing unit in a certain city has 3 rooms. So

7% probability that a unit chosen at random has less than five rooms

8 0

3 years ago

Which statement about these triangles is true?

stealth61 [152]

Answer:

we cant see the triangle

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers