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Marrrta [24]
3 years ago
15

To draw a line that is parallel to 9x+12y=16, what should the slope of the line be?(1 point)

Mathematics
1 answer:
erik [133]3 years ago
4 0

Answer:

Hi how are you doing today Jasmine

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PLEASE HELP ASAP! I don’t recall how to do this!
MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

(1.05)^x=1.885

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

ln(1.05)^x=ln(1.885)

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

x=\frac{ln(1.885)}{ln(1.05)}

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

ln(x*x^2)=5

Simplifying gives you

ln(x^3)=5

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

ln(x)=\frac{5}{3}

Take the inverse ln by raising each side to e:

e^{ln(x)}=e^{\frac{5}{3}}

The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

\frac{1}{2}=e^{.1x}

"Undo" that e by taking the ln of both sides:

ln(.5)=ln(e^{.1x})

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others.  Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

(2^2)^x-6(2)^x=-8

Now we will bring over the -8 by adding:

(2^2)^x-6(2)^x+8=0

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution.  Let's let u=2^x

When we do that, we can rewrite the polynomial as

u^2-6u+8=0

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

2^x=4,2^x=2

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

2^2=2^x

Now that the bases are the same, we can say that

x = 2

For the second solution, we will raise the 2 on the right to a power of 1 to get:

2^x=2^1

Now that the bases are the same, we can say that

x = 1

5 0
3 years ago
Which ordered pair makes both inequalities true y x 1 YX?
denis-greek [22]

The ordered pair which makes both inequalities true is (-2, 2).

It is given that inequalities are

y < -x + 1 and y > x

For  y < -x + 1

Substituting every ordered pair,

1) (-3, 5)

⇒ 5 < - (-3) + 1

⇒ 5 < 3 + 1

⇒ 5 < 4 is false

2) (-2, 2)

⇒ 2 < -(-2) + 1

⇒ 2 < 2 + 1

⇒ 2 < 3 is true

3) (-1, -3)

⇒ -3 < - (-1) + 1

⇒ -3 < 1 + 1

⇒ -3 < 2 is true

4) (0, -1)

⇒ -1 < -0 + 1

⇒ -1 < 1 is true

Now , for  y > x

1) (-3, 5)

⇒ 5 > -3 is true

2) (-2, 2)

⇒ 2 > -2 is true

3) (-1, -3)

⇒ -3 > -1 is false

4) (0, -1)

⇒ -1 > 0 is false

Therefore ,the ordered pair which makes both inequalities true is (-2, 2).

To know more about Inequalities here

brainly.com/question/11612965

#SPJ4

5 0
1 year ago
What is the measure of the highlighted angle
IgorLugansk [536]
Angle on a straight line sums up to 180
so
72+x + x+130 = 180
2x = 180-72-130
2x =-22
x= -11

so Angle on the LHS is 61°
while angle on the RHS is 119°
7 0
3 years ago
In a certain country, approximately 22 out of 100 people over the age of 12 smoke. How many smokers would you expect in a group
Elan Coil [88]

Answer:

121 smokers

Step-by-step explanation:

This can be calculated as a simple rule of 3.

In these problems, the first step is identifying the measures in the problem. Then, we must identify whether their relation is direct or inverse.

When it is direct, as one measure increases, the other will increase too.

When it is inverse, as one measure increases, the other will decrease.

In this problem, the measures are the number of people over 12 that smoke, and the total number of people over 12. Their relation is direct, because as the number of people increases, the number of smokers will increase too.

So we must solve the following rule of three:

22 smokers - 100 people

x smokers    - 550 people

x = 550*22/100

x = 22*5.5

x = 121 smokers.

So,  in a group off 550 people over the age of 12, there are 121 expected smokers.

8 0
3 years ago
If Dr. Suzuki rides his bike to his​ office, he averages 9 miles per hour. If he drives his​ car, he averages 27 miles per hour.
Helen [10]
Speed
Riding speed = 9 mph
Driving speed = 27 mph

Time
If x hours is the time taken when riding, (x - 1/3) hours  is the time taken when driving.

Distance in both instances is the same, D= Speed * time

Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours

Distance, D = 1/2 *9 = 4.5 miles
7 0
3 years ago
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