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dimaraw [331]
3 years ago
8

The function f(x) varies directly with x and f(x) = 12 when x = ¼. What is f(x) when x = 1/8?

Mathematics
1 answer:
Alexxandr [17]3 years ago
3 0

Answer:

6.

Step-by-step explanation:

f(x) = kx where k is a constant

Plugging in the given values:

12 = k * 1/4

48 = k

So the relation is

f(x) = 48x

So when x = 1/8

f(x) = 48 * 1/8 = 6.

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1. Dolores is on a bridge that is 42 feet above a lake. What is the distance from Dolores to the boat? G​
mrs_skeptik [129]

Answer:

See answer below

Step-by-step explanation:

You are missing data such as the angle of the boat next to Dolores. I found an exercise similar to this, and I'm going to show it here and use the missing data to show you how to do it:

<u>Dolores is on a bridge that is 45 feet above a lake. She sees a boat at a 30 degree angle of depression. What is Dolores' approximate horizontal distance from the boat?</u>

<u></u>

According to that, I will use the angle of 30° to do this, but the distance of 42 feet.

Now, we can see this as a triangle. Dolores is on a bridge 42 feet above a lake, this 42 feet distance should be one side of the triangle (The vertical forming the 90° angle), and the boat that is on the lake, is seen with an angle of 30°. So the distance of the boat, to the spot where dolores is, under the bridge would be the horizontal side.

With this, we have the opposite side (a) and the adyacent side (b) of the triangle, and we have the angle, therefore:

tanα = a/b

Replacing we have:

tan30° = 42/b

b = 42 / tan30°

b = 72.75 feet

Hope this helps

4 0
3 years ago
Find x<br> options;<br> a) 21√2/2<br> b) 21√2<br> c) 21√3/2<br> d) 7
pishuonlain [190]

The value of x is  21√2/2

The correct option is (A)

<h3>What is Trigonometry?</h3>

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

In triangle having angle 60.

sin 60 = P/ 7√3

√3/2= P/7√3

2P= 21

P= 21/2

Now again

cos 45= 21/2/x

1/√2 = 10.5/x

x=  21√2/2

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

6 0
2 years ago
The sum of two numbers is negative fifteen, and one number is five less than the other. Using the variables m and n to represent
Likurg_2 [28]

We need to use the variables m and n to represent both numbers.

Their sum must equal -15. Therefore, we can write the next equation:

m + n = -15

If one number is five less than the other, we need to choose one variable and then we can write it in terms of the other variable. Then:

n = m-5

To find the value for each number, we can replace the n equation on the first equation:

m + n = -15

m + (m-5)= -15

Then:

m + m - 5 = -15

2m -5 = -15

Solve the equation for m:

Add both sides 5 units:

2m - 5 +5 = -15+5

2m = -10

Divide both sides by 2:

2m/2 = -10/2

m = -5

Finally, replace the m value on the first equation:

m + n = -15

-5 + n = -15

Then, solve the equation for n:

Add both sides by 5:

-5+5 + n = -15 +5

n = -10

Hence, both numbers are m=-5 and n= -10.

The equations separated by a comma are m + n = -15,n = m-5.

The numbers separated by a comma are -5,-10.

6 0
1 year ago
Geometry help please! Match the reasons with the statements.
SSSSS [86.1K]

Given:

∠PRS and ∠VUW are supplementary.

To prove:

Line TV || Line QS

Solution:

Step 1: Given

∠PRS and ∠VUW are supplementary.

Step 2: By the definition of supplementary angles

m\angle {PRS}+m\angle {VUW}=180^{\circ}

Step 3: Angles forming a linear pair sum to 180°

m\angle {PRS}+m\angle {SRU}=180^{\circ}

Step 4: By transitive property of equality

step 2 = step 3

m\angle {PRS}+m\angle {VUW}=m\angle {PRS}+m\angle {SRU}

Step 5: By algebra cancel the common terms in both side.

{m} \angle {VUW}={m} \angle{SRU}

Step 6: By converse of corresponding angles postulate

Line TV || Line QS

Hence proved.

6 0
3 years ago
Sue had 5 identical bags of candy to share with the crew. Twenty-five pieces of candy disappeared. Ted had 4 bags with the same
inna [77]

Answer:

Each bag originally had 35 pieces of candy

Step-by-step explanation:

Since the bags are identical, Let them Number of candies in each bag sue had be x. Thus, she had 5x candies. Since she lost 25 pieces, then she now has;

5x - 25 candies left.

We are told that Ted had 4 bags with the same number of candies like Sue had. Thus, he has 4x candies.

He mysteriously found 10 additional pieces. Total Ted now has is;. 4x + 10

Finally, we are told that Sue and Ted now have an equal number of candies.

Thus;

5x - 25 = 4x + 10

Rearranging, we have;

5x - 4x = 25 + 10

x = 35

Thus, each bag originally had 35 pieces of candy

3 0
3 years ago
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