1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
matrenka [14]
2 years ago
12

Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.

Mathematics
1 answer:
Cloud [144]2 years ago
4 0

Answer:

y=0.3x

Step-by-step explanation:

Formula = K=\frac{y}{x}

y α x

y = kx

Where k is the constant of proportionality.

When y = 1.5; x = 5;

We substitute these known values in the equation,

y = kx

1.5 = k5

Dividing both sides of the equation by 5 to find the value for k, we have

1.5/5= k0.3/5

Therefore,

K = 0.3

Having found the value of k,

We substitute this value into the relationship

y = kx

Therefore we have,

y = 0.3x.

The direct variation function is therefore,

y = 0.3x.

[RevyBreeze]

You might be interested in
A student used the graph below to identify the minimum/maximum. The student said the graph had a maximum of 1. Explain the stude
11Alexandr11 [23.1K]

Answer: Answer is in the step.

Step-by-step explanation:

The student made a mistake by identifying the maximum point by the x coordinate value of the vertex. Minimum or maximum points are determine using the y coordinate value.The student can determine the difference between a maximum and minimum by identifying the y coordinate of the vertex.

7 0
3 years ago
X=-3y-5 3x+9y=7 how can u solve this?
pentagon [3]

Answer:


Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
Answer if you want to
prohojiy [21]

Answer:

B: 24(0.3)

Step-by-step explanation:

24 * 0.3 = 7.2

So Mandy spent $7.20 on arts and crafts.

24 - 7.2 = $16.80 remaining.

So this is the final answer is 24 * 0.3

5 0
3 years ago
Use the properties of quadrilaterals to complete the statements. A has exactly one pair of parallel sides. A must have two pairs
vesna_86 [32]

Answer:

1. Trapezoid

2. Kite

3. Square, Rhombus

Step-by-step explanation:

Given - Use the properties of quadrilaterals to complete the statements.

To find - A ..... has exactly one pair of parallel sides.

             A ....... must have two pairs of adjacent sides congruent.

             A ........ must have all congruent sides.

Proof -

A Trapezoid has exactly one pair of parallel sides.

A Kite must have two pairs of adjacent sides congruent.

A Square, Rhombus must have all congruent sides.

Reason -

  • A trapezoid is a quadrilateral with exactly one pair of parallel sides.
  • A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.
  • A rhombus is a parallelogram with four congruent sides.
  • A square can be defined as a rhombus which is also a rectangle . In other words, a square is a parallelogram with four congruent sides and four right angles.

5 0
3 years ago
Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b
trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) \cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}

( 2 ) \sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}

These two identities makes sin(π / 10) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and cos(π / 10) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}.

Therefore cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}. Substitute,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right]

And now simplify this expression to receive our answer,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right] = -\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i,

-\frac{3\sqrt{5+\sqrt{5}}}{4} = -2.01749\dots and \:\frac{3\sqrt{3-\sqrt{5}}}{4} = 0.65552\dots

= -2.01749+0.65552i

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}, cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}

We know that 6\sqrt{5+\sqrt{5}} = 16.13996\dots and -\:6\sqrt{3-\sqrt{5}} = -5.24419\dots . Therefore,

Solution : 16.13996 - 5.24419i

Which rounds to about option b.

7 0
3 years ago
Other questions:
  • One number is 6 more than twice another. If their sum is 51, find the numbers. Which of the following systems of equations repre
    10·1 answer
  • explain how the distributive property helps us multiply the following polynomials and why and how the final product differ
    10·2 answers
  • How is this solved please help anyone
    13·1 answer
  • 6,7,9 pleaseee !!!! I need help today I need it for tomorrow morning
    15·2 answers
  • A survey on healthy choices was given to gym members at Work It Out. The results showed that 90% of its members drank protein sh
    12·1 answer
  • Which expression is equivalent to 9(4p)?
    7·2 answers
  • What is this number in standard form? seventy-one and ninety-two thousandths
    6·2 answers
  • Please help me as soon as possible
    13·1 answer
  • Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two clas
    15·1 answer
  • On a coordinate plane, triangle A B C has points (negative 1, negative 1), (negative 2, negative 1) and (negative 2, negative 4)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!