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2 years ago

What transformation of the square root function comes from the constant

Mathematics

1 answer:

Leto [7]2 years ago

4 0

The required transformation is $p=(\frac{v}{10.35} )^2$

<h3>Transformation of functions</h3>

Given the function expressed as:

$v=10.35 \times\sqrt{p}$

We are to make p the subject of the formula. First, divide both sides by 10.35

$\frac{v}{10.35} =\frac{10.35 \times\sqrt{p}}{10.35}\\ \frac{v}{10.35}=\sqrt{p}$

Square both sides of the equation:

$p=(\frac{v}{10.35} )^2$

Hene the required transformation is $p=(\frac{v}{10.35} )^2$

Learn more on transformation here: brainly.com/question/17311824

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Perform the multiplication. Simplify the answers. 2 √30*( √5+ √6+ √10+ √15)

Delicious77 [7]

The simplified expression of $2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$ is $10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

The expression is given as:

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$

Expand the expression

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+ 2\sqrt{30} \times \sqrt6+ 2\sqrt{30} \times \sqrt{10} + 2\sqrt{30} \times \sqrt{15}$

Factor out 2

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+ \sqrt{30} \times \sqrt6+ \sqrt{30} \times \sqrt{10} + \sqrt{30} \times \sqrt{15})$

Combine the radicals

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} + \sqrt{180}+ \sqrt{300} + \sqrt{450})$

Expand the expression

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} + \sqrt{9 \times 20}+ \sqrt{100 \times 3} + \sqrt{225\times 2})$

Evaluate the roots

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} + 3\sqrt{20}+ 10\sqrt{3} + 15 \sqrt{2})$

Expand

$2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

Hence, the simplified expression of $2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})$ is $10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}$

Read more about simplified expressions at:

brainly.com/question/8008182

3 0

2 years ago

Arjun and Jessica each improved their yards by planting daylilies and shrubs. They bought their

Anvisha [2.4K]

Hi there! Let me know if you have questions about my answer:

One shrub is $11.

One daylily is $4.

Step-by-step explanation:

To find the cost of each item, write a system of equations, one equation for what each person bought, and solve for each variable.

Define your variables.

let 'd' be the cost of one daylily

let 'r' be the cost of one shrub

Create a system using the variables and information from the question.

Write an equation for what Arjun bought:

5d + 7r = 97 5 daylilies, 7 shrubs, totaling $97

Write an equation for what Jessica bought:

2d + 11r = 129 2 daylilies, 11 shrubs, totaling $129

Solve the system.

I will solve the system algebraically, using the substitution method. Isolate one variable in one of the equations.

I will isolate 'd' in Jessica's equation:

$2d + 11r = 129$ Start with Jessica's equation

$\frac{2d + 11r}{2} = \frac{129}{2}$ Divide everything in the equation by 2

$d + \frac{11r}{2} = \frac{129}{2}$ Simplify

$d = \frac{129}{2} - \frac{11r}{2}$ Isolate 'd' by subtracting $\frac{11r}{2}$ from both sides.

Now you have an expression for 'd'.

Substitute Arjun's equation with the expression for 'd'. Solve for 'r' to find the cost of one shrub.

$5d + 7r = 97$ Start with Arjun's equation

$5(\frac{129}{2} - \frac{11r}{2}) + 7r = 97$ Substitute 'd' for $d = \frac{129}{2} - \frac{11r}{2}$

$\frac{5*129}{2} - \frac{5*11r}{2} + 7r = 97$ Distribute the 5

$\frac{645}{2} - \frac{55r}{2} + 7r = 97$ Simplify the numerators

$\frac{645}{2} - \frac{55r}{2} + \frac{14r}{2} = 97$ Change 7r to a fraction over 2

$\frac{645}{2} - \frac{41r}{2} = 97$ Combine like terms, the terms with 'r'

$\frac{645-41r}{2} = 97$ Simplify

$645-41r = 194$ Multiply both sides by 2

$-41r = 194-645$ Subtract 645 from both sides

$-41r = -451$ Divide both sides by –41

$r = 11$ Solved for cost of one shrub

Substitute 'r' for 11 using either Arjun's or Jessica's equation. Then, isolate 'd' to solve for the cost of one daylily.

I will use Arjun's equation.

$5d + 7r = 97$ Start with Arjun's equation

$5d + 7(11) = 97$ Substitute 'r' for r = 11

$5d + 77 = 97$ Simplify. Subtract 77 from both sides.

$5d = 20$ Divide both sides by 5.

$d = 4$ Solved for the cost of one daylily

I hope this helped! Check out a similar problem about solving systems here to learn more:

brainly.com/question/11103098

7 0

2 years ago

Express 2x2 + 8x + 3 in the form 2(x + p) +9

Jet001 [13]

Answer is 2( x + 2 )^2 - 5 I think

4 0

2 years ago

There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance

Natali5045456 [20]

The answer is 7/69.

There are 8 black-haired children among 24 children. The probability of randomly selecting black haired children for the first time is:
P1 = 8/24 = 1/3

Now, there are 7 black-haired children left among 23 children. The probability of randomly selecting black haired children for the second time is:
P2 = 7/23

Since we want both of these events to occur together, we will multiply their probabilities:
P = P1 * P2 = 1/3 * 7/23 = 7/69

6 0

3 years ago

Hey! i’ll give brainliest please help

mart [117]

Answer:

Step-by-step explanation:

3 0

3 years ago