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3 years ago

Write an equation of the line with a slope of 2 and y-intercept of 9

Mathematics

1 answer:

spayn [35]3 years ago

7 0

Answer:

Y=2x+9 :)

Step-by-step explanation:

You might be interested in

T=21and u =4 what is \sqrt(t+U)

Aleks04 [339]

√(t + u)

√(21 + 4)

√25

6 0

2 years ago

Read 2 more answers

If AC equals 48 meters, what is the perimeter of the field

Alinara [238K]

Remark

A kite is constructed such that AB = BC and AD = DC. AB = sqrt( (1/2)AC + 18^2) see diagram. AD = sqrt(24^2 + 32^2)

Step One

Solve for AB

1/2 AC = 24 (AC is given as 48)

18 is a given length

AB = sqrt(24^2 + 18^2) = sqrt(576 + 324) = sqrt(900) = 30

Step Two

Find the length of AD

AD = sqrt(32^2 + 24^2) = sqrt(1024 + 576) = sqrt(1600) = 40

Step Three

Find the Perimeter.

P = 2 * 30 + 2*40 = 60 + 80 = 140

P = 140 <<<<< Answer

5 0

3 years ago

Read 2 more answers

Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 15 grams

hram777 [196]

Answer:

$X(16)=25.71grams$

Step-by-step explanation:

let $X(t)$ denote grams of $C$ formed in $t$ mins.

For $X grams$ of $C$ we have:

$\frac{2}{3}Xg$ of A and $\frac{1}{3}Xg$ of B

Amounts of A,B remaining at any given time is expressed as:

$40-\frac{2}{3}Xg$ of A and $50-\frac{1}{3}Xg$ of B

Rate at which C is formed satisfies:

$\frac{dX}{dt} \infty(40-\frac{2}{3}X)(50-\frac{1}{3}X)->\frac{dX}{dt}=k(90-X)\\\therefore \frac{dX}{(90-X)^2}=kdt->\int{\frac{dX}{(90-X)^2}} \, =\int {k} \, dt \\\therefore \frac{1}{90-X}=kt+c->90-X=\frac{1}{kt+c}\\\\X(t)=90-\frac{1}{kt+c}$

Apply the initial condition, $X(0)=0$ ,to the expression above

$0=90-\frac{1}{c} \ \ ->c=\frac{1}{90}\\\therefore\\X(t)=90-\frac{1}{kt+\frac{1}{90}} \ \ ->X(t)=90-\frac{90}{90kt+c}$

Now at $X(8)=15$ :

$15=90-\frac{90}{90\times 8k+1} \ ->75=\frac{90}{720k+1}\\k=0.0002778$

Substitute in X(t) to get

$X(t)=90-\frac{90}{0.0002778t\times 90+1}\\X(t)=90-\frac{90}{0.25t+1}\\But \ t=16\\\therefore X(t)=90-\frac{90}{0.025\times16+1}\\X(t)=25.71$

5 0

2 years ago

2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

________________________________________________________

<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

________________________________________________________

<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Cross out the common factor</h3>

$cos\ 4A=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

________________________________________________________

<h3>Reduce the fraction</h3>

$cos(-A)=0$

________________________________________________________

<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

5 0

2 years ago

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates ar

Sunny_sXe [5.5K]

Answer:

Range[4,24,44,64,84,104,124]

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs

20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in

pounds can be represented by f x( ) = 20x + 4.

What is the range of the function for this situation?

The range of a function can be defined as the difference between the maximum and minimum function. From the question, we can deduced that the minimum function of X is 0 and no plate is added, and the maximum is 6

The given function is

f(x) = 20x + 4 =

f(0) = 20(0) + 4

= 4

f(6) = 20(6) + 4

= 124

Which means the range is within 4 and 124.

But we are told from the question that Each pair of plates weighs 20 lb, which means there is difference of 20ib each between 4 and 24

Then we can compute the range as [4,124] or (4,24,44,64,84,104,124)

3 0

2 years ago