Rationalize the denominator. [tex]\frac{9}{\sqrt{x+3} }[/tex] Simplest form

Answer: [tex]\frac{15\pi}{4}[/tex]

Step-by-step explanation:

[tex]A=\pi(3^{2})\left(\frac{150}{360} \right)=\boxed{\frac{15\pi}{4}}[/tex]

Using proportions, it is found that the amounts are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The amount deposited is of $425 each month for 25 years, that is, $425 in 25 x 12 times, that is:

D = 425 x 25 x 12 = $127,500.

The amount of interest is the total amount subtracted by the amount deposited, hence:

I = 281,292.21 - 127,500 = $153,792.21.

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Answer:

[tex]x+4\geq 12[/tex]

Step-by-step explanation:

x - a number

x+4 - a number plus 4

x+4[tex]\geq[/tex] - a number plus 4 is greater than or equal to

x+4[tex]\geq[/tex]12 - a number plus 4 is greater than or equal to twelve

Answer:

Inequality:  x + 4 ≥ 12

Solution:  x ≥ 8

Step-by-step explanation:

Plus:  "+" →  to add something to something else

Greater than or equal to:  "≥" → the expression on the left side of the inequality sign is greater than the expression on the right side of the sign.

Let x be the unknown number.

A number plus four is greater than or equal to twelve:

x + 4 ≥ 12

To solve the found inequality, subtract 4 from both sides:

⇒ x + 4 - 4 ≥ 12 - 4

⇒ x ≥ 8

Therefore, the solution to the inequality is x ≥ 8.  The unknown number x can be any real number equal to or greater than 8.

It is wider and shifted 3 units to the left , Option A is the right answer.

Function is a mathematical statement that shows relation between two variables.

The parent function given is

f(x) = |x|

The transformed function is given by

f(x) = 0.1|x -3|

The function is shifted towards the left

and as the scale factor is 0.1 therefore , It is wider

Therefore Option A is the right answer.

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Answer:

The answer for this is B.

Step-by-step explanation:

Figured it out the hard way on EDGE. 2022

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Step-by-step explanation:

how does the picture fit into this question ?

I guess you mean

(a² + ab)

when a = 4 and b = 3. then we simply replace the variable names by the actual values and calculate :

4² + 4×3 = 16 + 12 = 28

.

now to the picture :

i am not sure what the requested result of procedure is.

so, I am just going to simplify the expression :

(log(25) - log(4)) / (log(55) - 1/2 × log(2)

remember the rules of the logarithm :

log(a) - log(b) = log(a/b)

k × log(a) = log(a^k)

a^(1/2) = sqrt(a) (the square root of a)

I assume we are using the logarithm to the base of 10.

so, we have here

log(25/4) / log(55/sqrt(2)) =

= 0.795880017... / 1.589847692... = 0.500601423...

260 inches of trim are needed to surround the​ window.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Actually, all we need is a trim that is the same size as our window and equal to the parallelogram's circumference, which is

The sum of the side is;

⇒Length of lower side + Length of the upper side

⇒ 90+90

⇒180 inches

The sum of adjacent sides;

Sum of adjacent sides  =  40+40

Sum of adjacent sides  = 80 inches

The length you should trim is needed to surround the​ window is found as;

⇒ 180 inches + 80 inches

⇒260 inches

Hence,260 inches of trim are needed to surround the​ window.

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Answer :Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:

first, check the directions to make sure they are opposite,

then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.

3 is not the opposite of -6

__

6 is the opposite of -6

Answer:

B

Step-by-step explanation:

Range is all the possible values of 'y'. As seen in the graph, the smallest value of 'y' is 20, where the point is (6, 20), and the largest value of 'y' is 60, where the point is (1, 60). Therefore, the range is B. 20≤y≤60

The complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The complete question is in the attachment

The given parameters are:

The vertex is represented as (h, k ± a).

So, we have:

h = -5

k + a = 14

k - a = -2

Add the last two equations

2k = 12

Divide by 2

k = 6

Substitute k = 6 in k + a = 14

6 + a = 14

Solve for a

a = 8

The ellipse equation is represented as:

[tex]\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1[/tex]

So, we have:

[tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The ellipse passes through the point (0,6).

So, we have:

[tex]\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1[/tex]

This gives

[tex]\frac{5^2}{b^2} + \frac{0}{8^2} = 1[/tex]

Evaluate the quotient

[tex]\frac{5^2}{b^2} = 1[/tex]

Cross multiply

[tex]b^2 = 5^2[/tex]

Take the square root of both sides

b = 5

Substitute b = 5 in [tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

[tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

Hence, the complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

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Answer:

6 $50 bills and 9 $5 bills

Step-by-step explanation:

Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:

5x + 50y = 345

x + y = 15

Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:

x + y = 15

x = 15 - y

Now, plug in (15 - y) for x into the other equation, and solve for y:

5(15 - y) + 50y = 345

75 - 5 y + 50y = 345

75 + 45y = 345

45y = 270

y = 6

Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)

Answer:

87.92

Step-by-step explanation:

We are given this expression:

3.14(a² + ab)

And we want to evaluate it if a is 4 and b is 3.

To solve this, we need to follow the order of operations, usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have their own variations on the acronym.

Despite this, let's start with P, which would be parentheses.

Because we have the a² + ab in parentheses, we should evaluate this first.

We should substitute the values  of a and b with 4 and 3 respectively, to get this (we can ignore the 3.14 for now):
(4)² + 4 * 3

First, let's go on to exponents.

We do have one exponent, which is the 4 being raised to the second power.

So let's evaluate that.

Raise 4 to the second power (multiply it by itself).

4 * 4 = 16

We can replace (4)² with 16.

16 + 4 * 3

Now, let's move on to multiplication.

We do have one multiplication operation, which is the 4 * 3, so let's evaluate that.

4 * 3 = 12

Replace 4 * 3 with 12.

16 + 12

We don't have any division in this, so we can skip that.

Moving on to addition:

We can add these two numbers together.

16 + 12 = 28

28 is the value of a² + ab.

We now multiply this by 3.14 to get the answer.

3.14 * 28 = 87.92

Topic: substituting values into an expression

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The value of expression 3.14([tex]a^{2}[/tex]+ab) when a =4 and b=3 is 87.92.

Given Expression :3.14([tex]a^{2}[/tex]+ab) and we have to find the value at a=4 and b=3

we know expressions are the combinations of numbers, symbols and coefficients and in the expression given the variable are a and b .Expression shows the relationship between the variables which are present in the expression. When we have to find the value of expression at a=4 and b=3 we have to just put the values of a and b in the expression .

[tex]a^{2}[/tex]=16 and ab=4*3=12

=3.14[tex]((4)^{2}+4*3)[/tex]

=3.14(16+12)

=3.14*28

=87.92

Hence the value of the expression 3.14(a2 + ab) at a=4 and b=3 is 87.92.

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Answer:

Below

Step-by-step explanation:

1. has

2. has

3. have

4. has

5. have

6. has

7. has

8. have

9. have

10. has

11. has

12. has

13. have

14. have

Answer: the +2

Step-by-step explanation: PEMDAS. Exponents are before addition in the sequence. I hope this helps!

(The E standing for exponents and the A standing for addition)

Answer:

Linear Equations In One Variable =

Next step :

in the equation y/6 = 156, it would be equivalent to y = 156 × 6.

so that :

y = 156 × 6

y = 936

this equation solved. (Answer : 936)

Answer:

  see attached

Step-by-step explanation:

You recognize the equation of the line as being given in point-slope form:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +3 = 2(x +3) . . . . . . given equation

This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.

__

You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.

The Sales Volume Variance of the car manufacturer for the twelve-month period is $96,000.

The sales volume variance measures the financial impact of not meeting or exceeding the budgeted sales for a period.

It can be computed by finding the difference between actual and budgeted sales quantities and then multiplied by the unit selling price.

Budgeted sales units = 50,000

Actual sales units = 48,000

Sales price per unit = $60

Actual sales revenue = $2,904,000

Budgeted sales revenue = $3,000,000 ($60 x 50,000)

Sales volume variance = $96,000 ($3,000,000 - $2,904,000)

Thus, the Sales Volume Variance is $96,000.

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Answer:

x = 5/2

Step-by-step explanation:

Given that,

[tex] \cfrac{x}{3} = \cfrac{5}{6} [/tex]

Solution:

Multiplying using criss-cross method;

Divide both sides by 6;

Done!

Hence x = 5/2.

Answer:

x = 2.5

Step-by-step explanation:

x = 3*(5/6)

Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.

The attached graph represents the graph of the constraints

The constraints are given as:

7x+11y≤ 1540

x+3y ≤ 360

x+y≤ 200

x ≥ 0, y ≥ 0

Next, we plot the graph of the constraints using a graphing calculator

From the graph (see attachment), we have the coordinates of the feasible region to be (66, 98), (120,80) and (165,35)

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Solving the given equations we get,

If the quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solutions of this are given by,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here in the problem given that,

The first quadratic equation is [tex]9x^2-25=-12-10x[/tex]

Converting it into standard form of quadratic equation we get,

[tex]9x^2-25=-12-10x\\9x^2-25+12+10x=0\\9x^2+10x-13=0[/tex]

So here a=9,b=10,c=-13

The solutions of the equation is given by,

[tex]x=\frac{-10\pm\sqrt{10^2-4\times9\times(-13)}}{2\times9}=\frac{-10\pm\sqrt{100+468}}{18}\approx\frac{-10\pm23.83}{18}[/tex]

So either,

[tex]x=\frac{-10+23.83}{18}=\frac{13.83}{18}\approx0.77[/tex]

Or,

[tex]x=\frac{-10-23.83}{18}\approx-1.88[/tex]

So the solutions are given by x=0.77 and -1.88

Second quadratic equation is [tex]4n^2-1=12n+3n^2+11[/tex]

Converting the equation in its standard form we get,

[tex]4n^2-1=12n+3n^2+11\\4n^2-1-12n-3n^2-11=0\\n^2-12n-12=0[/tex]

so here a=1,b=-12,c=-12

Solutions are given by,

[tex]n=\frac{-(-12)\pm\sqrt{(-12)^2-4\times1\times(-12)}}{2\times1}=\frac{12\pm\sqrt{144+48}}{2}\approx\frac{12\pm13.86}{2}[/tex]

So either

[tex]n=\frac{12+13.86}{2}=12.93[/tex]

Or,

[tex]n=\frac{12-13.86}{2}=-0.93[/tex]

Solutions are given by n = 12.93 and -0.93

Hence the solutions are x=0.77 and -1.88 for first equation and n=12.93 and -0.93 for second equation.

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Answer:

D. x=5

The answer is x=4.50 then it is rounded off to 5. So, the answer is 5.

Step-by-step explanation:

Find the domain of the inequality:[tex]2x-1\geq 0[/tex]

Rearrange terms to the left side of the equation:[tex]2x\geq 1[/tex]

Divide both sides of the inequality by the coefficient of the variable:

=> [tex]x\geq \frac{1}{2}[/tex]

The domain of the inequality is:[tex]x\geq \frac{1}{2}[/tex]

Convert logarithm to exponential form:[tex]2^{3}=2x-1[/tex]

Calculate the power:[tex]8=2x-1[/tex]

Rearrange terms to the left side of the equation:[tex]-2x= -8-1[/tex]

Calculate:[tex]-2x=-9[/tex]

Divide both sides of the equation by the coefficient of the variable:[tex]x=\frac{-9}{-2}[/tex]

=> [tex]x=\frac{9}{2}[/tex]

=>[tex]x=4.5\\[/tex]

Round the number: [tex]x=4.50[/tex]

Answer: [tex]x=4.50[/tex]

=> [tex]x=5[/tex]

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Answer:

x = 9/2

Step-by-step explanation:

Step-by-step explanation:

1) the equation of the line represented is

y=0.5x+3 (slope-interception form), the slope is 0.5, the intercept is 3.

x-2y+6=0 (common form);

2) x-intersection is at -6, y-intersection is at 3.

Answer:

7%

Step-by-step explanation:

[tex] \frac{14766 - 13800}{13800} \times 100 = 7 [/tex]

The percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766

Percentage increase:

[tex]= \rm \dfrac{14766-13800}{13800}\times 100[/tex]

= 7%

Thus, the percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.

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Answer:

h(-7) = 44

Step-by-step explanation:

h(x) = h (-7) means x= -7

h(x) = (-7)² - 5

49 - 5

44

Answer:

43

Step-by-step explanation:

63-3/3=20 63-20

Answer:

mark has 18

don has 45

Step-by-step explanation: