How do I solve the following equation?

Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]

Step-by-step explanation:

You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.

Answer:  1 question Solve for x

x=

3

−y−2z−10

​

Solve for y

y=−3x−2z−10

Step-by-step explanation: Steps for Solving Linear Equation

3x+y+2z=−10

Subtract y from both sides.

3x+2z=−10−y

Subtract 2z from both sides.

3x=−10−y−2z

The equation is in standard form.

3x=−y−2z−10

Divide both sides by 3.

3

3x

​

=

3

−y−2z−10

​

Dividing by 3 undoes the multiplication by 3.

x=

3

−y−2z−10

​

The distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

The points are (3, π/6) and (2, π/3)

The polar coordinate system is the system that represent a point by a distance from a fixed reference point and angles from a reference direction

The distance between the two points

d = [tex]\sqrt{r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)}[/tex]

(3, π/6) is the coordinates of first point

(2, π/3) is the coordinates of second point

Substitute the values in the equation

d = [tex]\sqrt{3^2+2^2-2(3)(2)cos(\pi/6 - \pi /3)}[/tex]

d = [tex]\sqrt{9+4-12(\frac{\sqrt{3} }{2} )}[/tex]

d = [tex]\sqrt{13-6\sqrt{3} }[/tex]

d = 1.614 units

Hence, the distance between the two points (3, π/6) and (2, π/3) in polar coordinates is 1.614 units

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The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.

To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.

100 - 45.75% = 54.25% or 0.5425

Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:

7g × 0.5425  = 3.7968

So, the total gram of fat for one serving of the low-fat yogurt is equal to:

3.7968g

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By performing some simple mathematical operations, the answers to all the subparts are:

So, the answers after multiplication are:

Therefore, by performing some simple mathematical operations, the answers to all the subparts are:

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Answer: mode is 94

Step-by-step explanation:

Answer:

[tex] = \frac{8(x + 3) {}^{2} }{2(x + 3)} = 4(x + 3) = 4x + 12[/tex]

Hopefully this will help u

Answer:

68°

Step-by-step explanation:

The angles are equal to each other.  Set them equal and solve for x

5x + 18 = 8x - 12  Subtract 5x from both sides of the equation

18 = 3x - 12  Add 12 to both sides of the equation

30 = 3x  Divide both sides by 3

10 = x

Now that you have found x plug is back into  5x + 18

5(10) + 18

50 + 18 = 68

Answer:

∠ FLJ = 68°

Step-by-step explanation:

∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then

8x - 12 = 5x + 18 ( subtract 5x from both sides )

3x - 12 = 18 ( add 12 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°

Answer: 17%

Step-by-step explanation:

If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.

Answer: over budget by $64



Step-by-step explanation:

$99 coat

$75 Shoes

$240 tv

Total=414

total-budget=

Budget =$350

414-350

= 64

The zeroes of the parabola is -1, -5.

What is parabola and zeroes of parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:

f(x) = y= ax2 + bx + c

To find zeroes of parabola

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

Given equation is

f(x) = [tex]x^{2} +6x+5[/tex]

a = 1, b = 6, c = 5

x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2

x = -6 ±[tex]\sqrt{16} /2[/tex]

x = -6 ± 4 /2

hence,

x = -6-4/2 and x = -6 +4/2

x = -5 or x = -1

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Check the picture below.

After solving the given equation for r, the value of r is √T/4π.

So, the formula equation is:

Now, solve for r as follows:

Therefore, after solving the given equation for r, the value of r is √T/4π.

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The answer is option (a)

Hope this answer helps you

The dimensions of the cup that minimize the construction cost are 2 x 2 x 5 in

Given:  Capacity = 20 in³, cost of material for the side = 12¢/in² and cost of material for the base = 60¢/in²

In order to calculate the dimension of the cup

Let h and x represent the height and square base respectively

Thus, the capacity (volume) of the pencil cup is can be represented as:

V = x²h     (where V = 20)

20 = x²h

h = 20/x²

At minimum cost, we have:

C(x) = 60x² +  12(4xh)

C(x) = 60x² +  48xh         (put h = 20/x²)

C(x) = 60x² +  48x(20/x²)

C(x) = 60x² +  960/x

Differentiating with respect to x, we have:

C(x) = 120x - 960/x²      (multiply through by x²)

120x³-960 = 0

120x³ = 960

x³ = 960/120

x³ = 8

x = ∛8 = 2 in

For the height:

h = 20/x²

h = 20/2²

h = 20/4 = 5 in

dimensions = 2 x 2 x 5 in

Therefore, the dimensions of the cup that minimize the construction cost are a 2 x 2  square base and  height of 5 in

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If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total time of the math test Raven took was 1 hour and 35 minutes.

Now he finishes the test at 1:20.

So, One hour before the time was 12:20.

20 minutes before that was exactly 12:00 and 15 minutes before that was

11:45 so a total of 1 hour and 35 minutes.

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The factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

According to the question,

We have the following expression:

6x²y-10xy+15x-25​

In this expression, we can not use any identity to solve it further.

Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.

Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:

2xy(3x-5)+5(3x-5)

Taking (3x-5) as a common factor from the above expression:

(3x-5) (2xy+5)

Hence, the factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

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The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]

The interior angles of a triangle are the angles formed by the sides sides of the triangle.

The question can be solved by making use of the known properties of a triangle.

The angle sum property of the interior angles in a triangle gives;

The sum of the interior angles of a triangle is 180°

Therefore; x + 2·x + 70 = 180

3·x = 180° - 70° = 110°

[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]

The measure of angle A is 2·x

Which gives;

[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]

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For Jeremy the new balance due was $8.9  .

In the question ,

it is given that ,

bill received by Jeremy with balance due =  $35.60  

also given that after an error occurred  ,

the new balance was 1/4 of the original balance due .

So , the new balance due is = (1/4) × (original balance due)

Substituting the value of original balance due ,

we get ,

new balance due = (1/4) × (35.60)

= 35.60/4

On Simplifying further ,

we get ,

= 8.9

Therefore , For Jeremy , the new balance due was $8.9  .

The given question is incomplete , the complete question is

Jeremy received a bill with a balance due of $35.60. After an error was corrected, the new balance was 1/4 of the original balance due. What was the new balance due ?

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Answer:

150 adult tickets where sold

Step-by-step explanation:

If we multiply 150 times 3 that gives us 450, which acounts for all the students. And 150 is the number thats left of adults that adds up to 600.

The distance between the eyes and the distance to the image of the toes will be 273.80 cm.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror.

The distance between the image of toes and eyes will be calculated as,

H² = P² + B²

H= √(P² + B²)

H = √(163² + 220²)

H = √(26569+48400)

H = √74969

H = 273.80 cm

Therefore, the distance between the eyes and the distance to the image of the toes will be 273.80 cm.

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The math shows the world is designed, and that design is symmetry and spirals.

How is math found in nature What is the significance of mathematical patterns in nature?

Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.

Here,

If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.

Hence, the math shows the world is designed, and that design is symmetry and spirals.

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Answer:  y intercept:  (0, -1/7)

Step-by-step explanation:

First you start with y = 10x - 1/7

Since your finding the y-intercept, you turn the 10x into a 0

So you would have y = -1/7

So y = -1/7

is your answer!

The angular value of x is 3° as per the given the given information in the question.

An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Given,

m ∠GQP=80

m ∠RQP=3+59x

m ∠RQG=32x+4

From the figure,

m ∠RQG+ m ∠GQP= m ∠RQP

32x+4+80°=3+59x

27x=81°

x=3°

Therefore, the value of x=3°

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The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Percentage of people who notice the speed limit = 84%

The percentage of people who notice the sign and follow the speed limit is 75%.

Therefore, 84% - 75%  = 9% are the percentage speeding and noticed.

Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".

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Answer:

192

Step-by-step explanation:

If 20% is the profit, then 80% is the cost.

.8 x 240 = 192

Answer:

Store B

Step-by-step explanation:

Store A: $2.50 ÷ 2 = $1.25

Store B: $3.25 ÷ 3 = $1.08 (to nearest cent)

Store B offers the better deal.

Answer:

[tex]\textsf{a.} \quad x = 1 - \sqrt{7},\quad x = 1 + \sqrt{7}[/tex]

b.  y = -6

c.  Minimum point at (1, -7).

d.  Domain:  (-∞, ∞)

e.  Range:  [-7, ∞)

f.  See attachment.

Step-by-step explanation:

Given function:

[tex]\text{f}(x)=x^2-2x-6[/tex]

As per the question, use a graphing calculator to graph the given function.

The x-intercept(s) are the points at which the curve crosses the x-axis.

The y-intercept is the point at which the curve crosses the y-axis.

From inspection of the graph:

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

The range of a function is the set of all possible output values (y-values).

As the function has a minimum point at y = -7, the range is restricted.

Graph label the axes using a scale of 1 (see attachment).