Write the equation of the linear relationship in slope-intercept form, using decimals as needed.


x 0 100 200 300
y 2.5 97.5 192.5 287.5

Answer: because the other half is used on the base solution

Step-by-step explanation:

The equation 2cos²x + sinx - 1 = 0 can be solved by converting terms involving cosine to sine, simplifying the equation, and then solving the resulting quadratic equation for sinx and consequently solving for x.

To solve the trigonometric equation 2cos²x + sinx - 1 = 0, we can first convert the terms in the equation involving cosine to terms involving sine.

We know that cos²x= 1 - sin²x. Substituting this into the equation, we will have 2(1 - sin^2x) + sinx - 1 = 0.

This simplifies to 2 - 2sin²x + sinx - 1 = 0. Reordering terms, we get 2sin²x - sinx + 1 = 0. If we solve this quadratic equation for sinx, we can then solve for x. Assuming the domain 0<=x<=2pi, this will give us the possible values of x that satisfy the original equation.

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194 children, 92 students, and 97 adults attended

Step-by-step explanation:

The given is:

We need to find how many children,

students, and adults attended

Assume that x represents the number of children, y represents the number of students, and z represents the number of adults

∵ There were x children, y students and z adult attended

∵ The movie theater has a seating capacity of 383

∴ x + y + z = 383 ⇒ (1)

∵ The theater charges $5 for children, $7 for students, and

   $12 for adults

∵ The total ticket sales was $2778

∴ 5x + 7y + 12z = 2778 ⇒ (2)

∵ There are half as many adults as there are children

- Half means 0.5

∴ z = 0.5x ⇒ (3)

Substitute equation (3) in equations (1) and (2)

∵ x + y + 0.5x = 383

- Add like terms

∴ 1.5x + y = 383 ⇒ (4)

∵ 5x + 7y + 12(0.5x) = 2778

∴ 5x + 7y + 6x = 2778

- Add like terms

∴ 11x + 7y = 2778 ⇒ (5)

Let us solve equations (4) and (5) to find x and y

Multiply equation (4) by -7 to eliminate y

∴ -10.5x - 7y = -2681 ⇒ (6)

- Add equations (5) and (6)

∴ 0.5x = 97

- Divide both sides by 0.5

∴ x = 194

Substitute the value of x in equations (4) and (3) to find y and z

∵ 1.5(194) + y = 383

∴ 291 + y = 383

- Subtract 291 from both sides

∴ y = 92

∵ z = 0.5 (194)

∴ z = 97

194 children, 92 students, and 97 adults attended

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Answer:h = y^2 / 27

Step-by-step explanation:

Volume of a cylinder = pi*(xx)^2*yy

= x^4*pi*yy

Volume of a cone = 1/3*pi*(9x^2)^2*h

= 27pi*x^4*h

x^4*pi*y^2 = 27pi*x^4*h

h = y^2 / 27

Answer:

4 inches

Step-by-step explanation:

The volume of the cylinder is:

V = π r² h

V = π (2)² (3)

V = 12π

The cone has the same volume, so its height is:

V = ⅓ π r² h

12π = ⅓ π (3)² h

12π = 3π h

h = 4

The height of the cone is 4 inches.

Answer:

Divide 85 by 9.24

Step-by-step explanation:

Answer:

x=-5.4

Step-by-step explanation:

0.6+0.2x=-0.48

0.2x=-0.48-0.6

0.2x=-1.08

x=-1.08/0.2

x=-5.4

Answer:

answer should be x = 18.

Step-by-step explanation:

25 = x + 7

we can also write it as

x + 7 = 25

as we see 7 is positive(+) on LHS( left hand side) so if we move it to RHS( right hand side) the sign will change so the equation will be:

x = 25 - 7

now just simplify it:

x = 18.

Volume of water will it take to fill in the well is 4710 cubic feet

Given that a cylindrical well has a radius of 10 feet

Height of cylindrical well = 15 feet

To find: volume of water will it take to fill in the well

Since, the well is in the form of cylinder, This means that we need to find the volume of cylindrical well

The volume of cylinder is given as:

[tex]\text { Volume of water in the well }=\pi r^{2} h[/tex]

Where "r" is the radius and "h" is the height of cylinder

Substituting the given values we get,

[tex]\begin{array}{l}{\text { Volume of water in the well }=(3.14) \times(10)^{2} \times(15)} \\\\ {=(3.14) \times(1500)=4710}\end{array}[/tex]

[tex]\text { Volume of water in the well }=4710 \text { feet }^{3}[/tex]

Hence, the amount of water that can be stored in the well is 4710 cubic feet

Final answer:

The volume of water that will fill the cylindrical well with a radius of 10 feet and height of 15 feet is 1500π cubic feet.

Explanation:

To calculate the volume of water that will fill the cylindrical well, we need to use the formula: V = πr²h. Given that the radius is 10 feet and the height is 15 feet, we can substitute these values into the formula as follows:

V = π(10)^2(15) = 1500π cubic feet.

Therefore, it will take 1500π cubic feet of water to fill the well.

Answer:

The solution for the given system of equations is ( 4,-3).

Step-by-step explanation:

Here, the given set of equations is:

7 x - 3 y = 37    ....  (1)

14 x + 11 y = 23   .... (2)

Now, we solve this equation by ELIMINATION METHOD,

Multiply the first given equation with ( -2), we get:

(-2) [7 x - 3 y = 37 ] ⇒   -14 x + 6 y = -74  .... (3)

Adding equation (2) and (3), we get:

14 x + 11 y  +   -14 x + 6 y  = 23 -74

or, 17 y = - 51

or, y = -51/17 = 3

⇒ y = -3

Now, out the value of y in the given second equation,we get:

14 x + 11 (-3)  = 23

or, 14 x  = 23 + 33 = 56

or, x =  56/14 =  4

⇒ x = 4

Hence, the solution for the given system of equations is ( 4,-3).

The total number of chairs there are in the theater and balcony is; 3027 chairs.

According to the question;

In essence, The number of chairs in the theater is;

Additionally, there are 102 chairs in the balcony;

In essence, the total number of chairs is;

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Final answer:

To find the total number of chairs in the theater, multiply the number of rows by chairs per row and add the chairs in the balcony, resulting in approximately 3027 chairs.

Explanation:

To calculate how many chairs there are in total, we need to add the number of chairs in the rows to the number of chairs in the balcony.

First, multiply the number of rows by the number of chairs per row to find the total number of chairs in the rows: 325 rows × 9 chairs per row = 2925 chairs.

Then, add the number of chairs in the balcony to this total: 2925 chairs + 102 chairs in the balcony = 3027 chairs. So, there are approximately 3027 chairs in the theater.

Answer:

slope of a line perpendicular to the line -3x + 6y = -15 is -2

Step-by-step explanation:

-3x + 6y = 15

solve for y,

y = 1/2 x + 15/6

slope of a line perpendicular is the "negative reciprocal" of the slope of the original line, thus

y = -2 x + b

Answer:

[tex]W_{f}  = 90 - 1.2w[/tex]

Step-by-step explanation:

I want to cut back on my calorie intake so that I can lose weight.

I plan to lose 1.2 kg a week from my current weigh 90 kg until I reach my goal.

Therefore, I can model my weight loss for the next several weeks by the equation  

[tex]W_{f}  = 90 - 1.2w[/tex]  

where [tex]W_{f}[/tex] is my final weight after w weeks of treatment. (Answer)

To model your weight loss, you can create a linear equation using your current weight as the starting point, and representing your weekly weight loss as a negative rate of change. The equation W(t) = 90 - 1.2t will allow you to predict your future weight based on this rate of weight loss.

To develop an equation to model your weight loss, you need to translate the information about your weight loss goals into mathematical terms. You mentioned that your current weight is 90 kilograms and you plan to lose 1.2 kilograms per week.

Imagining that each week is a step forward in time, we can say time is represented by the variable 't' in weeks. Likewise, your weight, which will change as time increases, can be represented by 'w' in kilograms.

Giving weight loss a negative sign (since you are losing, not gaining weight), the amount of weight you will lose per week is -1.2 kilograms. When we start, at time t = 0, your weight is 90 kilograms. So we could represent your weight as a function of time with the equation W(t) = 90 - 1.2t.

In this equation, simply substitute 't' for the number of weeks to predict your weight loss. For example, if you want to find out your weight after 3 weeks, you would calculate W(3) = 90 - 1.2 * 3 = 86.4 kilograms. This is a simplified model and actual weight loss may vary due to factors like metabolic rate, type of food ingested and the amount of calories burned per day.

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Answer:

7

Step-by-step explanation:

Start with $30.

Subtract $5 for the admission: $30 - $5 = $25.

Now he has $25 to spend on rides. Each ride costs $3.5, so we divide $25 by $3.50.

$25/$3.50 = 7.14

Since the number of rides must be a whole number, he can go on 7 rides.

by the time Paul got into the fair he would have already paid admission with his 30 bucks meaning that he would have 25 dollars left for rides and 25 divided by 3.50 is 7.blah blah blah the rest dosent matter so Paul could go on a maximum of 7 rides

Answer:

-10y+42.

Step-by-step explanation:

Distribute.

8y-18y+42

-10y+42

:D I hope this helped you!

Answer:

-10y + 42 would be the answer

Answer:

y=3.72

Step-by-step explanation:

y/2+3.2=5.06

y/2=5.06-3.2

y/2=1.86

y=1.86*2

y=3.72

Answer:

y= 3.72

Step-by-step explanation:

reverse the operations

5.06-3.2= 1.86

1.86*2= 3.72

y=3.72

Answer:

I believe the answer is 48

Step-by-step explanation:

Answer:

42/100

The drawings will help

Answer:

42/100

Step-by-step explanation:

Just looking at the fraction, you could guess that one of the fractions is larger. So my guess would be the first one, but I'm guessing which really is only a guess. I like to guess at things like this; it's a little like playing monopoly. Let's find out what the answer really is. So get out your calculator.

29/71: 29 ÷ 71 = 0.4085

42/100: 42/100 = 0.4200

Well if you guessed the second one you are a better guesser than I am

42/100  is larger that 29/71

Yeah, I think it is C...

I don't really have an explanation though.

If I'm wrong, correct me. Hope I helped! ☺☼

Answer:

Option D is the nearest answer.

Elizabeth invested = $45,714

Step-by-step explanation:

Given that:

Total amount = $80,000

Ratio given = 3:4

As the total is divided into 7 parts (3+4) so,

Each part equals = 80,000/7

Each part equals = 11,428.57

Now steive invested = 11,428.57 * 3 = $34,286

Elizabeth invested= 11,428.57*4 = $45,714

i hope it will help you

Answer: 3/100

Step-by-step explanation: Using the place value chart, we can see that 0.03 means 3 hundredths so 0.03 can be written as the fraction 3/100.

3/100 is a proper fraction so it can't be changed to a mixed number.

Answer:

5/100• X = 3.5

X=3.5÷5/100

X=70

The answer is 5% x 70 = 3.5

To solve for the blank in the equation 5% x __ = 3.5, we need to find a number that, when multiplied by 5%, equals 3.5.

First, express 5% as a decimal: 5% = 0.05.

Set up the equation:

0.05 x x = 3.5

Next, solve for x by dividing both sides by 0.05:

x = 3.5 / 0.05

x = 70

Thus, the blank should be filled with 70.

Answer:

C

Step-by-step explanation:

Inverse of function(x,y) is equal to (y,x)

Answer:

c = 10 , d = 26

Step-by-step explanation:

In the rectangular prism, we know the fact that the three faces are mutually perpendicular to each other. So, it has a rectangular base.

Given, the length and breadth of the rectangle are 8 and 6 units, and the diagonal is c.

Since it is a rectangle, length , breadth and diagonal from a right angled triangle.

So we have, c² = 6² + 8² = 36 + 64 = 100

⇒           c = 10 units

For the side face:

Length = 24 units.

As we can see, the edge of the side face is perpendicular to the base of the prism. Which means, any line on the base of the prism is perpendicular to the 24units side edge.

So we can say that , the diagonal of the rectangular base of the prism (c) is perpendicular to the 24 units side face edge.

Hence, 24 , d and c (which is 10units) form a right angled triangle

From pythagoras theorem:

   d² = 24² + 10² = 576 + 100 = 676

⇒ d = 26 units

First find slope.

slope=change in y/change in x (y2-y1/x2-x1)

slope=4-3/-2-(-4)=1/2

Now we need to find the x intercept.

y=mx+b

3=1/2(-4)+b

b=5

So the equation is y=1/2x+5.

Answer:

4

Step-by-step explanation:

The square of 4 is 16, or 4 times 4.

When you subtract 4 from it, it becomes 3 times 4.

Therefore, 4 is the answer.

Answer:

The positive solution is 4.

Step-by-step explanation:

x^2-4=3x

x^2-3x-4=0

factor out the trinomial

(x-4)(x+1)=0

zero property,

x-4=0, x+1=0

x=0+4=4

x=0-1=-1

-------------

x=4, -1

Answer:

A-1 Rentals

hopefully that helps!!

Answer:

rent all

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sqrt[3]{b^{27}}=\sqrt[3]{b^{(9)(3)}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt[3]{(b^9)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=b^9[/tex]

Answer:

b^9 :)

Step-by-step explanation:

Answer:

A² - B² = 0 (Proved).

Step-by-step explanation:

Given that  

[tex]A = \frac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta + 1}[/tex]

⇒[tex]A = \frac{\csc \theta + \cot \theta - (\csc^{2} \theta - \cot^{2} \theta)}{\cot \theta - \csc \theta + 1}[/tex]

{Since, we know the identity as [tex]1 = \csc^{2} \theta - \cot^{2} \theta[/tex]}

⇒ [tex]A = \frac{\csc \theta + \cot \theta - (\csc \theta + \cot \theta)\times (\csc \theta - \cot \theta)}{\cot \theta - \csc \theta + 1}[/tex]

⇒ [tex]A = \frac{(\csc \theta + \cot \theta) (\cot \theta - \csc \theta + 1)}{\cot \theta - \csc \theta + 1}[/tex]

⇒ [tex]A = \csc \theta + \cot \theta[/tex]

Again, given that [tex]B = \csc \theta + \cot \theta[/tex]

So, A = B . ⇒ (A - B) = 0.

Hence, A² - B² = (A + B)(A - B) = 0 (Proved)

Answer:

-3

Step-by-step explanation:

We must do the subtraction -3 + 2 BEFORE anything else, because any operations inside parenthesis always take first priority.

We end up with:

-3(-1) - 6.  

We must multiply before addiing or subtracting.  Therefore, multiply (-3)(-1), obtaining 3 and complete result 3 - 6.

Finally do that subtraction; the result is -3.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\p\%=\dfrac{p}{100}\to16.5\%=\dfrac{16.5}{100}=\dfrac{16.5\cdot10}{100\cdot10}=\dfrac{165}{1000}=\dfrac{33}{200}\\\\16.5\%\ of\ 33=\dfrac{33}{200}\cdot33=\dfrac{1089}{200}=5.445[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}100\%&-&33\\\\16.5\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\100x=(16.5)(33)\\\\100x=544.5\qquad\text{divide both sides by 100}\\\\x=\dfrac{544.5}{100}\\\\x=5.445[/tex]