Solve for x using trigonometry. Round to the nearest tenth. (hint: One decimal place) 17 x 19

Answer:

c for the first one and a for the second

(a) To find the area of the kitchen floor, we just have to multiply

(b) To find the number of tiles needed, we have to find the area of each tile, which is

Then, we divide the total area of the kitchen floor by the area of each tile.

Hence, David will need 80 tiles to cover the floor.

In Part (b) of this problem, we want to determine which function is the bes representation for the graph and table.

We are given:

To determine which function matches best, we can look at the parent function of a linear, logarithmic, and exponential function.

(see comparisons below):

Notice that our graph most closely resembles that of the exponential function. Therefore, the best model for the data would be an exponential function.

For them, let x = number of children of the party and

A=Adventure Plext cost

B= Bright Child cost

C= Chuck E Cheese cost

So,

Then, graphing each equation of the system of equations

Now, for determine the break even point for Chuck E Cheese and Bright Child you have

That is, the break even point for Chuck E Cheese and Bright Child occurs when x = 60 children.

For determine the break even point for Adventure Plex and Bright Child you have

That is, the break even point for Adventure Plex and Bright Child occurs when x = 40 children.

Finally, For determine the break even point for Adventure Plex y Chuck E Cheese you have

That is, the break even point for Adventure Plex and Chuck E Cheese occurs when x = 50 children.

The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.

Given,

Belinda wants to invest $1,000.

The Table is:
Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331

Now, According to the question:

When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.

For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:

1690/1300 = 1.3 = 1300/1000

Part A :
(Option 1) can be represented by exponential function.

(Option 2) can be represented by a linear function.

Part B:

For Option 1:

To find the value of the investment f(n), in dollars, after n years.

The generic form of an exponential function is ...

f(n) = a·b^n

Now, Amount after 1 year = 1100

Principle (P) is = 1000

Using the formula :

A = P[tex](1+r)^n[/tex]

1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]

1.10 = 1 + r

r = 0.10

Amount after t years can be given by :

A = 1000(1.10)^t

For Option 2,

The generic form of an exponential function is ...

f(n) = a·n + b

Rate of change (m) = (1100 - 1000) / 1 = 100

Amount after t years can be given by

A = 1000 + 100 x t .

Part C:

Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727

Investment in (2): $3000

Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.

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Ready

Points A = (-5, -2) C = (7, 2) E = (1, 0)

1.- Find the slope

m = (y2 - y1) / (x2 - x1)

m = (2 + 2) / (7 + 5)

m = 4/ 12

m = 1/3

2.- Find the equation of the line

y - y1 = m(x - x1)

y + 2 = 1/3(x + 5)

y + 2 = 1/3x + 5/3

y = 1/3x + 5/3 - 2

y = 1/3 x + 5/3 - 6/3

This is the equation:

y = 1/3 x - 1/3

my pleausre

Given: A figure is given.

Required: to determine the expression for the area of the figure. Also, determine the area when x=2.

Explanation: The area of the figure can be determined by dividing the figure as shown below-

Now, DEFG and ABCG represent rectangles. The dimensions of the rectangle DEFG is (2x+4) by (7x+2), and of the rectangle, ABCG is (4x+2) by BC where BC is-

Hence, the expression for the area is-

Further solving-

Substituting x=2 as follows-

Final Answer: The expression for the area of the figure is-

The area when x=2 is 158 sq units.

Question: Determine if the proportion is true 1/6= 3/18

Solution:

we have the following equation that it may be true or false:

But, the above equation is equivalent to:

But 1x 18 = 18, and 3x 6 = 18 so the above equation is equivalent to

The above equality always is true, so we can conclude that the proportion is true​.

The rational number is -91/100 or -0.91.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Given:

We have to find the rational number between -1/3 and -1/2

Tale LCM for 3 and 2 = 6

-1/3 x 2/2 and -1/2 x 3/3

-2/6 and -3/6

Now, multiply 10

-2/6 x 10/10  and -3/6 x 10/10

-20/60 and -30/60.

Hence, the rational number is -21/60.

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a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

We have been given a right circular conical tank.

h = 4 m and r = 1.20 m

We know that the formula for the volume of cone is,

V = πr²h/3

The volume of the tank would be,

V = (π × r² × h)/3

V = (π × 1.20² × 4)/3

V = 18.09/3

V = 6.03 m³

Let h1 be the height of liquid level in the tank and  V1 be the volume of the liquid in the tank.

h1 = 3.70 m

V1 = (π × r² × h1)/3

V1 = (π × 1.20² × 3.70)/3

V1 = 16.74 / 3

V1 = 5.58 m³

V1 = 5580 liters

The amount of liquid need to added to fill the tank 100% of capacity.

V2 = V - V1

V2 = 6.03 m³ - 5.58 m³

V2 = 0.45 m³

V2 = 450 liters

Therefore, a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

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Let:

Mp = Marked price = $310

r = Rate of discount = 20% = 0.2

D = Discount

Sp = Sale price

The discount will be given by:

And the sale price will be:

we have the following:

The correct answer is  A. 90 - d

Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.

And to find the other acute angle we use 90° - d.

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Given,

The speed of first plane is 450 miles per hour.

The speed of second plane is 550 miles per hour.

The total distance between plane required is 4000 miles.

As, the planes are moving in opposite direction, then distance cover by both is must be added.

Number of distance both plane becomes apart in one hour is,

The Number of hours required to complete 4000 miles is,

Hence, it will take 4 hours before they are 4,000 miles apart.

So, to solve the system:

To solve it, we could substitute the first equation in the second one and then solve for x:

We could solve the previous quadratic by factoring:

To find the values of y, just replace each vaue of x:

Therefore, the solutions of the system are

(x,y) = (-3,-1)

(x,y)=(1,3)

ANSWER;

Converse; Exterior alternate angles are equal

EXPLANATION;

Here, we want to get the value of x given that the lines l and m are parallel

From the diagram given, we can see that;

The reason for this is that they are a pair of exterior alternate angles

Mathematically, exterior alternate angles are equal

From here, we can proceed to solve for the value of x;

Answer: nonic

Step-by-step explanation:

1) In order to determine the perimeter of the figure, you take into account tht the perimeter is the sum of the values of all sides of a figure.

In this case, the sides of the triangle are s-4, s-8, and 6 respectivelly.

The perimer is the sum of the values of the sides, then, you have:

P = (s-4)+(s-8)+(6) "P is the perimeters"

= s-4+s-8+6 "sum simmilar terms, terms with variables and idependet term"

= 2s-6

Hence, the perimeter of the triangle is 2s - 6

2) The perimeter of a rectangle is P = 2w + 2l, in order to solve for w you proceed as follow:

P = 2w + 2l "subtract 2l both sides"

P - 2l = 2w "divide by 2 both sides"

(P - 2l)/2 = w

Hence, w = (P - 2l)/2

A logarithmic function is expressed as

y = a + blnx

We would substitute corresponding values of x and y into the function. This will give us two equations. We would solve the equations for a and b. We have

From the table, when x = 1, y = 60

Thus,

60 = a + b * ln1

60 = a + b * 0

60 = a

when x = 2, y = 54

Thus,

54 = a + bln2

54 = a + 0.693b

Substituting a = 60 into 54 = a + 0.693b, we have

54 = 60 + 0.693b

0.693b = 54 - 60 = - 6

b = - 6/0.693

b = - 8.65

The function would be

f(x) = 60 - 8.65lnx

The row echelon form of the matrix is presented as follows;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

The conditions of a matrix in the row echelon form are as follows;

Dividing Row 1 by -3 gives:

[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Subtracting Row 1 from Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]

Adding Row 2 to Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]

Dividing Row 2 by -2, and Row 3 by 18 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The above matrix is in the row echelon form

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Answer:

5 units

Explanation:

Given the points:

We use the distance formula below:

Substitute the given values:

The distance between the two points is 5 units.

Given the expression

Given:

80 feet is the final answer.

given data:

the amount needed to pay the downpayment of the car = $5280.

original financial plan = $220 per month.

The amount kara saved after 1 year = $2300.

the balance amount she needed to save

now, divide the balance amount by 12, because 1 year =12 months.

Thus, kara needs to save 248 dollors each month in order to have 5280 dollors after a year.

Answer:

$5304.25.

Explanation:

The simple interest formula is given by

where

A = future value

P = princple amount

r = interest rate /100

t = time interval.

Now in our case

A = unknown

P = $4900

r = 5.5 / 100

t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )

Putting the above values into the simple interest rate formula gives

which simplifies to give

Hence, the future value is $5304.25.

Solution:

Let t be the number of hours Mai works as a tutor.

Given that She earns $12 a hour as a tutor, this implies that for t number of hours, she will earn

For the month, she worked a combined total of 85 hours. This implies that

Her total eranings for the month is expressed as

Recall that she earnes $7 an hour while working as a waitress.

Thus, we have her combined total amount in dollars expressed as

Hence, the expression is

3.

We know that Hobby Land sells art supplies two different ways.

We can represent the situation with a system of equations

Where x is the cost of one easel and y represents the cost of one paint set.

Now, we must solve the system of equations.

We can multiply equation (1) by -4

Then, we can add (3) + (2)

Now, we can solve the equation for y

Finally, to find x we can replace the value of y in the equation (1)

So, the cost of one easel is $64.

Solution as either an ordered pair:

- (64, 75).

Four more than the product of a number and 8 is equal to

Let

x -----> the number

we have that

the algebraic expression is equal to

the product of a number and 8 ------> 8x

so

Four more than the product of a number and 8 is equal to 3

8x+4=3

solve for x

8x=3-4

8x=-1

x=-1/3

therefore

the number is -1/3

The area, in square feet, of the portion of the garden that excludes the border is 40.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We have been given that Angie added a stone border of 2 feet in width on all sides of her garden making her harder 12 by 6 feet.

Length = 12 ft

Width = 6 ft

The dimension of the garden  that excludes the border of 2 feet are;

Length = 12 ft- 2 = 10 ft

Width = 6 ft - 2= 4 ft

Thus, Area  =  length × Width

Area = 10 x 4

Area = 40 square feet

Hence, the area, in square feet, of the portion of the garden that excludes the border is 40.

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GIVEN

The function of the object's velocity is given as follows:

Also given:

SOLUTION

To get the position's function (s(t)), the velocity function needs to be integrated:

Therefore:

Recall that s(0) = 0. Therefore:

Hence, the position function is:

The THIRD OPTION is correct.