Solve each trigonometric function IN THE INTERVAL [0, 2).

sin(x) + 1 = cos(x)

The width of the arch at floor level is 18 inches.

Substitute x = 0 into the equation.
y = -1/9(0+18)(0-18)

Solve for y.
y = -1/9(-18)(18)
y = 18

Therefore, the width of the arch at floor level is 18 inches.

A linear system can be algebraically solved using the substitution approach. One y-value is substituted for another in the substitution procedure. Finding the value of the x-variable in terms of the y-variable is the method's most straightforward step.

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The graph of f(t) crosses the y-axis at t = 0, which represents the initial temperature of the ice cream (81°C below room temperature).

The graph of f(t) crosses the y-axis at y=81, which represents the initial temperature of the ice cream, 81°C below room temperature. This is the starting point of the graph, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. As time passes, the temperature of the ice cream decreases, and the graph of f(t) illustrates this change.

The y-intercept of a graph measures the initial value of the function. In this case, the initial temperature of the ice cream is 81°C below room temperature. As the time passes, the temperature of the ice cream decreases at a rate of 0.83°C per minute. This rate of decrease is represented by the slope of the graph, which is 0.83.

The point where the graph of f(t) crosses the y-axis illustrates the initial temperature of the ice cream, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. This is a helpful visual representation of the rate at which the temperature of the ice cream is decreasing. The graph of f(t) is a useful tool for understanding how the temperature of the ice cream changes over time.

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The true statements are:

A. KL=15

B. JL bisects IK

D. JL is the perpendicular bisector of IK

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign, ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

Given:

We have a triangle IJK.

m∠IJL=0.5 m∠JIK.

Side IJ ≅ side JK.

JL ⊥ IK.

It bisects the base.

That means,

JL bisects IK and JL is the perpendicular bisector of IK.

So, IL = LK.

3x = 2x + 5

x = 5

KL=15.

Therefore, A, B and D are the true statements.

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Answer:

14S -93

Step-by-step explanation:

(4s+7 -2S) +4 (3s-5^2)

= 2S +7 +12S -4*25

=14S -93

Answer:

6 Tables

Step-by-step explanation:

48 tables divided by 8 paintbrushes equals 6 tables.

The difference between the water levels for the high and low tide was 3. 6 feet. the equation to find the water level at high tide x = y + 3.6, where  High Tide Water Level = x and  Low Tide Water Level = y.

In simple form it will be  High Tide Water Level = Low Tide Water Level + 3.6. To explain this equation, the water level at high tide is equal to the water level at low tide plus 3.6 feet. The variable 'x' represents the water level at high tide, while the variable 'y' represents the water level at low tide. By adding 3.6 feet to the water level at low tide, we can find the water level at high tide.  

For example, if the water level at low tide is 4 feet, the water level at high tide would be 4 + 3.6 = 7.6 feet. To find the water level at high tide for any given low tide water level, one can simply add 3.6 feet to the known low tide water level. This equation can be used to accurately calculate the water level at high tide for any given low tide water level.

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The correct answer is 5/2. The median trapezoid is the line segment that bisects the area of the trapezoid and has its end points on the 2 bases of the trapezoid.

The median length is √( (3/2)^2 + (4/2)^2 ) = √(9/4 + 16/4) = √(25/4) = 5/2. So, the length of the median of the trapezoid is 5/2.

Since the diagonals of a median trapezoid bisect each other, the median of the trapezoid is the line segment that connects the midpoints of the diagonals. To find the median length, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the 2 points. In this case, the median length is the square root of the sum of the squares of 1/2 length of the diagonals.

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The length of the median of the trapezoid will be 5/2 units.

Given that the median trapezoid is the line segment that divides the trapezoid's area and has its ends on its two bases,

The median length will be:

√( (3/2)^2 + (4/2)^2 )

= √(9/4 + 16/4)

= √(25/4)

= 5/ units

So, the length of the median of the trapezoid is 5/2.

The median of a median trapezoid is the line segment that links the midpoints of the diagonals since the diagonals of a median trapezoid bisect one another. We may use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points, to get the length of the median. The median length in this instance is equal to the square root of the sum of the squares of the diagonals' half-lengths.

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Answer: To find the price of the car in May, we can use the formula:

New price = Original price - (Original price x Discount rate)

In this case, the original price is $22,800, and the discount rate is 5%, which can be written as 0.05.

So, the new price in May is:

New price = 22700 - (22700 x 0.05)

New price = 22700 - 1135

New price = $21,565

So, the price of the car in May was $21,565.

To find the percentage of the price of the car in May as compared to the price of the car in April, we can use the formula:

(New price / Original price) x 100

In this case, the new price is $21,565 and the original price is $22,800

(21565 / 22700) x 100 = 0.95 x 100 = 95%

Therefore, in May, the price of the car was 95% as compared to the price of the car in April.

Step-by-step explanation:

In order to replace the value in the explicit expression for h, one must evaluate a function h(x) for a particular value of the independent variable x.  h(-3)=30, h(0)=0, h(4)=-40

h(x)=-10x

Let's determine the values below:

h(0)= -10 * (0) = 0 and h(4)= -10 * (4) = -40, respectively.

h(-3)=30, h(0)=0, h(4)=-40.

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Lela had the highest score.

Now, According to the question:

A skewed distribution is neither symmetric nor normal because the data values trail off more sharply on one side than on the other. In business, you often find skewness in data sets that represent sizes using positive numbers.

In a negatively skewed distribution, higher values are more frequent than lower values causing the distribution to present a longer left-tail. This implies in a median higher than the mean and in a mode higher than the median:

mean < median < mode.

Therefore, since Lela scored at the mode, Lela had the highest score.

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All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.

2n8, 5n10, n2, 4n-14

2n8 : This expression is even for all values of n because the coefficient of n is an even number (2).

5n10 : This expression is even for all values of n because the coefficient of n is an even number (5).

2n3 : This expression is even for all values of n because the coefficient of n is an even number (2).

n2 : This expression is even for all values of n because the coefficient of n is an even number (1).

4n-14 : This expression is even for all values of n because the coefficient of n is an even number (4).

All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.

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The total number of four-digit parity-monotonic integers is 432*1 = 24.

We can solve this problem by counting the number of parity-monotonic integers in each of the four digits individually and then multiplying the counts together.

By counting the possible values of [tex]$a_1$[/tex], [tex]$a_2$[/tex], [tex]$a_3$[/tex] and [tex]$a_4$[/tex] independently, we have:

Thus, the total number of four-digit parity-monotonic integers is 432*1 = 24.

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Answer:

  D.  0.391

Step-by-step explanation:

You want the approximate solution to f(x) = x² -3x +1 = 0 on the interval [0, 1] using 5 iterations of the Bisection Method.

The Bisection Method makes one iteration by finding the function value at the midpoint of the interval. The midpoint replaces the end of the interval whose function value has the same sign. At the end of one iteration, the midpoint of the halved interval is calculated.

Start:

  f(0) = 1, f(1) = -1. Interval: [0, 1]; midpoint: 1/2

First iteration:

  f(1/2) < 0. Interval: [0, 1/2]; midpoint: 1/4

Second iteration:

  f(1/4) > 0. Interval: [1/4, 1/2]; midpoint: 3/8

Third iteration:

  f(3/8) > 0. Interval: [3/8, 1/2]; midpoint: 7/16

Fourth iteration:

  f(7/16) < 0. Interval: [3/8, 7/16]; midpoint: 13/32

Fifth iteration:

  f(13/32) < 0. Interval: [3/8, 13/32]; midpoint: 25/64

The approximate solution after 5 iterations is x ≈ 25/64 ≈ 0.391.

__

Additional comments

The approximate solution in the interval to full calculator precision is 0.38196601125. The exact solution is 1.5-√1.25.

You will notice that the function values for the ends of the interval [0, 1] are [positive, negative]. So, when the function value at the midpoint is negative, that point replaces the right end of the interval.

Of course, the midpoint is the average of the interval end values.

On average, it takes about 3.3 iterations to improve the accuracy of the solution by 1 decimal place.

A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly has coordinate (1.7, 0.6). The distance of the fly from the corner of the room is 1.8 meters.

Suppose we have a point having coordinate (x,y). Then the horizontal axes, vertical axis,  and the distance from the origin form a right triangle which its base is x and y.

Hence, we can find the distance of the point (x,y) from the origin using the Pythagorean Theorem.

In this case, the origin is a certain corner of the room. The coordinate of the fly is (1.7, 0.6) meters.

Using the Pythagorean Theorem:

distance = sqrt (1.7² + 0.6²)

distance = sqrt (2.89 + 0.36)

distance = sqrt (3.25)

distance = 1.8 meters

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The decimal 8. 33 written as a fraction is 8 3/10

A fraction can be defined as the part of a whole number, variable, element,

The several types of fractions are;

Examples of mixed fractions: 2 4/5, 7 1/2

Examples of simple fractions: 1/3, 1/4

Examples of improper fractions: 6/4, 7/5

Example of proper fractions: 2/3, 4/5

From the information given, we have that;

8.33

This is represented as;

8 3/10

Hence. the value is 8 3/10

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From the given example we can say that , the given expression is in the form of quotient of a powers property.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

3^9 / 3^4

= 3^(9-4)

= 3^(5)

So,

if a^m / a^n = a^(m-n)

Its in the form of quotient of powers property.

And from above we can say that, The given expression also in the form of quotient of powers property.

Hence, From the given example we can say that , the given expression is in the form of quotient of a powers property.

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Coordinates of the vertices of the octagon after dilation by scale factor 3 are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).

Original coordinates of the vertices of an octagon are :

(-4, 2), (-2,5), (1,5), (3, 2), (3, -6), (1, -3), (-2, -3), and (4, -6).

Scale factor is equal to 3

Figure transformed using dilation of scale factor of 3 with center of dilation at the origin.

Coordinates of the new vertices after dilation of the octagon.

(-4×3, 2×3) = ( -12, 6)

(-2 ×3,5×3) = ( -6 , 15)

(1 ×3,5×3) = ( 3 ,15)

(3×3, 2×3) = ( 9,6)

(3×3, -6×3) = ( 9, -18)

(1 ×3, -3×3) = ( 3 , -9)

(-2×3, -3×3) = ( -6 , -9)

(4×3, -6×3) = (12, -18)

Therefore, the new coordinates of the vertices after dilation are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).

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Chris owes $35 in interest to the back next month.

We know that a credit card's interest rate is nothing but the price one  pay for borrowing money. This is called the annual percentage rate (APR).

The Interest paid is calculated by the formula:

I = PTR ÷ 100

where P = Principal amount ,

R= rate of interest in percentage ,

and T= period.

Here, P = $2800,

R = 15%

T=  1 year

Using above formula,

I = (2800 x 15 x 1) ÷ 100

I = 420.

He will pay an interest of 420 ÷ 12= $35 per month.

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If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

What is Quadratic Equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0 .

Nature of Roots depending upon Discriminant

in step with the value of discriminant, we shall discuss the subsequent cases about the character of roots.

Case 1: D = 0

If the discriminant is same to 0 (b2 – 4ac = zero), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = zero, are real and equal. In this case, the roots are x = -b/2a. The graph of the equation touches the X axis at a single point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), a, b, c are actual numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are actual and unequal. The graph of the equation touches the X-axis at two unique points.

Case 3: D < 0

If the discriminant is less than 0 (b2 – 4ac < 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are imaginary and unequal. The roots exist in conjugate pairs. The graph of the equation does not touch the X-axis.

Case 4: D > zero and perfect square

If D > zero and an excellent square, then the roots of the quadratic equation are actual, unequal and rational.

Case five: D > 0 and now not an excellent square

If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

Therefore, If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

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The sum of the given expression will be 2a+7b+-d.

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now

Given expressions are 1.5b-2c+3-d 2.a+2b-c+d 3.2-d+3c+a

By adding these

=a+a+5b+2b-2c-c+3c-d+d-d

=2a+7b-d

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Answer: +8

Step-by-step explanation:

yes, it is going to be a positive product, since two negative signs multiply to give a positive sign.

⇒(4)(-0.5)(8)(-2/4)

⇒+8 ..Answer

hope that helps...

According to the elimination method, the solution of the system of equation has infinite number of solutions.

In math the term elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Here we know that the equations are

=> 6x - 2y = 8 ---------------(1)

=> -3x + y = -4 ------------------(2)

when we simplify the equation (1) by dividing the terms by 2, then we get

=> 3x - y = 4

Now, we have to add the two equation then we get the result as,

=> (-3x + 3x) +( -y + y) = (-4 + 4)

=> 0 + 0 = 0

Hence the system has an infinite number of solutions.

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The result of a histogram of the given data is 0.8.

There are a few steps to use a TI-83, TI-83 plus, or TI-84 calculator is used to create the histogram.

1. First, the process is to press the STAT key and then press ENTER.

2. Enter the data into column L1.

3. In the third step with all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu.

4. After that press ENTER and make sure that Plot1 is set to On.

5. Use the directional keys to navigate to the Type selector, move the selection to the third type in the top row, and press ENTER.

6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1.

7. Finally, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is finished, the correct histogram will display on the calculator.

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Answer:

15

Step-by-step explanation:

Given the expression:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5}[/tex]

We can apply the law of exponent of:

[tex]\displaystyle{\left(a^m\right)^n = a^{mn}}[/tex]

Therefore, we will have:

[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{\frac{5}{5}}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{1}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15}[/tex]

Hence, the value of expression is 15.

The 67th term of the arithmetic sequence -17,-23,-29 is -413.

What is the arithmetic sequence?

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same. This difference is called the common difference, and it can be represented by the variable d.

Given the sequence -17,-23,-29, we can see that the common difference is d = -23 - (-17) = -6

The nth term of an arithmetic sequence can be found using the formula:

a_n = a_1 + (n-1)d

where a_1 is the first term of the sequence, n is the term number and d is a common difference.

For the 67th term, a_1 = -17, n = 67 and d = -6

So the 67th term is:

a_67 = -17 + (67-1) * -6 = -17 + 66 * -6 = -17 - 396 = -413

Hence, the 67th term of the arithmetic sequence -17,-23,-29 is -413.

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Answer: -413

Step-by-step explanation:

Both equations are equivalent, which means that the two plants always have the same height.

We know that the height in inches for Kylie's plant is represented by the

equation y = 12x, where x is the time in months.

And the height of Glen's plant is represented by the equation 2y = 24x

Notice that if we take the second equation and we divide both sides by 2, we will get:

2y = 24x

2y/2 = 24x/2

y = 12x

This is the same equation than the one that represents the height of Kylie's plant.

Then the two plantes have the same height always.

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19N force act in upward direction with angle of elevation 28 degrees has horizontal and vertical force is given by 16.78N and 8.92N respectively.

Angle of elevation while thrown a ball upward 'α' = 28 degrees

Force 'F' is equal to 19N.

While throwing a ball force is applied in two possible direction are:

Horizontal direction and Vertical direction.

For horizontal direction :

let 'x' represents the horizontal direction

cosα = x / F

⇒ cos28° = x / 19

⇒ x = 19 cos 28°

⇒ x = 19 × 0.8829

⇒ x = 16.78N

For Vertical direction :

let 'y' represents the vertical direction

sinα = x / F

⇒ sin28° = y / 19

⇒ y = 19 sin 28°

⇒y = 19 × 0.4695

⇒ y = 8.92N

Therefore, the horizontal force and vertical force for the given angle of elevation is equal to 16.78N and 8.92N respectively.

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The probability that the number of first graders who have liked the hot dog is 15

In math the term probability is defined as a number that reflects the chance or likelihood that a particular event will occur

Here we have know that in a survey of 50 first graders, and then 30% said their favorite food is hot dog.

Here we have to find the probability that the number of first graders who have liked the hot dog

As we know that the number of first graders is 50.

And here we also know that 30% of them are liked the hot dog.

Then it can be calculated as,

=> 50 x 30%

=> 50 x 30/100

=> 15.

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