The ________ symbol indicates that some condition must be tested in a flowchart.
Rectangle
Square
Oval
Diamond
Parallelogram

The equation can be used to find the measures of angle LJK is LJK = 180 - (JKL + KLJ) This equation is based on the fact that the measures of the angles in any triangle add up to 180 degrees.

To find the measures of angle LJK, we can use the equation: LJK = 180 - (JKL + KLJ).  to find the measure of any given angle, we must subtract the measures of the other two angles from 180. In this case, we're looking for the measure of angle LJK, so we'll subtract the measures of the other two angles, JKL and KLJ, from 180. This will give us the measure of angle LJK. This equation is useful in finding the measure of any given angle, as long as we know the measures of the other two angles, as it is based on the fact that the measures of the angles in any triangle add up to 180 degrees.

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The measure of ∠5 is 35degree

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given:

In Quadrilateral ABCD, AB||CD

<M2=35

If a transversal line intersects two parallel lines then the alternate interior angles are congruent.

In the given figure In Quadrilateral ABCD, AB||CD<M2=35  .

So,

<5≅<2 (Alternate interior angles)

M<5=M<2

M<5=35degree

Therefore, the angle measure of M<5 will be 35degree

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The exact value of sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ is -0.707.

The right expression is sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰.

We have to find the exact value of sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰.

The angles and sides of a right-angle triangle are measured using these trigonometric values. Cotangent, secant, and cosecant are the other three significant values in addition to sine, cosine, and tangent.

To solve this question we use the formula

sin(A+B) = sinA cosB + cosA sinB

If we compare the given expression by the formula, we get

A = 170⁰ and B = 55⁰

So the exact value of

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = sin(170⁰ + 55⁰)

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = sin(225⁰)

Using the calculator the value of sin(225⁰) = -0.707

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = -0.707

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The exact value of sin 170° cos 55° cos 170° sin 55° is startfraction startroot 3 endroot over 2 endfraction negative.

The exact value of sin 170° cos 55° cos 170° sin 55° can be calculated using the trigonometric identities.

First, the double angle identities for sine and cosine can be used to express the given expression as:

sin 170° cos 55° cos 170° sin 55° = (sin 170°)2 cos 55° (cos 170°)2 sin 55°

Now, applying the double angle identities for sine and cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 + cos 340°) (1 + cos 110°)

Now, using the cosine addition formula, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (2 cos 170° cos 170°)

Now, applying the double angle identity for cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (sin 170°)2)

Now, applying the Pythagorean identity, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (1 - (cos 170°)2))

Now, using the cosine addition formula, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (2 cos 170° cos 170° - 1)

Finally, applying the double angle identity for cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (cos 340°)2)

Now, applying the Pythagorean identity, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (2 startfraction startroot 3 endroot over 2 endfraction)2)

Therefore, the exact value of sin 170° cos 55° cos 170° sin 55° is startfraction startroot 3 endroot over 2 endfraction negative.

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Answer:

10x^2 - 11x -6

Step-by-step explanation:

1/ First, distribute the brackets:

( multiply 5x to the other bracket, then 2 multiply it also to the other bracket)

After the distribution you'll get this:

10x^2 - 15x + 4x - 6

2/ finally, to simplify you'll have to combine the like terms:

( as you can see the only like terms we have are -15x and +4x)

combine them and you'll get:

10x^2 - 11x -6  ( this is the final answer)

The slope of the line is 0

It is important to note that the formula for the equation is expressed as;

y = mx + c

Where;

From the information given, we have the points

(0, 0) (0, 5)

The formula for calculating the slope of  a line is expressed as;

Slope, m = y₂- y1/x₂ - x₁

Substitute the values

Slope, m = 5 - (0)/ 0 - 0

Subtract the values

Slope, m = 5/ 0

Divide the values

Slope, m = 0

Hence, the value is 0

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Answer: Simplified

Step-by-step explanation: The question is already as simplified as it can get.

The first five terms of the given arithmetic sequence is; 36, 30, 24, 18, 12

The general formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

n is number of term

d is common difference

We are given;

First term; a₁ = 36

Formula for nth term of the sequence;

aₙ = aₙ₋₁ - 6

Thus;

Second term; a₂ = a₂₋₁ - 6

a₂ = a₁ - 6

a₂ = 36 - 6

a₂ = 30

Similarly;

Third term; a₃ = 30 - 6

a₃ = 24

Fourth term; a₄ = 24 - 6

a₄ = 18

Fifth term; a₅ = 18 - 6

a₅ = 12

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The side of the right angle triangle marked x have length equal to 7 using the Pythagoras rule

The Pythagoras rule states that in a right-angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

We shall evaluate the length of the side marked x as follows:

25² = x² + 24²

625 = x² + 576

x² = 625 - 576 {collect like terms}

x² = 49 {take square root of both sides}

x = √49

x = 7

Therefore, the length of the side of the right angle triangle marked x is equal to 7 using the Pythagoras rule.

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Answer:

Step-by-step explanation:

positive

Answer:

x-y=4, 3x-5y=-4

Step-by-step explanation:

step (1)

write the equation in the form ax+by=c

step (2)

put the equations below each other

x-y=4....(1)

3x-5y=-4....(2)

Multiply (1) by (-5) then add (1) and (2)

-5x+5y=-20

3x-5y=-4

-2x=-24 then x=12 from (1) y=8

S.S.={(12,8)}

The formula for [tex]R_{N}[/tex] for the function f(x) is [tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex] and the value of [tex]R_{N}[/tex] =  2688.

As per the given data, the given function f(x) is:

f(x) = [tex](8 x)^2[/tex]  on [-1, 5]

Here we have to determine the formula for [tex]R_{N}[/tex]

Let us consider the interval [a, b]

Then the value of a is -1 and the value of b is 5.

[tex]& \Delta x=\frac{b-a}{N}=\frac{5+1}{N}=\frac{6}{N} \\[/tex]

[tex]& x_j=a+\Delta x_j=-1+\frac{6 i}{N} \\[/tex]

Area Using Riemann Sum:

The Riemann sum of a function f(x) over a given interval [a, b] is given by:

[tex]$$S_n=\sum_{k=1}^n f\left(c_k\right) \Delta x$$[/tex]

When the points are chosen randomly, then the sum is called a Riemann sum and will give an approximation for the area of R that is in between the lower and upper sums.

Split the area into vertical slices then use the Riemann sum formula.

[tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex]

[tex]=\sum_{j=1}^N f\left(-1+\frac{6 j}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(-1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& R_N=\sum_{j=1}^N 64\left(1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(1+\frac{36 j^2}{N^2}-\frac{12 J}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =384 \sum_{j=1}^N\left(1+\frac{36 j^2}{N^2}-\frac{12 j}{N}\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(N+\frac{36}{N^2}\left(\frac{N(N+1)(2 N+1)}{6}\right)-\frac{12}{N}\left(\frac{N(N+1)}{2}\right)\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

[tex]& \lim _{V \rightarrow \infty} R_N=384 \lim _{N \rightarrow \infty}\left(-1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

= 384 (1 + 6(2) - 6)

= 384 (7)

= 2688

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Answer:

Step-by-step explanation:

p=12 q=4 r=10

2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

Given that,

We have to find which inequality is true for x=20

The inequality equations are

a. x-5 < 2x-35

b. 2x < x+22

c. x/4 > x-12

d. x+30 >3x

We know that,

We have to substitute x=20 in the inequality equation to check which equation is true.

a. 20-5 < 2(20)-35

15 < 40-35

15< 5

NO, the inequality is not true

b. 2(20) < 20+22

40 < 42

Yes, the inequality is true

c. 20/4 > 20-12

5>8

NO, the inequality is not true

d. 20+30 > 3(20)

50 > 60

NO, the inequality is not true

Therefore, 2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

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1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given, Anton realizes there is a linear relationship between the weight of the pet and the amount of food the pet should be fed.

The slope the slope of the line that represents the relationship is 1/8 cups.

the y-intercept of the line that represents the relationship is 1/4.

The slope is the value that will be multiplied by the weight of the cat  so as to know the amount of food that will be given to the cat.

The y intercept represent the fixed food that should be given to the cat after it has been using.

Hence, 1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

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The payments each month do not cover all interest and no principal. The correct answer would be an option (B).

A credit card trap occurs when the minimum payments required each month do not cover all the interest charges and do not reduce the principal balance. This means that even if the cardholder makes the minimum payments on time, they will still be paying only the interest charges and not reducing the amount of debt. This can result in a cycle of high-interest debt that is difficult to escape from.

Option A is incorrect as it's describing a common way payments work on credit cards.

Option C is not a trap, as it's describing a credit card issuer with a low-interest rate.

Option D is also incorrect, as it's describing a common way payments work on credit cards.

Hence, the correct answer would be an option (B).

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The relationship between angle 1 and 2 is alternate exterior angles.

When parallel lines are cross by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, same side interior angles, alternate exterior angles, vertically opposite angles.

The parallel lines are line m and line l. The parallel lines l and m are cut by a transversal line and the angles formed are angle 1 and 2. This establish an angle relationship.

Therefore, the angle 1 and angle 2 forms an angle relationships.

Hence, the special relationship of angle 1 and 2 are alternate exterior angles.

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Answer:

B

Step-by-step explanation:

Answer:

A)  Functions A and B have the same y-intercept.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Function A is a linear equation in slope-intercept form.

Therefore:

The x-intercept is when y = 0.

[tex]\begin{aligned}\textsf{$x$-intercept of Function A}: \quad -3x+2&=0\\-3x&=-2\\x&=\dfrac{2}{3}\end{aligned}[/tex]

Reading from the table, the x-intercept of Function B is x = 4.

Therefore, the two functions do not have the same x-intercept.

The y-intercept is when x = 0.

We have already determined that the y-intercept of Function A is y = 2.

Reading from the table, the y-intercept of Function B is also y = 2.

Therefore, both functions have the same y-intercept.

A linear function has one independent variable and one dependent variable.  The highest exponent of both variables is one.

Therefore, Function A is a linear function.

In a linear relationship, as one variable increases/decreases the other variable changes at the same rate.

For Function B, every time x increases by 2 units, y decreases by 1 unit.

Therefore, Function B is also a linear function.

We have already determined that the slope of Function A is -3.

[tex]\boxed{\sf Slope=\dfrac{change\:in\:y}{change\:in\:x}}[/tex]

For Function B, every time x increases by 2 units, y decreases by 1 unit for Function B.  Therefore, the slope of Function B is -¹/₂.

As 3 > ¹/₂, the slope of Function A is steeper than the slope of Function B.

The value of B-A of the matrices is:

            [0   5 -10]

B - A =  [-3 -4    7]​

            [-1   0   -6] ​

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

We can find the value of B - A of the matrices by subtracting corresponding values of the element of each matrix. That is:

      [4 -4 5]                        

A =  [3 2 -4]            

       [2 2 5]

       [4 1 -5]

B =  [0 -2 3] ​

       [1   2 -1​] ​

            [4-4  1-(-4)   -5-5]

B - A =  [0-3  -2-2  3-(-4)] ​

            [1-2    2-2     -1-5] ​

            [0   5 -10]

B - A =  [-3 -4    7]​

            [-1   0   -6] ​

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Complete Question

Given the matrices A and B shown below, find B − A .

      [4 -4 5]                        

A =  [3 2 -4]            

       [2 2 5]

       [4 1 -5]

B =  [0 -2 3] ​

       [1   2 -1​] ​

Answer:

32

Step-by-step explanation:

This is the step by step explanation

32×3=96

96÷4=24

Function rules will always be based on the formula y = mx + b.

You can use this formula to set up an equation with the numbers in your current problem.

y  = mx + b

-6 = 2(1) + -8

Hence, the function rule would be expressed as:

y = 2x + (-8)

Answer:

Step-by-step explanation:

Answer:

The shadow cast by the building is of the length 11.8 m.

Step-by-step explanation:

We consider the height of the building as the height of the triangle and the length of the shadow as the base of the triangle, then the distance from the top of the building to the tip of the shadow would be the hypotenuse of the triangle.

Using the Pythagorean theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse, which is 36m, a is the height of the building, which is 34m and b is the base of the triangle, which is the length of the shadow.

So by plugging the given numbers in:

b^2 = c^2 - a^2

b^2 = 36^2 - 34^2

b = √(36^2 - 34^2)

b ≈ 11.8m (if rounded to the nearest tenth)

So the length of the shadow in this scenario is approximately 11.8 m.

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The distance between the two cities located at latitude 19 degrees N, and the other has a latitude 26 degrees S is 5011 km

The distance between the two cities is calculated using the formula

= x/360 * 2 * pi * r

where

r = radius

x = the angle subtended by the distance

From the question we have that

x = 19 degrees N + 26 degrees S

x = 45 degrees

radius of the earth = 6380 km

distance between the points = x/360 * 2 * pi * r

distance between the points = 45/360 * 2 * pi * 6380

distance between the points = 0.125 * 12760 * pi

distance between the points = 5010.84 km

distance between the points = 5011 km

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The statements that complete the blanks are underlined as follows

From the question, we have the following parameters that can be used in our computation:

The graph

The given graph is a quadratic graph

All quadratic graphs are functions

So, the relation is a function

This statement is false,

This is so because one y value points to two different x values, as evident on the graph

As a general rule, the inverse of a quadratic function is not a function

This means that the inverse of the given relation is not a function

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Using ratio, the length of the tree is 1.9m

Ratio is a comparison of two or more related quantities, expressed as a fraction or a proportion. Ratios are used to compare values and to look for relationships between them. For example, if you have five friends and two of them are girls, the ratio of girls to boys is 2:3 (2 out of 5).

We can set up two ratio as a proportion to find the length of the tree.

1.2 / x = 4.2 / 6.5

Cross multiply both sides and solve for x

x = (1.2 * 6.5) / 4.2

x = 1.85m ≅ 1.9m

The height of the tree is 1.9m

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A line segment has two specific endpoints in a line. The length of the line segment is set, that is the distance between two fixed points.

The length here can be measured by metric units such as centimeters (cm), and millimeters (mm), or by conventional units like feet or inches.

A closed line segment contains both endpoints, but an open line segment is exclusive of the two endpoints. A line segment that has just one endpoint is called a half-open line segment.

A line segment has two endpoints. Now if we know the coordinates of the endpoints, then we calculate the length of the line segment by distance formula.

[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

Let a line segment has coordinates (2, –3) and (–1, –2). What is the length of a line segment?

Therefore, by distance formula,

[tex]D = \sqrt{(2 - (-1))^{2} + (-3 -(-2)^{2} }[/tex]

[tex]D = \sqrt{(2 + 1))^{2} + (-3 +2)^{2} }[/tex]

[tex]D = \sqrt{(3)^{2} + (-1)^{2} }[/tex]

[tex]D = \sqrt{10}[/tex] = 3.16

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Funsters inc. , the largest toy company in canada, sells its most popular doll for $35. It has just learned that its leading competitor toysorama is mass producing an excellent copy and plans to flood the market with their $10 doll in 6 weeks. Funsters should increase the supply of its doll now before the other doll hits the market.

1. Addressing Customer Needs

Often business competition motivates brands and businesses to meet customer needs, vying to be more effective than their competitors. This encourages brands to develop an understanding of audience needs.

This competition resulted in a focus on meeting customer needs including higher quality products, increased service value, and increased customer satisfaction.

2. Analyze Strengths and Weaknesses

Business competition can drive an evaluation of strengths and weaknesses, as well as optimizing sales strategies based on these findings. This enables a business to maximize resources, make informed decisions about marketing and sales strategies, and tailor offerings according to their strengths.

3. Increasing Demand

Business competition is an effective way to increase demand for a product or service. As more companies invest in their marketing and advertising efforts, the consumer demand for their products and services may increase as brand awareness increases.

3. Encouraging Innovation

In order to gain an advantage in the market, business competition can drive to innovate strategies and improve their products or services in creative ways. This is an important contribution to continuously improving the quality of goods and services, advancing product and service technology, and adapting to changing consumer needs.

4. Show Excellence

A business often tracks and analyzes competitors' performance to gain insight into their business strategy. By studying competitors' tactics, a business will be able to demonstrate their superiority in the market. So that many businesses can develop strategies that will result in success.

5. Promoting Business

Continuous business development can be an important factor in long-term success. Business competition is often challenging to continue to increase brand awareness, promote, analyze success, and develop new methods to achieve even bigger goals.

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The simplified form of the radical is 9i

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part I'm (z).  Also, it is called an imaginary number.

Given here, √-81 and we know √-1 = i

√-81 = √9² × √-1

        = 9 ×i

        = 9i

Hence 9i is the correct answer.

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Answer: 9i is the correct answer.

Step-by-step explanation:

Solving the given work.

The rate of change of the amount of gasoline in a storage tank at t=3 hours is -0.75 thousand gallons per hour, and the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

(a) To estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours, we can use the formula for the average rate of change over an interval: (G(b) - G(a)) / (b - a).

We can choose two points on the table that are closest to t=3 hours, such as t=2 and t=4. Using these points, we have:

G(2) = 22

G(4) = 20.5

Substituting these values into the formula, we get:

(G(4) - G(2)) / (4 - 2) = (20.5 - 22) / (4 - 2) = -1.5 / 2 = -0.75

The units of measure for this rate of change would be thousands of gallons per hour.

(b) Since G′′(t)>0 for 5≤t<10, this means that the second derivative of G(t) is positive for all values of t within this interval. The second derivative represents the rate of change of the rate of change, or the acceleration. A positive second derivative indicates that the rate of change is increasing, or that the function is accelerating. This means that the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

We can also conclude that G′(t)>0 for 5≤t<10 since the second derivative represents the rate of change of the first derivative, which is positive. This means that the first derivative, or the rate of change of the function, is also positive for this interval. This confirms that the amount of gasoline in the storage tank is increasing between t=5 and t=10.

Complete Question:

'A gasoline storage tank is filled by a pipeline from a refinery. At the same time, gasoline flows from the tank into trucks that will make deliveries to gasoline stations. The amount of gasoline in the storage tank at time t is given by the twice-differentiable function G, where t is measured in hours and 0≤t≤10. Values of G(t), in thousands of gallons, at selected times t are given in the table above. It is known that G′′(t)>0 for 5≤t<10.

(a) Use the data in the table to estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours. Show the computations that lead to your answer. Indicate units of measure.

(b) For 0 t (hours) 0 5 8 10 G (0 (thousands of gallons 22 18.5 19.5 22 24'

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