How many solutions does this system have?
Answers:
None
1
2
3
Infinite

The measure of the missing angle α is 62 degrees.

The sum of angles on the straight line adds up to 180 degrees.

From the diagram;

Since the sum of angles on a straight line adds up to 180 degrees.

Angle 1 + Angle 2 + Angle 3 = 180

Plug in the values

118 + α = 180

Subtract 118 from both sides

118 - 118 + α = 180 - 118

α = 180 - 118

α = 62°

Therefore, the value of angle α is 62 degrees.

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The lower quartile for the given data is -2, since it is the 25th percentile and is the value that lies at the 25th position when the data is sorted in ascending order.

1. Sort the data in ascending order: -4, -2, 1, 1, 6, 8, 12, 15

2. Calculate the 25th percentile: 25th percentile = (n + 1) * 0.25 = (8 + 1) * 0.25 = 2.25

3. The 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively.

4. The lower quartile is -2.

The lower quartile (also known as the 25th percentile) is the value that lies at the 25th position when the data is sorted in ascending order. To find the lower quartile of the given set of data (1, 8, 1, -4, 12, -2, 15, 6), the data needs to be sorted in ascending order. This gives us the following data: -4, -2, 1, 1, 6, 8, 12, 15. Now, to calculate the 25th percentile, we use the formula (n + 1) * 0.25, where n is the number of data points. In this case, n = 8, so the 25th percentile = (8 + 1) * 0.25 = 2.25. This means the 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively. Therefore, the lower quartile for the given data is -2.

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John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.

John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.

The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:

4 + 5x ≤ 15

To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:

5x ≤ 11

Next, we can isolate x by dividing both sides of the inequality by 5:

x ≤ 11/5

Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:

0 ≤ x ≤ 11/5

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Answer:

$51

Step-by-step explanation:

At each age his grandmother gives him three times his age in money.

3 x 5

3 x 8 ...

Answer:

?

Step-by-step explanation:

Factor the polynomial by factoring out the greatest common factor, 7x2 + 5 - x = 6x2 + 10

x = -5

Soultion:

→ 7 × 2 + 5 - x = 6 × 2 + 10

Multiply.

→ 14 + 5 - x = 12 + 10.

Combine like terms.

→ 19 - x = 24

Isolate x (I'm going to add x and subtract 24 from both sides to avoid changing signs)

Answer

→ = x = -5

Answer:

A ratio of 5 parts water to 1 part fertilizer for watering plants. This ratio ensures that the plants receive the proper amount of nutrients without being over-fertilized, which can harm their growth.

A ratio of 5 parts rest to 1 part exercise for a healthy lifestyle. This ratio helps to maintain a healthy balance between rest and physical activity, allowing for proper recovery and growth. It also ensures that a person does not over-exercise and become exhausted, which can lead to injury or burnout.

Answer:

x-8

Step-by-step explanation:

the answer is  x-8                                                             correct answer x-8

I know, I answer quick. What do you expect I'm Johnny Sins to help you with your homework. :)

Anyways,

The height of the nth bounce can be calculated using the formula:

h_n = h_1 * 0.68^(n-1)

Where h_1 is the height of the first bounce, h_n is the height of the nth bounce, and 0.68 is the percentage of the height lost with each successive bounce.

Substituting the given values, we have:

h_9 = 5 * 0.68^(9-1)

h_9 = 5 * 0.68^8

h_9 = 5 * 0.265

h_9 = 1.325

So the height of the 9th bounce would be approximately 1.3 feet, rounded to the nearest tenth.

_________________________________________________________

Thanks for the support, love you brother!

Love Johnny Sins

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The liquid should be in the cooler less than 10 minutes. Therefore, option C is the correct answer.

A thermometer can be used to measure the degree of hotness or coolness that is present. It also expresses the rate of motion of a substance's atoms and molecules. The Fahrenheit, Celsius, and Kelvin thermometers measure temperature in degrees.

Given that, the temperature of a liquid must stay above 60° F.

The starting temperature of the liquid is 90° F.

Difference in temperature = 90-60

= 30

It is placed in a cooler, which lowers its temperature 3° F each minute.

= 30/3

= 10° F

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

For an experiment, the temperature of a liquid must stay above 60°F. The starting temperature of the liquid is 90°F . It is placed in a cooler, which lowers its temperature 3°F each minute. Let m represent the number of minutes the liquid is in the cooler. Which statement determines how many minutes the liquid can stay in the cooler?

A) The liquid must be in the cooler fewer than 10 minutes.

B) The liquid must be in the cooler fewer than 15 minutes.

C) The liquid must be in the cooler fewer than 30 minutes.

D) The liquid must be in the cooler fewer than 60 minutes.

We solved the given inequality and found the values of x lie in the interval   ( -∞ , 4). This is graphed and shown on the number line as below.

What is meant by inequality?

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Given inequality is:

11x + 6 < 9x + 10

Solving,

11x - 9x < 10 - 6

2x < 4

x < 4

The values of x is in the interval : ( -∞ , 4)

The above inequality is shown below on the number line as well as on the graph.

We can see that all the values to the left of 4 but not including 4 can be taken as the value of x.

Therefore we solved the given inequality which is graphed and shown on the number line.

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Keenan has placed his solar panel at an optimal angle.

The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:

cos(C) = (a² + b² - c²) / 2ab

where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.

Check the attached image for labelling.

The angle we are trying to calculate is labelled C.

cos (C) = (20² + 18² - 19²) / (2*20*18)

cos (C) = 363/720

C = cos⁻¹(363/720)

C = 59.72°

Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.

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Complete Question

Check the attached image for complete question

Sipho earned R33.15 in simple interest.

The balance of the account at the end of the first 30 days was R2 133.15.

a. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.

Total amount deposited = R600 + R1 000 + R500 = R2 100

Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)

Therefore, Sipho earned R33.15 in simple interest.

b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:

Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15

Therefore, the balance of the account at the end of the first 30 days was R2 133.15.

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The area of field hockey is larger by 3162.85 [tex]m^2[/tex].

The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."

The hockey surface given here is in rectangular shape, so,

Area = length x breadth

Area of the hockey surface at a community centre is,

= 61 m x 30.5 m

=1860.5 [tex]m^2[/tex]

Area of field hockey played at outdoors,

= 91.5 m x 54.9 m

= 5023.35    [tex]m^2[/tex]

Clearly, we can see that area of field hockey is larger.

Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].

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The expression which is equivalent to the given expression 3/5 divided by 4/7 is given by option d.  3/5 multiply 7/4.

The expression which is equivalent to  the expression  3/5 divided by 4/7 is:

3/5 divided by 4/7 can be expressed as

= ( 3 / 5 ) ÷ ( 4 / 7 )

Convert division sign into multiplication sign we get,

= ( 3 / 5 ) × [ 1 / ( 4 / 7 ) ]

= ( 3 / 5 ) × ( 7 / 4 )

= 3/5 multiply 7/4

Therefore, the correct way of representing the expression 3/5 divided by 4/7 is equivalent to option d. 3/5 multiply 7/4.

The above question is incomplete, the complete question is:

Which of these expression is the same as 3/5 divided by 4/7?

a 3/5 divided 7/4

b 4/7 divided 3/5

c 3/5 multiply 4/7

d 3/5 multiply 7/4

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Answer:

0.2115

Step-by-step explanation:

probability the first lefty is the second person:

1. the first person must be right handed (1-13% = 0.87)

2. the second person must be left handed (0.13)

both must happen, so this is 0.87 * 0.13

probability the first lefty is the third person:

1. the first person must be right handed (0.87)

2. the second person must be right handed (0.87)

3. the third person must be left handed (0.13)

all must happen, so this is 0.87 * 0.87 * 0.13

either the second or third person must be left handed, so we add this to get

0.87 * 0.13 + 0.87 * 0.87 * 0.13 = 0.2115

Answer:

Step-by-step explanation:

Let's say that after the break, the group of friends watches m minutes of the movie.

We know that they watched 42 minutes before the break, so the total time they have watched before and after the break is 42 + m minutes.

Since the movie is 115 minutes long, the inequality that represents the number of minutes they will watch after the break is:

42 + m < 115

So, the inequality that represents the number of minutes, m, they will watch after the break is:

m < 115 - 42 = 73

This means that m has to be less than 73 for the group of friends to finish watching the movie.

The equation will be solved x = 2.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

The given equation 2/[tex]2^{(4-3x)}[/tex] = 8

[tex]2^{(4-3x)}[/tex]  = 2/8

[tex]2^{(4-3x)}[/tex] = 2⁻²

So we can take 4-3x = -2

3x = 4+2

x = 6/3 = 2

Hence, the equation will be solved x = 2.

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With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

The variable gets eliminated, then the equation has no solution.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

Simplify the equation, then we have

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

10x - 4 - 7 + x = 10x + 2 - 4 + x

11x - 11 = 11x - 2

11x - 11x = 9

The variable gets eliminated, then the equation has no solution.

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The correct equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

The given Expression simplifies to -8.1069556e+27

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.

Given an equation to solve,

6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456

Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal

By, the BODMAS rule,

First step: Multiply C, D, E. Let this be G

Now, the equation will look like this: A + B - G + F

Second step: We can add and subtract according to the signs now

On solving, the expression simplifies to -8.1069556e+27

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Answer:

8 to 2

Step-by-step explanation:

because u have 8 cocca and 2 sugar

Left and right multiplying a positive semi-definite matrix by another matrix will always result in a positive semi-definite matrix.

Positive semi-definite matrices are important in many areas of mathematics and science, including linear algebra, optimization, and physics.

Let A be a positive semi-definite matrix, and let B be an arbitrary matrix. We want to determine whether AB and BA are also positive semi-definite matrices.

First, let's consider AB. To show that AB is positive semi-definite, we need to show that for any non-zero column vector x, xT(AB)x ≥ 0. We can expand this expression as:

xT(AB)x = (xTA)Bx = yTBy

where y = Ax. Since A is positive semi-definite, we know that yTy ≥ 0 for any vector y. Therefore, we have shown that xT(AB)x ≥ 0 for any non-zero column vector x, and hence AB is positive semi-definite.

Next, let's consider BA. To show that BA is positive semi-definite, we need to show that for any non-zero column vector x, xT(BA)x ≥ 0. We can expand this expression as:

xT(BA)x = (xTB)Ax = zTAz

where z = Bx. Since A is positive semi-definite, we know that zTAz ≥ 0 for any vector z. Therefore, we have shown that xT(BA)x ≥ 0 for any non-zero column vector x, and hence BA is also positive semi-definite.

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The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.

Note that triangle ABC and triangle FBE are similar,(by AAA)

As [tex]\angle B[/tex] is common in both, and [tex]\angle F= \angle A[/tex] as they both are 90°

so, the [tex]\angle C[/tex] will also be equal to [tex]\angle E[/tex]

so [tex]\frac{BF}{FR} = \frac{AB}{AC}[/tex]

This can be written as [tex]\frac{4-x}{x} = \frac{4}{3}[/tex]

solving: 12 - 3x = 4x

7x = 12 or x = 12/7

Similarly, triangle A'B'C' and triangle RB'Q are similar,

so RB' = [tex]\frac{4}{3}y[/tex] and C'S= [tex]\frac{3}{4}y[/tex]

Thus, C'B' = C'S+ SR+ RB'

or  [tex]\frac{4}{3}y + y + \frac{3}{4} = 5[/tex]

solving y = 60/37

Now, x/y = [tex]\frac{12}{7} \times \frac{37}{60}[/tex] = 37/35

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It would take Tracy and Dave approximately 4.8 hours to complete the task together. So, the correct option is C.

To solve this problem, we can use the formula:

time = work / rate

where work is the amount of work to be done (in this case, collecting signal strength data from each house), and rate is the rate at which the work is being done.

Let's start by finding Tracy's and Dave's individual rates:

Tracy's rate: 1 job / 8 hours = 0.125 jobs per hour

Dave's rate: 1 job / 12 hours = 0.0833 jobs per hour

Now, let's find their combined rate when they work together:

Combined rate = Tracy's rate + Dave's rate

Combined rate = 0.125 + 0.0833

Combined rate = 0.2083 jobs per hour

Finally, we can use the formula time = work / rate to find how long it would take them to complete the task together:

time = 1 job / 0.2083 jobs per hour

time ≈ 4.8 hours

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Answer:

The equation is:

8x + 4 = 68

and the solution is:

x = 8

Step-by-step explanation:

The equation is:

8 time x and 4 is 68

8x+4 = 68

Solve:

8x + 4 - 4 =  68 - 4

8x + 0 = 64

8x = 64

x = 64/8

x = 8

Check:

8*8 + 4 = 68

The Distance between A, B based on the information will be 28.705 feet

From the information, the policewoman has positioned herself 500 ft from the intersection of two roads and she has carefully measured the angles of the lines of sight to the points.

Distance between A, B will be:

= 500 tan(15.4) - 500 tan(12.3)

= 500 (tan 15.4 - tan 12.3)

= 500(0.0574)

= 28.705 feet

The speed will be:

= 28.705 / 1.75

= 16.403 ft/s

= 12.3 mph

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Answer:

Step-by-step explanation:

Perimeter is equal to 2 times length and 2 times the width.

This problem says the length is twice the width.

Let's use 2w for the length:

Here's the equation:

2L + 2W = 156

Substitute 2W for the length,

2(2W) + 2W = 156

4W + 2W = 156

6W = 156

6W/6 = 156/6

w = 26

so length is 2 times 26 = 56 Length = 56 m

Answer:

The perimeter of △ABC is 144 cm.

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

Since points C and D are on the perpendicular bisector of AB, we have:

Find the length of AC using Pythagorean:

Find the perimeter of ΔABC: