PART A
How many solutions does the system have? Explain.
PART B
Identify the slope and y-intercept of each line. What do you notice about
the slopes of the lines?

Answer:

Step-by-step explanation:

y=kx+b

b=3

(1,5)

1*k+3=5

k=2

so, 2x+3=y

The solution to the inequality are the region in the shaded area and the graph is attached

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

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer: 4x2

Step-by-step explanation:

Answer:

[tex]4x^2[/tex]

Step-by-step explanation:

[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]

Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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The correlation between your daily calorie intake and your GPA is not likely to be immediately apparent, and it would require further investigation to determine whether there is a positive or negative correlation, or no linear relationship between the two variables.

It is difficult to predict the correlation between your daily calorie intake and your GPA as they are not obviously related variables. However, it is possible that there may be a weak or indirect relationship between the two variables.

          If a person is consuming a well-balanced diet with the right amount of nutrients, vitamins, and minerals, they may have the energy and focus necessary to perform well academically. In this case, there may be a positive correlation between calorie intake and GPA. Alternatively, if a person is consuming an excessive amount of calories from unhealthy foods, they may be more likely to experience health problems that could impact their academic performance. In this case, there may be a negative correlation between calorie intake and GPA.

      On the other hand, there may be no direct linear relationship between the two variables, and other factors such as sleep, stress, exercise, and overall health may have a greater impact on academic performance than daily calorie intake.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Shawns party will cost $16 if there are 8 guest

The tension forces are  1895 N and  2542 N.

Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart

We know that the third angle in the triangle that is formed is;

180 - [35 + 48]

= 97 degrees

We then have the tension in the ropes as T1 and T2

Using the sine rule;

T1/sin 35 = 3275/sin97

sin97T1 = 3275 sin 35

T1 = 3275 sin 35/sin97

T1 = 1895 N

For T2

T2/sin48 = 3275/sin97

sin97T1 = 3275 sin 48

T1 = 3275 sin 48/sin97

T1 = 2542 N

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None. There are no references in this line. This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.

This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.

This line of code does not contain any references at all. Therefore, it is not possible for any references to be null, and it is impossible for a NullPointerException to be thrown in response to this line. NullPointerExceptions are only thrown when a program attempts to use a reference that is null, but this line does not contain any references, so such an exception is not possible. Consequently, no references can be null in this line and no NullPointerException can be thrown.

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Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

The sum of expression is 8a + 5b - 9.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(8a + 2b -4) and (3b-5)

Now, adding the above expression we get

(8a + 2b -4) + (3b-5)

= 8a + 2b - 4 + 3b - 5

= 8a + 2b + 3b -4 - 5

= 8a + b(2+ 3) - 9

= 8a + b(5) -9

= 8a + 5b - 9

Hence, the simplified expression is 8a + 5b - 9.

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The exponential function from the decay function given is y = 30.5(0.7)ˣ

An exponential function is a mathematical function that models the growth of a quantity as a power of another quantity, typically as the exponent of a constant called the base. The general form of an exponential function is given by:

f(x) = a^x

where "a" is the base and "x" is the input. The value of "a" must be positive and greater than zero. When "a" is greater than 1, the exponential function grows very quickly, and when "a" is between 0 and 1, the exponential function decreases very quickly.

In this problem, we can find the exponential function by;

when x = 0

f(0) = 30.5

The function can be written as;

f(x) = 30.5(b)ˣ

To find the value of b,

We can take another point and solve;

f(0) = 30.5

f(1) = (21.35)

Looking at the graph, this is a decay function and we can easily find the value as 0.7.

The function is given as y = 30.5(0.7)ˣ

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Answer:

Howard's pencil is 750 millimeters

Step-by-step explanation:

[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]

Step-by-step:

75 cm = 75 × 10 mm

75 cm = 750 mm

Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00 then  the total cost of 1 tie and 1 shirt is $153.33.

What is system of equations?

A system of equations is a set of two or more equations that are solved simultaneously to find the values of the variables that satisfy all the equations in the system. The solution of the system is the set of values of the variables that satisfy all the equations. There are different methods to solve a system of equations, such as substitution, elimination, and matrix methods.

Let x be the cost of 1 tie and y be the cost of 1 shirt.

From the problem, we can set up a system of equations:

3x + 4y = 500 (equation 1)

6x + 7y = 920 (equation 2)

To solve for x and y, we can use elimination method. Multiply equation 1 by 2 and subtract it from equation 2:

6x + 7y = 920

(6x + 8y = 1000)

-y = -80

Therefore, y = 80. We can substitute y = 80 into equation 1:

3x + 4(80) = 500

Simplifying the equation, we get:

3x = 220

So, x = 220/3 = 73.33 (rounded to two decimal places).

Therefore, the total cost of 1 tie and 1 shirt is $73.33 + $80 = $153.33.

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The plane ticket to Barcelona is now £164.50. This is because 6% of £175 is £10.50 and if you subtract £10.50 from £175, it equals £164.50.

well, let's get the info first.

so going forth the Cheetah goes 70mph and going back it modestly does 40mph.

can we say that on average it did 55mph?

well, what's that?  on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.

well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.

A)

since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say

[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]

[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]

B)

[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]

The translation of a function and coordinates are given below..

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The following functions:

y = x²

y = 2x

The transformation is:

Translate two units to the left.

So,

y = (x - 2)²

y = 2(x - 2)

Translation 5 units up.

y = x² + 5

y = 2x + 5

The following coordinates:

Translate 2 units to the right.

(1, 4) = (1 + 2, 4) = (3, 4)

(5, 8) = (5 + 2, 8) = (7, 8)

Translation 5 units down.

(1, 4) = (1, 4 - 5) = (1, -1)

(5, 8) = (5, 8 - 5) = (5, 3)

Thus,

The translation of a function and coordinates are given above.

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The two plants would have the same height in 7 weeks and the height would be 31 inches.

The form of the expression that represents the length of the plant on the window sill is:

initial length + (length of growth per week x number of weeks)

3 + (4 x w)

3 + 4w

The form of the expression that represents the length of the plant on the coffee table is:

initial length + (length of growth per week x number of weeks)

17 + (2 x w)

17 + 2w

When the two plants have the same height, the two expressions would be equal:

17 + 2w = 3 + 4w

17 - 3 = 4w - 2w

14 = 2w

w = 14/2

w = 7 weeks

Height of the plant = 3 + 4(7)

3 + 28 = 31 inches

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The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Sin θ = Opposite Side to θ/Hypotenuse

Cos θ = Adjacent Side to θ/Hypotenuse

Tan θ = Opposite Side/Adjacent Side

Cot θ = Adjacent Side/Opposite Side

Sec θ = Hypotenuse/Adjacent Side

Cosec θ = Hypotenuse/Opposite Side

where, Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle)

The inverse ratios start with the ratio and then find the angle that produces this ratio.

(a) x=cos−1(a/c)

(b) x=sin−1(c/b)

(c) x=tan−1(c/a)

(d) y=sin−1(a/c)

(e)y=cos−1(c/b)

The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).

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The apothem is perpendicular distance from the center of a regular polygon to any one of it sides.

The Apothem is defined as a term that used in geometry to describe a characteristic feature of a regular polygon.

A Regular Polygon is a polygon that has all sides of equal length and all angles of equal measure.

The Apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to any one of its sides.

The Center of circle is also the center of polygon. So , apothem is the distance from the center of the circle to the midpoint of any side of the polygon .

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The given question is incomplete , the complete question is

The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.

The system of linear equations represented in the graph have (b) ne solution at (-3, 1)

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

0 = y - x - 4

3y + 9 = -4x

The above system represents two linear functions

The point of intersection of the linear functions represent the solution

In this case, the linear functions intersect at (-3, 1)

See attachment for graph

Hence, it has one solution at (-3, 1)

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Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:

                             [tex]a^2 + b^2 = c^2[/tex]

We can use the Pythagorean theorem to find the distance between the two ships at any given time:

d² = (20t)² + (15(t-4))²

Simplifying this equation, we get:

d² = 400t² + 225(t² - 8t + 16)

d² = 625t² - 1800t + 3600

d = √(625t²- 1800t + 3600)

We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:

100 = √(625t² - 1800t + 3600)

Squaring both sides, we get:

10000 = 625t² - 1800t + 3600

Rearranging, we get:

625t² - 1800t - 6400 = 0

Using the quadratic formula, we get:

t = (1800 ± √(1800² + 46256400)) / (2*625)

t = (1800 ± 3900) / 1250

t = 3.84 or t = 8.16

So the time elapsed for the second ship is:

t2 = t + 4

t2 = 7.84 or t2 = 12.16

We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:

d = √((163.2)² + (62.4)²) = 174.9 nautical miles

Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

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The resulting sum function if x is equivalent to 2 is 18

Composite functions are known as function of a function

Given the following functions

f(x) = 3x + 5 and;

g(x) = 4x - 1.

(f+g)(x) = f(x) + g(x)

(f+g)(x) = 3x + 5 + 4x - 1

(f+g)(x) = 7x + 4

Substitute x = 2 into the result

(f+g)(2) = 7(2) + 4

(f+g)(2) = 18

Hence the value of the sum of the function when x = 2 is 18

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Answer:

58

Step-by-step explanation:

4234 = 73x divide by 73 on both sides and x=58

The sequence is an arithmetic sequence.

A rule for each term is t(n) = 7 - 4(n - 1).

Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence is 7, 3, –1, –5, –9, ....

First term = 7

Second term = 7 + -4 = 3

Third term = 7 + (-4 × 2) = -1

....................

Here each term is getting by adding -4 to the preceding term.

So -4 is the common difference.

nth term of the sequence is t(n) = 7 - 4(n - 1).

Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).

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Answer: 1

Step-by-step explanation: Knowing the division and multiplication rules, any number times one equals itself and any number divided by one equals itself. Make sure not to put 0 as an answer because any number divided by 0 is undefined.

Answer: 1) 4 $3 and 4 $2; 2) 4 candles; 3) 4 adults and 6 students; 4) Small is 11.67 and Large is 83.75

Step-by-step explanation: 1. Total of $20 and needs 9 donuts. One is $3 and one is $2. Start with 3 $3 that 9 and let's do 3 for $2 which is 6. 9+6 is $15. 20-15 is 5. We have $5 left so we can buy in total 4 $3 donuts and 4 $2 donuts.

2. She has to make at least 4 candles. Booth is $40. And $2 per candle. 4*2 is $8. 40+8 = 48 and 48/12 is 4 candles.

3. They have a total of 120 sold. So let's start with adult tickets: $15 each. So let's start with 4 sold. 15*4 = 60. Students: $10 each. 10*4 is $40. 60+40 is 100 sold! So let's do 2 more student tickets to get 120 sold. 4 adults sold and 6 students sold.

4. Let's work with 6 and 8 you set up the equation 6x+8y=670 you get x = 11.67 and y is 83.75. So the large price is $83.75 and the Small is $11.67

Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

It is given that Gwen has a £5 note and a £2 coin.

Therefore, she has a total of £(5 + 2) = £7

A liter of cola costs £1.25.

Therefore, (7 ÷ 1.25) = 5.6

Therefore, Gwen can buy a total of 5 liters of cola.

Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75

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Complete question is:

Gwen has a £5 note and a £2 coin

a litre of cola cost £1.25

gwen buys as many liter bottles of cola as she can

how much money will she have left over