how many solutions does -x+y=-5,3x+5y=15 have

If we change the symbols, the system will have one solution.

x ≥ 2

x ≤ 2

Where the solution is x = 2.

Here we have the system of inequalities:

x > 2

x < 2

So, x can be smaller than 2 or larger than 2. Is easy to see that there are no values of x that are solutions of both inequalities, but if we replace both symbols by ≤ and ≥, then x = 2 will be a solution of both inequalities, and thus, a solution of the system.

x ≥ 2

x ≤ 2

That system has one solution.

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As per the borrowed amount, the value of IRR is 6.40%

The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.

Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.

Now, we have to calculate the value of IRR,

The general form of the IRR formula is written as,

=> NPV = [tex]\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0[/tex]

where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.

Here we apply the values on it, then we get,

=> [tex]NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000[/tex]

When we simplify this one then we get,

=> Internal Rate of Return = 6.402%

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His speed for the remaining 26 km of the course is given as follows:

24.3 km/h.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which the parameters are given as follows:

The time is obtained as the distance divided by the velocity, hence:

t = d/v.

Then the time taken for the first 29 km is given as follows:

t = 29/15

t = 1.93 hours.

180 minutes = 3 hours, hence he took 1.07 hours for the remaining 26 km, hence the velocity is of:

v = 26/1.07

v = 24.3 km/h.

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129 students had a private scholarship.

Out of the 843 students,

To calculate the total number of students with a private scholarship, we need to add the number of students who had a private scholarship (112) and the number of students who had both scholarships (17). This gives us a total of 129 students with a private scholarship. The rest of the students, who had either a government scholarship (80) or no scholarship (651), do not have a private scholarship.

209 students had only one of the two scholarships, so 209 - 129 = 80 students had a government scholarship.

So in total, 112 + 80 = 192 students had either a private or a government scholarship.

Therefore, 843 - 192 = 651 students did not have either a private or a government scholarship.

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Answer: there’s no attachment so I’m not sure what you need help with

Step-by-step explanation:

A rashguard costs $25 at full price, which is calculated as 3x - 15 = 60.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given Blue Tide Swim Shop is having its annual summer sale,

rashguards sell for $5 less than the full price,

let the actual price of rashguards be x

price to be payed = x - 5

Miguel purchases 3 rashguards,

at cost  = $60

cost of 3 rashguards is 3(x - 5) = 3x - 15

3x - 15 = $60

3x = 60 + 15

3x = 75

x = 75/3

x = 25

cost of rashguards is $25.

Hence the actual cost is $25, and the equation is 3x - 15 = 60.

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p(x) must be equal to (x-a)(x-b) where b is another number.

If p(a) = 0, then this implies that (x-a) is a factor of p(x). Therefore, p(x) can be factored into (x-a)q(x), where q(x) is a polynomial of degree one less than the degree of p. This means that p(x) must be equal to (x-a)(x-b) for some other number b. It does not mean that p(x) must be equal to the zero polynomial or (x-a)².

The product of two factors, (x-a) and (x-b), is a polynomial of degree two, p(x). This can be expressed in expanded form as p(x) = x² - (a + b)x + ab, where a and b are any two numbers

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The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

The par coupon rate of a four-year, default-free security with annual coupon payments can be calculated by taking the present value of all future coupon payments, plus the face value of the security, and dividing that amount by the face value of the security.

Par Coupon Rate = (Present Value of Coupon Payments + Face Value) / Face Value

Annual interest payment = [tex]\frac{12}{100} *1000[/tex]

Annual interest payment = $120

A face value of $1,000 and the present value of all future coupon payments is $120, the par coupon rate for this security would be 112%.

Par Coupon Rate = ($120 + $1,000) / $1,000

Par Coupon Rate = 1120 / 1000

Par Coupon Rate = $1.12

Par Coupon Rate = 112/100

Par Coupon Rate = 112 %.

Therefore,

The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

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Use the formula: time = distance / speed

time = 7 km / 21 km/h = 1/3 hours

To convert hours into minutes, you can multiply the number of hours by the conversion factor 60.

1/3 x 60 = 20

It takes Moses 20 minutes to ride 7 km on a segway scooter at a top speed of 21 km/h.

Answer:

h(13) = 3

h(25) = 7

h(34) = 10

Step-by-step explanation:

In this situation, you plug in the number inside h, replacing t because the original function is h(t).

So,

h(13) = (13-4)/3

9/3 = 3

h(25) = (25-4)/3

21/3 = 7

h(34) = (34-4)/3

30/3 = 10

Hope this helps!

Answer: Nora spent 11 ours working.

Step-by-step explanation: 3 + 2 + 2 + 4 = 11

Answer:

7

Step-by-step explanation:

meetings don't count

Kapitan Tiago borrowed 560,000 × 60 % = 336,000 from the bank.

To find the amount borrowed, we multiply the balance Kapitan Tiago paid in cash by the loan percentage he obtained. The loan percentage is expressed as a decimal, so we multiply 560,000 by 0.6 to get 336,000.

This means Kapitan Tiago borrowed 336,000 from the bank and paid

560,000 - 336,000 = 224,000     in cash.

The total amount he spent on the car is

336,000 + 224,000 = 560,000.

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John has 6 quarters, 12 nickels, and 6 dimes, for a total of 24 coins. This is because he has twice as many nickels as quarters (12 nickels, 6 quarters), and two more dimes than nickels (12 nickels, 6 dimes). With this combination, the total value of all the coins would be $3.50.

To calculate the number of coins John has, we can use the following steps:

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If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection is 120 °

The term angle of deflection in math is defined as  the angle of which the M particle is deviated

Here we know that the intersection point is the angle between the back tangent and forward tangent.

Here we have also know that the surveyor either computes its value from the preliminary traverse station angles or measures it in the field and it can be denoted by Δ.

Then the Tangent length is calculated as,

=> T = R tan ⁡ Δ/2

Similarly, the long chord is calculated as,

=> L = 2 R sin ⁡ Δ/2

Here we also know that Length of the long chord is defined as,

=> L = T

The it can be calculated as,

=>R tan Δ/2 = 2 R sin ⁡ Δ/2

Here we know tanθ = sinθ/cosθ then it can be written as

=> 1/2 = cos (Δ/2)

=> Δ/2 = 60°

=> Δ = 120 °

Therefore option (d) is correct.

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1. The variable in the solution is the population every year

2. The model can be presented as

y= 1175-20x

3. The value of slope is -20 which says that the population decreases by 20 members for every one year increase from 2010

Let y be the population after x years from 2010

So, the model can be presented as

y= 1175-20x

Now for example, in year 2011

x= 2011-2010= 1

The population is y = 1175-20(1) = 1155

The population in year 2012 is

x= 2012-2010= 2

Population is y= 1175-20(2) = 1135

The result obtained is satisfactory and hence ok

The population follows a linear trend with slope of -20 and intercept of 1175.

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Emily ran 731.6/12.4 = 59 meters per minute.

Hailey's plane climbed 1004.7/59.1 = 17 feet every second.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

1a.

Emily ran 731.6 meters in 12.4 minutes.

She ran 731.6/12.4 = 59 meters per minute.

1b.

Hailey's plane climbed 1,004.7 feet in 59.1 seconds.

Her plane climbed 1004.7/59.1 = 17 feet every second.

Therefore, all the required values are given above.

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The equation of line J that is perpendicular to line K is: 3. y = 1/2x + 6.

Perpendicular lines have slopes that are negative reciprocals to each other, that is, if the slope of one is 3, the other will be -1/3.

Given that the slope of line K is -2, the slope of line J that is perpendicular to line K would be 1/2.

Substitute m = 1/2 and (x, y) = (6, 9) into y = mx + b to find b:

9 = 1/2(6) + b

9 = 3 + b

9 - 3 = b

6 = b

b = 6

Substitute b = 6 and m = 1/2 into y = mx + b:

y = 1/2x + 6.

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R-squared is calculated as the square of the linear correlation coefficient (r). In this case, the linear correlation coefficient is 0.817, so the R-squared can be calculated as follows:

R-squared = r^2 = 0.817^2 = 0.67

R-squared measures the proportion of variation in the dependent variable that is explained by the independent variable in a regression analysis. A value of R-squared close to 1 indicates that a large proportion of the variation in the dependent variable is explained by the independent variable, while a value close to 0 indicates the opposite.

In this case, a value of 0.67 for R-squared indicates that 67% of the variation in the dependent variable is explained by the independent variable, while the remaining 33% is unexplained.

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You were on the right track, I totally understand why you'd get stuck where you are currently in the process. To start with, you technically found the wrong ratio between the two triangles. Your ratio is just 2x, while it should be 2x/5.

To start, let's find the ratio between triangle FEG and ABC by dividing angle F by and A:

[tex]R=\frac{2x}{5}[/tex]

Now, multiply angle B by this ratio:

[tex](x+4)(\frac{2x}{5} )=\frac{2x^2}{5}+\frac{8x}{5}=\frac{2x^2+8x}{5}[/tex]

We can now set this expression equal to angle E, as we have multiplied by the common ratio:

[tex]\frac{2x^2+8x}{5} =18[/tex]

This looks rather daunting, but let's keep calm... you can do this!!

Start by subtracting 18 from both sides:

[tex]\frac{2x^2+8x}{5}-18=0[/tex]

Now, let's get the whole expression under the denominator 5:

[tex]\frac{2x^2+8x-90}{5}=0[/tex]

Notice that the denominator can now be removed:

[tex]2x^2+8x-90=0[/tex]

Now, factor the equation (you could also use the quadratic eq if you want)

[tex]2(x-5)(x+9)=0[/tex]

Notice that we have two potential values for x (5 and -9).

Think about this logically... If we use -9 and plug it in for x, we will end up with values of -5 degrees for an angle, which is impossible! Therefore 5 is the only valid answer!

I encourage you to also approach the problem from a different angle and use the common factor (5/2x) and multiply it by 18 :)

3.5 capfuls of vitamin is required for the 350 liter fish tank, to keep the fish healthy.

An equation is an expression that shows the relationship between two or more numbers and variables.

To keep the fish healthy, 2 drops of vitamin is required per 5 liter of water. Hence, for 350 liter:

5 liter = 2 drops

350 liter = 350 liter * 2 drops per 5 liter = 140 drops

40 drops = 1 capful

Hence:

140 drops = 140 drops * 1 capful per 40 drops = 3.5 capfuls

3.5 capful is required for the 350 liter

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36 yards wide is the actual picnic area.

The drawing's length, a colon (":"), and the actual length that corresponds to it are used to illustrate the scale.

Given that this illustration is scaled at "1:10," everything depicted with a size of "1" would have a size of "10" in the real world, a measurement of 150 mm on the image would be 1500 mm on the actual horse.

One unit in the picture equals 100 actual units. In other words, you would draw the table on a piece of paper at a scale of 2 cm if we were to draw it at a scale of 1:50 and it was 100 cm wide by 200 cm long.

width of actual picnic area = 12 × 3 = 36 yards

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The statement which is strictly true for algorithms is :

Option d. Each step of algorithms should be very clear and unambiguous.

Therefore, the option d. each step of algorithms represents steps clearly and unambiguous is the true statement of algorithms.

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(a) the value of y-intercepts is 70 (b) In what year did people born that year have an average life expectancy of 75 years= 1990 (c) the average life expectancy =76.5 years.

The average life expectancy y of a person born x years after 1960 can be approximated by the linear equation y = 1/6 x + 70.

(a) What interpretation can be given to the y-intercept of the graph?

we know that the standard form of a straight line is = y=mx+c

where c is y-intercepts,

So, we have y=0.1666x+70

here the value of C=70

hence, it is y intercepts=70

b)

In what year did people born that year have an average life expectancy of 75 years,

we have y=75

x=30

So year = 1960+30=1990.

c)  What is the average life expectancy of people born in 1999?

1999-1960=39=x

y=76.5 year.

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The only correct option from the given graph is Graph X.

A function's derivative can be used to detect whether a function is rising or decreasing on any interval in its domain. If f′(x) > 0 at every point in an interval I, the function is said to increase on I. If f′(x) 0 at every point in an interval I, the function is said to be declining on I.

When we draw tangents to the curve, we can see that if the gradient of the tangent is positive, the function is rising, and if the gradient is negative, the function is dropping.

The given figure  Y is the graphs only increase when x = 0.

Let's look at each graph individually.

When x0, graph W really decreases, therefore it is erroneous.

Because graph X grows when x0 but not when x0, it is a plausible explanation.

Because graph Y drops at x0, it is erroneous.

Graph Z grows when x0, but it also increases when x0, indicating that Graph Z is erroneous.

The only right answer is Graph X.

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Answer:

Step-by-step explanation:

There are 16 ounces in 1 pound. Take 3/4 and multiply it by 16.

3/4 x 16 ounces = 12 ounces

There are 12 ounces in 3/4 lb.

The chef uses 1/8 of the 12 ounces (or 3/4 lb) of cheese for the top of the lasagna.

1/8 of 12 ounces

1/8 x 12 ounces = 1.5 ounces

The chef uses 1.5 ounces for the top of the lasagna.

To convert the ounces to pounds, use 1 lb/16 ounces. The ounces cancel and you are left with pounds.

1.5 ounces x (1 lb/16 ounces) = 0.09375 lb

Answer:2 + √3

Step-by-step explanation:

The value of tan 5pi/12 in decimal is 3.732050807. . .. Tan 5pi/12 can also be expressed using the equivalent of the given angle (5pi/12) in degrees (75°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)

⇒ 5pi/12 radians = 5pi/12 × (180°/pi) = 75° or 75 degrees

∴ tan 5pi/12 = tan 5π/12 = tan(75°) = 2 + √3 or 3.7320508