What is the solution to the system of equations?
3x+10y=-47
5x - 7y=40
O (1.-5)
O (1,5)
0 (-1,-5)
0 (-1,5)

it wont let me answer hold on

Answer:

52

Step-by-step explanation:

This is because the formula is dr

Answer:

tan 0 = -2.4

sin 0 = 0.42

Step-by-step explanation:

sec 0 = -13/12 => cos 0 = -12/13

cot 0 < 0 => tan 0 < 0

so, the angle is on second quadrant

=> tan 0 = -12/5 = -2.4

=> sin 0 = 5/12 = 0.42

Answer:

Solution given;

Sec θ=-\(\frac{13}{12}\)

cotθ< 0,

It lies in second quadrant.

where sin and cosec is positive.

Now

\( \frac{1}{cosθ}=-\frac{13}{12}\)

cosθ=\(\frac{12}{13}\)

\(\frac{b}{h}\)=\(\frac{12}{13}\)

b=12

h=13

By using Pythagoras law

p=\( \sqrt{13²-12²}=5 \)

Now

exact values of tan θ=\(\frac{p}{b}\)=\(\frac{5}{12}\)

since it lies in II quadrant

tan θ=-\(\frac{5}{12}\)

and

sinθ=\(\frac{p}{h}\)=\(\frac{5}{13}\)

since it lies in II quadrant

sin θ=\(\frac{5}{13}\)

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

Step-by-step explanation:

3x+8

Answer:

This known value does not match the measured value at the 95% confidence level.

The 95% confidence interval for value is calculated as 42.92 to 43.78%,

Step-by-step explanation:

The complete question is:

Police have a hit-and-run case and need to identify the brand of red auto paint. The percentage of iron oxide, which gives paint its red color, was determined to be 43.35 ± 0.33% by one method of analysis using five measurements. The color reference provide by the automotive manufacture is 44.21%. What can you conclude about whether the sample matches the reference at a 95% confidence level?

Student's t test is used to compare the two values .

Here n=5

Degrees of freedom =ν= n-1= 5-1=4

The value from t- table for 4 d.f at 95 % confidence interval is 2.776

The test statistic is

x`± t ∝/2(v). S/√n

43.35 ± (2.776)(0.33)/√5

= 43.35 ± 0.43

= 43.78, 42.92

Here the 95% confidence interval for μ calculated is 42.92 to 43.78%, where as color reference provided by the automotive manufacture is 44.21%.

This known value does not match the measured value at the 95% confidence level.

SOLUTION

The given question is

Simplify the expression

The difference of two cubes is given as

Hence the given expression becomes

This gives

An increasing linear function results in a graph that slants upward from left to right and has a positive slope. A decreasing linear function results in a graph that slants downward from left to right and has a negative slope. A constant linear function results in a graph that is a horizontal line.

In a right triangle, the sine of the angle opposite the side of length 4 cm is 0.8 cm.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The angle opposite the side of length 4 cm can be calculated as:

The hypotenuse is the side of length 5 cm.

The calculation of the sine of the angle can be calculated using the formula:

\(Sine = \dfrac{Opposite}{hypotenuse}\)

Substitute the value in the given formula.

\(Sine(A) = \dfrac{4}{5}\)

Sine(A) = 0.8

So, the sine of the angle opposite the side of length 4 cm is 0.8 cm.

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Julie has $250 to plan the party.

The room costs $175 to reserve plus $1.25 per person for food and drinks.

Let "x" represent the number of people she can invite, you can express the total cost for the party as follows:

From this expression, we can determine the number of people she can invite, without exceeding the $250 budget.

The first step is to pass 175 to the right side of the expression by applying the opposite operation "-175" to both sides of it:

Next, divide both sides of the equation by 1.25 to reach the value of x:

She can invite up to 60 people to the party

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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The result is that x = 8 is the smallest positive number such that f(x) surpasses g(x).

An integer is a whole number that may be positive, minus, or zero and is not a percentage. Integer examples include: -5, 1, 5, 8, 97, as well as 3,043. The following figures are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.

To find the smallest positive integer x for which f(x) exceeds g(x)

we need to set the two functions equal to each other and solve for x:

f(x) = g(x)

-x² + 5x = -10x + 10

Simplifying the equation, we get:

x² + 15x - 10 = 0

Using the quadratic formula, we can solve for x:

x = (-15 ± sqrt(15² - 4(1)(-10))) / (2(1))

x = (-15 ± sqrt(265)) / 2

The two possible solutions are approximately -0.372 and -14.628. Since we are looking for the smallest positive integer solution, we take the ceiling of the positive solution to get x = 8.

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Answer:

Step-by-step explanation:

make a right triangle to find the lenght of a side  which is also the hypotenuse of the triangle

c² = a² + b²

c² = 7² + 5²

c²  = 49 + 25

c²  =  = 74

Since the area of a square is s² and c = s

a = c²

a = 74 units²

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Answer:

144°

Step-by-step explanation:

First, find the area of the circle, with the formula A = \(\pi\)r²

Plug in 10 as the radius, and solve

A = \(\pi\)r²

A = \(\pi\)(10²)

A = 100\(\pi\)

Using this, create a proportion that relates the area of the sector to the degree measure of the arc.

Let x represent the degree measure of the arc of the sector:

\(\frac{40\pi }{100\pi }\) = \(\frac{x}{360}\)

Cross multiply and solve for x:

100\(\pi\)x = 14400\(\pi\)

x = 144

So, the degree measure of the sector arc is 144°

Answer:

We know that

Area = πr²

Area = 3.14 × (10)²

Area = 314/100 × 100

Area = 314 cm²

Now

40π/314 = x/360

40 × 3.14/314 = x/360

125.6/314 = x/360

0.4 = x/360

0.4 × 360 = x

144 = x

\( \\ \)

Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.

The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Answer:

x = -11

Step-by-step explanation:

7 - x = 18

+ x on both sides to cancel the negative one

7 = 18 + x

- 18 on both sides to get rid of the 18

solve:

7 - 18 = x

-11 = x

Answer:

collecting like terms

Step-by-step explanation:

step 1. Shift 7 to the right side

-x = 18 - 7

-x = 11

step 2. divide by -1 both sides

-x/-1 = 11/-1

x = -11

Answer:

$13564

Step-by-step explanation:

\(\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\% of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|\)\(\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\% of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\% of the amount over 77,100\end{array}\right|\)

\(\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\% of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\% of the amount over 349,700\end{array}\right|\)

Mary’s taxable income= $68,562

From the table, If taxable income is over $31,850 but not over $77,100

The tax = $4386.25 + 25% of the amount over 31,850

Amount over $31,850=$68,562-$31,850

=$36,712

Therefore:

Mary's tax = $4386.25 + (25% of $36,712)

=$4386.25 +9,178

=$13564.25

=$13564 (to the nearest dollar)

Income tax is the tax charged on individual's or entities' income

Mary owes $13564 income tax

Given that the taxable income is $68,562.

Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100

So, the tax is $4386 added to 25% of the excess over $31850

This is calculated as:

\(Tax = \$4386 + 25\% \times (Income -\$31850)\)

Substitute $68,562 for income

\(Tax = \$4386 + 25\% \times (\$68562 -\$31850)\)

Solve the expression in the bracket

\(Tax = \$4386 + 25\% \times \$36712\)

Evaluate the product

\(Tax = \$4386 + \$9178\)

Add the terms of the expression

\(Tax = \$13564\)

Hence, Mary owes $13564 income tax

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The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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The number of goals scored in a hockey game is a discrete random variable.

A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.

The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.

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Answer and Step-by-step explanation:

\(\frac{3}{t}\) + 5

Above is the answer.

#teamtrees #PAW (Plant And Water)

The value of x, given that Figure B is a scaled image of Figure A, can be found to be 24.

The value of x, can be found by taking into account, the scale factor that maps Figure A to Figure B, and the corresponding length of Side x in Figure A.

To find the value of x, the value is therefore:

= Scale factor x Corresponding length of side x on figure A

= 4 x 6

= 24 units

In conclusion, the value of x is 24 units.

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Answer:

For me I think 216 diapers for 39.98 is the best option

Step-by-step explanation:

Get the price of one diaper in each offer

216 = $39.98

1= ?

1×39.98÷216=0.19

Option 2

88=24.99

1 =?

1×24.99÷88=0.28

So I prefer buying 1 diaper for$0.19 and get 216 of them for $39.98 rather than buying 1 diaper for $0.28 and get 88 of them for $24.99