A submarine is passing by a solar station, located al (0,0), that can detect objects that
are as far away as 5km in any direction. A swiss submarine is traveling along a trajectory defined by y= -2/3x +26/3 where x and y represent distances measured in kilometers. Determine algebraically whether the sonar station will detect the submitline.​

Step-by-step explanation:

the area of a rectangle is

length × width.

so, the original area is

40 × 21 = 840 cm²

now, we add x to length and width, and we get :

(40 + x) × (21 + x) = 2262 cm²

let's do the multiplication :

40×21 + 40x + 21x + x² = 2262

840 + 61x + x² = 2262

x² + 61x = 1422

x² + 61x - 1422 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 61

c = -1422

x = (-61 ± sqrt(61² - 4×1×-1422))/(2×1) =

= (-61 ± sqrt(3721 + 5688))/2 =

= (-61 ± sqrt(9409))/2 =

= (-61 ± 97)/2

x1 = (-61 + 97)/2 = 36/2 = 18

x2 = (-61 - 97)/2 = -158/2 = -79

x2 would make the side lengths negative, and that does not make any sense for an actual shape, so

x = 18

is our valid solution.

that means the new length is

40 + 18 = 58 cm

the new width is

21 + 18 = 39 cm

Answer:

[tex] \frac{1}{2} \div 3 \frac{1}{6} [/tex]

[tex] \frac{1}{2} \div \frac{19}{6} = \frac{1}{2} \times \frac{6}{19} = \frac{3}{19} [/tex]

The answer is 3/19.

Answer:

1,975,906

Step-by-step explanation:

Answer:

The answer is 1975906

Explanation:
If you pick up a Calculator and you input this on it It will give you the answer if u don't have a calculator search on the internet how to multiply numbers

Answer: you good day

Step-by-step explanation:

The missing variables of the triangle is given as follows:

17.) X=20

18.) X= 32

19) X = 31

20) X= 149

21) X= 125

22.) X= 10

23.) X= 13

To calculate tye variables the formula SOHCAHTOA is used.

For question 17.)

The adjacent of the triangle = 14

The hypotenuse of the triangle = X

The given angle = 45°

Therefore Cos ∅ = 14/X

X = 14/cos∅

X = 14/0.707106781

X = 20( approximately)

For question 18.)

The opposite of the triangle = x

The hypotenuse of the triangle = 45

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin 45° = X/45

X = sin45°×45

X = 0.707106781×45

X = 32 (approximately)

For question 19.)

The opposite of the triangle = 22

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin∅ = opposite/hypotenuse

sin45° = 22/X

X= 22/0.707106781

X= 31

For question 20.)

The opposite of the triangle = x

The hypotenuse of the triangle = 210

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin45° = X/210

X= 0.707106781×210

X= 149 (approximately)

For question 21.)

The opposite of the triangle = 88

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin∅ = 88/X

X= 88/0.707106781

X= 125(approximately)

For question 22.)

The opposite of the triangle = 5√2

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

Sin∅= 5√2/X

X= 7.071067811/0.707106781

X= 10

For question 23.)

The opposite of the triangle = 9

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

Sin∅ = 9/X

X = 9/0.707106781

X = 13(approximately)

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Answer: 18/49

Step-by-step explanation:

P(Yellow) = 9/14

= 9/14 • 9-1/14

=9/14 • 8/14

= 72/196 or 18/49

The appropriate choice is for all actual x values of x 1.5, the function is declining.

A linear polynomial is a polynomial of degree one, which means it is a polynomial that has only one variable raised to the power of one and no other variables or exponents.

A function f(x), which is made up of two linear polynomials, is given as follows:

f(x)=(x-4)(x+1)

We now know that when we multiply the two linear polynomials, a quadratic polynomial results.

As a result, the function f(x) will be shown as:

f(x)=x(x+1)-4(x+1)

f(x)=x²+x-4x-4

f(x)=x²-3x-4

In order to determine which claims about the function are accurate, we shall plot the function's graph.

1) The function increases for all real x values greater than zero.

Since we get from the graph that function f(x) is decreasing for x<0.

This statement is false.

2)The function is increasing for all real values of x where x < –1 and where x > 4.

This option is incorrect as the function is decreasing for x<-1

whereas it is increasing for x>4.

3)Where -1 <x<4, the function decrements for all real values of x.

This is the incorrect choice.

Because of the function's dual trend of growing and dropping in the interval (-1,4).

4)For all actual x values of x< 1.5, the function is declining.

This choice is the best one.

since, it is obvious from the graph that the function declines for x<1.5.

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The complete question is;

The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.

2. IN THE ALPHABEIC ORDER IF WE GO A-B SO I THINK ITS 10

Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.

The Pythagorean theorem serves as the foundation for the distance formula. A line connecting two sites of interest is the hypotenuse of the a right triangle, and this particular line connects the two points of interest.

The neighbouring side is obtained by uniting the x-coordinates of both the two points in a horizontal line, whereas the opposing side is obtained by joining the y-coordinates. Let's assume that d is the hypotenuse's length. Given two locations' coordinates,  length of both the adjacent side:

(x1,y1) = A(3,7)

(x2,y2) = B(7,11)

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

[tex]d = \sqrt{(3 - 7) ^{2} + (7 - 11 ^{2})}[/tex]

[tex]d = \sqrt{16 + 16}[/tex]

d = [tex]\sqrt{32}[/tex]

d = 16√2

Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.

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Answer:

x = y = 10

Step-by-step explanation:

This is a 45-45-90 triangle. This means the values of x and y are equal.

The formula for hypotenuse of this type of triangle s[tex]\sqrt{2}[/tex] where s is the side length.

s[tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex]

Therefore, s = 10; x = y = 10.

Note that the side lengths of 45-45-90 triangles are equal because their angles are equal. 45-45-90 triangles are also isosceles right triangles.

The mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

What is standard deviation ?

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from their mean (average) value. It tells us how much the individual data points differ from the mean. In other words, it measures the spread of the data around the mean.

A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean.

The formula for standard deviation is the square root of the sum of the squared differences between each data point and the mean, divided by the number of data points minus 1. It is denoted by the symbol σ for a population, and s for a sample.

The mean of the number of lightning strikes on a square kilometer of open ground in a year is 6, and the standard deviation is 2.4. Since we are interested in the mean of a sample of 25 square kilometers, the mean of the sample means, denoted by ▁x, can be found by:

Mean of ▁x = Mean of the population = 6

The standard deviation of the sample means, denoted by σ(▁x), can be found by dividing the population standard deviation by the square root of the sample size:

σ(▁x) = Population standard deviation / √Sample size

= 2.4 / √25

= 0.48

Therefore, the mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

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Answer: 97445

Step-by-step explanation:

27.4% of x = 26,700

x = 26,700 divided by 27.4%

(convert 27.4% to decimal) x = 26,700 divided by 0.274

x = 97445 (note the answer is rounded because you cannot have .25 of a person)

Answer: J. 8 Coins

Step-by-step explanation: 5 quarters ($1.25 worth), 2 dimes ($0.20 worth ) and 1 nickel ($0.05 worth) is the only way you can get to the value of $1.50 total using 8 coins while using every coin at least once.

The length οn the map that represents 1 meter in real is 2/3 centimetres.

When twο numbers are cοmpared, the ratiο between them shοws hοw οften the first number cοntains the secοnd. As an illustratiοn, the ratiο οf οranges tο lemοns in a dish οf fruit is 8:6 if there are 8 οranges and 6 lemοns present.

Given that Each 12 centimetre οn a map represents an actual length οf 18 οf a meter. Therefοre, the ratiο can be written as,

=>Length οn Map / Actual Length = (12) centimetres / (18) meters

=>Length οn Map / Actual Length = 2/3 centimetres per meters

Nοw, the length οn the map that represents 1 meter in real is,

=>Length οn Map / Actual Length = 2/3 centimetres per meters

=> Length οn Map / 1 meter = (2/3) centimetres / 1 meters

=>Length οn Map = 2/3 centimetres

Hence the length οn the map that represents 1 meter in real is  2/3 centimetres.

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Answer: 2.5 (or 2 1/2 as a mixed number)

Step-by-step explanation:

Answer:

5/2 or 2.5

Step-by-step explanation:

[tex]5 \frac{1}{4} - 2\frac{3}{4}[/tex]  = 5.25 - 2.75 = 2.5 = 5/2

Answer: 402 is the workers should be picking in order to ship 110,550 units for the shift. Hence, option E is correct.

Step-by-step explanation:

The experimental prοbability that the card selected was a K οr 6 is fοur οver 25.

The study οf prοbability examines the likelihοοd that a particular οutcοme will οccur; this likelihοοd is determined by the ratiο οf the preferred and pοssible cases.

The frequency οf K and 6 is 8 and 7 respectively.

Therefοre, the tοtal frequency οf K οr 6 is 8 + 7 = 15.

The tοtal number οf cards drawn is 100.

Hence, the experimental prοbability οf drawing a K οr 6 is:

15/100 = 3/20

Hence, the answer is fοur οver 25.

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cot θ = 7/4 and θ in degrees = 29.744881 degrees. In this case, the adjacent side is 7 and the opposite side is 4.

Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle.

In this right angle triangle, cot θ can be calculated using the formula

cot θ = adjacent/opposite.

In this case, the adjacent side is 7 and the opposite side is 4.

Therefore, cot θ = 7/4.

Now, to find theta in degrees, we can use the inverse cotangent function, arccot.

arccot (cot θ) = θ.

Therefore, θ = arccot (7/4).

Using a calculator, arccot (7/4) = 29.744881 degrees

Therefore, cot θ = 7/4 and θ in degrees = 29.744881 degrees.

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Answer:

Question 1) $2150.74

Step-by-step explanation:

100 + 3.7 = 103.7
Divide this by 100 to give you 1.037
Then multiply this by 2,000
$2000 x 1.037^2 = $2150.74
Make sure the square is there to represent the years

This is your answer for 2 years.

To solve this problem, we can use the formula for probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

A. To find the probability that a student likes vanilla or chocolate ice cream, but not both, we need to subtract the number of students who like both from the total number of students who like vanilla or chocolate:

Number of students who like vanilla or chocolate = 258 + 142 = 400

Number of students who like both = 102

Number of students who like only vanilla or only chocolate = 400 - 102 = 298

Probability = 298/300 = 0.9933

B. To find the probability that a student likes neither vanilla nor chocolate ice cream, we need to subtract the total number of students who like either or both flavors from the total number of students:

Total number of students = 300

Number of students who like vanilla or chocolate = 258 + 142 = 400

Number of students who like both = 102

Number of students who like neither flavor = 300 - 400 + 102 = 2

Probability = 2/300 = 0.0067

C. To find the probability that a student likes vanilla ice cream but not chocolate ice cream, we need to subtract the number of students who like both from the total number of students who like vanilla:

Number of students who like vanilla = 142

Number of students who like both = 102

Number of students who like only vanilla = 142 - 102 = 40

Probability = 40/300 = 0.1333

Answer:

Step-by-step explanation:

Carl is boarding a plane. he has 2 checked bags of equal weight and a backpack that weighs 4kg. The total weight of Carls baggage is 35 kg.

2w + 4= 35

2w=31

w= 31/2

w=15.5

The weight of each bag is 15.5 kg.

Therefore , the solution of the given problem of function comes out to be  rate of change for O Function f is -4.

There will be questions on every subject, including created and real places as well as algebraic variable design, on the midterm test. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.

Here,

The appropriate statements, given the facts, are:

The range of function g includes all real values.

The y-intercepts of functions f and g are identical.

The domains of functions f and g are all real integers.

The appropriate answers are thus:

The range of the O Function g includes all real integers.

The steady percent rate of change for X Function g is 125%.

The y-intercepts of X Functions f and g are identical.

O Function f ultimately outperforms function g.

The domains of X Functions f and g are all real integers.

The steady rate of change for O Function f is -4.

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The 60 m length of PS and the 21° angle ∠QKR, 41° angle ∠KSR, 17° angle ∠KSR, and the time of flight of 2 minutes, indicates that the distance |PQ| and the aeroplane speed are;

(a) The distance |PQ| is about 2,020.5 meters

(b) The speed of the aeroplane is about 60.6 km·h⁻¹

The speed of an object is a measure of how fast the object is moving, and the unit of speed is the distance per unit time. The speed of an object is the magnitude of the velocity vector of the object.

(a) The direction of flight of the aeroplane = Horizontally

Therefore;

PS = QR

PS = 600 m (the dimension on the diagram)

Therefore; QR = PS  = 600 m

QR/KR = tan(21°)

KR = QR/tan(21°)

Therefore;

KR = 600/tan(21°) ≈ 1,563.05

PQ and SR are horizontal segments and PS and QR are vertical, therefore;

PQ ║ SR and PS ║ QR, therefore, quadrilateral PQRS is a parallelogram

PS and QR are vertical therefore, ∠PSR and ∠QRS are 90° angles, (definition of vertical segment PS is perpendicular to the horizontal segment segment SR)

Therefore, the parallelogram PQRS is a rectangle (Properties of a rectangle)

PQ ≅ SR (Facing sides of a rectangle)

∠SKR = 180° - (41° + 17°) = 122°

∠SKR = 122°

KR/sin(41°) = SR/sin(122°)

SR = sin(122°) × KR/sin(41°)

SR = sin(122°) × KR/sin(41°)

SR = sin(122°) × 1,563.05/sin(41°) ≈ 2,020.5

SR = PQ ≈ 2,020.5

(b) The aeroplane flies from P to Q in 2 minutes

The conversion of the units are obtained as follows;

2,020.5 meters = 2.0205 km

The time of 2 minutes = 120 seconds, therefore;

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The solution as an ordered quadruple:

(0, -6 - z, z, 5)

HOW TO SOLVE A LINEAR SYSTEM?

The given linear system is:

x + y - z + 2w = 4

w = 5

This system is already in row echelon form. We can use back substitution to solve for the variables. Since we already know the value of w, we can substitute w = 5 into the first equation:

x + y - z + 2w = 4

x + y - z + 2(5) = 4

x + y - z + 10 = 4

Simplifying, we get:

x + y - z = -6

Now we have two equations:

x + y - z = -6

w = 5

We can solve for x, y, and z using the first equation. To do this, we can use the fact that the system is in row echelon form, which means that the leading coefficients are all 1 and there are no variables to the left of the leading coefficients. We can start by solving for z since it has a leading coefficient of 1:

z = x + y + 6

Next, we can use the second equation to solve for y:

y = -x - z - 6

Finally, we can use the third equation to solve for x:

x = y + z + 6

Substituting the expressions for y and z into the equation for x, we get:

x = (-x - z - 6) + (x + y + 6) + 6

Simplifying, we get:

2x = 0

Therefore, x = 0. Substituting this value into the expressions for y and z, we get:

y = -z - 6

z = y + 6

We have now solved the system and found that:

x = 0

y = -z - 6

z = y + 6

w = 5

We can write the solution as an ordered quadruple:

(0, -6 - z, z, 5)

where z can take on any value. This means that the system has infinitely many solutions, since we can choose any value for z and obtain a corresponding solution for x, y, and w.

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Answer:

B.

Step-by-step explanation:

Just pick a point on the graph like F

( -1, 3)

(-5,-4)

so its -4 for x and -7 y

If the scooter travels 4.4km with the given radius, the wheel have number of revolutions about 1567 times.

In order to solve this issue, we must first determine the scooter wheel's circumference, which is given by the formula C = 2[tex]\pi[/tex]r, where r is radius of the wheel. Hence, the circumference of a wheel with a 14 cm radius would be:

C = 2[tex]\pi[/tex](14cm) = 28[tex]\pi[/tex] cm

We must translate the distance from kilometres to centimetres in order to determine how many revolutions the wheel completes if the scooter travels 4.4 kilometres. 1 km equals 100,000 cm, so 4.4 km is equal to 440,000 cm.

Now, we can calculate the number of rotations by dividing the distance travelled by the wheel's circumference:

Distance travelled divided by circumference equals the number of revolutions.

440,000 cm / 28 cm divided by the number of revolutions

1566.99 revolutions were made.

Therefore if the scooter travels 4.4km, the wheel will turn about 1567 times.

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Answer:

34

Step-by-step explanation:

5 ( x + 2 ) + 9 ( y - 1 )

Solve the brackets.

5x + 10 + 9y - 9

Combine like terms.

5x + 9y + 1

Given that,

x = 3

y = 2

So, to find the value of the expression replace x and y with 3 & 2 and solve the expression.

Let us solve it now.

5x + 9y + 1

5 × 3 + 9 × 2 + 1

15 + 18 + 1

34

Answer:

1

Step-by-step explanation:

5x + 1 / 4y²

5(3) + 1 / 4(2)²

15 + 1 / 4(4)

16 / 16 = 1

Answer:

see step by step

Step-by-step explanation:

so a laptop starts at 1450 this means the equation is

y=1450(0.75)^x and plug in 4 for x and you get $458.79

The length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm. In a right triangle, the side opposite the right angle is the hypotenuse, while the other two sides are the legs.

Let's label the sides of the triangle ABC as follows:

BC is the hypotenuse, opposite to the right angle at B.

AB is a leg, adjacent to the angle A.

AC is a leg, opposite to the angle A.

Given that the area of the triangle is 32√3cm^2, we have:

(area) = (1/2) x (base) x (height)

Substituting the values we know, we get:

32√3 = (1/2) x AB x AC

Simplifying, we get:

AB x AC = 64√3

We also know that <A = 30 degrees, which means that <C = 60 degrees (since the angles in a triangle add up to 180 degrees).

Now we can use the trigonometric ratios to find the lengths of the sides. We have:

sin(30) = AC/BC

cos(30) = AB/BC

Solving for AC and AB, we get:

AC = BC x sin(30) = BC/2

AB = BC x cos(30) = BC√3/2

Substituting these values into the equation we got earlier, we get:

(BC/2) x (BC√3/2) = 64√3

Simplifying, we get:

BC^2 = 256

Taking the positive square root, we get:

BC = 16

Substituting this value into the equations we got for AB and AC, we get:

AB = BC√3/2 = 8√3

AC = BC/2 = 8

Therefore, the length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm.

The complete question is:

right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.​

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