Solving Systems of Quadratic Equations
5. Solve this nonlinear system of equations. Show your work.
a. Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point)
b. Factor your equation from Part a. (1 point)
c. Identify the x-values of the solutions. (1 point)
d. Identify the solutions to the system. (1 point)

For the given graph of the function: Period = π, Domain = [0,π], Range = (-∞, + ∞), Asymptotes at x = 0.

Period:

A function is referred to as periodic if it repeats a pattern, such as sine or cosine. The shortest interval with exactly one instance of the repeating pattern is said to have a period, which is its length.

Period = π

Domain:

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

Domain = [0,π]

Range:

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Range = (-∞, + ∞)

Asymptotes:

The graph of the a function approaches an asymptote as either x or y approach positive or negative infinity, respectively.

Asymptotes at x = 0.

As a result, whenever x = 0, the function possesses a vertical asymptote.

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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 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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The relations that are functions are the ones in options 12 and 13

A relation is a function only if each one of the inputs is mapped to a single one output, so if you see a relation where the same input is mapped into different outputs, this is not a function.

Then the relations that are functions are options 12 and 13, in the other two we can see that there are multiple outputs for the same inputs.

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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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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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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:

[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.

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: 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.

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.

Answer:

y = (-3)2^x

Step-by-step explanation:

We can substitute the two points in the equation y = abˣ and we get two equations. By solving the two equations, we can find the values of a and b.

Substitute (0, -3)  in the equation y = abˣ            

-3 = a * b⁰            

-3 = a * 1              

[tex]\boxed{\bf a = -3}[/tex]

Substitute (4, -48) in the equation y =abˣ

-48 = (-3) * b⁴

[tex]\dfrac{-48}{-3}=b^4\\\\ b^4 = 16\\\\b^4 = 2^4\\\\ \boxed{\bf b = 2}[/tex]

Exponential function:

           [tex]y = (-3)2^x[/tex]

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

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:

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

In conclusion √-36 can be simplified to 6i.

How to simplify and what does a square root mean?

The square root of a negative number is not a real number, as any real number squared gives a non-negative result. Therefore, the expression √-36 cannot be simplified in terms of real numbers.

However, in some mathematical contexts, we define the imaginary unit i as √-1. With this definition, we can write:

√-36 = √(36)√(-1) = 6i

Therefore, in this context, √-36 can be simplified to 6i.

In mathematics, the square root of a non-negative real number is a number that, when multiplied by itself, gives the original number. The square root is denoted by the symbol √.

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Answer:

1

Step-by-step explanation:

5x + 1 / 4y²

5(3) + 1 / 4(2)²

15 + 1 / 4(4)

16 / 16 = 1

Answer:

A) 0.5%

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

0.5%

Step-by-step explanation:

7 out of 1400 walk

7/1400 = 1/ 200   divide by 2 equals   0.5/100=0.5%

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

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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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.

Answer: you good day

Step-by-step explanation:

Assumptions for above case:

1-Equal payments are made monthly.

2-Total amount deposited throughout the year are compounded by end of the year.

3-Annual interest is 6%

4-Total Amount invested plus interest at maturity are reinvested the following year.

Given above, if you create a table in excel for those calculations, you would get $296.330 /month which amounts to $12,000.00 in 3 years approximately.

Year 1 = $3,555.96 Pre-interest =>$3769.32 Post 6% interest

Year 2 = $7,325.28 Pre-interest =>$7,325.28 Post 6% interest

Year 3= $11,320.75 Pre-interest =>$12,000.00 Post 6% interest.

The way to calculate pre interest for each year is just $296.330*12=$3555.96

Afterwards just multiply by the annual interest rate to get the full amount invested + interest (6%) =>$3555.96*(1.06)= $3769.32

Then As per step 1, add another 3555.96 and multiply it all by 1.06, to get 305.06

x = $305.06

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.

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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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:

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

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.

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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