Find the values of x and y.

Answer:

[tex]-\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given a polynomial with rational coefficients, its irrational and complex roots would occur in conjugate pairs.

For example, if the roots of a polynomial are 2 + [tex]\sqrt{3}[/tex], 3 and 4 - 3i, then 2 - [tex]\sqrt{3}[/tex], and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are , [tex]\sqrt{2}[/tex] and  - [tex]\sqrt{13}[/tex], then -[tex]\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex] are also roots of the polynomial.

Answer:

(0,1)

Step-by-step explanation:

Complete question :

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnell is a middle school student with a height of 161.4 centimeters.

What proportion of student heights are lower than Darnell's height?

Answer:

0.716 (71.6%)

Step-by-step explanation:

Given that :

Mean, μ = 150

Standard deviation, σ = 20

Darnell's height, x = 161.4

(x < 161.4)

We obtain the standardized score, then find the proportion using a standard normal distribution ;

Zscore = (x - μ) / σ

Zscore = (161.4 - 150) / 20

Zscore = 11.4 / 20

Z = 0.57

P(Z < 0.57) = 0.71566 (Z probability calculator)

This means that about 0.716 (0.716 * 100% = 71.6%) of student's height are lower than 161.4 centimeters

Answer: 0.11

Step-by-step explanation:

Since we know the distribution of heights is normally distributed, the probability P(X>175)  can be found by calculating the shaded area above X=175  in the corresponding normal distribution:

P(X>175)≈0.11 is the answer.

Answer:

4in

Step-by-step explanation:

Answer:

46 feet

Step-by-step explanation:

23 x 2 = 46

Answer: 2 2/3

Step-by-step explanation:

Answer:

13 weeks

Step-by-step explanation:

Given that :

Cost of new tub = $312

Planned saving per week = $24

The number of weeks he'll have to save in other to be able to afford the tub can be obtained using the relation :

Number of weeks = cost of new tub / weekly saving

Number of weeks = $312 / $24

Number of weeks = 13 weeks

x = - 8 is the solution for 7x + 5 = - 19. This can be solved using the concept of equation solving.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

7x + 5 = -19

or, 7x = - 19 - 5

or, 7x = - 24

or, x = - 8

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Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Given

y  x² - 8x + 14

(a)

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 8x

y = x² + 2(- 4)x + 16 - 16 + 14

y = (x - 4)² - 2 ← in vertex form

(b)

Since the multiplier a = 1 > 0 then vertex is a minimum

(c)

(h , k ) = (4, - 2 ) ← coordinates of vertex

Answer:

look at the picture I sent

Answer:

69

Step-by-step explanation:

becuz

The scale factor of the image is 1/4 or 0.25.

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

To solve this question, use the coordinates of WX and W'X' as points of reference.

From the diagram, it can be obtained that -

W(-8,8) and X(8,0)

W'(-2,2) and X'(2,0)

First, calculate distance for WX -

Distance formula is -

d = √(x2-x1)^2+(y2-y1)^2

Distance for WX -

d1 = √(8+8)^2+(0-8)^2

d1 = √(16)^2+(-8)^2

d1 = √256+64

d1 = √320

d1 = 17.88

Distance for W'X' -

d2 = √(2+2)^2+(0-2)^2

d2 = √(4)^2+(-2)^2

d2 = √16+4

d2 = √20

The scale factor is then calculated using -

Scale = W'X'/WX

Scale = d2/d1

Substitute values of d1 and d2 -

Scale =√20/√320

Scale = √(20/320)

Scale = √1/16

Scale = 1/4

Therefore, the scale value is 0.25.

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Answer:

<DEB

Step-by-step explanation:

It's pretty simple actually. You just have to follow the letters to see if they make an angle. Please mark brainliest. :)

Answer: 360,000

Step-by-step explanation: First you would convert 12 kilometers to meters, which is 120,000. Then multiply that by 3. You get 360,000 meters. Therefore, the car can travel 360,000 meters on liters of gas.

Answer:

okok so you have all those numbers

remember area is multiplying

so multiply all that so that gives u

1,128,600

im not 100% sure but i think

Answer:

2+2i

Step-by-step explanation:

(-5+2i)+(3+4)

-5+3+4+2i

-5+7+2i

2+2i

Answer:

15 whistles

Step-by-step explanation:

12.5 feet is 150 inches

150 ÷ 10 = 15

Answer: Without estimation skills, students aren't able to determine if their answer is within a reasonable range.

Step-by-step explanation:

to make sure your answer at least make sense to the question

Answer:

5%

Step-by-step explanation:

6b - 0.78b it will result after expanding the expression.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.

There are three different expression types:

Let, b represent the original price of a loaf of bread.

Given that,

A grocery store has 13%-off sale on all bread.

This means that the amount by which the price of bread was reduced would be

13/100 × b = 0.13 × b = 0.13b

The new price for the loaf of bread would be: b - 0.13b

you decide to purchase 6 loaves of bread. The expression would be:

6(b - 0.13b)

Expanding the expression, it becomes: 6b - 0.78b

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Answer:

You want the area of the base to equal 20 ft^2

Step-by-step explanation:

Volume of a cube= (L)(w)(h)

Area of base = (L)(W)

60 cubic feet is the volume we are trying to acheive. Since the volume for a cube is (L)(w)(h), 3 needs to multiply by the area of the base to equal the volume. since 3 times 20 equals 60(You solve this by dividing 60 by 3) the base needs to equal 20ft^2.

Answer:

not enough information

Step-by-step explanation:

An expression that describes the team’s total points will be 2w + t.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator

In this case, the soccer team earns 2 points for a win and 1 point for a tie.

Let w represent the number of wins and t represent the number of ties.

The expression that describes the team’s total points will be:

= 2(w) + t

= 2w + t

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Answer:

Creo que la respuesta sería B: 2 horas y 15 minutos.

Step-by-step explanation:

Answer:

Yes (you are 75 mi from epicenter). Travel at least 7.91 mi south

Step-by-step explanation:

See the attached image.

The epicenter is the point at the upper right of the drawing.  You are 60 miles west (left) and 45 miles south (down) from the epicenter.  A right triangle is formed--apply the Pythagorean Theorem, (leg)^2 + (leg)^2 = (hypotenuse)^2.

[tex]x^2=60^2+45^2\\\\x^2=3600+2025\\\\x^2=5625\\\\x=\sqrt{5625}=75[/tex] This is within 80 mi, so you feel the quake.

Now (see image2) you go  y  miles south.  You want the distance between you and the epicenter to be at least 80 mi.  You have another right triangle with legs 60 and y + 45 and hypotenuse 80.

[tex](y+45)^2+60^2=80^2\\\\(y+45)^2+3600=6400\\\\(y+45)^2=2800\\\\y+45=\sqrt{2800}\\\\y=\sqrt{2800}-45 \approx 7.91 \rm mi[/tex]

Answer:

2,4,8

Step-by-step explanation:

The area of the oil spill is 2.924π square inches.

What is the radius of the circle?

Any line segment connecting a circle's center to its perimeter is considered a circle's or sphere's radius, and in more recent usage, their length is also considered. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

Here, we have

The radius of the circle of oil spread is modeled by the function r = ∛s where s = time in seconds.

The area of the oil spill A = πr²

= π(∛s)²

So, we need to find the area of the oil spill when s = 5.

So, A = π(∛s)²

A = π(∛5)²

A = π(1.7099)²

A = 2.924π square inches.

Hence, the area of the oil spill is 2.924π square inches.

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A polynomial is an expression involving variables and coefficients, which is formed by adding, subtracting, multiplying, and taking non-negative integer exponents of the variables. A mathematical statement that two expressions are equal is known as an equation.

A mathematical statement that two expressions are equal is known as an equation.

Example of a polynomial:

2x^2 + 3x + 5

Example of an equation:

2x^2 + 3x + 5 = 0

Let's say we are solving the equation 2x^2 + 3x + 5 = 0

Step 1: Subtract 5 from both sides.

2x^2 + 3x = -5

Step 2: Divide both sides by 2.

x^2 + 3/2 x = -5/2

Step 3: Use the quadratic formula to solve for x.

x = (-3 ± √17) / 4

Step 4: Simplify the answer.

x = (-3 ± 4.12) / 4

Step 5: Solve for the two values of x.

x = -0.78 or x = 3.28

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A three-degree equation is referred to as a cubic equation. The polynomials are referred to as cubic polynomials if they have a degree of three.

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. The polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

given

A three-degree equation is referred to as a cubic equation.

All cubic equations have roots that are either three real roots or one real root and two imaginary roots.

The polynomials are referred to as cubic polynomials if they have a degree of three.

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Ella can type faster than Andrew because the rate at which she types is faster than Andrew's rate by 0.5 text per second.

In Mathematics, rate of change can be defined as a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.

In this scenario, we would determine the rate of change with respect to the amount of words that Andrew and Ella can type per second as a ratio. For the amount of words that Andrew can type per second, we have:

Andrew = 7/21 = 28/84 = 1/3 or 1:3.

For the amount of words that Ella can type per second, we have:

Ella = 4/14 = 16/56 = 1/3.5 or 1:3.5

Difference = 3.5 - 3

Therefore, we can logically conclude that Ella can type faster.

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