find the missing side lengths​

Answer:

x = 6; y = 4

Step-by-step explanation:

y=4

-3x+5y=2

-3x + 5(4) = 2

-3x + 20 = 2

-3x = -18

x = 6

Answer: x = 6; y = 4

Answer:

(6,4)

Step-by-step explanation:

y=4

-3x+5y=2

Substitute y=4 into the second equation

-3x+5*4=2

-3x +20 = 2

Subtract 20 from each side

-3x +20-20 = 2-20

-3x = -18

Divide by -3

-3x/-3 = -18/-3

x=6

(6,4)

Answer:

(x-2)/3

Step-by-step explanation:

3x^2 -12

------------------

9x+18

Factor

3(x^2-4)

-------------

9(x+2)

Notice the numerator is the difference of squares

3(x-2)(x+2)

--------------------

3*3(x+2)

Canceling like terms

(x-2)

--------

3

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]\dfrac{3x^2-12}{9x+18}\\\\ \dfrac{3(x^2-4)}{9(x+2)}\\\\ \dfrac{3(x+2)(x-2)}{3.3(x+2)}\\\\ \dfrac{\cancel{3(x+2)}(x-2)}{3.\cancel{3(x+2)}}\\\\\dfrac{x-2}{3}[/tex]

Answer:

f (x) = x3 – 3x2 – 5x + 15

Step-by-step explanation:

i just took the test

The required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]

The correct answer is an option (C)

"It is an algebraic expression that consist of variables and coefficients."

For given question,

The polynomial function has the zeros 3, radical 5, and negative radical 5.

The polynomial function has zeros 3, √5, -√5

This means the factors of the polynomial function are (x - 3), (x - √5) and (x - (-√5)) = (x + √5).

Using the Factor theorem the polynomial function would be,

[tex]\Rightarrow f(x)=0\\\\\Rightarrow (x - 3)\times (x - \sqrt{5} )\times (x + \sqrt{5} ) = 0\\\\\Rightarrow (x-3)\times (x^{2} - (\sqrt{5} )^{2} )=0\\\\\Rightarrow (x-3)\times (x^{2} - 5)=0\\\\\Rightarrow x \times (x^{2} - 5) - 3\times (x^{2} - 5) =0\\\\\Rightarrow x^{3}-5x-(3x^{2}-15)=0\\\\\Rightarrow x^{3}-3x^{2}-5x+15=0[/tex]

Therefore, the required polynomial is [tex]\bold{f(x)=x^{3}-3x^{2}-5x+15}[/tex]

The correct answer is an option (C)

Learn more about the factors of the polynomial here:

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Answer:

[tex]\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}[/tex]

Step-by-step explanation:

The given numbers and their categories are;

1) [tex]-3\dfrac{3}{9}[/tex]  is not a natural number, because, natural numbers are whole number positive integers. It is not an integer, because it is a fraction.

It is a real number, because it has no imaginary part and it is a rational number because it can be expressed as a fraction

2) √11 is not a rational number, because it cannot be expressed as a fraction, and it is real number because it has no imaginary parts.

Therefore, is an irrational and real number

3) 125; The options selected are correct

4) 4·∛125 = 4 × 5 = 20; The options selected are correct

5) 7.[tex]\overline {17}[/tex] = 710/99; Therefore, 7.[tex]\overline {17}[/tex] is a rational number and it is also a real number as all natural, whole, integers, rational, and irrational numbers are real numbers

We get;

[tex]\begin{array}{ccccccc}&Natural&Whole &Integer&Rational&Irrational&Real\\-3\dfrac{3}{9}&&&& \checkmark&&\checkmark\\\sqrt{11} &&&&&\checkmark &\checkmark\\125&\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\4\cdot \sqrt[3]{125} &\checkmark&\checkmark&\checkmark&\checkmark&&\checkmark\\7.\overline {17} &&&& \checkmark&&\checkmark\end{array}[/tex]

Answer:

3

Step-by-step explanation:

assuming you forgot you ^ mark after x x^3 would be the highest x order here making it the order for the equation.

Answer:

O-2(x+5)=2x-10

Explanation

O-2(x+5)=2x-10

SOLUTION

-2x(x)= -2x

-2x+5 = -10

Answer:-7

Step-by-step explanation:

24-8i=10-10i

24-10=-10i+8i

14=-2i

I=-7

Answer:

1

Step-by-step explanation:

(a) i aint drawing a tree but basically, if left means a boy is born and right means a girl is born, the far left result (both boys) will happen with probability [tex](0.52)^2[/tex], the two middle results (one boy and one girl) will both happen with probablility [tex]0.48 \cdot 0.52[/tex], and the far right result (both girls) will happen with probability [tex](0.48)^2[/tex].

(b) binomial distribution table for what...?

Answer:

C

Step-by-step explanation:

By using a piece-wise function that models the cost as a function of the number of miles driven, we will see that the cost for 150 miles is $67.00

We know that there is a base fee of $40 plus $0.25 for the first 100 miles, and for each mile, after the 100 the cost is $0.18.

Then we have the piece-wise function:

c(x) = $40 + $0.25*x   0 ≤ x ≤ 100

c'(x) = $40+ $0.18*x   100 ≤ x

If x = 150, we need to use the second part, this will give:

c(150) = $40 + $0.18*150 = $67.00

So the cost is $67.00

If you want to learn more about piece-wise functions, you can read:

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Answer:

4049

Step-by-step explanation:

For a set of N numbers:

{x₁, x₂, ..., xₙ}

The mean is given by:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

So, if we have 2021 different positive integers, we have N = 2021.

We know that the mean is 3939.

We want to find the minimum possible value of the largest number in the set.

This is kinda trivial but:

We have 2021 numbers = 2020 numbers + 1 number

So we can assume that half of these 2020 numbers are consecutive to and smaller than 3939 and half are larger than and consecutive to 3939, and the remaining number is 3939, then our set is:

{ (3939 - 1010), (3939 + 1009),..., (3939), ..., (3939 + 1010)}

Obviusly, because the numbers are symmetrically distributed around 3939, the mean will be 3939.

And this is the case where we have the smallest largest value in the set, as the numbers are all clustered, for example, if one of the numbers in the lower side was 2 units smaller, then the largest number should be 2 units larger.

Then, the minimum possible value of the largest number is:

3939 + 1010 = 4049

Step-by-step explanation:

5 × 10[tex] {}^{-5} [/tex]

is in standard form or scientific notification. I have assumed that you meant what is 5 × 10[tex] {}^{-5} [/tex]

as a number

so here it is :-

[tex]5 \times {10}^{-5} = \frac{5}{100000} [/tex]

[tex] = 0.00005[/tex]

the Standard form 5x10-⁵ is 0.00005.

Answer:

[tex]\bold{5*10^{-5}=\frac{5}{100000}=0.00005}[/tex]

Answer:

Yes, she will be able to retrieve the item

Step-by-step explanation:

The information with regards to the research historian interest in finding a sunken treasure are;

The depth from which the equipment can recover items = 5,000 m

The speed of sound through water, v = 1,530 m/s

The time it takes the echo from the item to return to the sonar detector, t = 6.2 s

Let d, represent the depth at which the item is located

Given that an echo travels from the sonar detector to the item and back to the sonar detector, the distance traveled by the sound wave which is received as an echo by the sonar detector = 2 × d

Velocity, v = Distance/time

∴ Distance = Velocity × Time

The distance traveled by the echo = 2 × d = v × t

2 × d = v × t

∴ 2 × d = 1,530 m/s × 6.2 s

d = (1,530 m/s × 6.2 s)/2 = 4,743 m

The depth at which the item is located, d = 4,743 m is less than the maximum depth the equipment can recover items, therefore, she will be able to retrieve the item.

Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

by plugging on the number 2 to the equation, solve 3×2=6 and then subtract 1=5

Answer:

Splash Island.

Step-by-step explanation:

Magic Park = 32 - 7 = 25 you would have 25 dollars to spend on rides which would only get you 5 rides.

Splash Island = 32 - 14 = 18 this gives you 18 dollars to spend on rides, which would get you 6 rides.

Therefore you can go on more rides at Splash Island.

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\sqrt{8}-\sqrt{72}+\sqrt{50}[/tex] These cannot combine the way they are. The rule for adding and subtracting radicals is really picky. Not only does the index have to be the same (the little number that is sitting outside in the bend of the radical {ours is a 2, which isn't usually there, but is instead understood to be a square root}), but the radicand, the expression under the square root (or cubed root, or fourth root, etc) has to the same as well. All of our radicals are square roots, so that's good, but the radicands are all different. The first one is an 8, the next one is a 72, and the last one is a 50. BUT if we can rewrite them by simplifying them and then the radicands are the same, we're in good shape.

Simplify by taking the prime factorization of each of those numbers.

8: 4*2 and 4 is a perfect square, so we'll stop there

72: 36*2 and 36 is a perfect square, so we'll stop there

50: 25*2 and 25 is a perfect square, so we'll stop there.

Now, rewrite each one of them in terms of their prime factorization:

[tex]\sqrt{4*2}-\sqrt{36*2}+\sqrt{25*2}[/tex] and then pull out each perfect square as its root:

[tex]2\sqrt{2}-6\sqrt{2}+5\sqrt{2}[/tex] and now all the radicands are the same, so we can add them to get

[tex]1\sqrt{2}[/tex]  or simply  [tex]\sqrt{2}[/tex]

Answer:

[tex]A: \sqrt{2}[/tex]

Step-by-step explanation:

sqrt 8 = sqrt (2 * 2 *2 ) = [tex]2\sqrt{2}[/tex]

sqrt 72 = sqrt (2 * 2 *2 * 3 * 3 ) = [tex]6\sqrt{2}[/tex]

sqrt 50= sqrt (2 * 5 *5 ) = [tex]5\sqrt{2}[/tex]

Answer:

Yes, the function is symmetric about y-axis.

Step-by-step explanation:

To check whether the function is symmetric with respect to y-axis, replace each x as -x and simplify.

If h(x) = h(-x) then it is symmetric about y-axis.

Let's find h(-x) now.

h(-x)= [tex](-x)^4} -5(-x)^{2} +3[/tex]

Let's simplify it

h(-x)=[tex]x^{4}-5x^{2} +3[/tex]

Here, h(x) = h(-x). The function is symmetric about y-axis.

Answer:

[tex]WX=\sqrt{970}[/tex]

Step-by-step explanation:

The diagonals of a kite intersect at a 90-degree angle. In this figure, right triangle [tex]\triangle WRX[/tex] is formed by half of each of the diagonals.

In any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.

Segment WR is one leg of the triangle and is given as 21. XR forms the other leg of the triangle, and is exactly half of diagonal XZ. Therefore, [tex]XR=\frac{1}{2}\cdot 46=23[/tex].

The segment we're being asking to find, WX, marks the hypotenuse of the triangle.

Therefore, substitute our known information into the Pythagorean Theorem:

[tex]21^2+23^2=WX^2,\\WX^2=970,\\WX=\boxed{\sqrt{970}}[/tex]

Answer:

WX= 31.14

Step-by-step explanation:

Use the Pythagorean theorem- [tex]a^{2} +b^{2} =c^{2}[/tex]

XR=23 by taking half of 46

[tex]21^{2} +23^{2} =c^{2} \\441+529=c^{2} \\970=c^{2}[/tex]

sqrt both sides to get your answer of 31.14

Answer:

Step-by-step explanation:

1) ML // JK , MK is transversal,

∠LMK = ∠MKJ   {Alternate interior angles are congruent}

∠LMK = 30°

In ΔMKO,

30 + 115 + ∠ JLM = 180  {Angle sum property of triangle}

        145 +∠ JLM  = 180

∠ JLM  = 180 - 145

∠ JLM = 35°

2) AB // CD , AC is transversal

∠DCA = ∠BAC     {Alternate interior angles are congruent}

∠DCA = 23

∠BCD = ∠DCA + ∠BCA

          = 23 + 37

          = 60

3) EF // HG ; FH  is transversal

∠FHG = ∠HFE   {Alternate interior angles are congruent}

 ∠FHG = 77

4) ZY // WX ;  WY is transversal

∠ZYW = ∠XWY         {Alternate interior angles are congruent}

            = 65

ZY // WX ;  WY is transversal

∠ZWY = ∠WYX   {Alternate interior angles are congruent}

           = 36

In  ΔWZY

36 +  65 + ∠z = 180

        101 +∠Z = 180

∠Z = 180 - 101

∠Z = 79

Answer:

[tex]\sqrt{17}[/tex]

Step-by-step explanation:

[tex]\sqrt{4^2 + 1^2}[/tex]

[tex]\sqrt{17}[/tex]

Answer:

B

Step-by-step explanation:

A x - 36 <42 is wrong because its saying how many can be added

B x +36 < 42 this one is most likely correct because its displays x as how many can be added

C x - 36 > 42 this is wrong because the bus has less than 42 seats

D x + 36 >57 like i said cant be over 42

The inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. Inequality is used most often to compare two numbers on the number line by their size. There is always a definite equation to represent it.

Let x be the number of passengers that can be added to the bus.

It is given that the bus has less than 42 seats and 36 seats are already occupied.

The sum of the remaining seats which are to be filled by the passenger and the 36 seats which are filled, must be less than the total seats that is 42.

Therefore the inequality equation becomes,

x + 36 < 42.

Thus, the inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.

To learn more about inequality equation, refer -

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Answer:

sink at 1.28 g/cm^3

v = 4/3 [tex]\pi r^{3}[/tex]

v = 4/3 [tex]\pi 1.4^{3}[/tex]

v =11.49 /9 =1.28

Step-by-step explanation:

Answer:

m<ECB = 65°

Step-by-step explanation:

<ACB and <ACD are vertical angles. That means they are congruent and have equal measures.

m<ECB = 65°

Answer: 16:81

Step-by-step explanation:

Answer:

Perpendicular

Step-by-step explanation:

Perpendicular lines intersect and create 4 90 degree angles

Line AB and CD intersect and create 4 90 degree angles therefore line AB and CD are perpendicular

Answer:

3X +ky=8 eqn 1

X-2ky=5 eqn 2

but we want to eliminate ky to get our X.

So let's multiply eqn 1 by 2.

We will have 6x +2ky=16 now eqn 3

now we add eqn 1 and 2

We will have 7x=21

divide by 7

x=3

Answer:

Step-by-step explanation:

x = - 48/-8  = 6

c = c^2/c^1 = c^(2-1) = c^1

d = d^4 / d^1 = d^(4 - 1) = d ^3

x = 6

e = 1

f = 3

Answer:

86°

Step-by-step explanation:

180-(2*47)

= 180-94

= 86

Answered by GAUTHMATH

Answer:

isosceles

obtuse

Step-by-step explanation:

We know that one angle is 104 and angles greater than 90 and less than 180 are obtuse

We know that 2 sides are equal indicated by the lines on the sides.  That means the triangle is isosceles