If /61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang
answer in simplest radical form.
A. 5
B. 6
C. 2V15
D. 6V10

Answer:

(x+8)²-2=0

(x+8+√2)(x+8-√2)=0

x= - 8- √2 =  -9.41 lesser x

x= -8 + √2 = -6.59  greater x

Answer:

[tex]\mathrm{Decimal}:\quad x=-6.58578\ ,\:x=-9.41421[/tex]

Step-by-step explanation:

[tex]\left(x+8\right)^2-2=0\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\\left(x+8\right)^2-2+2=0+2\\Simplify\\\left(x+8\right)^2=2\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+8=\sqrt{2}:\quad x=\sqrt{2}-8\\x+8=\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=\sqrt{2}-8\\\mathrm{Simplify}\\x=\sqrt{2}-8[/tex]

[tex]\mathrm{Solve\:}\:x+8=-\sqrt{2}:\quad x=-\sqrt{2}-8\\x+8=-\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=-\sqrt{2}-8\\\mathrm{Simplify}\\x=-\sqrt{2}-8\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=\sqrt{2}-8,\:x=-\sqrt{2}-8\\\mathrm{Decimal}:\quad x=-6.58578 ,\:x=-9.41421[/tex]

Answer:

2/255

Step-by-step explanation:

In total, there are 18 books on the shelf.

The probability that person A will pick a novel is 6/18 = 1/3

There are now 5 novels and 17 total books on the shelf

The probability that person A then picks a mystery is 4/17.

There are now 3 mysteries and 16 total books on the shelf.

The probability that person B then picks a mystery is 3/16.

There are now 2 mysteries and 15 total books on the shelf.

The probability that person B then picks a poetry book is 8/15.

The probability that all these events occur back to back is the product of their individual probabilities. Therefore, the probability is:

1/3 * 4/17 * 3/16 * 8/15 = 2/255

Answer:

Yes, there is enough wrapping paper

The area of the wrapping paper is greater than area of the gift

Step-by-step explanation:

What to do is to check the area of the wrapping paper and the gift if equal.

Looking at the dimensions of the gift, it is a cuboid

Area of a cuboid = 2(lb + lh + bh)

where l, b and h are 50, 35,5 respectively

= 2(250 + 175 + 1750)

= 4350 cm^2

The area of the wrapping paper is just the product of its side = 75 * 60 = 4500 cm^2

We can see clearly that the area of the wrapping paper is greater than area of the gift.

so we can conclude that it is enough to wrap the gift

Answer:

$12.75

Step-by-step explanation:

Skubic Family-

22.75 = 5.25 + 7x

17.5 = 7x

2.5 = x

Therefore the cost for each person is equal to $2.5

Shaw Family-

2.5(3) + 5.25

7.5 + 5.25 = $12.75

Answer:

$12.75 is answer c

Step-by-step explanation:

Answer:

7-x

Step-by-step explanation:

49 - x^2 is a perfect square so

it factors to :(7+x)(7-x)

since there is a negative in 49 - x^2, it would make sense that the answer would be a negative to get that negative answer in the first place (negative times a positive equals a negative)

Forgive me for my lame explanation :')

Answer:

A

Step-by-step explanation:

1.5 does not equal 0.15 or the other values.

Answer:

[tex]V=122.5in^3[/tex]

Step-by-step explanation:

The volume of a right circular cone can be found with the formula [tex]V=\pi r^2\frac{h}{3}[/tex] .

So, just plug in the values that are given (by the way, the radius is found by dividing the diameter by 2 since it's half the value of the diameter).

[tex]V=\pi r^2\frac{h}{3}\\V=\pi (3.8)^2(\frac{8.1}{3} )\\V=\pi (14.44)(2.7)\\V=122.484\\V=122.5in^3[/tex]

Answer:

122.5

Step-by-step explanation:

Answer:

a. 54

b. 9.35

Step-by-step explanation:

a. First, divide 15.34 by 0.59 to find the number of songs you had to pay for.

15.34/0.59 = 26

then add it to the number of free songs you downloaded

26 + 28 = 54

b. divide 15.34 by 1.64

15.34/1.64 = 9.35

for c I would just multiply 1.65 by the usd exchange rate (1.64) which is 2.10 so you could afford 3 more songs but I don't know what equation exactly you would use or if what I did works.

Answer:

4.243

Step-by-step explanation:

To calculate the diagonal of a square, multiply the length of the side by the square root of 2:

d = a√2

d = 3√2=4.24264068

Answer:

x+2y=4

Hope this helped

Answer:

468

Step-by-step explanation:

Answer:

237

Step-by-step explanation:

This is written as 1+2+(3x78)

=3+234

=237

Answer:

A) 3

Step-by-step explanation:

The range is the highest value - the lowest value from the data

The data given is 1,2,3,4

Highest value: 4

Lowest value: 1

So range = 4-1

= 3

Answer:

a). A = -2x² + 200x

b). Widths = 40 feet and 60 feet

Step-by-step explanation:

It is given that length of the fencing material = 200 feet

a). Peg wants to cover the vegetable garden from three sides with the given fencing material.

If length of the garden = l

and width of the garden = x

l + x + x = 200

l + 2x = 200

l = (200 - 2x) feet

Therefore, area of the garden = Length × width

A = [tex](200-2x)\times x[/tex]

A = -2x² + 200x

b). Foe A = 4800 square feet,

4800 = -2x² + 200x

2x² - 200x + 4800 = 0

x² - 100x + 2400 = 0

x² - 60x - 40x + 2400 = 0

x(x - 60) - 40(x - 60) = 0

(x - 60)(x - 40) = 0

x = 40, 60 feet

Therefore, widths of Peg's garden will be 40 feet and 60 feet.

Answer:

65p

Step-by-step explanation:

375 divided by 750=0.50

0.50+15=65p

Answer:

0.65

Step-by-step explanation:

750 / 375 = 0.50, and he wanted to sell them for 0.15 more than the original cost, so the answer is 0.65

Answer:

The measure of each angle of the parallelogram.

37∘ , 143∘ , 37∘ , 143∘.

Step-by-step explanation:

Since opposite angles of a parallelogram are equal. Therefore,

3x − 2=50 − x⇒x = 13

(3x−2)∘ = 3(13)−2 = 37∘

The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary.

Another angle = 180−37=143∘

The measure of each angle of the parallelogram.

37∘ , 143∘ , 37∘ , 143∘

Answer:

Step-by-step explanation:

Twins born  call A

single child born called B

twins in family history 1

twins not in family history 2

my new table

          1.                                         2

A     8/34=0.23 (23.52%)      26/34=0.7647 (76.47%)

B. 125/966=0.1293 (12.93%) 841/966=0.8706(87.06%)

I hope u understand my table

Step-by-step explanation:

[tex]10x^2+2x-8\\2(5x^2+x-4)\\2(5x-4)(x+1)[/tex]

Answer:

[tex]2(5x-4)(x+1)[/tex]

You can check the answer by re-distributing the 2 and using the foil method :)

Answer:

7.96 ft

Step-by-step explanation:

Given;

Length of ramp L = 8 ft

Angle with the horizontal (ground) = 6°

Applying trigonometry;

With the length of ramp as the hypothenuse,

The horizontal distance d as the adjacent to angle 6°

Since we want to calculate the adjacent and we have the hypothenuse and the angle. We can apply cosine;

Cosθ = adjacent/hypothenuse

Substituting the values;

Cos6° = d/8

d = 8cos6°

d = 7.956175162946

d = 7.96 ft

The building is 7.96ft away from the entry point of the ramp.

Answer:

(2x+5)(x+4)

Step-by-step explanation:

After factoring we can find that it equals

(2x+5)(x+4)

Answer:

(2x +5) (x+4)

Step-by-step explanation:

2x*2+13x+20

(2x +   )(x+  )

Factoring 20 into 4 and 5  so we can get 13 in the middle

(2x +5) (x+4)

2*4 +5 = 13 for the middle term

Answer:

[tex]4\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{32}= \\\\\sqrt{2\cdot 16}= \\\\\sqrt{2\cdot 4^2}= \\\\4\sqrt{2}[/tex]

Hope this helps!

Answer:

[tex]4\sqrt{2} \\[/tex]

Step-by-step explanation:

4 times the square root of 2 is equivalent to the square root of 32.

Answer:

B→A

Step-by-step explanation:

I'm pretty confident in my answer.

Answer:

[tex] 2 \sqrt{71} \: units[/tex]

Step-by-step explanation:

Given is a right angled triangle in which third side is the hypotenuse.

Therefore, by Pythagoras theorem:

[tex]thid \: side = \sqrt{ {15}^{2} + ( \sqrt{59} )^{2} } \\ \\ = \sqrt{225 + 59} \\ \\ = \sqrt{284} \\ \\ = \sqrt{ {2}^{2} \times 71 } \\ \\ = 2 \sqrt{71} \: units[/tex]

Answer:

The Solution Set

Step-by-step explanation:

Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.

[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\S=\{3,4\}[/tex]

Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.

[tex](3)^{2}-7(3)+12=0\\-12+12=0\\0=0[/tex]

The output or possible values you could get as a result from an expression or equation is the solution set of the equation

Take for instance, we have the following equation

[tex]x^2 = 4[/tex]

When solved, the equation becomes

[tex]x = \pm 2[/tex]

This can be rewritten as:

[tex]x = \{-2,2\}[/tex]

This means that -2 and are the solution set of the equation [tex]x^2 = 4[/tex]

Hence, the output or possible values are called solution set

Read more about equations at:

https://brainly.com/question/14323743

Answer:

f⁻¹(f(6.022)) = 6.022

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Step-by-step explanation:

f⁻¹(f(x)) = x

so  f⁻¹(f(6.022)) = 6.022

inverse function flips y and x coordinates so look at table where f(x)=-10 and read x so f⁻¹(-10) = -6

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Answer:

Answers are: A,D, and  A

Step-by-step explanation:

I hope these are right

Answer:

9

Step-by-step explanation:

Let us look at the factors of each of these

36:

1 and 36

2 and 18

3 and 12

4 and 9

81:

1 and 81

3 and 27

9 and 9

When we look at the factors, we can see that 9 is the Highest Common Factor shared between them.

Answer: hope that's right

HCF OF 36 81 = 9

Step-by-step explanation:

Steps to find HCF:

Find the prime factorization of 36 36 = 2 × 2 × 3 × 3

Find the prime factorization of 81 81 = 3 × 3 × 3 × 3

To find the HCF , multiply all the prime factors common to both numbers:

Therefore, HCF = 3 × 3

Answer:

38^3+10^2+26x+3 over 18x+1

Step-by-step explanation:

Start by adding x's that are alike together.

4x^3+34x^3= 38^3

then do the same to the other x's

5x^2+5x^2= 10^2

Last x's

13x+13x=26x

For the final equation, you should have

38^3+10^2+26x+3

For the bottom equation, you do the same thing.

4x+14x= 18x

Final equation, really easy, is 18x+1

For the final answer you should have

38^3+10^2+26x+3 over 18x+1

Lmk if it helps!! :)

Answer:

A & D

Step-by-step explanation:

Vertical angles are equivalent angles made by intersecting lines. ISN and TSW, and TSN and ISW face each other and are equivalent.