If the legs of a right triangle are 8 and 10, find the length of the hypotenuse.

Answer:

Using the rational root theorem, we know to divide the function by (x - 1).

(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4

Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).

Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).

Using the factorized form above, the zeros of the function are 1, -2/7, and -2.

Answer:

x greater than equal to (-1)

x less than 2

all no. greater than -1 = -1,1, 0 , 1 ,2 ......

no. less than2 = 1, 0, -1,.......

-1,0, 1

Answer:

yes

Step-by-step explanation:

because bank

Answer:

x=80.8

Step-by-step explanation:

follow BODMAS

2015-(2015÷5(x-5)÷5)=2014

2015-(2015÷5x-25÷5)=2014

2015-(405/x-5)=2014

2015-(405-5x)=2014

2015-405+5x=2014

1610+5x=2014

5x=2014-1610

(5x=404)1/5

x=80.8

Answer:

first 1*3+1-3*4+1

then it is in fraction

the answer is -5

Answer:

ab+bc+ac = 7+21 + 28 =56

so the answer is 56

Observe that

[tex]a^2 + b^2 + ab = 7 \iff a^2 + b^2 - 2\cos(120^\circ) = \left(\sqrt 7\right)^2[/tex]

[tex]b^2 + c^2 + bc = 21 \iff b^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{21}\right)^2[/tex]

[tex]a^2 + c^2 + ac = 28 \iff a^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{28}\right)^2[/tex]

Drawing a comparison to the law of cosines, we see the first equation defines a triangle with sides [tex]a[/tex], [tex]b[/tex], and [tex]\sqrt 7[/tex]; the second equation defines one with sides [tex]b[/tex], [tex]c[/tex], and [tex]\sqrt{21}[/tex]; and the third equation defines another one with sides [tex]a[/tex], [tex]c[/tex], and [tex]\sqrt{28}[/tex]. We can then join these triangles at a point D to form a new triangle ABC with sides [tex]\sqrt7,\sqrt{21},\sqrt{28}[/tex]. (See attached sketch)

Now, the area of ABC is the sum of the areas of ABD, BCD, and ACD. The area of any of these triangles is equal to half the area of a parallelogram spanned by the sides involving the vertex D. The area of a parallelogram with adjacent sides [tex]x[/tex] and [tex]y[/tex] and with angle [tex]\theta[/tex] between them is [tex]ab\sin(\theta)[/tex].

For example, triangle ABD has area

[tex]\mathrm{area}_{\Delta ABD} = \dfrac12 \times ab \sin(120^\circ)[/tex]

Then the total area of triangle ABC is

[tex]\mathrm{area}_{\Delta ABC} = \dfrac12 \sin(120^\circ) (ab + ac + bc)[/tex]

We use Heron's formula to find the area of ABC. If [tex]s[/tex] is its semiperimeter, i.e.

[tex]s = \dfrac{\sqrt7 +\sqrt{21} + \sqrt{28}}2[/tex]

then, with a lot of algebraic simplification,

[tex]\mathrm{area}_{\Delta ABC} = \sqrt{s (s-\sqrt7) (s - \sqrt{21}) (s - \sqrt{28})} = \dfrac{7\sqrt3}2[/tex]

Finally, we find

[tex]\dfrac{7\sqrt3}2 = \dfrac12 \sin(120^\circ) (ab + ac + bc) \implies ab + ac + bc = \dfrac{\frac{7\sqrt3}2}{\frac12\times\frac{\sqrt3}2} = \boxed{14}[/tex]

Answer: 0 ≤ y < ∞

Step-by-step explanation:

   First, let us graph the function. See attached.

-> If I graphed the formatting of the square root sign incorrectly, please let me know so I can fix the answer.

  The range of the function is all of the function's output values. In this case, all of the y values.

        0 ≤ y < ∞

Answer:

24000

Step-by-step explanation:

6/5×20000

=24000

The approximate length of the side EF will be 1 unit.

The complete figure is attached below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is given below.

The length of EF will be

EF = CF – CE

Then the value of CF will be

CF = BC × cos 30

CF = 2 × 0.866

CF = 1.732

Then the value of CE will be

CE = BC × cos 42

CE = 1 × 0.743

CE = 0.743

Then we have

EF = 1.732 – 0.743

EF = 0.989 ≈ 1

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The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

To purchase 13700 worth of restaurant equipment for her business.

Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.

The total amount Maria ended up paying for the equipment will be

Total amount = 371.16 × 3 × 12 + 1500

Total amount = $14,861.76

The interest of Maria on the loan will be

Interset = [(14861.76 – 13700) / 13700] x 100

Interset = 8.48%

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Answer:

Step-by-step explanation:

plug in x try numbers

x = 14.2

Answer:

600

Step-by-step explanation:

Let's consider this question using algebra.

Imagine the number of bricks in the original pile is [tex]x[/tex].

We are told that [tex]\frac{3}{4}[/tex] of the bricks are used for a project, meaning that [tex]\frac{3}{4} x[/tex] has been used, leaving us with [tex]\frac{1}{4}x[/tex] as our remainder.

Then, we are told that [tex]\frac{2}{3}[/tex] of the remainder are used to leave us with 50 bricks. This means that [tex]\frac{1}{3}[/tex] of the remainder is left, and this is equal to 50 bricks. This means that the remainder's original amount is equal to 150, because we are told that [tex]\frac{1}{3}[/tex] of the remainder is equal to 50.

So, we know that the remainder is 150, and we also know that the remainder is [tex]\frac{1}{4} x[/tex]. Let's now use these to form an equation.

[tex]\frac{1}{4} x = 150[/tex]

Because we know that a quarter of the original amount of bricks is equal to 150, we can multiply both sides of the equation by 4 to get the original amount of bricks in the pile.

[tex]x = 150 * 4 = 600[/tex]

So, there were 600 bricks in the original pile.

Answer:

11 is best answer for it ....,..........

Answer:

10

Step-by-step explanation:

Jessica sells = 240 books,

Josh sells = 16 books.

The price of one book is = $15

Jessica sold 15 times more books than Josh.

In total, they have sold 256 books.

We can easily find the answer using variables.

Let,

Josh sold a total of x books whereas Jessica sold a total number of 15x books.

together they sold 16x books.

So we can form the equation

16x= 256

by solving this equation we will get x=16

So, Josh sold 16 books and Jessica sold 16×15=240 books in total.

Answer:

Jessica=240

Josh=15

Step-by-step explanation:

Answer:

K=-3/5

Step-by-step explanation:

y= -3x/5 - 11/5

Answer:

√2/4, √3/4, and √5/4.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer: 10

Step-by-step explanation:

The slope of the given line is 10, and since parallel lines have equivalent slopes, the slope of a line parallel to the given line is also 10

Probability that the salesperson has “Fair” potential or has Above Average Sales ability is; 90.8%

A) Probability that the salesperson has “Fair” potential for advancement = (16 + 45 + 93)/500 = 154/500 = 30.8%

B)  Probability that the salesperson has “Fair” potential or has Above Average Sales ability = 30.8% + (300/500)% = 90.8%

C) Probability that the salesperson has “Fair” potential given they have Above Average Sales ability = P(A|B) = P(A ∩ B)/P(B) = (93/500)/0.6 = 0.31 = 31%

D) P(selecting 2 salespersons and finding they both have Fair potential for advancement) = (154/500) * (153/499) = 9.44%

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Answer:

D

Step-by-step explanation:

the cordinate is at (-3,2)

Answer:

[tex]\boxed{\sf x= -29.5}[/tex]

Step-by-step explanation:

[tex]\sf \sqrt{-2x+5}-3=5[/tex]

[tex]\sf \sqrt{-2x+5}=8[/tex]

[tex]\sf -2x+5=64[/tex]

[tex]\sf -2x=59[/tex]

[tex]\sf \cfrac{-2x}{-2}=\cfrac{59}{-2}[/tex]

Therefore, x = -29.5.

Answer:

A

Step-by-step explanation:

In this case you have to show that 1 + 2 = 180

This way when you show that 2 + 3 = 180, that proves 1 & 3 are congruent.

Answer:

A. 2. ∡1 is supplementary to ∡2 (linear pair theorem)

Step-by-step explanation:

Given the following proof so far, we have:
1. Line a and line b intersect => given

2. ? => ?

3.  ∡3 is supplementary to  ∡2 => linear pair theorem

4.  ∡1 ≅ ∡3 => congruent supplements theorem

Now let's take a look at the reasoning for statement 4, which says that angle 1 and 3 are congruent due to congruent supplements theorem.

In this theorem, if 2 angles are supplementary (add up to 180 degrees) to the same angle, it means those 2 angles are congruent.

Why does this work?
________________________________________________________
Let's say x + y = 180, and z + y = 180

By transitivity (if a = b and b =c, then a=c), x + y is equal to z + y

x + y = z + y

Subtract y from both sides

x = z

________________________________________________________

Statement 3 says  ∡3 is supplementary to  ∡2, and because of congruent supplements theorem being our last reason (where  ∡1 and  ∡3 are congruent), we need to make statement 2 also have ∡1 being supplementary to ∡2, (∡2 is like y in the example above - it's the angle that  ∡1 and  ∡3 are both supplementary to).

This will eliminate choices B (which has  ∡1, but also  ∡4 which isn't necessary), C ( ∡which mentions nothing about  ∡1), and D (which also doesn't mention anything about  ∡1, and which also isn't necessary as we have statement 3 essentially saying the same thing), leaving A as the correct answer.

Answer: The function is odd and symmetric with respect to the origin.

Step-by-step explanation:

A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.

[tex]f(x)=x^{3}-2x\\\\f(-x)=(-x)^{3}-2(-x)=-x^{3}+2x=-f(x)[/tex]

Therefore, the function is odd, and thus the function is symmetric about the origin

The median of the distribution is 4.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The median is the number at the center of the data set.

Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10

1/2 x 22 = 11th number  4

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Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given Inequalities can be solved as,

5 - x > 7

-x > 7 - 5

-x > 2

x < -2

2x + 3 ≥ 13

2x ≥ 10

x ≥ 5

As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.

This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.

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Answer:

  145 square inches

Step-by-step explanation:

The surface area of a square pyramid can be found using the formula ...

  A = s(s +2h) . . . . . where s is the base side length, and h is the slant height

__

Using this formula with s=5 inches and h=12 inches, we find the area to be ...

  A = (5 in)(5 in +2(12 in)) = (5 in)(29 in) = 145 in²

The area of the pyramid is 145 square inches.

_____

Additional comment

This formula comes from the sum of the areas of the square base (s²) and the four triangular faces (4 × 1/2sh). That sum is ...

  A = s² +2sh = s(s +2h)

Answer:

D.

Step-by-step explanation:

He has to walk down 3 blocks and right 10

Answer:

33 elements

Step-by-step explanation:

Set A has 59 elements. Set A and Set B share 26 elements.

This means that 26 out of the 59 elements in Set A are also in set B.

Therefore, to find the number of elements not in Set B, you need to subtract the common elements from the total amount of elements in Set A.

59 (total in Set A) - 26 (common in Set A) = 33 (unshared elements).

The probability that both are red marbles is 0.2391

The given parameters are:

Red =12

Blue = 12

Total = 24

The probability of selecting the first red marble :

P(Red) = 12/24

Now, there are 11 red marbles and 23 marbles in all

The probability of selecting the second red marble :

P(Red) = 11/23

The required probability is:

P =  12/24 * 11/23

Evaluate

P = 0.2391

Hence, the probability that both are red marbles is 0.2391

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