Find the length of the third side. If necessary, write in simplest radical form

Answer:

hypotenuse = 13

shortest side = 5

third side = 12

Step-by-step explanation:

Given sides a, b, and c, with c representing the hypotenuse of a right triangle, we can say that

a²+b² = c² using the Pythagorean Theorem.

We are given that the hypotenuse (c) = 8 cm more than the shortest side. Representing the shortest side as a, we can say that c= 8 + a. Then, the third side, which we can represent as b, is 1cm shorter than the hypotenuse, so c-1 = b

c= 8+a

c-1 = b

a²+b² = c²

One thing we can do is to solve for everything in terms of c and solve the third equation from there

c= 8+a

subtract 8 from both sides

c-8 = a

a²+b² = c²

(c-8)²+b² =c²

b = c-1

(c-8)² + (c-1)² = c²

expand

c²-16c + 64 + c² - 2c + 1 = c²

2c² - 18c + 65 = c²

subtract c² from both sides to make this an equation that we can more easily solve

c² - 18c + 65 = 0

To factor, we can find two numbers that add to (-18) and multiply to 65. Two numbers that work at 13 and 5, so we have

c²-13c-5c + 65 = 0

c(c-13) -5(c-13) = 0

(c-5)(c-13) = 0

Therefore, the hypotenuse, or c, is 5 or 13. Because a=c-8, if c=5, a would be negative 3. This is not possible, so c cannot be 5. Therefore, c=13, a=c-8=5, and b=c-1= 12

Answer: No

Step-by-step explanation:

Because in a rhombus all sides are equal.

In this opposite sides are equal and not all sides.

please click thanks and mark brainliest if you like :)

Answer:

no

Step-by-step explanation:

the definition of a rhombus is a quadrilateral with 4 equal sides so we just have to either prove all the sides are equal or that two or more sides are not equal.

to do this use the distance formula: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

HIJK is a parallelogram but not a rhombus

Answer:

3.18%

2 between 89   91

Step-by-step explanation:

*Probability-Between 3.18%

Z1=0.04 Z2=0.12

x-1 89

x-2 (not required) 91

µ 88

σ 25

Answer:

4, 7, 14

Step-by-step explanation:

Because it's were it decreases

The maximum value of n (A ∩ B) occurs when A ⊂ B (i.e. when A is a subset of B), in which case A ∩ B = A, and so max{n (A ∩ B)} = n (A) = 11.

Question 10

Draw a 30-60-90 triangle template. Refer to the diagram below.

We have 1 as the short leg, 2 as the hypotenuse and sqrt(3) as the long leg.

Place the angle theta as the reference angle such that it's opposite the sqrt(3) side.

That allows tan(theta) = sqrt(3)/1 = opposite/adjacent

In other words, tan(60) = sqrt(3)/1

So theta = 60 is one solution. We add on 180 to get the other solution. So the other solution is 60+180 = 240

So tan(60) = tan(240) = sqrt(3)

======================================================

Question 11a

sin(theta) = -0.8

theta = arcsin(-0.8) or theta = 180-arcsin(-0.8)

theta = -53.1301  or theta = 180 - (-53.1301)

theta = -53.1301  or theta = 233.1301

Add 360 to the first angle to find a coterminal angle counterpart.

-53.1301 + 360 = 306.8699

So the two approximate solutions are

theta = 306.8699  or theta = 233.1301

and those round to 306.9 and 233.1 respectively.

======================================================

Question 11b

cot(theta) = 1.8

tan(theta) = 1/(1.8)

theta = arctan( 1/(1.8) )  or theta = 180+arctan( 1/(1.8) )

theta =  29.0546 or theta = 180+29.0546

theta = 29.0546 or theta = 209.0546

theta = 29.1 or theta = 209.1

Answer:

the negative just tell you you put a one over the number. Once that's done, the power will be positive, and you can square like normal

Are you asking about  [tex]7^{-2}[/tex]  ?

If so:

A negative in the exponent tells us that we must take the reciprocal of the number, in this case, 7, and then use the exponent like normal:

[tex]7^{-2}[/tex] =

[tex](\frac{1}{7})^{2}[/tex] =

[tex]\frac{1}{49}[/tex],

So our answer is 1/49.

Answer:

$121.81

Step-by-step explanation:

A=  4000(1+.03/365)^365

[tex]4000\left(1+\frac{0.03}{365}\right)^{365}=4121.81305\dots[/tex]

Total interest earned on Sandra’s card after 1 year is $4,121.81

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A=P(1+r/n[tex])^{nt}[/tex]

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

Given,

A=P(1+r/n[tex])^{nt}[/tex]

Sandra makes a credit card purchase for $4,000 that compounds interest daily.

P = $4,000

r =3%

t = 1 year

A=P(1+r/n[tex])^{nt}[/tex]

Substitute the values of P, r and t in the formula,

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 4,000.00(1 + 0.03/365)(365)(1)

A = 4,000.00(1 + 8.2191780821918E-5)(365)

A = $4,121.81

Therefore, total interest earned on Sandra’s card after 1 year is $4,121.81.

To learn more about the compound interest rate;

https://brainly.com/question/13307568

#SPJ5

angle B = ( arc ADB ) ÷ 2

46 = ( arc ADB ) / 2

Multiply both sides by 2

46 × 2 = 2 × ( arc ADB ) / 2

92 = arc ADB

arc AB = arc ADB

arc AB = 92

The measure of arc AB is 92°. Therefore, option B is the correct answer.

Given that, ∠B = 46°.

We need to find the measure of arc AB.

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

Now, ∠B = ( arc ADB ) ÷ 2

46° = ( arc ADB ) / 2

Multiply both sides by 2

46° × 2 = 2 × ( arc ADB ) / 2

92° = arc ADB

arc AB = arc ADB

arc AB = 92°

The measure of arc AB is 92°. Therefore, option B is the correct answer.

To learn more about the arc visit:

https://brainly.com/question/23117081.

#SPJ5

Answer:

98 ppl voted for Gordan

Step-by-step explanation:

a) 35% of 280=98

b)  15% of 280=42

   40% of 280=112

    10% of 280=28

Add 98, 42, 112, and 28 and you get 280! Hope this helps :)

Answer:

A. 6.75, divide 13.5 by 2.

B. It's 5.2, 26.2 rounded is 26 and 4.5 rounded is 5, divide. The average is 5.8 , 26.2 divide by 4.5

!This is the first part!

You want to try and get rid of one of the variables ( x or y) so you would multiply the second equation by 2 which would make the x variable -2x which then when added to the first equation would eliminate the x variable.

Answer: c. Multiply the second equation by 2.

hope it is help full

Step-by-step explanation:

mark me a brainlist

Answer and explanation:

Assume Almond is a

Cashew is c

Peanuts is p

The system of equations satisfies this thus:

a+c+p= 10

7a+5c+2p= $20

The system of equations has three unknowns. Solving for the unknown variables here would yield parametric equations or dependent system where given x y z we may find x in terms of y and z in terms of x, in that form. This would give many results for our problem which may not be very accurate.

Answer:

The radius vector is (-8, 7) and (-1 , 5).

Step-by-step explanation:

Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).

The end points are (- 8, 7) and (6, 3) .

The mid point is given by

[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]

So, the radius vector is (-8, 7) and (-1 , 5).  

Answer:

30 lamps

Step-by-step explanation:

30*2= 60

Answer:

60

Step-by-step explanation:

A circle is 360 degrees

1/6 of 360

1/6 * 360 = 60

Answer:

53640

Step-by-step explanation:

Answer:

a = 64

Step-by-step explanation:

The geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{28a}[/tex] = 16[tex]\sqrt{7}[/tex] ( square both sides )

28a = (16[tex]\sqrt{7}[/tex] )² = 1792 ( divide both sides by 28 )

a = 64

Answer:

a = 64

Step-by-step explanation:

The geometric mean for two numbers is given by :

GM = sqrt(ab)

16 sqrt(7) = sqrt(a*28)

Square each side

(16 sqrt(7))^2 = (sqrt(a*28))^2

256*7 = 28a

1792 = 28a

Divide each side by 28

1792/28 = 28a/28

64 = a

Answer:

264 Km²

Step-by-step explanation:

cross sectional perimeter of the triangular prism= 9+8+7= 24Km

now,

total surface area= C.S.P × height of the figure

= 24 × 11

= 264 km²

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

Answer:

Option A

Step-by-step explanation:

first calculate side b

which is 35.8

Using 2 lengths, calculate Angle G

Answer: c. always

Step-by-step explanation:edmentum

Answer:

try D

Step-by-step explanation:

Answer:

4) A

5) E

Step-by-step explanation:

#4

[tex]\frac{x}{y}=\frac{1}{10} * \frac{z}{y}[/tex]

[tex]\frac{x}{y} =\frac{1z}{10y}[/tex]

Cross multiply the equation and you get:

[tex]10xy=zy[/tex]

Since [tex]\frac{a}{b}=\frac{c}{d}[/tex]  is the same thing as [tex]ad=bc[/tex], you can change the equation into [tex]\frac{x}{z} =\frac{y}{10y}[/tex]

Cancel out the y on the top and bottom and you get 1/10

#5

[tex]\frac{2}{3} *\frac{x}{2} =5[/tex], simplify and you get [tex]\frac{x}{3} =5[/tex] so x=15

[tex]\frac{1}{5} * 3(x)[/tex] is equal to [tex]\frac{1}{5} *3(15)[/tex] after you plug in x, and that is equal to 9

Answer:

  x = 3

Step-by-step explanation:

A vertical line has undefined slope. Its equation is of the form x=c, for some constant c.

To make sure the line passes through a point with an x-coordinate of 3, the constant in the equation must be 3:

  x = 3 . . . . . . vertical line through (3, -7)

Answer:

Confidence Interval - "P" values  

(0.4433 , 0.5444 )

~~~~~~~~~~~~~~~~~~~~~~~

[tex]\mathrm{Expand\:}\left(x+4y\right)^3:\quad x^3+12x^2y+48xy^2+64y^3[/tex]

in you image it is the last on "D"

Step-by-step explanation:

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.4433 , 0.5444 )  

50 m

Step One: Every rectangle, opposite side are equal sides.

Area=2, the area of this rectangle is 2*(l+b).

Step Two: Simplify the numbers: 2*(l+b) is also equal to 2*(20+5) and 2*(20+5) is equal to 2*25, so:

50 meters.

I hope I've helped!

Answer:

4

Step-by-step explanation:

-2/5 x* 5y * -2x

Multiply the coefficients

-2/5 * 5*-2

-2*-2 *1/5*5

4