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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

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.

Answer:

2020³-1/4041

Step-by-step explanation:

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: 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

Step-by-step explanation:

f(X) = 5x+18= 18

so,

18 = 5x+18

18-18 = 5x

X= 0

so domain of the function is 0

Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

Answer:

1. La ecuación vectorial de la línea es [tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

[tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

Answer:

1093 tickets

Step-by-step explanation:

Take the total amount and divide by the amount per ticket to determine the number of tickets

6558/6

1093 tickets

Answer:

The band have to sell 1093 Ticket to meet its goal

Step-by-step explanation:

Total cost = $6,558

Per Ticket cost =$6

formula:

No of Tickets = Total cost of Ticket ÷  Per Ticket Cost

                       = 6558 ÷ 6

No of Tickets = 1093

Check:

Total Cost = No of Ticket × Per ticket cost

                 = 1093 × 6

Total Cost =$6558

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: $30

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

10% of 600 = 60

5% of 600 = 30

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:

B. on edge 2021

Step-by-step explanation:

y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4

Answer:

It's B :))

Step-by-step explanation:

hope it is help full

Step-by-step explanation:

mark me a brainlist

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.

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!

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:

30 lamps

Step-by-step explanation:

30*2= 60

Answer:

mean = 10

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{6+7+10+12+12+13}{6}[/tex]

        = [tex]\frac{60}{6}[/tex]

       = 10

Answer:

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

Answer:

filtration system is not working

filtration

Answer:

let x be the complementary angle

then x + 2 is the angle

x+2 +x =90

2x = 88

x = 44°

x + 2° = 46°

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:

228

Step-by-step explanation:

We are asked to convert 14 1/4 pounds into ounces, to do so, we need to multiply the amount of pounds by 16.

14 1/4 or 14.25

14.25 * 16

==> 228

Meaning there are 228 ounces in 14 1/4 pounds

Answer:

Answer is option C

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

try D

Step-by-step explanation:

Answer:

4th option, x = -1 and x = 9

Step-by-step explanation:

3(x-4)²=75

or, (x-4)²=25

or, x²-8x+16-25=0

or, x²-8x-9=0

or, x²-9x+x-9=0

or, x(x-9)+1(x-9)=0

or, (x-9)(x+1)=0

so, x-9=0 or, x=9

and x+1=0 or, x=-1

The two solutions of the quadratic equation are:

x = -1 and x = 9

The quadratic equation is:

3*(x - 4)^2 = 75

We can expand it as:

3*x^2 - 3*2*4*x + 3*16 = 75

3x^2 - 24x  -27 = 0

Now, using Bhaskara's formula we get:

[tex]x = \frac{-(-24) \pm \sqrt{(-24)^2 - 4*3*(-27)} }{2*3} \\\\x = \frac{24 \pm 30 }{6}[/tex]

So the two solutions are:

x = (24 + 30)/6 = 9

x = (24 - 30)/6 = -1

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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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).