Question on image. (4)

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Answer:

In a pyramid, line segment AD is the perpendicular bisector of triangle ABC on line segment BC. If AB = 20 feet and BD= 7 feet, find the length of side AC.

Step-by-step explanation:

Solution

It is given that AD is the perpendicular bisector on the line segment BC.

So, By Perpendicular Bisector Theorem, any point on line segment AD is at an equal distance from points B and C. It implies, AB = AC

AC = 20 feet.

Answer:

25 meters .

Step-by-step explanation:

The actual width of the rectangle is 24.5 meters.

The area of rectangle equals the base(width) times the height.

A = w × h

Given

Area of rectangle = 500 square meters.

Length of rectangle = 4x - 3 meters

Width of rectangle = 2x + 6 meters

Area of rectangle = length × width

500 = (4x - 3) (2x + 6)

⇒ 500 = [tex]8x^{2}+24x-6x-18[/tex]

⇒ 500 = [tex]8x^{2}+18x-18[/tex]

⇒ 500 = [tex]2(4x^{2}+9x-9)[/tex]

⇒ [tex]\frac{500}{2}=4x^{2}+9x-9[/tex]

⇒ [tex]250=4x^{2}+9x-9[/tex]

⇒ [tex]4x^{2}+9x-9-250=0[/tex]

⇒ [tex]4x^{2}+9x-259=0[/tex]

⇒ 4x(x + 7) -37(x + 7) = 0

⇒ (x + 7) (4x - 37) = 0

⇒ x = -7, x = [tex]\frac{37}{4}[/tex]

-7 is not satisfied because it is a negative number.

By substituting x = [tex]\frac{37}{4}[/tex] in width of rectangle

Actual width of rectangle = 2x + 6

= 2( [tex]\frac{37}{4}[/tex]) + 6

= [tex]\frac{37}{2}[/tex] + 6

= [tex]\frac{37+12}{2}[/tex]

= [tex]\frac{49}{2}[/tex]

= 24.5 meters

Hence, the actual width of the rectangle is 24.5 meters.

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Answer:

1st term = 14

2nd term = 29

3rd term = 44

Step-by-step explanation:

1st term = 3 x (5x 1) - 1

             = 3 x 5 - 1

             = 15 - 1 = 14

2nd term = 3 x ( 5 x 2 ) - 1

               = 3 x 10 - 1

                =30 - 1 = 29

3rd term = 3 x (5 x 3 ) - 1

               = 3 x 15 - 1

               = 45 - 1 = 44

Answer:

Area = 21.7777 m²

Step-by-step explanation:

Side of the square = 14 / 3.

Area of the square = side²

→ (14/3)²

→ 196/9

→ 21.7777 m²

Arithmetic

To round, go to the length behind it.

2,413

If it is four or under, you keep the four and, you must turn everything to the left side to zero.

If it is five and up, turn the number into 3000.

Note: This cannot be rounded to 2,500 and 2,400 due to the question being asked.

Meaning, the equation formed is:

5x2,000=10,000

Answer: 10,000

Step-by-step explanation:

the equation is 5 x 2000=10,000

because 1 - 4 let it stay and 5-9 higher up the grade so is was a 2 but you don’t look at the 2 it depends on the number that’s next to it which is 4 and that Means it stays and everything turns into a zero except the two remains it means 5×2000 = 10,000

i hope this helps

Answer:

Step-by-step explanation:

Solve this by adding the volume of the cylinder with the volume of the cone.  The volume of a cylinder is found from the equation:

pi * r^2 * h

In this case that gives pi * 50^2 * 30 = 75000pi

The area of the cone is found from the equation:

pi * r^2 * h *1/3

In this case you get pi * 50^2 * 10 * 1/3=  8333.pi

Add the two to ger 83333.333*pi ~261799

Answer:

[tex]f(10)= 236196[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (0,4)[/tex] --- y intercept

[tex]b = 3[/tex] --- growth factor

Required

[tex]f(10)[/tex]

An exponential function is represented as:

[tex]y = ab^x[/tex]

[tex](x,y) = (0,4)[/tex] means

[tex]4=a * b^0[/tex]

[tex]4=a *1[/tex]

[tex]a= 4[/tex]

So, we have:

[tex]y = ab^x[/tex]

[tex]y = 4(3)^x[/tex]

or

[tex]f(x)= 4(3)^x[/tex]

When x is 10, the value of the function is:

[tex]f(x)= 4(3)^x[/tex]

[tex]f(10)= 4(3)^{10[/tex]

[tex]f(10)= 236196[/tex]

Pretty sure it's the 6 month

Answer:

[tex]2\sqrt{6}[/tex] = x

Step-by-step explanation:

We can use the Tan ratio to figure this out;

[tex]Tan(60) = \frac{x}{\sqrt{8} }[/tex]

Tan(60) * [tex]\sqrt{8}[/tex] = x

[tex]2\sqrt{6}[/tex] = x

Hope this helps!

Answer:

The answer would be C. hope it helps goodluck

Answer:

y = 1/6x -4

Step-by-step explanation:

First find the slope

m= ( y2-y1)/(x2-x1)

m=(-5 - -3)/( -6 -6)

   = (-5+3)/ (-6-6)

       = -2/-12

       = 1/6

The slope intercept form is

y= mx+b where m is the slope and b is the y intercept

y = 1/6 x +b

Substitute a point into the equation

-5 = 1/6(-6) +b

-5 = -1+b

Add 1 to each side

-4 = b

y = 1/6x -4

Answer:

y=1/6x-4

Step-by-step explanation:

Answer:

Step-by-step explanation:

As,

Integers includes whole numbers, and negative of the whole numbers.

And Rationals includes every fraction, Integers and negative fraction.

So,

170, -25, and 74 are both Integers and Rationals.

But,

Only 3/10 is a fraction included only in rationals and not in Integers

Answer:

1.1+2. =3

2.1+2+3 =6

3.1+2+3+4 =10

4.1+2+3+4+5=15

5.1+2+3+4+5+6=21

6.1+2+3+4+5+6+7=28

triangle numbers

Answer:

Step-by-step explanation:

Diagram  (n)               Number of circles  ([tex]T_n[/tex])

 1                                       3

 2                                      6

 3                                      10

 4                                       15

 5                                       21  

 6                                       28

Pattern:

      [tex]T_n = \frac{(n+1)(n+2)}{2}[/tex]          

Where n = diagram number,        

OR

Diagram                                               Number of circles

 1                                                                  1 + 2

 2                                                                 1 + 2 + 3

 3                                                                  1 + 2 + 3 + 4

 4                                                                  1 + 2 + 3 + 4 + 5

 5                                                                  1 + 2 + 3 + 4 + 5 + 6

 6                                                                  1 + 2 + 3 + 4 + 5 + 6 + 7

 n                                                                  1 + 2 + 3 + 4 + 5 + . . . + (n + 1)  

Answer:

infinitely

many solutions hope that helps

Answer:

Infinitely many solutions

Step-by-step explanation:

Hi there!

When two graphs intersect each other at one distinct point, it has one solution.

When two graphs don't intersect each other at all, there are no solutions.

When two graphs completely overlap each other, there are infinite solutions. This is the case here; the two lines completely overlap each other and it's as if  we're looking at one line.

I hope this helps!

Step-by-step explanation:

Volume is the measure of the capacity that an object holds. For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object or solid shape.

Answer:

the amount of space that a substance or object occupies.

basically the volume of a container, like space in a container.

Answer:

V = 2261.9

Step-by-step explanation:

The formula to find the volume of a cylinder is:

V = pi • r² • h

Answer:

If you learned that you express pi is π: 720π [tex]cm^3[/tex]

If it says pi is 3.14: 2260.8 [tex]cm^3[/tex]

Step-by-step explanation:

oki, so the rule to find the area of a circle is r x r x π

which will be 36π in this situation!

So we multiply the area of the circle by the height next, and get 720π

if we have to say pi is 3.14, the answer should be 2260.8

Answer:

2.46 seconds (approximately)

Step-by-step explanation:

use ratio

T2/T1 = T2/3.3=sqrt(5): sqrt(9)

T2=3.3 (sqrt(5/9)=2.46 seconds

The time of oscillation for a pendulum of 5 meters will be 2.46 seconds.

A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity's restoring force will cause a pendulum to accelerate back toward its equilibrium position if it is sideways moved from its resting, equilibrium position.

Given that the time to complete one oscillation of a simple pendulum varies as the square root of the length of the pendulum. it is found that a pendulum 9 meters long makes a complete oscillation in 3.3 seconds.

The time will be calculated as below:-

T2/T1 = T2/3.3=√(5): √(9)

T2=3.3 (√(5/9)=2.46 seconds

Therefore, the time of oscillation for a pendulum of 5 meters will be 2.46 seconds.

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Answer:

a = -16  b = 8 and c =24

Step-by-step explanation:

h = -16t^2 + 8t + 24

A quadratic function can be in the form

ax^2 + bx+c

Replace x with t

-16 is the coefficient of the squared term  8 is the coefficient of the linear term and 24 is the constant

a = -16  b = 8 and c =24

Answer:

2

Step-by-step explanation:

if BF is the mid-segment of the triangle ADG then its measure will be half of the measure of AG so 0.5*8=4 by the (mid-segment theorem)

then CE is the mid-segment of triangle BDF, so its measure is will be half of BF, so 0.5*4=2

Answer:

CE = 2

Step-by-step explanation:

The midsegment is half the length of the third side of the triangle, then

BF = [tex]\frac{1}{2}[/tex] × DG = [tex]\frac{1}{2}[/tex] × 8 = 4 , and

CE = [tex]\frac{1}{2}[/tex] × BF = [tex]\frac{1}{2}[/tex] × 4 = 2

Answer:

Therefore the Answer would be (D) 73

Step-by-step explanation:

Let A = 65 feet and B = 33 feet.

Let C represent teh length of the hypotenuse, the length of the wire.

We use the Pythagroem Therom to find C.

(Hope this Helped  :)

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

Work Shown:

We use the first term to build to the second term.

Plug in n = 2

f(n) = -4f(n-1) + n

f(2) = -4f(2-1) + 2 ..... n replaced with 2

f(2) = -4f(1) + 2

f(2) = -4*4 + 2 ......... f(1) replaced with 4; since f(1) = 4

f(2) = -16 + 2

f(2) = -14

The second term is -14

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

Repeat for n = 3

f(n) = -4f(n-1) + n

f(3) = -4f(3-1) + 3 ..... n replaced with 3

f(3) = -4f(2) + 3

f(3) = -4*(-14) + 3 ......... f(2) replaced with -14

f(3) = 56 + 3

f(3) = 59

The third term is 59

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

We keep going until we get to f(5)

Plug in n = 4

f(n) = -4f(n-1) + n

f(4) = -4f(4-1) + 4 ..... n replaced with 4

f(4) = -4f(3) + 4

f(4) = -4*(59) + 4 ......... f(3) replaced with 59

f(4) = -236 + 4

f(4) = -232

The fourth term is -232

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

Just one more section

Plug in n = 5

f(n) = -4f(n-1) + n

f(5) = -4f(5-1) + 5 ..... n replaced with 4

f(5) = -4f(4) + 5

f(5) = -4*(-232) + 5 ......... f(4) replaced with -232

f(5) = 928 + 5

f(5) = 933

The fifth term is 933

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

As you can see, recursive sequences can get tedious for fairly large values of n. We need to compute every term before f(5) to figure it out. So if your teacher needed you to compute something like f(10), then it would get even worse. Sometimes it's possible to find a closed formula for it, but it may be tricky to find.

Answer:

19,23

Step-by-step explanation:

9+x-7≥ 21

Combine like terms

2+x≥21

Subtract 2 from each side

2+x-2 ≥21-2

x≥19

Any number greater than or equal to 19

Answer:

the triangle is not a right angle

Step-by-step explanation:

5²+12²=169

15²=225

Answer:

Step-by-step explanation:

First of all notice that slope has a negative value

Also notice that line cuts the y axis in -1

because of the symetry of the line you can deduce that the slope is -1, also you can calculate it using the fact that the points (-1, 0) and (0, -1) belongs to the line, the slope would be:

m=(0-(-1))/(-1-0)=-1

finally the equation is

y=-x-1

Answer:

x = 9.75

Step-by-step explanation:

We know that Triangle ABC and DEF are congruent, therefore;

[tex]\frac{CB}{FE} = \frac{AB}{DE}[/tex]

[tex]\frac{12}{9 }=\frac{13}{x}[/tex]

=> 12*x = 9*13

=> 12x = 117

=> x = 117 / 12

=> x = 9.75

Hope this helps!

Answer:

31.4

Step-by-step explanation: