The points A,B,C and D divide the line segment AD in the ratio 4:3:1 , respectively , and AD = 72cm . What is the length of BD?

Answers

Answer 1

Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;

XZ = XY + YZ

The length of the segment BD is 36  cm

The reason the above value is correct is as follows:

Known:

The ratio in which the points A, B, C, and D divide the line segment = 4:3:1

The length of segment AD = 72 cm

Required:

The length of BD

Method:

Calculate the length of BC and CD and add their values to get BD

Solution:

Let the ratios be given unit proportions of the segment AD such that we have;

AB = 4 units

BC = 3 units

CD = 1 unit

By segment addition postulate, we have;

AD = AB + BC + CD

∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm

∴ 1 unit = 72 cm/8 = 9 cm

1 unit = 9 cm

BD = BC + CD by segment addition postulate

BC = 3 units = 3 × 1 unit

∴ BC = 3 × 9 cm = 27 cm

BC = 27 cm

CD = 1 unit

∴ CD = 9 cm

∴ BD = 27 cm + 9 cm = 36 cm

The length of segment BD = 36 cm

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Related Questions

The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.

Answers

Answer:

Step-by-step explanation:

The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:

                          original                 new

length

width

And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:

                           original                  new

length                       L

width                       2L

Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.

The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:

                            original                        new

length                      L                       100%L + 50%L

width                       2L

The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:

                             original                       new

length                        L                     100%L + 50%L

width                        2L                  100%(2L) - 20%(2L)

And now we'll simplify that "new" column:

                              original                         new

length                        L                         150%L = 1.5L

width                         2L               80%(2L) = 160%L = 1.6L

Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:

248 = 2(1.5L) + 2(1.6L) and

248 = 3L + 3.2L and

248 = 6.2L so

L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)

aint the answer for this 10 just let me if im wrong​

Answers

Answer:

Yup

Step-by-step explanation:

The measure of two complementary angles are 2x degree and 3x degree, then value of x is​

Answers

Answer:

2x+3x=90

or ,5x=90

or,x=90/5

X=18

Answer:

90/5=18 degrees

Step-by-step explanation:

Second time posting this. Please help!! :)

Answers

Answer:

Step-by-step explanation:

[tex]\frac{480+24(x-40)}{x}[/tex]

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin

Answers

Answer:

A.

Step-by-step explanation:

85.9 > 85.31 > 85 > 84.52

Dallas, Fort Worth, San Antonio, Austin

Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.

Answers

Answer: £21007.22

Step-by-step explanation:

First, find the interest amount using the formula SI = (P × R × T) / 100.

SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2

SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22

The total amount = principle amount + interest amount

= £18790 + £2217.22 = £21007.22

Instructions: Find the measure of the indicated angle to the nearest degree.

Answers

Step-by-step explanation:

I don't have a calculator with me right now but I can give you the equation to work out your answer.

cos-1(35/38)

There should be a function of "cos-1" on you're calculator, not just "cos"

hope it helps :)

A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet

Answers

Answer:

Step-by-step explanation:

starting point: 140 feet below sea level.=-140

she then decends= 7(4.5)=31.5

-140-31.5=-171.5

finally she ascends 112.2 feet

-171.5+112.2=-59.3 feet or 59.3 feet below sea level

Answer:

It's B

Step-by-step explanation:

What is the area of this polygon

Answers

Answer:

51

Step-by-step explanation:

1. Approach

One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.

One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).

2. Find the area of (ABC)

The formula to find the area of a triangle is the following:

[tex]A=\frac{b*h}{2}[/tex]

Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:

[tex]A=\frac{b*h}{2}[/tex]

Substitute,

[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]

3. Find the area of (ACDE)

The formula to find the area of a rectangle is as follows:

[tex]A=b*h[/tex]

The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:

[tex]A=7*6\\\\A=42[/tex]

4. Find the area of the total figure

To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:

[tex]9+42= 51[/tex]

Find the value of both variables.

Answers

[tex] \cos(45) = \frac{5 \sqrt{2} }{x} \\ \frac{1}{ \sqrt{2} } = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ \\ \tan(45) = \frac{y}{5 \sqrt{2} } \\ 1 = \frac{y}{5 \sqrt{2} } \\ y = 5 \sqrt{2} [/tex]

I hope I helped you ^_^

Express 3.023 in P form where p and q are integers and q= 0 D​

Answers

Given:

The number is 3.023.

To find:

The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].

Solution:

The given number is 3.023. It can be written as:

[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]

[tex]3.023=\dfrac{3023}{1000}[/tex]

It cannot be simplified further because 3023 and 1000  have no common factors.

Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].

Please help me solve this

Answers

Answer:

The 2nd one is 3x+1

The 3rd answer is x+3

Step-by-step explanation:

Given g(x)=4x-1 and f(x)=x-2

Subtracting both

4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1

The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3

Find the measure of 2

Answers

Answer:

92

Step-by-step explanation:

Angle 2 and 92 are corresponding angles and corresponding angles are equal when the lines are parallel

Answer:

[tex]\angle 2=92^{\circ}[/tex]

Step-by-step explanation:

When two parallel lines are cut by a traversal, their corresponding angles are always equal. Corresponding angles can be found if you took each point of intersection and aligned them up with each other.

In this case, we see that [tex]\angle 2[/tex] and the angle marked as 92 degrees correspond with each other. Since all corresponding angles are equal, we have:

[tex]\angle 2=\boxed{92^{\circ}}[/tex]

If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n

Answers

[tex]n = \frac{6}{m + 1} [/tex]

Hope it helps you...

The value of n is n= 6/( m+1).

What is expression?

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

mn - 3 = 3 - n

mn + n = 6

n(m+ 1) =6

n= 6/( m+1)

Learn more about expression here:

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#SPJ2

Harry reads that a particular element has an atom with a mass of 0.000000000012 grams. What is the weight of the atom expressed in scientific notation?
A.
1.2 × 10-9 grams
B.
1.2 × 10-11 grams
C.
1.2 × 1011 grams
D.
1.2 × 1012 grams

Answers

Answer:

Since this number is small we know that the exponent will be negative.

In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.

1.2 x 10 ^-11

Step-by-step explanation:

order the set of irrational numbers from least to greatest

Answers

Answer:

answer is A

hope it helps please mark as brainliest answer and give me thanks

#Dhruv here

Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4

Answers

the order of symmetry is three as there are three of each repeated shape

The equation of line u is y = 9/2x+1. Line v is perpendicular to u. What is the slope of line v

Answers

Answer:

Step-by-step explanation:

The slope of line u is 9/2; the line perpendicular to that is the opposite reciprocal...opposite sign and the flip of the fraction. The perpendicular slope is -2/9

ASAP HELP!! PLEASEEEE!!

Answers

Answer:

Step-by-step explanation:

5.1, please this is just a guess from using my head to calculate

please help



yuffytdgtutidrysryrdf

Answers

Answer:

19 + 1 + 9 + 1

put any of those in the slots

Answer:

19 + 1 + 9 + 1

peace

Choose the graph that correctly corresponds to the equation y = −4

Answers

Answer:

e

Step-by-step explanation:

the graph should look something like this

What is the solution to this system of equations?
2x+y = 6
- - x - y = 2
0
0
(1, -1)
(0,8)
infinitely many solutions
no solution

Answers

Answer:

Step-by-step explanation:

{ 2/3 x+y=6

+

{ -2/3x-y=2

= 0=6

Hence,no solution.

The length of a rectangle is 3 times the width. The perimeter of the rectangle is 64 cm. Show the equation that would be used to find the dimensions of the rectangle.

Answers

Answer:

64 = 2(3x + x)

Step-by-step explanation:

Perimeter of the rectangle = 64 cm

Width of the rectangle = x

Length of the rectangle = 3x

Perimeter of a rectangle = 2(length + width)

The equation is

64 = 2(3x + x)

64 = 6x + 2x

64 = 8x

x = 64/8

x = 8 cm

Width of the rectangle = x = 8 cm

Length of the rectangle = 3x

= 3(8 cm)

= 24 cm

C=-(251x3+281)+3X251-(1-281)

Answers

Answer:

-1

Step-by-step explanation:

=-251x3+281 +251x3-1+281

=-1

Pleaseeee helppppppp

Answers

Answer:

d = 8t

Step-by-step explanation:

Use the parabola tool to graph the quadratic function f(x)=−x2+4. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

Answer:

see below

Step-by-step explanation:

f(x) = -x^2 +4

The vertex form is

y = a(x-h)^2 +k

Rewriting

f(x) = -(x-0)^2 +4

The vertex is (0,4) and a = -1

Since a is negative we know the parabola opens downward

f(x) = -(x^2 -4)

We can find the zeros

0 = -(x^2 -2^2)

This is the difference of squares

0 = -(x-2)(x+2)

Using the zero product property

x-2 =0   x+2 =0

x=2   x=-2

(2,0)  (-2,0) are the zeros of the parabola and 2 other points on the parabola

We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola

Answer:

Your vertex is (4,0)

Step-by-step explanation:

Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)

Answers

Answer:

y = -2x - 6

Step-by-step explanation:

Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise').  Thus, the slope of the line through these two points is m = rise/run =  16/(-8) = -2.

Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:

y + 8 = -2(x - 1), or

y = -8 - 2x + 2, or

y = -2x - 6 (in slope-intercept form)

Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=

Answers

Answer:

Step 1: 1.5

Step 2: Plot the points (0, 1.5)

Step 3: 3, then 0.75

Step 4: Plot the points (1, 3) and (-1, 0.75)

Step 5: y=0

Step-by-step explanation:

Ur welcome and have a nice day :>

The initial value of the function f(x) = 3/2 (2)^x is 3/2

How to calculate the initial value of the function?

The function expression is given s:

f(x) = 3/2 (2)^x

Substitute 0 for x

f(0) = 3/2 (2)^0

Evaluate the exponent

f(0) = 3/2 * 1

Evaluate the product

f(0) = 3/2

Hence, the initial value of the function is 3/2

Read more about exponential functions at:

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PLZZZZ HELPPPP… IF NOT 100% SURE PLZZ DONT ANSWER! BRAINLIEST TO FIRST AND CORRECT ANSWER!

Answers

Answer is 7/10 because you need the same denominator so you multiply 1/2 by 5 both top and bottom then multiply 1/5 by 2 both top and bottom and then add numerator

Answer:

7/10

Step-by-step explanation:

½ of a cup of cheddar=½ x 1=½

⅕ of a cup of parmesan=⅕ x 1=⅕

all cheese used=½ + ⅕= 7/10

A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.​

Answers

Answer:

Solutions given:

Velocity ratio V.R =5

effort =500N

efficiency =80%

magnitude of load=?

mechanical advantage [M.A ]

we have

efficiency =M.A/V.R*100%

80=M.A./5*100

80/100*5=M.A

M.A.=4

again

we have

M.A =load/effort

4=load/500

load=500*4

load=2000N

the magnitude of the load is 2000N.
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