The diagram shows the cross section of a solid metal prism of height 32
cm.
AD = 8.7 cm, AC = 8cm, AB = 6.4cm, BC = 4.8cm and CD = 3.3cm.
Find the volume of the prism in cm3
Type each step of your working on a separate line

Answer:

0.00001808958

Step-by-step explanation:

hope this helps you :)

Answer:

  B.  6

Step-by-step explanation:

The volume is proportional to the height. The ratio of the heights of the taller to shorter pyramids is 6 : 1. Since the pyramids have the same base ares, this is also the ratio of volumes.

The volume ratio is 6.

Answer:

slope is 4/5

y intercept is  -27/5  

f(x) =  4/5x -27/5

Step-by-step explanation:

The slope is

f(8) - f(3)

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

8-3

1 - -3

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

8-3

1+3

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

5

4/5

We can use the slope intercept form to find the y intercept

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

y = 4/5x +b

Using the point (8,1)

1 = 4/5(8)+b

1 = 32/5 +b

Subtract 32/5 from each side

5/5-32/5 = b

-27/5 = b

y = 4/5x -27/5

f(x) =  4/5x -27/5

Answer:

The correct answer is

n = 3038

Step-by-step explanation:

Where we have;

We note that 1000! = An even number

Since Even × Even = even

Even × Odd = Even

Also, 7ⁿ is an Odd number since odd × odd = odd

Therefore 7ⁿ will divide 1000! with some fractions as follows;

1000! divided by 7ⁿ

When 7ⁿ = 1000!

log(7ⁿ) = log(1000!) = log(4.02×10²⁵⁶⁷)

n·log(7) = 2567.604

n = 2567.604/(log(7)) = 3038.23

Therefore, the largest integer n such that 7ⁿ divides 1000! = 3038

Which gives, 1000! ÷ 7³⁰³⁸ = 1.5733.

Answer:

(4,3)-C

Step-by-step explanation:

this is a horizontal line so...

you need to keep the same y-values and find the average of the x-values

[tex]\frac{-2+10}{2} = \frac{8}{2} = 4[/tex]

this means that the x-coordinate is 4

and the y-coordinate is 3

(4,3)

Hope this helped

have a good day

Answer:

Let the points be A and B

A(-2,3)---->(X1,y1)

B(10,3)---->(x2,y2)

Now,

[tex]midpoint = ( \frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} ) \\ = ( \frac{ - 2 + 10}{2} \:, \frac{3 + 3}{2} ) \\ = ( \frac{8}{2} ,\frac{6}{2} ) \\ = (4 ,\: 3)[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

y ≤ 3

Step-by-step explanation:

All values will work all the way up to 3 (including 3). However, no solution would work after the value 3. So, your inequality would be y ≤ 3.

Answer:

y ≤ 3

Step-by-step explanation:

all y values lower than or equal to 3 are part of the shaded area.

Answer:

5ab + 8 - 1a^2.

Step-by-step explanation:

Combining like terms, we get 3a^2 - 4a^2 = -1a^2. We get 9ab - 4ab = 5ab. Then we get, 5 + 3 = 8. Together this is 5ab + 8 - 1a^2

Answer:

-[tex] {a}^{2} + 5ab + 8[/tex]

solution,

[tex]3 {a}^{2} + 9ab + 5 - 4 {a}^{2} - 4ab + 3[/tex]

collect like terms:

[tex]3 {a}^{2} - 4 {a}^{2} + 9ab - 4ab + 5 +3[/tex]

Simplify:

[tex] - {a}^{2} + 5ab + 8[/tex]

hope this helps ..

Good luck on your assignment..

Answer:

Part A ) Option A, Option C, Option E

Part B ) 1200 cm^2

Step-by-step explanation:

The area of a kite can be identified through 1 / 2 of the multiplication of each diagonal. The first diagonal is equivalent to the addition of 50 cm and 10 cm, while the second is of length 20 cm + 20 cm.

[tex]1 / 2 * ( 50 + 10 ) * ( 20 + 20 ),\\1 / 2 * ( 60 ) * ( 40 ),\\( 30 ) * ( 40 ),\\\\Area of Kite = 1200 square cm[/tex]

Consider the first option. If we take a look at the bit 2 * ( 1 / 2 * 20 * 50 ) the 2 and 1 /2 cancel each other out, leaving you with 20 * 50 = 1000 . Respectively in the expression 2 * ( 1 / 2 * 20 * 10 ) the 2 and 1 / 2 cancel each other out, leaving you with 20 * 10 = 200;

[tex]1000 + 200 = 1200 square cm,\\Option A - Correct![/tex]

The second option considers the expression 2 * ( 1 / 2 * 20 * 60 ). Again, the 2 and 1 / 2 cancel each other out, leaving you with 20 * 60;

[tex]20 * 60 = 1200 square cm,\\Option B - Correct![/tex]

Option C is a similar version of option a, besides the fact that the 1 / 2 doesn't exist. Thus, Option C is incorrect!

Option D is a similar version of option a as well, but as the 2 doesn't exist, it is incorrect!

This last option, option E is taken as 1 / 2 of the multiplication of the diagonals, and thus is correct!

[tex]1 / 2 * ( 40 * 60 ),\\1 / 2 * ( 2400 ),\\1200 square cm\\\\Correct![/tex]

Hope that helps!

Step-by-step explanation:

Hers your answer friend

Answer:

180 and 300

Step-by-step explanation:

We want to divide up the number 480 in a 3:5 ratio.

=> We should turn 480 into 3+5=8 portions, each portion is 480/8 = 60.

=> 480 could be divided into 2 smaller numbers that satisfy 3:5 ratio:

60x3=180 and 60x5 = 300.

Check:

180:300 ratio <=> 3:5 ratio (valid)

Hope this helps!

Answer:

Step-by-step explanation:

Given that,

ABC is an Isosceles triangle.

In an Isosceles triangle the opposite sides ( AB =AC) are equal; Their base angles ( < ABD = < ACD) are also equal to each other.

It is als given that D is the mid point of BC.

i.e., BD = CD

Therefore,

By SAS theorem of congruency of triangles,

ABD = ACD

If this is the answer required, hope it helps...

Answer:

120 sweets

Step-by-step explanation:

Bri:Jim:Kru

4: 3: 1

find the difference in the ratio of Bridget and Krutika

4-1=3

ratio 3 is equivalent to 45 sweets

total ratio(4+3+1)--------> ?

total no. of sweets= 8x45

3

=120sweets

Answer:

see below

Step-by-step explanation:

The domain is  the possible x values

For the top graph x goes from 0 to 240

0 ≤x≤240

For the bottom graph the domain is from -3 but not including -3 because of the open circle to 6

-3 < x ≤6

(-3,6]

The range is the possible y values

The lowest value of y is -5 and the largest is 7

-5 ≤y≤7

[-5,7]

Answer:

25% increase

Step-by-step explanation:

Apex

The percent increase in Soraya's monthly earnings is 2.5%

Increase expressed as a percentage is referred to as a percentage increase. When comparing growth in a quantity through time, from its beginning value to its ultimate value, the percentage increase formula is utilised.

Given:

Soraya earned $40 in October.

She earned $50 in November.

Change in amount= 50- 40= $10

So, percent increase = 10/ 40 x 100

                                   = 2.5%

Hence, the percent increase is 2.5%

Learn more about percent increase here:

https://brainly.com/question/13533684

#SPJ2

Answer:

107

Step-by-step explanation:

Median is the middle most no.

=> Here, Median are two numbers, 106 and 108 So, we'll find the mean of it to get the median

=> Median = [tex]\frac{106+108}{2}[/tex]

=> Median = 107

Answer:

b. Sorted and listed from the minimum to the maximum values

Step-by-step explanation:

A percentile can be defined a measure that is made use of statistics.

A percentile is a statistical measure that indicates or shows comparison amongst a given set of data.

A percentile tells us the value or scores below which a percentage of a given observation in a data set falls.

In other to be able to effectively obtain the percentile if a given set of data, the following steps must be taken.

Step 1: Arrange, sort and list the values of the given the data set in order from lowest to the highest

Step 2: Multiply the percentage (also represented by P ) by total number of values in the data set( also represented by N)

Step 3: The value obtained from step 3 is know as the rank and this would helps us to find the percentile f a given data set.

The formula for calculating a percentiles is given as

= (P/100) x N,

where

P = percentile

N = number of values in a data set (sorted or arranged from lowest to highest)

n = Rank of a given value.

Answer:

Step-by-step explanation:

[tex]3x^2+15x-5=0\\a = 3\\b = 15\\c = -5\\ x = -b\±\frac{\sqrt{b^{2} -4ac} }{2a} \\x = -(15)\±\frac{\sqrt{15^{2} -4(3)(-5)} }{2(3)} \\x = -15 \±\frac{\sqrt{225+60} }{6} \\x = -15\±\frac{\sqrt{285} }{6} = A[/tex]

Answer:

the answer is C

Answer:

The answer is C.

Step-by-step explanation:

We are given: [tex]\frac{3+2i}{1-5i}[/tex]. To find the quotient, simplify it. To do that, multiply by the conjugate of the denominator.

The conjugate of [tex]1-5i[/tex] is [tex]1+5i.[/tex]\

Thus, we have:

[tex]\frac{3+2i}{1-5i} \cdot\frac{1+5i}{1+5i} =\frac{3+15i+2i+10i^2}{1-25i^2}[/tex]

Recall that [tex]i^2[/tex] is simply -1.

Thus, we have:

[tex]\frac{3+17i-10}{1-(-25)}=\frac{-7+17i}{26}[/tex]

We can split this:

[tex]-\frac{7}{26}+\frac{17}{26}i[/tex]

Answer:

When the input is 4, the output of f(x) = x + 21 is 25.

Step-by-step explanation:

The given function is  

[tex]f(x)=x+21[/tex]

Here, x is input and f(x) is output.

We need to find the output of the given function f(x) if the input is 4.

Substitute x=4 in the given function.

[tex]f(4)=4+21[/tex]

[tex]f(4)=25[/tex]

So, the output value is 25.

When the input is 4, the output of f(x) = x + 21 is 25.

Answer:

[tex]\frac{3}{88}[/tex]

Step-by-step explanation:

Given

One-eighth times three-elevenths

Required

Solve

One-eighth means 1/8

Three-elevenths means 3/11

So, mathematically; the above expression is represented as thus:

[tex]\frac{1}{8} * \frac{3}{11}[/tex]

To solve this, we simply multiply the numerator and the denominator together.

After multiplying these together, the next is to check if the resulting can be simplified

If yes,we simplify it and if otherwise, we live it like that.

So,

[tex]\frac{1}{8} * \frac{3}{11}[/tex]

[tex]=\frac{1 * 3}{8 * 11}[/tex]

[tex]= \frac{3}{88}[/tex]

At this point, the fraction can't be simplified any further.

Hence,

[tex]\frac{1}{8} * \frac{3}{11} = \frac{3}{88}[/tex]

Answer:

A-4

B-5

C-1

D-3

E-2

Step-by-step explanation:

They all have the same explanation u have to find the point where the line coincides with the x and y axis

E.g on how to work out

Note when the value of y is zero u get the x coordinate and when x is zero u get the y coordinate

C=2x+y=4

To get x 2x+0=4 x=2

Y 0+y=4 y=4

After doing so u locate the line that passes through (2,0),(0,4)

Hope it helps

Answer:

Can you send a screen shot of each graph  because its hard to see the  coordinate

Step-by-step explanation:

Answer:

f(x) =1/3 × 4^x

f(4) = 1/3 × 4⁴

= 1/3 × 256

= 256/3

Hope this helps

Step-by-step explanation:

before tax it would be 6/100×48=$2.88

so therefore before tax = $48-2.88=$45.12

final price after tax =$48+2.88=$50.88

Answer:

The zeroes of a polynomial is the value of x when the polynomial is set to 0.

We can write x² - 2x - 8 = 0. This factors to (x - 4)(x + 2) = 0 and using Zero Product Property the solutions are x = 4, x = -2.

Answer:

[tex] 2\sin^2 A - 1 [/tex]

Step-by-step explanation:

[tex] \dfrac{\tan A - \cot A}{\tan A + \cot A​} = [/tex]

[tex] = \dfrac{\frac{\sin A}{\cos A} - \frac{\cos A}{\sin A}}{\frac{\sin A}{\cos A} + \frac{\cos A}{\sin A}} [/tex]

[tex] = \dfrac{\sin A \cos A \times (\frac{\sin A}{\cos A} - \frac{\cos A}{\sin A})}{\sin A \cos A \times (\frac{\sin A}{\cos A} + \frac{\cos A}{\sin A})} [/tex]

[tex] = \dfrac{\sin^2 A - \cos^2 A}{\sin^2 A + \cos^2 A} [/tex]

[tex] = \dfrac{\sin^2 A - \cos^2 A}{1} [/tex]

[tex] = \sin^2 A - \cos^2 A [/tex]

Since

[tex] \sin^2 A + \cos^2 A = 1 [/tex]

we know

[tex] \cos^2 A = 1 - \sin^2 A [/tex]

we now substitute to get

[tex] = \sin^2 A - (1 - \sin^2 A) [/tex]

[tex] = \sin^2 A - 1 + \sin^2 A) [/tex]

[tex] = 2\sin^2 A - 1 [/tex]

Answer:

-847

Step-by-step explanation:

Using PEMDAS, exponents come first. 6 ^ 3 is equal to 216. Then multiplication arrives.-4 * 216 = -864. Then addition has to be done. -864 + 17 =   -847

Answer:

-847

Step-by-step explanation:

10-4*6^3+7

PEMDAS

Parentheses first - there are none

Exponents

10-4*216+7

Multiply and divide from left to right

10-864+7

Add and subtract from left  to right

-854 +7

-847

Answer:

$250

Step-by-step explanation:

Total parts:

2+3+9 = 14

500/14 = 250/7

2×250/7 : 3×250/7 : 9×250/7

500/7 : 750/7 : 2250/7

The largest share is 2250/7, the smallest share is 500/7.

Find the difference.

2250/7 - 500/7 = 250

Answer:

$250

Step-by-step explanation:

2x+3x+9x= $500

9x-2x= 7x=?

14x= $500

7x= $500/2= $250

Show that the angles A and B are congruent

Answer:

[tex]\angle A =\angle B =90^\circ[/tex]

Step-by-step explanation:

The diagram of the sled kite is attached below.

The central part of the kite is square.

We know by the property of a square that all its angles are congruent and equal to 90 degrees.

Therefore:

[tex]\angle A =\angle B =90^\circ[/tex]

Angles A and B are congruent.

Answer:

1) 2

2) 1

Step-by-step explanation:

1) According to the law of exponents, [tex]x^0 = 1[/tex]

= [tex]2 (\frac{3}{5} )^0[/tex]

=2(1)

= 2

2) [tex](-7)^0[/tex]

= 1

Answer: 14000

Step-by-step explanation:

From the question, the first thing is to first calculate the simple interest (S.I). This will be:

S.I = (principal × rate × time)/100

where principal = 10,000

rate = 4%

time = 10 years

Simple interest = (10,000 × 4 × 10)/100

= 400000/100

= 4000

The total value after 10 years will be th addition of the amount invested and the interest. This will be:

= 10,000 + 4000

= 14000

Answer:

1 piece of UPS

Step-by-step explanation:

Here, we want to know the difference in the number of pieces handled at the different times

In 1995, amount handled = 1.8 * 10 = 18 pieces

In 2000, amount handled = 1.7 * 10 = 17 pieces

The difference between what was handled in the year 2010 and what was handled in 1995 is 18 -17 = 1