What is the surface area of the shaded front face of the composite solid?

A solid is comprised of 3 rectangular prisms. The first rectangular prism has a length of 2 centimeters, width of 4 centimeters, and height of 4 centimeters. The second has a length of 3 centimeters, width of 4 centimeters, and height of 2 centimeters. The third has a length of 3 centimeters, width of 4 centimeters, and height of 4 centimeters.
16 square centimeters
18 square centimeters
26 square centimeters
32 square centimeters

QUESTION 6

[tex]answer = 22.9 \: cm \\ solution \\ hypotenuse = 25 \: cm \\ perpendicular = x \\ base = 10 \: cm \\ now \\ using \: pythagorus \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {p}^{2} = {h}^{2} - {b}^{2} \\ or \: {x}^{2} = {25}^{2} - {10}^{2} \\ or \: {x}^{2} = 625 - 100 \\ or \: {x}^{2} = 525 \\ or \: {x} = \sqrt{525} \\ or \: x = 22.9 \: cm \\ hope \: it \: helps[/tex]

Answer:

4.

[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]

Step-by-step explanation:

[tex]18x^2-24x+87=0[/tex]

Using Quadratic Formula

[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

[tex]$x=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:18\cdot \:87}}{2\cdot \:18}$[/tex]

Solving the discriminant:

[tex]\Delta = \left(-24\right)^2-4\cdot \:18\cdot \:87\\\Delta = 576-6264\\ \Delta=-5688[/tex]

[tex]$x= \frac{24 \pm \sqrt{-5688} }{36} $[/tex]

[tex]$x= \frac{24 \pm \sqrt{5688i} }{36} $[/tex]

Once [tex]\sqrt{5688} =\sqrt{2^3\cdot \:3^2\cdot \:79}=6\sqrt{158}[/tex]

[tex]$x=\frac{24\pm6\sqrt{158}i}{36}$[/tex]

Dividing the denominator and numerator by 6

[tex]$x=\frac{4\pm \sqrt{158}i}{6}$[/tex]

Now rewrite it:

[tex]$x=\frac{4}{6} \pm i\frac{\sqrt{158}}{6}$[/tex]

[tex]$x=\frac{2}{3} \pm i \frac{\sqrt{158}}{6}$[/tex]

or

[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]

Answer:

20%

Step-by-step explanation:

Divided the two which is 80% so the increase is 20% I'm not good at explaining

Answer:

150-120=30

30/120=0.25

0.25=25%

25% is correct

120 x 0.25 = 30

120+ 30 = 150 so 25% is correct

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

2x+x = 3x

Answer:

3x

Step-by-step explanation:

2x + x.

Factor out the x

x(2+1)

x(3)

3x

Answer:

radius

Step-by-step explanation:

AJ is half the distance across the circle (radius).

Answer:

1

Step-by-step explanation:

l 10 - 11 l = |-1|= 1

Answer:

[tex]1[/tex]

Step-by-step explanation:

[tex]\left|10-11\right|[/tex]

[tex]\left|-1\right|[/tex]

[tex]=1[/tex]

Answer:

A piece of duct measures 48 inches.

In each connection, we lost 1 1/2 inches (i guess that it is what you wanted to write)

Then:

If we have 7 pieces of duct connected we have 5 connections (the ones in the extremes are not connected between them, so the number of connections is equal to the number of ducts minus two.)

So here we have 7 times 48 inches for the pieces, minus 5 times 1 1/2 in (i will write 1 1/2 = 1 + 0.5 = 1.5 in, so the math is easier)  for the connections, the length is:

L = 7*48in - 5*1.5in = 328.5 inches.

for the 12 pieces duct, we have 12 pieces and 10 connections, so the length is:

L = 12*48in - 10*1.5in = 561 in

Now, if we want to make only one duct with those two, then we must add their lengths, but if we connect them, we also need to subtract the 1.5in of the new connection:

L = 561in + 328.5in - 1.5in = 888in

Answer:

I think it is A

Step-by-step explanation:

the reason i am saying A is that you don't really know how many guests are coming it could be 10 or 15 or even more.

Answer:

Ok so it is A, I'm almost positive because the first fee is 100 but if you add ten people it is two hundred. the price is DEPENDANT on the amount of people so people is the Independent variable or (x) and cost is the dependent variable or (y) graph A lines up perfectly because if you have ten additional people you have 10 x the cost per person wich = 10 and 10 x 10=100, if you start with 100 as the base cost and add 100 in additional people you will owe 200

Step-by-step explanation:

HOLD ON if you are taking this test in plato/edmentum it will be a diffrent answer but the same graph, just try to find the same graph as graph A

Answer:

0.05

Step-by-step explanation:

3.25 divided by 9 is 0.35 and 2.4 divided by 8 is 0.3 (0.30)

theres a 0.05 gap

if im wrong im sorry

Answer:

f(x) = x²

f(-10) = (-10)²

f(-10) = 100

f(x) = x²

f(-7) = (-7)²

f(-7) = 49

f(x) = x³

f(-5) = (-5)³

f(-5) = -125

f(x) = x³

f(-3) = (-3)³

f(-3) = -27

f(x) = √x

f(0) = √0

f(0) = 0

f(x) = √x

f(2) = √2

f(2) = 1.414

f(x) = 1/x

f(5) = 1/5

f(5) = 0.2

f(x) = 1/x

f(7) = 1/7

f(7) = 0.143

FUNCTION NOT GIVEN. SOLVE LIKE THE ABOVE IF YOU KNOW THE FUNCTION

Answer: A

Step-by-step explanation:

Took the test

Answer: No, as the total cost of the 3 shirts w/ sales tax is $45.36 and she only has $45.

Step-by-step explanation:

Start by finding the price of one shirt on sale.

[tex]18*0.2[/tex]

This equals 3.6 which is how much will be deducted from the original price.

One shirt costs [tex]18-3.6\\[/tex] when its 20% off.

This is equal to $14.40.

Since she wants to buy 3 of them we just multiply the $14.40 by 3.

[tex]14.4*3=\\[/tex]

This equals $43.2 but this is without a 5% sales tax which is normally added to the total end price.

To add a sales tax you take the sales tax percent plus 1 and multiply it to the $43.2.

[tex]43.2*1.05=\\[/tex]

This means the total price of Kayla's purchase will be $45.36.

This is over her $45 she has so she can not buy it.

Answer: she does not and is over $45.36 (.36) cents over

Step-by-step explanation:

Answer:

D- Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x.

Step-by-step explanation: I did the test. Stay safe and have a good one!

Answer:

what the first person said "D"

Step-by-step explanation:

Answer:

26.442 litre

Step-by-step explanation:

total beverage sold= 117*226

= 26442ml

in litres= 26442/1000

= 26.442

Answer:

1/16

Events A+B are written (P) yellow : 1/4 * (P) green : 1/4

Ao event = (P) 1/4 * 1/4 = 1/16

Step-by-step explanation:

The probability of event A and event B is 1/16.

We have given that,

Event A: lands on yellow.

Event B: lands on green

Events A+B are written  

yellow(P) = 1/4 * (P) green= 1/4

Probability is defined as the likelihood of something occurring or the chance of something happening.

Ao event (P)=1/4 * 1/4

Event = 1/16

Therefore the probability of event A and event B is 1/16.

To learn more about the probability visit:

https://brainly.com/question/25870256

#SPJ2

Answer:

B

Step-by-step explanation:

To find DC

c²=a²+b² (pythagorean theory)

c²=6²+8²

c²=36+64. c²=100. √100. c=10cm

thus D =10.

AD= 15-6=9

To find AC

c²=a²+b²

c²=15²+8²

c²=225+64. c²=289 √289. c=17

AC=17

perimeter is the distance around a figure thus ADC=9+10+17

=36

Answer:

7 units to the right and 2 units up

Step-by-step explanation:

Answer:

Approximately 3.8 seconds

Step-by-step explanation:

H(x)=-16x^2+60x+4

We want to find when the ball hits the ground, or where the zeros are

0 =-16x^2+60x+4

Using the quadratic formula

-b ±sqrt(b^2 -4ac)

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

   2a

-60 ±sqrt(60^2 -4*-16*4)

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

   2(-16)

-60 ±sqrt(3600+256)

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

   -32

-60 ±sqrt(3856)

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

-32

We want the positive value for time

-60-62.09669879

---------------------------    

  -32

3.815521837

Approximately 3.8 seconds

Answer:

no

Step-by-step explanation:

suppose he will get exactly the score of 160 in the game four, the mean score this time will be (473+160)/4=158.25

which has already reached the mean score 158 and even higher than it

therefore, his statement is wrong

Answer: z = 28 degrees

Step-by-step explanation:

Since this is an isosceles triangle, two of the angles are congruent.

180 - 124 = 56

56/2 = 28

Answer:

x=7

Step-by-step explanation:

CE = 36

CE = 9+(3x+6) = 9+6+3x = 15+3x

36= 15+3x

36-15 = 15-15+3x (removing 15 from left side also means removing 15 from right side)

21 = 3x

x= 21/3 = 7

Answer:

x=7

Step-by-step explanation:

First, I wrote down the equation.

3x+6=36-9

Then, I simplified it.

3x+6=27

Then, I moved the six from the right to the left.

3x=21

After that, I divided both sides by 3.

x=7

Yay! You got your answer!

Answer:

The center is (-1,0) and the radius is 10

Step-by-step explanation:

We can write the equation of a circle as

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

where the center is (h,k) and the radius is r

(x+1)^2+y^2=100

(x - -1)^2+(y-0)^2=10^2

The center is (-1,0) and the radius is 10

Answer:

radius = 10

center = (- 1, 0)

Step-by-step explanation:

eqn. of the circle = (x - h)^2 + (y - k)^2 = r^2

= (x + 1)^2 + y^2 = 100

(x - (-1))^2 + (y - 0)^2 =10^2

The center is (- 1, 0) and the radius is 10

Hope this helps!

Answer:

[tex]3\dfrac{5}{8}[/tex] pizzas.

Step-by-step explanation:

It is given that Aisha and her friends ate [tex]2\dfrac{1}{2}[/tex] pizzas.

After the party, the remaining pizza is [tex]1\dfrac{1}{8}[/tex] pizzas.

Now,

[tex]2\dfrac{1}{2}=\dfrac{4+1}{2}=\dfrac{5}{2}[/tex]

[tex]1\dfrac{1}{8}=\dfrac{8+1}{8}=\dfrac{9}{8}[/tex]

Pizzas at the starting = Pizza eaten by Aisha and her friends + Remaining pizza

[tex]=\dfrac{5}{2}+\dfrac{9}{8}[/tex]

[tex]=\dfrac{20+9}{8}[/tex]

[tex]=\dfrac{29}{8}[/tex]

[tex]=3\dfrac{5}{8}[/tex]

Therefore, [tex]3\dfrac{5}{8}[/tex] pizzas were there at the start of the party.

Answer:

3 & 5/8

Step-by-step explanation:

i got it right

It's known as exterior angle theorem...The sum of angleB + angle C is equal to angle DAB....

That means 65+61 = 126...

Angle DAB =126

Answer: The Median: 78, The First Quartile: 63, and The Third Quartile: 99

Step-by-step explanation: Ok, so let's put the data set from least to greatest....

(63, 63, 76,) (77, 79,) (84, 99, 99)

First Quartile              Third Quartile

First, let's find the median, since you made a little mistake...

77 + 79 = 156

156 ÷ 2 = 78

The median is 78!

Now, let's determine the first quartile and the third quartile.

For the the first quartile/third quartile it'll be the middle number, if it's even we'll do the same extra step just like we'll do for the median. In this case it's not even therefore...

First Quartile: 63

Third Quartile: 99

I hope this helps!

Answer:

The answer is a

Step-by-step explanation:

I hoped i helped

a squared + b squared = c squared

576+100=c squared

676=c squared

c squared = 26

hope it helps