1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LUCKY_DIMON [66]
2 years ago
9

1) The dimensions of an irregular solid are as shown in the figure below.

Mathematics
1 answer:
Juliette [100K]2 years ago
8 0

Hello,

a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped

Volume of rectangular parallelepiped = lengh × high × height

Volume of light blue rectangular parallelepiped :

V = (x + 2) × (x + 5) × (2x + 1)

V = (x² + 5x + 2x + 10) × (2x + 1)

V = (x² + 7x + 10) × (2x + 1)

V = 2x³ + 15x² + 27x + 10

<u>Volume of dark blue rectangular parallelepiped :</u>

V = x × 3 × (x + 5)

V = 3x(x + 5)

V = 3x² + 15x

Polynomial function, in standard form, to model the volume of this solid :

V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)

V = 2x³ + 15x² - 3x² + 27x - 15x + 10

V = 2x³ + 12x² + 12x + 10

b) We have to solve 2x³ + 12x² + 12x + 10 = 208

⇔ 2x³ + 12x² + 12x - 198 = 0

⇔ 2(x - 3)(x² + 9x + 33) = 0

⇔ x = 3 or x² + 9x + 33 = 0

a = 1 ; b = 9 ; c = 33

Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution

So if the volume of the solid is 208 cubic inches, the value of x is 3

You might be interested in
Lauren's cat weighs 3 pounds more than half of Adrian's cat. Lauren's cat weighs 10 pounds.
monitta

Answer:

w = weight of Adrian's cat

c = weight of Lauren's cat

c = 3 + w/2

given: c=10

10 = 3 + w/2

Solve to get 'w':    20=6+w; w=14 pounds

Step-by-step explanation:

3 0
3 years ago
Learning Task 1: Illustrate the following fractions on your notebook.
Marizza181 [45]

Answer:

The illustration is found in the attachment below.

<em>Note: The correct order of the question is found below:</em>

<em>Learning Task 1: Illustrate the following fractions on your notebook.</em>

<em>a.)2/3 b.)7/9 c.)10/12 d.)8/12 e.)4/5 f.) 8/6 g.)9/4 h.) 28/10</em>

Step-by-step explanation:

a) Draw a rectangle of sides 3 cm by 1 cm. Divide the rectangle into three equal parts. Shade two out of the three parts to give the fraction 2/3

b)  Draw a rectangle of sides 9 cm by 1 cm. Divide the rectangle into nine equal parts. Shade seven out of the nine parts to give the fraction 7/9

c)  Draw a rectangle of sides 12 cm by 1 cm. Divide the rectangle into twelve equal parts. Shade ten out of the twelve parts to give the fraction 10/12

d)  Draw a rectangle of sides 12 cm by 1 cm. Divide the rectangle into twelve equal parts. Shade eight out of the twelve parts to give the fraction 8/12

e)  Draw a rectangle of sides 5 cm by 1 cm. Divide the rectangle into five equal parts. Shade four out of the five parts to give the fraction 4/5

f)  Draw two rectangle of sides 6 cm by 1 cm. Divide the rectangles into six equal parts each. Shade all the six parts of the first rectangle completely. Then, shade two out of the six parts of the second rectangle to give the fraction 8/6

g) Draw three rectangles of side 4 cm by 1 cm. Divide each of the three rectangles into four parts each. Shade completely the four parts of the first and second rectangle. Then, shade one part out of the four parts of the third rectangle to give the fraction 9/4

h) Draw three rectangles of side 10 cm by 1 cm. Divide each of the three rectangles into ten parts each. Shade completely the ten parts of the first and second rectangle. Then, shade eight parts out of the ten parts of the third rectangle to give the fraction 28/10

6 0
3 years ago
(7*5*2 / 7*3)^(2) *(5^(0) / 2^(-3) * 2^(-9)=??? does it make sense to anyone?? please help...
saul85 [17]
Evaluate
remember that x^0=1
and x^-m=1/(x^m)

simplify
PEMDAS
parenthasees exponentes mulitplciraon or diviosn additon or subtraction

parethasees first

inside to ut
lef to right
7*5*2/7*3
70/21
10/3

then in the next partnheasees
5^0/2^-3 times 2^-9
1/(1/2^3)(1/2^9)
1/(1/8)(1/512)
8/512
1/64

so now we have
(10/3)^2 times 1/64
100/9 times 1/64
100/576
25/144

you should group them better so it is easier to read


8 0
4 years ago
Read 2 more answers
154 is the same as the product of 158 and n, decreased by 132
grandymaker [24]

Answer:

Equation: 154 = 158n - 132 n = 11/6

Step-by-step explanation:

Let's start by converting this into an equation. Some keywords to look for are "is" which means an equal sign (=), "product" which is multiplication (*), and "decreased" which means a minus sign (-):

So this is our equation: 154 = 158n - 132

Now we have to solve for n:

First, we add 132 to both sides to isolate the n more:

286 = 158n

Then to completely isolate the n, we divide both sides by 158

286

------    =     n

156

<u>n = 11/6, final answer.</u>

8 0
2 years ago
What is 36/5 simplified by a whole number
goldfiish [28.3K]

Answer:

36/5 = 7 1/5

Step-by-step explanation: hope this help!

7 0
4 years ago
Read 2 more answers
Other questions:
  • How many times would you have to run back and forth across the length of a football field to run about 1 km?
    12·1 answer
  • How do you find the perimeter in a triangle
    15·1 answer
  • Find the circumference of a circle with radius 280 mm. Use 22/7 for π
    14·1 answer
  • On the first play of a football game, the Titans lost 31
    8·1 answer
  • Find the missing side
    9·1 answer
  • Please help asap will give you brainliest
    5·1 answer
  • 1. Find the equation of a line that is perpendicular to<br> y=-2/3+4 and goes through (0,5)
    10·2 answers
  • Help me out plzzzzzz
    11·2 answers
  • 1/2,5/16,3/32,3/4,3/8 make it in least to greatest order plz
    6·2 answers
  • Can someone help we with this problem?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!