MATHEMATICS MIDDLE SCHOOL

3 pineapples, 2 cabbages and 6 bananas cost a total of $27.2 pineapples, 3 cabbages and 4 bananas cost a total of $23.
4 pineapples, 1 cabbage and 8 bananas cost a total of $31.
Find the costs of:
-one pineapple -one cabbage -one banana
*Please show your work step by step*

Answers

Answer 1
Answer: 3p + 2c + 6b = 27
2p + 3c + 4b = 23
4p + 1c + 8b = 31
===============
take any 2 equations and eliminate a variable

3p + 2c + 6b = 27
4p + 1c + 8b = 31....multiply by -2
---------------------
3p + 2c + 6b = 27
-8p - 2c - 16b = - 62 (result of multiplying by -2)
--------------------add
-5p - 10b = - 35

Now take one equation, and the other equation that u have not used already, and eliminate the same variable.

4p + 1c + 8b = 31.....multiply by -3
2p + 3c + 4b = 23
---------------------
-12p - 3c - 24b = - 93 (result of multiplying by -3)
2p + 3c + 4b = 23
----------------------add
-10p - 20b = - 70

now take ur 2 equations that u eliminated the c in, and eliminate another variable

-5p - 10b = -35......multiply by -2
-10p - 20b = -70
---------------------
10p + 20b = 70 (result of multiplying by -2)
-10p - 20b = -70
-------------------add
0 = 0

when u get a result such as  0 = 0....this means there is infinite solutions to this problem

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A ladder, 14 feet long, is leaning againsta building. If the base of the ladder is 7
feet from the building, how high up the
building will the ladder reach?

Answers

Answer:

12.12ft

Step-by-step explanation:

14² = 7² + x²

x² = 14² - 7²

x² = 196 - 49

x² = 147

x = √147

x = 12.12ft

Answer:

12.6

Step-by-step explanation:

I rounded to the nearest tenth of a foot like it said to :)

What type of conic section is given by the equation 4x^2+9y^2=36? What are its domain and range?

Answers

Answer:

Ellipse

Domain:[-3,3]

Range:[-2,2]

Step-by-step explanation:

We are given that an equation

4x^2+9y^2=36

We have to find the type of conic section and find the domain and range of conic section.

Divide by 36 on both sides then, we get

(x^2)/(9)+(y^2)/(4)=1

(x^2)/(3^2)+(y^2)/(2^2)=1

It is an equation of ellipse.

Substitute y=0 then , we get

(x^2)/(9)=1

x^2=9

x=\pm 3

Domain :[-3,3]

Substitute x=0 then we get

(y^2)/(4)=1

y^2=4

y=\pm 2

Range=[-2,2]
4x^2+9y^2=36\n \n (4x^2)/(36)+(9y^2)/(36)=(36)/(36)\n \n \boxed{(x^2)/(9)+(y^2)/(4)=1}

This is a equation of a ellipse (0,0) centered

Domais: {x∈R/-3≤x≤3}
Range:{y∈R/-2≤y≤2}

The function f(x) = 5One-fifth is reflected over the y-axis. Which equations represent the reflected function? Select two options.f(x) = One-fifth
f(x) = One-fifthOne-fifthOne-fifth
f(x) = 5One-fifth
f(x) = 5(5)x
f(x) = 5(5)–x

Answers

Answer:

The equations that represent the reflected function are

f(x)=5((1)/(5))^(-x)

f(x)=5(5)^(x)

Step-by-step explanation:

The correct question in the attached figure

we have the function

f(x)=5((1)/(5))^(x)

we know that

A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.

therefore

f(−x) = f(x).

The reflection of the given function across the y-axis will be equal to

(Remember interchanges positive x-values with negative  x-values)

f(x)=5((1)/(5))^(-x)

An equivalent form will be

f(x)=5((1)/(5))^((-1)(x))=5[((1)/(5))^(-1))]^(x)=5(5)^(x)

therefore

The equations that represent the reflected function are

f(x)=5((1)/(5))^(-x)

f(x)=5(5)^(x)

Answer:

c,d

Step-by-step explanation:

Round the following numbers to 2 decimal places 0.273
1.595
6.473
2.571
0.425
44.5564
82.3643
325.1741

Answers

Before I give you the answers, there is a simple rule to observe when rounding a number to two decimal places. If the number in the third decimal place is less than five, then the number in the second decimal place stays the same. If the number in the third decimal place is five or greater than five, the number in the second decimal place is incremented by one. In our case the above numbers are rounded up as follows:

0.273 is rounded up to 0.27
1.595 is rounded up to 1.60
6.473 is rounded up to 6.47
2.571 is rounded up to 2.57
0.425 is rounded up to 0.43
44.5564 is rounded up to 44.56
82.3643 is rounded up to 82.36
325.1741 is rounded up to 325.17

Solve for x: 2x + 12 = 64

Answers

Answer:

X=13

Step-by-step explanation:
subtract 12 from 64,
2x=52
divide by 2,
x=26
answer: 26

Solve the equations in two different ways:6p=0.6(5p+15)

Answers

Answer:

Step-by-step explanation:

1st way:

Solve directly

6p=0.6(5p+15)

Open bracket

6p = 3p + 9

Collecting like terms

6p - 3p = 9

3p = 9

Dividing by 3

p = 9/3

p = 3

2nd way:

6p=0.6(5p+15)

Convert the decimal to fraction

6p= 6/10(5p+15)

6p= 3/5(5p+15)

6p= 3/5(5p) +3/5(15)

6p = 3p + 9

Collecting like terms

6p - 3p = 9

3p = 9

Dividing by 3

p = 9/3

p = 3
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