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Mekhanik [1.2K]
3 years ago
9

if two similar rectangles have a scale factor of 5:2 and the area of the smaller rectangle is 45 cm^2, what will be the area of

the larger rectangle?
Mathematics
1 answer:
Semenov [28]3 years ago
8 0

Answer:

281.25 cm^2

Step-by-step explanation:

Given that,

The scale factor of Two similar triangles = 5:2

Area of the smaller rectangle = 45 cm^2

To find,

The Area of the larger rectangle = ?

Procedure:

As we know, similar triangles have similar ratios of sides. Thus, this can be written in proportion with the sides' ratio to the left while ratio of areas on the right.

(5)^2/(2)^2 = a/45

∵ The area of the larger rectangle = 25/4 * 45

= 281.25 cm^2

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Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -
rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

D=b^2-4ac\\

Where

a= the coefficient of the x^{2}

b= the coefficient of x

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\

Hence we have two real roots for this equation.

y = 2x^2 - 6x + 5\\

y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D

Hence we do not have any real root for this quadratic

y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\

Hence D>0 and thus we have two real roots for this equation.

y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\

Hence we have one real root to this quadratic equation.

7 0
3 years ago
12=5x-13x-44. answer it in multi-step equations
fomenos

12=5x-13x-44

combine like terms

12 = -8x -44

add 44 to each side

12+44 = -8x

56= -8x

divide by -8 on each side

56/-8 = x

-7 =x


5 0
3 years ago
Read 2 more answers
The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72
Brut [27]

Answer:

The maximum number of songs that the symphonic choir can record is 14

Step-by-step explanation:

Let

x ----> the number of songs of the symphonic choir

we know that

The number of songs of the jazz choir multiplied by its average time per song plus the the number of songs of the symphonic choir multiplied by its average time per song, must be less than or equal to 72 minutes

so

The inequality that represent this situation is

3(7)+3.5(x)\leq 72

solve for x

21+3.5x\leq 72

subtract 21 both sides

3.5x\leq 51

divide by 3.6 both sides

x\leq 14.6\ songs

therefore

The maximum number of songs that the symphonic choir can record is 14

3 0
2 years ago
What is the value of the expression below? ( 9.5-3x1 1/2 ) / 0.5<br>PLEASE HURRY!!
GuDViN [60]
The answer would be 10!
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3 years ago
81.3 x 47.5 = i am lost............
Drupady [299]

Answer:

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Step-by-step explanation:

i hope its the good answer

5 0
3 years ago
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