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2 years ago

The perimeter of the rectangle below is 42 inches. Find the value of x.

Mathematics

1 answer:

elena-s [515]2 years ago

4 0

Answer:

x=7

Step-by-step explanation:

P=5x+x-3=42

=6x-3=42

=6x=45

x=45/6

x=7.5 closest answer is 7

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The sum of two integers is 6 and the difference between the numbers is 40. Find the numbers

nevsk [136]

Set up a system of equations.

X+y=6
Y-x =40

Substitution method.

Y=6-x

(6-x)-x =40
6-2x=40
-2x=34
X= -17

Plug it back into the equation.
-17+y=6
Y=33

(-17,33) is one of the possible answers.

8 0

3 years ago

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The circumference of a circle can be found using the formula C = 2 nr.

victus00 [196]

Radius = circumference/2(3.14)
OPTION 3

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2 years ago

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Jamal is making two paintings using canvases that are similar rectangles. The length of the smaller canvas is 3 ft and the width

Alex787 [66]

Let's start with what we know:

Smaller canvas:
Length ( $L_{1}$ ) = 3ft
Width ( $W_{1}$ ) = 5ft

Larger canvas:
Length ( $L_{2}$ ) = ?
Width ( $W_{2}$ ) = 10ft

Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:

$\frac{ L_{1} }{ L_{2} } = \frac{ W_{1} }{ W_{2} }$
So let's plug it all in from above:

$\frac{ 3 }{ L_{2} } = \frac{ 5 }{ 10 }$
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:

$(3)(10) = (5)(L_{2})$
$30 = 5L_{2}$
Now divide each side by 5 to isolate $L_{2}$

$\frac{30}{5} = \frac{ 5L_{2}}{5}$
The 5s on the right cancel out, leaving us with:

$6 = L_{2}$

So the length of the larger canvas is 6 ft

4 0

3 years ago

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What is the surface area of this rectangular pyramid?

Alexxx [7]

Answer:

304m^2

Step-by-step explanation:

First find the surface area of the base by multiplying the length by the width.

(12m) (8m)= 96m^2

Second, find the surface area of the front and back triangles using the formula 1/2 (base) (height). Use the length for the base.

1/2 (12m) (10m)= 60m^2

Next, find the surface area of the side triangles using the formula 1/2 (base) (height). Use the width as the base.

1/2 (8m) (11m)= 44m^2

Last, add the surface area of each section. Make sure you add the area of each face.(we only solved for 1 of the front/ back triangles and 1 of the side triangles) To make it easier to understand I wrote out an equation to show how I added the surface areas.

base=a, front/ back triangles= b, side triangles=c

SA= a + 2b +2c or SA= a +b +b +c +c

Using one of the equations above solve for the total surface area.

SA= (96m^2) + (60m^2) +(60m^2) +(44m^2) +(44m^2)

SA= (96m^2) + 2(60m^2) +2(44m^2)

SA= (96m^2) +(120m^2) +(88m^2)

SA= 304m^2

7 0

2 years ago

⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformati

goldenfox [79]

Answer:

Whereby circle $\bigodot$ P can be obtained from circle $\bigodot$ O by applying the transformations of a translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4, $\bigodot$ O is similar to $\bigodot$ P

Step-by-step explanation:

The given center of the circle $\bigodot$ O = (-2, 7)

The radius of $\bigodot$ O, r₁ = 5

The given center of the circle $\bigodot$ P = (12, -1)

The radius of $\bigodot$ P, r₂ = 12

The similarity transformation to prove that $\bigodot$ O and $\bigodot$ P are similar are;

a) Move circle $\bigodot$ O 14 units to the right and 8 units down to the point (12, -1)

b) Apply a scale of S.F. = r₂/r₁ = 12/5 = 2.4

Therefore, the radius of circle $\bigodot$ O is increased by 2.4

We then obtain $\bigodot$ O' with center at (12, -1) and radius r₃ = 2.4×5 = 12 which has the same center and radius as circle $\bigodot$ P

∴ Circle $\bigodot$ P can be obtained from circle $\bigodot$ O by applying similarity transformation of translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4, $\bigodot$ O is similar to $\bigodot$ P.

7 0

3 years ago