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3 years ago

Don’t mind the pencil writing

Mathematics

1 answer:

vesna_86 [32]3 years ago

8 0

Answer:

Length = 22 cm

Width = 4 cm

Step-by-step explanation:

Area = 88 cm²

Length = x + 7

Width = x - 11

Area of rectangle = length*width

Therefore:

(x + 7)(x - 11) = 88

x(x - 11) +7(x - 11) = 88

x² - 11x + 7x - 77 = 88

Add like terms

x² - 4x - 77 = 88

x² - 4x - 77 - 88 = 88 - 88

x² - 4x - 165 = 0

Factorize

x² - 15x + 11x - 165 = 0

x(x - 15) +11(x - 15) = 0

(x + 11)(x - 15) = 0

x = -11 or x = 15

Let's use the positive number.

Therefore:

Length = x + 7

Plug in the value of x

Length = 15 + 7 = 22 cm

Width = x - 11 = 15 - 11 = 4 cm

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how do you know what order to put the letters of a similarity statement in? ex. WZYX ~ ABCD (why would they be stated this way)

Nimfa-mama [501]

The order should be that of the corresponding equal angles
For example 2 triangles ABC and XYZ where <A=X, <B=Y and <C = < Z.

8 0

2 years ago

State whether the following coordinates on a Cartesian plane form an acute, obtuse or right triangle: a) (-1, 1), (7,-2) and (1,

LiRa [457]

Answer:

a) Acute triangle

b) Right triangle

Step-by-step explanation:

∵ A triangle having sides a, b and c is called,

Acute : If a² + b² > c² or a² + c² > b² or b² + c² > a²,

Obtuse : if a² + b² < c² or a² + c² < b² or b² + c² < a²

Right : a² + b² = c² or a² + c² = b² or b² + c² = a²,

a) Let A≡(-1, 1), B≡(7,-2) and C≡(1,-5),

By the distance formula,

$AB=\sqrt{(7-(-1))^2+(-2-1)^2}=\sqrt{(7+1)^2+(-3)^2}=\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}\text{ unit}$

Similarly,

$BC=\sqrt{45}\text{ unit}$

$CA=\sqrt{40}\text{ unit}$

∵ The sum of any two sides is greater than third side,

So, ABC is a triangle,

Now,

$AB^2 + BC^2 > CA^2$

⇒ ABC is an acute triangle.

b) Let P≡(0,6), Q≡(1,2) and R≡(5,3),

By the distance formula,

PQ = √17 unit,

QR = √17 unit,

RP = √34 unit,

∵ The sum of any two sides of PQR is greater than third side,

⇒ PQR is a triangle ,

Also,

$RP^2=PQ^2+QR^2$

Hence, PQR is a right triangle.

3 0

3 years ago

Please help with the question in the attachment. Do not give an improper answer or you will be reported.

____ [38]

9514 1404 393

Answer:

2876 books

Step-by-step explanation:

If we let y1 and y2 represent the costs from method 1 and method 2, then we have, for x books published, ...

y1 = 12841 +24.25x

y2 = 48072 +12x

These costs will be equal when ...

y1 = y2

12841 +24.25x = 48072 +12x

12.25x = 35231 . . . . . . . . . . . . . subtract 12841+12x

x = 2876 . . . . . . . . . . divide by 12.25

The costs will be the same for production of 2876 books.

3 0

2 years ago

Give that the line y=4x-14 passes through the point (k,k+1), find the value of k.

balandron [24]

Answer:

k = 5

Step-by-step explanation:

The given line is y = 4x - 14.

The given point is (k, k + 1).

For this point, x = k and y = k + 1.

You substitute these equations into the line's equation to find the value of k.

(x = k)

(y = k + 1)

y = 4x - 14

(k + 1) = 4(k) - 14

Solve for k.

k + 1 = 4k - 14

Subtract k from both sides.

1 = 3k - 14

Add 14 to both sides.

15 = 3k

Divide both sides by 3.

15/3 = k

Simplify.

5 = k

And that's the answer!

Please mark as Brainliest! :)

7 0

3 years ago

If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount

monitta

If the interest is compounded annually, then
A = P*(1+r/n)^(n*t)
A = 3000*(1+0.05/1)^(1*4)
A = 3646.51875
which rounds to 3646.52
Call this value x, so x = 3646.52
-----------------------------------
If the interest is compounded using simple interest, then
A = P*(1+r*t)
A = 3000*(1+0.05*4)
A = 3600
Call this value y, so y = 3600
-----------------------------------
Now subtract x and y
x-y = 3646.52-3600 = 46.52
-----------------------------------
Therefore the answer is choice C) $46.52

4 0

3 years ago