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fenix001 [56]
3 years ago
12

Write 8,840 in scientific notation.

Mathematics
1 answer:
Alborosie3 years ago
6 0
So, the final answer is 8.84 × 10^3
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A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti
yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have  b=\frac{42}{h}. Then, you can replace it in equation 1.

2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0

Now, you should solve the quadratic equation.

h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}

h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}

h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm

h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm

If h1=9.65 cm, then b_1=\frac{42}{9.65} =4.35 cm, and if  h2=4.35 cm, then b_1=\frac{42}{4.35} =9.65 cm.

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

8 0
1 year ago
Write the explicit<br> rule for the nth term.<br> Then find a71.<br> {O, -8, -16, -24 ...}
yulyashka [42]

Answer:

Step-by-step explanation:

{0, -8, -16, -24,...} here you add -8 each time so the rule is

a_{1} = 0, a_{n} = a_{n-1} -8

the 71 term is

a_{71} = 0 + (71 - 1) * (-8) = 70 * (-8) = -560

3 0
3 years ago
the sum of the digits of a certain two-digits number is 7.Reversing its digits increases the number by 9.What is the number
rusak2 [61]
Unit digit=y
tens digit=x
the number: 10x+y

We suggest this system of equations:
x+y=7
(10y+x)=(10x+y)+9
we solve it by substitution method.
x=7-y
10y+(7-y)=(10(7-y)+y)+9
9y+7=70-10y+y+9
9y+10y-y=70+9-7
18y=72
y=72/18=4

x=7-y
x=7-4=3

number=10x+y=10*3+4=30+4=34

solution: the number: 34

To check:
3+4=7
43=34+9
8 0
3 years ago
Read 2 more answers
Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....
Shalnov [3]

Answer:

63,127

Step-by-step explanation:

the interval between each number is multiplied by 2

such as between 1 and 3 we have 2 so 2×2=4

the 4+3=7 and so on

7 0
3 years ago
Read 2 more answers
In a fish tank, there are 24 goldfish, 2 angel fish, and 5 guppies. if a fish is selected at random, find the probability that i
Artist 52 [7]
There are a total of 31 fish in the tank. Therefore, the probability of it being a goldfish is 24/31 or about 77.4%, since there are 24 goldfish. The probability of it being an angel fish is 2/31 or about 6.45%, for the same reason as before. 
3 0
3 years ago
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