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3 years ago

To the nearest millimeter, a cell phone is 105 mm long and 66 mm wide. What is the ratio of the width to the length?

Mathematics

1 answer:

makvit [3.9K]3 years ago

3 0

Answer:

22:35

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 66 and 105 is 3

Divide both the numerator and denominator by the GCD

66 ÷ 3/105 ÷ 3

Reduced fraction:

22/35

therefore the ratio will be 22:35

You might be interested in

How much is 18 + 8 ÷ 2 + 4

Lisa [10]

Answer: 26

Step-by-step explanation: The order of operations says to divided 8 and 2 first, which gives you 4. 18+4=22. Plus 4 again is 26

4 0

3 years ago

A long paper strip with a width of 5 cm is folded, as shown in the picture. Find the smallest possible area of the gray triangle

Stolb23 [73]

By using some logic and the formula of the triangle's area, we will find that the smallest possible area is 12.5 cm²

How to start thinking about the problem.

First of all, for the configuration of this paper strip, we can see that the base of the triangle will always be equal of the width of the paper. Thus, the smallest area will be only dependent of the height of the triangle.

Now, we need to analyze the picture to figure out how we can get the smallest height possible for that triangle.

What is the smallest height possible.

Doing this, we shall see that the smallest height possible is actually when the height equals the width itself, as it's shown in the attached image.

How to calculate the smallest area possible.

Thus, to calculate the smallest area, we just have to use the formula of the area of the triangle, which is $\frac{b\times h}{2}$ , where b is the base and h is the height.

As we previously found, for this question, the

base = height = width of the paper = 5cm

Now, we just have to calculate it with the formula

$Area = \frac{base \times height}{2} \\\\
\\
Area = \frac{5 \times 5}{2} \\
\\
Area = \frac{25}{2}\\
 \\
Area = 12.5 cm^{2}$

learn more about the area of the triangle here: brainly.com/question/15442893

3 0

2 years ago

An Air Conditioner uses 850 Watts of electricity and local emissions from electricity produce 1.37 pounds of CO2 per kWh. If you

Zina [86]

Answer: 6,987,000 pounds fo CO₂ per kWh.

Step-by-step explanation: Quilowatt-hour (kWh) is a unit of energy that measures the amount of energy expended in 1 hour.

The AC uses 850 Watts, which in kW is 850,000 kW

If you leave the AC on for 6 hours, it will consume

850,000(6) = 5,100,000 kWh

Eletricity produces 1.37 pounds of CO₂ per kWh, then in 5,100,000 kWh:

1.37 $\frac{pounds}{kWh}$ .(5,100,000kWh) = 6,987,000 pounds

If you open a window for 6 hours, you would keep 6,987,000 pounds of CO₂ for entering the atmosphere.

7 0

3 years ago

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

vagabundo [1.1K]

Answer:

A) -2 - i√3 , -2 + i√3

Step-by-step explanation:

Solve using quadratic formula

x² + 4x + 7 = 0

The Almighty Formula

= -b ± √b² - 4ac/2a

Where ax + bx² + c = 0

From the above question

a = 1, b = 4, c= 7

Hence,

-4 ± √4² - 4 × 1 × 7/2 × 1

-4 ± √16 - 28/2

=( -4 ± √-12)/2

Since

b² - 4ac < 0

We have two complex roots

Simplifying

( -4 ± √-12)/2

= -4/2 ± √-12/2

= -2 ± 2√3i/2

= -2 ± √3i

Therefore,

-2 - √3i , -2 + √3i

-2 - i√3 , -2 + i√3

Option A , is the correct answer

3 0

3 years ago

Write the equation of the quadratic function whose graph passes through <img src="https://tex.z-dn.net/?f=%28-3%2C2%29" id="TexF

blagie [28]

Answer:

$f(x)=x^2+3x+2$

Step-by-step explanation:

We want to write the equation of a quadratic whose graph passes through (-3, 2), (-1, 0), and (1, 6).

Remember that the standard quadratic function is given by:

$f(x)=ax^2+bx+c$

Since it passes through the point (-3, 2). This means that when $x=-3$ , $f(x)=f(-3)=2$ . Hence:

$f(-3)=2=a(-3)^2+b(-3)+c$

Simplify:

$2=9a-3b+c$

Perform the same computations for the coordinates (-1, 0) and (1, 6). Therefore:

$0=a(-1)^2+b(-1)+c \\ \\0=a-b+c$

And for (1, 6):

$6=a(1)^2+b(1)+c\\\\ 6=a+b+c$

So, we have a triple system of equations:

$\left\{ \begin{array}{ll} 2=9a-3b+c &\\ 0=a-b+c \\6=a+b+c \end{array} \right.$

We can solve this using elimination.

Notice that the b term in Equation 2 and 3 are opposites. Hence, let's add them together. This yields:

$(0+6)=(a+a)+(-b+b)+(c+c)$

Compute:

$6=2a+2c$

Let's divide both sides by 2:

$3=a+c$

Now, let's eliminate b again but we will use Equation 1 and 2.

Notice that if we multiply Equation 2 by -3, then the b terms will be opposites. So:

$-3(0)=-3(a-b+c)$

Multiply:

$0=-3a+3b-3c$

Add this to Equation 1:

$(0+2)=(9a-3a)+(-3b+3b)+(c-3c)$

Compute:

$2=6a-2c$

Again, we can divide both sides by 2:

$1=3a-c$

So, we know have two equations with only two variables:

$3=a+c\text{ and } 1=3a-c$

We can solve for a using elimination since the c term are opposites of each other. Add the two equations together:

$(3+1)=(a+3a)+(c-c)$

Compute:

$4=4a$

Solve for a:

$a=1$

So, the value of a is 1.

Using either of the two equations, we can now find c. Let's use the first one. Hence:

$3=a+c$

Substitute 1 for a and solve for c:

$\begin{aligned} c+(1)&=3 \\c&=2 \end{aligned}$

So, the value of c is 2.

Finally, using any of the three original equations, solve for b:

We can use Equation 3. Hence:

$6=a+b+c$

Substitute in known values and solve for b:

$6=(1)+b+(2)\\\\6=3+b\\\\b=3$

Therefore, a=1, b=3, and c=2.

Hence, our quadratic function is:

$f(x)=x^2+3x+2$

5 0

3 years ago