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2 years ago

4) Sophie checks her bike for repairs every 9 days and Susan check hers every 12 days.

Mathematics

1 answer:

musickatia [10]2 years ago

6 0

Answer:

Step-by-step explanation:

12+9=20

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the area of a trapezium is 594 sq. cm. The lengths of its parallel sides are in the ratio 4 : 5. The height of the trapezium is

Sophie [7]

Answer:

1st side=44 cm, 2nd side= 55cm

Step-by-step explanation:

let a = '4x' , b = '5x'

h= 12cm

Area of trapezium=1/2*(a+b)h

area=594=1/2*9x*12

594*2/12=9x

594/6=9x

99=9x

99/9=11=x

therefore, 4x=4*11=44cm

&5x=5*11=55cm

5 0

1 year ago

Which measure is the largest? 1.2 km, 120,600 cm, 1,220,000 mm, 120 meters

aalyn [17]

The answer would be 1,220,000mm.

You can do this if you convert all the measures into one unit. Let us convert all into km.

The first one is already in km, so we do not need to covert it.

Let's start with converting 1,220,000mm to km.

There are 1, 000,000 mm in one km.

$1,220,000X \frac{1km}{1,000,000mm} = 1.22km$

So there are 1.22km in 1,220,000mm.

Next, we have 120m. There are 1,000m in 1km.

$120mX \frac{1km}{1,000} =0.12km$

There are 0.12km in 120m

Now you can see that 1,220,000mm is the longest.

4 0

2 years ago

Find all x in set of real numbers R Superscript 4 that are mapped into the zero vector by the transformation Bold x maps to Uppe

sukhopar [10]

Answer:

$x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the $\bar x$ so that $A \bar x = 0$

$\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right]$

Now the augmented matrix is

$\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right]$

After this, we decrease this to reduce the formation of the row echelon

$R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right]$

$R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]$

$R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right]$

$R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]$

$= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0$

$x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]$

By applying the above matrix, we can easily reach an answer

5 0

2 years ago

Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.

4 0

2 years ago

To complete one round of a jogging track, Samantha took 1.52 minutes. Which expression below represents the time taken by Samant

OleMash [197]

As there is no sample expressions which could be the given answer we will solve it by the equation

(amount of time it takes to complete one round)*(number of rounds completed)=

We know that it took Samantha 1.52 minutes to go around once and assume that she continues this pace for 3 rounds. To solve for this we plug in our numbers into our equation.

1.52*3=<span>4.56</span> minutes to complete 3 rounds.

Does that answer your question?

8 0

2 years ago

Read 2 more answers