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2 years ago

The length of a swimming pool is 8m longer than its width and the area is 105m2

2 answers:

8 0

$width : w \\ length : \ l = w + 8 \\ A = 105 \ m^2 \\ \\A= w \cdot l \\ \\w(w+l)=105 \\ \\w^2+w = 105 \\ \\w^2+w-105 =0 \\ \\(w+15)(w-7)=0 \\ \\w+15 =0 \ \ or \ \ w-7 = 0 \\ \\w = -15 \ \ or \ \ w=7 \\ \\ width \ cant \ be \ negative, \ so \\ \\ w = 7 \ and \ l = w+8 = 7 +8 =15 \\ \\chek : \\ \\ A=w\cdot l \\ \\A=7\cdot 15=105 \ m^2$

Talja [164]2 years ago

5 0

$l\ \rightarrow\ the\ length\\w\ \rightarrow\ the\ width \\\\l=w+8\ \ \ and\ \ \ l\cdot w=105\ \ \ and\ \ \ l>0,\ w>0\\\\(w+8)\cdot w=105\ \ \ \Rightarrow\ \ \ w^2+8w=105\\\\ w^2+2\cdot4w+4^2=105+4^2\\\\ (w+4)^2=105+16\ \ \ \Rightarrow\ \ \ (w+4)^2=121\\\\w+4=11\ \ \ or\ \ \ w+4=-11\\\\w=7\ \ \ \ \ \ \ \ \ \ or\ \ \ w=-15$

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Mason owns a trucking company. For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an

emmasim [6.3K]

Answer: The required system of equations are

y = 30x

13x + y = 258

Step-by-step explanation:

Let x represent the number of hours

that the driver worked.

Let y represent the number of miles that the truck drove.

For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that

13x + y = 258

On that particular day, the driver drove an average of 30 miles per hour.

Speed = distance/time

It means that

y/x = 30

y = 30x

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2 years ago

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If two or more polygons are congruent, which statement must be true about the polygons? Read all of the choices before deciding.

hodyreva [135]

The best correct answer is option E. If two or more polygons are congruent, then rigid transformations can be used to map one polygon onto the other. Two figures are said to be congruent when they have the same shape and size or if one object is a mirror image of the other object.

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2 years ago

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Michael went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 40 grams of sugar and

Fudgin [204]

40x+20y=300
x= amount of soda bottles
y= amount of juice bottles

Solving this equation, finding x&y will give you the number of each bottles!

I hope this helped!

~ Penny

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2 years ago

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A sociologist wants to determine if the life expectancy of people in africa is less than the life expectancy of people in asia.

Colt1911 [192]

Answer:

The sample statistics are attached.

First, we need to determine the hypothesis.

The null hypothesis should be: $H_{o} : u_{africa} \geq u_{asia}$ .

The alternative hypothesis should be: $H_{a}: u_{africa}$

The next step is about calculating the t statistics based on the samples. This t test will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is: $t=\frac{x_{1}-x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }$

Replacing all the values into the formula, we have:

$t=\frac{52.4-58.1}{\sqrt{\frac{(7.4)^{2} }{45}+\frac{(8.8)^{2} }{35} } } \\t=\frac{-5.7}{\sqrt{1.2+2.2} } =\frac{-5.7}{1.8} =-3.2$

Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

Therefore, according to the table attached, the p-value is less than 0.01, which is less than our level of significance. This result means that the null hypothesis is rejected. In other words, there's enough evidence to say that the life expectancy of people in Africa is less than the life of expectancy of people in Asia.

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2 years ago

Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta. 2cos2(θ)−1 2 c o s 2 ( θ ) − 1 = nothing

yulyashka [42]

We have to evaluate

=2 cos 2Ф - 1

⇒cos 2Ф

A =2cos²Ф-1

B =1 -2 sin²Ф

C = cos²Ф - sin²Ф

Possible Answers are

=2 ×(2cos²Ф-1)-1

=4cos²Ф-2-1

=4cos²Ф - 3

=2×(1 -2 sin²Ф)-1

=2- 4sin²Ф-1

=1 - 4sin²Ф

=2× ( cos²Ф - sin²Ф) -1

=2 cos²Ф - 2sin²Ф-1

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2 years ago