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3 years ago

E is the midpoint of DF, DE = 3x + 4 and EF = 5x - 2. Find DE, EF, and DF.

Mathematics

1 answer:

Alisiya [41]3 years ago

8 0

Since E is the midpoint of DF, DE and EF are two halves of DF. First, let's write down what we know.

DE = 3x + 4

EF = 5x - 2

DE = EF

DE + EF = DF

Now, let's plug our values for DE and EF into our first expression.

3x + 4 = 5x -2

Add 2 to both sides and subtract 3x from both sides.

6 = 2x

Divide both sides by 2

3 = x

Let's plug 3 in for x into DE.

DE = 3x + 4 = 3(3) + 4 = 9 + 4 = 13

DE = EF = 13

We can plug 13 in for DE and EF to get DF

DF = DE + EF = 13 + 13 = 26

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stephen and bridget win some money and share it in the ratio 5:2. stephen gets £65. how much does bridget get

katen-ka-za [31]

Answer:

Bridget will get the amount as £26.

Step-by-step explanation:

Given:

Amount Stephen gets = £65

Amount shared in ratio = 5:2

We need to find the amount Bridget gets.

Solution:

Let the common factor in the ratio be $'x'$ .

Amount Stephen gets = $5x$

Amount Bridget gets = $2x$

But we know that;

Amount Stephen gets = £65

so we can say that;

$5x=65$

Now dividing both side by 5 we get;

$\frac{5x}{5}=\frac{65}{5}\\\\x=13$

So now we get;

Amount Bridget gets = $2x=2\times 13 = \£26$

Hence Bridget will get the amount as £26.

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3 years ago

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Step-by-step explanation:

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2 years ago

Which polynomial can be simplified to a difference of squares

Mrrafil [7]

<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)$

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

$First=10a^{2}$

$Second=16a^{2}$

$Third=25a^{2}$

$Fourth=24a^{2}$

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

$16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}$

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

$16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)$

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

$25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}$

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}$

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If the mass of a material is 44 grams and the volume of the material is 6 cm^3, what would the density of the material be?

Svetlanka [38]

Density is mass per unit volume.

For the given material that has a mass of 44 grams occupying a volume of 6 cm^3, we divide the mass by the volume, i.e.

density of material = 44 grams / 6 cm^3 = 44/6 grams/cm^3 = 7.3 g/cm^3 (to two significant figures)

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