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3 years ago

Are these expressions equivalent 20d - 16 and 4(5d - 4)

Mathematics

2 answers:

ELEN [110]3 years ago

4 0

Answer:

Yes

Step-by-step explanation:

If we where to simplfy the 4(5d - 4) it would be 20d - 16 and that is equivalent to 20d - 16.

weqwewe [10]3 years ago

3 0

Answer: Yes they are equivalent

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The reason why is because

4(5d - 4) = 4*(5d) + 4(-4) = 20d - 16

You multiply the outer term 4 by each term inside the parenthesis

4 times 5d = 4*5d = 20d

4 times -4 = 4*(-4) = -16

I'm using the distributive property.

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Alternatively, you can start with 20d - 16 and factor out the GCF 4. Divide each term by 4 to get

20d/4 = 5d

-16/4 = -4

So after dividing each term of 20d-16 by 4, we get 5d-4 and the 4 will be pulled out to say 20d - 16 = 4(5d - 4)

As you can probably see, factoring is just thinking of distributing in reverse. Instead of multiplying each term by the same number, you divide each term by the same number. You can distribute the 4 back in to check your factorization.

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Consider this quadratic equation:

zhenek [66]

Answer:

a=2

b=0

c=12

Step-by-step explanation:

The standard form of a quadratic equation is ax²+bx+c=0

Here's the given equation:

2x²+12=0

You might notice that the term bx is not there (there is just ax² and c). That means that b is 0.

The term 2x² is the term ax² in this equation. The coefficient in the term is 2, so that means that a is 2

12 has no variable, so that means it'll be c in the equation.

Hope this helps!

6 0

3 years ago

Terri is rewriting 7^13 in expanded form. How many factors should she use in her expression?

Mazyrski [523]

She should use 13 factors.
All 13 factors are the same thing . . . 7 .

7^13 should be written as 7¹³ .

It means: 7·7·7 · 7·7·7 · 7·7·7 · 7·7·7 · 7

6 0

3 years ago

Read 2 more answers

2 ratios equivalent to 8\3

borishaifa [10]

Some equivalent fractions of 8/3 are:
8/3 = 16/6 = 24/9 = 32/12 = 40/15 = 48/18 = 56/21 = 64/24 = 72/27 = 80/30 = 88/33 = 96/36 = 104/39 = 112/42 = 120/45 = 128/48 = 136/51 = 144/54 = 152/57 = 160/60

3 0

3 years ago

Make g the subject of this relation

zhannawk [14.2K]

Answer:

see explanation

Step-by-step explanation:

Simplify the radical

$\frac{U}{\frac{1}{f}+\frac{1}{g} }$

= $\frac{U}{\frac{g+f}{fg} }$

= $\frac{Ufg}{g+f}$

Square both sides

T² = $\frac{Ufg}{g+f}$ ( multiply both sides by (g + f) )

T²(g + f) = Ufg ( distribute left side )

T²g + T²f = Ufg ← subtract Ufg from both sides

T²g - Ufg + T²f = 0 ← subtract T²f from both sides

T²g - Ufg = - T²f ← factor out g from each term on the left side

g(T² - Uf) = - T²f ← divide both sides by (T² - Uf)

g = - $\frac{T^2f}{T^2-Uf}$ = $\frac{T^2f}{Uf-T^2}$

6 0

3 years ago

In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

vredina [299]

Answer:

c) P(270≤x≤280)=0.572

d) P(x=280)=0.091

Step-by-step explanation:

The population of bearings have a proportion p=0.90 of satisfactory thickness.

The shipments will be treated as random samples, of size n=500, taken out of the population of bearings.

As the sample size is big, we will model the amount of satisfactory bearings per shipment as a normally distributed variable (if the sample was small, a binomial distirbution would be more precise and appropiate).

The mean of this distribution will be:

$\mu_s=np=500*0.90=450$

The standard deviation will be:

$\sigma_s=\sqrt{np(1-p)}=\sqrt{500*0.90*0.10}=\sqrt{45}=6.7$

We can calculate the probability that a shipment is acceptable (at least 440 bearings meet the specification) calculating the z-score for X=440 and then the probability of this z-score:

$z=(x-\mu_s)/\sigma_s=(440-450)/6.7=-10/6.7=-1.49\\\\P(z>-1.49)=0.932$

Now, we have to create a new sampling distribution for the shipments. The size is n=300 and p=0.932.

The mean of this sampling distribution is:

$\mu=np=300*0.932=279.6$

The standard deviation will be:

$\sigma=\sqrt{np(1-p)}=\sqrt{300*0.932*0.068}=\sqrt{19}=4.36$

c) The probability that between 270 and 280 out of 300 shipments are acceptable can be calculated with the z-score and using the continuity factor, as this is modeled as a continuos variable:

$P(270\leq x\leq280)=P(269.5$

d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:

$P(X=280)=P(279.5$

8 0

3 years ago