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3 years ago

Which expression is equivalent to 7x , if b > 0?

Mathematics

2 answers:

Lelechka [254]3 years ago

7 0

Answer:

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

AlladinOne [14]3 years ago

6 0

<h3>Answer: Choice C</h3>

Work Shown:

$7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\$

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

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The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle

Mama L [17]

Answer:

The circumference of the circle is $C=45.346 \:units$ .

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by $A_{circle}=\pi r^2$

The formula used to calculate the area of a sector of a circle is:

$A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2$

The circumference of a circle is the distance around the outside of the circle and its given by

$C=2\pi r$

We know the central angle $\theta$ = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

$50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}$

The radius can't be negative. Therefore,

$r=\sqrt{\frac{1800}{11\pi }}\approx 7.217 \:units$

Next, we apply the formula for the circumference of a circle.

$C=2\pi (7.217)=45.346 \:units$

7 0

3 years ago

X/4 < -1.5 for a million dollars and Brainliest. Send cash app too

pogonyaev

Answer:

x < -6

Step-by-step explanation:

X/4 < -1.5

Multiply each side by 4

X/4*4 < -1.5*4

x < -6

3 0

3 years ago

Any one can help with this Venn Diagram question?.Please note that there is an another language, ignore except if you can unders

zloy xaker [14]

Answer:

(i) 30

(ii) 8

Step-by-step explanation:

Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.

Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.

We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.

Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.

We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.

Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).

We know that BMW got 36 votes, so:

20 + x + x + 2x = 36

20 + 4x = 36

4x = 16

x = 4

We know that Citroën got 34 votes, so:

20 + x + x + z = 34

20 + 4 + 4 + z = 34

28 + z = 34

z = 6

We know that Audi got 48 votes:

y + 2x + x + z = 48

y + 2(4) + 4 + 6 = 48

y + 18 = 48

y = 30

Finally, we know that the total number of voters is 100.

20 + 20 + x + x + 2x + y + z + n = 100

20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100

92 + n = 100

n = 8

8 0

3 years ago

Y=3x+4 y=-2x-1 mathaaaaa

valentinak56 [21]

Answer:

the answer is x=−1 and y=1

Step-by-step explanation:

hoped I helped:)

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3 years ago

Evaluate the expression to find out how much she will pay if she drives 100 miles.<br> 250 + 0.80m

zmey [24]

We plug 100 miles into 0.80. 250 + 0.80(100) is 250 + 80. 250 + 80 is 330.

7 0

2 years ago