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marshall27 [118]
3 years ago
9

Use the substitution method to solve these simultaneous equations.

Mathematics
1 answer:
Amanda [17]3 years ago
4 0

Answer:

Step-by-step explanation:

a) 3x+2(41-5x)=33            as y=41-5x is given

3x+82-10x=33

-7x+82=33

-7x=33-82

-7x=-49        cut the negative signs as its LHS and RHS

<u>x=49/7=7</u>

b)-5x+3(3x-3)=3   as y=3x-3 is given

-5x+9x-9=3

4x-9=3

4x=3+9

<u>x=12/4=3</u>

<u>c</u>)4x+11-5x=9

-x+11=9

-x=9-11

-x=-2         cut the negative signs as its LHS and RHS

<u>x=2</u>

d) 5y+ -5-2y=-11      as x=-5-2y is given

3y+-5=-11

3y=-11+5

3y=-6

<u>y=-6/3=-2</u>

e)-5x-4(2x+1)=35       as y=2x+1

-5x-8x+4=35

3x+4=35

3x=35-4

3x=31

x=31/3

<u>x=10.3</u>

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Elena-2011 [213]
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18 ÷ 2 =9

A = pi(3.14)r^2
A = 3.14 × 9^2
A = 3.14 × 81
A = 254.34in^2
4 0
4 years ago
Find the diameter of a sphere with a surface area of 196π square centimeters
aleksandr82 [10.1K]

\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}

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2 years ago
What is the formula for a confidence interval?
ikadub [295]

Answer:

a) The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) \bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Part a

The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

5 0
4 years ago
Start with Chanel’s sequence. How does a 90-degree counterclockwise rotation about the origin change the coordinates of a shape?
zmey [24]

When a shape is rotated, it must be rotated through a point.

  • <em>90 degrees counterclockwise rotation negates the y-coordinates, and then swap the x and y-coordinates</em>
  • <em>Chanel is incorrect</em>

The rule of 90 degrees counterclockwise is:

(x,y) \to (-y,x)

This means that:

  • <em>The y-coordinate is negated</em>
  • <em>Then the y and x coordinates are swapped</em>

<em />

However, Charlies transformation is incorrect.

  • This is so because, the shape was not rotated, but instead it was reflected  across the x-axis.
  • Then, the shape was dilated

Using points L and Q

L=(1,1)

When L is reflected across the x-axis.

The rule is:

(x, y) \to (x, -y)

So, we have:

(1, 1) \to (1, -1)

Next, it is dilated by 2.

The rule of this is:

(x,y) \to k(x,y)

So, we have:

(1,1) \to2 \times  (1,-1)

(1,1) \to (2,-2)

From the diagram, the coordinate of Q is:

Q = (2,-2)

Same as the calculated point

Hence, Chanel is incorrect

Read more about transformation at:

brainly.com/question/11709244

8 0
2 years ago
Read 2 more answers
I AM GIVING BRAINLISEST AND 20 POINTS! Write the equation of the circle in standard form.
azamat

Answer:

(x-4)^2+(y)^2=1

Step-by-step explanation:

The general format for the equation of a circle is the following:

(x-n)^2+(y-m)^2=1

This circle will have its center at point (n,m). Please note that its center is shifted (n) units to the right of the origin, and (m) units up. Apply this knowledge to the given problem.

The circle in the given problem has its center at (4, 0). Therefore the following can be stated,

n=4\\\\m =0

Substitute these points into the general formula for the equation of a circle, then simplify,

(x-n)^2+(y-m)^2=1

(x-4)^2+(y-0)^2=1

(x-4)^2+(y)^2=1

6 0
3 years ago
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