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2 years ago

The rectangle shown below has an area of 4(x+3) square units.

Mathematics

1 answer:

Serga [27]2 years ago

3 0

Remark

The area = 4*(x + 3) to start with. If you remove the brackets,

A = 4(x + 3)

A = 4*x + 3*4

A = 4x + 12 <<<<<< Answer for A

Part B

The area will become 4 times larger.

A = 4*(4x + 12)

A = 16x + 48

Argument

You may not be wholly satisfied with an unproved statement. I could prove it with algebra but it might be easier just to give an example.

Area = L * W

L = 10

W = 5

Area = 10*5

Area = 50

Now double both L and W

L = 20

W = 10

Area = L*W

Area = 20*10

Area = 200 which is 4 times the size of 50.

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After the bank cashed a check Maureen wrote for $60, her balance was Negative 14 dollars. The equation b + (negative 60) = negat

RoseWind [281]

B + (-60) = -14
-60 -60
---------------
b = -74

What error, if any, did Maureen make?

Maureen's work is correct, and her original balance was -$74.

Maureen should have added 60 to both sides.

Maureen should have added 14 to both sides.

Maureen made a computational error when she subtracted -14 - 60
Maureen's work is correct, and her original balance was -$74.

--> Maureen should have added 60 to both sides.

Maureen should have added 14 to both sides.

Maureen made a computational error when she subtracted -14 - 60

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2 years ago

Read 2 more answers

I need to u substitution method to solve -5x-8y=17 , 2x-7y=-17

harina [27]

Answer:

Alright well solve for the variable in one of the equation's. then substitute the result of the other equation

Point form: - 175/51, 1/51

Equation form:

x = - 175/51 y = 1/51 Hope this help's :)

Step-by-step explanation:

8 0

2 years ago

In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

Perimeter = (2 + √3)·a

Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

3 0

2 years ago

Line WY is an altitude in triangle WXZ. If ΔYWZ ~ ΔYXW, what is true about XWZ? XWZ is an obtuse angle. XWZ is a right angle. XW

topjm [15]

In triangle WXZ,

Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
If ΔYWZ ~ ΔYXW
∠WXY = ∠WZY

Then, we can also conclude
∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)

Now, in any triangle, the sum of all the three angles is 180.

In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°

Similarly, in WZY.

Hence, we conclude that XWZ is a right angle.

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2 years ago

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A company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When

Tanya [424]

Answer:

$ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434$

Step-by-step explanation:

For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.

We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

$\hat p = \frac{24}{250}= 0.096$

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".

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.33$

And the margin of error would be:

$ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434$

4 0

2 years ago