What is the amount of the average rate of change?

Given:

The equation is:

[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]

To find:

The error in the given equation and correct it.

Solution:

We have,

[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]

Taking left-hand side, we get

[tex]L.H.S.=(2x+3y)(2x-3y)[/tex]

[tex]L.H.S.=(2x)^2-(3y)^2[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]L.H.S.=(2)^2(x)^2-(3)^2(y)^2[/tex]       [tex][\because (ab)^x=a^xb^x][/tex]

[tex]L.H.S.=4x^2-9y^2[/tex]

It is not equal to right-hand side [tex]4x^2+6y^2[/tex]. In the right hand side, there must be a negative sign instead of positive sign.

Therefore, [tex](2x+3y)(2x-3y)=4x^2-6y^2[/tex].

Answer:

3675

Step-by-step explanation:

Answer:

5 grams/metres squared = 50 kg/hectares

Step-by-step explanation:

We need to convert 5 grams/metres squared to kilograms/hectares.

We know that,

1 kg = 1000 g

1 hectare = 10000 m²

So,

[tex]5\ \dfrac{g}{m^2}=5\times \dfrac{0.001}{\dfrac{1}{10000}}\\\\=50[/tex]

Hence, 5 grams/metres squared = 50 kg/hectares

Answer:

2x²+5x-6 = 0

using the quadratic formula

x = 0.886 and x= -3.386

Answer:

4.50

Step-by-step explanation:

[tex] \sin(40) \times 7 = 4.499513268[/tex]

round it up

[tex] = 4.50[/tex]

Answer:

the second one

Step-by-step explanation:

Answer:

26 cm

Step-by-step explanation:

[tex]a^{2} +b^2=c^2[/tex]

[tex]24^2+10^2=c^2[/tex]

576 + 100 = 676

[tex]\sqrt{676}[/tex] = 26 cm

Answer:

Rhombus

Step-by-step explanation:

Rhombus: A quadrilateral with four congruent sides and two pairs of parallel sides.

Answer:

a. x=9

b. PR = 59

Step-by-step explanation:

a. 11x-40 = 6x+5

11x-6x=5+40

5x=45

x=9

b. PR = 11(9) -40

= 99-40

= 59

Answer:

B.

Step-by-step explanation:

4x + 4x - 4x = 4x

24x ÷ 2 = 12x

3x • 4x = [tex]12x^2[/tex]

15x - 3 = 15x - 3

Answer:

B. 24x/2

Step-by-step explanation:

12x

A. 4x + 4x - 4x = 8x - 4x = 4x

B. 24x/2  = 24/2 x = 12x

C. (3x)(4x) = 12 x^2

D. 15x - 3​ = 15x -3  ( no like terms

Answer:

jeff has 3 apples left. kyle has 2 apples left. kelsea had 4 apples left.

Step-by-step explanation:

5-2=3

3-1=2

8-4=4

Answer:

jeff 3 apples, kyle 2 apples, kelsea 4 apples

total apples left = 9 apples

total apples eaten = 7 apples

total apples = 16 apples

Step-by-step explanation:

Answer:

n = 28 degree

Step-by-step explanation:

2n + 17 + 2n - 5 + 2n = 180 degree (sum of interior angles of a triangle)

6n +12 = 180

6n = 180 - 12

n = 168/6

n = 28 degree

Answer:

153.86

Step-by-step explanation:

So first off, what is the formula for finding area of a circle?

Its [tex]\pi r^{2}[/tex]

We know that r(radius), is the distance from one point of the circle to its center.

In this case it is 7.

Note that in other cases, you might see a line going strait through the middle of the circle.

This is the diamater, and is 2x the radius. If you see the diamater, divide it in half, and you will find radius.

Now, back to the problem.

We know our radius is 7, so lets plug that into [tex]\pi r^{2}[/tex]:

[tex]\pi *7^{2}[/tex]

=

[tex]\pi *49[/tex]

=

153.93

So tecnically, this test is wrong. THe actual answer is .07 bigger than what they give.

However, it is the only possible answer, so it is correct.

Answer:

153.86

Hope this helps!

Answer:

r

Step-by-step explanation:

Answer:

$52 is the sale price.

Step-by-step explanation:

First find 35% of $80. Multiply .35 x 80 to do this.

.35 x 80 = 28

Then subtract 28 from the original price 80.

80 - 28 = 52

Answer:

No the shop did not meet the 65 mean.

Step-by-step explanation:

The mean is the same thing as the average of the sales. So the first six months sales were 52, 82, 71, 92, 51, and 28. the average of these six numbers is 62.66667 which is short of the 65 mean.

52+82+71+92+51+28=376

take that number 376 and divide by the number of months (6)

376/6=62.66667

Answer: The final value is 10

Step-by-step explanation:

We are given:

[tex]4\tan 45^o+(2\sin 45^o)(6\cos 45^o)[/tex]

We know that:

[tex]\tan 45^o=1\\\sin 45^o=\frac{1}{\sqrt{2}}\\\cos 45^o=\frac{1}{\sqrt{2}}[/tex]

Putting values in the given equation, we get:

[tex]\Rightarrow (4\times 1)+(2\times \frac{1}{\sqrt{2}})\times (6\times \frac{1}{\sqrt{2}})\\\\\Rightarrow 4+(\frac{2\times 6}{2})\\\\\Rightarrow (4+6)\\\\\Rightarrow 10[/tex]

Hence, the final value is 10

Answer:

Yes the answer is indeed 60%

the answer is 60% so you are correct

Answer:

A= 43.393 rounded

Step-by-step explanation:

A=2πrh

A= 2 [tex]\pi[/tex] 1.625 (4.25)

A= 13.8125[tex]\pi[/tex]

or

A= 43.393 rounded

Answer:

x = 7.75

Step-by-step explanation:

To solve this equation for x, start by consolidating the constant terms on the right side:  Add 7.25 to both sides, obtaining:

3x = 16 + 7.25, or

3x = 23.25

Dividing both sides by 3, we get        x = 7.75

Answer:

x = 7.75

Step-by-step explanation:

3 x - 7.25 = 16

3 x = 16 + 7.25

3 x = 23.25

x = 23.25/3

x = 7.75

Answer:

20%

Step-by-step explanation: The percent of error formula is |(theoretical value-actual value)/actual value|=percent of error. Substitute the values in. |(2.8-3.5)/3.5|=|(-0.7)/3.5|=0.2. The percent equal to 0.2 is 20%.

Answer:

$8.39 por pe rsona

Step-by-step explanation:

Answer: 13 degrees

Step-by-step explanation:

1. - 2<0

2. (- 2)-(-15)=(-2)+15=13

Answer:

Probability of an event = 1 / 10

Step-by-step explanation:

Given:

Total number of people in particular area = 1,600

Number of people vaccinated = 160

Find:

Probability[people vaccinated]

Computation;

Probability of an event = Number of favorable outcomes / Total number of outcome

Probability of an event = 160 / 1600

Probability of an event = 16 / 160

Probability of an event = 1 / 10

Answer:

15c+70b[tex]\leq[/tex]112000

Step-by-step explanation:

Truck could carry 7000 pounds.

There are 15 ounce cans and 70 ounce bottles.

There are 'c' number of 15 ounce cans and 'b' is the number of 70 ounce bottles.

So, C number of cans can  carry 15C ounces

'b' number of bottles can carry 70b ounces

So, we can set up inequality as

15c+70b[tex]\leq[/tex]112000

Answer: [tex]371.8\ \text{Pounds}[/tex]

Step-by-step explanation:

Given

Dimensions of rectangular granite countertop is [tex]72\times 42\times 1.25\ in.^3[/tex]

Density of granite is [tex]\rho=170\ \text{Pounds per cubic ft}[/tex]

Volume of granite countertop

[tex]\Rightarrow V=72\times 42\times 1.25\\\Rightarrow V=3780\ in.^3[/tex]

We know, 1 ft=12 inch

[tex]\therefore V=2.187\ cm^3[/tex]

Weight of granite

[tex]\Rightarrow m=\rho \times V\\\Rightarrow m=170\times 2.1875\\\Rightarrow m=371.8\ \text{Pounds}[/tex]

Answer:

∅ ≈ 34º

Step-by-step explanation:

sin = opp/hyp

∅ = arcsin opp/hyp

∅ = arcsin 14/25

Use calculator

∅ = 34.055797742567906

∅ ≈ 34º

Answer:

is 55

Step-by-step explanation:

×[tex]\frac{x}{1}*\frac{14}{25}[/tex]⇒0.56

cos0.56

55

Answer:

56.3 =c

44.1 =a

Step-by-step explanation:

Using the law of sines

sin 102        sin 28

----------  = ----------

c                 27

Using cross products

27 sin 102 = c sin 28

Divide by sin 28

27 sin 102

------------   = c

sin 28

56.25470702= c

Rounding to the nearest tenth

56.3 =c

To find a

We need Angle A

A = 180 - 102 -28

A = 50

sin 50        sin 28

----------  = ----------

a                 27

Using cross products

27 sin 50 = a sin 28

27 sin 50

------------   = a

sin 28

44.0563425= a

Rounding to the nearest tenth

44.1 =a