Expand the following expression.

Answer:

I may not know his balance but I think he's not making a good financial decision because he already has - $60 in his account and he's spending more making him more liable to burn money and it's not advisable

The proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

The given figure showing ΔABE ≅ ΔDCE is in the image attached below.

We know that:

E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.

E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.

∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.

This means that ΔAEB and ΔDEC have:

two pairs of congruent sides - AE ≅ ED and BE ≅ EC

one pair of congruent included side -  ∠AEB ≅ ∠CED

Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.

If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.

Therefore, AB∥CD by the CPCTC Theorem.

Thus, the proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

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Answer:

Hopefully this is the question: 7[tex]x^{2}[/tex] + 3x - [tex]x^{2}[/tex]

Step-by-step explanation:

7[tex]x^{2}[/tex] + 3x -[tex]x^{2}[/tex]

= 6[tex]x^{2}[/tex] + 3x

= 3x ( 2x + 1 )

Hopefully this helps.

Answer:

76%

Step-by-step explanation:

to make this a percentage we need to make the denominator 100. luckily 25*4=100, so multiply 19/25 by 4/4 to get 76/100. so our percentage is 76

Answer:

76%

Step-by-step explanation:

percent is out of 100, so 19*4/25*4=76/100=76%

Using the Central Limit Theorem, it is found that the correct option is:

(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.

By the Central Limit Theorem, for a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

A similar problem is given at https://brainly.com/question/24663213

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]

[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]

[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]

Finding the value of x at the maximum point, we get;

[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]

Therefore;

[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]

[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]

The length of the plot that will give the most area, y = 125 feet

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Answer:

Some answers for #4 I think!

a = 36

b = 90

c = 36

d = 90

e = 54

Sorry if they are wrong I tried my bestest!

Answer:

k = - [tex]\frac{16}{15}[/tex]

Step-by-step explanation:

Since x = - 2 is a zero , then p(- 2) = 0 , that is

2(- 2)² - 3(- 2)(5k + 4) = 0

2(4) + 6(5k + 4) = 0 ← distribute parenthesis

8 + 30k + 24 = 0

30k + 32 = 0 ( subtract 32 from both sides )

30k = - 32 ( divide both sides by 30 )

k = [tex]\frac{-32}{30}[/tex] = - [tex]\frac{16}{15}[/tex]

Given Polynomial P(x) = 2x^2-3x(5k+4)

Zero = -2

We know that

If -2 is zero of the Polynomial then it satisfies the given Polynomial

⇛P(-2) = 0

⇛ 2(-2)^2-3(-2)(5k+4)=0

⇛ 2(4)+6(5k+4) = 0

⇛ 8+30k+24 = 0

⇛ 30k+32 = 0

⇛ 30 k = -32

⇛ k = -32/30

⇛ k = -16/15

Answer:- The value of k = -16/15.

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Answer:

( iii)

a-x/a+x =b

a-x=b(a+x)

a-x=ab+ax

a-ab=ax+x

a-ab=x(a+1)

a-ab/a+1=x(a+1)/a+1

x=a-ab/a+1

x=a(1-b)/a+1

Answer:

A = 36√3 - 12π

Step-by-step explanation:

Make 2 identical 30-60-90 triangles out of the "wedge"

For each 30-60-90 triangle:

Since the short leg is 6 the long leg is 6√3

short leg is the base and long leg is the height

a = (1/2)bh

a = (1/2)(6)(6√3)

a = 3(6√3)

a = 18√3

Since there are 2 triangles

a = 36√3

--------------------------------

Then subtract off the area of the 120º sector

a = (120/360)πr^2

a = (1/3)π(6^2)

a  = (1/3)π(36)

a = 12π

Shaded area

a = 36√3 - 12π

Step-by-step explanation:

we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).

since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.

basically, the area of a triangle is

1/2 × b×c × sin(A)

A being the angle between the 2 sides b and c. for any 2 sides of the triangle.

one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.

we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.

remember, the sum of all angles in a triangle is 180 degrees.

so, via the law of sines we can then calculate all sides :

a/sin(A) = b/sin(B) = c/sin(C)

with the angles being opposite of the sides.

6/sin(30) = baseline/sin(90)

6/0.5 = baseline/1

12 = baseline

top side² + 6² = 12²

top side² = 12² - 6² = 144 - 36 = 108

top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.

the area of the 2 triangles is then

6×sqrt(3)×6×sin(90) = 36×sqrt(3)

and the circle segment to be deducted is

pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12

so, the complete answer is

A = 36×sqrt(3) - 12×pi

Answer:

i cant read the handwriting

Step-by-step explanation:

Answer:

solutions are all values greater than 6

Step-by-step explanation:

add 15 to each side to get:

3x > 18

divide each side by 3 to get:

x > 6

solutions are all values greater than 6

Answer:

$2.00

Step-by-step explanation

To solve this problem, divide $6 by 3 bars which is $2 a bar

Answer:

One bar= $2

Step-by-step explanation:

6 is the amount paid, 3 is the amount of bars he got. so to find the amount for one bar you divide, 6÷3= 2

Step-by-step explanation:

no cause 3/2 can't be changed

Answer:

r = 2.5 cm

Step-by-step explanation:

The radius is 1/2 of the diameter

r = 1/2 (d)

r = 1/2 (5)

r = 2.5 cm

Answer:

x2\2+3\2=h/2 therefore x= -3\2+h\2

Answer:

  y = K/(16z)

Step-by-step explanation:

  [tex]K=16yz\qquad\text{given}\\\\\boxed{y=\dfrac{K}{16z}}\qquad\text{divide by the coefficient of y}[/tex]

Number of marbles with Mallika = x

Number of marbles with Kishore = x (same number of marbles)

To get 100 marbles = x + x + 30

=》x + x + 30 = 100

2x + 30 = 100

2x = 100 - 30

2x = 70

x = 70/2

x = 35

■ Final answer =》Mallika & Kishore both have 35 marbles each.

■ Equation =》2x + 30 = 100

■ Equation type =》Linear equation in 1 variable

______

Hope it helps ⚜

The equation for the given situation will be;

⇒ 2x + 30 = 100

Where, 'x' is represent the number of marbles.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Mallika and Kishore have the same number of marbles.

And, To have 100 marbles they must pool their marbles together and then get 30 more.

Now,

Since, Mallika and Kishore have the same number of marbles.

Hence, Let the number of marbles = x

So, We can formulate;

⇒ x + x + 30 = 100

⇒ 2x + 30 = 100

⇒ 2x = 100 - 30

⇒ 2x = 70

⇒ x = 35

Thus, Number of marbles each have = 35

And, The equation for the given situation will be;

⇒ 2x + 30 = 100

Where, 'x' is represent the number of marbles.

Learn more about the mathematical expression visit:

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Answer:

16. Domain: [-3,5] and range : [-5,3]

17. Domain: [0,4] and range: [0,4]

=======================================================

Explanation:

1/5 of the beans are mung, so 4/5 of the beans are pinto. The two fractions add to 5/5 = 1.

Ignore the denominators and focus on the numerators for each fraction. We have 1 mung and 4 pinto. The values are read in this order to form the ratio 1:4 which is our answer. We cannot reduce this ratio any further.

The order is important because saying 4:1 would mean that we have 4 mung beans and 1 pinto, when it's the other way around.

Side note: The value 450 isn't needed. We could easily change it to any other multiple of 5 and get the same exact answer.

Step-by-step explanation:

6/2 (1+2) = 3(3) = 9.

hope this helps you.

Answer:

9

Step-by-step explanation:

First you need to multiply 6/2 or 3 by the numbers in the ( ) 6/2 x 1 and 6/2 x 2. You will get 3 and 6. 3+6= 9

Answer:

the answer is 15 bc 30-15=15

Step-by-step explanation:

Answer:11?

Step-by-step explanation:30 buldogs

                                             pirates 10 plus star 9 19 in 30 wwhats left

Answer:

the coomon factor is 3xy³

by factoring we get

3xy³(4y-7xy²z+12)

Answer:

Step-by-step explanation:

First you put the negative sign away for the end and then you switch the problem to 20.5 - 6. Then you put the 0.5 away for later too. 20 - 6 is equal to 14. Then you add the 0.5 back to the number. So it is equal 14.5 and the you put the negative sign back on to get the final answer of -14.5.

Answer:

243 km

precio de los kilómetros: $2357.10

Step-by-step explanation:

precio total = tarifa mínima + precio de los kilómetros

Para x kilómetros,

P = 490 + 9.7x

P = 2847.1

490 + 9.7x = 2847.1

9.7x = 2357.1

x = 243

precio de los kilómetros: 243 × $9.70/km = $2357.10

Respuesta: 243 km

precio de los kilómetros: $2357.10

Answer:

51840

[tex] 51840[/tex]

Answer:

518400

Step-by-step explanation:

7200 ÷ 10 is just the zero less:

= 720

Then

720 × 720 =

+1440

+5040

=518400

Answer: 0.6 Liters of powdered milk can produce 60 cups of milk.

Explanation: 120 grams of powdered milk makes 12 cups of milk. 120 divided by 12 is 10. 60 times 10 is 600. So 600 grams of powdered milk to make 60 cups of milk. That is equal to 0.6 kilograms and that is equal to 0.6 liters.

Answer:

Step-by-step explanation:

8/9    8 is a cube but 9 is not.  8/9 is not a cube

27      27 = 3^3, a perfect cube

30      Not a cube

8/27   Both 8 and 27 are perfect cubes, and so 8/27 is one also.

1/27    This is equivalent to 1^3 / 3^3 and is a perfect cube.

27/64  Both 27 and 64 are perfect cubes, so 27/64 is one also

64        64 = 4^3, a perfect cube

1/9        9 is not a cube, so 1/9 is not one either.

Answer:

There are 8 pieces of string cut

Explanation:

27.2 ÷ 3.4 = 8

Answer:

there is no graph though