Fully simplify the following expressions
1. (2⁴ x 5⁵)²
2. (2²+5)²
3. 2-²+3 ÷ 2-¹
​

Answer:

AE = ED/////  A MIDPOINT DIVIDES A SEGMENT INTO TWO CONGRUENT SEGMENTS

AB = DC ///// OPPOSITE SIDES OF A RECTANGLE ARE CONGRUENT

<A IS A RIGHT ANGLE ///// THE INTERIOR ANGLES OF A RECTANGLE ARE RIGHT ANGLES

<D IS A RIGHT ANGLE ///// THE INTERIOR ANGLES OF A RECTANGLE ARE RIGHT ANGLES

<A = <D ///// ALL RIGHT ANGLES ARE CONGRUENT

TRIANGLES ABE = DCE ///// SAS

Hope this might help you.

Step-by-step explanation:

Answer:

x=-3 and

x=-2 is the answer i watched a vid about it for you i can put more \

(x + 3 )(x+2) = 0

x+-3

x+2=0

x=-2

hope this helps?

Step-by-step explanation:

Answer:

6.5 ounce puppy would be 8.6

7.3 ounce puppy would be 9.4

6.4 ounce puppy would be 8.5

Step-by-step explanation:

6.5+2.1=8.6

7.3+2.1=9.4

6.4+2.1=8.5

hope this helps!

Answer: 8.6, 9.4, and 8.5.

Step-by-step explanation:

 6.5

+ 2.1

_____

 8.6

 7.3

+ 2.1

_____

 9.4

  6.4

+ 2.1

_____

  8.5

Hope this helps! :)

Step-by-step explanation:

you make a question we don't understand. can you explain

Answer:

it can be simplified to Y^(-5)X^(-2)

Step-by-step explanation:

So the exponents can be added because the terms are all being multiplied:

For Y: (-8)+(3)=(-5)

For X: (0)+(-2)=(-2)

So the simplified answer is Y^(-5)X^(-2)

That is also the same as 1/[(x^5)(y^2)]

Does that answer the question?

Answer:

A

Step-by-step explanation:

x³ - 4x² + 7x - 28

= x²(x - 4) + 7(x - 4)

= (x - 4)(x² + 7)

= A

As per the given data, the resulting expression after factoring by grouping is [tex](x^2 + 7)(x - 4)[/tex], which is option A.

Factoring is the process of finding the factors of an algebraic expression, which involves writing the expression as a product of simpler expressions.

There are different methods for factoring, depending on the type of expression. Some common methods include: Factoring by grouping, Factoring quadratics, and Factoring higher degree polynomials.

We can factor [tex]x^3 - 4x^2 + 7x - 28[/tex] by grouping the first two terms and the last two terms as follows:

[tex]x^3 - 4x^2 + 7x - 28= (x^3 - 4x^2) + (7x - 28)\\= x^2(x - 4) + 7(x - 4)\\= (x^2 + 7)(x - 4)[/tex]

Therefore, the resulting expression after factoring by grouping is (x^2 + 7)(x - 4), which is option A.

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Answer:

$7.00

Step-by-step explanation:

Each pound cost $2 and we have 3 pounds which means that's $6:

3 • 2= 6

But then we have half a pound (1/2), well whats half of 2? the answer is 1 which means we add another dollar making that $7.00! :)

Answer:

[tex]z \leqslant 29[/tex]

Step-by-step explanation:

[tex] - z \geqslant - 6 - 23[/tex]

[tex] - z \geqslant - 29[/tex]

[tex]z \leqslant 29[/tex]

The value of [tex]b[/tex] in the cubic polynomial is -4.

After a quick analysis, we find that given cubic function is equivalent to the following equivalence:

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x-1)^{2}\cdot (x-2)[/tex]

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x^{2}-2\cdot x + 1)\cdot (x-2)[/tex]

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-2\cdot x^{2}+x-2\cdot x^{2}+4\cdot x-2[/tex]

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-4\cdot x^{2}+5\cdot x -2[/tex]

After a quick observation, we conclude that the value of [tex]b[/tex] in the cubic polynomial is -4. [tex]\blacksquare[/tex]

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Considering the situation described, we have that:

a) The Poisson distribution is used because we only have the mean.

b) There is a 0.0907 = 9.07% probability that there will be no defects.

c) There is a 0.2177 = 21.77% probability that there will be one defect.

d) There is a 0.3084 = 30.84% probability that there will be fewer than two defects.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The Poisson distribution is used because we only have the mean.

We have 0.8 defects per m² and 3 m², hence the mean is given by:

[tex]\mu = 3 \times 0.8 = 2.4[/tex]

Item b:

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2.4}(2.4)^{0}}{(0)!} = 0.0907[/tex]

There is a 0.0907 = 9.07% probability that there will be no defects.

Item c:

The probability is P(X = 1), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 1) = \frac{e^{-2.4}(2.4)^{1}}{(1)!} = 0.2177[/tex]

There is a 0.2177 = 21.77% probability that there will be one defect.

Item d:

The probability is P(X < 2), hence:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0907 + 0.2177 = 0.3084.

There is a 0.3084 = 30.84% probability that there will be fewer than two defects.

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Suppose ABC be a triangle such that ∠A = 4x + 7 ,

∠B = 3x + 5 & ∠C = 6x + 12

We know, the sum of interior angles of a Triangle is 180°, therefore, ∠A + ∠B + ∠C = 180°

or, 4x + 7 + 3x + 5 + 6x + 12= 180°

or, 13x = 180 - 24

or, x = 156/ 13 = 12

Answer:

False

Step-by-step explanation:

3+2=5

3+2=55-1=4

3+2=55-1=44x4=16

3+2=55-1=44x4=16Hence, the equation is true.

Answer:

2 π R^2 = 72 π        area of the two circles

R^2 = 36

R = 6

Area of rectangle = 2 R * 4 R = 8 R^2

Area = 8 * 36 = 288

Note area of one circle = π R^2 = π  36 = 113

Area of two circles = 226 - somewhat less than the area of the rectangle

Given :

⠀

To Find :

⠀

Answer :

⠀

Explanation :

We know that,

⠀

Therefore,

[tex]{ \longrightarrow \sf \qquad \angle1 + \angle2 + \angle3= 180 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \sf \qquad 50 {}^{ \circ} + 58{}^{ \circ}+\angle3= 180 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \sf \qquad 108{}^{ \circ}+\angle3= 180 {}^{ \circ} }[/tex]

⠀

Subracting 108° from both sides :

[tex]{ \longrightarrow \sf \qquad 108{}^{ \circ} - 108 {}^{ \circ} +\angle3= 180 {}^{ \circ} - 108 {}^{ \circ} }[/tex]

[tex]{ \longrightarrow \pmb{\bf \qquad \angle3= 72 {}^{ \circ} }}[/tex]

⠀

Therefore,

Answer:

A=1/2b*h

Step-by-step explanation:

A=1/2b*h

a rectangle is b*h, and a right triangle is half a rectangle.

Answer:

9 is added by 4 times y is the correct answer.

The given option don't describe the expression 4y+9

Answer:

I think 5 because they both go into it

The base and height of the triangle is 16 meters and 7 meters respectively.

Scalene triangles are triangles which has all three sides having different side lengths and the measure of all the three angles is different.

Given that,

Area of a scalene triangle = 56 square meter

Base of the triangle = 2x - 6 meters

Height of the triangle = x - 4 meters

The formula to find the area of a triangle is,

Area = [tex]\frac{1}{2}[/tex] × base × height

Substituting,

[tex]\frac{1}{2}[/tex] × (2x - 6) (x - 4) = 56

[tex]\frac{1}{2}[/tex] (2x² - 6x - 8x + 24) = 56

[tex]\frac{1}{2}[/tex] (2x² - 14x + 24) = 56

x² - 7x + 12 = 56

x² - 7x - 44 = 0

Factoring,

(x - 11) (x + 4) = 0

So, x = 11 or x = -4.

x = -4 is not possible, since the negative lengths are not possible.

So, x = 11

So base = 2x - 6 = 16 and height = x - 4 = 7

Hence the base and height are 16 and 7 respectively.

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Answer:

E)

Step-by-step explanation:

It cannot be decided from the information given as we have only been given the side lengths of each of the squares.  We have not been told at what point along each side length the other square intersects, nor have we been told the angle at which the squares intersect each other.   We would need this information to be able to calculate the specified area.

Diagram is note done perfect according to question .

Use the shortcut trick mentioned below while these cases come .

Area left(Black part)=Area of biggest square- area of rest squares drawn

Now

Area left:-

[tex]\\ \rm\rightarrowtail 7^2-(5^2+3^2)[/tex]

[tex]\\ \rm\rightarrowtail 7^2-(25+9)[/tex]

[tex]\\ \rm\rightarrowtail 49-34[/tex]

[tex]\\ \rm\rightarrowtail 15cm^2[/tex]

Answer:

Infinitely Many Solutions

Step-by-step explanation:

There can be infinite solutions to this problem

Here are some examples

3   4

6   8

12  16

24 32

48   64

96   128

To get a solution, just multiply both numbers by the same term. I multiplied by 2 each.

Hope this helps :)

-jp524

yes

yes

Step-by-step explanation:

I am in the blooket

Answer:

ok

Step-by-step explanation:

Answer:

Hi , your answer is V = 4/3 πr³.

Hope this helps

Answer:

5 3/5 --> 5 12/20

3 3/4 --> 3 15/20

redistribute 1 into 20/20 and make

4 33/20 - 3 15/20

= 1 18/20

= 1 9/10

Answer: D

Step-by-step explanation:
Unit means 1, so it’s obviously D!

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$30000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &15 \end{cases} \\\\\\ A=30000[1+(0.06)(15)]\implies A=30000(1.9)\implies A=57000[/tex]

Answer:

The value of X is 1

Step-by-step explanation:

Trust me i did this already.

Answer:

x=3

Step-by-step explanation:

we can use the  pythagora thearom as it is a right angled triangle.

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

so in this example it would be like this

[tex]x^{2} +x^{2} =(3\sqrt{2})^{2}[/tex]

so lets simplify it to this

[tex]2x^{2} =18[/tex]

now all thats left is to get x on its own

[tex]x^{2} =9[/tex]

[tex]x=+or-3[/tex]

x cant be -3 so x =3

Answer: 16

Step-by-step explanation:

It divides evenly into (w-4)^2.

Answer:

$49

Step-by-step explanation:

16 - 9 =7

7 x 7 = 49

he would make $49.

Answer:

(x, y) ==> (-4, -3)

Step-by-step explanation:

-2(3x + y = -15) ==> -6x - 2y = 30

3x + 2y = -18

-6x - 2y = 30

3x + 2y = -18

-3x = 12

/-3    /-3

x = -4

Now, we solve for y:

-6x - 2y = 30

-6(-4) - 2y = 30

24 - 2y = 30

-24        -24

-2y = 6

/-2    /-3

y = -3

(x, y) ==> (-4, -3)

Hope this helps!

Answer:

The solution would be to solve two equations simultaneously.

Step-by-step explanation:

The solution would be to solve two equations simultaneously.

So let X = ml of 8 % SOLUTION and Y = ml of 20 % SOLUTION

We know that X + Y must = 60 ml.

So first equation is X + Y = 60

The second equation is the statement of the problem

0.2 X + 0.08 Y = 0.1 x 60 = 6

Second equation reduces to

0.2 X + 0.08 Y = 6

Solve the two equations for X and Y and you have your answer.