Find x if (3⋅5)⁴ ⋅ (2⋅3)⁵ ⋅ (2⋅5)⁷ = 2ˣ ⋅ 3ʸ ⋅ 5ᶻ

Answer:

1.

For triangle 1

[tex]a = 3\sqrt{5}[/tex]

For triangle 2

[tex]x = 2\sqrt{2}[/tex]

2.

Way 1

By reducing  the length of the side 4 to 3.60

Way 2

By increasing the length of side 7 to 7.21

Step-by-step explanation:

The complete question is attached in the image

Solution

1.

Both the triangles are right angled triangle

For triangle 1

[tex]7^2 = 2^2 + a^2\\49 = 4 + a^2\\a^2 = 45\\a = 3\sqrt{5}[/tex]

For triangle 2

[tex]4^2 = x^2+x^2\\2x^2 = 4*4\\x^2 = 8\\x = 2\sqrt{2}[/tex]

2.

Way 1

By reducing  the length of the side 4 to 3.60

Way 2

By increasing the length of side 7 to 7.21

Answer:

The answer is 5.66

Step-by-step explanation:

let the missing side be x

9² = 7² + x²

9² - 7² = x²

x² = 9² - 7²

x² = 81 - 49

x² = 32

x = √32

x = 5.66

Answer:

100-16π ft2

Step-by-step explanation

Answer:

100-16π ft2

Step-by-step explanation:

Answer:

[tex](1)\ [12]x^2 [-][37]x - 30 = (3x + 2)(4x - 15)[/tex]

[tex](2)\ x^2\ [\ -]\ 169 = (x \[+ ]\ 13){x\ [- ]\ [13 ])[/tex]

[tex](3)\ x^2 [-]\ [9]x + 20 = (x\ [-] 5)(x- [4])[/tex]

[tex](4)\ x^2 + [11]x + 28 = (x + 7)(x + [4])[/tex]

[tex](5)\ x^2 + [5]x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Complete the boxes

Solving (1):

[tex][ \ ]x^2 [ \ ] [\ ]x - 30 = (3x + 2)(4x - 15)[/tex]

Swap the equation

[tex](3x + 2)(4x - 15) = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]

Open bracket

[tex]12x^2 -45x + 8x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]

Simplify the like terms

[tex]12x^2 -37x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]

So, we have:

[tex][12]x^2 [-][37]x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]

i.e.

[tex][12]x^2 [-][37]x - 30 = (3x + 2)(4x - 15)[/tex]

Solving (2):

[tex]x^2\ [\ ]\ 169 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]

The above expression illustrates the difference of two squares.

So, complete the first equation with minus

[tex]x^2\ [\ -]\ 169 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]

Express 169 as 13^2

[tex]x^2\ [\ -]\ 13^2 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]

Apply difference of two squares

[tex](x + 13)(x - 13) = (x \[\ ]\ 13){x\ [\ ]\ [\ ])[/tex]

So, the complete expression is:

[tex]x^2\ [\ -]\ 169 = (x \[+ ]\ 13){x\ [- ]\ [13 ])[/tex]

Solving (3):

[tex]x^2 [\ ]\ [\ ]x + 20 = (x \ [\ ]5)(x - [\ ])[/tex]

20 can be expressed as: -5 * -4

So, the expression becomes

[tex]x^2 [\ ]\ [\ ]x + 20 = (x \ [- ]5)(x - [4 ])[/tex]

Expand

[tex]x^2 [\ ]\ [\ ]x + 20 = x^2 - 5x - 4x + 20[/tex]

[tex]x^2 [\ ]\ [\ ]x + 20 = x^2 -9x + 20[/tex]

So, the complete expression is:

[tex]x^2 [-]\ [9]x + 20 = (x\ [-] 5)(x- [4])[/tex]

Solving (4):

[tex]x^2 + []x + 28 = (x + 7)(x + [])[/tex]

28 can be expressed as 7 * 4

So, the expression becomes

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

Expand

[tex]x^2 + []x + 28 = x^2 + 7x + 4x + 28[/tex]

[tex]x^2 + []x + 28 = x^2 + 11x + 28[/tex]

So, the complete expression is:

[tex]x^2 + [11]x + 28 = (x + 7)(x + [4])[/tex]

Solving (5):

[tex]x^2 + []x - 24 = (x\ []\ [])(x\ []\ [])[/tex]

-24 can be expressed as -3 * 8

So, the expression becomes

[tex]x^2 + []x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]

Expand

[tex]x^2 + []x - 24 = x^2 +8x - 3x - 24[/tex]

[tex]x^2 + []x - 24 = x^2 +5x - 24[/tex]

So, the complete expression is:

[tex]x^2 + [5]x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]

An equation is formed of two equal expressions. The complete equations are:

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1. The first equation that is given to us is:

[tex](?x^2)\ ?\ (?x)-30 = (3x+2)(4x-15)[/tex]

Now, if we simply expand the right-hand side of the equation we will get the equation that is mentioned on the left side of the given equation, therefore,

[tex](3x+2)(4x-15)\\\\= 12x^2-45x+8x-30\\\\=12x^2-37x-30[/tex]

Thus, the complete equation will be

[tex]12x^2-37x-30 = (3x+2)(4x-15)[/tex].

2. The second equation that is given to us is,

[tex]x^2\ ?\ 169 = (x\ ?\ 13)(x\ ?\ ?)[/tex]

Now, if look closely at the equation, and substitute the '-' in the place of '?' the equation we will be in the form of an algebraic equation, therefore, the solution of the equation can be made using the algebraic expression,

[tex]a^2-b^2 = (a+b)(a-b)\\\\(x^2-13^2) = (x+13)(x-13)\\\\\(x^2-169) = (x+13)(x-13)[/tex]

Thus, the complete equation will be

[tex](x^2-169) = (x+13)(x-13)[/tex].

3. The third equation that is given to us is,

[tex]x^2\ ?\ (?x)+20 = (x\ ?\ 5)(x-?)[/tex]

As we can see in the equation, on the left side of the equation the last digit is +20, therefore, the digits on the right side of the equation should be such that their product should be +20, as 5 is already given therefore, the other term should be 4 also, the second term is positive but we need the product to be positive, therefore, the sign of the digit 5 will also be negative.

[tex]x^2\ ?\ (?x)+20 = (x\ ?\ 5)(x-?)\\\\x^2\ ?\ (?x)+20 = (x- 5)(x-4)[/tex]

Now, if we solve the right side of the equation we will get the left side of the equation,

[tex](x- 5)(x-4)\\\\= x^2 - 4x-5x +20\\\\=x^2-9x+20[/tex]

Thus, the complete equation is

[tex]x^2-9x+20=(x-5)(x-4)[/tex].

4. The fourth equation that is given to us is

[tex]x^2 + ?x + 28 = (x+7)(x+?)[/tex]

As we can see in the equation, on the left side of the equation the last digit is +28, therefore, the digits on the right side of the equation should be such that their product should be +28, as 7 is already given therefore, the other term should be 4. Also, 28 is a positive integer, and 7 is also a positive integer, therefore, the number in the last will be positive as well.

[tex]x^2 + ?x + 28 = (x+7)(x+4)[/tex]

Now, if we solve the right side of the equation we will get the left side of the equation,

[tex](x+7)(x+4)\\\\= x^2 + 4x+ 7x + 28\\\\= x^2 + 11x+28[/tex]

Thus, the complete equation is

[tex]x^2 + 11x + 28 = (x+7)(x+4)[/tex]

5. The fifth equation that is given to us is

[tex]x^2 + ?x -24=(x\ ?\ ?)(x\ ?\ ?)[/tex]

As we can see in the equation, on the left side of the equation the last digit is -24, therefore, the digits on the right side of the equation should be such that their product should be -24, Since the product is negative, therefore, either one of the digits on the right should be negative as well, but the middle term on the right is positive, therefore, the bigger number will be positive while the smaller ones will be negative.

[tex]x^2 + ?x -24=(x+8)(x-3)[/tex]

Now, solving the right side of the equation to get the complete left side of the equation we will get,

[tex](x+8)(x-3)\\\\=x^2 -3x + 8x -24\\\\=x^2 + 5x - 24[/tex]

Thus, the complete equation is

[tex]x^2 + 5x - 24=(x+8)(x-3)[/tex]

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

400 minutes

Step-by-step explanation:

20 *5 = 100

she needs 100 minutes to paint 1 wall

so for 4

100*4 =400 minutes

Answer:

[tex]P(2)=(32,46)[/tex]

Step-by-step explanation:

From the question we are told that:

Height of robot [tex]h=12 inches[/tex]

Weight of robot [tex]W=4[/tex]

Start position [tex]P(1)=(4,4)[/tex]

Per minute distance [tex]d=(4,6)[/tex]

Total time [tex]T=7min[/tex]

Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by

 [tex]d_T=d*T[/tex]

 [tex]d_T=(4.6)*7[/tex]

 [tex]d_T=(28,42)[/tex]

Generally the position of the robot after 7 minutes is  mathematically given by

 [tex]P(2)=P(1)+d_T[/tex]

 [tex]P(2)=(4,4)+(28,42)[/tex]

 [tex]P(2)=(32,46)[/tex]

Therefore the position of the robot after 7 minutes is

 [tex]P(2)=(32,46)[/tex]

Answer:

16 ft

Step-by-step explanation:

To find the perimeter of a square you must:

1. add all of the lengths together (4+4+4+4=16)

Have a great day.

48 + 54 = 102

102 / (8+9) = 6

48 + 54 = 6 x (8+9)

6 can be written on the blank line to make the expressions equivalent.

can i please get brainlist

Answer: 8+9

Step-by-step explanation:

Divide both by 6

48/6 = 8

54/6 = 9

This is the lowest point you can divide it by meaning 8+9 would be equivalent to 48+54.

I didn't see any multiple choice answers to choose from so this could be wrong.

Step-by-step explanation:

5x can also be written as " -3x + 8x " so:

[tex]x^2+5x-24 = x^2-3x+8x-24[/tex]

Using the distributive property:

[tex]x(x-3)+8(x-3)[/tex]

Then again, using the distributive property (but in reverse):

[tex](x-3)(x+8)[/tex]

The two numbers that the middle term should be split into in order to factor can be found by listing out pairs of factors for the product of the last term and the coefficient of the first term, and using the two factors whose sum is the middle term.

For eg (because that was a bit text heavy):

The product of the last term and the first coefficient (1 * (-24)) is -24

the factors of -24 include (and their sum)

-1, 24 (23)

1, -24 (-23)

-2, 12 (10)

2, -12 (-10)

-3, 8 (5)

3, -8 (-5)

-4, 6 (2)

4, -6 (-2)

The middle coefficient is 5 and the sum of the factors -3 and 8 are 5, so split 5x into -3x + 8x to be able to factor how I showed before.

Answer:

false

Step-by-step explanation:

Supplementary means that two angles added together must equal 180. An acute angle is one less than 90 degrees, and an obtuse one is greater than 90. They will not always add up to 180.

For example, 24 is an acute angle. 134 is an obtuse angle. But they do not add up to 180 degrees, thus not supplementary.

Answer: True

Step-by-step explanation: Hope that helped!

Answer:

A. 320 cubic centimeters

Step-by-step explanation:

First, you want to multiply 4 by 4 to get 16. Then what you want to be is multiply 16 by 20 and you will get 320 cubic centimeters.

Answer:

I'm assuming the order corresponds the student to the equation. Because of this, the answer is simple:

Bert, Etsuko, and Camille.

Step-by-step explanation:

2x-9=-1, 2x=8, x=4

2(x-10)=-12, x-10=-6, x=4

-2x+12=4, -2x=-8, x=4

Answer:

Explanation:

Volume of a right cylinder = area of the base × height

V = πr² × h

r = d/2

r = 34/2 = 17 m

V = π × 17² × 27

V = 24513.85 m³

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 2 √ 3 , − 2 √ 3

Answer: 240

Step-by-step explanation:

Given

Shop has 12 types of bagels, 10 types of cream and a option for roast

For making a bagel there are 12 choices to select a bagel, following this there are 10 choices for cream with a option to roast

So, total no different bagels that can be made out of the given is

[tex]\Rightarrow 12\times 10\times 2\\\Rightarrow 240\ \text{types}[/tex]

Answer:

1.99m²

Step-by-step explanation:

From the above question

1 ft = 3.281 m

1 ft² = (3.281 m)²

Converting 21.4 ft² to m²

1 ft² = (3.281 m)²

21.4 ft² = xm²

x m² = 21.4 ft²/ (3.281 m)²

x m² = 1.9879310292 m²

Approximately :

21.4 ft² = 1.99m²

Answer:

336 ft ²

Step-by-step explanation:

Find the area of the two triangles

In this case, both triangles are the same, so we can modify the formula for area of triangle

In the formula, we divide by two, but because we multiply the area by two for the two triangles, we can just use base x height

Triangles = 6 x 8 = 48 ft²

top rectangle = 10x12 = 120 ft²

bottom rectangle = 8x12 = 96 ft²

back rectangle = 6x12 = 72 ft²

Total = 48 ft² + 120 ft² + 96 ft² + 72 ft² = 336 ft²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

g(f(4)) = 41

Step-by-step explanation:

Evaluate f(4) then substitute the value obtained into g(x)

f(4) = 4² + 4 = 16 + 4 = 20, then

g(20) = 2(20) + 1 = 40 + 1 = 41

That is g(f(4)) = 41

Answer: [tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

A standard 52 card deck includes spades, clubs, hearts, and diamonds.

13 card of each category is present

So, there are 13 spades present in the deck

Probability is the ratio of favorable to the total outcomes.

[tex]\therefore P=\dfrac{13}{52}\\\\\Rightarrow P=\dfrac{1}{4}[/tex]

Answer:

No.

Step-by-step explanation:

25x + 20y = 5x(5 + 4y)

Distribute the 5x inside the (5 + 4y).

5x * 5 = 25x

5x * 4y = 20xy

25x + 20y ≠ 25 + 20xy, so the two expressions below are not equal.

Answer:

A. contract

Step-by-step explanation:

Answer:

1 hour and 35 mins

Step-by-step explanation:

Answer:

first of all chill lol

anyway here are the ways to factor the following trinomials:

6:

[tex]x^2-7x-30=(x-10)(x+3)[/tex]

7:

[tex]x^2-10x+24=(x-6)(x-4)[/tex]

:)

Answer:

t test for the slope of regression line

Step-by-step explanation:

Suppose a random sample is drawn from the bivariate normal population and the estimated regression equation is found Y^= a +bX , where, b , the sample estimate of β1 is normally distributed with mean β and standard deviation

σyx / √∑(x-x`)².

The test statistic has  t distribution where

t= b-β/sb

where sb=  Syx / √∑(x-x`)² with υ= n-2 degrees of freedom.

It is important to note that the testing of hypothesis that β= 0 is equivalent to testing the hypothesis that variable Y is independent of the variable X in the linear sense.

The test statistic then becomes  t= b/ sb .

If we reject H0 : β= 0 we conclude that the two variables are linearly independent.

Answer: - 58

Step-by-step explanation:

First, let us think of this number as x.

The first direction is to add 10 to it which is now x+10

After, we divide this by 6 getting -8.

This would look like (x + 10)/y = -8

Now, we solve

We go backwards so first step Is to multiply -8 by 6. This would get us -48. Then we subtract 10 since we added ten in the first place giving us -58.

The final answer is -58

Answer:

The original number was -58

Step-by-step explanation:

Step 1: Do -8*6 to find out what the numerator was.

Step 2: After finding that the numerator was -48 you would subtract 10 getting -58

Step 3: Check your work : -58+10 = -48

                                            -48/6 = -8

Answer:

You can make it to a rectangle and a square

Step-by-step explanation:

Answer:

you split it into 2 different parts, then add the area.

the answer to this question is 18in squared

Answer:

the second option

Step-by-step explanation:

Answer:

92.736

Step-by-step explanation:

A = L* W

A = 4.8 * 19.32

A = 92.736

Answer:

16/50 or 8/25

Step-by-step explanation:

Good luck. Hope you get a good grade