One more than the quotient of a number x and four

Step-by-step explanation:

4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same

8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same

2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2

Answer:

1. [tex]5\sqrt{2}[/tex]

2. [tex]4\sqrt{3}[/tex]

3. [tex]8\sqrt{6}[/tex]

Step-by-step explanation:

Number 1:

We can treat [tex]\sqrt{2}[/tex]  as a variable in which we are multiplying 4 by. Let's call [tex]\sqrt{2}[/tex] x.

This makes our expression [tex]4x + x[/tex]. Combining like terms, we get [tex]5x[/tex]. This means that [tex]4\sqrt{2} + \sqrt{2} = 5\sqrt{2}[/tex].

Number 2:

Again, we can use the same logic as we did in number 1. Let's treat [tex]\sqrt{3}[/tex] as a variable y.

[tex]8y-4y[/tex]

Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's [tex]4y[/tex]. This means that  [tex]8\sqrt{3}-4\sqrt{3}=4\sqrt{3}[/tex]

Number 3:

When we multiply radicals, we want to put the radicals in [tex]\sqrt{x}[/tex] form.

[tex]\sqrt{32}[/tex] is already in this form.

However [tex]2\sqrt{3}[/tex] is not.

[tex]2\sqrt{3}[/tex] is the same thing as [tex]\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}[/tex].

Now we multiply these radicals by multiply the term inside the square root sign

[tex]\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}[/tex]

384 is divisible by 64, so:

[tex]\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}[/tex]

Hope this helped!

Answer:

w = -4

Step-by-step explanation:

Answer:

w = -4

Step-by-step explanation:

[tex]-6=-2+w\\[/tex]

Switch sides

[tex]-2+w=-6[/tex]

Add 2 to both sides

[tex]-2+w+2=-6+2[/tex]

Simplify

[tex]w=-4[/tex]

Answer:

13, 16, 23

Step-by-step explanation:

The first side is x.

The second side is x + 3

The third side is 2x - 3

(x) + (x +3) + (2x - 3) = 4x

4x = 52

x = 13

Answer:

19 marshmallows per person.

Step-by-step explanation:

So, 38 marshmallows per bag and 12 bags were brought.

38 x 12 = 456

Walt and 23 of his friends - 24 people

456/24 = 19 marshmallows

Answer:

x = 2

Step-by-step explanation:

8(7x-2)=96

7x-2 = 96 : 8

7x-2 = 12

7x = 12 +2

7x = 14

x = 14 : 7

x = 2

Answer:

Step-by-step explanation:

[tex]8\left(7x-2\right)=96\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8\left(7x-2\right)}{8}=\frac{96}{8}\\\\Simplify\\7x-2=12\\\\Add\:2\:to\:both\:sides\\7x-2+2=12+2\\\\Simplify\\7x=14\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7x}{7}=\frac{14}{7}\\\\Simplify\\x=2[/tex]

Answer:

   3                                            

1 -----                          

    25

Step-by-step explanation:

Answer:

67-100

Step-by-step explanation:

This is the answer because the . is ones the 6 is tens and the 7 is the hundreds

Answer:

a. It is a negative pattern

b. Fourth term is 67

c. Explicit formula is Tn = 87 - 5n where n is the number of the term.

d. The value of the 100th term is -413

Step-by-step explanation:

1.Firstly, we want to know if the pattern is positive or negative.

Looking at the pattern, we can see our first term as 82, second as 77, third as 72.

What this show is that the pattern is decreasing as we move on from one term to another. So we can say it is a negative recursive pattern.

2. We are asked which term is the 4th.

This is quite obvious from the spelt out pattern.

82 77 72 67

1....2......3.....4

67 is the fourth term.

3. We want an explicit formula for the sequence.

What this question is asking us is a formula such that we can use at any point in time to calculate the value of the term at that point.

Firstly we have the first term as 82.

We need the common difference.

Mathematically this is the second term minus the first term which is same as the third term minus the second term.

That would be; 77-82 = 72-77 = -5

Mathematically the nth term of an arithmetic sequence is;

Tn = a + (n-1) d

Where in this case a is 82 and d is -5

Substituting these values, we have;

Tn = 82 + (n-1)-5

Tn = 82 -5n + 5

Tn = 82 + 5 -5n

Tn = 87 -5n

Where Tn is the term we are looking for while n is the number of the term.

4. Value of the 100th term

Simply substitute the value of 100 for n in the explicit formula.

That would be;

87 -5(100) = 87-500 = -413

Answer:

My answer is 28,250Rs.

Area of a triangle=1/2b×h.

1/2×7×5=17.5.

Area of a rectangle=l×b.

20×15=300.

Area of rectangle-Area of the triangle=300-17.5=282.5m^2.

If 1m^2=100Rs.

then 282.5m^2=282.5×100=28,250Rs.

Answer:

12.1

Step-by-step explanation:

To approximate this value, we simply need to know some perfect squares.  We know that the value 144 is the perfect square of 12.  And we know the value 169 is the perfect square of 13.

Note, that our value, 146 is far closer to 144 than to 169, so we know that we will be close to 12 as our approximation.

The distance from 144 to 146 is 2, while the distance from 169 to 146 is 23.

A rough fractional approximation can be found with 2/23 approximately 0.08.

For the solution then, our approximation of sqrt(146) ~= 12.08 ~= 12.1

Cheers.

Answer:

Step-by-step explanation:

L = ⁵/₂x + 10

W = ⁵/₂x + 5

A = L•W

A = (⁵/₂x + 10)(⁵/₂x + 5)

A = ⁵/₂x•⁵/₂x + ⁵/₂x•5 + 10•⁵/₂x + 10•5

A = ²⁵/₄x² + ²⁵/₂x + ⁵⁰/₂x + 50

A =  ²⁵/₄x² + ⁷⁵/₂x + 50

Or if yoy mean:

L = 5/(2x) + 10

W = 5/(2x) + 5

A = [5/(2x) + 10][5/(2x) + 5] = 25/(4x²) + 75/(2x) + 50

1. C) Rational Numbers and Integers only

2. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in c.

In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1

Answer:

The product of the terms in the given expression is -90k⁷

Step-by-step explanation:

10k⁴ · (-9k³)

When we multiply exponents, then we are going to add the exponential together. So, we will add 4 and 3 together which is 7. Since our base numbers are different, then we also multiply them together. So, we will multiply 10 by -9 which is -90.

-90k⁷

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-6,-10) & (-2,-10)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

36 cents

Step-by-step explanation:

In order to figure out how much one can cost you need to do 6.48/18 which then gets you 33 cents, the cost of one can.

Step-by-step explanation:

15) 50 ÷ 2 = 25

17) Mean = 301, Mode = 40-50

(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35

(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65

(70+80) ÷ 2 = 75

• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540

55×10 = 550, 65×4 = 260, 75×2 = 150

Mean = (60+200+350+540+550+260+150) ÷ 7

= 2110 ÷ 7

= 301.4285....

= 301

Mode : the highest frequency

Answer:

15) 50 ÷ 2 = 25

17) Mean = 301, Mode = 40-50

(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35

(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65

(70+80) ÷ 2 = 75

• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540

55×10 = 550, 65×4 = 260, 75×2 = 150

Mean = (60+200+350+540+550+260+150) ÷ 7

= 2110 ÷ 7

= 301.4285....

= 301

Mode : the highest frequency

Answer:

Hey there!

Angela will have 7+2, or 9 cups of rice.

Let me know if this helps :)

Answer:

7/2

Step-by-step explanation:

Answer:

108 seconds and 0.03 hours

Answer:

9z

Step-by-step explanation:

4th root of z = z^1/4

=> 3 * z^1/4

=> 3z^1/4

3z^1/4 * 3z^3/4

=> 3 x 3 x z^1/4 + 3/4

=> 9z^4/4

=> 9z^1

=> 9z

The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.

We are given:

  =  [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]

We need to write this in the form of :

  =   [tex]k~.~z^{n}[/tex]

We use exponents and powers when we want to write very large numbers or very small numbers in a simplified manner.

Example:

8 = 2 x 2 x 2 = [tex]2^{3}[/tex].

Where 2 is the base and 3 is the exponents.

72 = 8 x 9 = [tex]2^{3} \times3^{2}[/tex].

Here we have two bases 2 and 3 and two exponents 3 and 2.

8 / 9 =  [tex]\frac{2^{3} }{3^{2} }[/tex] =  [tex]2^{3} \times3^{-2}[/tex].

Here the bases are 2 and 3 and exponents are 3 and -2.

We have

[tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]

Here,

[tex]\sqrt[4]{z}[/tex] can be written as [tex]z^{\frac{1}{4} }[/tex].

  [tex]z^{\frac{1}{4} }~.~z^{\frac{3}{4} }[/tex]  can be written as :

                 [tex]z^{\frac{1}{4} +\frac{3}{4} }\\\\ z^{\frac{4}{4} } \\\\z^{1} = z[/tex]

Now we have,

3 x 3 x  [tex]z^{\frac{1}{4} }[/tex]  x [tex]z^{\frac{3}{4} }[/tex]

3 x 3 x z

[tex]3^{2}[/tex] x z

9 x [tex]z^{1}[/tex]

So, comparing with k . [tex]z^{n}[/tex]

we have,

k = 9 and n = 1.

The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.

Learn more about exponents and powers here:

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Answer:

x = 3.91039

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

4.32x + 1 = 17.8929

Step 2: Subtract 1 on both sides

4.32x = 16.8929

Step 3: Divide both sides by 4.32

x = 3.91039

Answer:

I believe it is 1.

Step-by-step explanation:

1. because thats half

Answer:

I think it's sum and difference

Answer:

less than and difference

Step-by-step explanation:

Answer:

We have 2 values to work with, both in terms of x. the first value is just x, our first number. The second value is 40% higher than the original.

x + (x + .4x) = 180

x + 1.4x = 180

2.4x = 180

x = 180/2.4

x = 75 1.4(75) = 105

Check:

75 * .4 = 30

75 + 30 = 105

Answer:

75, 105

Step-by-step explanation:

Let's let the two numbers be a and b.

The sum of them is 180. Thus:

[tex]a+b=180[/tex]

One of the number is 40% more than the other. In other words, let's let a be the bigger number:

[tex]a=1.4b[/tex]

Substitute this into the first equation:

[tex]1.4b+b=180[/tex]

Combine like terms:

[tex]2.4b=180[/tex]

Divide everything by 2.4:

[tex]b=75[/tex]

So, b is 75.

And their sum is 180. Thus, a is 180-75 or 105.

And we're done!

Answer:

8.4 in by 8.4 in

Step-by-step explanation:

The area of a square is the side length squared.

Let s be the side length:

s^2 = 70

s = \sqrt(70) = 8.4 in

Answer: x=11

Step-by-step explanation:

If m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.

Given,

m∠XWZ = 90.

Right angle ∠XWZ is divided into 2 acute angles labeled as:

- 5x + 5 degrees

- 2x + 8 degrees.

We need to find the value of x.

An acute angle means angles that are less than 90 degrees.

If an angle is divided, the sum of the divided angles must be equal to the angle divided.

Find the right angle.

m∠XWZ = 90

Find the acute angles that are being divided.

= 5x + 5° and 2x + 8°

Find x.

Since m∠XWZ is divided we have,

90° = 5x + 5° + 2x + 8°

Now,

Add the like terms.

90 = 7x + 13

Subtract 13 on both sides.

90 - 13 = 7x

77 = 7x

Divide both sides by 7.

11 = x

x = 11

We can crosscheck the angles:

90° = 5x + 5° + 2x + 8°

90 = 5x11 + 5 + 2x11 + 8

90 = 55 + 5 + 22 + 8

90 = 60 + 30

90 = 90

Thus if m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.

Learn more about finding the value of angles here:

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Answer:

[-9,0]

Step-by-step explanation:

You use brackets to indicate that the numbers, in this case -9 and 0, are included in the interval.

You use parentheses to indicate that the numbers are excluded from the interval.

Since we want to include the numbers in the interval, we use the brackets.

The answer is [-9,0]

Hope this helps!

Answer:

x = -7/2

Step-by-step explanation:

(1/4) ^ (x+1) = 32

Rewriting 32 as 2^5 and 1/4 and 2^-2

2^-2 ^ (x+1) = 2^5

  We know that a^b^c = a^ ( b*c)

2 ^ (-2x-2) = 2 ^ 5

Since the bases are the same, the exponents have to be the same

-2x-2 = 5

Add 2 to each side

-2x = 7

Divide by -2

x = -7/2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.7}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{12 + x = 16.7}[/tex]

Move 12 to right hand side and change it's sign

[tex] \dashrightarrow{ \sf{x = 16.7 - 12}}[/tex]

Subtract 12 from 16.7

[tex] \dashrightarrow{ \sf{4.7}}[/tex]

Hope I helped!

Best regards!

Answer:

[tex]\huge\boxed{\sf x = 4.7}[/tex]

Step-by-step explanation:

12 + x = 16.7

Subtracting 12 to both sides

x = 16.7 - 12

x = 4.7

Answer:

2 * 50/(y + 8)

Step-by-step explanation:

"twice the quotient of 50 and a sum of a number y and 8"

y + 8

"twice the quotient of 50 and a sum of a number y and 8"

50/(y + 8)

"twice the quotient of 50 and a sum of a number y and 8"

2 * 50/(y + 8)

Answer:

2*50/ (8+y)

Step-by-step explanation:

twice the quotient of 50=2*50 divided by something

the sum of a number= y and 8

So... 2*50/ (8+y) is the answer