Translating English to Algebra

Answer:

17x + 4

Step-by-step explanation:

Distribute: 4(5x + 1) - 3x

20x + 4 - 3x

Combine like terms: 20x + 4 - 3x --> 17x + 4

Hope this helps! :')

Answer:

A.) 2(-2) -y=10

     -4-y= 10

     +4      +4

        -y=14

      /-1     /-1

     y= -14

B.) 2(0)-y=10

      -y=10

     /-1    /-1

   y=-10

C.) 2(2)-y=10

        4-y=10

     -4       -4

       -y = 6

        /-1  /-1

     y=-6

According to the question, write the single logarithm of the given logarithmic expression and the expression is as follows:

Expression: [tex]log_{2}15 -log_{2}5[/tex]

Using logarithmic formula that is it divide when subtraction is there: [tex]log(a)-log(b)=log(\frac{a}{b} )[/tex].

Now, the expression can be re-written as:

Expression: [tex]log_{2}15 -log_{2}5=log_{2}(\frac{15}{5} )=log_{2}(3)[/tex]

The solution for the given expression is: [tex]log_{2}(3)[/tex].

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Answer:

the compound interest will be 365,809.5 naira.

The percentage of people living on boat in Florida is 15.4%. The equivalent of this percentage to decimal is 0.154 and to fraction is 77/500.

55% live in a house, 25% live in an apartment, 4.6% in condo while the rest live on a boat. If all the percentages are summed up, they must be equal to 100%.

Let a% equals to the percentage of adult living on boat

55+25+4.6+a = 100

84.6 + a = 100

Collect like terms

a = 100 - 84.6

a = 15.4%

Therefore, the percentage of adult living on boat is 15.4%

To convert the percentage to decimal equivalence, one must divide it by 100%

15.4%/100%

= 15.4/100

= 0.154

To convert the percentage to fraction equivalence, one have to divide it by 100%

15.4%/100%

= 15.4/100

One has to make both the numerator and denominator of the fraction whole numbers, to do that one has to shift the decimal place behind the last digit, for a number without decimal point a 0 is added to the back of the number.

= 154/1000

Reducing the fraction to its lowest term, this is done by diving the numerator and denominator by a common factor

= 77/500

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Answer:

The alternative form would be ≈ 21.213203

Step-by-step explanation:

The two consecutive integers in which the side length of the square fall between is 9 and 10

The formula for the area of a square is given as follows:

            A = (s)²

where A = area of square

            s = length of side of a square

According to the question we have been given that

the area of square = 90 inch²

Now putting the required values in the formula of area we get

          (s)² = 90

Taking square root both sides we get

           s = √90

 As 90 is not a perfect square but it lies between two perfect squares which are 81 and 100.

As     √81 = 9   and √100 = 10

Now,   √81 ≤ √90 ≤ √100

     ⇒    9 ≤ √90 ≤ 10

Hence two consecutive integers such that the side length of the square fall between is 9 and 10

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Answer:

huh?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: f(x) = x

Step-by-step explanation:

Answer:

elena

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes , the given logarithm is a common logarithmic.

We have given an logarithm function which is [tex]log_{10}100[/tex]   ..... (1)

As , we can see that this log has a base of 10 so , it is a common logarithm.

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The fourth coordinate for the given parallelogram are going to be (5, 7).

According to the statement

We have to find that the coordinate of the parallelogram.

So, For this purpose, we know that the

A parallelogram is a quadrilateral with opposite sides parallel

From the given information:

The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1).

Then

Now,

The slope of AB = Slope of CD

(y - 5)/(x - 11) = (1 - 3)/(8 - 2)

6(y - 5) = -2(x - 11)

⇒ 6y + 2x = 52 are going to be the primary equation.

Now,

The slope of BC = Slope of AD

[(y - 3)/(x - 2)] = [(5 - 1)/(11 - 8)]

[(y - 3)/(x - 2)] = 4/3

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

⇒ 3y - 4x = 1 are the second equation.

Now, By substitution

x = 5 and y = 7

Hence, The fourth coordinate for the given parallelogram are going to be (5, 7).

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Answer:

6t

Step-by-step explanation:

The simplified form of the expression is 11.

Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.

You may also hear the simplest form called "lowest term."

In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:

Combine Like terms

Factoring

Increasing (the opposite of factoring)

Clean out fractions by multiplying

Recognizing a pattern you have seen earlier, just like the difference between squares

Simplify the following:

sqrt(11) * sqrt(11)

sqrt(11)  * sqrt(11) = 11:

Answer: 11

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Answer:

-y

Step-by-step explanation:

i did the test

Answer:

Y=8

Step-by-step explanation:

Move all terms that don't contain y to the right side and solve.

Answer:

h =2

Step-by-step explanation:

10=h ×5

10=h5

DBS by 5

10÷5=h5÷5

h=2

Answer:

Step-by-step explanation:

3/9 can be a rational number.

Let me show you:

The Answer and/or 1 : 3 or 3 : 9.

It should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴

It should be noted that from the information, we want to calculate 215 * 107 in scientific notation.

It should be noted that 215 = 2.15 × 10²

It should be noted that 107 = 1.07 × 10²

Therefore, calculating 215 * 107 in scientific notation will be:

= 215 × 107.

= 2.15 × 10² × 1.07 × 10²

= 2.15 × 10⁴

Therefore it should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴

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Answer: the 2nd one

Step-by-step explanation: first term (a1) is -1

recursive formula goes like this

is the nth term

is the term before that

we normally have

we see each term is multipying by -3 to get next one

so that would be

where a1=-1

the 3rd option is correct except that it is the explicit formula

so answer is 2nd one.

Answer:

45

Step-by-step explanation:

run plus duck equals to the implement

Answer:

[ 5 4 2 ]

Step-by-step explanation:

The correct answer of the given expression is 4x².

It is given that ∛64 x⁶

 On simplifying , we get

=  ∛4³(x²)³

  =  4x²

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Using ratio we can calculate that Mr. Singleton used approximately 1.33  pounds of sausage .

A ratio demonstrates how frequently one number is found within another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

He uses 1 pound sausage for every 3/4 pound of cheese.

Ratio of sausage to cheese = 1 : 0.75 = 4 : 3 .

Now he uses 1 pound of cheese therefore let he uses x pounds of sausage.

Now using ratio:

x : 1 = 4 : 3

or , x / 1 = 4 / 3

or, x = 1.333..

or, x ≈ 1.33 pounds

Hence he uses 1.33 about pounds of sausage

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The is a parallel to b and m is parallel n.

Given that

To find

So, according to the question

We have,

and the value of two angles m∠2 and m∠4.

From diagram we can see a is parallel to b and m is parallel to n.

So, we can say that

   m∠4 = m∠3    { they are vertical congruent angles } and

   m∠3 = m∠2    { they are congruent angles}

∴  m∠4 = m∠2 -------------(1)

Now, putting the values in equation(1)

So, will be get

                m∠4 = m∠2 -------------(1)

              11x+16 = x²+5x

  x²+5x - 11x-16 = 0

         x²- 6x-16 = 0  

    x²-8x+2x-16 = 0  

  x(x-8)+2(x-8) = 0

        (x-8)(x+2) = 0

If               (x+8) = 0

                      x = 8

And if        (x+2) = 0

                      x = -2

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In the cuboid, the line segment parallel to AD is BC as they both lie on same plane and are directed in same direction.

Two lines are said to be parallel if they lie on the same plane and are directed towards the same direction.

Given in the question is a labelled cuboid.

From the definition of parallel lines, they should lie on the same plane. Therefore, we will eliminate EB and EH because they don't lie in the plane of AB. CD lies in the plane of AB, but is directed perpendicular to AB. BC is in the same plane in which AB lies and is also directed in the direction of AB.

Therefore, in the cuboid, the line segment parallel to AD is BC.

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If the 6% sales tax had been computed on the sale price instead of on the regular price, the tax will be $0.04 lower.

It should be noted that from the information, Samwell bought a packet of pens and his receipt is shown above as $2.04.

Assume that sales tax is rounded to the nearest cent, If the 6% sales tax had been computed on the sale price instead of on the regular price, the difference will be:

Sales price = $1.89

Tax = $1.89 × 0.06 = $0.11

Therefore, the difference will be:

= Former tax amount - New tac amount

= $0.15 - 0.11

= $0.04

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There will be $ 2249.728 in the account after 3 years .

Simple Interest : Each year interest is calculated on the principal amount ( the amount that was deposited initially ) .

Simple Interest = ( P * R * T ) / 100

P ( principal amount ) = 2000

R ( Rate of Interest ) = 4

T ( No . of years for which amount is deposited ) = 3

Substituting values

Simple Interest = ( 2000 * 4 * 1 ) / 100

                         = 80

Amount in account after 1 yr = 2000 + 80

                               = $ 2080

In second year amount will be = 2080 + [ ( 2080 * 4 * 1 ) / 100 ]

                                            = 2080 + 83.2

                                             = $ 2163.2

After three yrs . amount in account = 2163.2 + [ ( 2163.2 * 4 * 1 ) / 100 ]

                                       = 2163.2 + 86.528

                                         = $ 2249.728

Hence , there will be $ 2249.728 in the account after 3 yrs .

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The midpoint between two points A(0,0) and B(8,4) is (4,2)

The distance between two points A(0,0) and B(8,4) is 4√5

To find the midpoint of two points,

We need to take an average of both the x and y components of both points

Two points A(x ₁,y₁) and B(x₂ ,y₂) are (0,0) and (8,4) respectively

Let M be the mid-point M(x, y),

x = x₁+x₂/2

 = 0+8/2

= 8/2

= 4

Similarly

y = y₁+y₂/2

  = 0+4/2

  = 4/2

  = 2

So, the midpoint of the two points A(0,0) and B(8,4) is (4,2)

To find the distance between two points,

We need to take the square root of the difference square of x and y, which is

d² = Δx² + Δy²

d = √(Δx²+Δy²)

Δx = x₂-x₁

    = 8-0

   = 8

Δy = y₂-y₁

    = 4-0

    = 4

Thus,

d = √(8²+4²)

d = √(64 + 16)  

d = √80

d = 4√5

So the distance between the two points is 4√5

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Answer:

[tex]\sf \bf m^6[/tex]

Step-by-step explanation:

 In exponent multiplication, if bases are same, add the powers.

      [tex]\sf \boxed{\bf a^m*a^n =a^{m+n}}[/tex]

[tex]\sf m^9 * m^{-3}=m^{9 +(-3)}[/tex]

               [tex]\sf = m^{6}[/tex]