Given the following logarithmic equation, think about how you would solve each one. Now,
describe those processes using at least 3 to 4 sentences. Then solve, showing your work.
Equation 1: log2 + logx = log3

Answer:

None of the above

Step-by-step explanation:

the x coordinate tells us the duration, and the y-coordinate tells us the total cost of a phone call. The y coordinate of point aA represents the total cost of an 8 minutes phone call. not 8 phone calls. point a tells us that the cost is $2 for an 8-minute phone call, so the cost per minute is 2/8=$0.25, not $0.3.

Hope this helps!

Answer:

See explanation below.

Step-by-step explanation:

A right triangle is a triangle that has a right angle (90º). In math, the Pythagorean theorem allows us to calculate the length of the sides of a right triangle.

In a right triangle, the legs are the two sides that meet at the 90º angle and the hypotenuse is the side that opposes the right angle. The Pythagorean Theorem tells us that the square of the hypotenuse equals the sum of the squares of the legs. In other words: [tex]c^2 =a^2 +b^2[/tex] where c is the hypotenuse and a and b are the legs.

Now, we can use this formula to calculate the diagonal of the pool if we just have the length and the width (these would be the legs of the triangle). We need to measure both the length and the width and then square both of them and sum up the squares: this would give us the square of the diagonal so we will only need to find its quadratic root and we will have the length of the diagonal.

For example, let's say we have a pool that is 3 ft by 4ft, using the formula we have:

[tex]Diagonal^2=3^2 +4^2 \\Diagonal^2 = 9+16\\Diagonal^2 = 25\\Diagonal = \sqrt{25} \\Diagonal =5[/tex]

Therefore, in this case the diagonal would be 5 ft long.

Answer:

a

Step-by-step explanation:

Answer:

[tex]A=P+P\times S\%[/tex]

Step-by-step explanation:

For calculating the sales tax of a product, it is required to first multiply the original cost price of the product by the sales tax percentage.  

Once the sales tax has been computed add it to the original cost price in order to determine the total cost of the product.

The formula of final amount is:

[tex]A=P+P\times S\%[/tex]

Here,

A = final amount

P = original cost price

S = sales tax percentage

Answer:

1.$25.68

2.$51.36

3. 77.04

Step-by-step explanation:

I just took the test.

It is approximately equal to 0.1111

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

To get this answer, we use the rule

[tex]x^{-k} = \frac{1}{x^k}[/tex]

The negative exponent tells us to apply the reciprocal to get the exponent to be positive.

So,

[tex](-3)^{-2} = \frac{1}{(-3)^2}\\\\(-3)^{-2} = \frac{1}{9}[/tex]

Squaring -3 means you square the negative as well

[tex](-3)^2 = (-3)*(-3) = 9[/tex]

Answer:

1/9

Step-by-step explanation:

(-3)^-2 would be better written as (-3)^(-2).

                                                                                       1

(-3)^(-2) would be easier to evaluate if written as -------------

                                                                                   (-3)^2

The final answer is 1/9.

Answer:

The coin toss does not appear to be  fair

Step-by-step explanation:

 From the question we are told that

     The  sample size is  [tex]n = 400[/tex]

      The number of game won by team that won the coin toss at the beginning of overtime  [tex]x = 194[/tex]

     The level of significance is  [tex]\alpha = 0.10[/tex]

The population proportion  is  evaluated as  

                  [tex]p = \frac{194}{400}[/tex]

                 [tex]p = 0.485[/tex]

Since the population proportion is  0.485 [tex]\approx[/tex] 0.5 which implies that the coin toss is  fair then

The Null hypothesis is  

         [tex]H_o : p = 0.485[/tex]

and  The Alternative hypothesis is  

        [tex]H_a : p \ne 0.485[/tex]

The test statistics is evaluated as follows

         [tex]t = \frac{[x + p] - [\frac{n}{2} ]}{\frac{\sqrt{n} }{2} }[/tex]

substituting values  

         [tex]t = \frac{[194 + 0.485] - [\frac{400}{2} ]}{\frac{\sqrt{400} }{2} }[/tex]

         [tex]t = -0.5515[/tex]

=>     [tex]|t| = 0.5515[/tex]

now the critical value of  [tex]\alpha[/tex] for a two tail test(it is two tailed because we are test whether the critical value is  less than or greater than the test statistics ) is  

         [tex]t_{\alpha } = 1.645[/tex]

This is usually found from the critical value table  

     Now comparing the critical values and the calculated test statistics we see that the critical value is greater than the test statistics hence the Null hypothesis is  rejected

   This  means that the coin toss is not fair  

Answer:

(-2.3, 0.5)

Step-by-step explanation:

Step 1: Write out systems of equations

8x - 10y = -23

9x + 10y = -16

Step 2: Elimination (add the 2 equations together)

17x = -39

x = -39/17 = -2.29412 ≈ -2.3

Step 3: Plug in x to find y

8(-39/17) - 10y = -23

-312/17 - 10y = -23

-10y = -79/17

y = 79/170 = 0.464706 ≈ 0.5

Answer:

(-2.3, 0.5)

Step-by-step explanation:

Step 1: Write out systems of equations

8x - 10y = -23

9x + 10y = -16

Step 2: Elimination (add the 2 equations together)

17x = -39

x = -39/17 = -2.29412 ≈ -2.3

Step 3: Plug in x to find y

8(-39/17) - 10y = -23

-312/17 - 10y = -23

-10y = -79/17

y = 79/170 = 0.464706 ≈ 0.5

Step-by-step explanation:

Answer:

18π

Step-by-step explanation:

the area of a circle is :

A= r²*π     where r is the radius

here r²  =81⇒ r= 9

the circumference of a circle is :

P= 2*r*π

P= 18π

Answer:

18 pi inches

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

81 pi = pi r^2

Divide by pi

81 = r^2

Take the square root of each side

sqrt(81) = sqrt (r^2)

9 = r

We want the circumference

C = 2 * pi * r

C = 2 * pi * 9

C = 18 pi

Answer:

The correct answer is:

[tex]+6x^{2}\\-9y^2[/tex]

Step-by-step explanation:

We are given the term:

[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9[/tex]

We have to fill in to the empty spaces such that the above equation gets satisfied.

First of all, let us simplify the LHS (Left Hand Side):

[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9[/tex]

Now, let us equate the LHS and  RHS (Right Hand Side):

[tex]\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9[/tex]

Equating the coefficients of [tex]x^{2}\ and\ y^{2}[/tex] in LHS and RHS:

One box will have value = [tex]9x^{2} -3x^{2} =+6x^{2}[/tex]

Other box will have value = [tex]-y^{2} -9y^{2} =-10y^{2}[/tex]

The correct answer is:

[tex]+6x^{2}\\-9y^2[/tex]

So, if we fill the boxes with above values, the expression will be simplified as given.

Answer:

The correct answer is B. Positive 6 x squared and Negative 10 y squared

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

because all of the sides have the same measurement.

Answer:

Triangle C

Step-by-step explanation:

Triangle A: All sides have length 9 cm.

By SSS this is a unique triangle.

Triangle B: Two sides have length 10 cm, and the included angle measures 60°.

By SAS this is a unique triangle.

Triangle C: Two angles measure 50°.

This gives us at most SS Similarity, so we do not have a unique triangle. The triangle sides can be any length. This is not unique.

Triangle D: Base has length 8 cm, and base angles measure 45°. Which triangle is not a unique triangle?

This gives us ASA, so we have a unique triangle.

Answer: Triangle C

Answer:

I hope it will help you......

Answer:

ST is 5

Step-by-step explanation:

Divide the larger triangle's BC by 3.

Answer:

380 tickets were sold at the door and 440 tickets were sold before

Step-by-step explanation:

x = tickets sold before

y = tickets sold at the door

x + y = 820

x = y + 80

y + 80 + y = 820

   -80           -80

2y = 740

y = 370

820 - 380 = 440

x = 440

Answer:

The answer is given below

Step-by-step explanation:

The equation of a quadratic function is given by:

ax² + bx + c where a, b and c are the coefficients of the quadratic equation. The value of a determines whether the graph opens up or down (if a is positive opens up and if a is negative opes down), the value of c determines the y intercept (if c is positive, we have a positive intercept and if c is negative the intercept is negative).

The chosen equation is -x² -4x + 5. Since it has y-intercept of 5 and opens down (coefficient of x² is -1)

Let us assume a vertical stretch of 4, the new equation becomes:

4(-x² -4x + 5)

-4x² - 16x + 20

-4x² - 16x + 20 = 0

a = -4, b = -16 and c = 20

Using the quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}\\ x=\frac{-(-16) \pm \sqrt{(-16)^2-4(-4)(20)} }{2(-4)}=\frac{16 \pm 24}{-8} \\x= -5 \ or \ x=1[/tex]

Answer:

0.34134

Step-by-step explanation:

In other to solve for this question, we would be using the z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the probability that a worker selected at random makes between $350 and $400

let x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

From tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 =

0.34134

Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134

Answer:

34%

Step-by-step explanation:

Acellus sux

Answer:

32 hours and 65 minutes

Step-by-step explanation:

Answer:

The Answer is 33 hours and 5 minutes

Step-by-step explanation:

The reason being that 32.65 is 32 hours and 60 min is an hour so add that to the 32 it's 33hrs and the remaining 5 min

Answer:

(0,-6), (-2,0)

Step-by-step explanation:

-3x-y=6

-y=6+3x

y=-3x-6

when x=0, y=-6

when y=0 x=-2

You're looking for "parabola" like shapes in which the lowest point has a y coordinate of y = 0. In this case, it would be the "parabola" portion on the right that has its lowest point at (3,0). The only interval that fits is [tex]2 \le x \le 4[/tex] which in interval notation is written as [2,4]. So this fits with choice D.

Answer:

Option B

Step-by-step explanation:

The formula for geometric sequence is given by:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

Where,

[tex]a_{n}[/tex] = nth term of sequence

[tex]a_{1}[/tex] = 1st term of the sequence

[tex]r[/tex] = common ratio (ration of the second term to the first term)

So,

Here:

[tex]a_{1}[/tex] = 12

[tex]r[/tex] = 6/12 = 1/2

Plugging in the values of [tex]a_{1}[/tex] and r in the above formula:

=> [tex]a_{n} = 12 * (\frac{1}{2}) ^ {n-1}[/tex]

Answer:

1st option

2,4,8,16

Step-by-step explanation:

1st option is not an Arithmetic sequence, it is geometric sequence. Because, the common ratio is 2

the 2nd option has a common difference of 7, so it is arithmetic

the 3rd option has a common difference of 0.5,  so it is arithmetic

and 4th option has a common difference of -4.  so it is arithmetic

Answer:

9 roots

Step-by-step explanation:

(x+10)^9 = 0

If you would multiply it out, the highest power is x^9 so the equation has 9 roots

Solving (x+10)^9 =0

Taking the 9th root of each sdie

x+10 = 0

x = -10

The root is -10 with multiplicity of 9

Answer:

d. 12

Step-by-step explanation:

if you rewrite the first as 2x + y = 4 and then multiply it by 3, it is equal to the second equation if the right hand side is 12.

If a system of equations contains dependent equations (ie., equal give or take a scale factor), then there is not one single solution but many.

Answer: its d, 12

Step-by-step explanation:

Answer:

83.80 cm³

Step-by-step explanation:

volume of cone=

[tex] \frac{1}{3} \pi {r}^{2} h[/tex]

1/3×22/7×4×4×5=1760/21= 83.80 cm³

Answer:

Sammy delivered 10 pizzas to each party.

Step-by-step explanation:

34 pizzas - 4 pizzas

= 30 pizzas

30 pizzas/ 3 parties

= 10 pizzas per party

Answer:

Hey there!

Sammy delivered four to his colleagues. Thus, he has 34-4, or 30 pizzas left.

He split these between three parties, thus each party received 10 pizzas.

Hope this helps :)

Answer:

1. A. 12a^2 + 8a + 4

2. C. 4xy+16x-4y^2-16y

3. C. 64q^6r^8s^4

4. A. -4x^4y^6

Step-by-step explanation:

48a^3 + 32a^2 + 16a / 4a = (48a^3) / 4a + (32a^2) / 4a + (16a) / 4a = 12a^2 + 8a + 4.

So, the answer is A. 12a^2 + 8a + 4.

(2x-2y)(2y+8) = 4xy - 4y^2 + 16x -  16y.

So, the answer is C. 4xy+16x-4y^2-16y.

(-8q^3 * r^4 * s^2)^2 = (-8)^2 * q^6 * r^8 * s^4 = 64q^6r^8s^4.

So, the answer is C. 64q^6r^8s^4.

-12x^8y^8 / 3x^4y^2 = (-12 / 3) * (x^(8 - 4)) * (y^(8 - 2)) = -4x^4y^6.

So, the answer is A. -4x^4y^6.

Hope this helps!

Answer:

(2, 4)

Step-by-step explanation:

You can use a graphing calculator, and find the point where the lines intersect. Attached is the image.

Hope this helps! :)

Answer:

[tex]\frac{x^2}{2}[/tex] square units        [one-half x squared square units]

Step-by-step explanation:

As shown in the diagram attached to this response,

Since a square has all sides equal, let the sides of the square be each of a units.

The area, A, of the square = a x a = a²

i.e

A = a²    --------------(i)

Now,

The diagonal is x units such that applying Pythagoras rule gives;

x² = a² + a²

x² = 2a²

a² = [tex]\frac{x^2}{2}[/tex]           ----------------(ii)

Substitute the value of a² in equation (ii) into equation (i) to get;

A = [tex]\frac{x^2}{2}[/tex]

Therefore, the area of the square is [tex]\frac{x^2}{2}[/tex] square units

Answer:

1/2x^2 square units

Step-by-step explanation:

Answer:

Jane will run more than 30 miles this week, as thus far she ran 22.    

Step-by-step explanation:

X + 22>30

         X>8

She runs more than 8 miles.

Answer:

Well, it depends.

Step-by-step explanation:

In the problem, it doesn't specify if the miles she runs is a positive integer or not, but I will assume that it is.

There are  number of miles: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31.

So t = 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31

Answer:

[tex]\boxed{\sf \ \ \ 2^0*3^0*7*47=329 \ \ }[/tex]

Step-by-step explanation:

hello,

let's try to divide by 7 329 it comes

329 = 47 * 7

and 329 is not divisible by 2 or 3 so

the solution is

x = 0

y = 0

z = 47

[tex]2^0*3^0*7*47=329[/tex]

hope this helps

Answer:

Area of shaded part = 41.09733550

Perimeter of shaded part = 35.82011867

Step-by-step explanation:

Area of shaded part =  ((πr^2)   4) - (bh ÷ 2)

Area of shaded part = ((π(12)^2) ÷ 4) - ((12)(12) ÷ 2)

Area of shaded part = (452.3893421 ÷ 4) - (144 ÷ 2)

Area of shaded part = (113.0973355) - (72)

Area of shaded part = 41.09733550

Perimeter of shadedpart:

AC = √a^2 + b^2

AC = √12^2 + 12^2

AC = √144 + 144

AC = √288

AC = 16.97056275

Perimeter of whole circle ÷ 4:

C=2πr

C=2π(12)

C=75.39822369

C ÷ 4 = 75.39822369 ÷ 4

C ÷ 4 = 18.84955592

Perimeter of shaded part:

18.84955592 + 16.97056275 = 35.82011867