Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.

Given data:

The given function is f(x)= x^2 +3x-10.

The given inequality is,

ANSWER:

318

STEP-BY-STEP EXPLANATION:

We have the following operation:

So the answer is 318

Question:

Solution:

Remember the following theorem: the ratio of the areas of two

similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :

S1 : S2 = 5 : 8

then

now, A1 = 87.5. Thus, according to the theorem, we get the following equation:

this is equivalent to:

by cross-multiplication, this is equivalent to:

solving for A2, we get:

so that, we can conclude that the correct answer is:

The area of the larger triangle is

Answer:

(8, 0)

Explanation:

Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:

That is, the x-coordinate and y-coordinate change places.

Therefore, the image of the point (0,8) when reflected across the line y=x is:

The correct answer is (8,0).

Total number of defected radios is 18

Let the total number of defective radios be taken as y

If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y

Solve for y, by cross multiplying

Hence, the number of radios inspected, y, is 75000

Answer: The better buy is the the 12-inch deluxe for $5.99.

B. 12-inch pizza; $1.50

Explanation:

From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as

Area = πr^2

where

π = 3.14

r is the radius of the circle

For the 10-inch cheese and sausage pizza,

diameter = 10

r = 10/2 = 5

Area = 3.14 x 5^2 = 78.5

If it is divided among 3 people,

each person gets 78.5/3 = 26.2 in^2

Amount that each person pays = 4.99/3 = $1.66

This means that each person pays $1.66 for 26.2 in^2

For the 12-inch cheese and sausage pizza,

diameter = 12

r = 12/2 = 6

Area = 3.14 x 6^2 = 113.04

If it is divided among 4 people,

each person gets 113.04/4 = 28.26 in^2

Amount that each person pays = 5.99/4 = $1.5

This means that each person pays $1.5 for 28.26 in^2

Thus, the better buy is the the 12-inch deluxe for $5.99.

The amount that each person pays is

B. 12-inch pizza; $1.50

Given:

There is a function given as below

Required:

For what value of b the given function in decreasing

Explanation:

The given function is logarithm function

also written as

The base b is determines that if the function is increasing or decreasing

here

for

for

the given function is increasing

Final answer:

the coordinate of M is (-3, -5)

it is given that M is translated 6 unit right , and 5 unit up.

so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)

so, the distance between M and M' is,

d = 7.81

so, the closest to the unit distance is 8

thus, the answer is option D

Answer:40

Step-by-step explanation: 15 bars to a box.

600 bars in total.

600/15= 40

40 boxes of granola bars

You have:

sin 2A = -√7/4

In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:

sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin

2A = -41.41° divide by 2 both sides

A = -41.41°/2

A = -20.705°

however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.

To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:

20.705 + 180° = 200.705°

Next, use calculator to calculate sinA:

sin(200.705°) = -0.3535

Given:

g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}

So,

To find g(-3), we need to find the term that contains -3 in the location of x of the order pair

So, g(-3) = 3

And by the same manner, we will find the others

So,

g(-9) = 12

g(-7) = 9

ANSWER

EXPLANATION

To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,

Thus, dx is,

Replace the function and the differential in the integral,

The sin(x) cancels out,

We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,

Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,

Finally, we have to replace u with the function we substituted before,

Hence, the result of the integral is,

Explanation:

The number line is between 0 to 1. There are 10 smaller lines in between

Each of the small lines represent 1/10 or 0.1

one/twos is the same as 1/2 = 0.5

three/fifths is the same as 3/5 = 0.6

From the above, 0.6 is greater than 0.5

Showing both numbers on the number line:

The relation is decreasing by a factor of 2 each time, so:

Therefore:

Answer:

-191

We will determine the mean as follows:

So, the mean will be 6.

if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175

And when she found two $5 bills, it is like she received 2 times 5 = $10

Normally, expenses are negative numbers and earning are positive numbers, in this case

-$175 + $10 = - $165

Sothe answer is -165

Sample mean = 3.43

sample standard deviation = 2.07

Explanation:

Given: 2, 3, 2, 5, 7, 1, 4

Total numbers = 7

1) Sample mean is calculated by finding the average of the data set

2) We have sample standard deviation and population standard deviation.

SInce the question asked for sample mean, we will be calculating sample standard deviation.

Standard deviation is calculated as:

The expression has a value of -31 when a = 2 and b = –3

From the question, the expression is given as

5 – a(3² + (ab + 2)² – 7)

Also, we have the values of the variables to be

a = 2 and b = –3

Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)

So, we have the following equation

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)

Evaluate the expressions in the bracket

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)

Evaluate the exponents

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)

So, we have

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18

This gives

5 – a(3² + (ab + 2)² – 7) = 5 – 36

Evaluate the difference

5 – a(3² + (ab + 2)² – 7) = -31

Hence, the value of the expression is -31

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Given:

The angels and sides of the triangle are

A = 50°. B = 45°, and a=3

Aim:

We need to find the angle C and sides c and b.

Explanation:

Use sine law.

Substitute A = 50°. B = 45°, and a=3 in the equation.

Use the triangle sum property to find the angle C.

Substitute A = 50°. and B = 45° in the equation.

Substitute A = 50°. C= 85°, and a=3 in the equation.

Final answer:

Answer: $111 is earn by shoe salesman as commission .

Step-by-step explanation:

As given the statement in the question be as follow.

Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.

Total cost of the pair of shoes = 3 × 70 + 2 × 80

                                                 = 210 + 160

                                                 = $ 370

As given

shoe salesman earns a commission of 30% of all shoe sales made.

30% is written is decimal form

= 0.30

Commission earns = 0.30 × Total cost of the pair of shoes .

                              = 0.30 × 370

                              = $ 111

Therefore $111 is earn by shoe salesman as commission .

The sides of the triagle have lengths:

1.1 p + 9.5 q

4.5 p - 5.2 r

5.3 r + 5.4 q

Or:

1.1 p + 0 r + 9.5 q

4.5 p - 5.2 r + 0 q

0 p + 5.3 r + 5.4 q

If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:

(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q

= 5.6 p + 0.1 r + 14.9 q

The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;

This shows that when paying the bill, each of the four individuals will have to pay $7.52

A die can have 6 possible outcomes.

The probability of an event is calculated using the formula:

Therefore, the probability of rolling a 1 is gotten to be:

The probability is 1/6.

The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.

Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We can model the equation for Madeline's total pay as follows -

P = base pay + (number of sold computer) × (cost of 1 computer)

P = 80 + 20x

Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x

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Given: The function below

To Determine: If the function as a aximum or a minimum using the first principle

Solution

Let us determine the first derivative of the given function using the first principle

So,

So

Therefore,

Please note that at critical point the first derivative is equal to zero

Therefore

At critical point the range of value of x is 0 and 2

Let us test the points around critical points

The function given has both maximum and minimum point

Hence, the maximum point is (0,0)

And the minimum point is (2, 4)

Solution:

Given the dimensions of the composite figure below

To find the surface area, SA, of the composite figure, the formula

Substitute the values of the variables into the formula above

Hence, the surface area, SA, is

The consumption is 355 billion  .

Given,

In the question:

Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.

Now, According to the question:

Based on the given condition,

Formulate;

Aggregate expenditure (consumption)= Output - Savings= Investment

370 - 15

Calculate the sum or difference

= 355billion

Hence, The consumption is 355 billion  .

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Given:

Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.

The total number of sample space is, N = 10.

Head for female kitten

T for male kitten.

The objective is to find the probability that at least three of the kittens will be male.

Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4

Now, the probability of at least three of the kittens will be male can be calculated by,

Problem

Last month, Ebony had 110 dollars in a

checking account. The current balance is

146 dollars. What is the percent change in

the account balance from last month to this

month? Round your answer to the nearest whole percent.

Solutiion

For this case we can use the following formula:

And replacing we got:

And then the answer wounded to the nearest percent would be:

33%

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given information

The function for the cost price becomes:

STEP 2: Get the function for the selling price

The function for the selling price becomes:

STEP 3: Calculate the number of books required to break even

To get the breakeven, the cost price will be equal to selling price. Therefore,

Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519