Select the values that are solutions to the inequality x2 + 3x – 4 > 0.

Answer: 7/8

Step-by-step explanation:

[tex]\displaystyle\\3\frac{1}{2} :4=\\\\\frac{3*2+1}{2}:4=\\\\\frac{6+1}{2}:4=\\\\ \frac{7}{2}*\frac{1}{4} =\\\\\frac{7*1}{2*4} =\\\\\frac{7}{8}[/tex]

Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.

As discussed , the numbers that follow each other in an order are called consecutive numbers or consecutive integers. These integers go from smallest to the highest, i.e. in ascending order. Some of the examples are:

From the above examples, we can see, the integers follow each other in a sequence. The difference between preceding and succeeding integers is always equal to 1.

So, given question, we can write:

For a consecutive integers, the number either increases by 1 or decreases.

First we take option 1:

12,22,32

Find out difference,

22-12=10       ,        32-22=10

The difference is '10'

Hence it is not consecutive integer.

We take option 2:

100,99,98

Find out difference,

100-99=1        ,          99-98=1

The difference is '1'

Hence it is consecutive integer.

We take option 3:

-11,-10,-9

Find out difference,

=-10-(-11)      ,       =-9-(-10)

=11-10=1       ,       =-9+10=1        

The difference is '1'

Hence it is consecutive integer.

We take option 4:

10,11,12

Find out difference,

11-10=1        ,          12-11=1

The difference is '1'

Hence it is consecutive integer.

So, 12,22,32 is not contain consecutive integer, because the difference is '10'. For a consecutive integers, the number either increases by 1 or decreases.

Learn more about event correlation here: brainly.com/question/1767889

#SPJ9

The 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

Here, we have three numbers- 31, 18, and 20

To find 3 common multiples of these numbers, we first find the least common multiple or LCM of these 3 numbers.

31 is a prime number, hence it can be written as- 31 × 1

18 can be written as- 3 × 3 × 2

20 can be written as- 5 × 2 × 2

Thus, the LCM of 31, 18 and 20 will be-

3 × 3 × 5 × 2 × 2× 31 × 1

= 5580

Thus, we found the least common multiple of 31, 18 and 20.

Now, the other 2 multiples will be multiples of the LCM itself.

The other two numbers can be-

5580 × 2 = 11,160

5580 × 3 = 16,740

Thus, the 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

Learn more about the LCM here-

https://brainly.com/question/20739723

#SPJ9

The width and length of the rectangle are 11 and 13 cm respectively

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the perimeter

The given parameters about the rectangle are

Perimeter = 37 + Width

Length = Width + 2 i.e. consecutive odd integers, and width is smaller

Rewrite the above equations as

p = 37 + w

l = w + 2

The perimeter of a rectangle is

p = 2 x (l + w)

Substitute p = 37 + w in the above equation

So, we have

2 x (l + w)= 37 + w

Substitute l = w+ 2 in the above equation

So, we have

2 x (w + 2 + w)= 37 + w

Evaluate the like terms in the above equation

So, we have

2 x (2w + 2)= 37 + w

Open the bracket in the above equation

So, we have

4w + 4= 37 + w

Evaluate the like terms in the above equation

So, we have

3w = 33

Divide both sides of the above equation by 3

So, we have

w = 11

Recall that

l = w + 2

So, we have

l = 11 + 2

Evaluate

l = 13

Hence, the width and length of the rectangle are 11 and 13 cm respectively

Read more about perimeter at

https://brainly.com/question/18019422

#SPJ1

Answer:

Will Give Brainliest!!!! Match each step with the correct justification.

Given: QM MR

a. Given

Answer:

3

Step-by-step explanation:

You are asked to find the slope of the function.
You can find the slope using the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

For simplicity, I'll take the points (0, 0) and (1, 3) and substitute their coordinates into the formula.

[tex]m = \frac{3 - 0}{1 - 0} \to \frac31 \to 3[/tex]

Therefore, [tex]y = 3x[/tex]

Nine friends can arrange themselves on the nine rows of movie theatre in 362,880 ways.

For the given question;

The total number of friends went to watch movie = 9.

The initial number of seats in movie theatre = 10

The seats left after the removal of one seat = 9

Thus, the nine friends can arrange on the 9 seats in 9! ways.

9! = 9×8×7×6×5×4×3×2

9! = 362,880

Therefore, the possible arrangement of 9 friends on remaining seats is 362,880.

To know more about the combination, here

https://brainly.com/question/12915297

#SPJ9

The decimal that represents the portion of people who own dog will be 0.32.

It should be noted that decimal numbers are the numbers that are used for denoting numbers that have while numbers and fractions.

In this case, it was stated that Isaac read that 32% of people owned dogs.

Therefore, the decimal that represents the portion of people who own dog will be:

= 32 / 100

= 0.32.

The decimal that represents the portion of people who own dog will be 0.32.

Learn more about decimals on

brainly.com/question/1827193

#SPJ1

Isaac read that 32% of people owned dogs. What decimal represents the portion of people who own dog?

Answer:

(4a3-5a-3)(2a2-7a+3)

Step-by-step explanation:

use 4a3 to multiply everything in the both brackets=

8a⁵-28a⁴+12a³. then use -5a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a³+35a²-15a. then use -3a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a²+35a²-15a-6a²-21a-9.then you furthermore solve=

8a⁵-28a⁴+2a³+29a²-36a-9

The amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

A ratio is a comparison of two or more numbers that indicates their sizes and amount in relation to each other.

We have,

Patients weighing 195 pounds require 279 milligrams of medicine.

We can write this in ratio as:

= 279 / 195

Now,

We need to have both patients in proportion.

Proportion means their ratios must be equal.

Let the amount of medicine required for the second patient be M.

We have,

279 / 195 = M / 130

We will find M.

(279 x 130) / 195 = M

M = 186

Thus the amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

Learn more about ratios here:

https://brainly.com/question/1504221

#SPJ1

The division statement 1/4 ÷ 7/16 can be seen in a real-life situation when a ratio of boys in two different classes  is being ascertained to help use the ratio of said classes to derive the distribution of textbooks

This is further explained below.

Generally, The process of combining numbers to create new numbers is referred to as division, and it is one of the four fundamental operations of mathematics.

In conclusion,  the remark on the division In real life, the ratio 1/4 to 7/16 may be observed while determining the number of male students in two distinct classrooms in order to determine how many textbooks should be assigned to each of those classes based on the number of male students in each class.

Read more about  division

https://brainly.com/question/21416852

#SPJ1

The  triangle LMN is an isosceles and right-angled triangle.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

In a given triangle is LMN

According to given question we have

An isosceles triangle is a triangle with two congruent sides and one unique side and angle.

An equilateral triangle is a triangle with three congruent sides and three congruent angles.

A scalene triangle is a triangle with no congruent sides and no congruent angles.

A right triangle is a triangle that has one right angle.

The triangle is right-angled because the line segment LM is perpendicular to the MN.

Therefore, the  triangle LMN is an isosceles and right-angled triangle.

Learn more details about triangle. here:

https://brainly.com/question/2773823

#SPJ1

Answer: 1, 4 and 5

Step-by-step explanation:

LM ⊥ MN

The triangle is isosceles

The triangle is a right triangle

Answer:

45.10

Step-by-step explanation:

The "quotient" is the answer or result of a division problem.  Look up "significant digits" if you want to know why I have the answer to two decimal places.

[tex]f^{-1}[/tex](f(6.022)) is 6.022 and [tex]f^{-1}[/tex](-10) + f(6) is -4

The general evaluation of function is

[tex]f^{-1}[/tex](f(x)) = x

Here we have to find [tex]f^{-1}[/tex](f(6.022))

Therefore [tex]f^{-1}[/tex](f(6.022)) = 6.022

Now we have to find the value of [tex]f^{-1}[/tex](-10) + f(6)

Form the table of values, we have

[tex]f^{-1}[/tex](-10) = -6 and f(6) = -10

So we have

[tex]f^{-1}[/tex](-10) + f(6) = 6 + (-10)

                     = 6 -10

                     = -4

Therefore [tex]f^{-10}[/tex] (-10)+ f(6) = -4

To know more about the inverse function refer to the link given below:

https://brainly.com/question/11735394

#SPJ1

Answer:

You would travel 331.80 miles

Step-by-step explanation:

79 × 4.2 = 331.8 rounded to the nearest hundredth is 331.8

The revenue equation of the item is r = 3.56q

The given parameters are:

Expense equation, E = 3.2q + 56000

Selling price = 3.56 per item

This means that the selling price equation is

S = Selling price per item * Number of items

So, we have

S = 3.56 * q

This gives

S = 3.56q

The total selling price of the item is the same as the revenue equation

So, we have

r = 3.56q

Note that the revenue equation is also a linear equation

Where linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

Hence, the revenue equation of the item is r = 3.56q

Read more about revenue equation at

https://brainly.com/question/25623677

#SPJ1

The numbers in this problem are classified as follows:

A. Rational.

B. Rational.

C. Irrational.

Hence:

More can be learned about rational and irrational numbers at brainly.com/question/5186493

#SPJ1

Answer:

81°

Step-by-step explanation:

m∠1 + m∠2 + m∠3 = 180° because they add to form a straight angle.

The number of different purchases you could make is 11440

The given parameters are:

Number of chocolate, n = 16

Kinds of chocolate, r = 9

The number of different purchases you could make is calculated using the following combination equation

Purchases = C(n, r)

So, we have

Purchases = C(16, 9)

Apply the combination formula

Purchases = 16!/(9! * 7!)

Evaluate the expression

Purchases = 11440

Hence, the number of different purchases you could make is 11440

Read more about combination at

https://brainly.com/question/11732255

#SPJ1

Answer:

Step-by-step explanation:

Bro u just subtract...:)

547.25(day 1) - 327.875(day2) = 219.375 miles as the difference(just use a calculator)

Answer:

Hello,

P=(1,2)

Step-by-step explanation:

[tex]\overrightarrow{OP}=\overrightarrow{OA}+\dfrac{2}{3} *\overrightarrow{AB}\\\\=(-3,-4)+\dfrac{2}{3} *(3-(-3),5-(-4))\\\\=(-3,-4)+\dfrac{2}{3}*(6,9)\\\\=(-3,-4)+2*(2,3)\\\\=(-3,-4)+(4,6)\\\\\boxed{=(1,2)}\\[/tex]

after you open your keyboard click on the "?123" button then click on the "=\<" button then there u will look for the upside down V

Step-by-step explanation:

thank you !!

Answer:

a. [tex]f(x) = 3 + 0.2x[/tex]

b. 6$

c. 35 miles

Step-by-step explanation:

There is a fixed price of $3 per ride, therefore, the y-intercept of the function would be $3, as she has to pay that amount for any amount of miles ridden in the cab.

In addition, she must add an extra $0.2 for every mile she has ridden in the cab. We can represent the amount of miles using the parameter [tex]x[/tex].

Therefore, the function to represent the cost of a cab-ride would be [tex]f(x) = 3 + 0.2x[/tex].

b. To find out how much she must pay for a 15-mile trip, we must substitute [tex]x = 15[/tex], as she has ridden 15 miles in the cab.

[tex]f(x = 15) = 3 + 0.2 \times 15 \to 3 + 3 \to 6[/tex]

She must pay $6 for the ride.

c. To find out how far she can travel if she only has $10, we would have to equalize the function to 10, as that is the final price she has to pay.

[tex]f(x) = 10\\\to 3 + 0.2x = 10\\\to 0.2x = 7\\\to x = 35[/tex]

For $10, she can travel 35 miles.

Answer: For $10, she can travel 35 miles.

Step-by-step explanation:

In the shadow of the tree, Height = 4 feet

Given :

A  32-foot tree is directly between you and the sun

you are standing 105 feet away from the tree

the tree casts a 120-foot shadow

Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using trigonometric formulas, functions, or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians.

In this article, let us discuss the six important trigonometric functions, ratios, trigonometry tables, formulas, and identities that help to find the missing angles or sides of a right triangle.

Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle.

Solution :

Trigonometry

Length of shadow= 120-105

Length if shadow= 15 feet

height= x

X/15= 32/120

X= 15*32/120

x= 15* 16/60

x= 15*8/30

x= 15*4/15

x= 4

X = 4 feet

Height = 4 feet

In the shadow of the tree, Height = 4 feet

More details :

#SPJ9

The equation of the line will be x = -6, that is, option B.

Here, we are given that a line passes through point (-6,-9) and perpendicular to y = 1/4

If two line are perpendicular to each other, the product of their slopes is equal to -1.

Here, the slope of y = 1/4 will be 0 as y is a constant value and not changing.

Let the slope of the given equation be m

them m × 0 = -1

m = -1/0

Thus, the slope is not defined, this means that the line will be parallel to x axis of the form x = k.

Now, we know that the line passes through point (-6,-9). This means that if y = -9, x will be -6. But we know that x will take only one value for all values of y.

Thus, the equation of the line will be x = -6, that is, option B.

Learn more about equation of a line here-

https://brainly.com/question/13763238

#SPJ9

Your question was incomplete. Check for the full content below-

Select the correct answer.

Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6-9)?

OA. x= -9

OB. x=-6

Oc. y=9

OD. y= -4

Answer:

[tex] \sqrt[16]{5 |2| } sdh[/tex]

usmsks

Jeo need to pay $0.4 million to buy Thea’s share.

Given,

Ratio of investment of Joe, Thea, Taylor in the partnership = 1:2:3

Worth of partnership after some years = $1.2 million

Now, we can calculate the share of partners:

Total of investment = 1 + 2 + 3 = 6

1.2 / 6 = 0.2 million, this is the investment.

Now share of partners:

Joe’s share = 0.2 x 1 = $0.2 million

Thea’s share = 0.2 x 2 = $0.4 million

Taylor’s share = 0.2 x 3 = $0.6 million

From the above data’s we can conclude that Joe needs $0.4 million to buy Thea’s share.

Learn more about shares here:

https://brainly.com/question/1607231

#SPJ1

Answer:

[tex]2x[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the given number.

"Multiply the number by 4" [tex]\to 4x[/tex]

"Add 6 to the product" [tex]\to 4x + 6[/tex]

"Divide this sum by 2" [tex]\to \frac{4x + 6}2 \to 2x + 3[/tex]

"Subtract 3 from the quotient" [tex]\to 2x + 3 - 3 \to 2x[/tex]