Solve the following inequality algebraically.
x^2-3x-70< 0

The equation of the line that is perpendicular to given line is y = -x -2

From the question, we are to determine the equation of the line

From the given information,

We have that the two lines are perpendicular

If two lines are perpendicular, the product of their slopes is -1

That is,

m₁m₂ = -1

Where m₁ is the slope of the first equation

and m₂ is the slope of the second equation

In the given equation,

y = x - 2

Compare to the general form of the equation of a line

y = mx + b

Where m is the slope

and b is the y-intercept

Thus,

In the equation, y = x - 2

Slope = 1

Therefore,

The slope of the equation we are to determine is -1

Also, from the given information,

The line passes through the point (-12, 10)

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -12

y₁ = 10

Thus,

y - y₁ = m(x - x₁)

y - 10 = -1(x - -12)

y - 10 = -1(x + 12)

y - 10 = -x -12

y = -x -12 + 10

y = -x -2

Hence, the equation of the line that is perpendicular to given line is y = -x -2

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Answer:

See explanation

Step-by-step explanation:

f(x)=x² + x + 2 and g(x) = 2x² - 7

f(2) g(2)=

((2)² + (2) + 2)(2(2)² - 7)=

(4 + 2+ 2)(2(4) - 7)=

(8)(8 - 7)=

8*1=8

2 fg(2)=

2 f(g(2))=

2 f(2(2)² - 7)=

2 f(2(4)-7)=

2 f(8-7)=

2 f(1)=

2(1² + 1 + 2)=

2(1+3)=

2(4)=8

8=8

2 fg(2)=f(2) g(2) √

It takes the object about 26/49 minutes to travel 5 1/5 miles.

A mixed fraction is a non-integer that consists of a whole number and a proper fraction. An example of a mixed fraction is 1 1/2.

Speed measures how fast an object is moving with respect to time. Speed is the total distance travelled per time.

Speed = total distance / total time

In order to determine the total time it would take the object to travel the distance, divide the distance travelled by the speed.

Time = distance / speed

5 1/5 ÷ 9 4/5

26/5 ÷ 49 / 5

26/5 x 5/49 = 26 / 49 minutes

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The simplification by combining like terms of b -2(1 + c - b) is 3b -2c - 2.

According to the given question.

We have an expression b -2(1 + c - b).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression b -2(1 + c - b).

Here b and 2b both are the like terms.

So, we add and subtract coeffcients of b to simplify the given expression.

Therefore, the simplification of the expression b -2( 1 + c - b) is given by

b - 2( 1+ c - b)

= b - 2 -2c + 2b

= 3b -2c - 2

Hence, the simplification by combining like terms of b -2(1 + c -b) is 3b -2c - 2.

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Answer:

c) 0.67

c) 0.67 d) 2.4

c) 0.67 d) 2.4 e) 0.046

c) 0.67 d) 2.4 e) 0.046f) 0.26

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535k) 0.074

c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535k) 0.074 l) 0.4305

Step-by-step explanation:

Method 1: Without a calculator

To divide just move the decimal point to the right to how many zeros there are (for example 10 is one zero so you move the decimal point to the right one time).

Method 2: With a calculator

Type the equation press enter or "=" and you get your answer.

The total time needed for Elizabeth on the practice is 130 minutes.

It should be noted that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam,

Let the total time be represented by x.

Therefore, 70% × x = 91

0.7 × x = 91

0.7x = 91

Divide

x = 91/0.7

x = 130

The total time needed is 130 minutes.

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The tape diagram shows that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam, on conversation practice. What was the total time needed?

Answer:

+18 or -18

Step-by-step explanation:

Answer:

Step-by-step explanation:

jjjjjjjj

We can use the formula for the sum of a geometric series as Summation.

What is Geometric Series:

A geometric series is the sum of finite or infinite terms of a geometric sequence. For the geometric sequence a, ar, ar2, ..., arn-1, ..., the corresponding geometric series is a + ar + ar2 + ..., arn-1 + .... We know that "series" means "sum". In particular, the geometric series means the sum of the terms that have a common ratio between every adjacent two of them. There can be two types of geometric series: finite and infinite.

Now, Solution of the given problem

We can write

0.999...=9/10+9/100+9/1000+⋯

=9/10+9/10(1/10)+9/10(1/10)2+⋯

=∞∑n=0 9/10(1/10)n,

which is a geometric series

with a=9/10and r=1/10

.So, the sum is a/1−r=9/10 / 1−1/10 = 1.

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Answer:

3.2 + 3.2squared + 2 = 15.44

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + x^2 + 2

3.2 + 3.2^2 + 2

3.2 + 10.24 + 2 = 15.44

1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R.

Transformation is rearranging a graph by a given rule it could be either increment,decrement, reflection, or rotation.

Reflection is a mirror image of a graph about any axis.

It seems that figure R is the rotation of Q clockwise by 90°.

In figure Q,

The Coordinate of the bottom left point of it is (3,1) if we rotate by 90° then it will remain at (3,1).

The coordinate of the same point in figure R is (2,-1)

So,

3 + x = 2 → x = -1 (1 unit left)

1 + y = -1 → y = -2 (2 units down)

Hence "1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R".

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The amount of $123 will be equal to 1380 yens.

The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.

Given that the exchange rate of the Japanese Yen on a certain day was Rs 10.25. On the same day, if $3 was exchanged for Rs 345.

The amount of $123 in the yens will be calculated by forming the equations below:-

1 yen = 10.25 rs

1 rs = ( 1 / 10.25 ) yens  ........................(1)

$3 = 345 rs

1 rs = $3 / 345             .........................(2)

From both the equations:-

( 1 / 10.25 ) yens  = $ ( 3 / 345 )

$ 1 = ( 345 / ( 10.25 x 3 ) yen

$ 123 = ( 345 x 123  / ( 10.25 x 3 ) yen

$ 123 = 1380 yen

Therefore, the amount of $123 will be equal to 1380 yens.

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In logarithm , value of function is 1/4.

How should log be defined?

Log x + log 6= log(2x+1)

use log property log m + log n = log ( mn)

log ( 6x) =  log (2x + 1)

  6x = 2x + 1

   4x = 1

      x = 1/4

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Answer:

8

Step-by-step explanation:

200 ×4=800

OR

200+200+200+200=800

The function is increasing is f(x) = [tex]5^x[/tex]

For exponential functions: f(x) = [tex]a^{x}[/tex] (a>0 and a[tex]\neq 0[/tex] ), when A is greater than the function is increased.

0.5 <1, [tex]\frac{1}{15}[/tex]<1 , [tex]\frac{1}{5}[/tex]<1 , 5>1

so C is correct.

The exponential  is a mathematical function denoted by the argument x is written as an exponent. Unless otherwise specified, the term generally refers to the positive-valued function of  a true  variable, although it  are often  extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The  exponential  originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended  to all or any  real arguments, including irrational numbers. Its ubiquitous occurrence in pure and  applied math  led mathematician Walter  to opine that the exponential function is "the most important function in mathematics".

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Hello,

A - B = 7x² - 3x + 10 - (-4x² + 6x - 4)

A - B = 7x² -3x + 10 + 4x² -6x + 4

A - B = 11x² - 9x + 14

17 weeks

Step-by-step explanation:

you multiply the number of hours by the number of weeks, giving you 40, then divide the amount of total hours worked by 40, giving you 17

5 x 8 = 40

680/40 = 17

17 weeks.

Using the values of the first term and the sum of the first 40 terms of the given series, a(40) = 300

Suppose we are given a series:

  a(1) + a(2) + a(3) + ....+ a(n)

Then, the sum of the first n terms is given by:

S(n) = n/2 [a(1) + a(n)]

Parameters given in the problem:

a(1) = 4

S(40) = 6080

To find a(40), substitute n = 40, a(1) = 4, and S(40) = 6080 into the formula:

S(n) = n/2 [a(1) + a(n)]

S(40) = 40/2 [4 + a(40)]

6080 = 20 . [4 + a(40)]

Divide both sides by 20

304 = 4 + a(40)

Subtract 4 from both sides:

304 - 4 = 4 + a(40) - 4

a(40) = 300

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The distance between the coordinates is 2+√19.

According to the question, the given problem can be solved by using the standard distance formula.

Now, the coordinate values are:

p(a, 2a); q(4, 3) and Distance = 10 units

Therefore, from the given parameters we can write:

x1 = a; y1 = 2a; x2 = 4; y2 = 3

Now,

Distance^2 = (x1 - x2)^2 + (y1 - y2)^2

Substituting the given values, we get:

Distance^2 = (4 - a)^2 + (3 - 2a)^2 = 16 +a^2 - 8a + 9 +4a^2 - 12a

100 = 25 + 5a^2 - 20a

5a^2 - 20a - 75 = 0

a^2 - 4a - 15 = 0

a = 2+√19

Hence, the distance between the coordinates is 2+√19.

What is distance?

Distance can be defined as the resultant displacement between the two endpoints. It can measured in different units like meters, centimeters, kilometers, etc. And the respective values can be calculated by using the standard formula.

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The given statement is completely true.

This is because the definition of slant height is the altitude of the lateral face of a pyramid or cone which is true.

There are three dimensions of a cone.

The vertical height (or altitude) is the perpendicular distance from the top down to the base.

The radius of the circular base slant height is the distance from the top, down the side, to a point on the base circumference.

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Here mWXZ=108*and m1 is two times m2 so, The value of m2 is [tex]36[/tex]°.

The fundamental geometric shapes are lines and angles. Infinite points that stretch infinity in both directions make up lines, which are geometric objects. Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints. The most useful area of mathematics is the study of geometric shapes and their characteristics. As we've already mentioned, the foundation of any geometric shape is made up of lines and angles. Without employing lines and angles, it is impossible to draw a two-dimensional to three-dimensional shape. Consequently, it is imperative to discover the meanings of the two terminologies. Here, the fundamental definitions and characteristics of lines as well as angles are provided. A line is a simple, one-dimensional shape that can go on forever in opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right. When the ends of two rays collide at a single location, an angle is a geometry that results. They are expressed as radians or degrees (°). A 360-degree angle is the same as a whole rotation.

Let the angle m2 be x

so, according to the question m1= 2m2=2x

so, m1+m2=[tex]108[/tex]°

  ⇒2x+x=[tex]108[/tex]°

  ⇒3x=[tex]108[/tex]°

  ⇒x=[tex]36[/tex]°

means angle m2=[tex]36[/tex]°

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Answer:  It is not always true, so it's not an identity

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

Explanation:

Let's try replacing each 'a' with 1, and each b with 2. Feel free to pick two of your favorite nonzero numbers.

So we'll plug in a = 1 and b = 2

[tex](a+b)^2 = a^2+b^2\\\\(1+2)^2 = 1^2+2^2\\\\(3)^2 = 1^2+2^2\\\\9 = 1+4\\\\9 = 5\\\\[/tex]

The last equation is a false statement. This means the first equation is also false for a = 1 and b = 2.

This is one counter-example to disprove that (a+b)² = a² + b² is true in general.

Therefore, the equation is not an identity.

--------------

What is an identity however is this

(a+b)² = a² + 2ab + b²

If you were to plug in a = 1 and b = 2, then you'd get 9 on each side. This is one example to help partially confirm it's an identity.

More rigorous proof is in the form of using the FOIL method, the distributive property, or the box method.

Step-by-step explanation:

Tell me the problem and I may help u

The assumptions need to be made in the dart simulation is that the object lands within the target area, and that it is equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land anywhere in the region.

Dart game:

Basically, the dart game board consists of sisal fibers or boar bristles and cork. An 18 inch diameter board is divided into 20 sections.

Thin metal structures are used to design the dividing lines and with the same materials the numbers are designed.

Sometimes the manufactures opt for printing number formats. The board should be positioned on the wall in such a manner that the bull’s eye should be 5ft 8 inch above the floor.

Given,

Here we need to find When designing a simulation where darts are thrown at targets, what assumptions need to be made and why are they needed.

While looking at the definition of the dart game board,

We know that, we have to do the following,

We assume that the object lands within the target area, and that it is  equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land  anywhere in the region.

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Answer:

$10800

Step-by-step explanation:

$11,448 = 100% + 6%

          = 100%

$11,448 = 106%

          = 100%

Cross-multiply it :

$11,448 × 100% = × 106%

$11,448 × 100/100 = 106/100

$11,448 × 100/106 =

= $10800

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One year percent change is 14 percent.

A portion of a whole expressed in hundredths the number of students present was high. B: The outcome of dividing a number by a percentage is that the percentage equals the rate divided by the base. A portion of victories or profits (2a).

Given that,

Berkshire Hathaway closed at 185,690 per share on February 26.

One share's closing price from one year ago was 215,970.

So,the percentage of one year is 215970 × 185690/185690 × 100

So, the percent of one year is 14 percent.        

Therefore, One year percent change is 14 percent.

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According to the given statement;

object A is moving faster by 8.184-5= 3.184

3.184 mph faster.

The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.

The most crucial scientific concept is measurement. Base or physical fundamental units are used to measure a wide range of measurable quantities. One such measurable quantity is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.

According to the given valus;

Speed of object A = 12 ft per sec

I foot per second = 0.682 mph

12 ft per sec = 0.682x 12

= 8.184 mph

object В speed = 5 mph

object A is moving faster than B.

object A is moving faster by 8.184-5= 3.184

3.184 mph faster.

Hence,object A is moving faster than B by  3.184 mph.

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The solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.

According to the given question.

We have a linear equation in one variable.

12 -3(2w + 1) = 7w -3(7 + w)

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is given by

12 - 3(2w + 1) = 7w - 3(7 + w)

⇒ 12 - 6w -3 = 7w - 21 -3w                 (by distributive rule)

⇒ 9 - 6w = 4w - 21                          (subtracting the like terms)

⇒ 9 + 21 = 4w + 6w

⇒ 30 = 10w

⇒ 30/10 = w

⇒ w = 3

Hence, the solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.

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133.3333333333% (increase) is percent of increase 70%.

What is the percentage formula?

Use the formula percent change

Percent change = [tex]\frac{New - old}{old} * 100[/tex]

                           = 70- 30/30 * 100

                           = 40/30 * 100

                           = 133.3333333333% (increase)

Where: 30 is the old value and 70 is the new value.

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