David requires at least $250 to hold his birthday party. If David can save $43 a month, how many months will he need to save to be able to afford his birthday party?




a. Write an inequality that describes this situation.


b. Solve the inequality. Show all your work.


c. Write your answer in a complete sentence.

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

Given that;

Since ∠CDA is a right triangle, the sum of ∠ADB and ∠CDB sums up to 90 degrees.

∠ADB + ∠CDB = 90°

(7x +2) + (3x - 2) = 90

Solve for x

7x +2 + 3x - 2 = 90

7x + 3x - 2 +2 = 90

10x = 90

x = 90/10

x = 9

Now, the numerical measure of angle CDB will be;

m∠CDB = (3x - 2)

Plug in x=9

m∠CDB = 3(9) - 2

m∠CDB = 27 - 2

m∠CDB = 25 degrees

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

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Answer: X=365/83 OR x= 4.39

Step-by-step explanation:

Answer:

+18 or -18

Step-by-step explanation:

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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Answer:

8

Step-by-step explanation:

200 ×4=800

OR

200+200+200+200=800

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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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:

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

Answer: 203.057

Step-by-step explanation:

75.2+123.96+3.897

199.16+3.897

203.057

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.

Can someone help explain how to solve

In the picture there are 4 question that are

1) [tex]A(-6,-2)\rightarrow A^{'}(-6,2)\\B(-3,-6)\rightarrow B^{'}(-3,6)\\C(-2,-2)\rightarrow C^{'}(-2,2)\\[/tex]

2)[tex]D(15,10)\rightarrow D^{'}(6,4)\\E(5,10)\rightarrow E^{'}(2,4)\\F(10,-5)\rightarrow F^{'}(4,-2)\\[/tex]

3)[tex]G(-2,7)\rightarrow G^{'}(-7,-2)\\H(-4,8)\rightarrow H^{'}(-8,-4)\\I(-3,5)\rightarrow I^{'}(-5,-3)\\[/tex]

4) [tex]J(11,-8)\rightarrow J^{'}(1,-5)\\K(6,-1)\rightarrow K^{'}(-4,2)\\L(3,-7)\rightarrow L^{'}(-7,4)\\[/tex]

The transformation has the following form:

1)[tex](x,y)\rightarrow(x,-y)[/tex]

2)[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)[tex](x,y)\rightarrow(-y,x)\\[/tex]

4) It does not have transformation.

Geometric Transformation:

Images of triangles, quadrilaterals, pentagons, and other geometric shapes can undergo geometric transformations through the vertices in a Cartesian plane. Reflection, rotation, and translation are the three transformations; they only affect the geometric figure's location and not its size. Expansion and contraction are the two transformations that alter the geometric figure's size.

It is necessary to know the sort of transformation that took place given the points and their transformations.

1) We observe that point transformation A,B and C are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(x,-y)[/tex]

Every x-value remains constant, while every y-value flips from what it was.[tex](x,y)\rightarrow(x,-y)[/tex]

2)We observe that point transformations D, E, and F are contractions. Let's now identify the scalar that was applied to the transformation. We compute the product of the original point's coordinate and one of the transformation point's coordinates.

[tex]\frac{D^{'} _{y} }{D_{ y}} =\frac{4}{10} =\frac{2}{5}[/tex]

We multiply the coordinates of points E and F and check the results to make sure this is true.

For E:

[tex]\frac{2}{5} (5,10)=(2,4)\\Therefore,E^{'} =(2,4)[/tex]

For F:

[tex]\frac{2}{5} (10,-6)=(4,-2)\\Therefore,F^{'} =(4,-2)[/tex]

Therefore, The transformation has the following form:

[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)We observe that point transformation G,H and I are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(-y,x)[/tex]

Every y-value flips from what it was to the opposite. The x and y values are reversed.[tex](x,y)\rightarrow(-y,x)[/tex]

4)We observe that point transformation J,K and L are not transformed.

It does not satisfy the condition of the transformation.

Therefore, this is how we solve the transformation.

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Step-by-step explanation:

Question no 23 : Option d

Question no 21:

angles on a straight lin is equal to 180°

150-180 = 30 (option d)

I just answered question no 23 and 21

re check the answers if you can I am a student too just trying to help as much as I can.

Answer:

Step-by-step explanation:

jjjjjjjj

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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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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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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$2950 is the monthly salary of the other employee.

a. the given information = mean of two salaries =  3210

                                        = salary of 1st employee =3470

the unknown information = salary of 2nd employee = 2950

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We know that mean, [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]

Here is given the

mean = 3210

term₁ = 3470                 (salary of one of the employees)

term₂ = ?                          (salary of the 2nd employee)

So, if we simplify

⇒ [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]

⇒ [tex]3210 = \frac{3470 + term_2}{2}[/tex]

⇒ [tex]3210[/tex] × [tex]2 = 3470 + term_2[/tex]

⇒ [tex]6420[/tex] = [tex]3470 + term_2[/tex]

⇒ [tex]term_2 = 6420 - 3470[/tex]

⇒ [tex]term_2 = 2950[/tex]

So, the salary of the other employs is $ 2950

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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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Step-by-step explanation:

Tell me the problem and I may help u

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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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.

The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

A rigid transformation is a transformation that preserves the shape and size such as rotation, reflection and translation.

Given the points A(-1, 13), B(1, 5), A'(2, 3), and B'(6, 1), hence:

[tex]AB=\sqrt{(5-13)^2+(1-(-1))^2} =\sqrt{68}\\\\A'B'=\sqrt{(1-3)^2+(6-2)^2}=\sqrt{20}[/tex]

The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

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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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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:

It the square with 3/4 shaded. the point shows 0.75 and the square shows 75% which is 3/4.

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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The equation of line for m = 5/6 and the y -intercept is (0,12) is y = 5/6x + 12.

The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

The equation for line is y = mx + c

Given, m = 5/6, y-intercept = (0,12)

now putting the values in the equation,

y = 5/6x + 12

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to get the equation of any straight line, we simply need two points off of it, again, let's use the ones from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{11}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{11}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 4 }{ 2 }\implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{2}(x-\stackrel{x_1}{2}) \\\\\\ y-7=2x-4\implies {\LARGE \begin{array}{llll} y=2x+3 \end{array}}[/tex]

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: SA=326.56 inches

Step-by-step explanation:

[tex]SA=2\pi r^2+2\pi rh\\SA=2\pi r(r+h)\\r=4 \ inches\ \ \ \ \ h=9\ inches\ \ \ \ \ \ \pi =3.14\\Hence,\\SA=(2)(3.14)(4)(4+9)\\SA=(25.12)(13)\\SA=326.56\ inches[/tex]