What is the area of the rectangle in the coordinate plane?

The required sum of the 7 terms in the geometric sequence is 16.6.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
Given geometric series,
10, 4, 8/5 . . . . . .  

Common ratio = 4 / 10 = 2/5

first term = 10

the sum of the first seven terms is given as,
S₇ = a[r⁶ - 1] / r - 1
S₇ = 10[{2/5}⁶ - 1] / {2/5 - 1}
S₇ = 16.6

Thus, the required sum of the 7 terms in the geometric sequence is 16.6.

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Answer:20

Step-by-step explanation:

Answer:

the percent of 40 is 50

the answer to this is 10

Answer: The graph represents the solution to the following sentence is the option number 3:

-3 -2 -1 0 1 2 3 4 5

This is because the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2. The graph shows all the values of x that are greater than 4 and all values of x that are less than -2. The graph also includes the values of x between -3 and 5, it encompasses all the values that are greater than 4 and all values that are less than -2.

The graph represents the solution to the following sentence is (C).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

{x | x >4 } ∪ {x | x < -2}

Here the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2.

The graph displays all instances of x larger than 4 and all instances of x less than -2.

The graph covers all x values higher than or equal to 4, as well as all x values less than or equal to -2.

It also includes x values between -3 and 5.

Thus, the number line is C.

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Answer: 2nd picture

Step-by-step explanation: its rotating 90 degrees

Answer:

a. the 2% commission he receives

b. $138

c. He must make $47,500 in sales

Step-by-step explanation:

a. No work needed

b. E= 0.02 (4,400) +50, which simplifies to E= 88+50 which continues to 138 dollars

c. To find this you already know E, so you can work backwards

1,000= 0.02 (x) + 50

then subtract 50 from each side

950 = 0.02 (x)

then divide both sides by the 0.02 to get X alone

47,500 = X

Therefore , the equation problem is  15 fraction of 72 is the number 480. The expressions published here on left & right sides appear to be equivalent in their relationship.

Mathematical statements with two algebraic in the middle and also the means total (=) sign from either side are called equations. Variables, contractors, diffusion coefficients, terms, and the equatable to sign are just a few of the elements that compose an equation. The "=" sign but also terms both on sides are always necessary when writing an equation.

Here,

Using the value A = 480 as a guide

Let y become the ratio of the number, or the opposite.

It is equivalent to 72%.

The equation that results is

72 is equivalent to x% of 480.

When the expression is condensed, we get

72 = y % x 480

72 = ( y/100 ) x 480

Divide each side by 480 to obtain

y/100 = 0.15

Multiply by 100 on each side to arrive at

y = 15

Consequently, the value is y = 15.

Therefore, out of 480, 72 represents 15%.

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Answer:

-1

Step-by-step explanation:

Since -1 to a power will either be negative or postive 1, looking at whether the exponent is odd or even can determine if the answer is -1 or 0 (x + x^2 for instance  equals 0 but x + x^2 + x^3 is -1)

[tex]\it (-1)^{2k}=1;\ \ \ (-1)^{2k+1}=-1,\ \ \forall\ k \in\mathbb{N}\\ \\ S=-1+(1-1)+(1-1)+\ ...\ (1-1)=-1[/tex]

The interval over which h(t) has a negative rate of change is given as follows:

(-∞, -3).

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

The equation for this problem is given as follows:

h(t) = (t + 3)² + 5.

The leading coefficient is positive, hence the function is concave up.

Considering the t-coordinate of t = -3 at the vertex, the decreasing and increasing intervals are given as follows:

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Answer:

We can start solving this problem by using a system of linear equations. Let x be the number of gallons of the 20% pure slime mixture and y be the number of gallons of the 80% pure slime mixture. We know the following:

The total amount of slime mixture is 1000 gallons. This means that x + y = 1000.

The final mixture is 65% pure slime, which means that 0.65 = (0.20)x + (0.80)y. This is because we are mixing 20% pure slime and 80% pure slime to get the final mixture.

We can use these two equations to solve for x, which is the number of gallons of the 20% pure slime mixture needed.

First, we'll use the first equation to solve for y in terms of x:

y = 1000 - x

Then we'll substitute this expression into the second equation:

0.65 = (0.20)x + (0.80)(1000 - x)

Simplifying we get:

0.65 = 0.20x + 800 - 0.80x

0.45x = 200

x = 200/0.45

x = 444.44 gallons

So, you would need 444.44 gallons of the 20% pure slime mixture to make 1000 gallons of a 65% pure slime mixture.

Step-by-step explanation:

On solving the provided question, we can say that from the given graph, it is shown that it is a starlight line so the equation that represents is x = y => x-y = 0

Mathematicians use graphs to logically convey facts or values using the visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here, from the given graph

it is shown that it is a starlight line

so the equation that represents is x = y

x-y = 0

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The volume, V of box as a function of x that is V(x) = 4x³ - 64x² + 240x , where x is side of square cut out from each corner.

We have, a box open from top and constituted from rectugular pieces of dimensions 12 inches and 20 inches. As we know, The volume of a box is V

= width (w) × height(h) ×length (l).

Now, equal squares of side x are cut from each corner of box and folded. We draw our box it looks like as seen above figure. We will notice here that the height will be x and that the height and length depend on x. Length of box, l = 20 - 2x and

Width of box, w = 12 - 2x

So the volume is, V(x) = w×h×l

= (12 - 2x)(x)(20 - 2x)

Expand it for further calculation,

V(x) = ( 12 - 2x ) ( 20x - 2x²)

V(x) = 4x³ - 64x² + 240x

Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.

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The volume, V, of a box is defined as V(x) = 4x3 - 64x2 + 240x.

We have a box that opens from the top and is made of rectangular components that are 12 inches and 20 inches in length. As is common knowledge, a box's volume is V.

V = height (h) + width (w) + length (l).

From each corner of the box, equal squares of side x are now cut and folded. We create a box that resembles the image above. Here, we'll see that the height is x and that the relationship between height and length is x-dependent.

Box length, l = 20 - 2x, and

Box width, w = 12 - 2x

Thus, V is the volume (x) = W * H * I

V(x) = (12 - 2x) (x) (20 - 2x)

V(x) = ( 12 - 2x ) ( 20x - 2x²)

V(x) = 240x - 24x² - 40x² -4x³

V(x) = 4x³ - 64x² + 240x

Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.

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A graph which represents the system of inequalities for this scenario include the following: graph B.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of developed acres and number of open acres, and then translate the word problem into algebraic equation as follows:

Since a planned community must have at least 4 acres of developed and open space, a linear inequality which represents this situation is given by;

x + y ≥ 4

Additionally, since the difference between the number of developed acres and the number of open acres can be no more than 1, we have;

y – x ≤ 1

Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by graph B.

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The value of x, which is the measure of the remaining angle, is equal to 180° - 70° - 30°, or 80°.

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Variance and standard deviation are two common measures of spread in statistics. The standard deviation is √30.25 = 5.5.

OB. s² = The sample variance is a measure of the spread of a set of data. To calculate the sample variance, the sum of the squares of the differences between each data point and the mean is divided by the number of data points minus one. In this case, the mean of the data set is (22+15+4+7+9)/5 = 11.

The differences between each data point and the mean are 11-22=-11, 11-15=-4, 11-4=7, 11-7=4, and 11-9=2. The sum of the squares of these differences is (-11)² + (-4)² + 7² + 4² + 2² = 121.

Dividing this by the number of data points minus one, which is 5-1=4, gives us a sample variance of 121/4 = 30.25.

The standard deviation is the square root of the sample variance, so in this case, the standard deviation is √30.25 = 5.5.

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Answer: y= -3x+7

Step-by-step explanation:

the equation is y=Mx+b you gave me the slope (-3) and the y-intercept (7) so the answer is y=-3x+7

Of those who were not happy with their purchase, about 20% purchased model A, and about 36% purchased model B.

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Option A is appropriate since the table's function is linear.

The equals sign is used in equations to indicate the equality of two expressions in a formula. The expressions relate two or more variables with each other.

Given that:

x = 2 and y =4

x= 4 and y= 8 and so on.

In all the values given, the value of y is two times the value of x.

Also, these values satisfy the condition of linear expression:

y=mx

where, m =2 for the represented value.

This means that the function is linearly dependent on x.

The function shown in the table is linear.

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The truth table for  ~p ∨ q is as shown below.

~p ∨ q

   T

   F

   T

   T

A truth table is a table for evaluating the truth value of a truth-functional compound sentence on the basis of the truth value of its part

The truth tables for negation and disjunction are shown below:

Negation

p     ......    ~p

T                F

F                T

Disjunction

p  ..... q  ..... p v q

T        T         T

T        F         T

F        T         T

F         F        T

Note:

T and F stand for True and False respectively.

In disjunction, if one of the inputs is true then the output will be True.

Negation reverses the input i.e if the input is True, the output will be False. The symbol for negation is  ~ i.e the negation of p is  ~p

Truth table for ~p ∨ q?

p  -----  q  -----  ~p  -----  q  -----  ~p ∨ q

T          T            F         T              T  

T          F            F         F               F

F          T            T         T              T    

F          F            T         F              T  

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Answer:

45c-20c²

Step-by-step explanation:

You just multiply the number outside the bracets with the numbers inside.

5c×9= 45c

5c×-4c= -20c²

So the answer is 45c-20c²

Which is option 'B'

Answer: 400

Step-by-step explanation: Max has rounded off the difference of two numbers. Max's estimate of the difference is 400.

Given information:

The first number = 718.

The second number = 331

Now, according to the question, Max estimates their difference by taking the number rounded off.

Hence, the rounding off the given number to nearest 100,

we get,

First number as 700 and Second number as 300.

Hence the difference of the obtained number can be written as:

Hence, one can conclude that, max's estimate of the difference is 400.

From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.

Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate.

Let x and y be proportional relation

=> x ∝ y

=> x = ky    

=> x/y = k    [ where 'k' proportionality constant ]

Here we have

Table 1

x   2   3   4    5  

y   7   9   11   13    

=>  [tex]\frac{x}{y} = \frac{3}{7} = \frac{3}{9}[/tex]    [ which is not true ]

Hence,

Table 1 not shows any proportional relationship between x and y

Table 2

x  3   7.5  15  25

y  1    2.5  4    6    

=>  [tex]\frac{x}{y} = \frac{3}{1} = \frac{7.5}{2.5} = 3[/tex]  [ which is true ]

Hence, Table 2, shows a proportional relationship between x and y

Table 3

x   1      2     7     8

y  0.5    1    3.5   4    

=> [tex]\frac{x}{y} = \frac{1}{0.5} = \frac{2}{1} = 2[/tex]  [ Which is true ]

Hence, Table 3 shows a proportional relationship between x and y

Table 4

x    3    6    8   10  

y    12   15  18  20  

=> [tex]\frac{x}{y} = \frac{3}{12} = \frac{6}{15}[/tex]   [ Which is not true ]  

Hence, Table 4 not shows a proportional relationship between x and y

Therefore,

From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.

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The correct solution of the expression 3/4 ( 6x - 4) = 1/2 (x + 4) with the property that justify each step is shown below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

Now, Solve the expression as;

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

⇒ 9/2x - 3 = 1/2x + 2                        By Distributive property

⇒ 9/2x - 3 - 1/2x = 1/2x + 2 - 1/2x     Subtraction property of equality

⇒ (9/2 - 1/2)x - 3 = 2                        Combine like terms

⇒ 4x - 3 = 2                                     Subtraction property

⇒ 4x - 3 + 3 = 2 + 3                         Addition property of equality

⇒ 4x = 5

⇒ 1/4 × 4x = 1/4 × 5                          Multiplication property of equality

⇒ x = 5/4

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There are 24 red peppers and 8 yellow peppers.

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

Casey has 48 red peppers and 16 yellow peppers.

Now, Divide it into equal part.

Hence, Number of red peppers in two parts = 48/2

                                                                     = 24

And, Number of yellow peppers in two parts = 16/2

                                                                     = 8

Thus, After divide into parts, we get;

There are 24 red peppers and 8 yellow peppers.

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Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.

given

m∠V + m∠W + m∠X + m∠Y = 360

10x -27 + 2x + 19 = 180

12x - 8 = 180

188 = 12x

x = 15.66

m∠V + m∠X = 180

2x = 180

x = 90

Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

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Answer:

13

Step-by-step explanation:

the using the Pythagorean Theorem A^2+b^2=c^2

5^2 is 25

12^2 is 144

add 144+25=169 then you square root this and it should be 13

The solution of this equation is given by x = -10 ( option A)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The equation is

2x - 10 = 3x

⇒ x = -10

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In the circle the area of the shaded region and the length of arc ADB is 23/4 π and 23/6 π respectively.

What is length of arc?

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Given that the circle has a center O.

The radius of the circle is 3 yd.

The measure of ∠AOB is 130°.

First find the measure of ∠ADB -

∠ADB = 360° - ∠AOB

Substituting the values in the equation -

∠ADB = 360° - 130°

∠ADB = 230°

Now find the area of the shaded region.

The area of the shaded region can be determined using the formula -

A = (θ/360)πr²

Substituting the values in the equation -

A = (230/360) π(3)²

A = (230/360) π 9

A = 23/4 π or 5.75 π

Therefore, the area of the shaded region is 5.75 π yd².

Now, find the length of the arc ADB.

The length of arc ADB can be determined using the formula -

Arc Length = (θ/360)2πr

Arc Length = (230/360)2π3

Arc Length = 23/6 π or 3.83 π

Therefore, the length of arc is 3.83 π yd.

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Answer:

A) x= -4

Step-by-step explanation:

-7x+3x=7+9

-4x= 16

x= 16÷ -4 = -4

The given two lines are parallel to each other. The correct answer would be an option (A).

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The lines will be parallel if they have the same slope and they will be perpendicular if the product of the slopes of the two lines is -1.

The slope of the first line can be found using the formula:

m₁ = (-2 - (-5))/(5-9) = -3/4

The slope of the second line can be found using the formula:

m₂ = (1 - (-2))/ (-8 - (-4)) = -3/4

They have identical slope, so the lines will be parallel.

Hence, the given two lines are parallel to each other.

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