is it easier to describe the solution of a system of linear inequalities in words or to show it using a graph?

Answer:

we have

6x+2y > -106x+2y>−10

Isolate the variable y

Subtract 6x6x both sides

2y > -6x-102y>−6x−10

Divide by 22 both sides

y > -3x-5y>−3x−5

The equation of the line of this inequality is

y=-3x-5y=−3x−5

The slope is negative and is equal to m=-3m=−3

The y-intercept is the point (0,-5)(0,−5) ----> value of y when the value of x is equal to zero

The x-intercept is the point (-5/3,0)(−5/3,0) ----> value of x when the value of y is equal to zero

The solution of the inequality is the shaded area above the dotted line

Using a graphing tool

see the attached figure

Using proportions to find the radius of figure 2, we have that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The rule of three to find the radius of figure 2 is given as follows:

[tex]\frac{5}{9} = \frac{r}{4.5}[/tex]

Applying cross multiplication:

9r = 4 x 4.5

r = 4 x 4.5/9

r = 2 in

The circumference of a circle of radius r is given by:

[tex]C = 2\pi r[/tex]

In this problem, we have that r = 2 inches, hence:

[tex]C = 2\pi \times 2 = 4\pi[/tex]

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

[tex]A = \pi r^2[/tex]

Hence:

[tex]A = 4\pi[/tex]

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Answer: First one is 5, Second is 6.25

Step-by-step explanation: Correct on Edmentum/Plato

Answer: 156 degrees

Step-by-step explanation:

Answer: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

[tex]A=\frac{1}{2}(5+9)*3[/tex]

[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]

[tex]A=7*3[/tex] [Multiplying one-half by 14]

[tex]A=21[/tex] [Multiplying 7 and 3]

The area is 21 units².

Q1

Nominal - D

Ordinal-  B, G

Ratio - A, C, E, F

Q2

Quantitative- A, C, D, G

Qualitative -B, E, F, G

Q3

Simple Random - A, C

Systematic Sample - B

Nominal measures are the most accurate and meaningless, as they only show the "characteristics" or "identities" that we are interested in. In other words, in a nominal variable, a number just gives the attribute a unique "name". In this case, the number is just a label.

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Answer:

Step-by-step explanation:

hello

calculate x : 3x+2 =5

means : 3x+2-2 =5-2

3x = 3

so : x = 3/3 =1

1 is the  element in domain has the image 5 under function f(x)= 3x+ 2

Answer:

Step-by-step explanation:

The height of the pyramid (h) = 3.6m

The perimeter of the base = 4.1m

Volume of a pyramid = ?

Formula:-

[tex]\boxed{\sf Volume =\cfrac{1}{3} \: a^2h}[/tex]

So,

Perimeter = 4a

[tex]\sf 4.1=4a[/tex]

[tex]\sf a=1.025[/tex]

Now, let's put the value of a in the formula:-

[tex]\sf V=\cfrac{1}{3} \:(1.025)^{2} (3.6)[/tex]

[tex]\sf 1.26075m^2[/tex]

[tex]\sf \thickapprox 1.3m^3[/tex]

Therefore, the volume of the pyramid is 1.3m³.

Parallel cousins are found in the iroquois system of kinship and are defined as bifurcate merging.

Parallel cousins, or the offspring of one's mother's or father's brothers or sisters, were frequently referred to and regarded in the same way as one's siblings. Contrarily, cross-cousins, or the offspring of one's mother's brothers or father's sisters, were frequently regarded as the best source of children.

Bifurcate merging is the underlying idea of the Iroquois system. The ego divides his family into those on his mother's side and those on his father's side (bifurcation) and combines his father with his brother (A) and his mother with her sister (B) .

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Solving a system of equations we can see that:

First, let's define the variables:

With the given information we can write 3 equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

Then we need to solve a system of equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

We can first replace the first equation into the third to get:

(3/4)*V + V + K = $386.4

And rewrite the second to get:

k = V + $18

And replace that in the other equation:

(3/4)*V + V + V + $18 = $386.4

Now we can solve this for V:

V*(1 + 1 + 3/4) = $386.4 - $18

V*(11/4) = $368.40

V = (4/11)*$368.40 = $133.96

Now that we know the value of V, we can replace it in:

K = V + $18 = $133.96 + $18 = $151.96

A = (3/4)*V = (3/4)*$133.96 = $100.47

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The 95% confidence interval of the statistics is (7.795, 8.243).

Based on the information given, the 95% confidence interval will be:

= 8.019 + (1.962 × 3.183/✓1114)

= 8.243 and

= 8.019 - (1.962 × 3.183/✓1114)

= 7.795

In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).

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Considering the definition of an equation and the way to solve it, there are 10 apples in the bag.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "or" the number of oranges in the bag, and knowing that:

the equation in this case is:

or + apples= 15

or + 2or= 15

Solving:

3or= 15

or= 15 ÷ 3

or= 5

As a bag of apples and oranges contains twice as many apples as oranges, then 2or= 2×5= 10 apples

Finally, there are 10 apples in the bag.

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Answer:-----------

Step-by-step explanation:------------------

Answer:

???????

Step-by-step explanation:

Please tell the question so i can answer it

One sample Z Test is used by cate.

According to the statement

The average tuition in Illinois is $28,950 with a standard deviation of $3,470.

Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.

So, One sample Z Test is used by cate.

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The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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Y=4x+5 and y=4x-5 has no solution

What are Linear Equations in two Variables?

The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.

Steps

[tex]Y=4x+5\\ Y=4x-5[/tex]

Substitute y=4x+5

[tex][4x+5=4x-5][/tex]

Refine [tex][4x+5=4x-5][/tex]

-10=0

-10=0 is a false ,therefore the system of a equation have no solution

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The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

Linear inequalities are inequalities that have constant average rates of change, slope or gradient

A system of linear inequalities is a collection of at least two linear inequalities.

In this case, the system of linear inequalities is given as

7x+2y > 3

x-2y < 2

Rewrite the inequalities as equations

7x+2y = 3

x-2y = 2

Make x the subject in the second equation, by adding 2y to both sides of the equation

x - 2y +2y = 2 + 2y

This gives

x = 2 + 2y

Substitute x = 2 + 2y in 7x+2y = 3

7(2 + 2y) +2y = 3

Expand the brackets

14 + 14y + 2y = 3

Evaluate the like terms

16y = -11

Divide both sides by 16

y = -11/16

Substitute y = -11/16 in x = 2 + 2y

x = 2 - 2 * 11/16

Evaluate the product

x = 2 - 11/8

Evaluate the difference

x = 5/8

Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

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Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.

The steps involved are:

Given that,

Jamie is ordering cupcakes for an office party.

There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.

Jamie purchased a total of 18 cupcakes for $55.75

The cost for a single cupcake of each flavor is as follows:

Chocolate - $3

Strawberry  - $2.75

Peanut - $3.50

Consider the number of cupcakes of each flavor as x, y, and z respectively.

So, the equations we can write from this data are,

x + y + z = 18 and

3x + 2.75y + 3. 50z = 55.75

But it is given that,

There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.

So, z = 2x

Then the above two equations become,

3x + y = 18 and

10x + 2.75y = 55.75

By solving these two equations we get,

x = 3.57 ≅ 4

y = 7.28 ≅ 7

Since we know that z = 2x,

⇒ z = 2 × 3.57 = 7.14 ≅ 7

So,

There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.

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The polynomial expression that represents the profit of selling x tablets is 10x - 100

profit = revenue – cost

= (100 + 30x) - (20x + 200)

= 100 + 30x - 20x - 200

Profit = 10x - 100

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The total surface area of the composite figure is calculated as 444 m².

Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.

Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²

Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²

Area of shared surface = 2(16)(5) = 160 m²

Total surface area = 328 + 276 - 160 = 444 m².

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2 items should be placed on the ballot to maximize the total number of votes cast on all items.

According to the statement

items on which people vote = 30

people who will vote = 240

batch containing items = 3

number of batches formed = 10

now we find the number of items placed on ballot to maximize the number of votes.

we find the average number by each items got the vote.

Average = items in batch / total votes

Average = 3/240

but if we add 2 items in the ballot then average become half.

So, 2 items should be placed on the ballot to maximize the total number of votes cast on all items.

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Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

The data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9

A measure is considered an outlier in a data-set if it is very far from other measures, especially in these two cases:

In this problem, he data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9.

The second highest value is 5.3, which is considerably less than 22.6, hence 22.6 is an outlier in the data-set.

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Answer:

A and B

Step-by-step explanation:

A : (a²+b²=c²) 11²+13²=290 (c²); c=√290

B : 7²+24²=625; c=√625=25

C : 2²+5²=29≠7²

According to the Pythagorean triple, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

The Pythagorean triple are three set of sides that can form a right triangle if the square of the longest side equals the sum of the squares of the other two smaller sides.

11² + 13² = (√290)²

290 = 290 [correct]

7² + 24² = 25²

625 = 625 [correct]

2² + 5² = 7²

29 ≠ 49 [correct]

Therefore, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

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Answer:

9cm

Step-by-step explanation:

If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm

This gives us a ratio of 1:3

PQ = LM*3 = 3cm*3 = 9cm

The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

According to the statement

we have a given that the Among the 1000 respondents,

12​% chose chocolate​ pie, and the margin of error was given as

±5 percentage points.

and we have to explain the statement that the margin of error was given as ±5 percentage​ points.

We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

And this statements also indicates the interval between the like and unlike respondents of chocolate pie.

So, this statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

So, The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

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imagine the cd/cd as 1 which is a whole number. then, add the denominators (d+c-cd)/cd

The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards

Quadratic functions are functions that has a leading coefficient of 2.

According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.

The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.

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Total number of five letter strings formed by A,B,C and D with repetitions allowed

={4x4x4x4x4 = 4 power 5 = 1024

Now, fix BAD in a string at one place then we have 2 more places to be filled with 4 letters, total number of such strings

=4x4=16

Here, BAD can be at any of the 3 positions,

Hence the total number of strings with BAD in it

= 3 x 16=48

Now, The total number of strings not containing BAD

=1024-48

=976

Using 26 letters, the number of 5-letter words that can be formed when the letters are different is determined as follows: 26P5 = 26 × 25 × 24 × 23 × 22 = 7883600 different words.

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Answer:

x=17

Step-by-step explanation:

Since they are intersecting lines, 3x=51

x=17

Answer:

x = 17

Step-by-step explanation:

When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".

3x = 51

x = 17