Determine if the given point is a solution of the system of inequalities.
Help please.

In the expression 2t+8, 8 represents the number of seats at each table.

An expression is combination of variables, numbers and operators.

Given that A coffee shop has a group of seats at the counter and t individual tables.

where each able has the same number of seats.

2t + 8 represents the total number of seats in the restaurant.

8 represents the number of seats at each table and 2t is the number of individual seats.

Hence, in the expression 2t+8, 8 represents the number of seats at each table.

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By cancelative property, the roots of quadratic equation x² + 4 · x - 20 are: Exact: - 2 + 2√6, - 2 - 2√6, Approximate: 2.899, -6.899.

In this problem we must factorize a quadratic equation and use an algebraic property known as cancelative property, defined as:

If a · b = 0, then a = 0 or b = 0.

In addition, we can apply the following factorization rule:

x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)

First, factorize the quadratic equation:

x² - (- 2 + 2√6 - 2 - 2√6) · x + (- 2 + 2√6) · (- 2 - 2√6)

(x + 2 - 2√6) · (x + 2 + 2√6)

Second, apply cancelative property:

x + 2 - 2√6 = 0

x = - 2 + 2√6

x + 2 + 2√6 = 0

x = - 2 - 2√6

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Answer:

$1,684.25

Step-by-step explanation:

(.85 x 1250) = 1062.50  If we take off 15% we leave on 85% which as a decimal is .85

Now add the tax

1062.50 + .06(1062.50)

1620.50 + 63.75

1684.25

The original price of the sofa before the discount is $241.11.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Let the original price of the sofa be x.

Given that 72% of the original price is $173.60, this can be written mathematically as follows:

72/100 × x = 173.60

72x = 17360

x = 241.11

Hence, the original price of the sofa before the discount is $241.11.

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Answer:

5 hours

OR

300minutes

Step-by-step explanation:

1 degree lost 1 hour

5 degrees lost (5×1) hours

5hours

1 hour=60 minutes

5hours= (5×60)

300minutes

Answer: $5.55

Step-by-step explanation: 15% = 0.15

                                             37 / 0.15 = 5.55

A graph of the solutions of this inequality 3x + 2 ≥ 1/2(x + 5) is shown on the number line attached below.

In this exercise, we would solve the given inequality by making x the subject of formula as follows;

3x + 2 ≥ 1/2(x + 5)

By multiplying both sides of the inequality by 2, we have the following:

(3x + 2) × 2 ≥ 1/2(x + 5) × 2

6x + 4 ≥ x + 5

By rearranging and collecting like terms, we have the following:

6x - x ≥ 5 - 4

5x ≥ 1

x ≥ 1/5

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the greater than or equal to (≤) symbol.

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The equation has one solution

The solution to the equation is  x = 3

4(2x – 5) = 4

To solve this, we would first have to open the bracket.

4 * 2x - 4*5 = 4

8x - 20 = 4

We would want to have the variable x stand on its own

so we take like terms

8x = 4 + 20

8x = 24

To get the value of x divide through the equation by 8

x = 24 / 8

x = 3

The solution is just one at x = 3

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The variable 'time to destination' quantitative.

Quantitative variables are those whose values are obtained through measurement or counting. A qualitative variable, also referred to as a category variable, is a non-numerical variable. It describes information that can be categorized. Examples like Eye colors, States, Dog breeds etc.

Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. Generally speaking, a variable is considered to be quantitative if it can be used mathematically (such as addition). Otherwise, it's top-notch. You cannot, for instance, add blue and green.

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For the given similar triangles, the value of x = 5.

Similar triangles share the same associated angle measurements and proportional side lengths.

Due to their similar shapes, two figures that are not always the same size can appear comparable. We might claim, for instance, that all circles are equivalent. Squares and equilateral triangles share similar characteristics. Although similar figures need not be congruent in order to be comparable, congruent figures are always comparable.

Despite having the same shape, similar triangles have different diameters. In identical triangles, corresponding angles are equal. In analogous triangles, the ratio of the corresponding sides is the same. Any pair of equivalent sides' squares and any comparable triangle's area have the same ratio.

As the given triangles are similar,

the sides are in same ratio,

⇒ 56 / 8x - 5 = 24 / 15

⇒ 8x - 5 = 35

⇒ 8x = 40

⇒ x = 5

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Question 6:

The relationship between ∠2 and ∠7 is that they are corresponding angles.

Question 8:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=m∠1 so 180°

Question 9:

Options A, C, and D are correct.

*Note*

For option B the angles are supplementary.

For option E the angles are vertical angles.

Question 10:

∠1 and ∠2 lie in the interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal.

The probability of  4 in the tens place is [tex]\frac{1}{9}[/tex], the probability of  at least one 4 in the tens place or the units place is [tex]\frac{1}{5}[/tex], the probability no 4 in either place is [tex]\frac{4}{5}[/tex].

(a) total number of 2-digit terms =(99 - 10) + 1 = 90

n(s) = 90

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

number of 2 digits that have 4 in tens place = 40, 41, 42 ......49

n(a) = 10

P(A) =[tex]\frac{ n(a)}{n(s)}[/tex]

Substituting the values

P(A) = [tex]\frac{10}{90}[/tex]

P(A) = [tex]\frac{1}{9}[/tex]

Therefore, P(A) = [tex]\frac{1}{9}[/tex]

(b) From the previous one, we know the P(A) = [tex]\frac{1}{9}[/tex]

Number of 4's in units place = 14, 24, 34.....94 = 9

n(b) = 9

P(B) = [tex]\frac{ n(b)}{n(s)}[/tex]

Substituting the values

P(B) = [tex]\frac{9}{90}[/tex]

P(B) =[tex]\frac{1}{10}[/tex]

P(A and B) = [tex]\frac{1}{10}[/tex]

Using OR probability, we have

P(A or B) = P(A) + P(B) - P(A and B)

P([tex]\frac{1}{9}[/tex] or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{9}[/tex] + [tex]\frac{1}{10}[/tex] - [tex]\frac{1}{90}[/tex]

P([tex]\frac{1}{9}[/tex]or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex]

Therefore, P([tex]\frac{1}{9}[/tex]or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex]

(c) Probability of no 4 in either place = 1 - ( probability of 4 in either place)

= 1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Therefore, probability of no 4 in either place = [tex]\frac{4}{5}[/tex]

Therefore, the probability that the integer chosen has a 4 in the tens place is [tex]\frac{1}{9}[/tex], P([tex]\frac{1}{9}[/tex] or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex], and probability of no 4 in either place = [tex]\frac{4}{5}[/tex].

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The area of the tin box without the top is 39100 square cm.

The cost of making this tin box is  Rs. 19550.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, A tin box of 1 m in length, 85cm in width, and 60cm in depth is to be made.

We know the total surface area of a cuboid is 2(lw + wh + wl).

Therefore, The surface area of the cuboid without the top would be,

= 2(lw + wh + wl) - (l×w).

= 2(100×85 + 85×60 + 85×100) - (85×60).

= 2(22100) - 5100.

= 44200 - 5100.

= 39100 square cm.

The cost of making this tin box is Rs.(39100×0.50).

= Rs. 19550.

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She would be doing 9 hours of studying per day and 6 hours of other activities. This is because 15 hours divided by 9 hours of studying and 6 hours of other activities would equal the same amount of time allocated to each activity.

The amount of studying she is going to do per day is 9 hours, and the amount of other activities she is going to do per day is 6 hours.   This means that she will be dedicating roughly 60% of her waking hours to studying and 40% to other activities. This is a good balance between the two activities, and it will ensure that she is able to adequately focus on both her studies and other activities.

This balance will also help her to stay motivated and not become overwhelmed by her studies. Having a set amount of time for both activities will also help her to organize her day and stay on track. It will give her a sense of structure and allow her to plan her day accordingly.

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Answer:

Step-by-step explanation: using the y-intercept form, I see the y-intercept is 40 , at the point (0,40)

and we have a point (4,160), so

slope = (160-40)/(4-0) = 30

equqtion: y = 30x + 40 or 30x - y = -40

The inequality of the statement is y/4 ≤ 19

From the question, we have the following parameters that can be used in our computation:

A mathematical statement represented as

the quotient of y and 4 is at most 19

The variable in the above statement is y

This means that the quotient of y and 4 cannot exceed 19

The term cannot exceed implies less than or equal to

So, we have the following representation

y/4 ≤ 19

Hence, the statement is

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The surface area of the rectangular prism is 112 square metes.

The sum of all area of each surface that make up an object is referred to as its surface area.

So that in the given question,

Area of a rectangle = length x width

i. area of its base = length x width

                            = 8 x 2

                            = 16 sq. m

ii. area of its front surface = length x width

                                      = 4 x 8

                                      = 32 sq. m

iii. area of it one of its sides = length x width

                                    = 4 x 2

                                    = 8 sq. m

Therefore,

surface area of the rectangular prism = (2 x 16) + (2 x 32) + (2 x 8)

                                       = 32 + 64 + 16

                                       = 112

The surface area of the rectangular prism is 112 square meters.

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Answer:

24 days = 1500 tables

25 days = Fewer than 1500 tables

Step-by-step explanation:

So we have the inequality of < which is fewer than. Let's start by labeling all the numbers given.

What we want to find is how many days, so we'll make days = x

2100 is the initial and they sell 25 a day... 25 a x.

Combining them all we get a basic inequality of:

2100 - 25x < 1500

Let's get X alone.

Subtracting 2100 from both sides gives you

-25x < -600.

We have negatives on both sides. For me, if I see that, I make both of them positive;

25x < 600

Last step is to divide the 25 out of the X which means you'll divide 25 by 600 also

X = 24

Which means day 24 will be exactly 1500. We wanted fewer though, so adding a day gives you an answer of 25 days.

The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

where, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points.

Now putting the values

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)[/tex]

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)[/tex]

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)[/tex]

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = [tex]\sqrt{(-2-1)^2+(3-1)^2}[/tex]

r =[tex]\sqrt{(-3)^2+(2)^2}[/tex]

r = [tex]\sqrt{9+4}[/tex]

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

The result of the division of the number by 100 gives 3.05109 in decimal.

A decimal is really a number that is divided into two parts: another whole and a fraction.

For the given number.

= 305.109 ÷ 100

Then point will shift to 2 decimals towards left.

= 3.05109

Thus, the result of the division of the number by 100 gives 3.05109 in decimal.

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Answer:

Two statement are true.

O The function is increasing on the interval (-∞, 0).

O The function is increasing on the interval (0, ∞).

Step-by-step explanation:

The function h(x) = 3x is a linear function (straight line) with a slope of 3, and a y-intercept of 0.  The constant, positive slope means that h(x) will increase over the interval (-∞, ∞).

See the attached graph.

Answer:

d. Yes, this function is linear; the slope is -100 feet/second.

Step-by-step explanation:

Find the difference in height at two different time periods.

If

Δh = difference in height values

Δt = difference in seconds

then

[tex]\mathrm{slope = \dfrac{\Delta h}{\Delta y}}[/tex]

Take the difference in heights at t = 0 and t = 5

The height drops from 4000 to 3500 feet so Δh = 3500 - 400 = -500

Δt = 5- 0 = 5 seconds

slope = -500/5 = -100

If you compute the slope between any pair of heights and time difference you will get the same value

So slope is constant indicating a linear function

Answer: 8y-56

Step-by-step explanation: the equivalent expression is 8y-56

Answer: 8y - 56

Step-by-step explanation: Hello! Here are the steps to solve this:

8(y - 7)            Use the distributive property, distribute 8 to y and 8 to -7

8y - 56           8 x y = 8y, 8 x -7 = -56

8y - 56 is an equivalent expression to 8(y - 7) because it is simplified.   I hope this helps!

Answer

  5518

28/154504

154504

1 4 0      

 1 4 5    

 1 4 0    

     5 0  

     2 8  

     2 2 4

     2 2 4

         0

The distance travelled by Jasmine in 3 1/5 hours is 108 miles.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

Plug in given values into the above equation and solve for distance.

Speed = Distance / time

Distance = Speed × Time

Distance = 33 3/4 × 3 1/5

Convert to improper fraction

Distance = (33 × 4 + 3)/4 × ( 3 × 5 + 1)/5

Distance = 135/4 × 16/5

Distance = 2160 / 20

Distance = 108 miles

Therefore, the distance covered is 108 miles.

Option D) 108 miles is the correct answer.

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The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

A positive exponent indicates that the base should be multiplied by that many.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. Negative exponents like xn can be rewritten as 1 / rs. As an illustration, qr^-4  s^6 q ^-8 s^6 q^-1 rs^6

The Power Rule for Exponents is a further exponent rule that follows from this. You multiply the exponents while keeping the base constant to simplify a power of a power. As an illustration, b for any positive s^6 q ^-8 s^6 q^-1 rs^6 number x and integers q and s.

⇒ qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁸ × r⁻⁴ × s⁹

[tex]$ \Rightarrow \frac{1}{q^8} \times \frac{1}{r^4} \times s^9[/tex]

[tex]$ \Rightarrow \frac{s^9}{q^8r^4}[/tex]

Thus , The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

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Answer:

F(x)=-x^2

Step-by-step explanation:

The one example of function with range of only negative number is:

F(x)=-x^2

Why this? We know for every x, x^2 is positive. So -x^2 will be negative.