Without graphing, determine whether each linear system has:
one solution

no solution

or infinitely many solutions.

a) 3x - y = 17
6x + 2y = -8

b) y = 2x - 5
4x - 2y = 10

c) 5x - y = 4
-5x + y - 4 = 0

d) 2x - y = 3
x - 2y = 3

There were 4 speed bumps installed on the road leading into the house development.

What is the formula of speed when time and distance have given?

The formula is speed = distance/time

Here given,

The length of the road is 3/4 miles or 12/16 miles and the distance between each speed bump is 3/16 miles.

Now we want to obtain the number of speed bumps,

So, Number of speed bumps = (Total distance of road) / (Distance between each speed bump)

Number of speed bumps = [tex] \frac{ \frac{12}{16} }{ \frac{3}{16} } [/tex]

Number of speed bumps = [tex] \frac{12}{16} \times \frac{16}{3} [/tex]

Number of speed bumps = 4

Therefore, there were 4 speed bumps installed on the road leading into the house development.

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Triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

Given are two triangles as shown in the image given.

The given triangles are ΔKLM and ΔXYZ.

∠L = ∠Y

KM = XZ

∠M = ∠Z

So, by ASA criteria, the triangles ΔKLM and ΔXYZ are congruent.

Therefore, triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

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Grantly must place the chairs close enough so that people can easily speak with one another

Grantly is designing a sitting area that will be located outside of his client's master bedroom. He intends to furnish the area with a few rugs, an end table, and chairs.  The seats should be spaced apart just enough to allow for easy conversation while seated, but not too much that it seems crowded. For easy access, end table should be positioned close to the seats. The placement of rugs should be such that they both define seating area and add to overall attractiveness of the space.

To make sure that chairs, end table, and rugs fit properly without giving area a claustrophobic feeling, Grantly should take measurements of the available space in the sitting room. He should also consider how the master bedroom is organised as well as any existing furnishings or fixtures that could have an impact on how the sitting room furniture is arranged. Additionally, seating should be set up so that conversing with one another while seated is simple. Conversation can be facilitated and a cosy environment can be created by positioning chairs in a circula configuration, facing one another.

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t = 18, -18

To solve, we will isolate the variable t.

Given:

      0.5t² = 162

Divide both sides of the equation by 0.5:

      t² = 324

Square root both sides of the equation:

      t = 18, -18

The required solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18, as of the given condition.

To solve the equation [tex]0.5t^2 = 162[/tex], we need to isolate the variable t.

First, we can start by dividing both sides of the equation by 0.5 to eliminate it on the left side:

[tex]0.5t^2 / 0.5 = 162 / 0.5[/tex]

Simplifying:

[tex]t^2 = 324[/tex]

Next, we take the square root of both sides to solve for t:
[tex]\sqrt(t^2) = \sqrt(324)[/tex]

t = ±18

Therefore, the solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18.

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The ratio of the volume of the first cube to the volume of the second cube is 1:27. The correct option is (C).

Let's represent the length of the edge of the first cube "n" and the length of the edge of the second cube "3n".

The volume of the first cube is:

V1 = n³

The volume of the second cube is:

V2 = (3n)³ = 27n³

To find the ratio of the volume of the first cube to the volume of the second cube, we divide V1 by V2:

V1/V2 = n³ / (27n³) = 1/27

Therefore, the required ratio is 1:27.

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The correct question is as follows:

One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the

second cube?

A 1:3

B. 1:9

C. 1:27

D. 1:6

E. 1:81

The value of x is 7.99 centimeters to the nearest hundredth.

As per the given diagram, the value of x sits as the base length of the triangle.

And it is given that the hypotenuse's side length is 10 cm.

As per the cosine function,

The adjacent side to hypotenuse ratio is known as the cos function.

Adjacent Side/Hypotenuse = CosA.

Here, A = 37 degrees, adjacent side = x, and hypotenuse = 10cm.

So,

cos37° = x/10

x = 10 × cos37°

x = 7.9863551

x ≈ 7.99 cm.

Therefore, the value of x to the nearest hundredth can be described as x = 7.99 cm.

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The complete question:

Solve for x. x = [ ? ] cm, round to the nearest hundredth.

The image is attached below.

The thing that will be always true about quadrilateral ABCD is C. m∠A+m∠B=180°

The coordinates of the center of the circle is B. (6, 4)

Based on the fact that opposite angles in an inscribed quadrilateral are always equal, then m∠A+m∠B=180°. As a result, ∠A + ∠C = 180 degrees and likewise for ∠B + ∠D = 180 degrees.

The intersection of the two lines, namely, the perpendicular bisector of AB (passing through midpoint (6, 3.5) with a slope -12/7) and the vertical line whose undefined own slope penetrates the midpoint (6, 0) of AC, is exactly the center of circle, which has its coordinates as (6, 4).

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The approximation of g(-1.2) using the line tangent to the graph of g at x=-1 is 3.6.

We can use the formula for the equation of a tangent line to approximate the value of g(-1.2) using the given information:

y - y1 = m(x - x1)

m = g'(-1) = 2 (since g'(-1) = 2)

Substituting these values into the formula, we get:

y - 4 = 2(x + 1)

Simplifying:

y = 2x + 6

Now we can use this equation to approximate g(-1.2) by plugging in x=-1.2:

g(-1.2) ≈ 2(-1.2) + 6

g(-1.2) ≈ 3.6

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Answer:

Step-by-step explanation:

To find the area of the garden covered by the pond, we need to find the area of sector ACB.

First, we need to find the measure of the central angle of sector ACB. The central angle is the same as the angle formed by radii OA and OB.

Since the radius of the garden is 3 meters, we can use the Pythagorean theorem to find the length of the chord AB:

AB² = OA² + OB²

AB² = 3² + 3²

AB² = 18

AB = √18 ≈ 4.24 meters

Now, we can use the formula for the area of a sector:

A = (θ/360)πr²

where θ is the central angle and r is the radius of the circle.

The central angle of sector ACB can be found using the inverse cosine function:

cos(θ/2) = AB/2r

cos(θ/2) = 4.24/(2*3)

cos(θ/2) ≈ 0.707

θ/2 ≈ cos⁻¹(0.707)

θ ≈ 2cos⁻¹(0.707)

θ ≈ 144.1 degrees

Now we can calculate the area of sector ACB:

A = (θ/360)πr²

A = (144.1/360)π(3)²

A ≈ 10.6 square meters

Therefore, the area of the garden covered by the pond is approximately 10.6 square meters.

The volume of the triangular prism whose base = 4.8m , height = 3.2m, length = 9m is 69.12 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the base by the height and the length of the prism. The formula for the volume of a triangular prism is:

V = 1/2 x b x h x l

where b is the length of the base, h is the height of the base, and l is the length of the prism.

In this case, the base of the triangular prism has a length of 4.8m and a height of 3.2m, so the area of the base is:

A = 1/2 x b x h = 1/2 x 4.8m x 3.2m = 7.68m²

The length of the prism is 9m, as given in the problem.

Therefore, the volume of the triangular prism is:

V = A x l = 7.68m² x 9m = 69.12m³

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Two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

Let's denote the meteorologist's rainfall prediction by x.

The percent error can be calculated using the formula:

percent error = |(actual value - predicted value) / actual value| x 100%

We can use this formula to set up an equation and solve for x.

Since we want to find two possible values for x, we can use both the positive and negative versions of the percent error:

18.02% = |(43 - x) / 43| x 100% or

-18.02% = |(43 - x) / 43| x 100%

We have to find the values of x

18.02% = |(43 - x) / 43| x 100%

0.1802 = |(43 - x) / 43|

0.1802 x 43 = |43 - x|

7.7566 = |43 - x|

43 - x = 7.7566 or 43 - x = -7.7566

x = 35.2434 or x = 50.7566

Therefore, two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

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The speed of the car traveling is 42.96km/hr, under the condition  if d=0. 05v²+2. 2v.

The distance a car travels is 200. We can perform the formula d = 0.05v² + 2.2v to evaluate the speed of the car.
Staging d = 200 in the above equation, we get:

0.05v² + 2.2v - 200 = 0

Evaluating this quadratic equation gives us two values of v:

v = (-2.2 ± √(2.2² + 4 × 0.05 × 200)) / (2 × 0.05)

v ≈ -44.96 or
v ≈ 42.96

Since speed cannot be negative, we take v ≈ 42.96 as the speed of the car.
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The probability of selecting two different colors is 13/15.

The probability of selecting two different colors is determined using the complement rule as follows:

The probability of selecting two marbles of the same color from the first bag is:

P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)

P(same color) = 0 + 0 + 0 + 0 + (1/6)(2/5) + (1/6)(2/5)

P(same color) = 2/15

The probability of selecting two marbles of the same color from the second bag is:

P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)

P(same color) = 0 + 0 + 0 + 0 + (1/6)(1/3) + (1/6)(1/3)

P(same color)  = 1/9

The probability of selecting two different colors from both bags will be:

P(different colors) = 1 - (2/15) * (1/9)

P(different colors) = 13/15

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If Hi, Leon Sargetta, do you promise to pay Patrick Amina the sum of $3500. the minimum amount of Leon’s monthly payment is: c. $104.84.

Using this formula

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

where:

P = Principal = $3500

r = Monthly interest rate =  (5.5% / 12) = 0.00458333

n = Number of months in the loan term = 3 years 36 months.

Let plug in the formula

Monthly Payment = (3500 * 0.00458333 * (1 + 0.00458333)^36) / ((1 + 0.00458333)^36 - 1)

Monthly Payment  = 104.84

Therefore the correct option is C.

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Answer:

B

Step-by-step explanation:

1/3(9-6x+12)

    3-2x+4

      1-2x

Hayden can arrange his 5 trophies on the fireplace in 56 different ways.

The formula for combinations,

which is nCr = n!/r!(n-r)!, where n is the total number of items and r is the number of items being chosen. In this case, n=8 and r=5.
So, we can calculate the number of ways that Hayden can arrange his trophies as follows:
8C5 = 8!/5!(8-5)! = 8!/5!3! = (8x7x6)/(3x2x1) = 56
Therefore, there are 56 ways that Hayden can arrange his 5 trophies on the fireplace.

Hence,  Hayden can arrange his 5 trophies on the fireplace in 56 different ways using the formula for combinations.

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An equation that can be used to determine how many months Ely will need to save money to reach his goal of a total of $1,550 in his savings account is 200 + 150x = 1,550.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

Equations use the equal symbol unlike mathematical or algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.

The intended monthly savings = $150

The amount already in Ely's account = $200

The total amount Ely needs = $1,550

Let the number of months required to reach $1,550 = x

200 + 150x = 1,550

150x = 1,550 - 200

150x = 1,350

x = 9 months.

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In the year 2040, the populations of the two towns will be approximately equal.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To find the year when the populations of the towns will be approximately equal, we need to set the two equations equal to each other and solve for t:

8t² + 2000 = 100t + 3000

8t² - 100t - 1000 = 0

We can simplify this equation by dividing both sides by 4:

2t² - 25t - 250 = 0

Now we can solve for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -25, and c = -250. Plugging in these values, we get:

t = (25 ± √(25² - 4(2)(-250))) / (2(2))

t = (25 ± √(9375)) / 4

t = (25 ± 97.0) / 4

So t = 30.25 or t = -6.25. We can ignore the negative solution since we're looking for a year after 2010. Therefore, the populations of the two towns will be approximately equal in the year:

2010 + 30.25 = 2040.25

So, in the year 2040, the populations of the two towns will be approximately equal.

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An expression that is equivalent to (-3)^4/(-3)^2 is(-3)^2

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

(-3)^4/(-3)^2.

Applying the law of indices, we have

(-3)^4/(-3)^2 = (-3)^(4 - 2)

Evaluate

So, we have

(-3)^4/(-3)^2 = (-3)^2

Hence, the solution is (-3)^2

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Answer:

3^(2 + 7 - 8) = 3^1 = 3

The expression for the length of the rectangular prism is L = 9x² + 7x - 2

Given data ,

Let the length of the rectangular prism be L

Let the volume of the rectangular prism be V = 36x³ - 28x + 8

Let the height of the prism be H = 3x - 1

Let the width of the prism be W = 4

And , Volume of Rectangle = Length x Width x Height

On simplifying , we get

36x³ - 28x + 8 = L ( 3x - 1 ) ( 4 )

L ( 12x - 4 ) = 36x³ - 28x + 8

By long division , we get

       -----9x² + 7x - 2--------------------------------------

4(3x - 1) | 36x³ - 28x + 8

                  - (36x - 9x)

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

                           7x - 2

                           - (7x - 2)

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

                                          0

Hence , the length of the prism is L = 9x² + 7x - 2

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The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

The polygon is translated 6 units to the left

Given data ,

A ( 1 , 6 ) , B ( 3 , 2 ) , C ( 7 , 2 ) , D ( 5 , 6 ) transformed to A' ( -5 , 6 ) , B' ( -3 , 2 ) , C' ( 1 , 2 ) , D' ( -1 , 6 )

The given coordinates represent two sets of points, one for the original polygon ABCD and the other for the transformed polygon A' B' C' D'.

Now , we can observe that the x-coordinates of each vertex have changed, while the y-coordinates remain the same. Specifically, the x-coordinates of the original vertices have been decreased by 6 units to obtain the x-coordinates of the transformed vertices.

This indicates that a translation has been applied to the original polygon, shifting it 6 units to the left along the x-axis

Hence , the function is translated 6 units to the left

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Answer:

select me as brainliest

Feeling sleepy? Students in a high school statistics class responded to a survey designed by their teacher. One of the survey questions was “How much sleep did you get last night?” Here are the data

Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs. The Total amount Jeremiah will pay for s songs $7 + $1.25 s

We are given that Jeremiah signed up for a streaming music service that costs $7 per month.

Cost per month = $7

Cost of Offline download = $0.50 per song

Total amount Jeremiah will pay = $7 + $1.25(50)

= 7 + 62.5

= $69.5

Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs.

Therefore, Total amount Jeremiah will pay for s songs = $7 + $1.25* s

= $7 + $1.25 s

Total amount Jeremiah will pay for s songs = $7 + $1.25 s

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Answer:

1760

Step-by-step explanation:

10 x 16 x 11

160 x 11 = 1760

The number of miles driven if the cost of renting a car is $130 with a cost function of c(m) = 0.05m + 30 is 2000 miles.

We can start by setting up an equation to solve for the number of miles driven, m

c(m) = 0.05m + 30 (where c(m) is the cost of renting a car)

We know that the cost is $130, so we can substitute that into the equation

130 = 0.05m + 30

Now we can solve for m

130 - 30 = 0.05m

Subtract the numbers

100 = 0.05m

m = 100/0.05

Divide the numbers

m = 2000 miles

Therefore, the number of miles driven is 2000 miles

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The given question is incomplete, the complete question is:

If c(m)=0. 05m + 30 represents the cost of renting a car, how many miles were driven if the cost is 130$?

The length of the arc shown in red is 5.2359 radians

We know that the formula for the length of the arc of a circle.

s = r × θ

where s represents the arc length (in radians)

r represents the radius

and θ is the central angle in radians

From the attached figure of the circle, the radius of the circle r is 10 cm.

Here, the arc length is given in degrees.

We know that central angle = arc measure

So, the central angle θ = 30°

θ = 0.52359 radians

Using above formula of the arc length,

s = r × θ

s = 10 × 0.52359

s = 5.2359 radians

Thus, the arc length = 5.2359 radians

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