The solution to a system of two linear equations is x = 3; y = 9.
How could the intersection of the graphs of the two equations be located on a coordinate grid?
What does the solution to a system of two linear equations mean on the graph? The point where
Can you have more than one solution to a Linear system of equations? Yes, because the
Can you have exactly two solutions to a Linear system of equations? The point that th
Can you have no solutions to a Linear system of equations? No, because line
:: From the origin, move 3 units up and 9 units right
The point of inte!
:: From the origin, move 3 units right and 9 units up
:: Yes, if the lines are parallel
:: Yes, if both lines are the same exact line

Surface area of a rectangular prism is 136 sq. units.

Length of the base of prism, l = 4 units

Breadth of the base of prism, b = 3 units

Height of the base of prism, h = 8

Surface area of a rectangular prism is given as,

SA = 2(lb + bh + lh)

SA = 2[(4 x 3) + (3 x 8) + (4 x 8)

SA = 136 sq. units

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Answer:

If im not mistakeing

Step-by-step explanation:

(-15,2)

OR

2,15

or 2,-15

it's one of those three. im srry

Answer:

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

y = x² −7x + 7

Complete the square for y = x² −7x + 7

(x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Set y equal to the new right side.

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

So, the answer is y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Answer:

B

Step-by-step explanation:

I think that may be right if it is have a good day,:))

The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c)  At least one PE is 18 girls

How to determine the numbers?

Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

From the given parameters,

(a)  The number that play both PE is given as

13 - x + x + 17 - x + 1 = 25

Solving the equation to get the value of x

13+17-x = 25

⇒ 31 -x =25

Collecting like terms we have

-x = 25 - 31

- x = -6

Dividing by a minus we have

x = 6

This means that 5 girls play both PE

(b)  Number that play gymnastic but not acrobat is given as

Gymnastic only that is

13 - x

13 - 6 = 7 girls

(c)  Number that play at least one game is calculated thus:

n(G) ∪ n(A)

That is (13 - x )  + (17 - x)

= 13-6 + 17 -6

7 + 11 = 18 girls

The equations of the circles in standard form, obtained from the coordinates of the center and the points on the circle are;

5) (x + 16)² + (y + 16)² = 3²

6) (x - 15)² + (y + 7)² = 8

7) (x + 6)² + (y + 2)² = 6²

8) (x + 9)² + (y + 3)² = 89

The standard form of the equation of a circle is; (x - h)² + (y - h)² = r²

Where;

(h, k) = The coordinates of the center of the circle

5) The center of the circle is (-16, -16)

The coordinates of a point on the circle is (-13, -16)

Therefore; r² = (-13 - (-16))² = 3²

The equation of the circle in standard form is therefore;

(x - (-16))² + (y - (-16))² = 3²

(x + 16)² + (y + 16)² = 3²

6) The coordinates of the center of the circle = (15, -7)

The coordinate of a point on the circle = (17, -5)

r² = (17 - 15)² + (-5 - (-7))² = 8

The equation is; (x - 15)² + (x - (-7))² = 8

(x - 15)² + (x + 7)² = 8

7) The coordinates of the center = (-6, -2)

The coordinate of a point on the circle = (-12, -2)

The square of the radius is therefore; r² = (-6 - (-12))² = 6²

(x - (-6))² + (y - (-2))² = 6²

(x + 6)² + (y + 2)² = 6²

8) The coordinates of the center is; (-9, -3)

The point on the circle is; (-1, -8)

The square of the radius is; r² = (-1 - (-9))² + (-8 - (-3))² = 89

The equation of the circle is therefore; (x - (-9))² + (y - (-3))² = 89

(x + 9)² + (y + 3)² = 89

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The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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Given:

[tex]\sf y = 4x + 5[/tex]

Switch x and y.

[tex]\sf x = 4y + 5[/tex]

Solve for y.

[tex]\sf 4y = x - 5[/tex]

[tex]\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}[/tex]

[tex]\Rightarrow\boxed{\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}}[/tex]

Based on the tangent line and the radii, the value of x given that AB is tangent to the circle is 10

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

AB is tangent to the circle

As a general rule:

The radius of circle is perpendicular to the tangent line

This means that we can calculate x using the Pythagorean theorem

So, we have

x^2 = 6^2 + 8^2

Evaluate the sum of exponents

So, we have

x^2 = 100

So, we have

x = 10

Hence, the calculated value of x in the circle is 10

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The range of the function, in dollars, is

R: [50, 510]

The range of a function is the set of possible outputs of said function. In this case, we know that the function is:

E = 50 + 2v

Where v is the number of games sold.

Here the domain will go from v = 0 (no games sold)

to v = 230 (the number of the play's audience)

Then the range is:

E = 50 + 2*0 = 50

E = 50 + 2*230 = 510

R: [50, 510]

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The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

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The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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The area of the rhombus is 33 square unit.

We have,

x = 6 units, y = 3 units, and h = 5 units.

Now, area of Triangle

= 2 x 1/2 x b x h

= 2 x 1/2 x 6 x 3

= 18 square unit

and, area of Rectangle

= l w

= 5 x 3

= 15 square unit

Thus, the Area of Rhombus

= 18 + 15

= 33 square unit

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Answer: Its high

Step-by-step explanation: It just is

The probability that Brent draws mismatched socks is 32/153.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.

Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.

For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.

Let's consider the first case.

There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.

For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.

Therefore, the probability of Brent drawing mismatched socks is:

= (32 + 32) / 306

= 64 / 306

= 32 / 153

Thus, the probability that Brent draws mismatched socks is 32/153.

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Investing could help you grow your funds over time. For example, if you were to invest $30 per month in a stock mutual fund that has a long-term average annual return of 8%, after 10 years, your investment could grow to about $5,000.

This could provide you with more financial security and give you the opportunity to reach your financial goals faster than keeping your money in a savings account.

Some investment products that you could consider are stocks, bonds, mutual funds, and exchange-traded funds (ETFs). You could also consider robo-advisors, which use algorithms to create and manage investment portfolios for you based on your goals and risk tolerance.

When it comes to choosing investments, there are a few things you can consider. First, think about your financial goals and your time horizon. This will help you determine how much risk you can afford to take on.

Thus, if you have a long-term goal, such as saving for retirement, you may be able to afford to take on more risk than if you have a short-term goal, such as saving for a down payment on a house.

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The three adverbs in the sentence are:

hard (modifying the verb "raining")

clearly (modifying the verb "see")

almost (modifying the verb "crashed")

1) "Hard" is an adverb of manner that describes how the rain was falling. It indicates that the rain was falling with intensity or force, which made it difficult for the driver to see.

2) "Clearly" is an adverb of manner that describes how the driver was seeing. It indicates that the driver was having difficulty seeing due to the heavy rain, which was affecting their vision.

3) "Almost" is an adverb of degree that modifies the verb "crashed." It indicates that the driver came very close to crashing their shiny new car, but managed to avoid a collision at the last moment.

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Answer:

approximately 7.07 square feet

Step-by-step explanation:

To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius of the circle.

Given the radius of the circle is 1.5 ft, we can substitute this value into the formula:

A = π(1.5)^2

A = 7.07 square feet (rounded to the nearest hundredth)

Therefore, the area of the circle is approximately 7.07 square feet.

Answer:

A= 1.77 units squared.

Step-by-step explanation:

To find your answer, you would first need the formula. It would be A=πr2. In your image, 1.5cm is the diameter, twice the radius. How to find the radius is easy. To do that, you would divide by two.

1.5/2 <---- shown here (which would equal 0.75)

A=πr2

A=π(0.75)2

A=π(0.5625)

A= 1.76625

However, to round your answer, you would get 1.77

Answer: A.

Step-by-step explanation:

    The range is the difference between the minimum and maximum values. We look at the dashed lines for these values. Ava's Average Autos have a larger spread of prices, as shown by the longer box plot for their store.

[tex] \\ 7 \sqrt{ \\ + 45)4} [/tex]

Answer:

4 feet

Step-by-step explanation:

Their is one rectangular prison divided into two.

The volume of the first one is

V1= L X H X W=80.

Volume of the second one is

V2= L X H X W

V2= 6 X H X 5

V2 = 30H

Now from the question, the total volume is 200cubic feet which means V1 + V2 = 200, recall that V1=80 and V2=30H, so we say;

80+30H=200, collecting the like term we have, 30H=200-80.

30H=120, divide both side by 30

30H/30=120/30

H= 4feet.

Height is 4feet.

Answer: 2,556 seats

Step-by-step explanation

18 x 142 =2,556 seats

Answer: y = 2x + 2

Step-by-step explanation: First, you find slope between the points with point slope form. (8-(-6))/(3-(-4) = 2.

2 is the slope.

Now we have y = 2x + b.

To find b, we pick a coordinate and insert the values.

8 = 2(3) + b

8 = 6 + b

8 - 6 = b

b = 2

Put it together, you have y = 2x + 2

The simplified expression is  [tex]7 x^{3} - 14 x^{2} + 28 x - 55+\frac{124}{x + 2}[/tex]. The correct answer is an option (C).

The expression is given as follows:

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}[/tex]

We can use polynomial long division to simplify the expression:

         7x² - 14x² + 28x - 55

        ______________________

x + 2 ) 7x⁴ + 0x³ + 0x² + x + 14

          7x⁴ + 14x³

       ___________

               -14x³ + 0x²

               -14x³ - 28x²

               ____________

                        28x² + x

                        28x² + 56x

                        __________

                               -55x + 14

                               -55x - 110

                               ________

                                       124

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}=7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

Hence, the simplified expression is as follows:

[tex]7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

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Answer:

  $2080

Step-by-step explanation:

You want to know the annual cost of coffee purchased 5 mornings and 3 afternoons per week when each purchase amounts to $5.

Five morning visits and three afternoon visits to the coffee shop will be a total of 8 visits per week. At $5 each, the cost per week is ...

  8 × $5 = $40

The cost for a year will be the cost for 52 weeks:

  52 × $40 = $2080

Carla spends $2080 per year on coffee.

Whether this is a "little indulgence" or not will depend on Carla's budget.

The experimental probability that an arrangement will contain at least one yellow balloon is 0.767. Then the correct option is C.

Given that:

Each balloon arrangement in Ethan's class has four balloons in it. The likelihood of each balloon being red, blue, or yellow is equal. To represent this possibility, Ethan made a spinner.

ybrr, bybb, rbbb, rrry, rbbb, rryy, yybb, ryry, ryyr, rbyr, ryyr, rryy, rrrr, yrby, bbyy, byyr, byyr, byyb, rbby, ybry, rryy, rbrr, rybb, bbbr, rrbr, ybry, ryrr, rryb, rrrb, rryr

The experimental probability that an arrangement will contain at least one yellow balloon is calculated as,

P = 23 / 30

P = 0.767

Thus, the correct option is C.

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We can see here that x will be = 123.4°.

A polygon is actually known to be a two-dimensional geometric shape. It is a shape that is known to be defined by a closed path. It consists of finite sequence of straight line segments.

The segments are actually known as sides or edges and which are connected at vertices or corners.

Looking at the shape, we see that the regular pentagon and heptagon are joined together on one side.

Thus, exterior angle of a regular pentagon (5 sides) = 360°/5 = 72°.

The exterior angle of a regular heptagon (7 sides) = 360°/7 = 51.4°

Thus, x° = 72° + 51.4° = 123.4°

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Answer:

x = 5

y = 5√2

Step-by-step explanation:

In a 45-45-90 degree right triangle, the two legs form the right angle, and the hypotenuse is opposite the right angle.

The side lengths of a 45-45-90 right triangle are in the ratio

1 : 1 : √2

The legs are congruent, so if one leg has length 5, the other leg also has length 5.

The hypotenuse is √2 times the length of the legs.

x = 5

y = 5√2

The length of the line segment AB = 16 units

Given data ,

Let the length of the line segment AB = 2x - 4

Let the length of the line segment BC = 3x + 2

Now , AC = 48 units

So , AC = AB + BC

On simplifying the equation , we get

2x - 4 + 3x + 2 = 48

5x - 2 = 48

Adding 2 on both sides , we get

5x = 50

Divide by 5 on both sides , we get

x = 10 units

So , the length of AB = 2 ( 10 ) - 4

AB = 16 units

Hence , the length is AB = 16 units

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The length of each rope if all the ropes had the same length is 3 ft

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

The dot plot

From the dot plot, we can see that the data are normally distributed

This means that the length of each rope is the mean, the median and the mode

Given that the data on the dot plot is normally distributed, we have the following values

So, we can conclude that the length is 3 ft

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Answer:

To find 40% of a number, you can multiply the number by 0.4 or divide it by 2.5.

Using this method, we get:

40% of 100 is 40 (100 x 0.4 or 100 ÷ 2.5)

40% of 110 is 44 (110 x 0.4 or 110 ÷ 2.5)

40% of 140 is 56 (140 x 0.4 or 140 ÷ 2.5)

40% of 120 is 48 (120 x 0.4 or 120 ÷ 2.5)

Therefore, 40% of 100 is 40, 40% of 110 is 44, 40% of 140 is 56, and 40% of 120 is 48.