Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is (/,/)

The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.

A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.

When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.

So that we can find real solution of quadratic equation by finding discriminant of given equation.

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The equation for new function is,

⇒ f (x) = ∛( 1/4x - 6) - 5

A relation between a set of inputs having one output each is called a function.

Given that;

The parent function is,

⇒ g (x) = ∛x

Now, After  reflected and stretched by 4, we get;

⇒ g (x) = f (1/4x) = ∛ 1/4x

And, After translated 6 units to the right, we get;

⇒ g (x) = f (x - 6) = ∛ 1/4x - 6

And, After 5 unit down, we get;

⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5

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The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.

From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

The maximum time (in seconds) that she can take on her last lap and still make the team will be:

= (60 × 5) - (63 + 62 + 65 + 58)

= 300 - 248

= 52

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When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.

given

by Pythagoras theorem

[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]

When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

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Answer:

k = 9

Step-by-step explanation:

According to the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

given (x - 6) is a factor of f(x) then f(6) = 0 , that is

3(6)³ - 17(6)² - 6k + 18 = 0

3(216) - 17(36) - 6k + 18 = 0

648 - 612 - 6k + 18 = 0

36 - 6k + 18 = 0

54 - 6k = 0 ( subtract 54 from both sides )

- 6k = - 54 ( divide both sides by - 6 )

k = 9

Teaching two step equations is a standard that needs to be taught in both 7th and 8th grade middle school PreAlgebra Math.

Two step equations are algebraic equations that can be solved in exactly two steps and gives the final answer of the variable in two steps. Generally two step equations are of the form ax + b = 0  where a and b are real numbers.

A two-step equation is an equation that requires two steps to solve. We must eliminate any constant that is on the same side as the variable first. To solve first use the inverse operations to isolate the variable by itself. We can do only one operation in single step.

Now

we solve two steps equation in grade 7th and 8th.It is very easy to understand.

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Answer:

Each child will have 3/16 pound of Halloween candy.

Step-by-step explanation:

To find out how much candy each sibling gets, we need to divide 3/4 by 4

3/4 divided by 1/4 = 3/16

Therefore, our answer is 3/16.

The total number of rectangles you can draw using the grid lines exists 1296.

A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.

A square is a particular type of closed figure that has four straight sides, four right angles, and sides that are all the same length. As a result, we can say that: A square is a particular variety of rectangle. Rectangles are not always squares, but squares are always rectangles.

Number 2 × 2 squares have 4 black squares

all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.

there are 6 × 6 = 36   3 × 3 squares

there are 5 × 5 = 25   4 × 4 squares

there are 4 × 4 = 16    5 × 5 squares

there are 3 × 3 = 9     6 × 6 squares

there are 2 × 2 = 4     7 × 7 squares

there is   1          8 × 8 square

Summing we get 91 squares

The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.

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The total number of rectangles you can draw using the grid lines exists 1296.

A shape with two opposing sides that are equal and parallel is called a quadrilateral. It has four sides, four 90-degree angles, and is a polygon. A rectangle is a two-dimensional form.

An example of a closed form with four straight sides, four right angles, and all sides being the same length is a square. Therefore, we can state that a square is a certain type of rectangle. Squares are not always rectangles, but rectangles are always squares.

Number 2 × 2 squares have 4 black squares

all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.

there are 6 × 6 = 36   3 × 3 squares

there are 5 × 5 = 25   4 × 4 squares

there are 4 × 4 = 16    5 × 5 squares

there are 3 × 3 = 9     6 × 6 squares

there are 2 × 2 = 4     7 × 7 squares

there is   1          8 × 8 square

Summing we get 91 squares

The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.

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Answer:

$400

Step-by-step explanation:

If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment

The fraction expression as a product expression is 1/2 * 2/5

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

A mathematical expression

The mathematical expression is given as

1/5

In this case, the expression is a fraction

Using the above as a guide, we have the following:

Fraction = 1/5

Multiply the fraction by 1

So, we have the following representation

Fraction = 1/5 * 1

Express 1 as 2/2

This gives

Fraction = 1/5 * 2/2

Swap the factors of the expression

This gives

Fraction = 1/2 * 2/5

Hence, the product expression is 1/2 * 2/5

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The value of the PU in the given triangle is 19.

The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Given,

'p' is the centroid of triangle XYZ and XU is 57.

Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'

from the centroid Theorem, we can write;

XP = 2/3 * XU

plug the values 'XU' in the above equation:

XP = 2/3 *57

XP = 2*19

XP = 38

from figure:

XP + PU = XU

PU = XU - XP

Plug 'XU' and 'XP'

PU = 57 -38

PU = 19

therefore, the PU of the given triangle is 19 units.

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Complete question:

The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because ,  it is opposite to the angle 90°.

Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .

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The perimeter of the right triangle is 228 inches

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.

Since it is a right triangle,

c² = 57² +76²

c² = 3249 + 5776

c² =  9025

c=  √ 9025 = 95

Perimeter is the sum of all sides

Perimeter = 57+76+95 = 228 inches

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Answer:

1408 yards

Step-by-step explanation:

A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:

4224 feet / 3 feet/yard = 1408 yards

So a horse walks 1408 yards in 12 minutes.

The area of the triangular plot of land from the vertices is 20 square units

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

A(1,5), B(7,5), and C(8,0)

Represent the vertices properly

So, we have the following representation

A = (1,5)

B = (7,5)

C = (8,0)

The area of the triangle is calculated from the vertices using the following equation

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|

Evaluate the sum of products

Area = 0.5 * |40|

Remove the absolute bracket

Area = 0.5 * 40

Evaluate

Area = 20

Hence, the area of ABC with vertices is 20 square units

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Complete question

The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)

Calculate the area.

The smallest positive integer that is both multiple of 4 and 7 is 2

In mathematics, multiples are the results of multiplying an integer by a given number.

The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.

The multiples of 4

4 8 12 16 20 24 28 32 36 .......

The multiples of 7:

7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....

The smallest common multiple is 28

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There are 8 half dollars and 9 quarters inside the cup.

We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.

Let h be the number of half dollars and q be the number of quarters.

The first equation represents the total number of coins in the cup:

The second equation represents the total value of the coins:

To solve for h and q, we can use either the substitution or elimination method.

By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.

So, q = 17 - h

then substitute it into the second equation:

0.5h + 0.25(17 - h) = 5.50

By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9

So, there are 8 half dollars and 9 quarters inside the cup.

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Yes, the horizontal asymptote is at y = 4.

The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.

Here we have given the expression y = 4.

In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,

The first process is to label the graph with x and y axis.

And then we have to defines the scale for the for the graph.

Now, we have to input the expression y = 4 on the graph then we get the graph like the following.

While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.

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The scale factor for the length is 12/8 = 1.5 and the scale factor for the width is 15/10 = 1.5

So the scale factor used to make an enlarged version is 1.5.

A scale factor is a value used to multiply the dimensions of an object in order to increase or decrease its size. It is often represented as a ratio, such as 1:2 or 1/2, which indicates that the new object is half the size of the original object. Scale factors can also be expressed as a decimal or a percentage, such as 0.5 or 50%. Scale factors can be used in various fields such as architecture, cartography, and graphic design.

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The correct answer is (D) 0.75. The probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%

We know that there are 8 possible outcomes when rolling the number cube (1, 2, 3, 4, 5, 6, 7, 8). Of these 8 outcomes, 5 of them are numbers greater than 4 (5, 6, 7, 8). So, the number of favorable outcomes is 5.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: P(number greater than 4) = 5/8. As a decimal, this is 0.625. However, the question asked for P(number greater than 4) which means we have to add 0.125 to 0.625, the answer is 0.75.

Therefore, the probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%. This means that if we roll the cube many times, we expect 75% of the rolls to be numbers greater than 4.

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The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.

Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.

Given that:

A = $10,000

r = 4% = 0.04

t = 5 years

n = 12 (since the compounding is monthly)

P = ?

The compound interest is given as follows:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Substituting the values in the formula we have:

[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]

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The value of x is 10.66

Complementary angles  is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.

If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

Collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Therefore, the value of x is 10.66

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Answer:

x=3 y=1

Step-by-step explanation:

-2/3x+3=2x-5

x=3

y=-2/3(3)+3

y=1

y=2(3)-5

y=1

Answer: , P = 2 +3g

Step-by-step explanation:

Answer:

there's one solution bc the lines have one point in common

10.  This system has one solution with coordinates (1, -2)

11. This system has one solution with coordinates (0,-3)

12. This system has one solution with coordinates(-1, -2)

13. This system has no solution.

14. This system has no solution.

16.   This system has one solution with coordinates (0,-4)

According to question:-

10. y = x - 3 ------- 1

y = -5x + 3 ------- 2

substitute 1 in 2,

x - 3 = -5x + 3

x = 1

y = 1 - 3 = -2

y = -2

The co-ordinates is (1,-2)

11. y = -3

substitute in y = x-3

-3 = x - 3

x = 0

The co-ordinates is (0,-3)

12. y = 4x + 2 --------- 1

y = -2x - 4 ------------2

Substitute 1 in 2,

4x + 2 = -2x - 4

6x = -6

x = -1

substitute x = -1 in 2

y = -2

The co-ordinates is (-1, -2)

13. y = x - 6 -----1

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

It has no solution, so there is no co-ordinates.

14. x + y = 4

3x + 3y = 12

It has no solution, so there is no co-ordinates.

16. 2x + 3y = 12 ------1

2x - y = 4 --------2

from 2 we rewrite the equation as y = 2x-4

Sub in eq 1

2x + 3(2x-4) = 12

2x + 6x - 12 = 12

8x = 24

x = 3

y = 2

The co-ordinates is (3,2)

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Answer:

The difference in costs including tax between the two nights is $53

Step-by-step explanation:

To find the cost of the hotel suite on Monday including tax, we first calculate the amount of tax by multiplying the room rate by 6% (0.06):

$299.00 * 0.06 = $17.94

So the total cost of the room on Monday including tax is:

$299.00 + $17.94 = $316.94

Next we find the cost of the hotel suite on Friday including tax:

$349.00 * 0.06 = $20.94

So the total cost of the room on Friday including tax is:

$349.00 + $20.94 = $369.94

Finally, to find the difference in costs between the two nights, we subtract the cost of the room on Monday including tax from the cost of the room on Friday including tax:

$369.94 - $316.94 = $53

The difference in costs including tax between the two nights is $53.

Answer:

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

The cost x including a 6% tax is:

The difference in costs including tax is:

Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.

The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.

T = 2 × π × (square root of 1.00 m / 9.81 m/s²)

T = 2 * 3.1416 * (square root of 0.101936799)

T = 6.2832 * 0.319275428

T = 2.00 seconds

The period of this pendulum correct to 3 significant figures is 2.00 seconds.

The frequency of this pendulum is solved by the formula f = 1/T

f = 1/2.00 seconds

f = 0.500 hertz

Answer: 9.76 m/s^2

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.

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The reason behind horizontal asymptote is defined as the end behavior of the function.

The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.

Here we need to list down the reason behind horizontal asymptote.

As we all know that the horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞. Here we also know that the slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞.

Therefore, through the definition we know that the horizontal line to which the graph of the function appears to coincide with but it doesn't actually coincide.

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