Is the ordered pair (- 2 2 A solution of the linear inequality?

The newer pump will take 6.25 hours to drain the pool working alone

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

According to the data we can state:

x = time new pump to drain the pool alone

4x = time older pump

Together they drain the pool in 5 hours, therefore:

1/x + 1/4x = 1/5

Multiply everything by x:

1 + 1/4 = 1/5 x

(4+1)/4 = 1/5x

5/4 = 1/5x

5/4 * 5 = x

25/4 = x

x = 6.25 hours

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So, the midpoint of the line segment joining the points (1,2) and (3,4) lies in the Quadrant 2.

To find the midpoint of a line segment, we need to average the x-coordinates and the y-coordinates of the two given points.

The given points are (1, 2) and (3, 4)

The x-coordinate of the midpoint = (x1 + x2)/2 = (1 + 3)/2 = 2

The y-coordinate of the midpoint = (y1 + y2)/2 = (2 + 4)/2 = 3

So the midpoint of the line segment joining the points (1, 2) and (3, 4) is (2, 3)

The point (2,3) is in Quadrant 2 as x is positive and y is positive.

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The angle at which the ladder is leaning according to the base and length of the ladder is 62°.

The angle formed between ladder and house is right angled triangle. Thus, the trigonometric formula to be used for calculation is -

cos theta = base ÷ hypotenuse

Keeping the values in formula to find the value of theta which represents angle of leaning of ladder

cos theta = 7/15

Performing division on Right Hand Side of the equation to find the value of theta

cos theta = 0.47

theta = [tex] { \cos }^{ - 1} [/tex] 0.47

theta = 61.97

Thus, the angle is 61.97 or 62°.

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The length of each scarf is given by the equation A = 4.9 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the length of each scarf be represented as A

Now , the equation will be

The total length of all the scarves = 470.4 inches

The total number of scarves = 8 scarves

So , the length of each scarves = total length of all the scarves / total number of scarves

Substituting the values in the equation , we get

The length of each scarf A = 470.4 / 8

The length of each scarf A = 58.8 inches

Now , 12 inches = 1 foot

So , 1 inch = ( 1/12 ) foot

The length of each scarves A = 58.8 ( 1/12 ) feet

On simplifying the equation , we get

The length of each scarf A = 4.9 feet

Hence , the length of each scarf is 4.9 feet

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2^x=32

Rewrite 32 as 2^5

2^x = 2^5

Since the bases are the same, the exponents have to be the same

x=5

2^x=32

Take log base 2 on each side

log2(2^x) = log2(32)

x = log2(32)

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Answer: 2 [tex]\sqrt{170}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem, 14^2 + 22^2 = x^2

196 + 484 = x^2

680 = x^2

x = [tex]\sqrt{680}[/tex]

   [tex]2\sqrt{170}[/tex]

Answer:

sqrt317

Step-by-step explanation:

Using the Pythagorean theorem, we know that a^2+b^2=c^2.

So, (14)^2+(11)^2=x^2

We multiply it out, giving us 196+121=x^2
This means that 317=x^2

We square root both sides, giving us x=sqrt317

The base of the triangle x, with an area of 5 units square is equal to 2 units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

we have the area as 5 units square and the height as 5 units, so we solve for the base x as follows:

1/2 × x × 5 units = 5 units²

divide through by 5 units;

1/2 × x = 1 unit

multiply both sides by 2;

x = 2 units

Therefore, the base of the triangle x, with an area of 5 units square is equal to 2 units.

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Possible question:

The triangle with an area of 5 units square and height 5 units has the length of its base as x. Solve for x.

The functions f(x) and 9(x) are not inverse functions because their graphs are not reflected across the line y=x. is not true.

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Multi-step equations are those that must be solved over the course of two or more steps.

An equation that needs to be solved in two or more steps is known as a multi-step equation. There may be a combination of addition, subtraction, multiplication, and division in these questions. For proper equation solving, we could additionally need to combine like terms or apply the distributive property.

Similar to multi-step equations, multi-step inequalities might require combining like terms, the distributive property, and variables on both sides. Again, the only distinction when resolving inequalities is that when multiplying or dividing by a negative number, the sign must be reversed.

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A line graph, sometimes referred to as a line chart or a line plot, is frequently used to display data that varies over time. Several points connected by straight lines can be used to plot it.

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Answer:

ang tanga mo naman para di malaman ang sagot

The solutions of this quadratic inequality are x ≤ -2 and x ≥ 1.

Step 1: Factor the quadratic expression on the left side of the inequality.

X² - 3x + 2 = 0

Step 2: Set the factors equal to zero and solve for x.

(x - 2)(x - 1) = 0

Step 3: Solve the individual equations.

x - 2 = 0

x - 1 = 0

Step 4: Set up the solutions in terms of x.

x ≤ -2

x ≥ 1

The quadratic inequality X² 3x 2 ≤ 0 can be solved by factoring the expression on the left side of the inequality. Setting the factors equal to zero and solving for x will give us the solutions for x. The solutions are x ≤ -2 and x ≥ 1, which can be read as 'x is less than or equal to -2' and 'x is greater than or equal to 1'. In other words, any value of x that is less than or equal to -2 or greater than or equal to 1 will satisfy the inequality.

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The axis of symmetry f(x) = x2 is 0 using standard form of axis of symmetry.

Given: y = x2

Using axis of symmetry formula,

x = -b/2a

x = -(0)/2(2)

x = 0

Therefore, axis of symmetry of parabola y = x2 is x = 0.

Formula for Axis of Symmetry

The axis of symmetry formula is used to quadratic equations when the line of symmetry and the equation's standard form are used. The axis of symmetry is a line that splits or bifurcates any object into two equal halves that are mirror images of one another. Any one of the three types of axis—horizontal (x-axis), vertical (y-axis), or inclined line—can be used to divide the objects.

The equation for the axis of symmetry can be shown when the parabola is in one of two forms:

1) standard form

2) Vertex form

1) standard form

Y = ax2 + b x + c is the quadratic equation in standard form.

with real numbers a, b, and c.

The axis of symmetry formula in this instance is x = - b/2a.

2) Vertex form

Y = a (x-h)2 + k is the quadratic equation in vertex form.

where the parabola's vertex is (h, k).

The axis of symmetry equation in this case is x = h.

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The probability that the three new numbers still sum to 100 is 0.9.

The three positive real numbers that sum to 100 can be any combination of numbers that add up to 100. If we round them to the nearest tenth, we will lose some precision, and it is possible that the new numbers will not sum up to 100.

We can think of this problem in two steps: first, we pick any three positive real numbers that add up to 100, then we round them to the nearest tenth.

The total number of possible sets of three positive real numbers that add up to 100 is infinite, but we are only interested in the sets that will round to 100 after the transcription.

To find the probability of this happening, we can think of the rounding as a rounding error. There is a probability of 0.05 that the rounding error will make the sum greater than 100 and a probability of 0.05 that the rounding error will make the sum less than 100.

So the probability that the three new numbers still sum to 100 = 100-0.05-0.05 = 0.9

Therefore, the probability that the three new numbers still sum to 100 is 0.9.

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Answer:

line segment

Step-by-step explanation:

the answer is above

The greatest possible perimeter  26  the least possible perimeter of the parallelogram 20

[ -1 + 2 , 0 + 4 ]  - [ 2 , -4 ]  =  [  [ 1 , 4] - [2 , - 4 ] =   ( -1, 8  )

The perimeter of this parallelogram =

2  [  sqrt  [ (-1-2)^2 + (8-4)^2]  + 8  ]  =

2 [ sqrt [ 9 + 16 ] +  8 ]  =

2 [ 5  + 8 ] =

26

Another possible  point is

[ 2 + 2, 4 - 4]  - [-1,0] =  [ 4, 0]  - [ -1,0]  = (5,0)

The perimeter of this parallelogram =

2 [ sqrt [ (5-2)^2  + (0 - 4)^2]  + sqrt [ (2- -1)^2 + (4 - 0)^2) ] ] =

2 [ sqrt (3^2 + 4*2)  + sqrt (3^2 + 4^2) ]  =

2 sqrt (25)  + sqrt (25) ] =

2 [ 5 + 5 ] = 20

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The percentage of the adult population that reports having been "sick with a cold" on any given day throughout the year ranges from a little more than 2% to nearly 11%.

What is meant by Population ?

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The quotient for the given expression  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]  is ,   1/4

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]

⇒  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]

⇒  [tex]\frac{2-2\sqrt{2} }{4+2\sqrt{3} }[/tex]

by rationalization of of denominator

⇒   [tex]\frac{2-2\sqrt{2} }{16-12 } \frac{4-2\sqrt{3}}{}}[/tex]

⇒   [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{16-12 }[/tex]

⇒   [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{ 4 }[/tex]

Hence, the quotient is 1/4

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The required value of k will the system of linear equations has infinite number of solutions is 8.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given set of equations is

kx + 4y = k - 4 ...(i)

16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)

= k² - 64

= (k + 8) (k - 8)

D1 = k (k - 4) - 4k

= k² - 4k - 4k

= k² - 8k

= k (k - 8)

D2 = k² - 16 (k - 4)

= k² - 16k + 64

= (k - 8)²

= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,

since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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The distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, the distance formula:

d=(((x 2-x 1)2+(y 2-y 1)2)

The points we have are: (-5, 7) and (-1, 3)

d=(((x 2-x 1)2+(y 2-y 1)2)

d= (−5−(−1))2 +(7−3)2

d= 16+16

d= 32

d= 4√2

​

Therefore, the distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

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Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

A) f (0)

Substituting the value of x = 0

f (0) = 6(0) -3

      = 0 - 3

      = -3

B) f (2)

Substituting the value of x =2

f (2) = 6(2) -3

      = 12 - 3

      = 9

C) f (-2)

Substituting the value of x = -2

f (2) = 6(-2) -3

      = -12 - 3

      = -15

D) f (1)

Substituting the value of x =1

f (1) = 6(1) -3

      = 6 - 3

      = 3

E ) f (-3)

Substituting the value of x =2

f (2) = 6(-3) -3

      = -18 - 3

      = -21

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Natalie would have $136 more in her account than Tamika

The formula for compound interest is given by:

A = P (1 + r/n)^(nt)

Where:

A = the final amount (principal + interest)

P = the initial principal or starting amount

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years for which the interest is calculated.

For Natalie:

P =  $470, r = 8 7/8% = 0.08875, n = 365 and t = 14

A = P (1 + r/n)^(nt)

A = 470 (1 + 0.08875/365)^(365×14)

A = $1628

The formula for compound interest compounded continuously is:

A = P e^(rt)

For Tamika:

P =  $470, r = 8 1/4% = 0.0825, and t = 14

A = 470× e^(0.0825×14)

A = $1492

Difference = $1628 - $1492 = $136

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The average speed of the car is 50 km/hour.

To find the average speed of a car, you can use the formula:

Speed = Distance / Time

In this case, the distance is 100 km and the time is 2 hours. So, to find the average speed of the car:

Speed = 100 km / 2 hours = 50 km/hour

So the average speed of the car is 50 km/hour.

In mathematics, distance refers to the measurement of the difference between two points in a space or a geometric figure. It can be represented by a numerical value, and is often used to determine the shortest path between two points. The most common distance formula used in Euclidean geometry is the distance between two points (x1, y1) and (x2, y2) is the square root of ((x2 - x1)^2 + (y2 - y1)^2). This is known as the Euclidean distance.

Therefore, the average speed of the car is 50 km/hour.

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Answer:

0.5045

Step-by-step explanation:

9.081 ÷ 18

Answer: -8

Step-by-step explanation: 1/4 + 1/4 = 1/2, -8 1/2 + 1/2 = -8

Answer:

No, they not equal

Step-by-step explanation:

23+37+9=60+97

It not equal

69 ≠ 157

A function is a relation in which each element of the domain is paired with exactly one element of the range.

Determine whether each relation is a function. Find the domain and range?

(-2,2) (0,0) (2,-2)

This is a function because it is a many to one relation(-2 map to 2,0 map to 0,2 map to -2

Domain( -2,0,2)

Range(-2,2)

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The value of the composite function are as follows:

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

A composite function is a function that depends on another function. In other words, a composite function is a function that is within another function.

Therefore, let's solve the function as follows:

f(x) = 2x²

g(x) = x + 1

Therefore,

(f - g)(x) = f(x) - g(x) = 2x² - (x + 1) = 2x² - x - 1

(f + g) =  f(x) + g(x) = 2x² + (x + 1) = 2x² + x + 1

(f .g)(-2) = f(g(-2))

g(-2) = -2 + 1 = -1

Hence,

(f .g)(-2) = 2(-1)² = 2

Therefore,

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

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