Choose the most accurate relationship between ∠1 and ∠2. A horizontal line is shown with a ray extending upward from a point near the center of the line. A second line runs diagonally from the lower left to the upper right, intersecting the line at the point of origin of the upward pointing ray. The angle formed by the two lines below the horizontal line on the left is labeled 1. The angle formed just left of the horizontal line and upward pointing ray is labeled 2. The angle just right of the upward ray formed by the upward ray and diagonal line is labeled 4. The angle formed just right of the diagonal line and above the horizontal line is labeled 5. The angle formed below the horizontal line and just right of the diagonal line is labeled 6. A. adjacent B. linear pair C. supplementary D. vertical

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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18  bottles of lemonade did the shop fill

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Answer:

0.5045

Step-by-step explanation:

9.081 ÷ 18

Answer:

ang tanga mo naman para di malaman ang sagot

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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Both "negative 1" and "minus 1" refer to the same value, which is -1. They both indicate that a value is less than zero.

"Negative 1" and "minus 1" are ways to represent the value of -1 in mathematics. In general, a negative number is any number that is less than zero. For example, -1, -2, -3, etc. are all negative numbers.

When we use the word "minus" in front of a number, it indicates that we want to subtract that number from a given value. For example, if we say "5 minus 2," we mean 5 - 2 = 3. Similarly, when we say "minus 1," it means we want to subtract 1 from a given value.

So, "negative 1" and "minus 1" are both ways to indicate the value of -1, which is less than zero.

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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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The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.

Angle measurements and side lengths are identical for congruent triangles. These are the criteria for triangle congruence: "Side-Side-Side" SAS (Side-Angle-Side)

If the five conditions for congruence are met, two triangles are congruent. These are right angle-hypotenuse-side (RAHS), side-side-side (SSS), angle-side-angle (ASA), angle-angle-side (AAS), and side-angle-side (SSS) (RHS).

Triangles are said to be congruent if two sets of corresponding angles and the pair of included sides are also so. The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.

You would need at least one pair of comparable sides that are likewise congruent to demonstrate the congruence of two triangles with three congruent, corresponding angles. Then, you might demonstrate congruence using the ASA or AAS congruence theorems or rigid transformations.

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Answer: Hi

We can use the information given to set up the inequality:

Weight of refrigerators + weight of pianos <= 6900 (since the truck can carry no more than 6900 lb)

We can use the weight of each item to write the inequality in terms of x (number of refrigerators) and y (number of pianos):

300x + 525y <= 6900

To graph the inequality, we can use the x and y values as coordinates and plot them on a coordinate plane. The line representing the inequality would be a boundary line, with all the points that satisfy the inequality on one side of the line, and all the points that do not satisfy the inequality on the other side of the line.

To check if 12 refrigerators and 9 pianos will overload the truck, we can substitute these values into the inequality:

300(12) + 525(9) = 3900 + 4725 = 8625

Step-by-step explanation:

To sum up, the inequality 300x + 525y <= 6900 represents the weight that the truck can carry. The points that satisfy the inequality (such as (4, 6) or (10, 3)) would represent a combination of refrigerators and pianos that the truck can carry, while the points that do not satisfy the inequality (such as (12, 9)) would represent a combination that overloads the truck.

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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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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To determine if an ordered pair (X,Y) is a solution to a linear inequality in two variables, substitute the values for X and Y into the inequality and check if the inequality holds true.

To determine whether an ordered pair (X,Y) is a solution of a linear inequality in two variables, we must first understand what a linear inequality is. A linear inequality is an equation with two variables (X and Y) that is either greater than or less than an expression. To determine if an ordered pair is a solution to a linear inequality, we must substitute the values for X and Y into the inequality and check if the inequality holds true. If the inequality is true, then the ordered pair is a solution. If the inequality is false, then the ordered pair is not a solution. For example, if we have an inequality of 2X + Y > 5 and the ordered pair (3,1), we can substitute the values for X and Y into the inequality (2(3) + 1 > 5). Since this inequality holds true, the ordered pair (3,1) is a solution

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The absolute value of the inequality |2x -1| >3  will have a union type of solution set.

By using the absolute rule that states:

An inequality equation's absolute value can be solved.

where the "or" functionality symbolizes the union between the solution sets.

Given that:

|2x - 1| > 3

Applying the absolute rule, we have:

2x - 1 < - 3 or 2x - 1 > 3

2x < -4 or 2x > 4

x < -4/2 or x > 4/2

x< -1 or x > 2    

This denotes the union of between the solution sets.

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The ratio of the edge lengths of the large and small cubes is 6:1

The ratio that compares the edge lengths of the large and small cubes is the ratio of the length of the edge of the large cube to the length of the edge of the small cube.

The edge length of the large cube is 12 cm and the edge length of the small cube is 2 cm. To find the ratio, we divide the length of the large cube by the length of the small cube.

So the ratio of the edge length of the large cube to the small cube is:

12cm/2cm = 6

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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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Answer:

f = 5

g = -3

Step-by-step explanation:

11f + 14g = 13        Q1

11f + 10g = 25       Q2

Q1 - Q2  =

4g = -12

g = -3

put it back in the equation

11f + 10g = 25

11f + 10 (-3) = 25

11f + -30 = 25

11f = 55

f = 5

Answer:

f = 5 , g = - 3

Step-by-step explanation:

11f + 14g = 13 → (1)

11f + 10g = 25 → (2)

subtract (2) from (1) term by term to eliminate f

(11f - 11f) + (14g - 10g) = 13 - 25

0 + 4g = - 12

4g = - 12 ( divide both sides by 4 )

g = - 3

substitute g = - 3 into either of the 2 equations and solve for f

substituting into (1)

11f + 14(- 3) = 13

11f - 42 = 13 ( add 42 to both sides )

11f = 55 ( divide both sides by 11 )

f = 5

solution is f = 5 , g = - 3

When multiplying a number by a sum, you can apply the distributive property of multiplication over addition. Say you want to multiply 3 by the sum of 10 plus 2, for instance: 3(10 + 2) =? This attribute allows you to add the integers and then multiply the result by three.

The distributive property of multiplication is used when multiplying each integer by the sum of two or more addends. The subtraction and addition of two or more numbers are both subject to the distributive property of multiplication.

Boost the equation's size. Divide (multiply) the initial number in each set, the outer number in each set, the inner number in each set, and the last number in each set. Join similar phrases. If necessary, simplify the equation after solving it.

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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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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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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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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 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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Answer:

3 (x + 4)

Step-by-step explanation:

3x = 3 × x

12 = 3 × 4

3x + 12

Take 3 common,

3 (x + 4)

Hence, factorised.

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 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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Answer:

No, they not equal

Step-by-step explanation:

23+37+9=60+97

It not equal

69 ≠ 157

A customer earns 1 free night per 10 nights stayed.

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

f(x)=x/10

When we put x=10, we get f(1)=10/10=1

Here f(1)  represents the number of free nights earned by the customer is 1 per 10 nights stayed.

When we put x=20, we get f(2)=20/10=2

Here f(2)  represents the number of free nights earned by the customer is 2 per 20 nights stayed.

When we put x=30, we get f(3)=30/10=3

Here f(3)  represents the number of free nights earned by the customer is 3 per 30 nights stayed.

When we put x=40, we get f(4)=40/10=4

Here f(4)  represents the number of free nights earned by the customer is 4 per 40 nights stayed.

Then, the pattern permits you to conclude that a customer earns 1 free night for every 10 nights stayed.

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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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