What Is The Initial Value Of The Function Represented By This Graph? 0457 (2024)

Solve each equation in steps:

2(3b + 6) =78 Given3b + 6 = 39 Divide both sides by 23b = 33 Subtract 6 from both sidesb = 33/3 Divide by 3b = 11 Answer

-2(6c - 3) = -72 Given6c - 3 = 36 Divide both sides by - 26c = 39 Add 3 to both sidesc = 39/6 Divide by 6c = 6.5 Answer

Answer:

b = 11 c = 6.5

Step-by-step explanation:

1) 2(3b + 6) = 78, value of b?

→ 2(3b + 6) = 78

→ 6b + 12 = 78

→ 6b = 78 - 12

→ 6b = 66

→ b = 66/6

→ [ b = 11 ]

Hence, the value of b is 11.

2) -2(6c - 3) = -72, value of c?

→ -2(6c - 3) = -72

→ -12c + 6 = -72

→ -12c = -72 - 6

→ -12c = -78

→ c = (-78)/(-12)

→ c = 78/12

→ [ c = 6.5 ]

Hence, the value of c is 6.5.

The side-length of square C as required in the task content is; 5 ft.

What is the side length of square C?

It follows from the task content that the side length of square C is to be determined according to the given diameter.

Recall that the Area, A of a square in terms of its side length, s is; A = s².

Therefore, s = √A.

On this note, for each of the given squares their side lengths are as follows;

For square A; side length is; √9 = 3ft.

For square B; side length is; √16 = 4ft.

Hence, since sides A, B and C form a right triangle;

C² = A² + B²

C² = 3² + 4²

C² = 9 + 16

C² = 25

C = 5.

Ultimately, the side-length of square C is; 5 ft.

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Answer:

a. A + C < B + C

Step-by-step explanation:

when we know that A < B, then adding the same amount to both sides did not change the relationship between both sides.

this is like having a balance with 2 cups. one side is heavier than the other, so the heavier cup is down.

if we add the same weight to both cups, the situation will not change.

that is why a. is the right answer.

b. would only be right, if C is negative.

for positive C the same argument as for A applies. a smaller amount (or weight) stays smaller also after multiplying both sides by the same number.

but because this option would only be right for a subset of the possible values, this is not true in general.

c.

this is not true at all.

if we multiply the expression by -1, then the inequality sign has to flip. < becomes >, > becomes <.

which did not happen here.

Answer:

7 < x < 11

Step-by-step explanation:

A square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

What is the conversion factor?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equals 1 foot.

A square yard of carpet is equivalent to 9 square feet because 1 yard = 3 feet and 1 square foot = 1 foot x 1 foot.

So, to find the cost of a square yard of carpet that is selling for $8.95 per square foot, we need to multiply the price per square foot by the conversion factor of 9 square feet per square yard.

$8.95/square foot * 9 square feet/square yard = $80.55/square yard

Hence, a square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

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Step-by-step explanation:

graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2

Answer:

it's c if you are taking pre algerbra 8th on question 5 if ur on flvs

Step-by-step explanation:

line passing through the points (-2,-3) (0,-2)

The equation of the quadratic function y = x² + 6x + 3 in vertex form is y = (x+ 3)² - 6

Quadratic function in math is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two.

Here we have given the quadratic function y = x² + 6x + 3 and we need to find the vertex form of the given quadratic function.

As we all know that the vertex form of the equation is given by

=> f(x) = a(x - h)² + k

Here we have given the expression that can be written as,

=> y = x² + 6x + 3

Now, we have to convert it into vertex form, then we get,

=> x² + 6x + 3

Expand the expression as follows:

=> x² + 6x + 3 + 9 - 9

Now, we have rewritten the expression like the following,

=> y + 9 = (x + 3)² + 3

Here we have to subtract 9 on both sides, then we get

=> y = (x+ 3)² + 3 - 9

Then the resulting equation is written as,

=> y = (x+ 3)² - 6

Complete Question:

What is the equation of the quadratic function y = x² + 6x + 3 in vertex form?

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No, a star does not have 5 angles.

A star is a two-dimensional shape that is made up of multiple straight lines. Each straight line must meet at a point, known as a vertex, which forms an angle.

The number of angles in a star depends on the number of points or vertices it has. A five-pointed star, for example, has five angles, each of which is equal to 36 degrees.

However, stars can have any number of vertices, meaning the angles may vary depending on the star.

A star is a two-dimensional shape that has a symmetrical arrangement of points. The points can vary in number, but typically a star has five or more points.

Each point corresponds to a corner of the star, but since a star does not have any sides, it is not possible for it to have five angles. Instead, the corners of the star form vertices, but no angles.

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The length of the rectangle is L = 29 meters

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the length of the rectangle be represented as L

Let the width of the rectangle be represented as W

Now , Perimeter P of rectangle = 2 ( Length + Width ) = 74 meters

And , length of a rectangle is three meters less than four times its width

Substituting the values in the equation , we get

L = 4W - 3

And , 74 = 2 ( 4W - 3 + W )

Divide by 2 on both sides of the equation , we get

37 = 5W - 3

Adding 3 on both sides of the equation , we get

5W = 40

Divide by 5 on both sides of the equation , we get

W = 8 meters

Now , the length of the rectangle L = 4 ( 8 ) - 3

Length of the rectangle L = 32 - 3 = 29 meters

Hence , the length of the rectangle is 29 meters

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Answer:

D is the answer

A 20 degree angle called an acute angle.

Any angle which is less than 90 degree but greater than 0 degree is called an acute angle. For example - 20, 30, 40 , 50 etc are acute angles.

Polygons with at least one acute angle include triangles, parallelograms, trapezoids, and so on.The acute angle that are present in the triangle they are known as acute angle triangle.

Properties of acute angle triangles:

Acute triangles are all equilateral triangles. An equilateral triangle has three equal-length sides and three equal-measure angles, i.e. 60°.The longest side of an acute triangle is opposite the highest angle.Isosceles, equilateral, and scalene triangles are examples of acute triangles.

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A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side. The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is opposite the other at a specific angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side. The terms hypotenuse, opposite, and adjacent are used to define the trigonometric functions sine, cosine, and tangent.

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Answer:

A

Step-by-step explanation:

Answer:

of course it would be 45

Step-by-step explanation:

it right trusss

Truth serum has 91% accuracy when guilty, 94% accuracy when innocent, 6% false positive, 9% false negative.

What is percentange ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%" (percent sign) and it's used to express a proportion or ratio. For example, if a student scored 80 out of 100 in an exam, the percentage score would be 80%, which means the student answered 80 out of 100 questions correctly.

A truth serum given to a subject is known to have a 91% reliability rate when the person is guilty and a 94% reliability rate when the person is innocent. This means that when the person is guilty, there is a 91% chance that the truth serum will indicate that the person is guilty, and a 9% chance of a false negative (indicating the person is innocent when they are guilty). Similarly, when the person is innocent, there is a 94% chance that the truth serum will indicate that the person is innocent, and a 6% chance of a false positive (indicating the person is guilty when they are innocent).

Truth serum has 91% accuracy when guilty, 94% accuracy when innocent, 6% false positive, 9% false negative.

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Answer:738

Step-by-step explanation:

Answer:2 = x

The missing step is:

Take the square root of both sides of the equation to get the value of x, which is:

x = 2 ± √(19/6)

Now we have our solutions, x = 2 + √(19/6) and x = 2 - √(19/6) which are the solutions of the quadratic equation.

Step-by-step explanation:

Answer: 1) Add 4 2) Subtract 24 from 5 3) 2

Correct on Edge 2023 :)

Answer:4

Step-by-step explanation:12/3=4

There are two solutions to the given equation 3x + 4y = 12.

Finding two solutions for the equation 3x + 4y = 12

Putting the value of x = 0 in equation 3x + 4y = 12

⇒3(0) + 4y = 12

⇒ 4y = 12

⇒y = 3

Thus, (0, 3) is a solution to the equation 3x + 4y = 12

Putting the value of y = 0 in the equation 3x + 4y = 12

Thus,

⇒3x + 4(0) = 12

⇒3x = 12

⇒x = 4

Thus, (4, 0) is a solution to equation 3x + 4y = 12

Therefore, (0, 3) and (4, 0) are two solutions to the equation 3x + 4y = 12.

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If the area of the triangle is 120 cm^2, the value of x is equal to 6.

How to calculate the area of a triangle?

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = 1/2 × b × h

Where:

b represents the base area of a triangle.h represents the height of a triangle.

According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]

Where:

s = (a + b + c)/2

s = (x + x + 1 + 2x - 1)/2

s = 4x/2

s = 2x

Substituting the parameters into Hero's Formula formula, we have the following;

x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]

x√10 = x√2(x − 1)

√10 = √2(x − 1)

Taking the square of both sides, we have:

10 = 2(x - 1)

10 = 2x - 2

2x = 12

x = 12/2

x = 6.

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Answer:

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

Step-by-step explanation:

The first equation is missing a + or - sign

Regardless, it is easier to solve using elimination since the y coefficients are the same.

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

What is SAS Triangle Congruence Theorem?

Congruence, in mathematics, a term employed in several senses, each connoting harmonious relation, agreement, or correspondence .Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout. Thus two triangles are congruent if two sides and their included angle in the one are equal to two sides and their included angle in the other.

This idea of congruence seems to be founded on that of a "rigid body," which may be moved from place to place without change in the internal relations of its parts. The position of a straight line (of infinite extent) in space may be specified by assigning four suitably chosen coordinates. A congruence of lines in space is the set of lines obtained when the four coordinates of each line satisfy two given conditions. For example, all the lines cutting each of two given curves form a congruence.

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The profit percent for the pencils is equal to 10%.

What is the profit percent of the pencils?

If C is the cost and P is the price, then the formula for the profit percent is:

p = 100%*(P - C)/C

Here we know that the selling price of 10 pencils is equal to the cost price of 11 pencils, then we can write the eqation:

10*P = 11*C

We can solve this for P.

P = (11/10)*C = 1.1*C

Replacing that in the given formula we will get:

p = 100%*(1.1*C - C)/C

p = 100%*(1.1 - 1)*C/C

P = 10%

The profit percent is 10%.

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Answer:

Solving a system of equations by substitution involves isolating a variable in one equation, then substituting that expression into the other equation. This allows you to solve for the remaining variable in one equation and then substitute it back into the first equation to find the solution for the other variable.

Here is the general process for solving a system of equations by substitution:

Isolate a variable in one of the equations. This is typically done by adding or subtracting one of the variables from both sides of the equation.

Substitute the isolated expression into the other equation by replacing the corresponding variable with the expression you found in step 1.

Solve the new equation for the remaining variable.

Substitute the value you found for the remaining variable back into the first equation and solve for the other variable.

Check your solution by substituting the values you found for the variables back into both equations to make sure they are true statements.

Write your solution in the form of an ordered pair (x, y)

An example of solving a system of equation by substitution :

2x + 3y = 8

4x - 3y = 2

Isolate a variable in one of the equations, for example:

3y = 8 - 2x

Substitute this expression into the other equation:

4x - 3(8 - 2x) = 2

Solve the new equation for the remaining variable:

4x - 24 + 6x = 2

10x = 26

x = 2.6

Substitute the value you found for x back into the first equation and solve for y:

2(2.6) + 3y = 8

5.2 + 3y = 8

3y = 2.8

y = 0.93

Check your solution by substituting the values you found for the variables back into both

Answer: C). Yes, by HL

Step-by-step explanation:

The scale factor for the triangle is 8 : 1.

The first option is the correct option.

What is a scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A triangle with a perimeter of 24 meters was created from a triangle,

with a perimeter of 3 meters using a scale factor.

Then the scale factor,

= Actual triangle / scale triangle

= 24 / 3

= 8/1

= 8: 1

Therefore, 8: 1 is the scale factor.

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Answer:

8:1

Step-by-step explanation:

0.5 is equivalent to the fraction 1/2.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

We are given 0.5 which is to be converted into a fraction.

So, for this we will take 0.5 as the numerator and 1 as the denominator because anything divided by 1 is the number itself.

Thus, we get

⇒0.5/1

Now, we will multiply both numerator and denominator by 10.

From this, we get

⇒(0.5*10)/(1*10)

⇒5/10

Now, we will reduce the fraction to the lowest form by dividing both numerator and denominator by 5.

From this, we get the fraction as 1/2.

Hence, 0.5 is equivalent to the fraction 1/2.

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The sum of an irrational number and a rational number can either be rational or irrational.

Depending on the specific numbers involved. There is no general expression for the sum of an irrational number and a rational number being irrational. If the sum of two numbers is irrational, it means that the result cannot be expressed as a simple fraction, and its decimal representation either goes on forever without repeating or repeats after a certain number of digits.

One example of the sum of an irrational number and a rational number being irrational is:

√2 + 1/2 = 1.732 + 0.5 = 2.232 (irrational)

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the angle between 0 and 2pi in radians that is coterminal to 44pi/9 then terminal angle for 43pi/10 is 3pi/10.

How do you find Coterminal angles?

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.

The coterminal angle lie in between [0, 2pi].

Simplify the coterminal angle 43pi/10 to obtain in [0, 2pi].

43pi/10= 4pi+3pi/10

So coterminal angle for 43pi/10 is 3pi/10.

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A system of equations is a set of two or more equations with two or more variables. The number of solutions to a system of equations depends on the number of equations and the number of variables.

A system of equations can have one unique solution if the equations are consistent and independent. This means that there is one specific set of values that makes all equations true.A system of equations can have infinitely many solutions if the equations are consistent and dependent. This means that there are infinitely many sets of values that make all equations true. This is usually represented by a line or a plane in the case of systems of 2 or 3 equations with 2 or 3 variables.A system of equations can have no solution if the equations are inconsistent. This means that there are no values that can be assigned to the variables that make all equations true.

It's important to note that the number of solutions is not determined by the number of equations, but by the relationship between the equations and the variables.

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