Solve the following quadratic by
completing the square.
f(x) = x² + 2x - 12
+√[]
x = [?] +

Answer:

CD = 27

Step-by-step explanation:

2(4x - 1) + 2(3x + 3) = 116

8x - 2 + 6x + 6 = 116

14x + 4 = 116

14x = 112

x = 8

3(8) + 3

= 24 + 3

= 27

Answer:

not enough info

Step-by-step explanation:

Let h = number of history books.

Let m = number of math books.

"The number of history textbooks sold was three times the number of math textbooks sold."

h = 3m

"A textbook store sold a combined total of history and math textbooks in a week."

h + m = t

t = total number of books sold.

We have a system of equations:

h = 3m

h + m = t

Since we do not have a value for t, and we have a system of 2 equations in 3 variables, we cannot find the numbers of history or math books sold.

Step-by-step explanation:

[tex]volume \: of \: cylinder = \pi \: {r}^{2} h \\ volume = 3.14 \times {7}^{2} \times 19 \\ = 2923.34 \: millimetres[/tex]

The required two-column proof that the triangles are congruent is explained below.

A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.

When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).

The two-column proof required in the question is given below:

       STATEMENT                                     JUSTIFICATION

1. <WXZ ≅ <YXZ                               Property of an angle bisector.

2. <XZW  ≅ <XZY                             Definition of a perpendicular bisector.

3. WX ≅ YX                                       Congruent sides of a triangle.

4. WZ ≅ YZ                                        Definition of a midpoint.

Therefore,

ΔWXZ ≅  ΔYXZ                                  Angle-Angle-Side theorem

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The value of x is equal to 9 for the two-variable equation -2x - 7y = 17 when y is equal to -5.

A two-variable equation is an equation that has 2 variables, typically x and y

For the two-variable equation;

-2x - 7y = 17

we shall evaluate for the value of x when y = -5 as follows:

-2x - 7(-5) = 17

-2x + 35 = 17

subtract 35 from both sides of the equation

-2x = 17 - 35

-2x = -18

divide through by -2

x = -18/-2

x = 9

Therefore, 9 is the value of x when y is equal to -5 for the two-variable equation -2x - 7(-5) = 17.

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By using the given formula and solving we get, the original value of the vase is 5000 pounds.

A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.

A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.

The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.

To find the original value of the vase, we need to know the value of the vase when n = 0.

Substituting n = 0 into the formula, we get:

value in pounds = 5000*1.28^0

When n = 0, 1.28^0 = 1, so the original value of the vase is:

value in pounds = 5000*1 = 5000 pounds

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The value of b can be -32 or +32 to ensure that the equation has only one true solution.

The discriminant is the quadratic formula section behind the square root symbol: b2-4ac. The discriminant indicates whether there are two solutions, one solution, or none at all. The "discriminant" is the argument (that is, the contents) of the square root, which is the equation b2 4ac, because by utilizing its value, you may "discriminate" between (that is, determine the difference between) the various solution types.

Here,

The discriminant of the equation is ...

d = b² -4ac

d = b² -4(2)(128)

d = b² -1024

In order for there to be one real solution, we must have d=0. So ...

0 = b² -1024

1024 = b²

±√1024 = ±32 = b

The value of b can be -32 or +32 to cause the equation to have one real solution.

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Therefore , the solution of the given problem of graphs comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

Graphs are used by mathematicians to rationally represent or chart facts or values. Typically, a graph tip will show a connection amongst two or more objects. A graph is a type of non-linear data structure that is made up of nodes, and vertices, and edges. affix the nodes, also referred as as vertices. This graph includes elements E=3,2,14,5 , having (2.5) and vertex V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistics charting (bar charts, charts, line charts, etc.). the form of a triangle-shaped logarithmic graph

Here,

If she is first driving toward the gas station, then the graph will be declining.

She fills up her tank at the gas station, which causes the graph to move upward.

After that, the graph will start to decline as she approaches the market.

From the information,

we can simply deduce that the graph will initially start out declining, then quickly increase, and finally have a continuous reduction until we achieve our target.

Therefore , the solution of the given problem of graph comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.

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The solution of the trigonometric equation sin^2(2x+3)+cos^2(2x+3)=2x+3 is x = -1.

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

sin²(2x+3) + cos²(2x+3) = 2x + 3

Remember, the trigonometric identity, sin²θ + cos²θ = 1.

Thus, we can say sin²(2x+3) + cos²(2x+3) = 1. We now have:

sin²(2x+3) + cos²(2x+3) = 2x + 3

1 = 2x + 3

2x = 1-3

2x = -2

x = -2/2

x = -1

Therefore, the solution of the equation is x = -1

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The original amount is (100%) if you have an increased by 30%

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.

In the given question, the percentage increase can be calculated with the help of the percentage increase formula,

Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100

To get the original amount,

Just add the percentage increase to 100, divide 100 by it, then multiple by the final number to get the original number.

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Equation 4x222-12x+9=5 has a solution of x=  -√4-3.  It is said to be linear when an equation has the form y=mx+b .

In algebra, a linear equation is one with the form y=mx+b. B is the slope, and m is the y-intercept. Because y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are those with two variables. There are various examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

4x²2²-12x+9=5

8x2 - 12x +4 = 0

8x2 - 6x - 6x +4 = 0

2x(4x - 3) - 2(3x +2) = 0

Equation 4x222-12x+9=5 has a solution of x=  -√4-3 . It is said to be linear when an equation has the form y=mx+b .

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The length of the straw placed inside the rectangular box is [tex]\sqrt{73}[/tex] inches.

A quadrilateral with parallel sides equal to one another and four equivalent vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel. The area of a rectangle is given as the product of the length and breadth of the rectangle.

The given parameters are:

The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

[tex]s=\sqrt{l^{2}+w^{2}+h^{2} }\\[/tex]

The equation becomes:

[tex]s=\sqrt{6^{2}+6^{2}+1^{2} }\\[/tex]

Evaluate the exponents:

[tex]s=\sqrt{73}[/tex] inches

=> s≈8.544 inches

Hence, the length of the straw is 8.544 inches.

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

The quadratic pattern with value of p and q has been proved.

A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word for square, is where the word "quadratic" originates.

Here,

Given : 1st difference

p−4;

11−p;

q−11;

22−q;

2nd difference−2p+15;

q+p−22;

33−2q−2p+15=1−2p=−14p

=733−2q

=1q+p−22

=1−2q=−32or/of

q+7−22=1

q=16

Therefore , the solution of the given problem of quadratic comes out to be q =16

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Answer:

Two possible ways Arvin can complete his training plan are:

Biking 35 miles a week, 3 days a week, biking 11.67 miles per day.

Biking 41 miles a week, 4 days a week, biking 10.25 miles per day.

In the first option, Arvin bikes 35 miles a week, 3 days a week, which means he bikes 11.67 miles per day to achieve his goal.

In the second option, Arvin bikes 41 miles a week, 4 days a week, which means he bikes 10.25 miles per day to achieve his goal.

It is important to note that these are just examples, and there could be other options that Arvin can consider, as long as it meets his requirement of biking between 35 and 41 miles a week, either 3 or 4 days a week, and the same number of miles each day.

Step-by-step explanation:

Answer: False

Step-by-step explanation:

-3/7 roughly equals -0.428

-2/5 equals -0.4

-0.4>-0.428

-2/5>-3/7

Argument A is deductive and Argument B is inductive.

Deductive reasoning uses broad premises to arrive at specific conclusions, while inductive reasoning starts with specific premises and draws general conclusions.

If the premises are valid, deductive reasoning's conclusions cannot be false. This is so because there is nothing in the conclusion that isn't already there in the premises. Yet, an inductively drawn conclusion goes beyond the information in the premises, unlike deductive reasoning.

Argument A is deductive because from the premise it is saying that the Grand Canyon was carved out by aliens from Jupiter, which is not sure.

Argument B is inductive because from the premise it is saying that Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old, which is true.

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The complete question is:

INDUCTIVE /DEDUCTIVE ARGUMENT

Argument A: The Grand Canyon could not have been made by humans, so it follows that the Grand Canyon was carved out by aliens from Jupiter.

Argument B: Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old.

The correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.

Relationships between two variables that are proportional occur when their ratios are equal.

Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.

The "constant of proportionality" is the name of this constant.

Observing the graph, the line traverses (0, 0). We obtain y=0.5(0)=0 if x=0.

Since this is the point's y-coordinate, it passes through this.

Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form equation for this line.

m=0.5 and b=0 in this equation.

This indicates that the slope is 0.5 or 1/2; as slope = rise/run, this indicates that the line rises one for every increase in the horizontal dimension of two.

This implies that starting from (0, 0), we would climb 1 and cross 2 to make the spot (2, 1).

When examining the graph, the line passes through this location.

We would then ascend 1 and cross over 2 once more to (4, 2). Once more, the line passes through this spot.

Therefore, the correct statement is (A) the points on the line would indeed be a part of the equation y = 0.5x.

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Complete question:

Which statement best explains if the graph correctly represents the proportional relationship y = 0.5x?

A. Yes, the points shown on the line would be part of y = 0.5x

B. Yes, all proportions can be shown on a graph of this line

C. No, the points shown would not be part of y = 0.5x

D. No, proportions cannot be represented on a graph

By algebra properties, the values of algebraic expression x³ - 4 · x are - 3 and 0 for x² + x = 3.

In this question we must derive the value of algebraic expression x³ - 4 · x based on the fact that x² + x = 3. First, determine the value of x by algebra properties:

x² + x = 3

x² + x - 3 = 0

x² + (2 - 1) · x + 2 · (- 1) = 0

x² + 2 · x - x - 2 = 0

x · (x + 2) - (x + 2) = 0

(x - 1) · (x + 2) = 0

x = 1 or x = - 2

The roots of x² + x = 3 are 1 and - 2.

Second, determine the values associated with the two roots found in previous step:

x = 1

y = x³ - 4 · x

y = 1³ - 4 · 1

y = 1 - 4

y = - 3

x = - 2

y = x³ - 4 · x

y = (- 2)³ - 4 · (- 2)

y = - 8 + 8

y = 0

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The equation of the relationship between the price of oranges last week and this week is y = 1.2x

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

Price last week = x

Rate of increment = 20%

Price this week = y

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

Price this week = Price last week * (1 + Rate of increment)

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

y = x * (1 + 20%)

Express as decimal

y = x * (1 + 0.2)

Evaluate the sum

y = x * 1.2

So, we have

y = 1.2x

Hence, the equation is y = 1.2x

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The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.

Answer:

2(3b+6) =78 : b=11

-2(6c-3) = -72 : c=6.5

Step-by-step explanation:

They are correct

By solving an exponential equation, we can see that the investment will be doubled after 10.6 years.

The investment can be modeled by the exponential equation:

P(x) = A*(1 + 6.75%/100%)^x

Where A is the initial value of the investment (the amount invested).

We can simplify this to get:

P(x) = A*(1 + 0.0675)^x

The investment will be doubled when:

2*A = A*(1 + 0.0675)^x

We want to solve this for x.

2 = (1 + 0.0675)^x

2 = (1.0675)^x

If we apply the natural logarithm in both sides:

ln(2) = ln((1.0675)^x)

ln(2) = x*ln(1.0675)

ln(2)/ln(1.0675) = x

10.6 = x

The investment will be doubled after 10.6 years.

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Answer:

2

Step-by-step explanation:

Answer::b.

Step-by-step explanation:

Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.

A straight line of numbers is shown visually as a number line.

This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.

The collection of integers can be shown on a number line much like other sets of numbers..

Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.

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The x and y-intercepts of the given equation of line 8x - 5y = -11 are (-11/8,0) and (0,11/5) respectively.

Given the equation of line in the question;

8x - 5y = -11

To find the x-intercept, substitute in 0 for y  and solve for x.

8x - 5y = -11

8x - 5(0) = -11

8x - 0 = -11

8x = -11

x = -11/8

Hence, the x-intercept is (-11/8,0)

To find the y-intercept, substitute in 0 for x  and solve for y.

8(0) - 5y = -11

0 - 5y = -11

-5y = -11

y = -11 / -5

y = 11/5

Hence, the y-intercept is (0,11/5).

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Answer:

-3c

Step-by-step explanation:

During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?

Answer:

-3c

Step-by-step explanation:

c+-4c+10+-10=  c+-4c= -3c

39

40-32÷8+5-2

40-4+3

40-1

39