Please help me

Given the quadratic function, describe in words the transformations and then
provide a sketch of the graph.
y = − 1/²(x+4)² - 7

Answer:

paper and pencil

Step-by-step explanation:

get a paper then a pencil and solve it

-6 × 2 + 6 × 200.

Hope this helps! :D - your friendly neighborhood Jxro!

The following results for the algebraic equation according to algebra properties are listed below:

In this problem we find an algebraic equation that must be expanded and simplified by means of algebra properties. Now we proceed to present the complete procedure. First, write the complete expression:

(x² + y²)² + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)

Second, expand the perfect square binomial:

x⁴ + 2 · x² · y² + y⁴ + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)

Third, use distributive property and add similar terms:

x⁴ + 4 · x² · y² = x² · (x² + 4 · y²)

Fourth, use distributive property once again:

x² · (x² + 4 · y²) = x² · (x² + 4 · y²)

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In the system of linear equations given, only option b have exactly one solution

A system of linear equations is a collection of two or more linear equations that are solved simultaneously. A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are real numbers and a is not equal to 0.

In this given problem, we have four system of linear equations and we need to determine which has exactly one solution.

a)

2x - 4y = 8 ...eq(i)

x + y = 7 ...eq(ii)

Solving both equations

x = 6, y = 1

b)

3x + y = - 1 ..eq(i)

8x + 2y = -2 ..eq(ii)

Solving both equations

x = 0, y = - 1

c)

3x + 3y = 3 ...eq(i)

-6x - 6y = 3 ...eq(ii)

Solving both equations;

There's no solution to this problem.

d)

3x - 2y = 4 ..eq(i)

-3x + 2y = 4 ..eq(ii)

Solving for both equations;

There's no solution to this problem

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Answer:

Step-by-step explanation:

Part A.

An appropriate design for the new study to examine whether vitamin E oil reduces pain in patients suffering from bulging disks in the thoracic region of the back would be a randomized controlled trial (RCT). The study should include the following elements:

1.Treatments: The study should include two treatment groups, one receiving vitamin E oil injections and the other receiving a placebo (e.g. a neutral oil) injections.

2.Method of treatment assignment: Patients should be randomly assigned to either the vitamin E oil treatment group or the placebo group, to control for potential confounding variables.

3.Variables that should be measured: The study should measure the following variables:

-Pain levels: Pain should be measured using a validated self-reported pain scale (such as the Visual Analog Scale or the Numeric Rating Scale) before and after each treatment session.

-Patient's demographics: Age, sex, and medical history should be recorded to evaluate the effect of these factors on the treatment outcome.

-Number of treatments: The number of treatments should be recorded for each patient.

-Adverse effects: Any adverse effects should be recorded, such as redness or swelling at the injection site.

It is important to note that this is a simplified design and a real study would need to consider many other aspects such as sample size, statistical analysis, and ethical considerations.

Part B

If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20-40, I would likely modify the study design. One reason is that age can be a confounding variable and could affect the outcome of the study. Studies have shown that age can affect pain perception and management, older adults have been found to have more chronic pain, and different pain management strategies might be more effective for different age groups.

I would modify the study design by including an age variable in the analysis and stratifying the sample by age, creating two subgroups (young and old patients) and comparing the results separately. This would allow us to see if there is any age-related differences in the effectiveness of vitamin E oil in reducing pain in patients suffering from bulging disks in the thoracic region of the back.

Another modification would be to include a larger sample size to ensure that there are enough patients in each subgroup to detect any potential differences in the effect of vitamin E oil on pain reduction between young and old patients.

It is important to note that this is a simplified design and a real study would need to consider many other aspects such as sample size, statistical analysis, and ethical considerations.

Part C

To construct 90% confidence intervals for the proportion of pain reduction for each treatment group, we can use the following steps:

1.Calculate the sample proportion of pain reduction for each treatment group:

For the Vitamin E oil group, the proportion of pain reduction = (52 / 100) = 0.52

For the Placebo group, the proportion of pain reduction = (35 / 100) = 0.35

2.Calculate the standard error (SE) for each proportion:

SE = sqrt( (p * (1-p)) / n )

Where p is the sample proportion and n is the sample size.

For the Vitamin E oil group, SE = sqrt( (0.52 * (1-0.52)) / 100) = 0.049

For the Placebo group, SE = sqrt( (0.35 * (1-0.35)) / 100) = 0.045

3.Calculate the margin of error (ME) for each proportion:

ME = z * SE

Where z is the critical value for a 90% confidence level, which is approximately 1.645.

For the Vitamin E oil group, ME = 1.645 * 0.049 = 0.0806

For the Placebo group, ME = 1.645 * 0.045 = 0.0743

4. Calculate the lower and upper bounds of the 90% confidence intervals for each proportion:

Lower bound = p - ME

Upper bound = p + ME

For the Vitamin E oil group, the 90% confidence interval is:

0.52 - 0.0806 = 0.4394 and 0.52 + 0.0806 = 0.6006

For the Placebo group, the 90% confidence interval is:

0.35 - 0.0743 = 0.2757 and 0.35 + 0.0743 = 0.4243

Therefore, the 90% confidence interval for the proportion of pain reduction for the Vitamin E oil group is (0.4394, 0.6006) and the 90% confidence interval for the proportion of pain reduction for the Placebo group is (0.2757, 0.4243)

Answer: 6.79

Step-by-step explanation: divide them

The equation of the line in standard form is 2x + 4y = 18.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

The equation of a line in standard form is,

Ax + By = C, where A, B and C are integers.

The equation given is,

(2/3)x + (4/3)y = 6

We need the coefficients to be integers.

Multiply throughout the equation by 3.

2x + 4y = 18, which is the standard form.

Hence 2x + 4y = 18 is the standard form.

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To find the area of a triangle with 3 unequal sides, you can use Heron's Formula.

This formula states that the area of a triangle (A) is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.

1. Calculate the perimeter of the triangle by adding together the lengths of all three sides.

2. Divide the perimeter by two to find s.

3. Plug in the lengths of the three sides and the value of s into Heron's Formula to calculate the area of the triangle.

A = √s(s-a)(s-b)(s-c)

To find the area of a triangle with 3 unequal sides, you can use Heron's Formula which states that the area of a triangle (A) is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.

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Answer: company B charges $10 and 2 cents more

Step-by-step explanation:

The graph with x 3 is called a cubic graph.

A graph is a visual representation of data, usually plotted on a two-dimensional plane. When graphing a function, the x-axis is used to represent the independent variable and the y-axis is used to represent the dependent variable. A graph with x 3 is a graph that shows the relationship between the independent variable, x, and the dependent variable, x3. This type of graph is called a cubic graph, as the graph follows a cubic equation.

The graph with x 3 is called a cubic graph.

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No, Root 3x 5 is not a polynomial, because it does not meet the definition of a polynomial.

A polynomial is a mathematical expression consisting of variables and coefficients, which only uses the operations of addition, subtraction, multiplication, and non-negative integer exponents. In other words, it must be an expression that can be written in the form ax^n + bx^(n-1) + cx^(n-2) + dx^(n-3) + ... + z, where n is an integer, and a, b, c, d, ... and z are real numbers.

Root 3x 5 does not fit this definition, because it contains a square root (√) which is not one of the operations listed. Additionally, it does not fit the form of a polynomial, as it does not contain any coefficients or exponents. The formula for root 3x 5 is simply √3x 5, and the calculation is the square root of 3x 5, or √15, which is equal to 3.75.

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y = -4x - 6 and -4x - y - 6 = 0 are both representations of the same linear equation.

The first equation, y = -4x - 6, is in slope-intercept form, where y is the dependent variable, x is the independent variable, -4 is the slope and -6 is the y-intercept. This means that when you graph this equation, the slope of the line will be -4 and the y-intercept will be -6.

The second equation, -4x - y - 6 = 0, is in standard form, where the variables are on one side of the equation and the constants are on the other side. To get this equation, you can move the y term to the other side by adding y to both sides, and then move the constants to the other side by adding 6 to both sides.

Both equations represent the same line. They are just in different forms, one is in slope-intercept form and the other is in standard form.

Answer:

infinite number of solutions

Step-by-step explanation:

y = - 4x - 6 → (1)

- 4x - y - 6 = 0 → (2)

substitute y = - 4x - 6 into (2)

- 4x - (- 4x - 6) - 6 = 0 ← distribute parenthesis and simplify left side

- 4x + 4x + 6 - 6 = 0

0 = 0 ← true statement

when both sides have the same numeric value

this indicates the system has an infinite number of solutions.

Answer:

amplitude=2

period=[tex]\pi[/tex]

A monomial is an algebraic expression that consists of only one term. Examples of monomials include 4x², a + 6, and a + b + c + d.

In the given example, (a) 4x² is a monomial because it consists of only one term, 4x². (b) a + 6 is also a monomial because it consists of only one term, a + 6. (c) a + 6 + c is not a monomial because it consists of more than one term, namely a + 6 and c. (d) a + b + c + d is also not a monomial because it consists of more than one term, namely a, b, c, and d.

To calculate the value of a monomial, we must first determine its degree. The degree of a monomial is the sum of the exponents of its variables. For example, the degree of 4x² is 2 because it consists of only one variable, x, with an exponent of 2.

Once the degree of a monomial is determined, its value can be calculated by substituting the values of its variables. For example, if x = 3, then 4x² = 4(3)² = 36.

In summary, a monomial is an algebraic expression that consists of only one term. Its degree is the sum of the exponents of its variables. To calculate its value, substitute the values of its variables into the expression.

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Answer: G = 15-D/20

Step-by-step explanation:

Using the variables given,

G = 15 - D/20

The following equations will have the same value of x as the one provided: 18x - 9 = 72.= 4.5

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

According to our question-

3/5(30x-15)=72

18x - 9 = 72

4.5

Hence, The following equations will have the same value of x as the one provided: 18x - 9 = 72.= 4.5

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The 3 types of sides in a right triangle are hypotenuse, base, and perpendicular.

A triangle is a form of a two-dimensional polygon with three edges and vertices. It is divided on the basis of sides as a Scalene triangle, Isosceles triangle, and Equilateral triangle. It is also divided on the basis of angles as acute, obtuse, and right-angle triangles.

A right-angle triangle has one angle equal to 90° and the other two angle sums up to be 90°.  The angle formed by the base and perpendicular is 90°.

The hypotenuse is the longest side of the triangle and it is opposite of the right angle. The relation between the three sides is Hypotenuse∧2 = Perpendicular∧2 + Base∧2. this relation is also called Pythagoras theorem.

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On solving the provided  question, we can say that value for the function g[h(−3)] is 12.

A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed.

In mathematics, a function is an expression, rule, or law that establishes the relationship between independent and dependent variables.

For equation h(x)

x = -3

then h(-3) = x²-1

h(-3) = (-3)² -1

h(-3) = 9-1 = 8 now using this value in g(x)

g(x) = x+ 4

g(8) = 8+ 4 = 12

Hence the value for the function is g[h(−3)] = 12

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Therefore, when two segments c, d, and a, b, cross at point e to form two triangles, the value of x is 30 cm.

Triangles are shapes with three sides and three vertices, making them polygons. It is one of geometry's fundamental forms. A triangle containing vertices A, B, and C is known as a triangle ABC. In Euclidean geometry, a singular plane and triangle are discovered when the three points are not collinear. A polygon with three sides and three corners is called a triangle. The corners of the triangle are the points where the three sides meet one another end to end. The sum of the angles in a triangle is 180 degrees.

given

From the diagram shown, the following equation is true:

x/75 = 12/30

Cross multiply

30x = 12 * 75

30x = 900

Divide both sides by 30

30x/30 = 900/30

x = 30

Therefore, when two segments c, d, and a, b, cross at point e to form two triangles, the value of x is 30 cm.

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The radical form of the given exponential form of a number 11x^(1/4) is written as ( 11 ) × [tex]\sqrt[4]{x}[/tex].

As given in the question ,

Given exponential form is equal to :

11x^(1/4)

Using th formula to convert exponential form into radical form in standard form we have :

( y )^ ( a / b ) = [tex]\sqrt[b]{y^{a} }[/tex]

Here y is equal to x

a is equal to 1

b is equal to 4

Substitute the value of the given expressions in the formula we have,

11x^(1/4)

= ( 11 ) ×  [x^(1/4) ]

= ( 11 ) × [tex]\sqrt[4]{x^{1} }[/tex]

Any thing raise to one is the number or variable itself the required radical form is equal to:

=  ( 11 ) × [tex]\sqrt[4]{x}[/tex]

Therefore, the radical form of the given expression 11x^(1/4) is given by :

( 11 ) × [tex]\sqrt[4]{x}[/tex].

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The volume of the storage compartment is 1246 cube ft.

In the given question, we have to find the volume of the storage compartment.

The diagram of the question is given below.

If we see the diagram it forms two recatangle with the lengths given below.

As we know that the volume of the cuboid is

V = LBH

where, L = length, B = breadth, H = Height

Now finding the volume of the cuboid A.

So V(A) = 10*8*15

V(A) = 1200 cube ft

Now finding the volume of the cuboid B.

So V(B) = 2*8*3

V(B) = 48 cube ft

Now the volume of the storage compartment is the sum of the volume of cuboid A and volume of the cuboid B, then we subtract 2 ft because we count the 2 ft of height two times.

The volume of storage compartment = volume of the cuboid A + volume of the cuboid B - 2 ft

The volume of storage compartment = 1200 + 48 - 2

The volume of storage compartment = 1248 - 2

The volume of storage compartment = 1246 cube ft

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The triangles Illustrated are not similar. The correct option is 4. no not similar

If two pairs of corresponding angles in two triangles are congruent, then the triangles are similar. All three corresponding sides of the acronym SSS (side-side-side) are congruent. SAS (side-angle-side) (side-angle-side) Congruence exists between two sides and their angle.

The triangles are congruent if all three sets of corresponding sides are present. The side-side-side shortcut is a congruence technique (SSS). Side-angle-side (SAS), which uses two pairs of sides and an angle between them that is known to be congruent, is another shortcut.

In this case, they aren't similar. The correct option is 4.

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The number of weeks it would take is 24 weeks.

The first step is to determine how many weeks it would take to learn one piece. In order to determine his value, divide 18 by 36.

Number of weeks = 18 / 36 = 0.50

Now, multiply the answers gotten in thee previous step by 48

Number of weeks it would take to learn 48 songs = 0.50 x 48  = 24

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The operational costs a business bears in order to make money are referred to as expenses.

The Complete Question is expenses.

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Step-by-step explanation:

what is the area of the whole circle ?

pi×r²

what is the segment length of the whole circle ?

right, that is the circumference :

2×pi×r

and a whole circle stand for 360°.

if we have only a part of these 360°, then all the attributes of the circle apply only to the corresponding fraction of 360°.

the "segment area" is (I assume) the shaded area.

that is the area of the whole segment XZY minus the triangle area.

let's start with the arc length (the easier part) :

again, for 360° it is

2×pi×r

for 135° it is

2×pi×r × 135/360 = 2×pi×8 × 135/360 =

= 18.84955592... cm

for the segment area :

the area of the full segment is

pi×r² = pi×8² = 64pi

for 135° it is

64pi × 135/360 = 75.39822369... cm²

the inner triangle is an isoceles triangle (both legs are equally long : 8 cm).

when we have the 2 legs and the encoded angle, the area of the triangle is

area= (a x b x sin(c))/2, where a, b are the two legs, and c is the angle between them.

area of the triangle = 8×8×sin(135)/2 = 22.627417... cm²

the shaded area is then

75.39822369... - 22.627417... = 52.77080669... cm²

The formula which we would use to know the probability that it is a defective tire of brand A is P(A|D) = P(D|A)P(A) / P(D). P(D) is the probability that a tire produced is defective.

Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.

A car producer stocks three types of tires. They are A, B, and C.

The percentage of defective tires is 2%, 1% and 5%, respectively. Someone picks a tire randomly and he gets brand A.

Find the formula to know the probability that it is a defective tire!

The options are

a) P(A|D) = P(D|A)P(A) / P(D)

b) P(D|A) = P(A|D)P(D) / P(A)

c) P(A|D)= P(D/A)P(D) / P(A)

d) P(D|A)= P(A|D)P(A) / P(D)

From the information, we get:

The probability that it is a defective tire of brand A = P(A|D). The formula is

P(A|D) = P(A∩D) / P(D)

P(A|D) = P(D|A)P(A) / P(D)

Hence, if we want to know the probability that it is a defective tire, the formula would be P(A|D)= P(D|A)P(A) / P(D).

The answer is (a).

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When evaluated [tex]\frac 23+\frac 34+\frac 42$[/tex] into simplified form we get [tex]3\frac{5}{12}[/tex] as the answer.

If the top and bottom have no common factors other than one, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and remain whole numbers.

You may also hear "lowest terms" when referring to the simplest form.

The fraction 4/5, for example, is in its simplest form. Except for 1, there is no number that divides both 4 and 5.

To evaluate in simplified form

[tex]$\frac 23+\frac 34+\frac 42$[/tex]

Lets simplify!

[tex]$ \Rightarrow \frac 23+\frac 34+\frac 42$[/tex]

[tex]$ \Rightarrow \frac{8}{12} + \frac{9}{12} +\frac{24}{12}[/tex]

[tex]$ \Rightarrow \frac{8+9+24}{12}[/tex]

[tex]$ \Rightarrow \frac{41}{12} = 3\frac{5}{12}[/tex]

Thus, when evaluated [tex]\frac 23+\frac 34+\frac 42$[/tex] into simplified form we get [tex]3\frac{5}{12}[/tex] as the answer.

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The solution to the given equations y = 1.5x - 4, y = -4 is (0, -4).

We can solve the given system of equations by the substitution method.

The substitution method is the algebraic approach to solving simultaneous linear equations. As the word tells, in this method, the value of one variable from one equation is substituted in the other equation and gets the value of the one variable.

y = 1.5x - 4     eqn(1)

y = -4       eqn(2)

Put the value of y in eqn(2)

- 4 = 1.5x - 4

Solve the above equation for x, by transferring the terms,

1.5x = - 4 + 4

1.5x = 0

x = 0

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The value of t in the trigonometric equation are The value of t is cos-1(-3 ± 1)

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

One of the most significant areas of mathematics is trigonometry. The terms "Trigonon" and "Metron," which imply triangle and measure respectively, are combined to produce the word "trigonometry." It is the examination of how a right-angled triangle's sides and angles relate to one another. It is therefore helpful to use formulae and identities based on this connection to determine the measure of a right-angled triangle's unknown dimensions.

In trigonometry, there are six fundamental ratios that are used to create a connection between a right triangle's side-to-angle ratio and its angle. If the angle created by the base and hypotenuse of a right-angled triangle is, then

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

Now,

sin2(t) = Gcos(t)

I — cos2(t) — 6cos(t) = O

cos(t) = -3 ± 1

The value of t is cos-1(-3 ± 1)

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