Amy works 15 hours a week at the movie theater. She earns $8 an hour. What statement is true about her weekly income? A) Her net income is more than $120. B) Her gross income is less than $120. C) Her net income is less than $120. D) Her gross income is more than $120.

The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

Given that,

The function is f(x)= (x-5)³(x+2)²

We have to find at which root does the graph function touch the x-axis.

We know that,

Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.

Take the function

f(x) = (x-5)³(x+2)²

f(x) = 0 if a curve touches the x-axis.

⇒ (x - 5)³(x + 2)² = 0.

But if ab = 0

So, a=0 and b=0

⇒ (x - 5)³ = 0 and (x + 2)² = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x=5 and x=-2.

Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

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Continuity of a function can be checked by examining the limits of the function as x approaches a certain value and ensuring the function's output is equal to the value of the function at that point.

Continuity of a function is an important concept in calculus and other branches of mathematics. In order to check the continuity of a function, the limits of the function must be examined as x approaches a certain value. This means that the left-hand limit and the right-hand limit must be equal. If the limits are equal, then the function is continuous at that point. If the limits are not equal, then the function is not continuous at that point. Additionally, the value of the function at that point must also be equal to the limits in order for the function to be continuous. If the function is discontinuous at any point, then it is not considered continuous. Continuity is necessary for certain properties of functions, such as derivatives and integrals, to be defined.

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Answer:

1. y=x    2. x=4   3. y=3x-10   4. y=-2/5x-1/5    5. y=-8x-13    6. y=-x+3

Step-by-step explanation:

The factors form of the given equation 3x²−6x is 3x(x−2)

Given that:

3x²−6x

To find : The factor form of 3x²−6x

The splitting or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. You will mostly learn this idea in your lower secondary studies, which run from grades 6 to 8.

=3×x×x−2×3×x, factor each monomial

=3x(x−2), factor out common factor 3x

The factors form of 3x²−6x is 3x(x−2)

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If we can move one thing without affecting its size or shape such that it perfectly overlays the other picture, then two objects are congruent. These motions are what are known as congruence transformations.

While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

In order for two items to be congruent, one of them must be able to be moved over the other without affecting its size or form. Congruence changes are what we refer to as these motions. The transformation of an object into a congruent object is known as a congruence transformation.

∠A = ∠B

And, also

AB = BC

AD = BD

Therefore,

ΔABC ≅ ΔDEF

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If q ║ r, value of x is 17.

When a transversal connects two or more parallel lines at different locations, alternate exterior angles are created. The word exterior refers to something that is located outside. Whenever the transversal intersects two lines, alternate external angles are always outside of those two lines and are situated on the opposing sides of the transversal. As a result, the pair of alternate external angles—two outside angles—that arise at the opposing ends of transversals in the exterior section are always equal. When a transversal splits two parallel lines, we obtain two of these pairs of alternate exterior angles.

Given

q ║ r

Alternate exterior angle,

7x - 10 = 9x - 44

9x - 7x = 44 - 10

2x = 34

x = 17

If q ║ r, value of x is 17.

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The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a summation symbol (∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the starting value of the index, and a colon (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.

To rewrite the given expression using the summation notation, we can use the following steps:

Identify the series of terms: 1 + 2 + 3 + ... + n.

Write the series of terms below the summation symbol: ∑ k = 1

Replace the variable in each term with the index: 1! + 2! + 3! + ... + (n+1)!

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

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The polynomial 3xA² is a linear monomial having one term and a degree one.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

There are many types of polynomials according to the number of terms they have.

If a polynomial has one term it is called a monomial, Has two terms called a binomial, and having three makes it a trinomial.

Given, A polynomial 3xA².

Now, The variable is 'x' and raised to the power of 1 so it is linear and consists of only one term so it is a monomial as 3 and A are constants.

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The roots of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the nature of the roots is real and equal.

The nature of the roots of a quadratic equation ax2 + bx + c = 0 with real coefficients a, b, and c can be determined by using the quadratic formula. The quadratic formula states that the two roots of the equation are given by:

x = (-b ± √(b2 - 4ac)) / 2a

For the equation 2x2 + 4x = 0, a = 2, b = 4, and c = 0. Substituting these values into the quadratic formula, we get the two roots of the equation as:

x = (-4 ± √(42 - 4(2)(0))) / 2(2)

x = (-4 ± 0) / 4

x = -1, 0

Therefore, the roots of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the nature of the roots is real and equal.

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Answer:

6/4

1 2/4

1 1/2

Step-by-step explanation:

3 x 2/4 = 3/2 or 1 1/2

6/4 reduces to 3/2 as factors of 2

1 2/4 simplifies to 1 1/2

1 1/2 is equal to 3/2

As per the given height of the wall, the approximate weight is 149kN

The term Hydrostatic refers to the force exerted by static water on the plate or object and its magnitude depends upon the positioning of the object inside the water.

Here we have given the following values,

Height = 2.76 upright

Width = 10 m

Here we have to consider the hydrostatic force acting on the wall about the pinned point say P then the expression is looks like,

=> F = ωAx

=> F =  9810(10 × 4) × 2

=> F = 784800 N = 785KN

Now, the weight is calculated as per the Hydrostatic method as,

=> W = (1.33/7) x 785

=> W = 149 kN

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Step-by-step explanation:

To find the ratio between Rohit's savings and expenditure, we need to divide his savings by his expenditure:

Savings / Expenditure = (1500 - 1250) / 1250 = 250 / 1250 = 1/5

The ratio between Rohit's savings and expenditure is 1/5.

To find the ratio between Rohit's expenditure and income, we need to divide his expenditure by his income:

Expenditure / Income = 1250 / 1500 = 5/6

The ratio between Rohit's expenditure and income is 5/6.

To find the ratio between Rohit's income and savings, we need to divide his income by his savings:

Income / Savings = 1500 / (1500 - 1250) = 1500 / 250 = 6/1

The ratio between Rohit's income and savings is 6/1.

The height of the tower where surveyor positions a transit that is 2 m tall  = 45.19 m

Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent are the six trigonometric functions. The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of the lengths of the two sides.

given:

transit height = 2 m

distance from the base of the tower = 35 m

angle of elevation = 51°

Utilize trigonometric functions to solve this problem. The tangent trigonometric function connects the opposite side and the neighboring side.

Opposite side / Adjacent side = tan Ф

solving opposite side = Opposite side = Adjacent side x tan Ф

Opposite side = 35 x tan 51°

Opposite side = 35 x  1.234

Opposite side = 43.19 m

calculating the tower height = 43.19 + 2 m

= 45.19 m

therefore the height of the tower = 45.19 m

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Answer:

{ X = 5} {Y = 3} pls mark brainliest

Step-by-step explanation:

Add the two equations: 4x + 7y + (x-7y) = 41 + (-16)

Remove parentheses: 4x + 7y + x-7y = 41 + -16

Cancel one variable:4x + x + = 41 + -16

Combine like terms: 5x = 41 - 16

Calculate the sum or difference: 5x = 25

Divide both sides of the equation by the coefficient of variable: x = 25/5

Cross out the common factor: X = 5

Substitute into one of the equations: 5 - 7y = -16

Rearrange unknown terms to the left side of the equation:  5 - 7y = -16 - 5

Calculate the sum or difference: -7y = -21

Divide both sides of the equation by the coefficient of variable: -21/-7

Determine the sign for multiplication or division: y = 21/7

Cross out the common factor: y = 3

The solution of the system is: { X = 5} {Y = 3}

We are asked to find the first derivative of,

[tex]\longrightarrow g(x) = \sqrt{x^2+2x}[/tex]

Here we can write the term [tex]x^2+2x[/tex] by adding and subtracting 1 as,

[tex]x^2+2x = x^2+2x+1-1[/tex]

[tex]x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2][/tex]

Thus,

[tex]\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)[/tex]

Now take,

[tex]x+1=\sec\theta\quad\dots(2)[/tex]

[tex]x=\sec\theta-1[/tex]

[tex]dx=\sec\theta\tan\theta\, d\theta[/tex]

[tex]\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)[/tex]

Then (1) becomes,

[tex]\longrightarrow g(x) = \sqrt{sec^2\theta-1}[/tex]

We have,

[tex]\sec^2\theta-1=\tan^2\theta[/tex]

So we get,

[tex]\longrightarrow g(x) = \tan\theta[/tex]

Now,

[tex]\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta][/tex]

By chain rule,

[tex]\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}[/tex]

[tex]\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}[/tex]

[tex]\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)[/tex]

But we have,

[tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]

[tex]\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}[/tex]

Hence (4) becomes,

[tex]\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}[/tex]

This is the first derivative of the given function.

More than 2 in mathematical expression is written as >2.

The relationship between two quantities can be described using comparison terms. There are primarily three comparison terms: more than (>), less than (<), and equal to (=).

More than (>): When one quantity is greater than the other quantity, we use “more than”. For example, 5 > 3.

Less than (<): When one quantity is less than the other quantity, we use “less than”. For example, 8 < 10.

Equal to (=): When two quantities are the same, we use “equal to”. For example, 15 = 15.

More than 2 means, greater than but not including 2, which is written as >2

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Answer:

m = 5

Step-by-step explanation:

The equation is y = mx + b

The m here is the slope; in this case, the slope is 5

The number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44 is one of this {798, 1726, 2654}.

There exists a, b∈N such as

N= 30+32a=44+58b

Therefore,

16a-29b= 22-15=7

Let us notice that 5×29-9×16=1

Therefore, 35×29-63×16=7

Hence, a= -63 is a non-fundamental solution to our equation.

We can show that the other solution are of the form a=-63+29k, with k∈Z

Therefore, the first positive solutions are

a= -63+3×29= 24

N= 798

a= -63+4×29= 53

N= 1726

a= -63+5×29=82

N= -63+6×29= 111

N= 3582

Therefore, the number is one of {798, 1726, 2654}.

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15  is the mean of 20 and 10 .

What are the mean, median, and example?

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

x = 20 + 10/2

x = 30/2

x = 15

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Answer:

Additional root of 7+√5 and 1/4 is:

D.5-√7

A corporate bond has a face value of p dollars. The interest each year is 6% of the face value.  the total interest /, in dollars, as a function of the age f, in years, of the bond is

a)I(f) = 0.06 * f * p

b) P(f) = I(f) + p

Generally, (a) The total interest, in dollars, as a function of the age f, in years, of the bond can be expressed as:

I(f) = 0.06 * f * p

This represents the total interest paid over f years, which is calculated by multiplying the annual interest rate (0.06), the number of years (f), and the face value of the bond (p).

(b) The payout P, in dollars, as a function of f can be expressed as:

P(f) = I(f) + p

This represents the total payout over f years, which is calculated by adding the total interest paid (I(f)) and the face value of the bond (p).

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The image of the point after the translation is (5,3)

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

Point =(4, 4)

This point can be represented as

(x, y) = (4, 4)

The translation equation is given as

(x,y)-->(x+1,y-1)

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

(x,y)-->(4+1,4-1)

Evaluate

(x,y)--> (5,3)

Hence, the image is (5,3)

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Answer:

Step-by-step explanation:

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Probability of event to happen P (E) = Number of favourable outcomes/Total Number of outcomes

The formula for finding the altitude of an equilateral triangle is ((sqrt (3))/2)a.

As we know, the sides of an equilateral triangle are equal. Let the side of the triangle be 'a'.

Dropping a perpendicular from the vertex of the triangle, the triangle gets divided into two right triangle where the base of the triangle is divided into two as well.

Therefore, by using the Pythagoras' theorem,

we can get the altitude (say 'h') of the triangle by:

h^2 = a ^ 2 - (a/2) ^ 2 = 3a ^ 2/4

h = sqrt (3a^2/4) = ((sqrt (3))/2)a.

The question is incomplete, the complete question is:

What is the formula for finding the altitude of an equilateral triangle?

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Answer:

Answer is 4, but in the answer choices provided it is 4b.

Step-by-step explanation:

Use PEMDAS! (Order of PEMDAS: Parenthesis, exponent, Multiplication, division, addition, subraction)

1. Multiply 6b x 2= 12b.

2. Divide 12b by 3b = 4. or 4b

Answer:

---------------------------

Correct choice is D.

The length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

Given :

What is average?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

There were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

The average length  = 9.04 feet

The length of the line can be found as follows:

= 9.04 * 1,000,000

The length of the line  = 9,040,000 feet/5280 feet (1 mile)

= 1712.12 miles

Thus, the length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

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Answer:

A = 3

B = 6

C = 4

D = 5

left rectangle = 4 x 6 = 24

mid = 5 x 6 = 30

right = 6 x 3 = 18

both triangles = 4 x 3 = 12

24 + 30 + 18 + 12

= 84 cm²

Answer: 84

Step-by-step explanation:

The 16% variability in weight can be explained by the relationship with height.

What is correlation?

In statistics, there are three different forms of correlation: positive, negative, and no correlation.

The link between two variables is said to be positive correlated when both variables move in the same direction. When one variable decline (or grows) while the other variable lowers (or increases), there is a positive perfect correlation, denoted by the number +1.

When two variables are correlated negatively, both of the variables are moving in the opposing direction. When one variable rises (or falls) while the other rises (or falls), there is a negative perfect correlation, which is symbolised by the number -1.

No correlation, which is represented by 0, means that there is no connection or reliance between the two variables.

On the basis of provided information, the correlation between the height and weight for adults is,

r = +0.4

So, the coefficient of determination is calculated as,

[tex]r^{2} = (0.40)^{2}[/tex] = 0.16 = 16%

Based on the provided information, the required answer is 16%.

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