-8(i - 6) = 32
Solve equation with distributive property

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

-20x^4y + 40x^3y^2.

Step-by-step explanation:

-5x^3y(4x-8y)

= -5x^3y * 4x + -5x^3y * -8y

= -20x^4y + 40x^3y^2

The sprinkler for the Cook family uses 15 liters of water per hour, whereas the Gonzalez family uses 40 liters of water per hour.

We can set up the following system of equations based on the given information:

Equation 1: x * 15 + y * 40 = 1825 (total water output equation)

Equation 2: x + y = 55 (sum of the two rates equation)

We can solve this system of equations to find the values of x and y.

Multiplying Equation 2 by 15, we get:

15x + 15y = 825

Subtracting this equation from Equation 1, we get:

25y = 1000

y = 1000 / 25

y = 40

Substituting the value of y in Equation 2, we get:

x + 40 = 55

x = 55 - 40

x = 15

Therefore, The sprinkler for the Cook family uses 15 liters of water per hour, whereas the Gonzalez family uses 40 liters of water per hour.

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Answer:

?????????????????

Step-by-step explanation:

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Answer:

n=91

Step-by-step explanation:

(n×7)+2=100

n+9=100

-9 from both sides

n=91

The length of AB is 78 units.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure is given below shows a line segment AB , where the length of line segment AB refers to the distance between its endpoints, A and B.

Given that C is the midpoint of AB

AC = 8x - 1 and BC = 4x + 19,

A______________C______________B

⇒ AB = AC+ BC

Since C is the bisects of AB, So AC = BC

⇒ AB = AC+ BC

⇒ AB = 2AC

Substitute the values of If AC = 8x - 1 and BC = 4x + 19,

⇒ 8x - 1 = 4x + 19,

Rearranging the terms in the above equation,

⇒ 8x - 4x  = 1 + 19,

⇒ 4x = 20,

⇒ x = 20/4,

⇒ x = 5

So AB = 2AC

⇒ AB = 2(8x - 1) = 16x -2

Substitute the value of x = 5 in the above equation,

⇒ AB = 16(5) -2

⇒ AB = 78

Hence, the length of AB is 78 units.

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Answer:

y=-4x-1

Step-by-step explanation:

All you have to do is isolate the "y", so you subtract 4x from the left and right side, leaving you with the answer above.

There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The phrase "If every element x of X is associated with the equivalent one-term sequence (x)" states that there's a corresponding one-term sequence (x) appropriately represents each element x in collection X.

Sequences are ordered sequences of integers (called "terms") like 2,5,8. Certain sequences follow a specific pattern that can be utilised to expand them forever. For example, 2,5,8 follows the pattern "add 3," allowing us to continue with the series. Sequences contain formulas that tell us how to discover any term in a series.

You should be familiar with four sorts of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.

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While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:

Theorist Approach to Learning Key Concepts

Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.

Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.

Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

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Answer:

Common ratio r = \(\dfrac{2}{3}\)

Sequence  is described by
\(a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\\)

Step-by-step explanation:

\(S_n = \dfrac{a_1(1-r^n)}{1-r}\)

where
r = common ratio
a₁ = first term

Sum of first two terms

\(S_2 = \dfrac{a_1(1-r^2)}{1-r}\)

Sum of first four terms:
\(S_4 = \dfrac{a_1(1-r^4)}{1-r}\)

\(\dfrac{S_4}{S_2} = a_1 \cdot \dfrac{1-r^4}{1-r} \div a_1 \cdot \dfrac{1-r^2}{1-r}\\\)

To divide, flip the divisor and multiply

\(\dfrac{S_4}{S_2} =\dfrac{a_1(1-r^4)}{1-r} \times \dfrac{1-r}{a_1(1-r^2)}\)

The a₁ and (1-r) terms cancel out from numerator and denominator leaving

\(\dfrac{S_4}{S_2} =\dfrac{1-r^4}{1-r^2} \cdots [1]\)  

Using the identity
\(a^2 - b^2 = (a- b)(a+b)\)

\(1- r^4 = 1^4 - r^4 = (1^2 - r^2)(1^2+r^2) = (1-r^2)(1+r^2)\)

Plugging this into equation 1 we get
\(\dfrac{S_4}{S_2} =\dfrac{(1-r^{2})(1+r^{2})}{1-r^{2}}\)

The \(1- r^2\) terms cancel out leaving:
\(\dfrac{S_4}{S_2} =1 + r^2\)

We are given

\(S_4 =\dfrac{65}{18}\\\\S_2 = \dfrac{5}{2}\)

\(\dfrac{S_4}{S_2} = \dfrac{65}{18} \div \dfrac{5}{2}\)

To divide, flip the denominator \(\dfrac{5}{2}\) and multiply
\(\dfrac{S_4}{S_2} = \dfrac{65}{18} \times \dfrac{2}{5}\\\\= \dfrac{13}{9}\)

Therefore
\(1 + r^2 = \dfrac{13}{9}\\\\r^2 = \dfrac{13}{9} - 1\\\\= \dfrac{13}{9} - \dfrac{9}{9}\\\\= \dfrac{4}{9}\)

\(r = \sqrt{\dfrac{4}{9}}\\\\= \dfrac{\sqrt{4}}{\sqrt{9}}\\\\= \dfrac{2}{3}\)

So the common ratio
\(r = \dfrac{2}{3}\)

To find the first term  we have sum of first two terms = 5/2

\(S_2 = \dfrac{a_1(1-r^2)}{(1-r)} = a_1 (1+ r)\)

Plugging in knowns
\(\dfrac{5}{2} = a_1(1+\dfrac{2}{3})\\\\= a_1 \cdot \dfrac{5}{3}\)

Multiply both sides by 3/5 to get
\(a_1 = \dfrac{5}{2} \times \dfrac{3}{5}\\\\a_1 = \dfrac{3}{2}\)

The nth term of a GP is
\(a_n = a_1 \cdot r^{n-1}\\\)

Plugging in the values obtained
\(a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\\)

The solution is, 29/h is the quotient of twenty-nine and a number h​.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

give that, we have to find  the quotient of twenty-nine and a number h​

i.e. 29/h which is the quotient of twenty-nine and a number h​

as, we know.

quotient is the result of division so you divide 29 by h which gives you 29/h or h/29

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The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.

Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

\(g(h(10)) = 2\sqrt 2\)

Step-by-step explanation:

Given

\(g(x) = \sqrt {x - 4\)

\(h(x) = 2x - 8\)

Required

\(g(h(10))\)

First, calculate \(g(h(x))\)

We have:

\(g(x) = \sqrt {x - 4\)

This gives:

\(g(h(x)) = \sqrt {h(x) - 4\)

Substitute \(h(x) = 2x - 8\)

\(g(h(x)) = \sqrt {2x - 8 - 4\)

\(g(h(x)) = \sqrt {2x - 12\)

Substitute \(x = 10\)

\(g(h(10)) = \sqrt {2*10 - 12\)

\(g(h(10)) = \sqrt {20 - 12\)

\(g(h(10)) = \sqrt {8\\\)

Split

\(g(h(10)) = \sqrt {4} * \sqrt 2\)

This gives

\(g(h(10)) = 2\sqrt 2\)

Answer:

Step-by-step explanation:

Answer:

A. 4×0= 0

Step-by-step explanation:

since it shows that any number you multiply by 0 still gives you 0

Answer:

1.125 x 1000/1 x 1000 = 1125/1000

[(1125/125)/(1000/125)] = 9/8

1 1/8

Answer:

I think its 32, I don't know how to put it into a linear equation I hope it helps enough though.

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

An equation is formed of two equal expressions. The equation of the new graph will be y=|1/(2x-4)|+3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation given is  \(y=\left|\dfrac{1}{2x-2}\right|+3\), which is needed to be translated 1 unit to the right therefore, the value of x should be decreased by 1. Therefore, the equation of the new graph will be,

\(y=\left|\dfrac{1}{2(x-1)-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-2-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-4}\right|+3\)

Hence, the equation of the new graph will be y=|1/(2x-4)|+3.

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Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The empirical rules states that for a normal distribution, 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within three standard deviations from the mean.

Given that:

mean (μ) = 71 inches, standard deviation (σ) = 4.3 inches

One standard deviation = μ ± σ = 71 ± 4.3 = (66.7, 75.3)

Two standard deviation = μ ± 2σ = 71 ± 2*4.3 = (62.4, 79.6)

Three standard deviation = μ ± 3σ = 71 ± 3*4.3 = (58.1, 83.9)

The graph is attached