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Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x³ feet, and the rectangular plot of land has a length of 3x⁵ feet and a width of 7x² feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3.

The value of the discriminant for 2x² + 5x + 7 = 0 is -31.

The discriminant of a quadratic equation is the part of the equation used to determine the number and type of solutions. It is calculated by subtracting 4 times the coefficient of the squared term, a, from the coefficient of the linear term, b, squared. This is then divided by four times the coefficient of the squared term, a.

In this case, the equation is 2x² + 5x + 7 = 0.

The discriminant for this equation is calculated as follows:

Discriminant = b² - 4ac

Discriminant = (5)² - 4(2)(7)

Discriminant = 25 - 56

Discriminant = -31

Therefore, the value of the discriminant for 2x² + 5x + 7 = 0 is -31.

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Answer:

Step-by-step explanation:

To find the time it takes for the rock to hit the water, we need to find the value of t when h is equal to zero. This is because the rock will hit the water when it reaches a height of zero feet above the water.

Substituting zero for h in the equation h = -16t^2 + 12t + 40, we get:

0 = -16t^2 + 12t + 40

This equation is a quadratic in t, so we can use the quadratic formula to solve for t:

t = (-12 +/- sqrt(12^2 - 4 * (-16) * 40)) / (-32)

Simplifying, we get:

t = (-12 +/- sqrt(144 + 640)) / (-32)

t = (-12 +/- sqrt(784)) / (-32)

t = (-12 +/- 28) / (-32)

t = -40/-32 or t = 16/-32

t = 1/8 or t = -1/2

Since the time cannot be negative (because the rock was thrown upwards), the only solution that makes sense is t = 1/8 seconds.

Therefore, it will take 1/8 seconds for the rock to hit the water.

x-1 is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1

if we equate x-1=0

=> x=1

after putting the value of x=1 in the equation  [tex]x^2-2x+1[/tex] to find the remainder.

so the value of [tex]x^2-2x+1[/tex] when x=1

=>1 -2*1 +1

=>0

so the value is 0 which means that x-1 completely divides the given equation  [tex]x^2-2x+1[/tex]

since the given equation is quadratic equation and one factor is linear so other factor which is quotient also need to be linear.

let the quotient after division is ax+b

and according to rule of division

[tex]x^2-2x+1[/tex] = (x-1)*(ax+b)

as remainder is 0

so (x-1)*(ax+b) = a[tex]x^2[/tex] +(b-a)x -b

comparing a[tex]x^2[/tex] +(b-a)x -b with  [tex]x^2-2x+1[/tex]

we observe that a=1 ,b=-1

so the quotient of the above divsion is x-1

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Complete question:

what is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1

Answer:

3+(t/2) or 3+t/2

Step-by-step explanation:

sum is addition

quotient is division

so, a quotient of T and 2 is t/2 (t divided by 2), and a sum of that and 3 is 3+(t/2)

Adding the parenthesis is optional :)

Answer:

these are okayish grades but great effort.

Answer:

B. 2.2 kilometers

Step-by-step explanation:

⭐What is the change in the cyclist's elevation?

Thus, we need to solve for the value of the height (x) of the hill.

Notice that the hill is in the shape of a right triangle. In order to find an unknown side length for right triangles, we need to use a trigonometric function.

⭐What is a trigonometric function?

First, let's see what kind of side lengths we are given (opposite, hypotenuse, or adjacent).

We are given a side length of 10km, which is the hypotenuse of the triangle, and we are given a side length of x, which is the opposite of θ (13°).

Therefore, we will use the trigonometric function sin(θ) to solve for x.

Substitute the side lengths and angle measures we are given:

[tex]sin(13) = \frac{x}{10}[/tex]

Set the equation equal to x:

[tex]10sin(13) = x[/tex]

Solve for x. I recommend using a scientific calculator (e.g. Desmos Scientific Calculator):

[tex]2.2 = x[/tex]

∴ The cyclist's change in elevation is 2.2 kilometers.

Answer:

integers have signs like -&+ while whole numbers are ALWAYS positive

There are some postulates, such as Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side, that can be applied to demonstrate the congruence of triangles.

The Angle-Side-Angle (ASA) postulate asserts that two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

The basic components, primarily the three angles as well as the three sides of a triangle, must be equal to the corresponding angles and sides of the other triangle for two triangles to be congruent.

To demonstrate that the triangle ABC is congruent, we must show that two of its angles and one of its sides are congruent.

If the lengths of the matching sides and angles of two triangles match, the triangles are said to be congruent. In maths, congruence relates to the similarity of two figures in terms of their size and shape. The mirror image of one shape is the same as the other if two shapes are congruent.

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Answer: The angle is 90 degrees.

Step-by-step explanation:

A triangle that has a diameter as its hypotenuse inside a inscribed circle has a right angle opposite of its hypotenuse. This is true for any right triangle inscribed in a circle, because the equation to get measure B is:

(angle ABC) = 1/2 * (angle AOC)

Angle AOC is 180 degrees. Putting 180 into the euqation, we get 90 degrees for angle ABC.

Answer:

[tex]Option C) 120cm^{3}[/tex]

Step-by-step explanation:

As we know the formula to find the volume is,

[tex]V=LXBXH[/tex]

[tex]V=5cm x 3cmx8cm[/tex]

[tex]V=120cm^{3}[/tex]

Hope it helps you

Based on the graph provided, the range of the function is the set of all real numbers. Therefore, the correct answer is (B) y is all real numbers.

Generally, To find the range of a function, you need to find the set of all possible output values of the function.

In this case, the range of the function is given by the set of all y-values that appear on the graph of the function.

The set of all real numbers is considered to represent the range of the function according to the graph that has been supplied. As a result, the response that is accurate is (B), which states that y only contains real values.

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Congruent shapes or figures can be said to be congruent if they can be related to each other by a transformation, such as a translation, rotation, reflection or scaling.

For example, two triangles are congruent if they can be related to each other by a rotation of 180 degrees.

To establish a student experience that yields significant and equitable improvements in outcomes and educational value, an institution's structures, culture, and business model must be realigned. This process is known as transformation.

Any action or set of actions that takes one or more inputs, changes and adds value to them, and then produces outputs for consumers or clients is referred to as a transformation process.

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When X=3 a polynomial has a value of 61 and when X=3 a value of 143.

Given that,

Let p(x)=3x²−4x²+7x−5 is our polynomial.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Substitute x=3 in above expression,

∴p(3)=3(3) 3−4(3) 2 +7(3)−5

=3(27)−4(9)+21−5

=81−36+21−5

=61

Now,

p(−3)=3(−3)

3 −4(−3) 2 +7(−3)−5

=3(−27)−4(9)−21−5

=−81−36−21−5

=−143

So, value of polynomial when X=3 is 61 and when x=−3 is −143

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Answer: (n-2) * 180

Step-by-step explanation:

The formula for the sum of the interior angle measures of a polygon with n sides is (n - 2)180 degrees.

Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent. Due to the stiff transformations' preservation of the distance and angle scales, all related sides and angles are congruent.

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In a given year, a member may get illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward. For the same condition, the sickness benefit cannot be awarded for more than 240 days.

A daily cash payment is made for each day a member is unable to work as a result of illness or accident.

Qualification Requirements

If a member meets the following criteria, they may be eligible to receive this benefit: Is unable to work due to illness or injury and is confined to a hospital or their home for a minimum of four (4) days;

Has duly notified the SSS directly of the fact of sickness or injury;

Has paid at least three (3) months' worth of payments within the 12-month period immediately preceding the semester of illness or injury.

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Answer:

2/1

Step-by-step explanation:

Answer:

the answer is 2!

Step-by-step explanation:

you count the rise over run

count from where it meets a whole number to where it meets another whole number and then you have your answer!

for this you count from (3,3) to (2,1) which is 2/1 making it 2

As per the concept of inverse function, the domain of f is the range of f⁻¹, and the domain of f⁻¹ is the range of f.

The term inverse function in math is referred as the function y=f(x) can be obtained by switching x and y and solving for y and then the value y will be replaced with f⁻¹ as this denotes the inverse of the function f.

Here we need to find the domain of f is the _____of f⁻¹, and the _____ of f⁻¹ is the range of f.

As we all know that the domain refers the set of all inputs of the function and range refers the set of all outputs of the function.

Based on these definition we have identified that the domain of function is always be the range of inverse function f.

Similarly, the range of inverse function f is always the domain of the function f.

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Answer:

m=1/5

Step-by-step explanation:

SImplify

4m-8=-6m-6

then 10m=2

so m=1/5

4(m - 2) = -2(3m + 3)

4m - 8 = -6m -6

4m + 6m = -6 + 8

10m = 2

m = 1/5   or 0.2

4(0.2 - 2) = -2[3(0.2) + 3]

4(-1.8) = -2(0.6 + 3)

- 7.2 = -2(3.6)

- 7.2 = - 7.2

Step-by-step explanation:

Choices B and C are both correct statements.

Choices A and D are both false.

The y-intercept of the line tells us about the situation when Justine started the race she was 10 kilometers from the finish line.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given, a line whose y-intercept is at y = 10 which is represented by the distance remaining in kilometers. Since x shows the time spent running that means at x = 0 she started running.

Therefore, The y-intercept of the line reveals that Justine was 10 kilometers from the finish line when she started the race.

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The value of y are when x = -2, -1, 0, 1, 2 are -4, 1, 0, -1, 4. The graph of the function attached.

What is coordinate plane?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

Given function is y = x³ - 2x

Putting x = -2 in the equation y = x³ - 2x:

y = (-2)³ - 2×(-2)

y = -4

Putting x = -1 in the equation y = x³ - 2x:

y = (-1)³ - 2×(-1)

y = 1

Putting x = 0 in the equation y = x³ - 2x:

y = (0)³ - 2×(0)

y = 0

Putting x = 1 in the equation y = x³ - 2x:

y = (1)³ - 2×(1)

y = -1

Putting x = 2 in the equation y = x³ - 2x:

y = (2)³ - 2×(2)

y = 4

The points on the equations are (-2,-4), (-1, 1), (0,0), (1,-1), (-2,4).

Plot the points and joint them by curve.

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Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

We can use rational zero theorem to find rational zeros.

Given,

Rational zero theorem;-

According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(x constant )'s term and q is a factor of P's leading coefficient (x). The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.

Purpose of rational zero test;-

It is also known as the rational root test and the rational zero test. It can be used to locate the polynomial function's zeros. One uses it to determine whether a polynomial has rational zeros or roots. A comprehensive list of the polynomial's potential rational roots is also provided.

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There are 50 odd integers from 1 to 100.

Odd integers  are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd integer by 2, then it will leave a remainder. In other words, numbers in the form of [tex]2k + 1[/tex], where [tex]k[/tex] ∈ [tex]Z[/tex] (i.e. integers) are called odd numbers.

First odd number is 1 from 1 to 100.

Last odd number is 99 from 1 to 100.

Total odd numbers = 99+1 ÷ 2 = 50

There are 50 odd integers from 1 to 100.

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Answer:

[tex] \displaystyle{\frac{2810}{3}} \pi \: \: \text{cm} ^{3} [/tex]

Step-by-step explanation:

The solid shape is composed of a cone and a hemisphere.

Let's work out the radius of the cone since the hemisphere and the cone share the same radius.

Let the radius be r cm.

Volume of cone= [tex] \displaystyle{\frac{1}{3} \pi {r}^{2} h}[/tex]

Substituting the volume and height of the cone:

[tex]270\pi = \displaystyle{\frac{1}{3} (\pi)( {r}^{2} )(10)}[/tex]

Simplify:

[tex] \frac{10}{3} {r}^{2} = 270[/tex]

[tex]81 = {r}^{2} [/tex]

Square root both sides:

[tex]r = \sqrt{81} [/tex]

r= 9

The volume of a hemisphere is half the volume of a sphere.

Volume of hemisphere

[tex] = \displaystyle{ \frac{1}{2}( \frac{4}{3} )(\pi )( {r}^{3}) }[/tex]

[tex] = \displaystyle{ \frac{2}{3}\pi {r}^{3} }[/tex]

Substituting the value of r:

Volume of hemisphere

[tex] = \displaystyle{ \frac{2}{3} (\pi)(10^{3} )}[/tex]

[tex] = \displaystyle{ \frac{2}{3}(1000)(\pi) }[/tex]

[tex] = \displaystyle{\frac{2000}{3} \pi}[/tex]

Volume of the shape

= volume of cone + volume of hemisphere

[tex] = \displaystyle{(270 + \frac{2000}{3} })\pi[/tex]

[tex] = \displaystyle{ \frac{2810}{3} \pi} \: \: \text{{cm}}^{3} [/tex]

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It is impossible to create an equation for a circle given exactly two points.

Let's consider the two basic equations of circle, i.e, the standard equation and general equation.

Now, Standard equation of circle with center (h, k) and radius r is represented as

(x−h)² +(y−k)² =r²

Note here we need values of three unknowns, h, k, r to get equation of a certain circle.

The other general equation of circle is of the form

x² + y² + 2gx + 2fy + c = 0

Again, values of three unknowns (g, f and c) are necessary for obtaining equation of a certain circle. So in both cases, values of three unknowns are required to have an equation of a distinct circle. In order to calculate, the values of these three unknowns, we must first require three conditions that would be produced by three equations. Solving those equations, allows us to construct the equation of circle. So if only two points are given, then these gives two equations with three unknowns. It would be impossible to get three distinct values from two equations. So, there is no possible distinct circle for two points.

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Both were multiplied by 100 and the quotient of both expressions is 2.5.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

3.75 ÷ 1.50 is equivalent to 375 ÷ 150.

Moving the decimal point 2 places to the right is equivalent to multiplication by 100.

so, both were multiplied by 100.

The quotient is:

3.75 ÷ 1.50 = 2.5

375 ÷ 150 = 2.5

Hence, both were multiplied by 100 and the quotient of both expressions is 2.5.

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The answers to the equation x2 – 6x = 16 are x = -2 and x = 8.

Two approaches to the equation x2 - 6x = 16 will be examined. First, factoring is used; second, the quadratic formula.

We shall employ the subsequent steps when factoring a solution:

Put all of the terms that are not zero on one side of the equation and zero on the other.

Add the non-zero component of the equation.

Solve the equation by setting each factor to 0.

Getting all non-zero terms on one side of the equation is the first thing want to do.

They are 8x and -2x, respectively. Therefore, (x+8) are the factors of x2 + 6x - 16 = 0. (x-2).

Therefore, the answers to the equation  is x2 – 6x = 16 are x = -2 and x = 8.

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