What is the area of the figure below?
3 in.
3 in.
5 in.
5 in.
3 in.
3 in.
7 in.

We can find the base of the isosceles triangle with legs using the formula:

2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base

Let us assume that the leg of the isosceles triangle is 'h' and one side is 'a'. Let the base be 'x'.

As there is a leg (altitude) in the isosceles triangle, then it forms a right triangle in the isosceles triangle, such that the sides form the hypotenuse.

Therefore, by using the Pythagoras' theorem,

hypotenuse ^ 2 = (altitude)^2 + (base / 2)^2

Hence, we get the base by deriving this expression from the above formula:

2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base

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The correct option is option (4) ASA is not a test for similarity

Triangles' similarities can be described based on their features. If two triangles have corresponding sides and have the same ratio and their corresponding angles are equal, then two triangles are said to be similar. The following are the criteria that are used to determine the similarity between two triangles:

1. AAA (Angle-Angle-Angle)

2. SSS (Side-Side-Side)

3. SAS (Side-Angle-Side)

The criteria ASA does not prove the similarity between two triangles as this property does not guarantee that the rest of the sides of one triangle will be similar to those of the other triangle. Thus, ASA criteria are not used to check the similarity between two triangles.

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Taking the function given in the question [tex]f(x) = \frac{10}{x^{2} +1}[/tex] , there are no vertical asymptotes since there no any real values for x , which makes the function undefined.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

To calculate the vetical asymptotes of a function simply equate the denominator of the equation to zero , which when solved gives the values of x at which the function is undefined. Thus the obtained values of x are the vertical asymptotes to the given function.

In the given function f(x), let's equate the denominator to zero to find the vertical asymptotes,

[tex]x^{2} +1 =0[/tex]

Solving the above equation, we get

x = [tex]\sqrt{-1}[/tex]

which is imaginary, hence there is no vertical asymptote for the given function.

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A continuous function is a function that is defined for all values of the independent variable, and its graph has no breaks or jumps. A discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph.

A continuous function is a function that can be graphed without any breaks or jumps. This means that the graph of a continuous function is a single, unbroken curve that passes through all its points. Furthermore, a continuous function is defined for all values of the independent variable. This means that the function is defined for all points in its domain. On the other hand, a discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph. This means that the graph of a discontinuous function will have jumps or breaks. Furthermore, a discontinuous function is not defined for all values of the independent variable, meaning that there are certain points in the domain for which it is not defined. In conclusion, the main difference between continuous and discontinuous functions is that a continuous function is defined for all values of the independent variable and has no jumps or breaks in its graph, whereas a discontinuous function is not defined for all values of the independent variable and has jumps or breaks in its graph.

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The domain and the range of this function shown in the graph include the following;

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent 1 unit and the less than or equal to (≤) would be used because the dotted point is shaded (closed).

By critically observing the graph shown above, we can reasonably and logically deduce the following:

Domain = -5 ≤ x < 1 or [-5, 1].

Range = -4 ≤ y < 7 or [-4, 7].

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The symmetries of the graphs are mentioned below -

Given are the graphs as shown in the image.

For each graph we can discuss the symmetry below -

Graph {A} -

Graph {B} -

Graph {C} -

Therefore, the symmetries of the graphs are mentioned below -

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Four areas known as quadrants are created by the coordinate axes.

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The sponsor will donate 750 dollars.

1 kilo is 1000 meters

5 kilos is 1 kilo x 5

1000 meters x 5 is 5000 meters

0.15 x 5000 = 750

Answer:

12345678900987654321

Answer:

The answer is C(t)=0.07t+20

Step-by-step explanation:

20 is the starting value, or y-intercept in this case. The rate of change is 7 cents, or, 0.07. If we put this in y=mx+b format, it will come out as:

C(t)=0.07t+20

Answer:

YZ = 20 cm

Step-by-step explanation:

Δ XYZ and Δ CBA are similar ( AA postulate )

The corresponding sides are then in proportion , that is

[tex]\frac{YZ}{BA}[/tex] = [tex]\frac{XY}{CB}[/tex] ( substitute values )

[tex]\frac{YZ}{8}[/tex] = [tex]\frac{25}{10}[/tex] = 2.5 ( multiply both sides by 8 )

YZ = 8 × 2.5 = 20 cm

The foci of the ellipse  are  (4,0) (9,0)

In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics.

The center of that ellipse is the midpoint of the major axis,

half way between (0,0) and (13,0) on line y=0.

The coordinates of that midpoint are the averages of the coordinates of the vertices.

The midpoint is (6.5,0) , and that is the center of the ellipse.

The distance from the center to each vertex is called the semi-major axis and represented as a .

In this case a=6.5 .

Half of the minor axis is called the semi-minor axis and is represented with b .

That is the distance from the center to each co-vertex.

In this case b= 12/2=6 .

The distance from the center to each focus is represented with c ,

and is related to a and b by a²=b²+c²

In this case 6.5²=6²+c²

Solving for c :

6.5²-6²=c²

A calculator can do that

6.5 -6

0.5*12.5=c²

c=√6.25

c=2.5 .

That is the distance from center (6.5,0) to each focus.

The foci are on the same line as the vertices, line y=0,

on either side of the center,

so the x-coordinate of one focus is 6.5-2.5=4 ,

and the x-coordinate of the other focus is 6.5+2.5=9 .

So, The foci of the ellipse  are  (4,0) (9,0

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The coordinates of that midpoint are the averages of the coordinates of the vertices.

The midpoint is (6.5,0) , and that is the center of the ellipse.

In this case a=6.5 .

Half of the minor axis is called the semi-minor axis and is represented with b .

That is the distance from the center to each co-vertex.

In this case b= 12/2=6 .

and is related to a and b by a²=b²+c²

In this case 6.5²=6²+c²

6.5²-6²=c²

A calculator can do that

6.5 -6

c=2.5 .

That is the distance from center (6.5,0) to each focus.

The foci are on the same line as the vertices, line y=0,

on either side of the center,

so the x-coordinate of one focus is 6.5-2.5=4 ,

and the x-coordinate of the other focus is 6.5+2.5=9 .

So, The foci of the ellipse  are  (4,0) (9,0)

Answer:

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

20% of 575 is 116

Answer:

Apple: $2.50

Orange: $1.75

Step-by-step explanation:

Let A represent apples and Y represent Orange

We have equations

9A + 6Y = $33

18A  + 20 Y = $80

Let's find out the cost of oranges first. Multiply the first equation by -2

-18A - 12Y = $-66

18A + 20 Y = $80

8Y = $14

Y = $1.75

Now let's put 1.75 back in the Y to find the cost of apple

18A  + 20(1.75) = $80

18A + 35 = $80

18A = $45

A = $2.50

Answer:2 50

Step-by-step explanation:

In the graph of a function there exist a point where function is not defined is known as a hole of a function.

Hole of a function is defined as:

Therefore, the hole of a function is a point where function does not defined only approaches.

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Yes, f(x) = π is a Polynomial function with the highest power = 0.

Let's First understand what is a polynomial function.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Given function f(x) = π is also a polynomial function.

Given function is known as constant polynomial function.

A function of the form f(x) = c, where c is a real number with a degree of zero at its highest, is known as a constant polynomial. Simply described, a constant polynomial is an algebraic polynomial whose output value does not change regardless of changes made to the input values.

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The dimension of actual plane is 300 inches.

What are ratios?

A ratio is the comparison of quantities which have same parameters or units of measurement.

Why are calculation of ratios significant?

It helps to identify how big or small a quantity is as compared to other thing having same parameter of measurement.

NOTE: Things which have different measurement cannot be compared by ratio;

Example: 1 litre of milk cannot be in ratio with 1 kg of sand, as milk is measured in volume and sand is in weight.

Solution:

Given, ratio of model of plane and actual plane = 1 : 40

           x = 7.5 inches

Let, x be the dimension of model of the airplane

      y be the dimension of actual airplane

Using the formula by equating the ratios,

1/40 = x/y

⇒ 1 x y = 40x

⇒ y = 40 x 7.5

⇒ y = 300 inches

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We can prove that two right triangles are similar by:

Hypotenuse-Leg (HL) Theorem.

Leg-Acute (LA) Angle Theorem.

Hypotenuse-Acute (HA) Angle Theorem.

Leg-Leg (LL) Theorem.

Two triangles are congruent if they have the same three sides and exactly the same three angles. Two right triangles can be considered to be congruent, if they satisfy one of the following theorems.

Theorem 1 : Hypotenuse-Leg (HL) Theorem :

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

Theorem 2 : Leg-Acute (LA) Angle Theorem :

If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.

Theorem 3 : Hypotenuse-Acute (HA) Angle Theorem :

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

Theorem 4 : Leg-Leg (LL) Theorem :

If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.

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Ramon should buy the rug of 169 square feet area because the room area is 160 square feet.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in the model ½ inch represents 2 feet and Ramons room measures 2.5 inches by 4 inches. Ramon wants to purchase a rug that will take up 169 square feet of space.

1/2 inch = 2 feet

1 inch = 4 feet

2.5 inch = 10 feet

4 inch = 16 feet

Area of room = L x W

Area of room = 10 x 16

Area of room = 160 square feet

The area of the rug is 169 square feet and the area of the room is 160 square feet which will cover the whole area.

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Standard form: [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]

Degree: 4

Leading coefficient: 6

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power.

Looking at the equation the highest power of the polynomial is 4;

The leading coefficient is nothing but the coefficient of the term which is having the highest power i.e.., 6;

Now arranging terms in the descending order(according to power of term) we get [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]

Standard form: [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]

Degree: 4

Leading coefficient: 6

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The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.

a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1).  Complex numbers can take a variety of shapes.

z=a+bi is the general form of complex number

As by definition

i^2=-1

So

i^4=(i^2)^2

    =(-1)^2

    =1

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The Possible rational roots of the equation "x³- x² - 10x - 8 = 0" are x = -1 , x = -2 and x = 4  .

The Rational roots of the equation are defined as the values of the variable such that value of the entire equation becomes 0 .

the function is f(x) = x³- x² - 10x - 8 ,

By the Rational Roots Theorem , we know that is p/q is the root of the equation , then p is a factor of 8 and q is a factor of 1 .

the possible values of p are ±1 , ±2 , ±4 , ±8 , and

the possible values of q are ±1 .

So , the possible rational roots (p/q) are  ±1 , ±2 , ±4 , ±8 .

So , on substituting the all the possible values of the rational roots ,

we get ;

f(1) = (1)³- (1)² - 10(1) - 8 = -18

f(-1) = (-1)³- (-1)² - 10(-1) - 8 = 0

f(2) = (2)³- (2)² - 10(2) - 8 = -24

f(-2) = (-2)³- (-2)² - 10(-2) - 8 = 0

f(4) = (4)³- (4)² - 10(4) - 8 = 0

f(-4) = (-4)³- (-4)² - 10(-4) - 8 = -48

f(8) = (8)³- (8)² - 10(8) - 8 = 360

f(-8) = (-8)³- (-8)² - 10(-8) - 8 = -446.

we get , the value as 0 at x = -1 , -2 and 4 .

Therefore , the possible rational roots are x = -1 , x = -2 and x = 4 .

The given question is incomplete , the complete question is

What are the possible rational roots of x³- x² - 10x - 8 = 0 ?

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Answer:

A. Triangle PNQ is translated along the vector <5,6> to map onto triangle P'N'Q'   OR
A. Triangle PNQ is translated right 5 units and up 6 units to map onto P'N'Q'
P (2,5) --> P' (7,11)
N (-3,-1) --> N' (2,5)
Q (4,0) --> Q' (9,6)

Step-by-step explanation:

The simplified form of the expression 10x⁻⁵/-5x¹⁰ is -2/x¹⁵. So Anja wrote the numerator as 15 instead of -2.

Exponentiation is the method of writing large numbers as the number in terms of power.

Exponent indicates how much time a number is multiplied to itself.

aᵇ read as a raise to b, implies that a is multiplies to itself b times.

We have to simplify the expression  10x⁻⁵/-5x¹⁰.

[tex]\frac{10x^-5}{-5x^1^0}[/tex] =  10 × [tex]\frac{1}{-5}[/tex] × x⁻⁵ × x⁻¹⁰

        = -2 x⁻¹⁵

        = [tex]\frac{-2}{x^1^5}[/tex]

Hence Anja simplified the expression as  [tex]\frac{15}{x^1^5}[/tex] which is not true. The correct simplified form is  [tex]\frac{-2}{x^1^5}[/tex].

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Answer:

its B

Step-by-step explanation:

i did the test

The largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulation is 11664 cubic inches.

The volume of a rectangular parcel with dimensions l, w, and h is lwh. We can express the volume of the rectangular parcel in terms of one variable, say l, as lwh = l(108 - 2l)h. We want to maximize this expression subject to the constraint that l is a positive number less than 54 (the maximum value for l that still allows the parcel to fit within the 108-inch limit).

Taking the derivative of the volume with respect to l and setting it equal to zero, we find that the maximum volume occurs when:

l = (27 inches)

At this value, the dimensions of the parcel are:

l = 27 inches

w = 27 inches

h = 2(108 - 2l) = 2(72) = 144 inches

The volume of the parcel is then:

lwh = (27)(27)(144) = 11664 cubic inches

This is the largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulations.

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The number of terms in the expression 5xy² 3xyz is 1.

Various parts of an algebraic expression , which are separated by + or – are called terms of the algebraic expression.

Calculation:

The given expression 5xy²3xyz.

Step 1: Write down the given expression    

          The given expression is 5xy²3xyz.

Step 2: Find number of terms in the expression

We know that Various parts of an algebric expression , which are separated by + or – are called terms of the algebric expression.

In the expressions the term is 5xy²3xyz.

Hence number of terms in the expression 5xy²3xyz is 1.

The number of terms in the expression 5xy² 3xyz is 1.

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Similar triangles are those with the same form but different sizes. The expression's measure for the value of x is 32.5.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.

In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

From the given diagram, since the triangle ABC is similar to DCE, hence the measure of the angle CDE is equal to ABC that is;

<CDE = <ABC

2x = 65

x = 65/2

x = 32.5

Hence the measure of the value of x from the expression is 32.5

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The Slope of the line passing through the points (0,3) and (5,8) is 1 .

The Line is passing through the points (0,3) and (5,8) .

we know that the formula to calculate the slope of the line passing through the points(x1,y1) and (x2,y2) is denoted by  ;

Slope(m) =   ;

It is given that points through which line is passing is (0,3) and (5,8) .

substituting the values in the above formula ,

we get ;

Slope(m) = (8 - 3)/(5 - 0)

On simplifying further ,

we get ;

slope(m) = 5/5 = 1 .

Therefore , the slope of line is = "1" .

The given question is incomplete , the complete question is

What is the slope of the line passing through the points (0,3) and (5,8) ?

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Using the formula T1/2 = 0.693/λ, we may determine decay from half-life.

The half-life is the amount of time needed for half of the initial population of radioactive atoms to decay.

T1/2 = 0.693/λ describes the relationship between the half-life, T1/2, and the decay constant.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

Nearly all decay processes that are exponential, or nearly exponential, are referred to by the phrase "half-life".

Therefore, using the formula T1/2 = 0.693/λ, we may determine decay from half-life.

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Answer:

perpendicular

Step-by-step explanation:

7y = -x - 3

y = -1/7 x - 3/7

-1/7 is the reciprocal of the opposite, so the lines are perpendicular