Geometry find length of third side !

The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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From a point (x, y) on a circle with radius r , we know that cos θ represents tha ratio  of x/r .Therefore, cos θ = x/r. On the unit circle the radius of the circle is 1, which means x = cosθ.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

From the figure below,

We see that,

The point (x, y) = (x, 0)

Cos θ = x/r

Unit circle means r = 1.

So,

Cos θ = x/1

Cos θ = 1

Thus,

The given statement is filled as above.

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We know that the volume of a rectangular box is given by length times width times height. So, we have:

V = x * (x - 5) * (x + 2) = 180

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

We can use this equation to find the length of the box.

Expanding the equation:

x^3 - 5x^2 + 2x = 180

Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52

So the length of the box is 9.52 inches.

The answer is B. 9.52 in

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Number of green chairs in the inventory is 208.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total number of chairs in the inventory = 520

Fraction of chairs that are green = 2/5 of 520

2 parts out of 5 parts are green.

Number of green chairs = 2/5 × 520

                                        = 1040 / 5

                                        = 208

Hence there are 208 green chairs in the inventory.

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Answer:

640

Step-by-step explanation:

Answer:

=297/7

PEMDAS Hope this helps :)

The number for the expression is 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = x

Now,

50 + x = 6x

Subtract x on both sides.

50 = 5x

Divide 5 into both sides.

x = 10

Thus,

The number is 5.

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Answer:1/4

Step-by-step explanation:3/8-1/8=1/4

Answer:

In solving any mathematical equation carrying x,we mainly begin by first understanding the question and breaking them down little by little and solving them separately to know which to add to get x,or which to subtract to get x,e.t.c,as the case may be

Answer:

HERE ARE FOLLOWS

Step-by-step explanation:

The population of a city was five-sevenths of a million in 2010 and five million in 2016. The population growth can be described as an arithmetic sequence. Find its common difference, which represents the annual growth of the population.

In this question, we’re told that we have an arithmetic sequence. This is a special type of sequence that has a common difference between each term. For example, the sequence two, seven, 12, 17, and so on has a common difference of five, as we add five each time to get the next term. The general term of any arithmetic sequence, written sub , is equal to sub one plus minus one multiplied by , where sub one is the first term in the sequence and is the common difference. It is this common difference that we are trying to calculate in this question.

In this question, we are told that the initial population in 2010 was five-sevenths of a million. So, we will let sub one, the first term, be five-sevenths. We are also told that the population in 2016 was five million. We can see that this would correspond to the seventh term in our sequence. This means that sub seven is equal to five. We can now substitute our values into the formula for the general term. The seventh term five is equal to five-sevenths plus seven minus one multiplied by . The right-hand side simplifies to five-sevenths plus six .

Noting that we can write five as 35 over seven, when we subtract five-sevenths from both sides of our equation, we get thirty sevenths is equal to six . We can then divide both sides of this equation by six, giving us is equal to 30 over 42. Both the numerator and denominator of our fraction are divisible by six. As 30 divided by six is five and 42 divided by six is seven, our fraction simplifies to five-sevenths.

We can therefore conclude that the common difference which represents the annual growth of the population is five-sevenths of a million.

Answer:

Graph 1- No, Graph 2- No, Graph 3- Yes, Graph 4- Yes, Graph 5- No, Graph 6- No

One can say that two triangles are congruent if their measurements and appearance match. The other two triangles remain true even if we rotate, flip, or shift one of them.

Two triangles with the same dimensions and appearance are said to be congruent. Even if we flip, rotate, or shift one of the triangles, the other two still hold true. If two triangles' sides are the same, they must have the same angles and, as a result, must be congruent.

Given that the bases of the triangle PWZ are the same (1 and 2) and that W and Z are the same distance from X and Y, where XY is the base of another triangle inside PWZ.

For PWZ

PWZ's two angles are the same, thus we know it is an isosceles triangle.

Because of this, another PXY is on the same base as a PWZ and is also located at the same distance from its point. These triangles are hence congruent triangles.

When viewed from that angle, we can claim that 1 and 2 are congruent pairs of alternate angles.

∠1 ≅ ∠2

In the same way, 3 and 4 are.

∠3 ≅ ∠4

As a result, the Triangles are congruent according to the ASA Theorem. The sides that the two angles encompass are similar.

Therefore, the correct answers are:

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The correct answers are Isosceles triangle theorem, SAS, CPCT( Corresponding parts of a congruent triangles are congruent), The converse of Isosceles triangle theorem.

Two triangles with the same dimensions and appearance are said to be congruent. Even if we flip, rotate, or shift one of the triangles, the other two still hold true. If two triangles' sides are the same, they must have the same angles and, as a result, must be congruent.

Given that the bases of the triangle PWZ are the same (1 and 2) and that W and Z are the same distance from X and Y, where XY is the base of another triangle inside PWZ.

For PWZ

PWZ's two angles are the same, thus we know it is an isosceles triangle.

Because of this, another PXY is on the same base as a PWZ and is also located at the same distance from its point. These triangles are hence congruent triangles.

When viewed from that angle, we can claim that 1 and 2 are congruent pairs of alternate angles.

∠1 ≅ ∠2

In the same way, 3 and 4 are.

∠3 ≅ ∠4

As a result, the Triangles are congruent according to the ASA Theorem. The sides that the two angles encompass are similar.

Therefore, the correct answers are:

Given

Isosceles triangle theorem

SAS

CPCT( Corresponding parts of a congruent triangles are congruent)

The converse of Isosceles triangle theorem

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Answer:

2x + 40

Step-by-step explanation:

Given ,

L = x

B = 20cm

To Find: Expression that represents the Perimeter

Perimeter of rectangle = 2(l+b)

                                       = 2(x+20)

                                        = 2x + 40

An image is always formed at the back of a mirror. Thus, the flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = opposite / adjacent

         = 1.65 / 1.7

Tan θ = 0.9706

θ =  Tan⁻¹(0.9706)

 = 44.2°

θ = 44.2°

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = opposite / adjacent

        = h / 8.75

0.9706 = h / 8.75

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m tall.

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The line ED has a length of 4 units.

Given,

Points E and D in the ΔCAB

equation represent the midpoints of the segments AC and BC, respectively.

AB is 8 units as well.

The length of segment ED needs to be determined.

We are aware that a triangle's third side and the line segment connecting its midpoint are both said to be parallel to the triangle's third side and to be half its length. The mid point theorem is what is known as this.

E and D are the midpoints of AC and BC in the equation CAB, and E's length is equal to half of AB's length is

=> 8/2  

=> 4 units

so the length of the segment ED is 4 units

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The measure of segment ED is 4 units.

4 units

We know that the measure of segment AB is 8 units and that point E is the midpoint of segment AC and point D is the midpoint of segment BC. This means that the measure of segment AC is 8/2, or 4 units. Since point E is the midpoint of segment AC, it is also the midpoint of segment ED, meaning that the measure of segment ED is 4 units.

The measure of segment ED is 4 units.

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The equation of this function is f(x) = 2(x - 2) / x - 1

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The parent function is given as:

y = 1.

we can see that the function is translated 3 units down and  2 units right.

This means that the transformation rule

(x, y) -> (x - 2, y - 3)

So, we have graph contains the point (-1, 2) and the y-intercept is less than 2.

Since the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

Hence, the equation of the graph is

f(x) = 2(x - 2) / x - 1

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Applying the perpendicular bisector theorem, the values of the measures are:

y = 12

x = 7

PQ = 29

SR = 32

PT = 18

PR = 36

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment.

In other words, if a point P is the perpendicular bisector of line segment AB, then the distances from P to points A and B are equal. This is true no matter where point P is located on the perpendicular bisector.

Since QT is the perpendicular bisector of PR, we would therefore have the following based on the above stated theorem:

PQ = QR

Substitute:

5y - 31 = 2y + 5

5y - 2y = 31 + 5

3y = 36

3y/3 = 36/3

y = 12

SP = SR

Substitute:

4x + 4 = 7x - 17 [congruent segments]

4x - 7x = -4 - 17

-3x = -21

x = 7

PQ = 5y - 31 = 5(12) - 31 = 29

SR = 7x - 17 = 7(7) - 17 = 32

PT = 6x - 2y = 6(7) - 2(12)

PT = 18

PR = 2(PT)

PR = 2(18)

PR = 36

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All the lengths in the original figure are multiplied by the same number to get a scaled replica.

Every length in the original figure is multiplied by the same number in a scaled copy, which is a copy of the original figure. For instance, triangle ABC is a scaled version of triangle DEF.

To find the matching side length on triangle DEF, each side length on triangle ABC was multiplied by 1.5. A figure that is geometrically identical to the original figure is called a scale copy. This indicates that the scale copy and the original figure are identical in shape but may vary in size.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

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The equivalent expression when we apply distributive property is -10w -20

You should understand that distributive property states that every term inside a grouping symbol multiplied by every term outside the grouping symbol yields the same result.

To this effect, the formula to do this is x(y+z) = xy+xz

The given expression is

5×(−2w−4)

= 5*-2w- 5*4

= -10w -20

In the expression every term outside the symbol is multiplied by every term inside the symbol to give the result of the expression

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The value of the trigonometric relation tan D = 15/8 = 1.875

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as CDE

The triangle CDE is a right triangle with ∠CDE = 90°

Now , the measure of side CD = 8 units

The measure of side CE = 15 units

The measure of side DE = 17 units

From the trigonometric relations ,

tan θ = opposite / adjacent

Substituting the values in the equation , we get

tan D = 15 / 8

Hence , the value of tan D = 15/8

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Equation reads C=25n+2500, and the price to make 3000 toys is $77,500. Additionally, 1200 toys may be created for $32500.

A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

Let's use the equation y=mx+b, where n is the number of toys and C is the overall cost. The total cost of producing n toys would be equal to the initial development cost plus the production cost of each toy.

The cost to make a toy will equal m since m is multiplied by n, the quantity of toys. B will always equal the development cost since it is a constant and its value is unaffected by the number of toys.

Therefore, [tex]C=25n + 2500[/tex]

by above, equation put

[tex]n=1750\\C= 25(3000) + 2500\\C= $77,500[/tex]

Now, again by same equation, but C instead of n.

[tex]= > 32500= 25n +2500\\= > 30000=25n\\= > n = 1200[/tex]

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The function is defines for all (x,y,z) ∈ R³

Hence the domain of this equation is,

D = {(x, y, z) | 9x² + 9y² + z² ≤ 81

The function is bound by sphere.

The set of inputs that a function will accept is known as the domain of the function in mathematics.  (f),  " (f), where f is the function, are other ways to refer to it.

More specifically, the domain of f is X given a function  Xto Yfcolon Xto Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.

The function f can be graphed in the Cartesian coordinate system in the particular situation where X and Y are both subsets of  R  In this instance, the graph's x-axis shows the domain as the projection.

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The ordered pair that is the best estimate for the solution to the system is (0.5, 0)

You should know that any equation whose highest power of its variable is one is linear

Also, the graph of linear equation is always straight line.  The solution set of the linear equation is the values of x and y where the two lines intersect.

From our graph, the coordinate of the points of intersection are 0.5 and 0

Reading from the graph to get the coordinates of points, We therefore conclude that the ordered pair is the best estimate for the solution to the system is (0.5, 0) respectively

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The solution of the algebraic equation is 37/2

An algebraic equation is a statement that says that two algebraic expressions are equal. For example, the equation 3x + 2 = 6x

The algebraic expression 4/(x-4) -3/(x²-16) = 6/(x+4)

To solve this algebraic equation, you need to find the value of x.

4/(x-4) -3/(x²-16) = 6/(x+4)

4/(x-4) -3/(x-4)(x+4) = 6/(x+4)

The LCM of (x-4) and (x-4)(x+4) is (x-4)(x+4):

(4(x+4) -3)/(x-4)(x+4) = 6/(x+4)

(4x+16 -3)/(x-4)(x+4) = 6/(x+4)

4x+13/(x-4)(x+4) = 6/(x+4)

Multiply both sides by (x+4):

4x+13/(x-4) = 6

4x+13 = 6(x-4)

4x+13 = 6x-24

6x-4x = 13+24

2x = 37

x = 37/2

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Answer:

1, 5 6 10 15 30 because these numbers times certain numbers can also give 30 for instance 1 by 30 is30, 5 by6 is 30 6 by 5 is 30 10 by 3 is 30 15 by 2 is 30 30 by 1 is 30

Answer:

3.75

Step-by-step explanation:

Just divide 1.5 by 0.4

just ask your teacher for extra help if needed

The values of f ◦ g is equal to (x + 2)^2 + 1 and g ◦ f is equal to x^2 + 3.

f ◦ g is the composition of functions f and g, which means that for any x in the domain of g, we substitute g(x) into f(x) to get f(g(x)) = (x + 2)^2 + 1.

g ◦ f is the composition of functions g and f, which means that for any x in the domain of f, we substitute f(x) into g(x) to get g(f(x)) = x^2 + 1 + 2

So f ◦ g = (x + 2)^2 + 1 and g ◦ f = x^2 + 3

It's important to notice that the order of the functions matters when composing them, f ◦ g is not the same as g ◦ f. The composition of functions is a fundamental concept in mathematics and it's used to chain multiple functions together to create a new function.

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Answer:

3

Step-by-step explanation:

Let's disect this sentence.

Three more (+3) than four times (x4) a number is 15 (=15)

So x · 4 + 3 = 15

Now we do algebra:

x · 4 + 3 (-3)  = 15 (-3)

x · 4 = 12

x · 4 (÷4) = 12 (÷4)

x = 3

Answer:3

Step-by-step explanation:

Answer:

48 free throws

Step-by-step explanation:

25:36 is the ratio

Now divide 25 by 36 to find the probability of the basketball player scoring:

25/36=0.694

Now multiply this probability with the total number of free throws (70) in order to get the number of free throws that would be made:

70 * 0.694 = 48.6

You can't make 48.6 free throws, so you have to round down to the nearest integer since you can't make 0.6 free throws.

Hence, 48.6 ==> 48 free throws

Solving the equation

An equation is a mathematical expression that shows the relationship between two variables.

Since together donal, yolanda, and iris made 27 birdhouses for a school fair. yolanda made n birdhouses. donal made one more birdhouse than yolanda, and iris made one more than donal. So, we solve the equation n +(n + 1) + (n + 1 + 1) = 27 to find the number of birdhouses each one made.

So, n + (n + 1) + (n + 1 + 1) = 27

Colecting like terms, we have that the equation is

n + (n + 1) + (n + 1 + 1) = 27

n + n + n + 1 + 1 + 1 = 27

3n + 3 = 27

Subtracting 3 from both sides of the equation, we have

3n = 27 - 3

3n = 24

Dividing oth sides by 3, we have

n = 24/3

n = 8

So, n + 1 = 8 + 1 = 9

and n + 1 + 1 = 8 + 1 + 1 = 10

So,

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The metal is most likely to be Silver (Ag).

Density, d = 10.5 g/cm3.

z = 4 (as it is an FCC)

a = edge length = 409 pm = [tex]4.09 * 10^{-8} cm[/tex]

We have to find the Atomic Mass (M).

Perhaps the most common crystal structure is Face-Centered Cubic (FCC). The crystal structure is based on the Bravais lattice of the same name, with a single atom at each lattice point on the cube’s corners and faces. FCC is one of the most stable crystal structures and has the highest packing density. In some textbooks, FCC may also be abbreviated as CCP, which stands for Cubic Close-Packed.

The formula for density, d =

[tex]D = \frac{z * M}{N_{A} * V }[/tex]

where, V = volume.

Volume, V = a x a x a = a^3

V =[tex](4.09 * 10^{-8}) ^ 3 = 68.417 * 10^{-24} = 6.841 * 10^{-23}[/tex]

Using the density formula,

[tex]M = \frac{d * N_{A} * V }{z}[/tex]

[tex]M = \frac{10.5 * 6.023 * 10^{23} * 6.841 * 10^{-23} }{4}[/tex]

[tex]M = 108.15 amu[/tex]

The atomic weight is close to that of Silver (Ag).

Thus, the metal is most likely to be Silver (Ag).

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