GFH and HFJ are adjacent and congruent what are two conclusions you can draw from this infomation?

On solving the provided question, we can say that - the of the function f(x) = 0.5x + 7.8 = 9.8

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here, we are provided with the function -

f(x)= 0.5x + 7.8

and given from question, x = 4

f(x) =  2 + 7.8 = 9.8

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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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Answer:

3.75

Step-by-step explanation:

Just divide 1.5 by 0.4

just ask your teacher for extra help if needed

-090

Step-by-step explanation:

The probability that the Canadian Rounders have 0 players injured for their next match is 1/4 or 25%.

This implies the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happeing of the event.

The total number of matches = 4+5+2+3+2

The total number of matches = 16

Total, that has zero injured players = 4

The probability will be:

= 4 / 16

= 0.25

The probability is 0.25.

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Complete question

The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.

Number of injured players Number of matches

0 | 4

1 | 5

2 | 2

3 | 3

4 | 2

Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 0 players injured for their next match?

Step-by-step explanation:

if the three numbers are x,x+1,x+2

2x+3(x+2)=(x+1)4+14

5x+6=4x+18

×=12

The area of the deck in terms of s is 2s^2 + 7s + 15. The expression can be written in standard form as A = 2s^2 + 7s + 15.

The area of the deck can be expressed in terms of s using the standard form of a rectangular area equation, A = lw, where l is the length and w is the width. The side length of the pool is s and the length of the deck is twice the side length of the pool plus 5, or 2s+5. The width of the deck is 3 units longer than the side length of the pool, or s+3. Substituting these values into the area equation gives us:

A = (2s+5)(s+3)

A = 2s^2 + 7s + 15

Therefore, the area of the deck in terms of s is 2s^2 + 7s + 15.

The expression can be written in standard form as A = 2s^2 + 7s + 15.

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The area of the rectangular deck built around the square pool of side, s in terms of s is 2s² + 11s + 15.

Therefore the answer is 2s² + 11s + 15.

The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool, that is

l = 2s + 5

The width of the deck is 3 units longer than the side length of the pool, that is

b = s + 3

Deck is in rectangular shape, thus the area of the deck in terms of s can be calculates by

A = lb = (2s + 5)×(s + 3)

= 2s² + 6s + 5s + + 15

= 2s² + 11s + 15

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At the point where x = 0, the equation simplifies to 8e^y = 8e, which can be rearranged to e^y = 1. This means that y = 0.

1. Substitute x = 0 into the equation: xy + 8e^y = 8e

2. Simplify the equation: 8e^y = 8e

3. Rearrange the equation to isolate the exponent: e^y = 1

4. Take the natural logarithm of both sides: y = ln(1)

5. Evaluate the natural logarithm: y = 0

At the point where x = 0, the given equation simplifies to 8e^y = 8e. Rearranging this equation to isolate the exponent on the left hand side, we get e^y = 1. Taking the natural logarithm on both sides, we get y = ln(1). Finally, evaluating the natural logarithm of 1, we get y = 0. Therefore, the value of y" at the point where x = 0 is 0.

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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

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 maximum load that can be applied to the wire made of that kind of steel is 21195 N. The result is obtained by using the tensile strength equation.

Tensile strength is the maximum load or stress that a material can withstand without fracture when being stretched or pulled per its cross-sectional area.

The statement can be expressed as

σ = F/A

Where

The tensile strength of a certain steel wire is 3000 MN/m². The diameter of the wire is 3.0 mm. Find the maximum load that can be applied to the wire!

Let's count the cross-sectional area!

A = πr²

A = 3,14 (½d)²

A = 3,14 [½(3.0 × 10⁻³)]²

A = 3,14 (1.5 × 10⁻³ m)²

A = 3,14 (2.25 × 10⁻⁶) m²

A = 7.065 × 10⁻⁶ m²

The maximum load is the maximum value of the force acting on it.

σ = F/A

3000 MN/m² = F / 7.065 × 10⁻⁶ m²

3000 × 10⁶ N/m² = F / 7.065 × 10⁻⁶ m²

F = 3 × 10⁹ × 7.065 × 10⁻⁶  N

F = 21.195 × 10³ N

F = 21195 N

Hence, the steel wire can have the maximum load of is 21195 N.

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A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).

∠1 ≅ ∠5 (corresponding angle theorem)

∠7 ≅ ∠5 (vertical angle theorem)

∠1 ≅ ∠7 (Transitive property of congruence)

Complete question is at the end of solution.

As per the given data, a transversal line intersects two parallel lines a and b.

The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)

Line a is parallel to line b.

Therefore,

a ║ b

Let's prove ∠1 ≅ ∠7

Hence,

∠1 ≅ ∠5 (corresponding angle theorem)

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.

∠7 ≅ ∠5 (vertical angle theorem)

Vertical angles theorem or vertically opposite angles theorem:

According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.

Vertical angles are the angles formed when two lines intersect each other.

∠1 ≅ ∠7 (Transitive property of congruence)

Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.

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The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

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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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Answer:1/4

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

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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Answer:

3/4

Step-by-step explanation:

1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.

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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Answer:

1200

Step-by-step explanation:

12 multiplied by 2 is 24.

24 divided by 2 is 12.

12 times 100 is 12 plus 2 zeros, or 1200.

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.

The value of the expression (x != 7) && (x <= y) is: B. true

The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.

Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.

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Answer:

x = 2

Step-by-step explanation:

6/3 = 2

To find 1/3 of a line segment, divide the line segment into three equal parts. Measure the length of one of these parts and this will be 1/3 of the line segment.

This can be done by using a ruler or a measuring tape. Alternatively, if the length of the line segment is known, divide it by 3 to find 1/3 of the line segment. For example, if the line segment has a length of 12 inches, then the length of 1/3 of the line segment is 4 inches. If the line segment is curved, you can divide it into three equal arc lengths using a compass.

You can then measure the length of one of these arcs to find 1/3 of the line segment. To make sure that the three parts are equal, you can use the Pythagorean theorem or the triangle inequality theorem. This will help you to accurately divide the line segment into three equal parts.

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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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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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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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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

According to the question quadrilateral pqrs, the russell jamie both neither is neither.

The Quadrilateral pqrs is located at p (−4, 1), q (−2, 3), r (1, 1), and s (−2, −2).

Russell:

PQRS is a parallelogram because both pairs of opposite sides are parallel

Segment pq is p (−4, 1), q (−2, 3).

Slope=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]& m=\frac{3-1}{-2+4}=\frac{2}{2}=1[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& m=\frac{1+2}{1+2}=\frac{3}{3}=1[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& m=\frac{-2-1}{-2+4}=\frac{-3}{2}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]m=\frac{1-3}{1+2}=\frac{-2}{3}[/tex]

Segments pq and sr are parallel, and segments ps and qr are parallel.

Jamie:

pqrs is a parallelogram because both pairs of opposite sides are congruent

Distance between two points is the length of the line segment that connects the two points in a plane

Segment pq  is p (−4, 1), q (−2, 3).

[tex]& d=\sqrt{(-2+4)^2+(3-1)^2}=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}[/tex]

Segment SR is s (−2, −2) and  r (1, 1)

[tex]& d=\sqrt{(1+2)^2+(1+2)^2}=\sqrt{9+9}=\sqrt{18}=3 \sqrt{2}[/tex]

Segment ps is p (−4, 1), s (−2, −2)

[tex]& d=\sqrt{(-2+4)^2+(-2-1)^2}=\sqrt{4+9}=\sqrt{13}[/tex]

Segment qr is q(-2,3) and r(1,1)

[tex]d=\sqrt{(1+2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}[/tex]

Segments pq and sr are congruent, and segments ps and qr are congruent.

Therefore, the correct option is neither.

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Both Russell and Jamie are correct. PQRS is a parallelogram with slope because both pairs of opposite sides are parallel, and it is also a parallelogram because both pairs of opposite sides are congruent.

Russell is correct because he used the slope of the lines to prove that both pairs of opposite sides are parallel. He calculated the slope of the lines using the equation m = (y2 - y1)/(x2 - x1) and found that the slopes of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are parallel.

Jamie is also correct because he used the distance formula to prove that both pairs of opposite sides are congruent. He calculated the distance between the points using the equation d = √((x2 - x1)^2 + (y2 - y1)^2) and found that the distances of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are congruent.

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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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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