Given: AD∥BC and AB∥CD
Prove: AD≅BC and AB≅CD

An expression is defined as a set of numbers, variables, and mathematical operations. The value of (3√x + 7), when the value of x is 25 is 22.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of (3√x + 7), when the value of x is 25 is,

3√x + 7

= 3√25 + 7

= 3(5) + 7

= 22

Hence, The value of (3√x + 7), when the value of x is 25 is 22.

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The probability of randomly selecting a student that is either a female or a senior is 3/4.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

                            Males          Females             Total

Freshman                8                   17                      25

Sophomores          15                   10                      25

Juniors                   12                    13                       25

Seniors                   15                   10                        25

Total                       50                   50                      100

Now, the probability of randomly selecting a student that is either a

female or a senior

= 50/100 + 25/100

= 75/100

= 3/4

Hence, the probability of randomly selecting a student that is either a female or a senior is 3/4.

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Answer:

acos(bxc)+d

h(x)=acos(bxc)+d

The function has a maximum point at (3,6) and a minimum point at (6.5,-9) so

h(x)=6-acos(3bx)+9

or

h(x)=-acos(3bx)+15

Step-by-step explanation:

Please analyze and reasure that this answer is correct.

An exact expression of h(x) is  7.5cos(51.4x - 154.3)-1.5.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions.

the difference in y values from max to min = 15. 15/2 = a

max cosine = 1, min cosine =-1

7.5 x 1 - 1.5 = 6

7.5x -1 -1.5 = -7.5-1.5= -9

h(x) = 7.5cos(bx+c) -1.5

now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c

at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...

if x=3, then 3b +c=0 and c=-3b

for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180

c= 180-6.5b

c=-3b

180-6.5b =-3b

add 6.5b to both sides to get

180= 3.5b

b = 180/3.5 = 51 1/7

c=-3b = -153 3/7

h(x) = 7.5cos(51.4x - 154.3)-1.5

Therefore, exact expression of h(x) is  7.5cos(51.4x - 154.3)-1.5.

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Answer:

SR and RZ

Step-by-step explanation:

A perpendicular bisector is a line segment that passes through the midpoint of a side of a triangle. In other words, If it goes through a side, it should split the segment in half perfectly. Furthermore, it must be perpendicular to the side it passes through (it should form a ninety-degree angle with the side). Given these two rules, one can say that one of the perpendicular bisectors is SR. SR forms a right angle with (and is thus perpendicular to) side AB. Furthermore, AS is congruent to (has the same length as) SB, which means SR cuts AB in half exactly. Another bisector would be RZ (for similar reasoning). Let me know if that doesn't make sense.

The reflection of the quadrilateral DEFG will be given in the figure.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the quadrilateral DEFG will be given in the figure.

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Answer:

Answers all found below.

Step-by-step explanation:

1) Given from diagram, RT = RS + RT

RT = 2cm + 2.5cm = 4.5cm

2) Given from diagram, AC = AB + BC

BC = AC - AB

= [tex]6 in-2\frac{3}{4} in\\=3\frac{1}{4} or 3.25in[/tex]

3)Given from diagram, XZ = XY + YZ

XZ = [tex]3\frac{1}{2} +\frac{3}{4} \\=4\frac{1}{4} or 4.25in[/tex]

4)Given from diagram, WX = XY and WY = 6cm

WX = WY / 2

= 6 / 2

= 3cm

For Questions 5,6 and 7, refer to the attached photos, apologies for the terrible drawing.

5) From the diagram,

RS + ST = RT

5x + 3x = 48

8x = 48

x = 48 / 8

= 6

6) From the diagram,

RS + ST = RT

2x + 5x+4 = 32

7x + 4 = 32

7x = 32 - 4

7x = 28

x = 28 / 7

= 4

7) From the diagram,

RS + ST = RT

6x + 12 = 72

6x = 72 - 12

6x = 60

x = 60 / 6

= 10

The function will begin to have real output when the input value is 2

The function is given as:

[tex]f(x) = -\sqrt{x - 2} + 2[/tex]

Set the radical greater than or equal to 0

[tex]x - 2 \ge 0[/tex]

Add 2 to both sides

[tex]x \ge 2[/tex]

This represents the domian

Hence, the function will begin to have real output when the input value is 2

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Complete question

At what input value will the function [tex]f(x) = -\sqrt{x - 2} + 2[/tex] begin to have real outputs?

Using the definitions of local maximum and minimum, it is found that:

In this problem, we have that the function is as follows:

Hence:

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Answer:

-2,0  0,2

Step-by-step explanation:for anyone needing it in the future cause I couldn't find the answer

The radius of the area the sprinkler has watered is 8.06 yards.

Rotation is spinning around a fixed point with a fixed radius in circular motions.

It is given that a sprinkler rotates 360 degree

The area watered is 204 sq. yards

Radius = ?

A sprinkler rotates in circle

Therefore the area of the circle = π r²

204 = π r²

204 * 7 /22 = r²

r² = 64.91

r = 8.06 yards

Therefore the radius of the area the sprinkler has watered is 8.06 yards.

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Answer: = 14a + 9b

Step-by-step explanation:

distribute:

2(a+3b) + 3(4a+b)

2a + 6b + 12a + 3b

combine like terms:

2a + 6b + 12a + 3b

14a + 6b + 3b

14a + 6b + 3b

= 14a + 9b

A quadratic equation in the form of ax²+bx+c. The zeroes of the polynomial are -2.4 and -7.5.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Root of the quadratic equation are given as,

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The zeroes of the polynomial are:

f(x)=x² + 9.9x + 18

0 = x² + 9.9x + 18

[tex]x= \dfrac{-9.9\pm \sqrt{(9.9)^2-4(1)(18)}}{2(1)}\\\\[/tex]

x = -2.4, -7.5

Hence, the zeroes of the polynomial are -2.4 and -7.5.

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Using translation concepts, the value of k is given as follows:

B) 1/5.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this graph, we have that g(x) = f(kx), hence since g(-2) = f(-10):

-2 = -10k

k = 2/10

k = 1/5.

Hence option B is correct.

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Answer:

9m²-n²

Step-by-step explanation:

(3m+n)(3m-n)

This is so easy algebraic expression.

Just rewrite as,

Simplifying,

[Alternate method is there]

The value of y, the length of each leg, must be greater than 7.

This is a type of triangle with two equal sides.

Let the first, second and third side = a, b and c respectively

     (b - a) < c < (a + b)

For an isosceles triangle with base of 14 units, the two other sides must be equal.

c <  (a + b)

c = 14

a = b = y

14 < (y + y)

14 < 2y

7 < y

Thus, the value of y, the length of each leg, must be greater than 7.

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Answer: C. greater than 7.

Step-by-step explanation:  Trust Me!

Did it on Edge got the answer correct! :)  

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

The set of the whole numbers is {0, 1, 2, 3...}

Then the first possible value is when g = 0.

0^2 + 3 = 3

The second possible value is when g = 1

1^2 + 3 = 4

The third possible value is when g = 2.

2^2 + 3 = 7

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

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Answer:

3,4,7

Step-by-step explanation:

jus took the test

The equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.

The slope-intercept form of a line is written as y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) can be calculated using the formula, slope (m) = (y₂ - y₁)/(x₂ - x₁).

Therefore, slope of the line passing through the points (-25, 50) and (25, 50) can be calculated as m = (50 - 50)/(25 - (-25)) = 0/(-50) = 0.

We can find the equation of the line using the point-slope formula, according to which, a line having a slope m and passing through the point (x₁, y₁) can be written as y - y₁ = m(x - x₁).

Therefore, the equation of the given line can be written as:

y - 50 = 0(x - 25)

or, y - 50 = 0,

or, y = 50.

Therefore, the equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.

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Answer:

d.)

Plot these inequalities:

Graphed below (shaded yellow region):

where all the inequalities meet or touches each other.

The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment

The complete question is in the attached image

From the image, we have:

PS = 8 units

This means that:

P'S' = 1/2 * PS

So, we have:

P'S' = 1/2 * 8

Evaluate

P'S' = 4

Also, the segment PS and P'S' do not lie on the same segment

Hence, the true statement is (c)

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The perimeter of the rectangular rose garden distance outside the path is 57.6m.

Two equal lengths and two equal widths make up a rectangle. We must sum up the lengths of the rectangle's four sides in order to get its perimeter.

Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.

Perimeter = 2(length + breadth)

Calculation for the outside of the path.

Th initial length of park is 15m.

The increment of the length after the width of path is included is;

= 15 + 1.2 + 1.2 (for both side)

= 17.4m

Similarly, the initial width of the park is 9m.

After the increment of the path the width becomes,

= 9 + 1.2 + 1.2 (both side included)

= 11.4m

The perimeter of the rose garden is ;

P = 2( 17.4 + 11.4)

  = 2×28.8

  = 57.6m

Therefore, the rectangular rose garden has the perimeter of 57.6m.

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1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.

What Is percent in simple words?

Based on the given conditions, formulate = [tex]6500 * (1 - \frac{45}{100} )^{( 0.1 * 60/2)}[/tex]

Evaluate the equation/expression=  1081.4375

Round the number: 1081.44

Therefore, 1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.

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Step-by-step explanation:

c-5-(7)=0

c-12 = 0

Ethnographic research is the type of sample is specifically used for gathering information about clandestine or difficult-to-identify groups.

Cultures have a set of rules and beliefs about what is correct for that specific culture. Ethnocentrism is the measuring and judging of one culture by another culture. This can be either a positive or negative judgment about the difference between the beliefs of the two cultures. Ethnocentrism is also believing in the inferiority of other cultures compared to the superiority of one's own culture.

Additionally, ethnocentrism is defined by individualistic or collective cultures. Many Western cultures are individualistic; they tend to focus on what is best for the individual.

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The correct answer is 108° i.e Option A.

.

.

.

HOPE IT HELPS! :)

The skew lines are CG, DH, AD, BC.

The parallel lines are  BC, EH, FG.

Two or more lines which have no intersections but are not parallel.

As, by the definition

The lines skew to EF is CG, DH, AD, BC

The parallel to AD is BC, EH, FG.

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Answer:

The equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Step-by-step explanation:

In the question, it is given that a line passes through (-2,-15) and (2,-3). Another line perpendicular to the first line passes through (6,4).

It is required to find the equation of the second line. of b and substitute all these values to find the equation of second line.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-3-(-15)}{2-(-2)} \\&m_{1}=\frac{12}{4} \\&m_{1}=3\end{aligned}$$[/tex]

Therefore, the slope of second line is [tex]$m_{2}$[/tex].

[tex]$$m_{2}=-\frac{1}{3}$$[/tex]

Step 2 of 2

Substitute the values of [tex]$m_{2}[/tex],x and g(x) to find the b.

[tex]$$\begin{aligned}&g(x)=m x+b \\&4=-\frac{1}{3}(6)+b \\&b=4+2 \\&b=6\end{aligned}$$[/tex]

Therefore, the equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-3-(-15)}{2-(-2)} \\&m_{1}=\frac{12}{4} \\&m_{1}=3\end{aligned}$$[/tex]

Therefore, the slope of second line is [tex]$m_{2}$[/tex].

[tex]$$m_{2}=-\frac{1}{3}$$[/tex]

Step 2 of 2

Substitute the values of [tex]$m_{2}[/tex], x and g(x) to find the b.

[tex]$$\begin{aligned}&g(x)=m x+b \\&4=-\frac{1}{3}(6)+b \\&b=4+2 \\&b=6\end{aligned}$$[/tex]

Therefore, the equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Answer:

113.1 m

Step-by-step explanation:

The value of x that makes sense in this context is; 32.

The dimensions of the new garden is; 64 by 16.

The expression that represents the problem statement is;

x² = (2x)(x – 16)

Expanding the bracket gives us;

x² = 2x² – 32x

x² - 32x = 0

x(x - 32) = 0

Thus; x = 0 or x = 32

x can't be 0 and as such the value of x is 32.

Thus;

The length of the new garden is; l = 2x = 64.

The width of the new garden is; w = x - 16 = 32 - 16 = 16

The dimensions of the new garden are therefore; 64 by 16

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Answer:

Who is the youngest in your family?

Answer:

Number 1 is 55

Number 2 is 60 :)

Step-by-step explanation:

(115 - 5)/2

110/2

55

Number 1 is 55

Number 2 is 60 :)

60 + 55

110 + 5

115 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

the first number is 55 and the second is 60