Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.



Angles 1 and 5 are
because they are
angles.



Angles 4 and 6 are
because they are
angles.

Answer:

Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.

For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.

Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.

Draw squares on each of these sides.These squares have areas p²,b² and h².

For any right angled triangle with sides of length p,b and h;

[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]

[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]

From (i); p²=h²-b²

[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

Similarly,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

Step-by-step explanation:

[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.

[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]

Answer:

x = 15

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

sum the 5 exterior angles and equate to 360

5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is

23x + 15 = 360 ( subtract 15 from both sides )

23x = 345 ( divide both sides by 23 )

x = 15

Answer: 212

Step-by-step explanation:

13 * 22 - 68 - 6 = X

286 - 68 - 6 = X

286 - 74 = X

X = 212

Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

Answer: R62,500

Step-by-step explanation:

To find the discount, simply multiply 12.5% (0.125 in decimal form) with 500,000

500,000 x 0.125 = 62,500

Answer:

  ₹62,50

Step-by-step explanation:

The amount of discount is found by multiplying the discount rate by the amount being discounted.

  discount = 0,125 × ₹500,00 = ₹62,50

You will receive a discount of ₹62,50.

_____

Additional comment

Here, a comma is used to separate the units part of the number from the fractional part of the number. This decimal separator is an alternative to the use of a period or centered dot (·) for that purpose.

Answer:

The probability of pulling a blue marble and the coin landing tails up is 360/2500

The tables of values are given as:

Color     Times

Blue        18

Green     20

Yellow    12

Heads    Tails

20          30

The probability of obtaining a blue marble is:

P(Blue) = 18/50

The probability of landing tails up is:

P(Tail) = 20/50

The required probability is:

P = P(Blue) * P(Tail)

This gives

P = 18/50 * 20/50

Evaluate the product

P = 360/2500

Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500

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The domain of the function is all real numbers, the range of a function is y ≤ 4

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = –(x + 6)(x + 2)

If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.

Here the no other details are given.

But we can say:

Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4

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Answer:

-x-y=1

-x= 1+y

x= -1-y

3x+2y=0

3(-1-y) +2y=0

-3-3y+2y=0

-3-y=0

y= -3

x= -1-(-3)

x= -1+3

x= 2

Therefore, x= 2 and y= -3

Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 65, \sigma = 3.5[/tex]

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{54.5 - 65}{3.5}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.

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Answer:The answer is 8 sides

Step-by-step explanation:

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

The representation of complex number in polar form is expressed as;

y = r(cosФ + isinФ)

where;

r is the modulus

Ф is the argument

Given the vector t = –5i + 12j, the modulus of the vector is given as;

r = √(-5)²+(12)²

r = √25 + 144

r = √169

r = 13

Determine the angle between the vectors

Ф = arctan(-12/5)

Ф = -67.38

Since tan is negative in the second quadrant, hence;

Ф = 180 - 67.38

Ф = 112.62°

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

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Answer:

67 m/s

Step-by-step explanation:

Formula for range :

Solving with the given values :

Answer:

[tex]\sf u=67\:ms^{-1}[/tex]

Step-by-step explanation:

Assuming the distance traveled is the horizontal distance.

Horizontal Range Formula

[tex]\sf R=\dfrac{u^2 \sin 2\theta}{g}[/tex]

where:

Given:

Substituting the given values into the formula and solving for u:

[tex]\implies \sf 400=\dfrac{u^2 \sin 60^{\circ}}{9.8}[/tex]

[tex]\implies \sf 3920=u^2 \sin 60^{\circ}[/tex]

[tex]\implies \sf 3920=\left(\dfrac{\sqrt{3}}{2}\right)u^2[/tex]

[tex]\implies \sf u^2=\dfrac{7840}{\sqrt{3}}[/tex]

[tex]\implies \sf u=\sqrt{\left(\dfrac{7840}{\sqrt{3}} \right) }[/tex]

[tex]\implies \sf u=67.2787196...[/tex]

[tex]\implies \sf u=67\:ms^{-1}\:(nearest\:whole\:number)[/tex]

The arrangement of the rose plants on the triangular plot is such that they

form a series or progression that is defined.

The number of rows on Bill's plot is; 8 rows

The given parameters for the triangular plot are;

Number of plants at the corner = 1 plant

Number of additional plants per row = 6 plants

Number of rose plants = 150 rose plants

The number of rows in the plot.

The difference between successive rows, d = 6

The number rose at the top vertex, a = 1

Therefore, the rose in the garden forms an arithmetic progression

The first term, a = 1

The common difference, d = 6

The number of rows Bill's plot will have, n is given by the sum of n in terms of

an arithmetic progression, Sn, is given as follows;

[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]

When Sn = 150, we get;

[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]

150 = 3·n² - 2·n

3·n² - 2·n - 150 = 0

Taking only the positive solution for n, we have;

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]

[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]

The number of rows Bill's plot has, n ≈ 7.3965

Given that the 7th row is completed, an 8th row will be present on Bill's plot

The number of rows Bill's plot will have = 8 rows

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Answer:

Step-by-step explanation:

3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b)   [commutative property]

                      = (6×ab) × (12×ab)  [associative property]

                      = (6×12) × (ab×ab)  [commutative + associative]

                      = (72) × (ab)²

                      = 72× (ab)²

                      = 72a²b²  [exponent property]

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Step-by-step explanation:

[tex]5 = {a}^{x} [/tex]

[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]

[tex] \frac{5}{a} = {a}^{x - 1} [/tex]

The mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

Mean is the sum total of the number divided by number of terms

Median is the middle number when arranged in ascending or descending order.

Midrange is the average of the sum of the maximum number and the minimum number.

Given that;

First, we arrange in ascending order.

60, 62. 64, 66, 68, 70, 72

Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7

Mean = 462 / 7

Mean = 66

Median = 66

66 is the middle number.

Range = ( Max + Min ) / 2

Range = ( 72 + 60 ) / 2

Range = 132 / 2

Range = 66

Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

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[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]

See the attached files!!!!

The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)

An intercept is the point where a straight line or a curve meets with the x or y axes.

Analysis:

The rate of change is the same as slope. The slope of y = -3x + 4 is -3,

All other functions Except A have a slope of -3.

for linear function A,

if y = mx + c, c = -4, x = -3, y = -13

-13= -3m - 4

-3m = -9

m = 3

In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4

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[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]

Answer:

The answer is B.) 3

Step-by-step explanation:

Answer:

jesse got right

Step-by-step explanation:

branliest.

Answer:

She would have received $5.49 change

Answer:

$5.49 ~$5.50

Explanation: $20 - $15.51 = $5.49 therefore you have to round off which would initially equal to $5.50

Answer:

x = 28

Step-by-step explanation:

By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28

Answer: (8, -4)

Step-by-step explanation:

-5x - 3y = -28
  x + 2y = 0

1. Multiply both sides of the bottom system by 5 to cancel the x out

   5(x+2y=0)

   5x + 10y = 0

2. rewrite

   -5x - 3y = -28

    5x + 10y = 0

3. add

   0x + 7y = -28

4. divide by 7

   7y = -28

5. y = -4

6. plug in -4 for y in one of the original equations

   x + 2(-4) = 0

7. simplify

   x = 8

9. solution is

   (8, -4)

Answer:

2.5 kilometers

Step-by-step explanation:

One kilometer is 1000 meters

To convert from metres to kilometers, we divide by 1000

2500 ÷ 1000 = 2.5km