In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR ≅ ∠SQR.

Answer:

m∠M=98º

Step-by-step explanation

Sum of interior angles;

  3x-16+x+6+x = 180

                   5x = 180-6+16

                   5x = 190

                      x = 38º

Angle M;

      m<M= 3x - 16 = 3(38)-16= 98º

      m∠M=98º

Answer:

<M = 98

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

< M + < N + < O = 180

3x-16 + x + x+6 = 180

Combine like terms

5x - 10 = 180

Add 10 to each side

5x-10 + 10 = 180+10

5x = 190

Divide by 5

5x/5 = 190/5

x=38

We want to find <M

<M = 3x-16  = 3*38 -16 = 114-16 =98

The total cost of 6 wave pool tickets with the discount included would be $73.5.

To calculate the total cost we must multiply the value of each ticket by the number of tickets to be purchased, in this case there are 6:

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In the imaged attached, the most precise name for ABCD  is known to be rhombus.

Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.

Using the Diagonal midpoints of AC and BD, the equation will be:

(A+C)/2

(B+D)/2

To find if the midpoints are similar, then:

A +C = (3, 5) +(6, 2) = (9, 7)

B +D = (7, 6) +(2, 1) = (9, 7)

Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.

In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:

 AC = C -A = (6, 2) -(3, 5) = (3, -3)

BD = D -B = (2, 1) -(7, 6) = (-5, -5)

So the lengths will be (3√2 vs 5√2).

Note also that the dot-product of these values need to be zero if they are perpendicular and as such:

 AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.

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Answer:

Length of pipe = 21 cm

Internal diameter = 4 cm

Internal radius = \frac{4}{2} = 2 cm24=2cm

Thickness = 0.5 cm

Outer radius = 2+0.5=2.5 cm

Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h

Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3

=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3

Hence The volume is 148.5 cubic cm.

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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm

Answer:

Step-by-step explanation:

THIS WILL BE A STRAIGHT LINE rising to the left as the coefficient of x is negative ( -3/2),

When x = 0  y = -3 so mark the point (0, -3) on your graph paper.

When x = 6, y = -3/2 * 6 - 3 =  -9 - 3 = -12

So mark  the point (6, -12)

The graph will be the straight  line passing through the above 2 points.

Considering that 160,000 is the y-intercept of the function, it's significance is given by:

the initial population at the time of the estimation.

The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.

Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:

the initial population at the time of the estimation.

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The equation will be given as y = 6x for the given information in the question.

The complete question is as below:-

Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.

And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be

y = 6x

Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.

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Answer:

Do you like having a pet? - statistcal question

Step-by-step explanation:

^^^^

Answer:

2×3.14×r=75

6.28 r=75

r=75/6.28=11.943=12 inch (nearly)

The equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4) would be Y=-1/9(x^2-36).

Since the zeros are symmetrical to the y axis, the equation can be written as;

y = a(x-b)(x+b),

where a is a scale factor and b is x-intercept.

From the given zeroes

y = A(x-6)(x+6).

Now we can plug in the y-intercept (0,4)

4 = A(0-6)(0+6)

4 = A(-36)

-36A=4

A = -1/9

Therefore the equation would be

Y = -1/9(x-6)(x+6),

or Y=-1/9(x^2-36)

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Answer:

5x - 2 = (-9x) + 8

5x + 9x = 8 + 2

14 x = 10

x = 10 / 14

x = 5/7

Answer:

5 / 7

Step-by-step explanation:

Step 1: Move the variables to one side and the numbers to the other. We get 14x = 10.

Step 2: Then we solve for x. x is equal to 10 / 14, which simplifies to 5 / 7.

The standard deviation will be 6816.9645.

From the information given, the mean is 74000 and X is given as 60000.

P[(Z < (-60000 - 74000)/SD] = 0.02

Note that 0.02 will be -2.0537 under the normal distribution table.

-14000/SD = -2.0537

SD = -14000/-2.0537

SD = 6816.9645

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Answer: Option 1

Step-by-step explanation:

Here, a = -3, b = -2, c = 6.

Answer:

quadrant 4

Step-by-step explanation:

(2,-5) would be in the 4th quadrant

Answer: 62.5%

Step-by-step explanation:

First, you must simplify 5/8 into a decimal and then multiply that by 100 to get the percentage of the fraction.

[tex]\frac{5}{8}=0.625[/tex]     [tex]0.625*100=62.5[/tex]%

I hope this helps!! Pls give brainliest :)

Answer:

[tex]b + n = 18[/tex]

[tex]6b + 5n = 101[/tex]

Answer:

2

Step-by-step explanation:

the additive inverse of - 2 is 2 , since

- 2 + 2 = 0

Answer:

or 3162.2776601683795

Step-by-step explanation:

what is the square root of 10,000,000​?

√10000000

= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5

= √26 x 2 x 56 x 5

= 1000√10

or 3162.2776601683795

The length side AB is 64 ft , Option D is the correct answer.

A triangle that has one angle 90 degree is called Right angled Triangle.

From the figure it can be seen that

The triangle CDE is a right Triangle

Applying Pythagoras theorem to find the length of CE

CE² = 12² + 16²

CE = 20 ft

As both the triangles are similar therefore the ratio of the sides will be equal

BC : CD = AC : CE

48 / 12 = AC / 20

AC = 80ft

As Triangle ABC is also a right angled triangle

Applying Pythagoras theorem to find the length of AB

AC² = BC² +AB²

6400 = 48² +AB²

AB² = 4096

AB = 64 ft

Therefore Option D is the correct answer.

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Answer:

64 ft.

Step-by-step explanation:

Keep it simple, just givin' the answer :)

Answer:

a

Step-by-step explanation:

we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value

*DO THE TRIAL AND ERROR METHOD*

take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.

[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]

Answer:

$20 × 14 days = $280

&30 × 3 = $90

&280 + $90 = $370

Answer:

For car she owes=

$20 x 14 = $280

For tank she owes=

$30 x 3 = $90

Therfore in total she owes,

$280 + $90 = $370

Answer:

f(x) = (x/8)^2       for x ≥ 0

Step-by-step explanation:

y = 8 sqrt x      switch   x and y

x = 8 sqrt y       now solve for y

(x/8)^2 = y

Answer:

See below

Step-by-step explanation:

q = quarters       value   = .25 q

n = nickels =  4q     value = .05 (4q)

    summed = 12.60

.25q   + .05(4q) = 12.60      <====== can be used to solve the problem

.45q = 12.60

q = 28     quarters     then nickels = 4q = 112  

The transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).

A dilation transformation is a transformation that changes the size of the original figure but the shape remains unchanged.

If any figure is dilated by a scale factor k with the center of dilation as the origin.

Then the change of transformation in each of the vertices of the figure is given:

(x,y) → (kx, ky)

It is given a point C which is located at C(9,3).

Hence, here k=3

We get:

C(9,3) → C'(9×3,3×3)

C(9,3) → C'(27,9) = C'(3,1)

Hence, the transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).

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Answer:

(5,5)

Step-by-step explanation:

count from the center

The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12

The expression is given as:

1/3y

Express 1/3y as 1/6y + 1/6y

So, we have:

1/6y + 1/6y

Factor out y

1/6y + 1/6(y)

Add 0 to the above equation

1/6y + 1/6(y + 0)

Express 0 as 12 - 12

1/6y + 1/6(y + 12 - 12)

Expand

1/6y + 1/6(y + 12) - 1/6 * 12

Evaluate the product

1/6y + 1/6(y + 12) - 2

Hence, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12

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The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12

The expression is given as:

1/3y

Express 1/3y as 1/6y + 1/6y

So, we have:

1/6y + 1/6y

Factor out y

1/6y + 1/6(y)

Add 0 to the above equation

1/6y + 1/6(y + 0)

Express 0 as 12 - 12

1/6y + 1/6(y + 12 - 12)

Expand

1/6y + 1/6(y + 12) - 1/6 * 12

Evaluate the product

1/6y + 1/6(y + 12) - 2

Therefore, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12

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Answer:

Step-by-step explanation:

2.5

4 quarts per gallon

8 quarts per 2 gallons

2 quarts is half a gallon since 4 quarts is a full gallon

answer: 2.5

Answer:

I think A or C.

Step-by-step explanation: