Write a two-column proof. Given: Triangle ACD is isosceles; <1 is congruent to <3 Prove: Segment AB || Segment CD

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Answer:

g(3) = 11.

Step-by-step explanation:

Given g(x) = x² + 2

Plug '3' into 'x' to solve for g(3):

g(3) = (3)² + 2

g(3) = 9 + 2

g(3) = 11.

Answer: g(3)=8

Step-by-step explanation:

If g(x)=x2+2 and you wish to find g(3), you simply sub in the 3 from g(3) into the x from the original equation, making it g(3)=3x2+2. 3 times 2 is 6, plus 2 equals 8.

Answer:

1.1 hour or 1 hour and 6 minutes

Step-by-step explanation:

Time is given by the distance divided by the velocity. If the time it takes the tugboat to travel 20 km downstream in the same time it takes it to travel 10 km upstream, then:

[tex]t_1=t_2\\\frac{20}{v_b+v_c}=\frac{10}{v_b-v_c}\\v_c=5\ km/h\\20v_b-100=10v_b+50\\10v_b=150\\v_b=15\ km/h[/tex]

The velocity of the boat is 15 km/h. When traveling downstream, the current will favor the boat, therefore, the time required for it to travel 22 km downstream is:

[tex]t=\frac{22}{v_b+v_c} \\\t=\frac{22}{15+5}\\ t=1.1\ hour[/tex]

It will take the boat 1.1 hour or 1 hour and 6 minutes.

Answer:

A

Step-by-step explanation:

We know that the y-coordinate has to be 1 so we can eliminate options C and D. If we plug y = 1 into y = -5x + 3 to solve for x we get:

1 = -5x + 3

-2 = -5x

x = 0.4 so the answer is A.

Answer:

25

Step-by-step explanation:

By Geometric mean theorem:

[tex] {12}^{2} = y \times 16 \\ \\ 144 = y \times 16 \\ \\ y = \frac{144}{16} \\ \\ y = 9 \\ \\ x = y + 16 \\ \\ x = 9 + 16 \\ \huge \red{ \boxed{ x = 25}}[/tex]

The missing length AC is approximately 25.61 units.

In the right-angled triangle ABC, the hypotenuse is AC, and the other two sides are AB and BC. We are given that BD = 12, DC = 16, and triangle ABC is right-angled at B.

To find the missing length AC, we can use the Pythagorean theorem:

[tex]AC^2 = AB^2 + BC^2[/tex]

Since triangle ABC is right-angled at B, we can use the given lengths to find AC.

We know that BD is perpendicular to AC, so it divides triangle ABC into two smaller right-angled triangles: ABD and BDC.

In triangle ABD:

[tex]AB^2 = BD^2 + AD^2\\\\AB^2 = 12^2 + AD^2\\\\AB^2 = 144 + AD^2[/tex]

In triangle BDC:

[tex]BC^2 = BD^2 + DC^2\\\\BC^2 = 12^2 + 16^2\\\\BC^2 = 144 + 256[/tex]

We also know that AB = BC (since they are opposite sides in an isosceles right-angled triangle), so we can equate the two expressions:

[tex]144 + AD^2 = 144 + 256[/tex]

Simplifying, we get:

[tex]AD^2 = 256[/tex]

Taking the square root of both sides:

AD = 16

Now we can substitute the value of AD back into the expression for [tex]AB^2[/tex]:

[tex]AB^2 = 144 + AD^2\\\\AB^2 = 144 + 16^2\\\\AB^2 = 144 + 256\\\\AB^2 = 400[/tex]

Again, since AB = BC (in an isosceles right-angled triangle), we can say:

[tex]400 = 144 + BC^2\\\\BC^2 = 400 - 144\\\\BC^2 = 256[/tex]

Taking the square root of both sides:

BC = 16

Finally, we can substitute the values of AB and BC into the Pythagorean theorem equation to find AC:

[tex]AC^2 = AB^2 + BC^2\\\\AC^2 = 400 + 256\\\\AC^2 = 656[/tex]

Taking the square root of both sides:

AC = √656

AC ≈ 25.61

Therefore, the missing length AC is approximately 25.61.

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Answer:

Use a graphing calc.

Step-by-step explanation:

Answer:

[tex] \frac{6}{18} = \frac{p}{36} \\ p = 36 \times \frac{6}{18} \\ p = 12[/tex]

Answer:

13%

Step-by-step explanation:

[tex]percentage \: increase = \frac{565 - 500}{500} \times 100 \\ \\ = \frac{65}{500} \times 100 \\ \\ = \frac{65}{5} \\ = 13 \% [/tex]

Answer:

Step-by-step explanation:

From the question, we are informed that Michael and Tyler both ran a half marathon and that Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 97 minutes and 49 seconds.

First, we should know that 60 minutes makes 1 hour, therefore we need to change Tyler's time taken to finish the marathon appropriately. Since Tyler finished in 97 minutes and 49 seconds, this will be converted to 97 minutes equals 1 hour 37 minutes. Therefore, Tyler used 1 hour, 37 minutes and 49 seconds.

Since Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 1 hour, 37 minutes and 49 seconds. We can see that Tyler is faster than Michael.

To know how much faster Tyler was, we subtract Tyler's time from Michael's. This will be:

= (1 hour, 42 minutes 13 seconds) - (1 hour, 37 minutes, 49 seconds)

= 4 minutes, 24 seconds.

Tyler was faster by 4 minutes, 24 seconds.

For this case we must represent the following expression algebraically:

"eight more than the product of a number and two"

Let "x" be the variable that represents the unknown number

We have to:

the product of a number and two is represented as: 2x

Then, the full expression will be:

2x + 8

Thus, we use multiplication and addition.

hope this answer correct

Answer:

x = 5.85641

Step-by-step explanation:

Step 1: Find missing leg of left triangle

sin30° = x/16

16sin30° = x

x = 8

Step 2: Find missing leg of right triangle

8² + b² = 16²

b² = 192

b = 8√3

Step 3: Find x by taking the difference

8√3 - 8 = 5.85641

Answer:

  D.  m∠C = 34, b = 25, c = 16

Step-by-step explanation:

If all you want is an answer, your friendly triangle solver can provide it. (See below)

__

When you have two angles and a side length, the law of sines can be helpful.

  b/sin(B) = a/sin(A)

  b = sin(B)/sin(A)·a = sin(119°)/sin(27°)·13 ≈ 25.04 ≈ 25

Similarly, you have C = 180° -27° -119° = 34°, so ...

  c = sin(C)/sin(A)·a = sin(34°)/sin(27°)·13 ≈ 16.02 ≈ 16

These values match answer choice D.

  m∠C = 34, b = 25, c = 16

Answer:

804.25 cm² (corrected to 2 decimal places)

Step-by-step explanation:

Radius = diameter / 2

= 16/ 2

=8 cm

Surface area of sphere = 4πr²

= 4π8²

=804.25 cm² (corrected to 2 decimal places)

By using multiplication, [tex](2x+3)^{2}[/tex] =  [tex]4x^{2} +12x+9[/tex].

Multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life. Multiplication is used when we need to combine groups of equal sizes.

Given

[tex](2x+3)^{2}[/tex]

= (2x + 3)(2x + 3)

= 2x (2x) + 2x(3) + 3(2x) +3(3)

= [tex]4x^{2} +6x+6x+9[/tex]

= [tex]4x^{2} +12x+9[/tex]

Hence, by using multiplication, [tex](2x+3)^{2}[/tex] =  [tex]4x^{2} +12x+9[/tex].

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Answer:

x=88° a=+3 b=4a-3

Step-by-step explanation:

as triangles ADE and BCE are congruent by sss axiom

so correponding angles are equal

i.e<AED = <BEC

and <DAE =90-60

=30°

so

62°+x+30°=180°

therefore x=88°

Answer: (9, 40, 41)

Step-by-step explanation:

There are an infinite number of Pythagorean triples.

Any value a, b, c such that a² + b² = c²

Here are a few of them:

3, 4, 5

5, 12, 13

7, 24, 25

8, 15, 17

9, 40, 41

Answer:

​(x²-y²)² + (2xy)² = (x²+y²)²

Find the missing x- and y-values and Pythagorean triples using the identity given

A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).​

​We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :

​a = (x²-y²)

​b = (2xy)

​c = (x²+y²)

​Question 1)

X Value = 4​

​Y Value = 3

​Pythagorean triples: ?

We can replace the values of x and y, to determine a, b and c.​

​a = (x²-y²) = (4²-3²) = 16-9 = 7

​b = (2xy) = (2*4*3) = 24

c = (x²+y²) = (4²+3²) = 16+9 = 25​

​Answer 1 : Pythagorean triples : (7,24,25)

Question 2) ​

​X Value = 5

Y Value = ?​

Pythagorean Triples: (9,40,41)​

​Now we have a, b, and c, to determine Y

​b = (2xy) = 40

Y = 40/2x = 40/2*5 = 40/10 = 4​

Answer 2 : Y = 4​

​Question 3)

X Value = ?​

Y Value = 3​

Pythagorean Triples: (27,36,45)​

Now we have a, b, and c, to determine X​

b = (2xy) = 36​

​X = 36/2y = 36/2*3 = 36/6 = 6

​Answer 3 : X = 6

Question 4)​

​X Value = 7

Y Value = 5​

​Pythagorean Triples: ?

We can replace the values of x and y, to determine a, b and c.​

a = (x²-y²) = (7²-5²) = 49-25 = 24​

b = (2xy) = (2*7*5) = 70​

c = (x²+y²) = (7²+5²) = 49+25 = 74​

Answer 4 : Pythagorean triples : (24,70,74)​

Hope this helps!​​​​​

Step-by-step explanation:

From Spymore

Step-by-step explanation:

if parabola has a vertex not in x-axis, it should have 2 x intercept

x-vertex = -2

first x intercept = 3

second x intercept should -7

so the equation will like this

y = a(x-x1)(x-x2)

y = a (x-3)(x+7)

y = a(x² + 4x - 21)

5 = a((-2)² + 4(-2) - 21)

5 = a(4 - 8 - 21)

5 = a(-25)

a = 5/(-25)

a = -1/5

then the equation is

y = (-1/5)(x² - 4x - 21)

or you can write as

y = -x²/5 + 4x/5 + 21/5

or as this one

5y = -x² + 4x + 21

This given equation represents a parabola that is downward facing, has a vertex at (-2, 5), and has an x-intercept of x = 3.

The equation of a parabola with vertex (h, k) is given by:

y = [tex](ax - h)^{2}[/tex] + k

We know that the vertex of the parabola is (-2, 5), so h = -2 and k = 5.  We also know that the parabola has an x-intercept of x = 3, so when x = 3, y = 0.  Substituting these values into the equation of the parabola, we get:

0 = [tex](a(3 - (-2))^{2}[/tex] + 5

0 = a × 25 + 5

-5 = 25a

a = -1/5

Therefore, the equation of the parabola is:

y = -(1/5)(x + 2) + 5

or

y = -(x + 22/5 + 5

We can also write the equation in vertex form as:

y = -(x - (-2))2 + 5

This equation represents a parabola that is downward facing, has a vertex at (-2, 5), and has an x-intercept of x = 3.

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Step-by-step explanation:

last years was $2500.00

20% of $2500 = $500.00

profit this year is $3000.00

Answer:

D

Step-by-step explanation:

Answer:

0.45 litres

Step-by-step explanation:

2/5 multiplied by 2 = 0.8

0.8+0.75= 1.55

2-1.55 = 0.45

Answer:

9.35975609756

Step-by-step explanation:

Its about this I just put it into a calculator

Answer:9.353658

Step-by-step explanation:

Answer: 2/4x

Step-by-step explanation:

Answer: x^2

Step-by-step explanation: X/x^2-4

2x/x^2-8x+12

Answer:

(2×1+2)+(2×2+2)+(2×3+2)+(2×4+2)

=28

Answer:

The answer is given below

Step-by-step explanation:

Given that the location of the points are W = (3, 1) , X = (7, -1), Y = (7, -3) and Z = (3,-3)

The distance between two points A(x1, y1) and B(x2, y2) is given by the formula:

[tex]|AB|=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Therefore, the side length of the quadrilaterals are:

[tex]|WX|=\sqrt{(-1-1)^2+(7-3)^2}=\sqrt{20} =4.47[/tex]

[tex]|XY|=\sqrt{(-3-(-1))^2+(7-7)^2}=\sqrt{20} =2\\\\|YZ|=\sqrt{(-3-(-3))^2+(3-7)^2}=\sqrt{20} =4\\\\|ZW|=\sqrt{(-3-1)^2+(3-3)^2}=\sqrt{20} =4[/tex]

The Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units

Answer:

4.47,

2

4

14.47

Step-by-step explanation:

Answer:

see explanations below.

Step-by-step explanation:

The shown sides are all equal.

If it is a regular polygon, it must have all interior angles equal, and all sides equal.

IF

all sides are equal and all angles are equal,

THEN

it is a regular polygon, with 12 sides, because in regular polygons, all exterior angles are equal, and add up to 360 degrees.

No. of sides = 360/(180-150) = 360/30 = 12 sides.

Answer:

oasis

Step-by-step explanation:

Step-by-step explanation:

[tex]y = 4x - 1 \\ m = 4 \\ c = - 1[/tex]

Answer:

m = 4, c = -1

Step-by-step explanation:

Given equation si

=> y-4x = -1

=> y = 4x-1

Comparing it with the standard form of slope intercept equation:

=> [tex]y = mx+c[/tex]

We get,

m = 4, c = -1

Answer:

2/9 , 3/7 , 1/5

Step-by-step explanation:

The pattern in matching the x value / y value, kind of like getting a gradient.

For example: Look at first paragraph, the points it corresponds are on x = 9, and y = 2, y/x = 2/9

The unit rate of first, second and third graph respectively are 2/9, 3/7 , and 1/5.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To determine unit rate to the graph that represents

The pattern that results from matching the ratio x value to the y value resembles that of a gradient.

According to the first graph,

the points it corresponds are on x = 9, and y = 2, y/x = 2/9

According to the second graph,

the points it corresponds are on x = 7, and y = 3, y/x = 3/7

According to the third graph,

the points it corresponds are on x = 5, and y = 1, y/x = 1/5

Hence, the unit rate of first, second and third graph respectively are 2/9, 3/7 , and 1/5.

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Answer:

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

Step-by-step explanation:

The translation is horizontal translation.

The value of x is subtracted from 4, since the function is shifted 4 units to the right.

f(x - 4)

f(x) = (x - 4) + 6

f(x) = x + 2

Answer:

Rule = 759375(1/15)^(n-1)

Where n represent the number of term

Step-by-step explanation:

a5= ar^4= 15

a6= ar^5= 1

ar^4=15... Equation 1

ar^5=1.... Equation 2

Dividing equation 2 by equation 1

r= 1/15

For the value of a

ar^5=1

a(1/15)^5= 1

a(1/759375)= 1

a= 759375

Rule = 759375(1/15)^(n-1)

Where n represent the number of term

Answer:

H(0, -7)

Step-by-step explanation:

x:

(16 + x)/2 = 8

16 + x = 16

x = 0

y:

(-2 + y)/2 = -4.5

-2 + y = -9

y = -7

H(0, -7)

Answer:

LJ = CB

Therefore, CJ is 50km