For the system of equations:
-4s + 2t = -5
8s - 6t=7
What is the value of s?

tienees que fijartelos extrreemos

The given transformations are rigid transformations, such that

the image and the preimage have the same dimensions.

Correct responses:

Given;

The images of triangle 1 are; Triangle 2, and triangle 3

Taking the image of line m as line m, we have;

Required:

The degree of the intersection of lines m and n

Solution:

Triangle 2 is the reflection of triangle 1 across line m, and

triangle 3 is the reflection of triangle 2 across line n

The distance of triangles 1 and 2 from line m are equal

The distance of triangle 2 and 3 from line n are equal.

Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is

equal to the degree of rotation of triangle 2 to triangle 3, θ₂,

we have;

θ₁ = θ₂

100° = θ₁ + θ₂ = 2·θ₁

θ₁ = θ₂ = 100° ÷ 2 = 50°

The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°

The transformation to give triangle 2 from triangle 1 is a reflection about line m.

Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.

Therefore;

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Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

Five trigonometric functions of θ are

sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]

"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."

Let θ be an acute angle of a right angle triangle

"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."

"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."

"An 'opposite' side is the one across from a given angle."

"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."

we have,

cosθ = [tex]\frac{5}{12}[/tex]

secθ = [tex]\frac{12}{5}[/tex]

Hypotenuse side = 12

Adjacent side = 5

∴ Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]

sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]

tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]

cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]

cotθ  = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]

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Answer:

54 and 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park , then

45% of 120 = 0.45 × 120 = 54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 more students chose the amusement park than the water park

Answer:

54, 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park

45% of 120 = 0.45×120=54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 students chose the amusement park than the water park

Answer:

6a+17

Step-by-step explanation:

This is an algebra 'expression' where you have to rearrange the question to the correct 'expression'

4a+2a= 6a

8+9= 17

Answer:

= 4a+2a+8+9

=6a+17

Answers:

============================================================

Explanation:

Let's solve the first equation for y

[tex]18 = (x+y)\frac{1}{3}\\\\18*3 = x+y\\\\54 = x+y\\\\x+y = 54\\\\y = 54-x\\\\[/tex]

Then we'll plug this into the second equation and solve for x

[tex]18 = (x-y)*\frac{3}{5}\\\\18 = (x-(y))*\frac{3}{5}\\\\18 = (x-(54-x))*\frac{3}{5}\\\\18 = (x-54+x)*\frac{3}{5}\\\\18 = (2x-54)*\frac{3}{5}\\\\18*5 = 3(2x-54)\\\\90 = 6x-162\\\\6x-162 = 90\\\\6x = 90+162\\\\6x = 252\\\\x = 252/6\\\\x = 42\\\\[/tex]

This is the average airspeed of the plane, in miles per hour (mph). It's the speed without accounting for the wind. If there's no wind at all, then this would be the ground speed of the plane.

Use this value of x to find y

y = 54-x

y = 54-42

y = 12

The average speed of the wind is 12 mph.

Answer: pi/6

explanation: took test

The value of θ on a unit circle where the terminal point of θ is (1/2,square root 3/2), is 60°.

The measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane is known as terminal point

Thus the value of θ at terminal point on a unit circle (1/2,square root 3/2) is 60 degrees.

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Answer:

340 miles per hour

Step-by-step explanation:

To find the speed, take the distance and divide by the time

510 miles / 1.5 hours

340 miles per hour

Answer:

340 miles

Step-by-step explanation:

Speed= Distance/ Time=

510/ 1.5= 340 miles

Answer:

20 quarts

Step-by-step explanation:

There are  4 quarts in a gallon

5 gallons * 4 quarts / 1 gallon = 20 quarts

Answer:

20 US quarts

Step-by-step explanation:

there are 4 quarts in a gallon so you have to multiply 5 x 4 to get the total amount of quarts in a gallon.

Hope it helps c:

Answer:

[tex]\sqrt{41}[/tex]

Step-by-step explanation:

think of this triangle being made up of 2 triangles with the lengths of 5, 4, and x.

x being the hypotenuse, 5 being one of the legs, and 4 being one of the legs. (8/2).

pythagorean theorem:

a^2 + b^2 = c^2

5^2 + 4^2 = x^2

25 + 16 = x^2

41 = x^2

x = sqrt 41

Answer:

The denominator will be [tex]5\sqrt{3} +5\sqrt{2}[/tex]

Step-by-step explanation:

This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).

Answer:

A & D

First and last

Step-by-step explanation:

Answer:

x = 78

Step-by-step explanation:

We can find angle y

D + B + y = 180 since the sum of the angles of a triangle are 180

31+47+ y =180

78+y = 180

y = 180 - 78

y = 102

x+y = 180 since they form a straight line

x + 102 = 180

x = 180-102

x = 78

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

we have to find the value of the x°=<GHC

In the triangle BDH,

we know that,

Sum of three angle of a triangle is 180°

According to the question,

But,

<GHC and <BHD forms a straight line

so,

Therefore,

The value of x is 78°

Answer:

A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.

Step-by-step explanation:

Answer:

It would take him 5.9 weeks (rounded). basically almost 6 weeks

Step-by-step explanation:

he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6

he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10

he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing

so add the numbers 6, 10, and 18, and you get 34.

he makes 34 dollars a week

divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.

he wants to get 200$, so the equation is

200 / 34 = 5.88

Its 5.9 rounded or 5.88 weeks exact.

Answer:

6 weeks

Step-by-step explanation:

Job 1:

2 x 3 = 6

$6 per week

Job 2:

2.50 x 4 = 10

$10 per week

Job 3:

15 + 3 = 18

$18 per week

6 + 10 + 18 = 34

$34 per week

200/34 = 5.88

Answer:

3.16, 3.16, 3.16

3.16, 3.16, 3.16

1.41, 1.41, 1.41

3.16, 3.16, 3.16

Step-by-step explanation:

Answer:

Length Length  Length

3.16         3.16   3.16

3.16 3.16   3.16

1.41   1.41   1.41

3.16  3.16  3.16

Step-by-step explanation:

(x-h)²+(y-k)²=r²

(3-h)²+(3-0)²=5²

h²-6h+9+9=25

h²-6h-7=0 —> (h-7)(h+1)=0

h=7 , h=-1

h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>

x²-14x+49+y²=25 —> x²+y²-14x+24=0

h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>

x²+2x+1+y²=25 —> x²+y²+2x–24=0

I hope it helped you ^_^

Answer:

the last one

Step-by-step explanation:

Answer:

37.68

Step-by-step explanation:

40 -2.32

= 37.68

Answer: is C. 22

Step-by-step explanation:

Answer:

( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Step-by-step explanation:

x^2 = - 7x - 8

x^2 + 7x + 8 = 0

Here,

a = 1

b = 7

c = 8

D = b^2 - 4ac

= 7^2 - 4 ( 1 ) ( 8 )

= 49 - 32

D = 17

x = - b ± √D / 2a

= - 7 ± √17 / 2 ( 1 )

x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Answer:

D

Step-by-step explanation:

Pythagorean

[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)

=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]

Answer:

120 / 561

Step-by-step explanation:

An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected

16/34 X 15 X 33

6a²+11x-10= (3a+5)(3a-2)

Answer:

Solution given:

6a²+11x-10

doing middle term factorisation

6a²+(15-4)x-10

6a²+15x-4x-10

3a(3a+5)-2(3a+5)

(3a+5)(3a-2)

Step-by-step explanation:

if

6a²+11x-10=0

(3a+5)(3a-2)=0

either

a=-5/3

it

a=⅔

Answer:

The last answer

Step-by-step explanation:

We can check

For example,

a5=-6×a4

a5=-6×(-216)

a5=1296

Answer:

Step-by-step explanation:

If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:

-.414t + 129.549 ≤ 64  We subtract 129.549 from both sides to get

-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:

t ≥ 158.3 minutes which is about 2.6 hours

Answer:

t ≥ 158.33, or rounded, t ≥ 160.

Explanation:

The equation we're given is

W = -0.414t + 129.549, which an be written as

-0.414t + 129.549 = W.

We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups.  Plugging this information in, we have:

-0.414t + 129.549 ≤ 64

To solve this, we first cancel 129.549 by subtracting from both sides:

-0.414t + 129.549 - 129.549 ≤ 64 - 129.549

-0.414t ≤ -65.549

Now divide both sides by -0.414:

-0.414t/-0.414 ≤ -65.549/-0.414

t ≥ 158.33

(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)

Answer:

18

Step-by-step explanation:

4*3 = 12

1/2 * 3 * 4  = 6

x + y = 32 (1)

3x + 4y = 120 (2)

x = 8; y = 24

Step-by-step explanation:

Total students = 120

Number of groups = 32

If the number of three person groups = x

Number of four person groups = y

write a system of equations that models this situation

x + y = 32 (1)

3x + 4y = 120 (2)

From (1)

x = 32 - y

Substitute x = 32 - y into (2)

3(32 - y) + 4y = 120

96 - 3y + 4y = 120

- 3y + 4y = 120 - 96

y = 24

Substitute y = 24 into (1)

x + y = 32

x + 24 = 32

x = 32 - 24

x = 8

x = 8; y = 24

Answer:

60

Step-by-step explanation:

To get the value of x;

3x:90

(90/3) = 30

x = 30

To get the value of 2x;

(2×X);

2 × 30

=60