write and expression for the perimeter of a rectangle with length L and width 6

(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:

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:

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;

Learn more about rigid transformations here:

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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:

y = x

Step-by-step explanation:

So what we're going to want to do here is use the slope formula and the general equation y = mx + b.

Let's start.

The slope formula is y2-y1/x2-x1. So, put our points in here. 4-0/4-0. Slope: 1.

Okay, we have that. Now, a line that passes through the origin (0,0) is not going to have a y-intercept because it hits the y-axis at 0. So, that cancels out the b.

With our slope 1, the answer is just y = x. Very simple equation.

Hope this helped!

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:

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°

tienees que fijartelos extrreemos

Answer:

A & D

First and last

Step-by-step explanation:

Answer:

[tex]y = \boxed0[/tex]

Step-by-step explanation:

we are given a sin function

[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) [/tex]

we want to figure out the midline of the function graphically The midline of a sinusoidal function is the horizontal line that passes exactly in the midline of its extreme value however since we a function recall that,

[tex] \displaystyle f(x) = a \sin(bx -c) + d[/tex]

where the midline is

to figure out the midline rewrite the function

[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) + 0[/tex]

therefore the midline is

[tex]y = \boxed0[/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

Given:

Diameter of the tennis ball = 14 inches.

Three tennis balls are fit in a cylindrical tennis ball cane.

To find:

The volume of air left between the balls and the cane​.

Solution:

Diameter of the tennis ball = 14 inches.

Radius of the tennis ball = 7 inches

Radius of tennis ball is equal to radius of cane. So,

Radius of the cane = 7 inches

Height of cane is:

[tex]3\times 14=42[/tex] inches

Volume of a ball is:

[tex]V_1=\dfrac{4}{3}\pi r^3[/tex]

Where, r is the radius of the ball.

So, the volume of 3 ball is:

[tex]V_2=3\times V_1[/tex]

[tex]V_2=3\times \dfrac{4}{3}\times \dfrac{22}{7}\times (7)^3[/tex]

[tex]V_2=4312[/tex]

Volume of the cane is:

[tex]V_3=\pi r^2h[/tex]

Where, r is the radius of the cane and h is the height of the cane.

[tex]V_3=\dfrac{22}{7}\times (7)^2\times 42[/tex]

[tex]V_3=6468[/tex]

Now, the volume of air left between the balls and the cane​ is:

[tex]V=V_3-V_2[/tex]

[tex]V=6468-4312[/tex]

[tex]V=2156[/tex]

Therefore, the volume of air left between the balls and the cane​ is 2156 cubic inches.

b) ( 7, 21)

Step-by-step explanation:

5(7)=2(21)-7

35=42-7

35=35

Answer:

None of them

Step-by-step explanation:

a: 5*0=2*6-7 False

b: 5*21=2*7-7 False

c: 5*18=2*8-7 False

d: 5*4=2*-3-7 False

Step-by-step explanation:

here's the answer to your question

Answer:

Step-by-step explanation:

this is a question about two similar triangles  , one is from  Amelia , the other is the tree.

1.5/4 = x/12

solve for x

4.5 = x

the tree is 4.5 meters tall

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:

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:

1. Multiply by 3

2. Multiply by 1/3

Step-by-step explanation:

6x - 3y = 3

-2x + y = -14

1. In order to eliminate the x-terms, they would both have to equal the same number with opposite signs (positive and negative). Since we are only touching the second equation, how can we get from 2 to 6? We can multiply 2 by 3 to get to 6 (negative 6 in the end.) This would result as follows:

6x - 3y = 3

-6x + 3y = 42

2. In order to eliminate the y-terns through multiplying with the first equation, we have to figure out how to make 3y into 1y. We can do this by adding its reciprocal, 1/3. 1/3 × 3 = 1. This would result as follows:

2x - y = 1

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]

Learn more about trigonometric functions, acute angle and right angle triangle here

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#SPJ2

Answer:

The distance is 7[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{The formula for \underline{distance between} is: }\mathsf{\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}}[/tex]

[tex]\large\textsf{Whereas }\mathsf{x_2}\large\textsf{ is }\mathsf{2}\large\textsf{ and }\mathsf{x_1}\large\textsf{ is }\mathsf{ -5}\\\\\large\textsf{And also }\mathsf{y_2}\large\textsf{ is }\mathsf{ -2}\large\textsf{ and }\mathsf{ y_1}\large\textsf{ is }\mathsf{5}[/tex]

[tex]\mathsf{\sqrt{(2 - -5)^2+ (-2 + 5)^2}}\\\mathsf{2 - -5}\\\mathsf{= 2 + 5}\\\mathsf{= \bf 7}\\\\\mathsf{-2 + 5}\\\mathsf{= \bf -7}\\\\\mathsf{= \sqrt{(7)^2+ (-7)^2}}\\\\\mathsf{7^2}\\\mathsf{= 7\times7}\\\mathsf{= \bf 49}\\\\\mathsf{(-7)^2}\\\mathsf{= -7\times-7}\\\mathsf{= \bf 49}\\\\\mathsf{= \sqrt{49 +49}}\\\\\mathsf{49+49}\\\mathsf{=\bf 98}[/tex]

[tex]\mathsf{= \sqrt{98}}\\\mathsf{= 7\sqrt{2}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf 7\sqrt{2}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

abcd is a quadrilateral so ,

a is ( 0,-5 )

b is ( 2,-5 )

c is ( 1,-7 )

and d is ( 0,-7 )

Answer:

18

Step-by-step explanation:

4*3 = 12

1/2 * 3 * 4  = 6

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

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:

The last answer

Step-by-step explanation:

We can check

For example,

a5=-6×a4

a5=-6×(-216)

a5=1296

Hi there!

[tex]\large\boxed{0, 3}[/tex]

Find the y-intercept by substituting in 0 for x:

f(0) = 0² + 2(0) + 3

Simplify:

f(0) = 3

Answer:

0,3

hope this helped !!!

Step-by-step explanation:

Answer:

The answer is C!

Step-by-step explanation:

Answer:

D

NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"

Step-by-step explanation: