WRITE A SIMPLIFIED EXPRESSION FOR THE PERIMETER OF THE TRIANGLE.

We need to know about scaling of measurements to solve the problem. The length of the bird's beak is 5.29 inches.

In the given question we know that the height of the bird in the photo is 3.4 inches and the real height of the bird is 3.75 feet. We know that the length of the beak in the photo is 0.4 inches, we need to find out the real length of the beak. We need to find by how much the measurement of the bird is scaled down to fit in the photo. We need to convert feet to inches first to get the scaling factor, we can then divide the length of the beak given by the scaling factor.

3.75 feet= 3.75x12 =45 inches

scaling factor= 3.4/45=0.0756

real length of beak=0.4/0.0756=5.29 inches

Therefore the length of the beak of the bird is 5.29 inches.

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Answer:

Trapezoid

Step-by-step explanation:

The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid)

Answer:  m=1/5

Step-by-step explanation:

Solution:

Given that;

To find the amount in 5 years, we will apply the compound interest formula below

Substitute the values of the variables into the formula above

Hence, the answer is B

EXPLANATION

The area of the figure can be obtained by applying the following relationship:

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

Multiplying both sides by 6.4:

Solving the argument:

Switching sides:

Now that we have the height, we can compute the area as follows:

The answer is 53.24 squared inches.

The probability that, before the low fuel light comes on the car will travel is 0.2576

Given,

The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320

It follows the standard deviation of ( δ ) = 30

For the normal distribution,

P(X < x) = P( Z < x - μ / δ)

a)

P( X < 330) = P( Z < 330 - 320 / 30)

                   = P( Z < 0.3333)

                   = 0.6306

b)

P( X > 308) = P( Z > 308 - 320 / 30)

                  = P( Z > -0.4)

                  = P( Z < 0.4)

                  = 0.6554

c)

P( 305 < X < 325) = P( X < 325) - P( X < 305)

                             = P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)

                             = P( Z < 0.1667) - P( Z < -0.5)

                             = 0.5662 - ( 1 - 0.6915)

                             = 0.2576

d) P(X = 340) = 0

Since X is a continuous random variable (For normal distribution).

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The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)

Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.

Given is a triangle coordinate on x - y plane.

The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.

Now, initially the coordinates of the triangle are -

(-2, 2) , (-3, 8) , (-7, 0)

After transforming the graph by the rotation of 180°, the new coordinates will be -

(2, - 2) , (3, -8) , (7, 0)

Plot the coordinates on the graph and you will get the rotated image.

Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).

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The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .

In the question ,

it is given that

the coordinates of the end points of A and B is A(-1,2) and B(5,8) .

also AC = 2/3(AB)

So , AC/AB = 2/3

and given that point C is on the line AB , hence AC+CB=AC

2+CB=3

So , CB=1

hence AC/CB = 2/1

so , the point C divides the line AB in the ration 2:1 .

and we have the coordinates of end points ,

that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .

Substituting the above values in the section formula ,

which states that the coordinate of point C will be

((m*x₂+n*x₁)/(m+n)  ,  (m*y₂+n*y₁)/(m+n))

= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))

= ((10-1)/3 , (16+2)/3)

= (9/3 , 18/3)

= (3,6)

Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .

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Answer:

A)  8/15

Step-by-step explanation:

3 / 5 x 8/9

(3/5)(8/9)

(3*8)/(5*9)

(24/45)

8/15

Answer:

8/15

Step-by-step explanation:

3 / 5 x 8/9

Multiplying fractions

Rewriting

3/9 * 8/5

Simplify

1/3 * 8/5

Multiply the numerators

1*8 =8

Multiply the denominators

3*5 = 15

8/15

Let's begin by identifying key information given to us:

Principal (p) = $690

Interest rate (r) = 7% = 0.07 per year

Time (t) = 8 years

The amount of money that Ji-yoon has in 8 years is calculated as shown below:

You can see the three points where the result is equal to an integer in the photo below. Good luck!

Answer:

x=15

Step-by-step explanation:

5x+25=100

Subtract 25 from both sides.

5x+25−25=100−25

5x=75

Divide both sides by 5.

5x÷5=75÷5

x=15

[tex]5x+25=100\\x=[/tex]

Subtract 25 from both sides:

[tex]5x+25-25=100-25\\5x=75[/tex]

Divide both sides by 5:

[tex]\frac{5x}{5} =\frac{75}{5}[/tex]

[tex]\fbox{x=15}[/tex]

Answer:

Step-by-step explanation:

(4x + 50)° = 150°

4x = 150° - 50°

4x = 100°

x = 100° / 4 = 25°

The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following function:

We solve the polynomial as follows:

When the expression (m²/³ n⁻¹/³)⁵ is rewritten, the equivalent expression is   ∛m¹⁰n⁻⁵

From the question, the expression is given as

(m2/3n-1/3)^5

Rewrite the expression properly

So, we have the following representation

(m²/³ n⁻¹/³)⁵

Express the radicals as roots

So, we have

(m²/³ n⁻¹/³)⁵ = (∛m² ∛n⁻¹)⁵

Remove the brackets in the expression

This is done by multiplying the exponents

So, we have

(m²/³ n⁻¹/³)⁵ = (∛m¹⁰ ∛n⁻⁵)

Combine the roots

(m²/³ n⁻¹/³)⁵ = ∛m¹⁰n⁻⁵

Hence, the equivalent expression is  ∛m¹⁰n⁻⁵

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The required simplified expression is given as ∛[m¹⁰/n⁵].

Given that,
For an expression (m²/³n-¹/³)⁵ we have to deduce the function that the solution only consists of the positive integer exponents.

Here,
Rewriting the given expression,
= (m²/³n-¹/³)⁵
Simplifying the expression,
using the property, (xᵃ)ᵇ = xᵃᵇ
= m¹⁰/³n⁻⁵/³
= [m¹⁰n⁻⁵]¹/³
we imply cube root for the exponent 1/3.
= ∛[m¹⁰n⁻⁵]
= ∛[m¹⁰/n⁵]   (using the property x⁻¹ = 1 / x )

Thus, the required simplified expression is given as ∛[m¹⁰/n⁵].

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The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Lisa buy new clothes for spring under $200.00

She spent $125.88 for buying some shirts that has each cost $20.80.

Let the number of shirts = x

Then, We can formulate for the given condition is;

The inequality for solution of the value of x is,

⇒ $20.03x + $125.99 < $200.00

Because we can solve for x, which is the number of shirts Lisa can buy with the money she has left.

Therefore,

The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

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sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) is equivalent to sin(-pi/2)

Define Trigonometric functions

A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.

We know the formula of sin(A - B) = sinAcosB - cosAsinB

And the given expression is

sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

Which is in the form of given formula of sin(A - B)

where,  A = π/12  and B = 7π/12

put A and B values in sin(A - B),

sin(π/12 - 7π/12) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

sin(-6π/12) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

sin(-π/2) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

Hence, sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12) is equivalent to sin(-π/2).

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Answer:

B

Step-by-step explanation:

before finding the sum we require to find first term and common difference.

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then

a₁ + 9d = - 5 → (1)

a₁ + 14d = - 7.5 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 5d = - 2.5

5d = - 2.5 ( divide both sides by 5 )

d = - 0.5

substitute d = - 0.5 into (1) and solve for a₁

a₁ + 9(- 0.5) = - 5

a₁ - 4.5 = - 5 ( add 4.5 to both sides )

a₁ = - 0.5

the sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

here a₁ = - 0.5 and d = - 0.5 , then

S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]

      = 10 (- 1 -9.5)

     = 10 × - 10.5

    = - 105

All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.

Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.

The inequality is given as,

$25 < x ≤ $30

All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

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Answer:

4 Eggs are left since he uses 2 eggs per 1 loaf so 2x4=8

Step-by-step explanation:

t(x) = x² + 8x - 20

Coordinate(s) of the solutions/roots

x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0

roots: x= 2 and x = -10

coordinate of the y-intercept

y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20

y-intercept: y = -20

location of the line of symmetry

x = -4

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4

coordinate of the vertex

(-4, -36)

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)

whether the graph opens up or down and how you know

Opens up

Because the coefficient of x² is positive

we get that:

so the answer is x=-6

Solution

For this case we can do the following:

tan x = 35/30

And we can solve for x and we got:

And rounded to the nearest degree is:

49º

Answer:

x-intercept (-2,0)

y-intercept (0,-3)

Step-by-step explanation:

to find the x-intercept we set y=0

so 3x=-6

x=-2

to find the y-intercept we set x=0

so 2y=-6

y=-3

- 5 < x < 5

Number line:

The expression for the total cost is 75 + 22h

From the information, the plumber charges a flat fee of 75 to visit a home and examine a clogged drain and also charges an additional 22 per hour spent fixing the drain.

Therefore, the amount that will be charged for each hour will be:

= 75 + (22 × h)

= 75 + 22h

where h = number of hours.

For example if the number of hours is 5 hours. This will be:

= 75 + 22h

= 75 + 22(5)

= 75 + 110

= 185

Your information was incomplete but an overview was given.

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Answer: y=x/3 + 4

Step-by-step explanation: