a) Write 2 expressions for the area of the shaded region.
b) Find the length of the shaded region if the perimeter is 48cm.
c) Find the area of the shaded region if perimeter is 48cm.

Answer: Choice C  [tex]f(x) = 5(x+4)^2 - 80[/tex]

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

Reason:

The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.

The -5(16) simplifies to -80

Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]

Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)

Answer:

c) 5(x+4)² - 80

Step-by-step explanation:

You have already gotten the third (second-last) step for finding the vertex as follows:

f(x) = 5(x² + 8x + 16) -5(16)

= 5(x+4)² - 80

Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).

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The zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.

A quadratic function is a function that has a degree of 2.

Given the following equation

f(m) = m^2 + 5m + 4

The x-intercept occurs at the point where f(m) is zero and same is applicable to the zeros of the function.

This shows that the zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.

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The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

[tex]\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units[/tex]

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The distance Leah would have to walk home is 1.5 miles

From the question, we are to determine the distance Leah will have to walk home

From the given information,

Price of journey in pounds = 3 + 2 × distance in miles

Let the distance be d

Then,

Price of journey in pounds = 3 + 2d

Since Leah has £5, we can write that

5 = 3 + 2d

5 - 3 = 2d

2 = 2d

∴ d = 2/2

d = 1 mile

This means her money can only cover 1 mile

But the journey to her home is 2.5 miles

Therefore, she will have to walk

2.5 mile - 1 mile  = 1.5 miles

Hence, the distance Leah would have to walk home is 1.5 miles

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Refer to the figure given below while reading the solution.

Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.

And then position B when traveled 5 m towards the right turning 90°.

We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).

Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).

Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.

So, the average of the shortest distances of B from each side is [tex]\frac{(AC-AD)+44-(AC-AD)+(AC+AD)+44-(AC+AD)}{4}=\frac{44+44}{4}=22[/tex]

Hence, the average of the shortest distance of B from each side is 22 m

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Answer:

A

Step-by-step explanation:

Givens

y2 = 15

y1 = 0

x2 = 3

x1 = 0

Equation

slope = (y2 - y1) / (x2 - x1)

Solution

The question is a bit unfair. It looks like you should be answering one. It's not true. What makes it not so is that the axis (x and  y) have different intervals.

Substitute the givens into the equation

slope = (15 - 0) / (3 - 0)

slope = 15 / 3

slope = 5

Answer Slope = 5 or A

Answer:

it's A

Step-by-step explanation:

that's what i put on that question

Finding the proportionality constant :

Finding y when x = 7 :

The value of y is 4/49 when x = 7.

[tex]y = \frac{k}{ {x}^{2} } \\ \\ 64 = \frac{k}{ { (\frac{1}{4}) }^{2} } \\ \\ 64 = \frac{k}{ \frac{1}{16} } \\ \\ 64 = 16k \\ \\ k = \frac{64}{16} \\ \\ k = 4.[/tex]

Finding 'y'

[tex]y = \frac{4}{ {7}^{2} } \\ \\ y = \frac{4}{49} .[/tex]

Answer:

33.3333%

Step-by-step explanation:

Total number of kg- 2+3=5

Total money- (2×8)=16

(3×6)=18

16+18=34

$34=5000g

=250g

(250×$34)÷5000=$1.7

profit-2.55-1.7=0.85

(0.85/2.55)×100=33.333%

0 planes contain points J, K, and N.

Given that, planes X and Y and points J, K, L, M and N.

We need to find exactly how many planes contain points J, K, and N.

From the figure, we can see Point J doesn't belong to the planes X and Y and Point K and N belong to the plane X.

Since, points J, K, and N together do not belongs to any single plane, the planes contain points J, K, and N is 0.

Therefore, 0 planes contain points J, K, and N.

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Answer:

2 planes.

Step-by-step explanation:

The third option is correct.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

5x+2x(x-4)=5x+x-10

5x+2x-8=5x+x-10

5x-5x+2x+x=-10+8

x+3x=-2

4x=-2

x=-2

Answer:

6/- 3

Step-by-step explanation:

Answer:

B. $5.20

Step-by-step explanation:

18 decrease 20% =

18 × (1 - 20%) = 18 × (1 - 0.2) = 14.4

14.4 increase 8.25% =

14.4 × (1 + 8.25%) = 14.4 × (1 + 0.0825) = 15.588

15.588/3 = 5.196

Answer:

2 times a number more than 4

Answer:B

Step-by-step explanation:

Answer:

15 (second option listed)

y = 15

x = 30

Step-by-step explanation:

setting up this statement algebraically:

[where x = one of our numbers, y = other number]

x + y = 48

x = (2y + 3)

x = 2y + 3

plug x [now in terms of y] into the original equation

(2y + 3) + y = 48

3y  + 3 = 48

  - 3        - 3

3 y = 45

÷3       ÷3

y = 15

from this value, we can plug it back into the y-value of the original equation to find our x-value

x + y = 48

x + 15 = 48

  - 15    - 15

x = 33

{to check: 33 is 2y + 3}

we know that y = 15 (smaller number) and that x = 33 (larger number)

so, the solution to the question of which is the smaller number is 15

The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.

The triangle is having three sides in an isosceles triangle the two opposite sides are equal and the two adjacent angles with similar sides are equal.

The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent.

Therefore the isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.

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Answer:

-11 < x < 7

(first option listed)

Step-by-step explanation:

we know that x² + 4x < 77

first, we should rewrite our expression in standard

x² + 4x - 77 < 0

factor {find two numbers that multiply to c (77) and add to b (4)  }

(x - 7) (x + 11) < 0

set both roots to 0:

x - 7 < 0

  + 7  + 7

x < 7

x + 11 < 0

x > -11

so, x will be < 7 and > -11

which can be expressed as

-11 < x < 7

So, -11 < x < 7

Answer:

-11 < x < 7

Step-by-step explanation:

1st option;

The gym location is (15th street, 14th Avenue). so the option D is correct.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location is 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home will be

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari will be

= (18th , 12th )

We know that

Gym distance = 2/3 × (18),  2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

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Answer:

x12×x5x×x-2×9) ____=((140)5

60x × (x-18)x _______=(140)5

60x×x-10x _______=(140)5

60x-18x______=140×5

42x_______=700

42x-42x ____=700-42x

658x

Answer:

A 3 and 8

Step-by-step explanation:

if a/b=c/d, the extremes are "a" and "d". The means would then be "b" and "c"

The extremes of the proportion are 3 and 8.

To find the extremes of a proportion, we need to identify the numbers that are positioned at the far ends of the proportion. In the given proportion:

3/4 = 6/8

The numerator of the first fraction, 3, and the denominator of the second fraction, 8, are the extremes. These numbers form the far ends of the proportion.

Therefore, the extremes of the proportion are 3 and 8.

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The score of Jane is 27 and the score of Claire is 18.

A linear equation is an equation where highest degree of variables is 1.

Let the score of Jane's mark is x

Given, that score Jane is 9 more than the score of Claire.

So, the score of Claire= x-9

Given, the score of Jane is 60% of the sum of their scores.

the sum of their scores is = x+x-9= 2x-9

from the above it is clear that

the linear equation will be

x=60%(2x-9)

⇒x=0.6(2x-9)

⇒x= 1.2x -5.4

⇒1.2x-x= 5.4

⇒0.2x= 5.4

⇒x= 5.4/0.2

⇒x= 27

So the score of Jane is 27.

As score Jane is 9 more than the score of Claire.

the score of Claire is = x-9= 27-9=18

Therefore the score of Jane is 27 and the score of Claire is 18.

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Passengers under the age of 8 and whose height is less than 57 inches must be in the back seat of a vehicle.

When you journey in the backseat of a automobile, you take a seat within the row of seats behind the motive force. Kids once in a while combat over the front seat, not wanting to take a seat within the backseat. you may tour within the backseat of a car except you're the driver or are using a two-seat sports activities vehicle.

The cushion in which the driving force or passenger sits is either known as a horizontal cushion or seat cushion. The back of the automobile seat is called the seat again however it could additionally be called a backrest.

An infant protection seat every so often referred to as an toddler protection seat, infant restraint device, baby seat, child seat, car seat, or booster seat is a seat designed particularly to shield youngsters from injury or death throughout automobile collisions.

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Step-by-step explanation:

eq of a circle is

(x-h)^2+(y-k)^2=r^2

h is 0

k=3

r is 1.5 this is radius of the circle

x^2+(y-3)^2=1.5^2

Answer:

Un= 1 + (n-1)4

Step-by-step explanation:

a=1

d=5-1=9-5=4

using the formula Un=a+(n-1)d

The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

[tex]\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\[/tex]

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

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The number of biscuits each friend can get would be 2.5.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Margret divides a packet of 20 biscuits among her 8 friends.

In order to find the number of biscuits each friend gets.

20 / 8

= 2.5

Hence, the number of biscuits each friend can get would be 2.5.

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Answer:

DEF

Step-by-step explanation:

it is mathematically similar as the sides have a scale factor of 4

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

The equivalent is the expressions that are in different forms but are equal to the same value.

Then the equation is given below.

-11(x - 2) = 8

By simplifying, we have

x - 2 = - 8 / 11

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

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