What are the ratio of the perimeters and the ratio of the areas?

A circle is a curve sketched out by a point moving in a plane. The area of the circle will be equal to 28.26 in².

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The area of the circle will be approximately equal to the area of the parallelogram. Therefore, the area of the parallelogram can be written as,

[tex]\text{Area of parallelogram} = 9.42 \times 3 = 28.26\rm\ in^2[/tex]

Hence, the area of the circle will be equal to 28.26 in².

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Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Let the length of the other leg can be represented by x.

Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,

Hypotenuse² = 3² + x²

6² = 3² + x²

36 = 9 + x²

x² = 27

x = √27

x = 5.1961

Hence, the measure of the other leg of the triangle is 5.1961 units.

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A) factor f(x) are 3/5 and -1.

B) x-intercepts of the graph of f(x)  are (3/5, 0) and (-1, 0).

C)  The end behavior is explained by vertex of the graph which is (-0.2, -3.2)

D) The graph is symmetrical about x = -0.2. shown below

Factorizing is a way of writing an expression as a product of its factors using brackets.

Given function is : 5x² + 2x − 3

A)5x² + 2x − 3

= 5x² + 5x-3x − 3

= 5x(x+1)-3(x+1)

=(5x-3)(x+1)

So, factors will be 3/5 and -1.

B) f(x)= 5x² + 2x − 3

The x-intercepts are when f(x) = 0.

So, x-intercepts are (3/5, 0) and (-1, 0).

C) The x-coordinate of the vertex is the midpoint of the zeros.

 midpoint= (3/5-1)/2

                =-0.2

To find the y-coordinate of the vertex, substitute the found value of x into the given equation:

f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

=-3.2

So, the end behavior is explained by vertex of the graph which is (-0.2, -3.2)

D) By plotting the zeroes and the vertex of the f(x).

The axis of symmetry is the x value of the vertex.

Thus,   the graph is symmetrical about x = -0.2.

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Answer:

2210

Step-by-step explanation:

390 =15%

390*3 = 130=5%

130*17=2210

Answer:

  60 gallons

Step-by-step explanation:

The amount of 10% solution he should add can be found by writing an equation for the total amount of chocolate in the mix.

__

Let x represent the amount of 10% solution that Augustus needs to add to the 30 gallons of 25% solution. The amount of chocolate in the resulting 15% mix is ...

  0.10x +0.25(30) = 0.15(x +30) . . . . gallons of chocolate in the mix

  0.10(30) = 0.05x . . . . . . . . subtract 0.10x +0.15(30)

  60 = x . . . . . . . . . . . . divide by 0.05

Augustus should add 60 gallons of the 10% solution to make a 15% mixture.

For this case we have the following equation for the volume:

[tex]x^3+6x^2-27x=140 < br/ >[/tex]

Rewriting the equation we have:

[tex]x^3+6x^2-27x=140=0 < br/ >[/tex]

We factor the equation to find the roots of the polynomial.

We have then:

[tex](x-5)(x+4)(x+7)=0 < br/ >[/tex]

Then, we discard the negative roots, because the dimensions of the figure must be positive.

We have then that the length is:

[tex]x=5 < br/ >[/tex]

The height is:

[tex]x+9=5+9=14 < br/ >[/tex]

The width is:

[tex]x-3=5-3=2 < br/ >[/tex]

Thus, the dimensions are:

[tex]5*14*2 < br/ >[/tex]

Answer:

The length is 5 inches, the width is 2 inches, and the height is 14 inches.

Answer:

y < 1 and y > x

Step-by-step explanation:

Let's find each equation without any inequalities first.

We have a dotted line at y = 1

Now, a dotted line represents exclusivity, and hence; it should not include the = sign

Therefore, the answer is y < 1 and y > x

the answer is A 47

Step-by-step explanation:

48+24÷8-2²

48+3-2²

48+3-4

=47

hope it helps!

Answer:

1 1/8 cups of flour

Step-by-step explanation:

hi!

If Chef Johnson needs 4 1/2 cups of flour to make 4 fruitcakes and he wants to make one, he has to divide the recipe by 4. 4 1/2 / 4= 1 1/8

Answer:

no graph un asnwerable

Step-by-step explanation:

Answer: 56.7%

Step-by-step explanation:

1) First we need to find the number of girls out of the class of 30:

30-13 = 17 -> 17 girls in the class

2) Then we can set up a part-whole equation like this (I don't know if this is how you learned it, I recommend searching up "part whole percent" if you're confused):

[tex]\frac{17}{30} \frac{x}{100}[/tex]      it follows this template: [tex]\frac{part}{whole} \frac{percent}{100}[/tex]

Since we're trying to find the percent and the problem gives us the rest of the info (by the way, that 100 will always stay there, it will never change)

3) Then we cross multiply

17 x 100 = 1700

1700/30 = 56.6666666

4) And since the answer has to be in the 1 decimal place, it would be 56.7

So that means approximately 56.7% of the class are girls

Answer:

72.

Step-by-step explanation:

2 x{15 plus[24-(1.5 x2)]}

Using PEDMAS:

= 2 x {15 + [24-(3)]}

= 2 x (15 + 21)

= 2 x 36

= 72.

The  most likely correlation coefficient for the set of data shown is: -0.21.

We would be using CORREL in excel to determine the correlation coefficient by inputting the set data below

X Y

A (1,4)

B (2, 1.5)

C (3,3)

D (4,4)

E (5,2)

Hence:

Correlation coefficient=-0.20801

Correlation coefficient=-0.21 (Approximately)

Therefore the  most likely correlation coefficient for the set of data shown is: -0.21.

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Answer:

B) -0.21.

Step-by-step explanation:

Step-by-step explanation:

[tex] = 1 - ( \frac{1}{6} + \frac{1}{5} )[/tex]

[tex] = 1 - ( \frac{5}{30} + \frac{6}{30} )[/tex]

[tex] = 1 - \frac{11}{30} [/tex]

[tex] = \frac{30}{30} - \frac{11}{30} [/tex]

[tex] = \frac{19}{30} [/tex]

So, he keeps [tex] \frac{19}{30}[/tex]

Answer:

Sanjeev kept 19/30 of his cake.

Step-by-step explanation:

So, if Sanjeev ate 1/6 of the cake there will be 5/6 of the cake left over.

He gave 1/5 of this 5/6 to his friend.

He did not give 1/5 of the entire cake, he gave 1/5 of the remainder of his cake, which was 5/6.

To solve this, we must first convert both fractions to the same denominator.

1/5 and 5/6 becomes 6/30 and 25/30

He gave away 6/30 of this 25/30

It is now clear that we must take away how much he gave away from the remainder of the cake.

25/30 subtract 6/30 becomes 19/30

We cannot simplify this.

Therefore, Sanjeev kept 19/30 of his cake.

Answer:

6x - y < -3

Step-by-step explanation:

When graphing inequalities:

< or > = dashed line

≤ or ≥ = solid line

< or ≤ = shade below the line

> or ≥ = shade above the line

Create an equation for the line

Choose 2 points on the line:

Calculate the slope:

[tex]\sf \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-3)}{0-(-1)}=6[/tex]

Determine the equation for the line using the point-slope formula:

[tex]\implies\sf y-y_1=m(x-x_1)[/tex]

[tex]\implies \sf y-(-3)=6(x-(-1))[/tex]

[tex]\implies \sf y+3=6(x+1)[/tex]

[tex]\implies \sf y=6x+3[/tex]

As the shading is above the line:

⇒ y > 6x + 3

Compare with answer options

Rearrange each answer option to make y the subject:

Option (a)

-6x + y < 3

⇒ y < 6x + 3

Option (b)

6x + y < 3

⇒ y < -6x + 3

Option (c)

6x - y < -3

⇒ -y < -6x - 3

⇒ y > 6x + 3

Therefore, as option C matches the calculated inequality, the answer is

6x - y < -3

Answer:

6x - y < 3

Step-by-step explanation:

Finding the equation of the inequality :

Slope :

⇒ m = 3 - (-3) / 0 - (-1)

⇒ m = 6/1

⇒ m = 6

Y-intercept :

⇒ (0, 3)

Equation :

⇒ y = 6x + 3

Here :

⇒ Above the origin, so it is greater than ( > )

⇒ y > 6x + 3

⇒ 6x - y < 3

Step-by-step explanation:

we assume day and night are equally long.

and the mouse will start at night of day 1.

then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).

so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).

with a starting value of 14 (the first night).

so, we are getting an arithmetic sequence

an = an-1 + c

c = 12 in our case.

a1 = 14

a2 = a1 + 12 = 14+12 = 26

a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38

an = a1 + (n-1)×12 = 14 + 12(n-1)

at what n will it reach 86 ?

86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n

84 = 12n

n = 7

so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).

Answer:

841854.7 ft²

Explanation:

[tex]\sf Formula \ for \ area \ of \ sector = \dfrac{\theta}{360 } \ x \ \pi r^2[/tex]

Here given:

Hence solve for area of sector:

[Insert values]

[tex]\rightarrow \sf \dfrac{60}{360 } \ x \ \pi (1268)^2[/tex]

[simplify]

[tex]\rightarrow \sf 841854.6778[/tex]

[round to nearest tenth]

[tex]\rightarrow \sf 841854.7[/tex]

Answer:

  841,854.7 ft²

Step-by-step explanation:

The area of the sector can be found using the appropriate area formula. The central angle in radians is required.

  A = 1/2r²θ . . . . where r is the radius, and θ is the central angle in radians

__

The 60° angle corresponds to 60° × π/180° radians, or π/3 radians. The area of the 60° sector is then ...

  A = 1/2(1268 ft)²(π/3) = 803912/3π ft² ≈ 841,854.7 ft²

Devin does not have to plow an area of about 841,854.7 square feet.

__

Additional comment

At 43560 ft² per acre, that's about 19.3 acres.

Answer:

See below

Step-by-step explanation:

Part A:

⇒ Y represents the amount of swimming

⇒ X represents the amount of tennis

Now, creating to equations:

Part B:

⇒ First equation is substituted for X in the other equation.

Gives us the plug in:

⇒ Y = 35 minutes of swimming

⇒ Adding :

35 + 40 = 75 minutes of swimming per day.

Part C:
No, due to the equation ⇒  70 + (70 - 40) = 100

Therefore, making this statement impossible.

A rhombus is a quadrilateral whose all sides are of equal length. The measure of the ∠QPR is 42°.

A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other.

The diagonals of a rhombus intersect each other at 90°. Therefore, the measure of ∠QTR can be written as,

∠QTR = 90°

(6y+6) = 90°

6y = 90 - 6

6y = 84

y = 14

Also, the diagonals of the rhombus divide the angle into two equal angles, therefore,

∠QPR = ∠SPR

∠QPR = 3y

∠QPR = 3(14)

∠QPR = 42°

Hence, the measure of the ∠QPR is 42°.

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Answer:

each friend will get 5/4 or 1.25 cups of lemonade

Step-by-step explanation:

5 divide by 4 since there are 4 friends.

so 5/4 of the lemonade will be shared by each friend.

Step-by-step explanation:

each friend would get 1.25 cups each

Answer:

The inequality is: 5<c<19

Length of third side "c" can have values greater than 5 but less than 19

Solution:

Given that,

Length of two sides of triangle are 7 inches and 12 inches respectively

Let the length of third side be "c"

The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side

So we get a inequality as:

Case 1:

Sum of length of two sides of triangle > length of third side

Rewrite,

Case 2:

Let 12 inches be the length of third side

Sum of sides of length 7 and c > 12

Therefore from case 1 and case 2,

Which can be combined,

Therefore the possible values of "c" are:

"c" can have values greater than 5 but less than 19

Answer:

46.77 cm

Step-by-step explanation:

Perimeter of the semicircle = Circumference + 2r

Answer:

[tex]f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]

Step-by-step explanation:

Recall the power series [tex]\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex].

In this case, [tex]x[/tex] is replaced with [tex]\displaystyle \frac{1}{1+e^x}[/tex], so our power series actually works out to be [tex]\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}[/tex]! Amazing, huh?

Now, we find the derivative of the function by using the chain rule:

[tex]\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]

You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.

Answer:

x = 43

Step-by-step explanation:

the angle in the triangle is vertically opposite 47° and is congruent

the sum of the 3 angles in the triangle = 180° , then

90 + 47 + x = 180

137 + x = 180 ( subtract 137 from both sides )

x = 43

Answer:

y = 96

Step-by-step explanation:

given that y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

to find k use the condition when y = 24 , x = 2 , then

24 = k × 2² = 4k ( divide both sides by 4 )

6 = k

y = 6x² ← equation of proportion

when x = 4 , then

y = 6 × 4² = 6 × 16 = 96

Answer:

Yes, it is correct.

Step-by-step explanation:

7x≥20x-39

39≥13x

x≤39/13

x≤3

The equation of the circle is :  [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84

A circle is a loci or a continuous line that equidistant from the center to any point on the line. it drawn starting from a point and ending on that same  point.

The equation of a circle is an equation used to find points on a circle so the circle can be drawn with accurate measurement. it can also be used to find the missing points.

In conclusion, The equation of the circle is :  [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84

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