In a school,The ratio of the number of boys to the number of girls is 8:5. One quarter of the boys and 1/15 of the girls wear glasses. When another 48 students who wear glasses join the school,the total number of students becomes 216. How many boys wore glasses at first?

Answer:

81

Step-by-step explanation:

Hello!

We can plug in 6 for x in x² + 8x - 3

When x = 6, the expression evaluates to 81.

There are two negative roots to the provided polynomial function

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

[tex]\rm f(x) =\left(x+1\right)\left(x^6-x^5+x^4-3x^3+3x^2+4x-2\right)[/tex]

Using the zero product property:

[tex]\rm \left x+1\right = 0 \ \ \ or \left x^6-x^5+x^4-3x^3+3x^2+4x-2\right = 0[/tex]

After solving:

x = -1, x = -0.853, and x = 0.418 (using the graph method)

Thus, there are two negative roots to the provided polynomial function

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

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The solution to the initial value problem is determined as y = e³ˣ.

The auxiliary equation is determined as follows;

y'' - 7y' + 12y = 0

m² - 7m + 12 = 0

m² - 3m - 4m + 12 = 0

m(m - 3) - 4(m - 3) = 0

m = 3 or 4

[tex]y = c_1e^{3x} + c_2e^{4x}\\\\y(0) = 1\\\\1 = c_1e^{3\times 0} + c_2e^{4\times 0}\\\\1 = c_1 + c_2 \ --(i)\\\\y' = 3c_1e^{3x} + 4c_2e^{4x}\\\\y'(0) = 3\\\\3 = 3c_1e^{3\times 0} + 4c_2e^{4\times 0}\\\\3 = 3c_1 + 4c_2 \ \ --(ii)[/tex]

solve (i) and (ii)

3 = 3c₁ + 4(1 - c₁)

3 = 3c₁ + 4 - 4c₁

3 = -c₁ + 4

c₁ = 1

c₂ = 0

[tex]y = e^{3x}[/tex]

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Answer:

660 miles.

Step-by-step explanation:

385 m/7 h = 55 m/h

55 m/h * 12 h = 660 m

Answer:

One Rectangular Pan

Step-by-step explanation:

Part C cannot be answered since the dimensions of the pool are not given.  Please check the question.

The cake pans may be compared by calculating the volume of each shape:

Rectangular pan:  Volume = Length x Width x Height

  Volume Rectangle = (13")*(9")*(2") = 234 in^3

Round pan:  Volume = [tex]\pi r^{2} h[/tex]

  Volume Round = (3.14)*(4")^2(2") = 100.5 in^3

Two round pans will hold 2*(100.5 in^3) or 201 in^3 of batter

One rectangular pan holds 234 in^3.

Go with the rectangular pan if you want more cake.

Answer:

274

Step-by-step explanation:

i used a calculator. You can try long division

Answer:

274

Step-by-step explanation:

7,124 ÷ 26 =274

0 2 7 4

2 6 7 1 2 4

0  

7 1  

5 2  

1 9 2

1 8 2

1 0 4

1 0 4

0

Work Shown:

54% = 54/100 = 0.54

54% of 77 = 0.54*77 = 41.58

That rounds to 42 if your teacher wants you to round to the nearest whole minute.

The differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵

The method of determining the derivative, or rate of change, of a function in mathematics.is termed as the differentiation.

Given that:-

[tex]g(t)= \dfrac{7}{t^4}[/tex]

The derivative will be calculated as:-

[tex]g'(t)=7 \dfrac{d}{dt}(t^{-4})\\\\\\g'(t)=7\times (-4t^{-5})\\\\\\g'(t)=\dfrac{-28}{t^5}[/tex]

Therefore the differentiation of the function g(t) = 7/t⁴ will be equal to g¹(t)=-28/t⁵

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Answer:

see the attachment photo!

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

The correct answer is option A which is j'(1,3) , E'( -2,1) and V'( 1,3).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Given that:-

So we will transform the points given in the figure.

V(-1,-1) , J(-4,-5) and E(-4,-3).

The transformation will be given as:-

V(-1,-1)  → V'(-1+2 , -1 + 4)      → V'( 1,3 )

J(-4,-5) → J'( -4 +2 , -5 + 4 )  → J'( -2,-1 )

E(-4,-3). → E'( -4+2 , -3+4 )   → E' ( -2, 1 )

Therefore  correct answer is option A which is j'(1,3) , E'( -2,1) and V'( 1,3).

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Step-by-step explanation:

normally the perimeter of a rectangle is

2×length + 2×width

in this case here one of the sides in that calculation has to be replaced by the outer circumference of the semicircle.

but which one ? you did not say, whether the semicircle is attached to a length or to a width of the rectangle.

the circumference of a circle is

2×pi×r

r being the radius (= half of the diameter).

so, the outer circumference of a semicircle is

2×pi×r/2 = pi×r

since we don't know the side of the rectangle, I am giving you both calculations here, and you have to pick the right one that fits your original problem definition.

if it is attached to a length (25 ft), then the radius of the semicircle is

25/2 = 12.5 ft

and the whole perimeter is

length + semicircle + 2×width =

= 25 + pi×12.5 + 2×29 =

= 25 + 39.26990817... + 58 = 122.2699082... ft

if it is attached to a width (29 ft), then the radius of the semicircle is

29/2 = 14.5 ft

and the whole perimeter is

2×length + semicircle + width =

= 2×25 + pi×14.5 + 29 =

= 50 + 45.55309348... + 29 = 124.5530935... ft

the exact value of sin A  to the nearest ten- thousandth is 0. 6625

a² + b² = c²

The opposite side is unknown, so use the pythagorean theorem to find it

c = hypotenuse = 4

a= opposite site = ?

b= adjacent side = 3

Substitute into the formula

4² = a² + 3²

16 = a² + 9

a² = 16 -9 = 7

Find the square root

a =√7 = 2. 65

To find Sin A, use

Sin A = opposite side ÷ hypotenuse

Sin A = 2. 65 ÷ 4 = 0. 6625

Thus,  the value of sin A is 0. 6625

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The angle m1 will be equal to 50°. The correct answer is option A.

The complete question is as below:-

Mr Jefferson is building a seesaw for the playground using the diagram shown. (see picture) In the diagram, the seesaw board is parallel to ground level and the triangle is an isosceles triangle.

What is m1?

A. 50º

B. 65º

C. 115º

D. 130º

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

We can find the angle using the opposite angles theorem.  When two are lines are crossed, there are four angles formed between them, and the opposite angles will be always equal.

Now, since the seesaw board is parallel to the ground, we can deduct (applying the opposite angles theorem) that both angles formed at the base of the triangle are equal to 65°.

Also, we must remember that the sum of the three interior angles of a triangle will be always equal to 180°, so:

m1 = 180 - ( 65 + 65 0

m1 = 50°

Therefore the angle m1 will be equal to 50°. The correct answer is option A.

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Answer:

for a) the next three would be 36, 49 and 64

for b) the next three would be 25, 36 and 49

for c) the next three would be 13, 16, and 19

for d) the next three would be 27, 33, and 39

Step-by-step explanation:

Answers:

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

Explanations:

Answer:

b

Step-by-step explanation:

ig becuase the line goes through 0,0 so it starts from negative

The height is represented by h = -16t² + 4t + 20 and There is only one solution, because the solutions indicate time and time cannot be negative.

We are given the vertical model of the diver's jump as;

h = -16t² + vt + s

where;

h is height

t is time

v is velocity

s is distance

A) We are given;

Distance; s = 20 ft

velocity; v = 4 ft/s

Thus;

h = -16t² + 4t + 20

B) The solution of the model is gotten from;

-16t² + 4t + 20 = 0

Solving this quadratic equation gives;

t = 1.25 seconds or -1 second

C) B. There is only one solution, because the solutions indicate time and time cannot be negative.

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The slope of a line is the rate of change of the line. The slope of the line is 1

The slope of a line is the rate of change of the line. The slope os calculated as:

Slope = y2-y1/x2-x1

Using the coordinate points (-1, 0) and (0, 1)

Substitute

Slope = 1-0/0-(-1)

Slope = 1/1

Slope = 1

Hence the slope of the line is 1

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Answer:

  about 101°

Step-by-step explanation:

The bearing back to the parking lot is the reverse of the bearing from the parking lot to the lake. That bearing can be found two ways. One of them uses the bearing and distance of each leg of the hike. The other uses what Zach remembers about the map.

__

The location of the lake from the parking lot can be found by adding the vectors to the campsite from the lot and to the lake from the campsite. That sum will be ...

  12.4∠315° +7.0∠180° ≈ 8.94∠281.4°

A suitable calculator can be used to find this sum, as shown in the second attachment. (Angles are displayed by the calculator in the range (-180°, 180°].)

__

The direction of the parking lot from the lake will be the opposite direction. It can be found by subtracting 180° from the angle:

  bearing to parking lot = 281.4° -180° = 101.4°

Michael and Zack should follow a compass direction of about 101°.

__

Northwest is a compass bearing of 315°. Points south of that bearing will have a smaller angle. Zach remembers the direction of the lake to be about 30° less than that angle, so at 315° -30° = 285°.

The bearing back to the parking lot is the opposite direction, so ...

  285° -180° = 105°

Based on Zack's memory, they should follow a compass direction of about 105°.

They will come within about 560 meters of the parking lot using this heading.

_____

Additional comments

When doing these vector calculations by hand, a couple of different methods can be used. One is to convert the vectors to component form, add the components, then convert back to polar form. The other is to make use of the Law of Cosines and the Law of Sines to solve the relevant triangles.

Here, the lake-lot distance is the third side of a triangle with two sides and the included angle known. The Law of Cosines applied to this situation is ...

  c² = a² +b² -2ab·cos(C) . . . . . generic Law of Cosines equation

  c² = 12.4² +7.0² -2(12.4)(7.0)cos(45°) ≈ 80.0063

  c ≈ √80.0063 ≈ 8.9446

Using the Law of Sines, we find the obtuse angle of the triangle to be ...

  sin(L)/12.4 = sin(C)/8.9446 . . . . . L and C are vertex angles in the diagram

  L = 180° -arcsin(12.4/8.9446×sin(45°)) ≈ 101.4°

__

If translation to rectangular coordinates is used, this can be done using the usual translation ...

  (x, y) = (r·cos(θ), r·sin(θ)) . . . . rectangular coordinates for r∠θ

The value of θ used can be the bearing angle (measured clockwise from north), or it can be the corresponding Cartesian plane angle (measured counterclockwise from +x). As long as the angles are consistently measured, the math works either way.

__

We have assumed that "northwest" is a bearing of 315°. If the compass rose is divided into 32 segments, the name "northwest" will be given to any bearing within 5° of this value. This makes our detailed vector calculations be somewhat approximate, and means that Zach's memory of the required bearing may be sufficiently accurate after all. Or not.

Since the line is a solid line and the graph is shaded below, the required equation will be 3y-  x≤ -4

The standard equation of a line in slope intercept form is expressed as y = mx+b

Using the coordinate points (4,0) and (1, -1)

Determine the slope

Sope = -1/-3
Slope = 1/3

For the y-intercept

0 = 1/3(4) + b

b = -4/3

Substitute

y = 1/3x - 4/3

Rewrite in standard form

3y = x - 4
3y - x = -4

Since the line is a solid line and the graph is shaded below, the required equation will be 3y-  x≤ -4

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Answer:

Yes, x = 0 is a solution to the given equation

Step-by-step explanation:

Hi Student!

The goal of this question is to determine x = 0 is a solution of the expression that was provided.  The first step that we must take is input 0 into all of the x's that we have in the expression.  Then we just simplify both sides and determine if the end expression is true and if it is then x = 0 is a solution.

Plug in the values

Simplify both sides

Looking at the final expression, we can see that 1 is indeed equal to 1 and since the expression is true, we can say that x = 0 is a solution of the expression that was provided in the problem statement.

The 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

We have:

The loudness L of sound in decibels is given by

[tex]\rm L=10log(\dfrac{I}{I_0})[/tex]

Here I is the intensity of the sound.

[tex]\rm I_0=10^{-12} \ W/m^2[/tex]

Loudness for 108 decibel sound:

[tex]\rm 108=10log(\dfrac{I}{10^-^1^2})[/tex]

I = 0.06309

Similarly, for:

100 decibel sound:

i = 0.01

I/i = 0.06309/0.01 = 6.31

I = 6.31i

Thus, the 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.

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Answer:

Step-by-step explanation:

Answer:

50cm squared

Step-by-step explanation:

Imagine the width is 'a'

Then the length will be 2a as it's twice as wide as it's long.

The formula for perimeter is 2(L+W)

If we subsitute the algebra/numbers in we get

P = 2(L+W)

30 = 2(2a+a)

30 = 2(3a)

30 = 6a

5 = a

a = 5cm

Then the area is the following

A = LW

A = 2a(a)

A = (2(5))(5)

A = 10(5)

A = 50cm squared

Answer:

The answer is the second option

Step-by-step explanation:

Let u=x^2.

[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8( {x}^{2} ) {}^{0} [/tex]

[tex] {u}^{2} - 9u + 8[/tex]

[tex](u - 1)(u - 8)[/tex]

[tex]u = 1[/tex]

[tex]u = 8[/tex]

Set this equal to x^2

[tex] {x}^{2} = 1[/tex]

[tex]x = 1[/tex]

or

[tex]x = - 1[/tex]

[tex] {x}^{2} = 8[/tex]

[tex]x = 2 \sqrt{2} [/tex]

or

[tex]x = - 2 \sqrt{2} [/tex]

Answer:

Whole integers

Step-by-step explanation:

0, 1, 2, 3, 4, 5... are all whole numbers, or the counting numbers. If we didn't specify "whole", then that would also include decimals, and we don't count usually with decimals.

Hope this helps!

Answer:

5 hours 3 minutes

Step-by-step explanation:

Add all of the times together, but remember that minutes only goes up to 60 minutes. So when you add all the minutes and you get 63, subtract 60 and add an hour, and you are left with 3 minutes.

Answer:

A

Explanation:

Formula for the volume of a cone :Volume (cone) = 1/3πr²h

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

Given :

⇒ r = 4 units

⇒ h = 21 units

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

Solving :

⇒ Volume (cone) = 1/3 × π x 4² × 21

⇒ Volume (cone) = 16 × 7 × π

⇒ Volume (cone) = 112π units²