When the length of each side of a square is increased by 5 cm, its area is increased by 895 cm2. Find the length of a side before the increase.

The length of a side before the increase is...

Answer:

Step-by-step explanation:

C -> Percentage of people who take cold drinks

H -> Percentage of people who take hot drinks

J - > Percentage of people who take Juice

i) At least one of drinks = 17 + 3 +15 +18 +7 + 15 + 5 = 75%

ii)  Exactly two types of drinks = Percentage of people who take cold  and hot drinks + Percentage of people who take cold and Juice + Percentage of people who take hot drinks and Juices

= 15 + 13 + 7

= 35%

iii) Exactly one type of drink =  Percentage of people who take only cold drinks + Percentage of people who take only hot drinks + Percentage of people who take only juices

= 17 + 3 + 15

= 35%

iv) None of the drinks = Total percentage - at least one of the drinks

                                    = 100 - 75

                                    = 25%

Answer:

B

Step-by-step explanation:

At - infinity, the function will tend to 0 and at +infinity, the function will tend to +infinity. Those are the two extremas of the function and extremas define the range. Range is all positive real number

cosine 122.2 = -0.532876276......

Step-by-step explanation:

100Km/hours......V/T

Answer:

30.28 yd²

Step-by-step explanation:

Area enclosed = area of trapezoid + area of semicircle

= ½(a + b)*h + ½(πr²)

Where,

a = 5 yd

b = 2 + 5 = 7 yd

h = 4 yd

r = ½(4) = 2 yd

Plug in the known values

Area enclosed = ½(5 + 7)*4 + ½(π*2²)

Area enclosed = ½(12)*4 + ½(π*4)

= 6*4 + π*2

= 24 + 2π

= 30.2831853

≈ 30.28 yd² (2 decimal places)

Answer:

A = 18 units²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h ( b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

By counting squares

h = 3, b₁ = 3, b₂ = 9 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (3 + 9) = 1.5 × 12 = 18 units²

Answer:

466.67

Step-by-step explanation:

Let p be the original price

p - 10 % p = 420

p - .10p = 420

.9p = 420

Divide each side by .9

.9p/.9 = 420/.9

p =466.666666

Rounding to the nearest cent

p = 466.67

Answer:

The angle in decimal form is 167.009°.

Step-by-step explanation:

We know an angle in terms of integer angles, minutes and seconds, whose conversion into decimal degrees is expressed by the following formula:

[tex]\theta = n + \frac{m}{60}+\frac{s}{3600}[/tex] (1)

Donde:

[tex]n[/tex] - Integer angle, in sexagesimal degrees.

[tex]m[/tex] - Minutes.

[tex]s[/tex] - Seconds.

If we know that [tex]n = 167[/tex], [tex]m = 0[/tex] and [tex]s = 31''[/tex], then the angle in decimal form is:

[tex]\theta = 167^{\circ}+\frac{0}{60}^{\circ} + \frac{31}{3600}^{\circ}[/tex]

[tex]\theta = 167.009^{\circ}[/tex]

The angle in decimal form is 167.009°.

Answer:

A' : {2, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 18}

Answer:

19.4 cm

Step-by-step explanation:

Hi there!

This is a right triangle. We're given an angle, the side adjacent to the angle and we're solving for the hypotenuse. Given this information, we can use the cosine ratio:

[tex]cos\theta=\frac{adj}{hyp}[/tex]

Plug in the given angle and side

[tex]cos71=\frac{6.3}{BC}\\BC=\frac{6.3}{cos71} \\BC=19.4[/tex]

Therefore, the length of BC is 19.4 cm when rounded to 3 significant figures.

I hope this helps!

Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

The image of the bar chart is missing and so i have attached it.

Answer:

Bus = 75

Cycle = 20

Walk = 45

Step-by-step explanation:

We are told that 50 students said they travel to school by car.

However, in the bar chart, we see that we have a portion for boys and girls

Under car, when we count along the y-axis, we will see that, there are 6 units for boys and 4 units for girls.

Thus, to find the value of a unit since number of people that took cars is 50, we have;

(6x + 4x)/2 = 50

Where x is the value of one unit. Thus;

10x/2 = 50

5x = 50

x = 50/5

x = 10

Thus, a unit is 10

Under bus;

Boys have 7 units while girls have 8 units.

Thus;

Frequency by bus = ((7 × 10) + (8 × 10))/2 = 150/2 = 75

Under cycle;

Boys have 1 unit while girls have 3 units.

Thus;

Frequency by cycle = ((1 × 10) + (3 × 10))/2 = 20

Under walk;

Boys have 5 units while girls have 4 units.

Thus;

Frequency by cycle = ((5 × 10) + (4 × 10))/2 = 45

Answer:

(For the image) A

Step-by-step explanation:

Answer:

she should add 2 cups of water.

Step-by-step explanation:

2 : 1 = 4 : 2

Answer:

As the x-values go to negative infinity, the function´s values go to positive. infinity.

--------------------------

Hope it helps...

have a great day!!

Answer:

(B) As the x-values go to negative infinity, the function's values go to positive infinity.

Step-by-step explanation:

The x-values the answer choices are talking about are the values on the x-axis.

Looking at the graph, when the x-values go to negative infinity (meaning it keeps on going left, or negative), the function goes up, meaning the function goes to positive infinity.

When the x-values go to positive infinity (meaning it keeps on going right, or positive), the function goes up, meaning the function goes to positive infinity.

Out of all the answer choices, only B agrees with the observations written above.

Hope that helps (●'◡'●)

Answer:

x=13.6

Step-by-step explanation:

By Pythagoras theorem, 5.5^2+x^2=14.7^2. x^2=14.7^2-5.5^2. x=13.6

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

Answer:

B. 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4(2)ˣ

Step 2: Evaluate

Answer:

a, 14.13. b, 39.25

Step-by-step explanation:

so for a the diameter is 6 so the radius is 3. The equation for the area of the circle is πr2. So 3x3=9. then 9x3.14=28.26. But then we have to divide by two cause we are finding only the shaded area. 28.26/2=14.13.

A is 14.13

for b, its the same thing, so the radiu is 5 and 5x5=25. 25x3.14=78.5, and divide two, so 78.5/2=39.25.

B is 39.25

WARNING: I am not sure this is correct, so if this is wrong i'm sorry, i'm learning too :)

Answer:

18225 cm²

Step-by-step explanation:

Divide 540 by 4 to get the length of all sides

540/4 = 135

Square 135 to get the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given

Divide 540 by 4 to obtain the length of all sides

540/4 = 135

Square 135 to acquire the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.        

To learn more about area refer to:

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Answer:

Step-by-step explanation:

There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.

We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:

[tex]3^2=1^2+y^2[/tex] which simplifies to

[tex]9=1+y^2[/tex] and

[tex]y^2=8[/tex] so

[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that

[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]

Now we have everything we need to fill in the identity for sin2θ:

[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get

[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]

Answer:

£32.50

Step-by-step explanation:

my first question to the teacher : so, no windows in the living room ?

so, it is a square living room with 5.5 m side length.

but each wall is a rectangle of 2.2 × 5.5 m.

for one wall we have to deduct a door area of 1.8×0.9 m.

so, one wall

2.2 × 5.5 = 12.1 m²

4 walls

4 × 12.1 = 48.4 m²

minus one door area

1.8 × 0.9 = 1.62 m²

48.4 - 1.62 = 46.78 m² total paint area

1 L paint covers 8 m².

so, we need 46.78/8 = 5.85 liters.

she gets the paint in 2 L tins. so, she needs 3 tins (6 L).

each tin costs £13.

and because she buys 3 tins, she gets the third one for half the price (13/2 = £6.50).

so, she has to pay

2×13 + 6.50 = 26 + 6.50 = £32.50

Answer:

3x10=30   30x178=5,430

Step-by-step explanation:

[tex]3 \times 10 \times 178 \\ 30 \times 178 \\ 5340 \: \: answer[/tex]

Answer:

34

Step-by-step explanation:

We are here given a modulus expression and we need to find out the value when m = -5 and n = 3 .

Modulus :- It always gives positive value . For example ,

[tex]\rm\implies |-a| = a [/tex]

[tex]\rm\implies |a| = a [/tex]

The given modulus expression is :-

[tex]\rm\implies |m^2+ n^2| [/tex]

As the number inside the modulus operator are already squared therefore they will always give positive value for real numbers . Here we can omit the modulus .

[tex]\rm\implies m^2 + n^2 [/tex]

Plug in the given values ,

[tex]\rm\implies (-5)^2 + 3^2 [/tex]

Solve 5² and 3² and add them ,

[tex]\rm\implies 25 + 9 [/tex]

On adding ,

[tex]\rm\implies 34 [/tex]

Therefore ,

[tex]\rm\implies \boxed{\blue{\rm |m^2+n^2| = 34 }}[/tex]

Hence the required answer is 34 .

Answer:

see below

Step-by-step explanation:

f(x) = -x^2 +4

The vertex form is

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

Rewriting

f(x) = -(x-0)^2 +4

The vertex is (0,4) and a = -1

Since a is negative we know the parabola opens downward

f(x) = -(x^2 -4)

We can find the zeros

0 = -(x^2 -2^2)

This is the difference of squares

0 = -(x-2)(x+2)

Using the zero product property

x-2 =0   x+2 =0

x=2   x=-2

(2,0)  (-2,0) are the zeros of the parabola and 2 other points on the parabola

We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola

Answer:

Your vertex is (4,0)

Step-by-step explanation:

Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

To know more about an expression follow

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Answer:

total balls = 18 .... 3/x = 1/6

blue = 10 ... 18-(5+3) = 10

p of green = 5/18 = .277

Step-by-step explanation:

Answer:

f(n+1) = f(n) - 5

Step-by-step explanation:

Just find some relationship between 2 numbers that are next to each other.

Answer:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

Step-by-step explanation:

I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified

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

so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:

[tex] \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)[/tex]

recall that,Sum-to-Product Formula of cos function:

[tex] \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }[/tex]

notice that we have two pair of function with which we can apply the formula thus do so,

[tex] \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)[/tex]

simplify addition:

[tex] \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)[/tex]

simplify division:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)[/tex]

By Opposite Angle Identities we acquire:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)[/tex]

factor out 2cosθ:

[tex] \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )[/tex]

once again apply Sum-to-Product Formula which yields:

[tex] \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )[/tex]

distribute:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

and we're done!