b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.​

[tex](2x + 1)(x + 1)[/tex]

•Distribute

[tex](2x + 1)(x + )[/tex]

[tex]2x(x + 1) + 1( x + 1)[/tex]

•Distribute

[tex]2x(x + 1) + 1(x + 1)[/tex]

[tex]2x² + 2x1(x + 1)[/tex]

•Multiply

[tex]2x² + 2x + 1(x + 1)[/tex]

[tex]2x² + 2x + x + 1[/tex]

•Combine like terms

[tex]2x² + x + x + 1[/tex]

[tex]2x²+ 3x + 1[/tex]

Solution:

[tex]2x² + 3x + 1[/tex]

Explanation:

see the graph

The volume of the cone will be 10 cubic units.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the cube or cuboid.

Given that:-

The volume of the cone will be:-

Vc   =   Vcyl

[tex]\dfrac{1}{3} \pi r^2h\ \ \ =\ \ \pi r^2h[/tex]

Vc         =    (1  /  3)  Vcyl

Vc         =    ( 1  /  3  ) x  30

Vc         =     10  cubic units

Therefore the volume of the cone will be 10 cubic units.

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Case 1

Case 2

Option A

It's impossible thing

Answer:

y out put x input and 3 is input and as 5 . tell me if you get it right

The expected value of one ticket at a raffle where 100 tickets are sold at $2 each for three prizes valued at $100,$ 50 and $25, $1.75.

The expected value is used to calculate the weighted average of all the possible values of a random variable.

[tex]\sum_{i=1}^n=P_i\times V_i[/tex]

Here, P is the probability of winning a prize and V is the value of the price.

At a raffle, 100 tickets are sold at $2 each for three prizes valued at $100,$50 and $25. The probability of winning one person in 100 persons is,

[tex]P=\dfrac{1}{100}[/tex]

There are three prices of $100, $50 and $25. Thus, the ticket price expected to win is,

[tex]E=100\times\dfrac{1}{100}+50\times\dfrac{1}{100}+25\times\dfrac{1}{100}\\E=1+0.5+0.25\\E=1.75[/tex]

Thus, the expected value of one ticket at a raffle where 100 tickets are sold at $2 each for three prizes valued at $100,$ 50 and $25, is $1.75.

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The table that correctly describes the given quadratic equation is table D.

A general quadratic equation is written as:

[tex]y = a*x^2 + b*x + c[/tex]

The y-intercept is the point (0, c), and the sign of the coefficient a determines if it opens up or down.

In this case, the quadratic equation is:

[tex]y = -2x^2 + 4[/tex]

Then we have:

The y-intercept is (0, 4), and because a is negative, the parabola opens down.

Then the correct table is table D.

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Both methods of solving for lengths of a right triangle are effective. That being said, the Pythagorean theorem is well-known and only requires a student to know one equation (as well as where the legs/hypotenuse should be plugged in). The six trigonometric ratios are also helpful, and over time are something that students begin to recognize when looking at right triangles.

I believe that the Pythagorean theorem is more effective because of its simplicity and wide application. The six trigonometric ratios will not apply to every right triangle, and require more memorization.

Hope this helps!

The possible number represented by the 9 counter is 27

The counters are given as:

12 counters and 15 counters

When added, we get a number that can be represented by 9 counters.

This means that:

12 + 15 = 9x

Evaluate the sum

27 = 9x

Divide by 9

x = 3

When subtracted, you need more than 9 counters.

This means that:

x = 15 - 12 = 3

So, we conclude that the number is a multiple of 3 and 9

In other words, the decimal number is a multiple of 9 (i.e. 27)

Hence, the possible number is 27

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total no of cards = 40

p(blue) = 8 out of 40

p(orange) = 8 out of 40

p(blue or orange ) = 16 out of 40

16÷40 = 2/5.

The quadrants in which the tangent is positive are I and III.

Option B is the correct answer.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle.

It is positive when the opposite side and the adjacent side are both positive or both negative.

In the first quadrant (I), both the opposite and adjacent sides are positive, so the tangent is positive.

In the second quadrant (II), the opposite side is positive and the adjacent side is negative, so the tangent is negative.

In the third quadrant (III), both the opposite and adjacent sides are negative, so the tangent is positive.

In the fourth quadrant (IV), the opposite side is negative and the adjacent side is positive, so the tangent is negative.

Therefore,

The quadrants in which the tangent is positive are I and III.

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Answer:

1.5 gallons

Step-by-step explanation:

(3/4) × (2 gallons) = 1.5 gallons

HOPE THIS HELPS AND HAVE A NICE DAY <3

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\:Important\: point's }}}[/tex]

[tex]{ \rule{70mm}{2.9pt}}[/tex]

[tex] \underline{ \boxed{ \sf{✵\: let's\: solve\:✵}}}[/tex]

[tex] \sf ➛\angle \: 120 \degree + \angle \:t = 180\degree \\ \sf ➛\angle \:t = 180 \degree - \angle \:120 \degree \\ \sf ➛\angle \: t = \:60 \degree[/tex]

[tex]{ \rule{70mm}{2.9pt}}[/tex]

[tex] \boxed{✛\underline{ \boxed{ \sf{ \: \angle \: t = 60 \degree \: }}}✛}[/tex]

Hope it helps !

Answer:

  1900 cm²

Step-by-step explanation:

We can use the given ratios and volume to find the scale factor for the dimensions. Knowing the dimensions, we can compute the surface area using the formula for a cuboid.

__

Let k represent the scale factor. Then the actual dimensions will be 5k, 4k, and 2k. The actual volume will be ...

  V = LWH

  5000 cm³ = (5k)(4k)(2k) = 40k³

  k³ = (5000 cm³)/40 = 125 cm³

  k = ∛(125 cm³) = 5 cm

The cuboid dimensions are 5(5 cm) = 25 cm, 4(5 cm) = 20 cm, and 2(5 cm) = 10 cm.

__

The surface area of the cuboid can be computed from ...

  A = 2(LW +H(L +W))

  A = 2((25 cm)(20 cm) +(10 cm)(25 +20 cm))

  A = 2(500 cm² +(10 cm)(45 cm)) = 2(950 cm²) = 1900 cm²

The surface area of the cuboid is 1900 cm².

Answer:

2.5

Step-by-step explanation:

The radius of a cylinder formula is

Plug in

So . .

R = 2.5

( I rounded to the tenth decimal place so you know!)

Answer:

-2

2

Step-by-step explanation:

just use common sense. what does "local maximum" mean ?

it means a point, where the curve in the nearest neighborhood does not have a higher value. where the curve comes from smaller values, turns around and leaves with smaller values again.

(a) there is one point in this graph : at x = -2

(b) and that maximum value at that point is y = 2

Answer:

Hope the picture will help you..............

Answer:

A function means that we get one input and one output.  In this example that means for every x-value that we have, we only have one y-value.

Looking at the first option, we can see that there is no x-value that has more than one y-value which means that it is a function.

The rest of the options are seen with at least two values for one x-value in one of the points.  Therefore, they wouldn't be considered a function leaving us with only option A as the solution.

Answer:

Answer with explanation is below~

Step-by-step explanation:

We could easily obtain the formulae/formula of an equilateral triangle not only through Pythagoras Theorem, but also through Heron's formula.

INTRODUCTION:

What's equilateral triangle?

What's Heron Formula?

[tex] \boxed{\rm \: Area= \sqrt{s(s - a)(s - b)(s - c)} \: units ^{2}} [/tex]

Where,

What's Pythagoras' Theorem?

SOLVING:

Let,ABC an equilateral triangle of sides a.

Now:Draw a perpendicular straight line AM to the side BC(Name each part of triangle)

So it's clear that ∆AMB is a right angled triangle at M, BM = (1/2)BC = a/2.

Please note AM here represents the height of ∆ ABC.

[tex] \boxed{\rm \: AM = \sqrt{AB^2-BM^2}}[/tex]

[tex] \rm \: AM = \sqrt{a {}^{2} - { \bigg( \cfrac{a}{2} \bigg) }^{2} } [/tex]

[tex] \rm \: AM = 3 \: \cfrac{a {}^{2} }{4} [/tex]

[tex] \rm \: AM = \cfrac{ \sqrt{3} }{2} \: a[/tex]

Now find the area of ∆ABC:

[tex] \rm \triangle \: ABC = \cfrac{1}{2} \times \: BC \times A [/tex]

[tex] \rm \: \triangle \: ABC = \cfrac{1}{2} \times a \times \cfrac{ \sqrt{3}}{4}a [/tex]

[tex] \boxed{\rm\triangle \: ABC = \cfrac{ \sqrt{3 } }{4} a {}^{2} \: units {}^{2}} [/tex]

Hence,the formulae of equilateral triangle using Pythagoras' theorem is {√(3)/4} a^2

[tex] \rule{225pt}{2pt}[/tex]

Extras:

Now let's find the area using Heron's Formula.

Solving:

Let each side of an equilateral triangle be a.

SO, then:

s = (3a/2)

We know that, (Heron's formula)

[tex] \rm \: A = \sqrt{s(s - a)(s - b)(s - c)} [/tex]

Now the area A :

[tex]\rm AR(A)= \sqrt{ \cfrac{ 3a } 2 \bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)} [/tex]

[tex]\rm AR(A)= \sqrt{ \cfrac{3a}{2} \bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)}[/tex]

[tex]\rm \boxed{ \rm AR(A)= \cfrac{ \sqrt{ 3a}}{4} \: a {}^{2} \: \: units {}^{2}} [/tex]

And voila! we're done!

I hope this helps! :)

[Figure of Equilateral triangle is attached, it denotes the triangle we need to draw while finding the formulae through Pythagoras' theorem. ]

The number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where 'a' is a constant and a>1

Total coins = 500 gold coin

Each sheep costs 12 gold coins, while each chicken costs 7 gold coins.

If purchased 32 sheep, so the total cost for the 32 sheep:

= 32×12

= 384

Remaining gold coin = 500 - 384 = 116 gold coin

Number of chicken can purchase in 166 gold coin = 116/7 = 16.57 ≈ 16

Inequality for the above scenario:

Let x be the number of sheep and y be the number of chickens.

12x + 7y ≤ 500

If you want to buy twice as many chickens as sheep.

y = 2x

12x + 7y = 500

After solving both the equation:

x = 19.23 ≈ 19 (Number of sheep)

y = 38 (double the number of sheep)

For the part 2:

The exponential equation for the sheep:

[tex]\rm y = 30(2)^x^-^1[/tex]

After 5 years, plug x = 5

[tex]\rm y = 30(2)^4[/tex]

y = 480 sheep

The exponential equation for the chicken:

[tex]\rm y = 20(2.2)^x^-^1[/tex]

After 8 years, plug x = 8

[tex]\rm y = 20(2.2)^7[/tex]

y = 4988.71 ≈ 4988 chickens

Similarly, you can find the rest of the data using the above equation.

Thus, the number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.

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Answer:

8 futballs

basketballs 18

beisballs 36

softballs 24

Step-by-step explanation:

dos mas del doble (2) de balones de fut = 8x2 = 16, 16+2 = 18

cuatro menos de 5 veces las pelotas de fut = 8x5 = 40, 40-4 = 36

seis mas de la mitad de beis = 36/2 = 18, 18+6 = 24

LISTO

The similarities and differences in a non-fiction text look at how the subject or events are portrayed.

Comparing non-fiction texts can focus on the similarities between the texts - things they have in common. You can also contrast texts and focus on their differences - things that set the texts apart from each other. You could compare and contrast the following:

Form – What types of text (letter, news report, etc) are they?

Purpose – What job (persuading, informing, advertising) is each text doing?

Audience – Who is the intended reader of the text?

Subject matter – What are the texts about?

Language choices – What kinds of words, images or rhetorical devices are being used?

Structure – How is the text ordered?

Tone – What is the overall tone or mood of the writing?

Non-fiction texts are all around us, and comparing them can help you become more aware of how language is being used in society. Comparing non-fiction texts can often prompt you to notice things that you might not have considered about a text in isolation.

Hence the similarities and differences in a non-fiction text look at how the subject or events are portrayed.

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Answer:

The answer is The function h because the graphs of f and h are symmetrical about the line y = x.

Step-by-step explanation:

A function and its inverse function become symmetrical across the line y = x.  

Answer:

Based on the given conditions;

50÷(1-15℅)

=50/1-0.15

=50/0.85

=1000/17

The probability is that a randomly selected tire that has a depth less than 0.50 mm will be 0.085121.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm.

Then the probability is that a randomly selected tire has a depth less than 0.50 mm will be

The value of the z-score will be

z = (0.50 - 0.98) / 0.35

z = -1.3714

Then the probability will be

P(x < 0.50) = P(z < -1.3714)

P(x < 0.50) = 0.085121

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Answer:

a) Time spent, x (minute): 50 < x ≤ 60

b) Time spent, x (minute): 20 < x ≤ 30

Step-by-step explanation:

a) The modal class is the class interval with the highest frequency in a frequency table which is 21 (right column)

b) Find the total amount of Frequency:

12 + 18 + 11 + 9 + 8 + 21 = 79

to find mid number through the data set divided by 2:

79 / 2 = 39.5

so add up the frequency till you reach 39.5 (max)

12 + 18 = 30

30 + 11 = 41   this passes through 39.5 so the median is in the 3rd row

Answer:

  A.  200 packages

Step-by-step explanation:

The number of packages per roll can be found by dividing the length of a roll by the length of tape needed for each package.

__

For each package:

  (2.375 in/piece)×(4 piece/package) = 9.5 in/package

Per roll:

  (1900 in/roll) / (9.5 in/package) = (1900/9.5) packages/roll

  = 200 packages/roll

The machine can seal 200 packages with a roll of tape 1900 inches long.

Answer:

x=12

Step-by-step explanation:

Every triangle has interior degrees that all together add up to 180. We already know we have 50 degrees and 75 degrees, so we can subtract that to see how much we have left to work with. If we do that, we get 55 degrees left. Now, we have to set up a two step equation to find x:

5x-5=55

The first thing to do is to add 5 to both sides to get rid of -5:

5x-5=55

   +5  +5

    __ __

     0   60

So now, it's 5x=60

Now, we have to isolate x. To do this, we have to divide both sides by 5. If you do this, you get:

x=12

Hope this helped!

Answer: b) x = 12

Step-by-step explanation:

   The sum of a triangle's angles add up to 180°. We will add together all the angles, set them equal to 180°, and then solve.

Given:

(50°) + (75°) + (5x - 5°) = 180°

Combine similar terms:

120° + 5x = 180°

Subtract 120° from both sides of the equation:

5x = 60°

Divide both sides of the equation by 5:

x = 12

       Your answer is;

           b) x = 12

Answer: 42 easy!

Step-by-step explanation: 42 hope this helps