HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answer:

Step-by-step explanation:

put (x+2)/(x-2)=a

a-1/a=5/6

[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]

[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]

2.

put (x+3)/x=a

a+1/a=4  1/4

[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]

Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.

The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713

Given that:

[tex]Entrance\ Fee = \$18[/tex]

[tex]Rate = \$0.08[/tex] per ball

Let:

[tex]B \to Balls[/tex]

The amount (A) Carolina can spend on B balls is:

A = Entrance Fee + Rate * B

This gives:

[tex]A = 18 + 0.08 * B[/tex]

[tex]A = 18 + 0.08B[/tex]

To get $10, Carolina must spend $75 or more.

This means:

[tex]A \ge 75[/tex]

So, the inequality is:

[tex]18 + 0.08B \ge 75[/tex]

The smallest number of balls is calculated as follows:

[tex]18 + 0.08B \ge 75[/tex]

Collect like terms

[tex]0.08B \ge 75 - 18[/tex]

[tex]0.08B \ge 57[/tex]

Divide both sides by 0.08

[tex]B \ge 712.5[/tex]

Round up

[tex]B \ge 713[/tex]

Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713

Learn more about inequalities at:

brainly.com/question/20383699

Using a linear function, it is found that:

-----------

The linear function for the cost of B paintballs has the following format:

[tex]C(B) = C(0) + aB[/tex]

In which

-----------

Question 1:

Thus:

[tex]C(B) = 18 + 0.08B[/tex]

[tex]C(B) \geq 75[/tex]

[tex]18 + 0.08B \geq 75[/tex], given by option B.

-----------

Question 2:

[tex]18 + 0.08B \geq 75[/tex]

[tex]0.08B \geq 57[/tex]

[tex]B \geq \frac{57}{0.08}[/tex]

[tex]B \geq 712.5[/tex]

Rounding up, she has to buy at least 713 paintballs.

A similar problem is given at https://brainly.com/question/24583430

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

Answer:

First one is 41

Second one is 87

Step-by-step explanation:

Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.

The unshaded part will be 16*8 then subtracts the shaded part which is 41.  Then you get the answer 87.

Answer:

¿De que solución habla?

Step-by-step explanation:

Answer:

B, D, F

Step-by-step explanation:

edge 2020

Answer:

52.0 m

Step-by-step explanation:

The triangle formed by the flagpole, the ground and the 30° line is a right triangle, with x as the required length to be found.

Using the tangent ratio

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{30}{x}[/tex] ( multiply both sides by x )

x × tan30° = 30 ( divide both sides by tan30° )

x = [tex]\frac{30}{tan30}[/tex] ≈ 52.0 m

Answer:

B. √16 × √6

C. √96

Step-by-step explanation:

4√6

4 can be written as a square root.

4 = √16

√16 × √6

The square roots are multiplied, they can be written under one whole square root.

√(16 × 6)

√96

Answer:

Y=x(t)(0.06) + x

Y =predicted population

X= population currently

t= number of years

Y= 60000(t) + 1000000

Step-by-step explanation:

Let the current population be x

X= 1000000

The rate of increase= 6% each year

Let the the predicted population= y

If the population is to increase by 6% each year the function predicting the population at the future will be

Y=x(t)(0.06) + x

The only changing value in the above formula is the time.

Y= 1000000(0.06)(t) +1000000

Y= 60000(t) + 1000000

Answer: The actual answer is:

next = now x 1.06, starting at 1,000,000

Answer:

Step-by-step explanation:

7(42 ÷ 3) + 4 (72 + 53) + 8 (-3)4

7(14) + 4(125) + 8(-12)

98 + 500 - 96

    598 - 96

        502

Answer:

Step-by-step explanation:

[tex]7(42 \div 3) + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Divide the numbers

[tex] = 7 \times 14 + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Add the numbers

[tex] = 7 \times 14 - 4 \times 125 + 8 \times ( - 3) \times 4[/tex]

Calculate the product

[tex] = 7 \times 14 + 4 \times 125 - 96[/tex]

Multiply the numbers

[tex] = 98 + 500 - 96[/tex]

Add the numbers

[tex] = 598 - 96[/tex]

Subtract the numbers

[tex] = 502[/tex]

Hope this helps..

Best regards!!

Answer:

Probability that one type of candy will be chosen more than once in 10 trials = 0.2639

Step-by-step explanation:

This is a binomial experiment because

- A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

- It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (10 trials, with the outcome of each trial being that we get the required candy or not)

- The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 10 trials

x = Number of successes required = number of times we want to pick a particular brand of candy = more than once, that is > 1

p = probability of success = probability of picking a particular brand of candy from a bulk with 10 different types of candies = (1/10) = 0.10

q = probability of failure = Probability of not picking our wanted candy = 1 - p = 1 - 0.1 = 0.90

P(X > 1) = 1 - P(X ≤ 1)

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = 0) = ¹⁰C₀ (0.10)⁰ (0.90)¹⁰⁻⁰ = 0.3486784401

P(X = 1) = ¹⁰C₁ (0.10)¹ (0.90)¹⁰⁻¹ = 0.387420489

P(X ≤ 1) = 0.3486784401 + 0.387420489 = 0.7360989291

P(X > 1) = 1 - 0.7360989291 = 0.2639010709 = 0.2639

Hope this Helps!!!

If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].

We're given

[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:

[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]

Multiply both sides by 2:

[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]

Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:

[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]

Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].

Answer:

26.4ft²

Step-by-step explanation:

I first converted the centimeter values to feet

140Cm x 30.48 = 4.59

70cm x 30.48 = 2.3

the paper required is approximately equal to the area of the pyramid.

area of pyramid is equal to area of triangle + base²

Are of triangle = 1/2 x b xh

= 4 x 1/2 x4.59x2.3 + (2.3)²

= 2 x 4.59 x 2.3 + 5.29

= 26.4 feet²

therefore it will take 26.4 feet² paper to make each tree, including the bottom.

Answer:

It is actually 24500

Step-by-step explanation:

Hope this helped! I had the same lesson.

Answer:

[tex]\boxed{x < 7.5}[/tex]

Step-by-step explanation:

=> 2x < 15

Dividing both sides by 2

=> x < 15/2

=> x < 7.5

Answer:

[tex]\boxed{x<\frac{15}{2}}[/tex]

Step-by-step explanation:

[tex]2x<15[/tex]

Divide both parts by 2.

[tex]\displaystyle \frac{2x}{2} <\frac{15}{2}[/tex]

[tex]\displaystyle x<\frac{15}{2}[/tex]

Answer:

  (-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)

Step-by-step explanation:

To make it easier to differentiate, we'll rewrite the function as ...

  h(x) = 2/(x-5) -1/(x-2)

Then the derivative is ...

  h'(x) = -2/(x-5)^2 +1/(x-2)^2

This will be zero when ...

  -2(x-2)^2 +(x-5)^2 = 0

  -2(x^2 -4x +4) +(x^2 -10x +25) = 0

  -x^2 -2x +17 = 0

  x^2 +2x +1 = 17 +1

  x +1 = ±√18 = ±3√2

  x = -1 ±3√2

The values of the function at these locations are ...

  h(-1-3√2) = -1 +(2/3)√2 ≈ -1.9428

  h(-1+3√2) = -1 -(2/3)√2 ≈ -0.0572

Then the range of h(x) is ...

  (-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)

Complete question is;

Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy

material. The Height is 0.5 m and the

Base is 1 m.

What is the length of the pillow?

Give an exact answer (do not round)

Answer:

length of Pillow  = 1.4 m

Step-by-step explanation:

This wedge will be the shape of a triangular prism. The volume of a triangular prism is given as;

V = area of base x length = ½ × base × height × length

Thus;

Volume of Wedge = ½ × base × height × length

We are given;

base = 1 m

height = 0.5 m

Volume = 0.35m³

And we want to find the Length(L)

Thus;

½ × 0.5 × 1 × L  = 0.35

L/4 = 0.35

Multiply both sides by 4 to give;

L = 0.35 × 4

L = 1.4 m

length of Pillow  = 1.4 m

Answer:

1.4

Step-by-step explanation:

Khan

Answer:

1/2*base*height

Step-by-step explanation:

All triangles have the area of 1/2*base* height.

Answer:

1/2 * b * h

Step-by-step explanation:

Answer:

27 terms

Step-by-step explanation:

a1 = 7

nth term is -175

common difference d= 0-7 = -7 or -7 - 0 = -7

nth term = first term + ( n-1) * common difference

-175 = 7 + ( n - 1 ) * (- 7)

-175 = 7 - 7n + 7

-175 = 14 - 7n

-175-14 = -7n

-189 = - 7n

n= -189 /-7

n=27

Answer:

397.7 m²

Step-by-step Explanation:

Step 1: find m < W

W = 180 - (33+113) (sum of ∆)

W = 34°

Step 2: find side UV using the law of sines

[tex] \frac{UV}{sin(W)} = \frac{VW}{sin(U)} [/tex]

[tex] \frac{UV}{sin(34)} = \frac{29}{sin(33)} [/tex]

Multiply both sides by sin(34)

[tex] \frac{UV}{sin(34)}*sin(34) = \frac{29}{sin(33)}*sin(34) [/tex]

[tex] UV = \frac{29*sin(34)}{sin(33)} [/tex]

[tex] UV = 29.8 m [/tex] (approximated)

Step 3: find the area using the formula, ½*UV*VW*sin(V)

area = ½*29.8*29*sin(113)

Area = 397.7 m² (rounded to the nearest tenth.

Answer:

x = 12 units

Step-by-step explanation:

In the picture attached,

Since, DE and BC are the parallel lines,AC and AB are the transverse.

Therefore, ∠AED ≅ ∠ABC [Alternate angles]

∠ADE ≅ ∠ACB [Alternate angles]

ΔADE ~ ΔACB [By AA postulate of similarity]

By the property of similarity,

If two triangles are similar then their corresponding sides will be proportional.

[tex]\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}[/tex]

[tex]\frac{(4+8)}{4}=\frac{(6+x)}{6}[/tex]

[tex]3=1+\frac{x}{6}[/tex]

x = 12

Therefore, length of missing segment is 12 units.

Answer:

x=3 y=11

Step-by-step explanation:

2x+3=9

2x=6

x=3

y-4=7

y=11

Answer:

88

Step-by-step explanation:

The original number ⇒ 100

100 is increased by 10%

The result is 20% reduced.

Calculate increase.

100 × (1 + 10%)

100 × (1.1)

= 110

Calculate decrease.

110 × (1 - 20%)

110 × 0.8

= 88

Answer:

6 bags

Step-by-step explanation:

Hey there!

Well first we need to find the area of the circle using,

π r^2

4*4 = 16

16 * pi ≅ 50.27

So now to find how much bags needed we do,

50.27 ÷ 9.42 = 5.34

Meaning 6 bags of soil is needed.

Hope this helps :)

Answer:

Caisha will need 6 bags of soil.

(B.) 6 bags :)

The distance between the points (0, 10) and (–9, 1) is 12.73 units.

Given the following data;

Points ([tex]x_1, x_2[/tex]) = 0, -9

Points ([tex]y_1, y_2[/tex]) = 10, 1

To find the distance between the points;

In Mathematics, the distance between two points on a plane is calculated by using the formula;

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }[/tex]

Substituting the points into the formula, we have;

[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]

Distance = 12.73 units

Therefore, the distance between the points is 12.73 units.

Find more information: https://brainly.com/question/13272812

Answer:

  927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

  A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

  A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

  V = Bh

where B represents the area of the base, and h is the height.

  V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

the answer on edg is 927

Answer:

10% off

Step-by-step explanation:

When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

x -y =4

Step-by-step explanation:

First find the slope

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

   = (1- -4)/(5 - 0)

    = (1+4)/(5-0)

   5/5

   = 1

Then we can use slope intercept form

The slope is 1 and the y intercept is -4

y = mx+b

y = 1x-4

We want it in standard form

Ax + By = C where A is a positive integer

Subtract x from each side

-x +y = -4

Multiply by -1

x -y =4

Answer:

x -y =4

Step-by-step explanation:

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

[tex]P + B = 14[/tex] ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

[tex]130P + 150B = 1920[/tex] --- Equation 2

Make P the subject of formula in equation 1

[tex]P = 14 - B[/tex]

Substitute 14 - B for P in equation 2

[tex]130(14 - B) + 150B = 1920[/tex]

Open Bracket

[tex]1820 - 130B + 150B = 1920[/tex]

[tex]1820 + 20B = 1920[/tex]

Subtract 1820 from both sides

[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]

[tex]20B = 100[/tex]

Divide both sides by 20

[tex]\frac{20B}{20} = \frac{100}{20}[/tex]

[tex]B = 5[/tex]

Substitute 5 for B in [tex]P = 14 - B[/tex]

[tex]P = 14 - 5[/tex]

[tex]P = 9[/tex]

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

x = 65°

y = 25° (equations in explanation)

Step-by-step explanation:

We know that EKD is 25° and we know that DKB is 90°.

EKD, DKB, and BKF are supplementary. This means that their angle measures add up to 180°.

So, since we know two, we can find the other very easily.

[tex]180 - (25+90)\\180 - 115\\65[/tex]

This means that BKF is 65°.

Now, BKF and EKC are alternate interior angles, so they have the exact same measurement. Therefore, EKC, x, is 65°.

Again, EKC, CKA, and AKF are supplementary. AKF is 90° and EKC is 65°, so we can find the measure of CKA easily.

[tex]180 - (65+90)\\180-155\\25[/tex]

Therefore y is 25° and x is 65°.

Hope this helped!

Answer:

Susan and 4 quests

5 people

Step-by-step explanation:

Take 9/10 and divide by 1/6

9/10 ÷1/6

Copy dot flip

9/10 * 6/1

54/10

50/10 + 4/10

5 4/10

We can only serve whole numbers

5 people

Susan and 4 quests

Answer:

a) 28 units

b) 0.0262 seconds

c) Minimum height of the nail = 1.923 units

Step-by-step explanation:

a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)

Where:

d = The mid line

a = The amplitude

The period  = 2π/b

c/b = The shift

Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28

b) Given that three revolution = 6×π, we have;

At t = 0

cos(720(t-10) = cos(720(0-10))  = cos(7200) = 1

Therefore, for three revolutions, we have

720(t - 10) = 720t - 7200

b = 720

The period = 2π/b = 6·π/720 = 0.0262 seconds

c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;

f(x) = -14×cos(720(t - 10)) + 14

At t = 0 gives;

f(x) = -14×cos(720(0 - 10)) + 14

Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923

Minimum height of the nail = 1.923