What is the distance between the points (4, -8) and (10,8)?

Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

Answer:

46666

Step-by-step explanation:

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer: The Lions scored 41 points.

53 - 12 = 41

Answer: 41

Step-by-step explanation: if the Lions scored Less than the Tigers. Then you would subtract the points the from the Tigers to the Lions. Therefor they scored 41.

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

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Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Answer:

\(x = 2\)

Step-by-step explanation:

Given

\(b(x) = -1\)

See attachment for graph

Required

Find x

To do this, we simply read the coordinates of the attached graph.

When \(b(x) = -1\)

\(x = 2\)

i.e.

\((x,b(x)) = (2,-1)\)

 409/99

 4  13/99

Hi there !

4.131313.. = 4.(13) = 4  13/99 = (4*99+13)/99 = 409/99

Good luck !

Answer:

x = 30

y = 2

Step-by-step explanation:

Please note: the value for x is correct only if this triangle is a right triangle.

This can be solved because 2(5y) = 20 and because if a triangle has all congruent angles then its side lengths are also congruent.

Answer:

∠1 = ∠8

Step-by-step explanation:

Because they are ALTERNATE EXTERIOR ANGLE

Answer:

∠1 = ∠8

Step-by-step explanation:

Because alternate exterior angles are equal.

Also there is no angle given so you cant work them out.

simply put:

∠1 = ∠8

∠1 = ∠4

∠3 = ∠2

∠1 = ∠5

∠2 = ∠6

∠2 = ∠7

∠5 = ∠8

∠4 = ∠8

∠7 = ∠6

∠7 = ∠3

Let me know if I missed out on anymore! It was long that's why.

Hope this kind of explained it :)

Steps to solve:

5x - 4 = 4x

~Subtract 5x to both sides

-4 = -x

~Divide -1 to both sides

4 = x

Best of Luck!

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4}}}}}\)

Step-by-step explanation:

\( \sf{5x - 4 = 4x}\)

Move 4x to left hand side and change it's sign

Similarly, move 4 to right hand side and change it's sign

\( \longrightarrow{ \sf{5x - 4x = 4}}\)

Collect like terms

\( \longrightarrow{ \sf{x = 4}}\)

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

you cant change the numerator if you cant change the denominator

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

5=x

Step-by-step explanation:

Q=2(2x-5)=3x+x-2x

SOLUTION:

4x-10=4x-2x

-10=2x-4x

-10= -2x

(-+-=+ so 10 and 2 are positive now)

10/2=x

5=x

Answer:

538

Step-by-step explanation:

l x w

7x39

12x20

5x5

538

Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

An astronaut is a person who has been prepared, outfitted, and sent into space as part of a human spaceflight program to serve as a commander or crew member.

How much more time does it take an astronaut to install a light than a cable?

The time an astronaut is a person who has been prepared, outfitted, and sent into space as part of a human spaceflight program to serve as a commander or crew member.

How much more time does it take an astronaut to install a light than a cable?

The time it takes to put on the unique undergarments that keep astronauts cool is included in the 45-minute period it takes to put on a spacesuit.

it takes to put on the unique undergarments that keep astronauts cool is included in the 45-minute period it takes to put on a spacesuit.

In the near future, pilot astronauts may pilot and command space shuttles as well as command missions to Mars or the moon. Astronauts with a focus on missions collaborate with pilots to launch satellites, conduct experiments, and repair spacecraft and equipment. Engineers, scientists, and doctors are all examples of mission experts.

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Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

Multiplication (150x4=600 25x4=100%)

Answer:

\frac{25}{100}  \times x = 150

So,

x =  \frac{150 \times 100}{25}  = 600

Hank will use this equation.

Ans: A total of 600 pages are in the book.

Step-by-step explanation:

Answer:

x = 2√10  =   6.325

Step-by-step explanation:

a² +b² = c²      a = 6     b = 2    c = x

c = √(a² +b²)

c = √(6² +2²)

c = √(36 +4)

c = √(40)

c = 2√10        

Answer:

0.40

Step-by-step explanation:

the constant rate of change is given to you in the problem.

The number of miles driven (n) and the total cost of renting the car (c) are related by a constant (k) as follows -

c - \(\frac{2}{5} n\) = k

We have a rental car company charges an upfront fee to rent a car, and then charges $0.40 per mile driven.

We have to determine the constant rate of change through which number of miles driven (n) and the total cost of renting the car (c) are related.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to the question, we have -

Charge per mile driven = $0.40

n - represents the varying number of miles that you drive in the car.

c - represent the total cost (in dollars) you will have to pay for the rental car.

Assume that the upfront fee to rent a car is - $k

Total charge for driving 'n' miles after paying the upfront fee - $0.40n

The total cost for driving 'n' miles in a rental car -

c = k + 0.40n

c - \(\frac{2}{5} n\) = k

Where k is a constant and is equal to upfront fee.

Hence, number of miles driven (n) and the total cost of renting the car (c) are related by a constant (k) as follows -

c - \(\frac{2}{5} n\) = k

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Let the number be y

The statement can be interpreted as

85% of y = 646