A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m.
With each swing, she travels along an arc that is half as long as the arc of the previous swing.
Which expression gives the total length the monkey swings in her first n swings?

Answer:

x=2

x=-5

Step-by-step explanation:

You need to get everything on one side to have a quadratic equation:

x^2+6x-4 -(3x+6) = x^2+3x-10

All factors of 10 are 1*10 and 2*5.

5-2 = 3 and 5*-2 = -10

Factoring x^2+3x-10 gives us (x-2)(x+5)

x=2

x=-5

Answer:

x=-5      x=2

Step-by-step explanation:

x^2+ 6x - 4 = 3x + 6

Subtract 3x from each side

x^2+ 6x-3x - 4 = 3x-3x + 6

x^2+ 3x - 4 =  6

Subtract 6 from each side

x^2+ 3x - 4-6 = 6 - 6

x^2 +3x -10 =0

Factor

What 2 numbers multiply to -10 and add to 3

5*-2 =-10

5+-2 = 3

(x+5) (x-2) =0

Using the zero product property

x+5 =0   x-2 =0

x=-5      x=2

Answer: ( - ∞ , 10 ] , { y| y ≤ 10 }

Step-by-step explanation: You have to find the domain by finding where the function is defined. The range is the set of the values that correspond with the domain.

The range of the function f(x) = 10 - x^2 is all real numbers less than or equal to 10.

To find the range of the function f(x) = 10 - x^2, we need to consider the maximum and minimum values that f(x) can take. The parabola opens downwards since the coefficient of x^2 is negative, which means it has a maximum value and no minimum value. The vertex of this parabola occurs at x = 0, which gives us the maximum value of f(0) = 10. Therefore, the range of f(x) is all real numbers less than or equal to 10, which can be expressed as f(x) ≤ 10 or in interval notation, \\[10, -∞).

Option b:

[tex]\boxed{ d=\sqrt{(7-x)^2+(-4-y)^2+(9-z)^2}}[/tex]

Let two points be:

[tex]P_{1}(x_{1},y_{1},z_{1}) \\ \\ P_{2}(x_{2},y_{2},z_{2})[/tex]

The distance formula is defined as:

[tex]d=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2+(z_{1}-z_{2})^2}[/tex]

Therefore, if we define:

[tex]P_{1}(7,-4,9) \ and \ P_{2}(x,y,z) \\ \\ \\ Then: \\ \\ d=\sqrt{(7-x)^2+(-4-y)^2+(9-z)^2}[/tex]

Finally, correct option is b

Answer:

The Answer is correct, he just has the wrong letter.

Step-by-step explanation:

The correct answer is C

Answer:

$1,335.60

Step-by-step explanation:

6% of $1,260 is $75.60. $1,260 + $75.60 = $1,335.60

Hope this helps!!

Step-by-step explanation:

The word form of the number 700.06 will be;

'' Seven hundred point zero six.

What is Place value?

The value represented by a digit in a number on the basis of its position in the number is called a Place value.

Given that;

The number is,

⇒ 700.06

Now,

The word form of the number 700.06 will be;

'' Seven hundred point zero six.

Thus, The word form of the number 700.06 will be;

'' Seven hundred point zero six.

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The probability of a quarter, a dime, and a penny all landing on heads is found by multiplying the individual probabilities for each coin, resulting in a 12.5% likelihood.

The question asks about the probability of a quarter, a dime, and a penny all landing on heads when accidentally dropped. To determine this, we assume each coin has a 50-50 chance of landing on heads or tails, i.e., the probability of heads is 0.5 for each coin toss. Since each coin is independent of the others, we apply the product rule of probability for independent events.

Therefore, the probability of all three coins landing on heads is:
Probability(Quarter on heads) × Probability(Dime on heads) × Probability(Penny on heads) = 0.5 × 0.5 × 0.5 = 0.125 or 12.5%.

This represents an application of the product rule, as each coin toss is an independent event and the final probability is the product of the individual probabilities.

The value of x in the expression given is 72.

From the equation given, we can calculate the value of x thus :

cross multiply

9(366 + x) = 6(585 + x)

3294 + 9x = 3510 + 6x

9x - 6x = 3510 - 3294

3x = 216

x = 216/3

x = 72

Hence, the value of x is 72

Complete Question:

A basketball team scored 366 points in 5 games. Another basketball team scored 585 points in 8. What is the value of x? A 65 B 73 C 61 D 72 games. Each team played one additional game, making the average number of points scored per game the same for both teams. The equation below can be used to find x, the number of points scores by each team in the additional game. (366+x)/6 = (585+x)/9 .

Add 2x and 4x together you'll get 6x then add 5 to 37 and get 42 then divide 42 by 6x and 7=x

Answer:

x=7

Step-by-step explanation:

2x + 4x - 5= 37

Combine like terms

6x-5 =37

Add 5 to each side

6x-5+5 = 37+5

6x = 42

Divide each side by 6

6x/6 = 42/6

x =7

Answer:

c

Step-by-step explanation:

i am a really good guesser and i think it is c

Answer:

6/0.8 = 7.5

She'll have to jog around the park 7 and a half times.

Answer:

16.56 in

Step-by-step explanation:

4 sides of the squares are exposed

The radius of each semicircle is 1 since they are against 2 squares.

2pi*r=circumfrence

2pi*1=6.28

6.28/2=3.14 because it's a semicircle

3.14*4=12.56 because there are 4 equal semicircles

12.56+4=16.56

Answer:

the answer is -12>x or x< -12

Step-by-step explanation:

multiply both sides by 3

Answer:

[tex]\quad x<-12[/tex]

(Please vote me Brainliest if this helped!)

Step-by-step explanation:

[tex]-4>\frac{x}{3}[/tex]

[tex]\mathrm{Switch\:sides}[/tex]

[tex]\frac{x}{3}<-4[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}3[/tex]

[tex]\frac{3x}{3}<3\left(-4\right)[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x<-12[/tex]

Answer:

Option C.

Step-by-step explanation:

It is given that Rusty’s favorite meal consists of a corn dog, tater wedges, and a fudgesicle.

Rusty has decided to order a corn dog and to choose his side and dessert randomly.

We need to find the probability that Rusty will not end up with his favorite meal.

Total number of sides = 4

Total number of desserts = 4

Total possibilities = 4 × 4 = 16

Possible ways of selecting tater wedges and a fudge sickle = 1

Probability that Rusty will end up with his favorite meal is

[tex]P=\dfrac{1}{16}[/tex]

Probability that Rusty will not end up with his favorite meal is

[tex]P'=1-P=1-\dfrac{1}{16}=\dfrac{15}{16}[/tex]

Hence, the correct option is C.

Answer:

[tex]D(t) = 1\,m + (0.2\,m)\cdot \sin \left[\right(2\,\frac{rad}{s} \left)\cdot t\right][/tex]

Step-by-step explanation:

The sinusoidal expression has the following form:

[tex]D(t) = D+A\cdot \sin (B\cdot t)[/tex]

Where:

[tex]D[/tex] - Initial distance from the floor of the lake, in meters.

[tex]A[/tex] - Amplitude of oscillation, in meters.

[tex]B[/tex] - Angular frequency, in radians.

Now, each coefficient is derived as follows:

Initial distance from the floor of the lake

[tex]D = 1\,m[/tex]

Amplitude of oscillation

[tex]A = 1.2\,m - 1\,m[/tex]

[tex]A = 0.2\,m[/tex]

Angular frequency

From the statement it is known that boat reaches its maximum height in a quarter of its oscillation. Then, the angular frequency is:

[tex]B = \frac{\frac{1}{2}\pi \,rad}{\frac{1}{4}\pi \,s}[/tex]

[tex]B = 2\,\frac{rad}{s}[/tex]

The expression is:

[tex]D(t) = 1\,m + (0.2\,m)\cdot \sin \left[\right(2\,\frac{rad}{s} \left)\cdot t\right][/tex]

Answer:

0.2sin(2t)+1

Step-by-step explanation:

This is a simplified version of the answer above me.

Answer:

a) 30m

b) 50.6m²

Step-by-step explanation:

Perimeter = 2(length + width)

= 2(9.96 + 5.08)

= 30.08 m

Area = length × width

9.96 × 5.08

50.5968 m²

Answer:

A right angled triangle is a triangle where one of the internal angles is 90°.

Consider the general right angle triangle, in figure 1 below, with angle β and sides labeled as shown below

Right-Angle-Triangle

The sides are labeled with respect to the angle β, so that the nearest side is called the adjacent side, the side that is directly opposite is called the opposite side while the longest side is called the hypotenuse.

Therefore, given any angle in a triangle, it should be easy to identify the adjacent, the opposite side and the hypotenuse.

Example

Reference to the figure below.

Example1

1. Identify the right angle triangles in the above diagram.

Solution: A right angled triangle is a triangle where one of the internal angles is 90°. Such triangles are ABC, ABN, DAC and DNC.

2. Identify the adjacent sides to angles θ, α, β and µ.

Solution:

   Angle θ is in triangle DAC. The angle is nearer to line AC hence, it is the adjacent line.

   Angle α is in triangle ABN. The angle is nearer to line AB hence, it is the adjacent line.

   Angle β is in triangle DNC. The angle is nearer to line DC hence, it is the adjacent line.

   Angle µ is in triangle ABC. The angle is nearer to line AB hence, it is the adjacent line.

3. Identify the opposite sides to angles θ, α, β and µ.

Solution:

   Angle θ is in triangle DAC. The angle is opposite to line DC hence, it is the opposite line.

   Angle α is in triangle ABN. The angle is opposite to line AN hence, it is the opposite line.

   Angle β is in triangle DNC. The angle is opposite to line CN hence, it is the opposite line.

   Angle µ is in triangle ABC. The angle is opposite to line AC hence, it is the opposite line.

4. Identify hypotenuse with respect to angles θ, α, β and µ.

Solution:

   Angle θ is in triangle DAC. The longest side in that angle triangle is AD hence, it is the hypotenuse.

   Angle α is in triangle ABN. The longest side in that angle triangle is NB hence, it is the hypotenuse.

   Angle β is in triangle DNC. The longest side in that angle triangle is DN hence, it is the hypotenuse.

   Angle µ is in triangle ABC. The longest side in that angle triangle is CB hence, it is the hypotenuse.

We will cover the following. Feel free to skip any section as you prefer.

Step-by-step explanation:

Answer:

14.5

Step-by-step explanation:

since the hypotenuse is 16 you multiply that by (sin(65)) and 14.5 is the answer.

Answer:

Step-by-step explanation:

It's 500 so yeah there you go

Answer:

y-intercept=32

Step-by-step explanation:

You can find the y-intercept using the slope-intercept form:

[tex]y=mx+b[/tex]

M is the slope and b is the y-intercept. To find the y-intercept, first find the slope. Take two of the points from the table (x,y) and use the slope formula:

[tex](64,12)(48,17)\\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis:

[tex](64(x_{1}),12(y_{1}))\\(48(x_{2}),17(y_{2}))[/tex]

[tex]\frac{17-12}{48-64}= \frac{5}{-16}=-\frac{5}{16}[/tex]

Now that we have the slope, insert into the equation:

[tex]y=-\frac{5}{16} x+b[/tex]

Take a point from the table and insert into the x and y values:

[tex](64_{x},12_{y})\\\\12=-\frac{5}{16}(64)+b[/tex]

Solve for b. Simplify parentheses:

[tex]-\frac{5}{16}*\frac{64}{1}=-\frac{320}{16}=-20[/tex]

[tex]12=-20+b[/tex]

Add 20 to both sides to isolate b:

[tex]20+12=-20+20+b\\32=b\\b=32[/tex]

If b equals 32, then the y-intercept is 32.**

Finito.

**The y-intercept is where x is equal to 0 (0,32)

Answer:

Upward

Step-by-step explanation:

The first term is positive meaning it will open upward

Answer: The answer is A: Upward.

Step-by-step explanation: When the first term is positive, the graph open upward.

Answer:

decay function

Step-by-step explanation:

took the usa test prep

The area of a square is equal to the side squared.

[tex]s^{2} = A[/tex]

We can plug in 24 for A and then take the square root of each side to

find s.

[tex]s^{2} = 24[/tex]

[tex]s = \sqrt{24}[/tex]

We can simplify √24.

The prime factorization of 24 is 2 x 2 x 2 x 3.

Since we have 2 x 2 inside the radical we can simplify to have 2

outside the racial.

[tex]\sqrt{24} = \sqrt{4*6} = 2 \sqrt{6}[/tex]

We can then use a calculator to find an approximate decimal value

2√6.

(You could technically calculate it by hend using the Babylonian

method, I don't think youre expectited to do that, though)

[tex]2\sqrt{6} = 4.9 ft[/tex]

Answer:

(x-6)^2 + (y-2)^2 = 64

Step-by-step explanation:

We can write the equation of circle as

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

Where (h,k) is the center and r is the radius

(x-6)^2 + (y-2)^2 = 8^2

(x-6)^2 + (y-2)^2 = 64

Circle equation: (x - h)² + (y - k)² = r²

The center is (h, k) and the radius is r.

(x - 6)² + (y - 2)² = 8²

(x - 6)² + (y - 2)² = 64

Best of Luck!

Answer: 1335.2 ft^2

Step-by-step explanation: The volume of a cylinder formula is V=πr^2h. Just plug in 17 into h and 5 into r. Also the 2 is an exponent

The volume of the cylinder with a height of 17ft and a base radius of 5ft is approximately 1335.2 cubic feet.

The volume of a substance is the total space occupied by the substance in the three-dimensional space.

The volume of a cylinder with the radius of the base r units, and a height of h units is given by the formula:

The volume of a cylinder = πr²h cubic units.

In the question, we are asked to determine the volume of a cylinder with a base radius of 5ft and a height of 17ft.

We are given base radius r = 5ft, height h = 17ft.

To determine the volume, we use the formula of the volume of a cylinder:

The volume of a cylinder = πr²h cubic units.

or, Volume = π*(5²)*17 cubic feet

or, Volume = 3.1415*25*17 cubic feet (Taking π ≈ 3.1415)

or, Volume = 1335.1768 cubic feet ≈ 1335.2 square feet (Nearest tenths)

∴ The volume of the cylinder with a height of 17ft and a base radius of 5ft is approximately 1335.2 cubic feet.

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In this Age and Texting question, The true statement based on this information is that the younger a person is, the more likely they are to text. So the correct answer is option 3rd.

The two equations given represent the lines of best fit for the data collected by Keiko and Eric regarding peoples' age and the number of texts they send per day on average.

By analyzing the equations, we can make inferences about the relationship between age and the number of texts. Keiko's equation, t = -1.63a + 92.14, suggests that as age increases, the number of texts decreases.

Eric's equation, t = -1.05a + 80.97, also indicates a negative relationship between age and the number of texts, but with a slightly smaller slope. Therefore, the true statement based on this information is that the younger a person is, the more likely they are to text.

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Answer:

The correct answer for the question is 7

Answer:

2x + 4y

$40

Step-by-step explanation:

Equation for x small balloons and y large balloons

2x + 4y

Total cost of 10 small balloons and 5 large balloons

x = 10, y = 5

2(10) + 4(5)

= 20 + 20

= $40

Answer:

Step-by-step explanation:

2*pi*r

here r=D/2=60/2=30

so

s=2*3.14*30=188.4

Answer:

4/8

Step-by-step explanation:

bc the ate 4 muffins of a total of 8

Answer:4:8

Step-by-step explanation:

For each cube there are 6 outcomes, so there are 6*6 = 36 outcomes for two dice. Visually you can have a table that is 6 rows and 6 columns leading to 36 cells overall.