The nth term of the sequence is n-4.
a) Work out the first three terms of the sequence.
b)Work out the tenth term of the sequence.

Answer:

22.5° and 67.5°

Step-by-step explanation:

The sum of complementary angles equal 90°.

Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.

Thus, the following expression can be written to represent this case:

[tex] x + 3x = 90 [/tex]

Solve for x

[tex] 4x = 90 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{90}{4} [/tex]

[tex] x = 22.5 [/tex]

The measure of the complementary angles are:

x = 22.5°

3x = 3(22.5) = 67.5°

Answer:

y = x/4 - 1/2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write equation

x = 4y + 2

Step 2: Subtract 2 on both sides

x - 2 = 4y

Step 3: Divide both sides by 4

x/4 - 1/2 = y

Answer:

[tex]y=\frac{1}{4} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To get slope-intercept form (y=mx+b), you have to solve this equation for y by using inverse operations. First, we can subtract by 2 on both sides to eliminate the +2 on the right side. This results in x-2=4y. To get y by itself, we can divide by 4 on both sides. This becomes (x-2)/4=y. To make this in slope-intercept form, we have to separate the terms into x/4 and -2/4. This is (x/4)+(-2/4)=y. We can reduce the second fraction to -1/2 and rewrite x/4 as 1/4x. The equation is y=1/4x-1/2.

Answer:

See below

Step-by-step explanation:

The sequence given

We see the pattern: triple the previous term plus 1

Next two terms

Following two terms

Answer:

D is the answer

Step-by-step explanation: Explanation:

The domain is the set of

x

-values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be

≥

0

.

Therefore we need all of the

x

-values that result in the value of

4

−

x

being

≥

0

.

4

−

x

≥

0

4

≥

x

x

≤

4

So all

x

-values

≤

4

will work in the equation. Now we right this in terms of all real numbers:

The Domain of

x

is all the real numbers expect when

x

>

4

(This produces a negative under the square root)

brainliest please

Answer:

Option 4.

Step-by-step explanation:

We know if under the square root is a negative, then it will become an imaginary number i.

We see that in order to make the square root negative, we would have to have a number smaller than 4.

√(x - 4)

√(4 - 4) = √0 = 0

√(3 - 4) = √-1 = i

Therefore, in order for f(x) to be real numbers, x ≥ 4, [4, ∞), or {x | x ≥ 4}

Answer:

[tex]x = 21.[/tex]

Step-by-step explanation:

[tex]m \angle \: bce = m \angle \: bcd + m \angle \: dce \\ 6x = 74 + (3x - 11) \\ 6x - 3x = 74 - 11 \\ 3x = 63 \\ \boxed{ x = 21.}[/tex]

♨Rage♨

Answer:

10b

Step-by-step explanation:

Answer:

83.4

Step-by-step explanation:

(16.2x2) +1/2x8.5x12

32.4 +1/2x8.5x12

lets spilt this up

32.4+ (1/2x8.5x12)

32.4 + 51

83.4

Answer:

it's the letter "B" 83.4

The probability that Ken will use all the toothpaste in the tube is 7.64%.

From the given information,Mean, μ = 0.13 ounceStandard deviation, σ = 0.02 ounceNumber of times Ken brushes his teeth, n = 6.

The amount of toothpaste Ken squeezes out of the tube each time he brushes is independent and can be modeled by a Normal distribution.

From this information, we can obtain that:Mean of toothpaste used in 6 brushes = n × μ = 6 × 0.13 = 0.78 ounceStandard deviation of toothpaste used in 6 brushes = $\sqrt{n}$ × σ = $\sqrt{6}$ × 0.02 = 0.049 ounce.

To find the probability that Ken will use all the toothpaste in the tube, we need to calculate the probability of the amount of toothpaste used in 6 brushes being more than or equal to 0.85 ounce,
which is the total amount of toothpaste in the tube.P(X ≥ 0.85) = P( Z ≥ (0.85 - 0.78) / 0.049) = P(Z ≥ 1.43) = 1 - P(Z < 1.43)Using standard normal distribution table, we find the value of P(Z < 1.43) as 0.9236. Therefore,P(X ≥ 0.85) = 1 - P(Z < 1.43) = 1 - 0.9236 = 0.0764 or 7.64%.

The amount of toothpaste that Ken squeezes out each time he brushes is modeled by a normal distribution with mean 0.13 ounces and standard deviation 0.02 ounces.

The amount of toothpaste squeezed out at each brushing is independent of the previous amount of toothpaste squeezed out. We want to determine the probability that Ken will use all of the toothpaste in a 0.85-ounce tube if he brushes his teeth six times.

To do so, we first find the mean and standard deviation of the amount of toothpaste squeezed out in six brushes. If Ken brushes his teeth six times, then the mean amount of toothpaste squeezed out is nμ = 6(0.13) = 0.78 ounces. If the amount of toothpaste squeezed out at each brushing is independent, then the standard deviation of the amount of toothpaste squeezed out in six brushes is sqrt(6) * 0.02 = 0.049 ounces.

We now want to find the probability that Ken will use all of the toothpaste in the tube.

This is equivalent to finding the probability that the amount of toothpaste squeezed out in six brushes is greater than or equal to 0.85 ounces, which is the total amount of toothpaste in the tube.

If X is the amount of toothpaste squeezed out in six brushes, then we want to find P(X >= 0.85).We can standardize the distribution of X by subtracting the mean and dividing by the standard deviation.

Z = (X - μ) / σ is the standard normal random variable associated with X. In this case, Z has mean 0 and standard deviation 1. We want to find P(Z >= (0.85 - 0.78) / 0.049), which simplifies to P(Z >= 1.43). Using a standard normal distribution table, we can find P(Z < 1.43) = 0.9236. Therefore, P(Z >= 1.43) = 1 - P(Z < 1.43) = 1 - 0.9236 = 0.0764, or 7.64%.Therefore, the probability that Ken will use all the toothpaste in the tube is 7.64%.

Therefore, the probability that Ken will use all the toothpaste in the tube is 7.64%.

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We are asked to apply Axiom 2, also known as the "unique fold" axiom, to find the line that maps point p1 = (1,4) onto point p2 = (3,1). We will use the formula for the equation of a line to determine the equation of the line that satisfies this condition. We can then verify our answer by plotting the two points on a graphing tool like Desmos.

Axiom 2 states that for any two distinct points p1 = (x1, y1) and p2 = (x2, y2), there exists a unique line that maps p1 onto p2. The equation of a line passing through two points can be found using the point-slope formula:

y - y1 = m(x - x1)

where m is the slope of the line. To find the slope, we use the formula:

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

In this case, p1 = (1,4) and p2 = (3,1), so we can substitute these values into the formulas to find the equation of the line. The slope is:

m = (1 - 4) / (3 - 1) = -3 / 2

Using the point-slope formula with p1, we have:

y - 4 = (-3/2)(x - 1)

Simplifying the equation, we get:

y - 4 = (-3/2)x + 3/2

y = (-3/2)x + 11/2

This is the equation of the unique line that maps p1 onto p2. To verify our answer, we can plot the two points (1,4) and (3,1) on a graphing tool like Desmos and observe that they lie on the same line with the equation

y = (-3/2)x + 11/2.

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Answer:

Angle 50 and common side, in triangle MNT the sum of angles m and t is 130. In triangle PMN the sum of angles n, m is 130

Step-by-step explanation:

Answer:

Got 100% on the test

Step-by-step explanation:

We have to prove that triangle NMT is similar to triangle PMN  

Statement:    Angle NPT = 50, Angle TNM = 50                                                                                                Reason:         Given

Statement: Angle NPT equals Angle TNM                                                                             Reason: Given

Statement: Angle M is congruent to Angle M                                                               Reason: Reflexive property of congruence

Statement: NM = NM                                                                                                     Reasom: Reflexive property of equality

Statement:Therefore ΔNMT is similar to ΔPMN

Reason: AA Similiraty                                                                  

Answer:

0.32 mL

Step-by-step explanation:

d = m/v

v = m/d

v = 4.0 g ÷ 12.5 g/mL

g ÷ g cancels out the unit g

v = 0.32 mL

Answer:

3/4

Step-by-step explanation:

9-6/-2 -(-6= 3/4

I hope this helps! :D

Answer:    m = ¾

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

The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes is found as  `0.7475`. Hence, the option D is correct.

The length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 2.5 minutes and a standard deviation of 0.75 minute.

We are supposed to find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

So, we need to find `P(x < 3)` where `x` is the time taken to find a parking spot in the library parking lot.

Now, z-score will be

`z = (3 - 2.5)/0.75

= 0.67`

By looking at the z-score table, the probability that corresponds to z = 0.67 is 0.2514.

Therefore,

`P(x < 3) = P(z < 0.67)

= 0.2514 + 0.5

= 0.7514

≈ 0.7475 (approx)`

So, the correct option is `0.7475`. Hence, the answer is option D.

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Answer:

Step-by-step explanation:

The equation of the line through the points (10, 54) and (42, 48)

Slope

y-intercept

So the line is

The support beam has y-intercept 12 feet below

Required equation

The slope of the line that goes through the points (3, 7) and (-1, 4) is 3/4.

The slope formula is: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line. This will allow us to determine the slope of the line that passes through the points (3, 7) and (-1, 4).

When we enter the provided coordinates into the formula, we get:

m = (4 - 7) / (-1 - 3) = -3 / (-4) = 3/4

The pace at which the y-coordinates vary in relation to the x-coordinates is shown by the slope, which expresses how steep the line is. In this instance, the slope of 3/4 means that the y-coordinate increases by 3 units for every 4 units that the x-coordinate increases. Likewise, the y-coordinate falls by 3 units for every 4 units decrease in the x-coordinate.

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Answer:

The slope of the line that goes through (3,7) and (-1,4) is 3/4

Step-by-step explanation:

Apply the formula m = (y₂ - y₁) / (x₂ - x₁) to find the slope.

(x₁, y₁) = (3, 7)

(x₂, y₂) = (-1,4)

= (4 - 7) / ((-1) - 3)

= -3 / -4

Since both of them are negative, they cancel out to 3/4.

Answer:(-12,-15)

Step-by-step explanation:

The new coordinate of point (-4,-5) after dilation by a scale factor of 3 centered at the origin is (-12,-15).

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

Given the coordinate (-4,-5)

If we apply a scale factor by 3 on any general coordinate (x,y)

Then,

x → 3x and y → 3y

Similarly

-4 → 3(-4) = -12

-5 → 3(-5) = -15

So the new coordinate will be (-12,-15)

Hence "The new coordinate of point (-4,-5) after dilation by a scale factor of 3 centered at the origin is (-12,-15)".

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Answer:

(0,2)

Step-by-step explanation:

I think this answer is right

Answer:

Step-by-step explanation:

First, convert to slope intercept form

-x+2y=4

Add x to both sides:

-x+2y+4

+x      +x

Simplify:

2y = 4+x

Divide both sides by 2:

2y/2 = 4/2 + x/2

Simplify:

y = 1/2x + 2

And then the graph looks like this:

Answer: 1/20

Step-by i hope you have a great day

The exponential function f with f(2) = 3 and a doubling time of 5 results in f(27) = 096.

To find f(27) given that f(2) = 3 and the doubling time is 5, we can use the general form of an exponential function: f(x) = a * (2^(x/d)), where a represents the initial value, x is the input value, and d is the doubling time.

Given that f(2) = 3, we can substitute these values into the exponential function equation: 3 = a * (2^(2/5)).

To find the value of a, we can solve the equation for a: a = 3 / (2^(2/5)).

Now, we can substitute a into the exponential function to find f(27): f(27) = (3 / (2^(2/5))) * (2^(27/5)) = 096.

Therefore, the value of f(27) is 096.

---

Supporting answer:

In this problem, we are given an exponential function with an initial value of f(2) = 3 and a doubling time of 5. The doubling time represents the time it takes for the function to double its value. We can use the general form of an exponential function, f(x) = a * (2^(x/d)), to find the value of f(27).

Substituting the given values, we have 3 = a * (2^(2/5)). To solve for a, we divide both sides of the equation by (2^(2/5)): a = 3 / (2^(2/5)).

Now, we can substitute the value of a into the exponential function to find f(27). By plugging in x = 27, we get f(27) = (3 / (2^(2/5))) * (2^(27/5)). Evaluating this expression gives us f(27) = 096.

Therefore, the value of f(27) is 096, which is the answer.

In summary, the exponential function f with f(2) = 3 and a doubling time of 5 results in f(27) = 096.

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Answer:

Fantasia's family's car is more fuel-efficient.

Step-by-step explanation:

Given that, Tiyleah's family's car is getting 40 miles per gallon, and Fantasia's family's car uses 7 liters per 150 km.

The comparison can be done by observing the distance traveled by the cars in an equal amount of fuel. The car which covers more distance in an equal amount of fuel is more fuel-efficient.

First, convert the given units to have the same unit of measurement,

As 1 gallon =3.7854 liters and 1 mile = 1.609344 km

So, 40 miles =40 x 1.61=64.40 km

Now, The distance covered by Tiyleah's family's car is 64.40 km in 3.7854 liters.

So, the distance covered by Tiyleah's family's car in 1 liter of fuel is [tex]\frac{64.40}{3.7854}=17.01[/tex] km

In a similar way,

As Fantasia's family's car uses 7 liters per 150 km.

So, the distance traveled by Fantasia's family's car in 1 liter of fuel =150/7=21.43 km

Observe that, in 1 liter of fuel, Tyleah's family's car covered 17.01 km while Fantasia's family's car covered 21.43 km which is more.

Hence, Fantasia's family's car is more fuel-efficient.

Answer:

(see first pic attached)

Step-by-step explanation:

The working to the problems shows the factorization method of solving quadratic equations.

A polynomial equation of degree 2 is a quadratic equation because it includes terms with variables raised to the power of 2.

We have that;

[tex]x^2 + 10x + 16 = 0\\x^2 + 8x + 2x + 16 = 0[/tex]

x(x + 8) + 2 (x + 8) = 0

(x +2) (x + 8) = 0

x = -2 and -8

2)

[tex]x^2 - 6x + 5 = 0\\x^2 -5x - x + 5 = 0[/tex]

x(x - 5) -1 (x - 5) = 0

(x - 5) (x - 1) = 0

x = 1 or 5

3)

[tex]x^2 - 2x - 8 = 0\\x^2 -4x + 2x - 8 = 0[/tex]

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

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

x = -2 or 4

4)

[tex]2x^2 - 8x - 10 = 0\\x^2 - 4x - 5 = 0\\x^2 +x - 5x - 5 = 0[/tex]

x(x + 1) -5(x + 1) = 0

(x + 1) (x - 5) =0

x = -1 or + 5

5)

[tex]4x^2 - 36 = 0\\x^2 - 9 = 0[/tex]

x = ±3

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Answer: 35 pounds

Step-by-step explanation: To solve this problem, we need to set up a system of equations. Let x be the number of pounds of Chex cereal, and y and z be the number of pounds of peanuts and pretzels, respectively. Then, we have x + y + z = 100, z = 2y, and (0.7x + 4.25y + 2.75z)/100 = 35

Therefore, the correct answer to this problem is 35 pounds of Chex cereal

Answer:

65%

Step-by-step explanation:

uhhhhh

Answer:

-11

Step-by-step explanation:

Answer:

No the Answer is 24

Step-by-step explanation:

The number (x) in: "9 more than three times a number is 24" is what we are solving here. In other words, you are looking for a number (x) that if you multiply it by three (same as three times) and then add 9, you get 24.

The equation for the line in slope-intercept form is: y = (-2/9)x + 41/9 This is the required equation for the line that passes through the points: (-2, 5) and (7, 3) in point-slope form.

The equation for the line that passes through the points: (-2,5) and (7,3) in point-slope form can be found as follows:

Solution:

Given points are (-2, 5) and (7, 3).

Let (x1, y1) = (-2, 5)and (x2, y2) = (7, 3)

Formula used: Point-slope form of a line: y - y1 = m(x - x1)

Slope of the line: m = (y2 - y1) / (x2 - x1)

Substitute x1, y1, x2, and y2 in the slope formula: Slope m = (3 - 5) / (7 - (-2)) = -2 / 9

Slope-intercept form of the line: y = mx + b

Substitute slope m, and any one point (x1, y1) in the slope-intercept formula: 5 = (-2/9) * (-2) + b

Simplify and solve for b: 5 = 4/9 + b b = 41/9

The equation for the line in slope-intercept form is: y = (-2/9)x + 41/9

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Answer:

1 5/16

Step-by-step explanation:

subtract 1 3/4 from 3 1/16

Answer:

13

Step-by-step explanation:

We replace each X with a 3, so

4 + 3 + 3 + 3

which equals to 13

To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.

To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).

In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.

While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.

For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.

Number of trees per acre: 1 tree per acre

Total yield: 1185 peaches per acre

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