Find the 52nd term of the sequence
3,7,11,15

Answer:

A

Step-by-step explanation:

We will get y = -7x + 6  in graph y-intercept 6 and slope-7.

The equation of the line with a y-intercept of 6 and a slope of -7 can be written in slope-intercept form as:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the given values, we get:

y = -7x + 6

So the equation of the line is y = -7x + 6.

slope -7 and y - intercept 6.

Slope intercept form: y = mx + b, m=slope, b = y-intercept

y = -7x + 6

Just plug in a value for x and solve for y

x     y=-7x+6

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

0           6

1          -1

If you plot these two points and draw a straight line through them,

that is the graph of the line.

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Answer:

less than.

Step-by-step explanation:

Any negative number is less than 0

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer: It is 3/17 :)

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

it’s SAA

Step-by-step explanation:

ur wlcm, i am sure of my answer

brainliest please?

Answer:

30

60

90

120

180

210

240

hope it helped have a good day mate

Answer:

Step-by-step explanation:

A= 2AB+(a+b+c)h

AB= s (s﹣a) ( s﹣b) (s﹣c)

s = a+b+c

2

Solving for A

A= ah +bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=17·8+14·8+15·8+1

2·﹣174+2·(17·14)2+2·(17·15)2﹣144+2·(14·15)2﹣154≈ 567.35897

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

A) 12 inches by 20 inches

Step-by-step explanation:

Dilation of a scale factor means to increase by a factor of 4.
That basically mean multiply the object by 4.

Therefore 3 inches x 4 = 12 inches

And 5 inches x 4 = 20

9514 1404 393

Answer:

  -26, -25

Step-by-step explanation:

The average of the two is their sum divided by 2: -51/2 = -25.5. The average of consecutive integers is halfway between them.

Hence, one is -26 and one is -25.

Answer:

Step-by-step explanation:

3:7 = ___: 49

3 : 7 = x : 49

x = 3 × 49 ÷ 7

x = 147 ÷ 7

x = 21

3 : 7 = 21 : 49  (your answer)

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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Answer:

Hope the picture will help

\(\frac{16}{7}\)Answer:

X = -16/7

Step-by-step explanation:

Multiply the numbers

4 x 2 + 8 = -7x

8 + 8 = -7x

Add the numbers

8 + 8 = -7x

16= -7x

Divide both sides by the same factor

16= -7x

16 divided bu -7x and -7x divided by -7x

Simplify

-16 divided by 7 not negative 7 and -7 divided by -7

Cancel terms that are in both the numerator and denominator

cancel out -7 divided by -7 and you get -16/7 left

so, therefore x= -16/7

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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\(28+24=4(7)+4(6)=4(7+6)[=4(13)=52]\)

The answer: 4(7+6)

ok done. Thank to me :>

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer:

Its b)6

Step-by-step explanation:

I just did it on edge and got it correct

The value of y is 6 centimeters.

Given that,

The length of RU = 12 centimeters

The length of UT = 4 centimeters

The length of QU = 8 centimeters.

The length of US = y centimeters

The intersecting chords theorem states that, the product of one whole chords segment and its external segment is equal to the product of the other whole chords segment and its external segment when two chords cross at an exterior point.

According to the intersecting chords theorem,

US x QU = RU x UT

Substitute the values in above formula,

y x 8 = 12 x 4

y = 48/8

y = 6 centimeters,

Hence, the value of y is 6 centimeters.

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Answer:A

Step-by-step explanation:

edge 2021

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

d. 4

Step-by-step explanation:

the numbers in the sequence keep increasing by a unit of 4.

-5 + 4 = -1

-1 +4 = 3

3 + 4 = 7

Answer:

B -4

Step-by-step explanation:

The period of the sine function representing the position of the band members is 60 feet, and the amplitude is approximately   \(170.3 feet.\)

Since the band members are standing in the shape of a sinusoidal function, we can assume that their positions can be represented by the equation:

\(y = A sin(Bx)\)

where y is the vertical position of a band member, x is the horizontal position on the field, A is the amplitude, and B is the period.

Since Darla is positioned in the exact center of the field, and the person closest to her on the same horizontal line stands 10 yards away, we can assume that the sinusoidal function has a phase shift of 0. This means that the midline of the function passes through the point (0, 0).

To find the amplitude, we need to determine the maximum and minimum heights of the function.

Since the playing area of the football field measures 300 feet by 160 feet, the distance between the two farthest points on the field is the diagonal distance, which can be calculated using the Pythagorean theorem:

\(sqrt(300^2 + 160^2) \approx 340.6 feet\)

Since the distance between the farthest points on the field is equal to the distance between two peaks or two valleys of the sinusoidal function, the amplitude is half of this distance:

\(A = 340.6/2 \approx170.3 feet\)

To find the period, we can use the fact that the distance between two consecutive peaks or valleys is equal to the period of the function.

Since the person closest to Darla stands 10 yards away, or 30 feet away, we can assume that this person is standing at a peak or a valley of the function. This means that the period is twice the distance between Darla and the person closest to her:

\(P = 2(30) = 60 feet\)

Therefore, the period of the sine function representing the position of the band members is 60 feet, and the amplitude is approximately   \(170.3 feet.\)

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Answer:

Step-by-step explanation:

true

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.

The function will be:

F = 2.40 + (0.40 × m)

F = 2.40 + 0.40m

where m = number of miles

F = taxi fare.

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Answer:

5 feet

Step-by-step explanation:

\(f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}\)

Answer:

B. 56°

Step-by-step explanation:

We are given that m∠R is 66° and m∠T is 122°.

We can apply the supplementary rule since ∠S and ∠T are a linear pair. So, we can use ∠T to find ∠S through 180° - 122° = 58°.

Now, we can use ∠R and ∠S to find ∠Q.

66° + 58° = 124°

180° - 124° = 56°

Answer:

m∠Q is 56°.

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the two interior angles that are not adjacent to that exterior angle.

In this case, ∠T is an exterior angle of the triangle, and ∠Q and ∠R are the two interior angles that are not adjacent to ∠T.

So, the measure of ∠T is equal to the sum of the measure of ∠Q and the measure of ∠R.

Therefore, m∠Q is 56°.

The maximum load that a beam can withstand before breaking is known as the critical load. The SI unit of a critical load is the Newton, which is the same as the unit of a load.

The articulation for the snapshot of dormancy of a circle is,

IC=πd432=0.098174 d4

Here the measurement of the circle is d.

As a result of the materials' identical cross-sectional area, A C = A S, substitute the given values.

I S = 1 6 A 4 = 1 6 (0.88622 d) 4 = 0.102805 d 4

The materials have the same cross-sectional area,

so, A C = A T 4 d 2 = 3 4 B 2 B = 1.34677 d

Here, the side of the triangle is B. I S = 1 6 A 4 = 1 6 (0.88622 d) 4 = 0.102805 d 4

The expression for the rectangle's moment of inertia is I T = 1 12 (4 d 2 ) (1.34677 d) 2 = 0.11872 d 4.

The expression for the critical load is P C = 2 E I L 2. It is evident from the aforementioned expression that the critical load is directly propositional to the moment of inertia.

The ratio of moment of inertia can be expressed as P 1:

P2:P3=IC:IS:

I T Replace the given values.

P1:P2: P3=0.098174:0.102805:

As a result, the critical load-to-weight ratio for these columns is 0.11872:

0.102805: 0.11872

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