Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...

Naoki shifted the base of ladder by 14 feet as the updated distance is 39 feet and old distance was 25 feet.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc). Finding the elements of vectors, modeling the mechanics of waves (both electromagnetic and physical), summarizing the strength of fields, and using dot and cross products are all physics applications of trigonometry. You can use trigonometry quite a bit in projectile motion.

Here,

The length of ladder= 65 foot

It rest at a wall at height of 60 foot.

So distance of foot of ladder from wall,

=√(65²-60²)

=√625

=25 foot

Now, as the ladder is shifted, it rest on the wall at height of 52 foot.

=√(65²-52²)

=√1521

=39 foot

Shift in the base of ladder,

=39-25

=14 foot

As the updated distance is 39 feet and the previous distance was 25 feet, Naoki moved the base of the ladder up by 14 feet.

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Answer:

2.5 - 2(-3-0.5) + 2(n) > 10.75

Step-by-step explanation:

Step 1: two and 5 tenths is 2.5

Step 2: 2 times the quantity of the difference of negative three and one half is 2(-3-1/2)

Step 3:  two times a number is at least ten and three quarters = 2(n) > 10.75

Combine: 2.5 - 2(-3-0.5) + 2(n) > 10.75

What is Angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

From the figure, we can tell that a transversal is passing through the two parallel lines which makes corresponding angles.

In the given figure 14x+7 and 10x+5 are the two angles formed by the transversal.

14x+7=10x+5

Now take all the variable terms to one side

14x-10x=5-7

4x=-2

Divide both sides by 4

x=-2/4

Divide numerator and denominator by 4

x=-1/2

Hence the value of x is -1/2

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Answer:

  $1280

Step-by-step explanation:

You want the cost of flooring a cubic 4096 ft³ room at $5 per square foot.

Each dimension (length, width, height) of the room is the edge length of a cube with a volume of 4096 ft³.

  V = s³

  4096 = s³

  ∛4096 = s = 16 . . . . feet

The floor area is the square of the edge length:

  A = s²

  A = (16 ft)² = 256 ft²

At $5 per square foot, the cost of flooring will be ...

  ($5/ft²)(256 ft²) = $1280

The hardwood floors will cost $1280.

Answer: 5468.9

Step-by-step explanation:

Answer:

I think its $90.75

Hopefully its right :)

A sampling distribution of the sample proportion with n=15 and p=0. 65 is stimulated here when The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

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Answer:

87.08.

850.08 - 763 = 87.08.

Answer:

x = 36

The measure of the exterior angle is 114°

The remote interior angles are 24° and 90°.

Step-by-step explanation:

The angle marked 3x + 6 is the exterior angle. The other two marked angles are called "remote interior angles"

The two remote interior angles added together equals the exterior angle.

3x+6 = 24° + 2x + 18

Combine like terms.

3x + 6 = 2x + 42

Subtract 2x from both sides.

x + 6 = 42

Subtract 6 from both sides.

x = 36

If required, use the x=36 to find the measure of the exterior angle.

3(36) + 6

= 108 + 6

= 114°

Or find the measures of the remote interior angles.

2(36) + 18

= 72 + 18

= 90°

The remote interior angles are 24° and 90°.

Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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the correct answer is A

Always concentrate on point where X or G(X) equals Zero.

For example, here point (0,2), G(X)=2 when X=Zero.

If u tried to Replace X and G(X) in the equations below with these numbers, you would figure out the right answer so easily. Have a nice day!

There are 52 cards in the deck and so the probability of guessing the card right is 1/52.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

We can find this probability by seeing that

=1/4×1/13

=1/52

Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.

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Answer:

u=8

Step-by-step explanation:

48+3u=9u

-3u both sides

48=6u

divide by 6 on both sides

8=u

The end behavior of the function is f(x) → -∞, as x→ -∞ and f(x) → -∞, as x→ +∞.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

For extremely big or very tiny values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behavior based on the sign of the leading coefficient.

The given function is -x⁴ -x³ +3x² +2x +6

The degree of the given function is even and the leading coefficient is negative. So,

End behavior is given by

f(x) → -∞, as x→ -∞

f(x) → -∞, as x→ +∞

The graph looks as follows:

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The value of x is 22.5528.

Let ABC be the triangle , <A = 70, <B = 30 ,<C = 80.

Sum of angles in a triangle is 180.

70 + 30 + <C = 180

<C = 180 - 100

<C = 80.

Let sides be a = x , b = 12 and c = ?

According to sines law,

a/sin A = b/sin B = c/sin C

substitute a ,b,A,B values

a/sin A = b/sin B

x/sin 70 = 12/sin 30

x = 0.9397*12/1/2

= 11.2764*2/1

x = 22.5528.

Therefore the value of x is 22.5528.

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Check the picture below.

Answer:

y = -1.5

Step-by-step explanation:

use the method y2 - y1 / x2 - x1

Salinity and density decrease as temperature rises. Salinity and density, therefore, have a negative relationship with temperature. The density rises as salinity rises. As the temperature drops, ocean water becomes denser. Therefore, water becomes denser as it becomes colder. The density of seawater also rises as salinity does.

Water that is less dense floats above water that is denser. The warmer water will float on top of the colder water if there are two layers of water with the same salinity. However, there is a catch! Salinity has less of an impact on water density than temperature does. Therefore, if the layer with higher salinity is considerably warmer than the layer with lower salinity, the layer with higher salinity can actually float on top of the layer with lower salinity.

As you descend to the ocean's bottom, the temperature of the water continues to drop. So, as you descend to the ocean's bottom, the density of the water keeps rising. The deep ocean is divided into layers, with the lightest water at the top and the densest water at the bottom. The ocean's depths have horizontal circulation. In other words, water flows in strata of equal density.

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(a) Probability that third apple is red from three selected apple one after one is 22/23.

(b) Probability that exactly two of the three apples are red is 0.3012

In the question we have,

total number of apples in a box = 25

number of red apples in a box = 22

number of green apples in a box = 3

Now, three apples are selected at random,one after other without replacement and first two apples are green .

(a) Then number of apples remained in a box after two green apples withdraw = 23

probability that third apple is red = 22/23

(b) The following are possible number of sample spaces for exactly two of the three apples are red

where , R--> red apple and G--> green apple

For first sample space , RGR i.e first and last apples are red

probability that first and last apples are red from three withdraw apples or P(RGR) = 22/25× 3/24× 21/23 = 0.1004

similarly, P(RRG) = 22/25×21/24×3/23 = 0.1004

P(GRR) = 3/25×22/24×21/23 = 0.1004..

Probability that exactly two apples are red = P(RRG)+ P(RGR)+ P(GRR) = 3(0.1004) = 0.3012

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Step-by-step explanation:

those are the answers if I am wrong you can correct

Answer:

(0.5, 1.5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (- 4, 4 ) and (x₂, y₂ ) = B (5, - 1 ) ,then

M = ( [tex]\frac{-4+5}{2}[/tex] , [tex]\frac{4-1}{2}[/tex] ) = ( [tex]\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = (0.5, 1.5 )

Answer:

The midpoint is at ( 1/2, 3/2)

Step-by-step explanation:

Midpoint

To find the x coordinate of the midpoint

Add the x coordinates of the endpoints and divide by 2

( -4+5)/2 = 1/2

To find the y coordinate of the midpoint

Add the y coordinates of the endpoints and divide by 2

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

The midpoint is at ( 1/2, 3/2)

When the directrix is at x = 5 and  point in the vertex is at h = 2. Then P would be -3

In the equation of parabola, P is defined as the distance between the directrix and the vertex

The vertex is defined by the points V ( h, k )

h is for the x coordinate

k is for the y coordinate

when the directrix is given in the x, we solve for P using h

P = h - point given for directrix

P = 2 - 5

P = -3

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Answer:

k = - 6 , c = 8

Step-by-step explanation:

f(x) = x² + kx + c

given f(2) = 0 , substitute (2, 0 ) into f(x)

0 = 2² + 2k + c

0 = 4 + 2k + c ( subtract 4 from both sides )

- 4 = 2k + c → (1)

given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)

35 = (- 3)² - 3k + c

35 = 9 - 3k + c ( subtract 9 from both sides )

26 = - 3k + c → (2)

subtract (2) from (1) term by term to eliminate c

- 4 - 26 = 2k - (- 3k) + (c - c)

- 30 = 2k + 3k

- 30 = 5k ( divide both sides by 5 )

- 6 = k

substitute k = - 6 into (1) and solve for c

- 4 = 2(- 6) + c

- 4 = - 12 + c ( add 12 to both sides )

8 = c

then

k = - 6 and c = 8

Answer:

Step-by-step explanation:

1 / 3

Reason being: 100 / 3 = 33.333333333

The formula that plots the radius against the area of such water puddle here on floor; A = πr².

For the given question,

Let the area of the water puddle on the floor be 'A'.

Let the radius of the water puddle be 'r'.

Then, using the area of the circle,

The function for the area of the water puddle be,

A = πr²

Thus, the formula that plots the radius against the area of such water puddle here on floor; A = πr².

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1.

The slope intercept form is y=mx+b

4x-3y=2

subtract 4x from both sides

3y=2+(-4x)

Divide by 3

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

simplify:

y=2/3-4x/3

reorder:

y=-4/3x+2/3

slope= -4/3, y intercept= 2/3

2.

In the same way,

3x+2y=-3

2y=-3-3x

y=-3/2 - 3x/2

y+3/2=-3x/2

y=-3x/2-3/2

y=-3/2x-3/2

slope=-3/2, y intercept= -3/2

I hope this helped you.

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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An ordered pair which makes both inequalities true is: C. (1, 2).

In this exercise, we would test each of the ordered pair with the given system of inequalities in order to determine which is true.

For ordered pair (-1, 3), we have:

y < 5x + 2

3 < 5(-1) + 2

3 < -5 + 2

3 < -3 (False).

For ordered pair (0, 2), we have:

y < 5x + 2

2 < 5(0) + 2

2 < 0 + 2

2 < 2 (False).

For ordered pair (1, 2), we have:

y < 5x + 2

2 < 5(1) + 2

2 < 5 + 2

2 < 7 (True).

y > x/2 + 1

2 > 1/2 + 1

2 > 3/2 (True)

For ordered pair (2, -1), we have:

y < 5x + 2

-1 < 5(2) + 2

-1 < 10 + 2

-1 < 12 (True).

y > x/2 + 1

-1 > 2/2 + 1

-1 > 2 (False)

For ordered pair (2, 2), we have:

y < 5x + 2

-1 < 5(2) + 2

-1 < 10 + 2

-1 < 12 (True).

y > x/2 + 1

2 > 2/2 + 1

2 > 2 (False)

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Answer:

B , C

Step-by-step explanation:

Which ordered pairs make both inequalities true? Select two options.

y < 5x + 2

y > One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded.  

(–1, 3)

(0, 2)  

(1, 2)

(2, –1)

(2, 2)                                                                                          Edge  2022

The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.

In this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:

y = m · x + b

Where:

And the relationship between the slopes of two perpendicular lines:

m · m' = - 1

Where:

And the slope of the original line can be found by the secant line formula:

m = Δy / Δx

And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:

M(x, y) = 0.5 · A(x, y) + B(x, y)

Where:

First, find the slope of the line segment by secant line formula:

m = [- 1 - (- 5)] / (- 5 - 9)

m = - 4 / 13

Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:

m' = - 1 / m

m' = - 1 / (- 4 / 13)

m' = 13 / 4

Third, determine the midpoint of the line segment by the midpoint formula:

M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)

M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)

M(x, y) = (2, - 3)

Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:

b = y - m' · x

b = - 3 - (13 / 4) · 2

b = - 3 - 26 / 4

b = - 3 - 13 / 2

b = - 19 / 2

The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.

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