Find the equation of the line.
6
The line is parallel to y =--x + 1 and passes through the point (-7, -3).
7
The equation of the line is

The first five terms of the given sequence are:

C: 18, 30, 42, 54, 66

The formula for the nth term of an arithmetic sequence is expressed as:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is number of term

The formula for the sequence is 12x + 6. Thus:

First term = 12(1) + 6 = 18

Second term = 12(2) + 6 = 30

Third term = 12(3) + 6 = 42

Fourth term = 12(4) + 6 = 54

Fifth term = 12(5) + 6 = 66

Thus, the sequence is : 18, 30, 42, 54, 66

Read more about nth term of sequence at: https://brainly.com/question/7882626

#SPJ1

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

For more questions on angle.

https://brainly.com/question/31615777

#SPJ8

The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

More can be learned about similar triangles at https://brainly.com/question/11920446

#SPJ1

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer: 40 dollars

Step-by-step explanation:

i hope the explanation is right:)

If he invites 5 friends for 40 bucks each then one friend that he knows will go is 40 dollars. So the only thing you have to do for this problem is multiply 40 by the number of friends which in this case i believe is 1.

Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

Answer:

The perimeter p of the square is:

\(p=4x\)

And in terms of x:

\(\displaystyle x = \frac{1}{4}p\)

Step-by-step explanation:

Part A)

We are given a square with side lengths x.

Recall that all four sides of a square are equivalent. Therefore, our perimeter is:

\(\displaystyle \begin{aligned} p & = x + x + x + x \\ \\ & = 4x\end{aligned}\)

Part B)

To make x the subject of the equation, divide:

\(\displaystyle \begin{aligned} p & = 4x \\ \\ x & = \frac{p}{4} \end{aligned}\)

Answer:

173.15 yards is the distance from tee to hole.

Step-by-step explanation:

Please refer to the image attached.

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation, \(\angle BAC = 12^\circ\)

To find: side AC.

Using trigonometric functions, we know that value of sine is:

\(sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\)

Here \(\theta = \angle BAC = 12^\circ\)

Perpendicular is side CB.

Hypotenuse is side AC.

\(sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards\)

Hence, 173.15 yards is the distance from tee to hole.

The statements about the quadrilateral and/or the transformed quadrilateral that are correct are:

The quadrilaterals will be congruent.

Option A is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

Quadrilateral WXYZ.

We see that,

Quadrilateral WXYZ is in the III Quadrant.

Step 1:

Rotated 180° about the origin.

This means,

Quadrilateral WXYZ is in the I Quadrant.

Step 2:

Reflection across the y-axis.

This means,

Quadrilateral WXYZ is in the II Quadrant.

Now,

Since there is no dilation the transformed quadrilateral will be congruent.

Thus,

The quadrilaterals will be congruent.

Quadrilateral WXYZ is in the II Quadrant.

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

The complete question is:

Quadrilateral WXY will be rotated about the origin and then reflected across the y-axis. Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

Learn more about logarithmic functions here:

https://brainly.com/question/28033379

#SPJ1

The length of the rectangle-shaped classroom is 15 meters.

We have a classroom. The shape of the classroom is rectangular. The length of the classroom is 3 meters more as compared to its width. The area of the rectangular classroom is 180 square meters. We need to find the length of the classroom.

Let the width of the rectangle be represented by the variable "x". The length of the rectangle is "x + 3". We will use the formula for the area of a rectangle. The area of a rectangle is the product of its length and width.

A = x*(x + 3)

180 = x² + 3x

x² + 3x - 180 = 0

We will use the quadratic formula to solve for the values of "x".

x = [-3 ± √(3² - 4(1)(-180))]/2(1)

x = [-3 ± √(9 + 720)]/2

x = [-3 ± √729]/2

x = [-3 ± 27]/2

The values of the variable "x" are -15 and 12. The negative value is rejected because the measure of a dimension cannot be negative. Hence, the value of "x" is 12. The length of the rectangular classroom is x + 3 = 12 + 3 = 15 meters.

To learn more about rectangle, visit :

https://brainly.com/question/15019502

#SPJ1

The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

Learn more on intervals of a function here;

https://brainly.com/question/1503051

#SPJ1

17.29162

\(\sqrt{18^2-5^2}\)

__________________________________________

\(17.29162\)

I hope this helps you

:)

Answer:

Step-by-step explanation:

148 people

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

Learn more about coordinates at:

https://brainly.com/question/17206319

#SPJ1

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

For such more questions on Vector Calculations and Addition

https://brainly.com/question/31866215

#SPJ11

Answer:

i need points and this is a long question from before

thanks for the points

Step-by-step explanation:

An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

Answer:

the answer is 27/10j + 1/8

\(139\) Days from September \(25\) will be \(11\) February.

Calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years.

So,

To find out \(139\) days from September \(25\);

We know that,

September has \(30\) days.

As it ask to count \(136\) days from \(25\) September ,

So,

Days left after September  \(=139-5=134\)

Now,

October has \(31\) days.

Days left after October \(=134-31=103\)

Now,

November has \(30\) days.

Days left after November \(=103-30=73\)

Now,

December has \(31\) days.

Days left after December  \(=73-31=42\)

Now,

January has \(31\) days.

Days left after January \(42-31=11\)

So, Left days are \(11\) these will be of February.

Hence, we can say that \(139\) Days from September \(25\) will be \(11\) February.

To know more about Calendar click here

https://brainly.com/question/4657906

#SPJ3

The vertices of the feasible region is (4, 3)

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

Read more about linear programming at

https://brainly.com/question/14309521

#SPJ1

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

\( \purple \bold{a^2 - b^2} \)

Step-by-step explanation:

X+4 is prime. X2-9can be factored using the \( \purple \bold{a^2 - b^2} \) formula

\( x^2 - 9\\

=x^2 - 3^2 \\

= (x+3)(x-3)\)

Answer: difference-of-squares

next one is (x+3)(x-3)(x+4)

Step-by-step explanation:

just took it on ed genuity :)

Answer:

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

Answer:

$582.68

Step-by-step explanation:

Total amount will be,

→ $266.63 + $317.29 + $62.78

→ 266.63 + 380.07

→ $646.7

Then the final price will be,

→ ($646.7 - 15%) + 6%

→ (646.7 - (646.7/100) × 15) + 6%

→ (646.7 - 97.005) + 6%

→ 549.695 + (549.695/100) × 6

→ 549.695 + 32.9817

→ 582.6767

→ $582.68

Hence, the answer is $582.68.

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

0.1241

Step-by-step explanation:

Given that:

Critical path = 37 days

Variance total = 27 days

Completion date (x) = 43 days

We obtain the Zscore :

Zscore = (x - critical path) / variance total

Zscore = (43 - 37) / √27

Zscore = 6 / √27

Zscore = 1.1547

Zscore = 1.155

Hence, probability of completing in 43 days :

P(Z > 43) = 1 - P(Z < 43)

P(Z < 43) = 0.8759

P(Z > 43) = 1 - 0.8759 = 0.1241

The marginal revenue at 8 units is given as follows:

MR(8) = 288 dollars per unit.

The revenue function is defined as follows:

R(q) = -7q² + 400q.

The marginal revenue function is the derivative of the revenue function, hence it is obtained as follows:

MR(q) = -14q + 400.

At 8 units, the marginal revenue is found with the numeric value of MR(q) at q = 8, hence:

MR(8) = -14(8) + 400 = 288 dollars per unit.

More can be learned about marginal revenue at https://brainly.com/question/13444663

#SPJ1

Answer:

−617.785

Step-by-step explanation: