Given rectangle DEFG, if FD = 3x - 7 and EG = x + 5, find EG

The trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ is 11/√2 cos θ.

The write the  trigonometric expression in the required, we can start by using the second formula:

a sin Bθ + b cos Bθ = a^2 + b^2 cos(Bθ − C)

where;

Let a = 11 and b = 11/√2, and Bθ = θ − π/4.

Then C = arctan(a/b) = arctan(11/(11/√2)) = arctan(√2).

Substituting these values, we get:

11 cos (θ − π/4) = 11/√2 cos (θ − π/4 + arctan(√2))

= 11/√2 cos (θ - π/4 + π/4)

= 11/√2 cos θ

Thus, we have written the trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ as 11/√2 cos θ.

Learn more about trigonometric expression here: https://brainly.com/question/26311351
#SPJ1

Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.

Here,

The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:

=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)

Condensing each term:

=> 3x³ - 5x²- 3x - 3x² + 5x + 3

=> 3x³ - 8x²+ 2x + 3

Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The slope of the line is 1. Two different points have the same slope.

Rise or fall is a number or ratio that determines the direction or slope of the line. The slope of a straight line is the ratio of the slope of the straight line to the course of the straight line. The point is:

-XY

twenty-five

−2 1

0 3

-7 -4

The slope of a straight line is generally calculated using the formula:

slope = [tex](y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]

Points (2, 5) and (-2, 1) of part (A).

Slope = [tex]( 1 - 5 ) / ( -2 - 2 )[/tex]

Slope = -4 / -4 = 1

Split (B) at the points ( 0, 3 ) and ( -7, - 4 ).

Slope = [tex]( -4 - 3 ) / ( -7 - 0 )[/tex]

Slope = -7 / -7 = 1

The slope of the line at two different points is the same. 

To know more about slope visit:

brainly.com/question/3493733

#SPJ1

Complete question is: A table with certain points is shown. x 2 −2 0 −7 y 5 1 3 −4 Part A: Choose two points from the table and calculate the slope between them. Show all necessary work. (4 points) Part B: Choose two different points from the table and calculate the slope between them. Show all necessary work. (4 points) Part C: What do the slopes from parts A and B tell you about the relationship between the points? Explain.

The probability of awarding the scholarship to a student who is either a math major or an engineering major is 0.2787 .Option (c) is the correct answer.

In this question, we are asked to find the probability of awarding the scholarship to a student who is either a math major or an engineering major. Total students (n) = 61 Chemistry majors (C) = 23 Math majors (M) = 12 Engineering majors (E) = 9 Undecided (U) = 17Students with declared majors in Math and Engineering (M ∩ E) = 4

We have to find P(A) = P(student is either a math major or an engineering major).To solve this problem, we will use the addition rule of probability. The addition rule states that the probability of event A or B occurring equals the probability of event A plus the probability of event B minus the probability of both A and B occurring. P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)

Here, P(M) = probability that the student is a math major= number of math majors / total students = 12/61 P(E) = probability that the student is an engineering major= number of engineering majors / total students = 9/61 P(M ∩ E) = probability that the student has declared both math and engineering majors = 4/61So,P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)P(A) = 12/61 + 9/61 - 4/61= 17/61≈ 0.2787

To know more about probability, refer here:

https://brainly.com/question/30034780#

#SPJ11

Answer:

We can use proportions to find out the tax on goods worth $60.00:

Let x be the tax on goods worth $60.00.

Then, we can set up the following proportion:

tax/sales = tax rate

or

2.42/44 = x/60

To solve for x, we can cross-multiply and simplify:

44x = 2.42 * 60

44x = 145.20

x = 145.20/44

x = 3.3 (rounded to the nearest cent)

Therefore, the tax on goods worth $60.00 would be $3.30.

Step-by-step explanation:

Answer:

F(x)=x^3+2x^2+15

Step-by-step explanation:

The probability is 0.05.

When using two water heaters as the inspection unit, the center line and control limits consistent with the past 22 days of inspection data are calculated as follows:

Center line (CL) = (X1 + X2)/2

Upper control limit (UCL) = CL + 3 * s/2

Lower control limit (LCL) = CL - 3 * s/2

Where X1 and X2 are the means of the two water heaters, and

s is the standard deviation of the sample data.

The probability of type I error for the control chart in part (b) is typically set at 0.05,

meaning that there is a 5% chance of rejecting the null hypothesis when it is actually true.

Complete question:

When using two water heaters as the inspection unit, (b) calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?

To know more about probability:

https://brainly.com/question/29381779

#SPJ11

Answer:

2.05 yards, Fredic and Fioana's answers are in the same range.

From the given data, the probability that the sample proportion is between 0.45 and 0.51 is approximately 0.7372 and between 0.42 and 0.54 is 0.9772.

To solve this problem, we can use the central limit theorem, which states that the distribution of sample proportions will be approximately normal for large sample sizes.

Given that the population proportion is p = 0.48 and the sample size is n = 350, we can calculate the standard error of the sample proportion as:

SE = √(p × (1 - p) / n) = √(0.48 × 0.52 / 350) = 0.025

We want to find the probability that the sample proportion is within three percentage points of the population proportion, or in other words, between 0.45 and 0.51. To do this, we can standardize the sample proportion using the standard error:

z = (P - p) / SE = (0.45 - 0.48) / 0.025 = -1.2

z = (P - p) / SE = (0.51 - 0.48) / 0.025 = 1.2

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values, which represents the probability that the sample proportion is within three percentage points of the population proportion:

P(-1.2 < z < 1.2) = 0.7372

To find the probability that the sample proportion is within six percentage points of the population proportion, or between 0.42 and 0.54, we can use the same approach:

z = (P - p) / SE = (0.42 - 0.48) / 0.025 = -2.4

z = (P - p) / SE = (0.54 - 0.48) / 0.025 = 2.4

Again, using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values:

P(-2.4 < z < 2.4) = 0.9772

Learn more about probability here: brainly.com/question/25839839

#SPJ1

Answer:

meaning the computer is $1246

Step-by-step explanation:

$1895-$649=$1246

Answer:

Below

Step-by-step explanation:

Area of a triangle = 1/2  base * height

  this triangle has base = 4 ( 3 in) = 12 in    and height = 3 (3 in) = 9 in

 area = 1/2 * 12 * 9 = 54 in^2

54 in^2 *  $ 2.75 /in^2 = $ 148.50

If the window is scaled down by .5 then the dimensions would be

  base = 6 in   height = 4.5 in

    area = 1/2 * 6 * 4.5 = 13.5 in^2

      cost would be    13.5 in^2   *  $ 2.75/in^2  =~ $37.13

Answer:

6

Step-by-step explanation:

y is 6..

In conclusion, a yardstick or ruler can be a reasonable tool to use to measure the length of a canoe paddle.

Then, move the yardstick along the length of the paddle, counting the marks until you reach the other end. This will give you an estimate of the length of the paddle in terms of the number of yardstick marks.
For a more precise measurement, you can also use a ruler. Place the zero mark of the ruler at the tip of the paddle and move the ruler along the length of the paddle, counting the small marks that correspond to 1/16th of an inch. This will give you a more precise estimate of the length of the paddle.

For more such yardstick related questions

https://brainly.com/question/29096010

#SPJ11

Step-by-step explanation:

See image below

Answer: 61 degrees

Step-by-step explanation:

just trust me

Answer:

You must know the value of x

The correct answer is B Parametric equations for the path of each player is Receiver: x=5, y=50-10t Defensive: x=10-0. 9t, y=54-10. 72t

The given paths of the receiver and defensive player can be described parametrically, using the parameter t, as:

Receiver: x = 5, y = 50 - 10t

Defensive: x = 10 - 0.9t, y = 54 - 10.72t

We can use the parameter t to represent the time that has elapsed since they started moving. The parametric equations describe the x and y coordinates of each player as functions of t.

By plugging in different values of t, we can determine the positions of the players at different points in time. In this case, the receiver moves horizontally while the defensive player moves at an angle, so their equations are different.

To know more about Parametric equations:

https://brainly.com/question/28537985

#SPJ4

Answer:

the midpoint is at -8

Step-by-step explanation:

The true statements based on the shape in the given image are:

The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.

Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.

With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.

Read more about math reflections here:

https://brainly.com/question/26642069

#SPJ1

Answer:

Stephanie Mary and Nicole

Step-by-step explanation:

In the triangle , the cοrrect οptiοn is  B) b = CD sin(A) and a = CD sin(B).

A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.

Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.

Here the given triangle CD is altitude.

According to the given statement table , in 4th statement we have definition of sine , Then

=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]

Here simplifying this sine equation for a and b then,

=> b = CD sin(A) and a = CD sin(B).

Hence the correct option is B) b = CD sin(A) and a = CD sin(B).

To learn more about triangle refer the below link

https://brainly.com/question/17335144

#SPJ1

Answer:

3.44827586

Step-by-step explanation:

1450:10,000::x:2

=10,000x=2900

x= 10,000

----------

2900

x=3.44827586 km

The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.

Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.

From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,

FG ⊥ HB.

Also, DE ⊥ HB, thus the segments FG ║ DE.

Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.

Learn more about perpendicular lines here:

https://brainly.com/question/28558890

#SPJ1

The system of equations that represents the number of each type of basket Jake scored is  given by:

x  + y = 13

2x +  3y = 28

A system of equations is   when two or more variables are related, and equations are built to find   the values of each variable.

In this problem,   the variables are:

Variable x: Number of  2-point shots.

Variable y: Number of 3-point shots.

Jake scored 28 points in his   basketball game   by shooting only 2-point and 3-point   shots, hence:

2x  +  3y = 28.

He scored a total   of 13 baskets, hence:

x  + y  = 13.

To learn more about System of equations, visit:

brainly.com/question/24342899

#SPJ1

The surface area of the cone is 1,966.896 mm²

We can see that the surface area of a cone of slant height H and radius R is:

SA = pi*R² + pi*R*H

Here we can see that R = 27mm/2 = 13.5mm

And H = 32.9 mm

And we know that pi = 3.14

So, replacing that we will get:

SA = 3.14*(13.5mm)²  + 3.14*13.5mm*32.9mm

SA = 1,966.896 mm²

Learn more about surface area at:

https://brainly.com/question/16519513

#SPJ1

Answer: 42

Step-by-step explanation:

We start by looking at the 49 degree angle. A common method of solving geometric problems is to bring things together. To follow this concept, we can say that the 49 degree angle has a vertical angle inside the triangle, which means that angle is 49 degrees. We now work with the 91 degree angle. We can see the 91 degree angle falls on a line, so the other side of the angle equals 180-91=89. All angles in a triangle add up to 180 degrees, so x + 49 + 89 = 180, so x=180 - 138 = 42.

Option B, 18 million, is the answer to this question.

In September 1998, the population of West Goma in millions was modeled by the function f(x) = 17.9e0.002x, and the population of East Goma in millions was modeled by the function g(x) = 13.6e0.017x. Here, x represents the year, with x=0 corresponding to September 1998.

To find out the point of intersection where the populations are equal, we equate both formulas and solve for x:

17.9e0.002x = 13.6e0.017x

Taking the natural logarithm of both sides of the equation gives:

x ln(17.9) + 0.002x = x ln(13.6) + 0.017x

Simplifying and rearranging terms, we get:

ln(17.9) - ln(13.6) = (0.017 - 0.002)x

0.079 = 0.015x

Solving for x, we get:

x = 5.27 years

Since x is the year, when x = 5.27, it corresponds to the year 1998 + 5.27 ≈ 2003.

When the populations are equal, the population will be f(5.27) ≈ 18 million for West Goma.

For further information on logarithms, refer below:

https://brainly.com/question/30085872

#SPJ11

A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.

A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:

= Length + Length + Width + Width

Slotting the figures in will give:

= 27 + 27 + 17 + 17

= 88 m

learn more about the perimeter.

https://brainly.com/question/6465134

#SPJ4

After the 15% increase in her hourly rate, Carmen's new hourly rate will be $18.40 per hour.

Carmen currently makes $480 in a month by working 30 hours. To find her hourly rate, we can divide her total earnings by the number of hours she worked:

Hourly rate = Total earnings ÷ Number of hours worked

So Carmen's current hourly rate is:

Hourly rate = $480 ÷ 30 = $16 per hour

If Carmen gets a 15% increase in her hourly rate, we can calculate her new hourly rate by multiplying her current hourly rate by 1.15 (since a 15% increase means the new rate is 115% of the current rate):

New hourly rate = Current hourly rate x 1.15

New hourly rate = $16 x 1.15

New hourly rate = $18.40 per hour

This means she will earn $2.40 more per hour than she did before the increase.

To learn more about hourly rate click on,

https://brainly.com/question/21186333

#SPJ4