6x + -2y² + 4xy² + 3x² + 5xy² simplify it​

Answer:

$50.40

Step-by-step explanation:

To find how much Lana will pay in total follow these steps.

First, multiply 40 by 1.05.

40×1.05=42.

This is how much she will pay for the food plus tax.

Now, multiply 42 by 1.2.

42×1.2=50.40

This is how much she will pay for the food, tax, and tip.

Lana will pay a total of $50.40.

Hope this helps!

Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.

To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.

Thus, we have:

FO = √(GF² - GO²)

FO = √(30² - 24²)

FO = 18 ft.

FJ = FO + GH

Plug in the values

FJ = 18 + 24

FJ = 42 ft.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/654982

#SPJ1

Answer:

x is 14

1st is 14

2nd is 20

Step-by-step explanation:

4/7 (x ) = (34 - x )(2/5)

4x/7 + 2x/5 = 34 x 2/5 = 68/5

34x/35 = 68/5

x = 14

https://brainly.in/question/1110296

Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]

⇒ [tex]E(X)=\infty[/tex]

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]

⇒ [tex]E(X)=\infty[/tex]

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

Learn more about discrete random variable here

https://brainly.com/question/27014983

#SPJ4

Answer:

Step-by-step explanation:

Part A:  

CIRCLE A : Circumference is (pi)(diameter) so if they give you the circumference (21.98), divide it by 7 which gives you 3.14.

CIRCLE B: 18.84/6 = 3.14

Part B:

CIRCLE A: Area is (pi)(radius^2) so if they give you the area (38.465), divide it by radius^2 (7/2 = 3.5^2 = 12.25) = 3.14

CIRCLE B: 28.26/(3^2) = 3.14

Part C:

The value of pi stays the same for circle A and B.

Hope this helps :)

The range is -6.

To find the answer, calculate as follows:

Range = Maximum - Minimum

Range = 8 and Maximum = 2

Let, the minimum be x.

Now, substitute values in the formula.

8 = 2 - x

x = 2 - 8

x = -6

Therefore, the answer is -6.

Know more about a range here:

https://brainly.com/question/26098895

#SPJ4

Answer: Options (2), (4), (5)

Step-by-step explanation:

When x = 1, y = 1. So, g(1)=1.

Using similar logic to test the other options, we see that the correct answers are options (2), (4), and (5).

180-180=100

2+3=5

100÷5= 20

x = 20

Answer:

[tex]5x+80=180[/tex]
I hope this helps and that you can give a brainliest!

Step-by-step explanation:

This is a straight line which is always 180°.

Here there are 3 angles adding up to the total 180°.

So the initial equation is [tex]3x+80+2x =180[/tex].

But there are coefficients that share the same variable.
So by simplifying the equation, you end up with:

[tex]5x+80=180[/tex]

Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅

The question has to deal with proportion

Proportion is the measure of a variable or quantity relative to another.

Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is

= 1/5

So, each sub-unit measure 1/5

Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5

= 9/5

= 1⁴/₅

So, the number represented by point B is 1⁴/₅

Learn more about number and proportion here:

https://brainly.com/question/25640375

#SPJ1

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

The time dilation using the Lorentz transformation formula is presented as follows;

[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]

From the question, we have;

The spaceship's speed, v = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]

The time that elapses as measured by Andrea = 8 years

Andrea's age, A, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

Learn more about the Lorentz transformation formula here:

https://brainly.com/question/15544452

#SPJ1

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

Learn more about hexagon here:

https://brainly.com/question/28016053

#SPJ4

Answer:

x = 80 , y = 50

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact is 90°

given the angle between the tangent and the chord is 40° , then

angle inside triangle = 90° - 40° = 50°

the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then

y = 50°

the sum of the 3 angles in the triangle = 180° , then

x = 180° - 50° - 50° = 180° - 100° = 80°

Answer:

x = 80°

y = 50°

Step-by-step explanation:

the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.

that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.

the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.

one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.

since both leg angles must be equal (as described above), y = 50° too.

and as the sum of all angles in a triangle must be 180°, that gives us for x

180 = 50 + 50 + x

x = 180 - 50 - 50 = 80°

The value of angle CFE in the diagram attached is 51 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Rectangular Prism

Step-by-step explanation:

We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.

The solution to the questions are:

1) Generally, the equation for  m∠ACB is  mathematically given as

CA= CB

CA = radius of the circle

Therefore,

∠CAB =

[tex]\angle CBA = 60 \textdegree[/tex]

the sum of all the angles of a triangle

the sum of all the angles of a triangle is 180°

[tex]< CAB + < CBA + < ACB = 180 \textdegree[/tex]

[tex]60\textdegree + 60\textdegree + < ACB = 180\textdegree[/tex]

[tex]120\tetxtdegree + < ACB = 180\tetxtdegree[/tex]

[tex]< ACB = 60\textdegree[/tex]

The value of [tex]< ACB\ is\ 60\textdegree[/tex].

2. What is the length of segment AB?

In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.

In a triangle with equilateral sides, each of the triangle's three sides has the same length.

AB = BC =CA = R

As a consequence, the radius of the circle is equal to the length of the segment AB.

The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.

The circumference of the hexagon is equal to 6 times a.

The circumference of the hexagon is equal to six times each side (AB)

The perimeter of the hexagon is equal to r times 6.

As a result, the number 6r represents the hexagon's perimeter.

4. The perimeter of the hexagon is  6r the circumference of the circle.

[tex]P=2*\pi*r[/tex]

P=2*3.14*r

P=6.28r

As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.      

5. The circumference of the circle is 6.28r.

the perimeter of the circle = [tex]2 \pi r[/tex]

[tex]P=2*\pi*r[/tex]

P=2*3.14*r

P=6.28r

As a result, the diameter of the circle is a fraction of a unit bigger than.

Read more about the circumference

https://brainly.com/question/426821

#SPJ1

Answer:

1. 60 degrees

2. r

3. 6r

4. slightly less than

5. slightly greater than 6r

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer:

Step-by-step explanation:

Dilation about the origin multiplies each coordinate value by the dilation factor.

For dilation factor k, the new coordinates are ...

  (x, y) ⇒ (kx, ky)

Your dilation factor is 3, so the transformation is ...

  (x, y) ⇒ (3x, 3y)

  A(-1, 4) ⇒ A'(-3, 12)

  B(3, 2) ⇒ B'(9, 6)

  C(-2, -2) ⇒ C'(-6, -6)

Your question is incomplete. please read below for the missing content

y = -3/4x + 14 is the answer.

y = 4/3x+ 7...slope here is 4/3. A perpendicular will have a negative reciprocal slope. All that means is to flip the slope and change the sign.

4/3....flip it....3/4....change the sign....-3/4. So our perpendicular equation has to have a slope of -3/4

y = mx + b

slope(m) = -3/4

(4,11)...x = 4 and y = 11

now we sub and find b, the y int

11 = -3/4(4) + b

11 = - 3 + b

11 + 3 = b

14 = b

so ur line is : y = -3/4x + 14

The perpendicular line has the opposite slope of the reciprocal, so the slope of the line you want to find is 1/2. Inserting the given points into the equation y = 1 / 2x + b and solving b yields b = 6. Therefore, the linear equation is y = ½x + 6. When relocated, it becomes –x / 2+. y = 6.

Q)  What is the equation of the line that passes through the point (4,11) and is perpendicular to the line with the following equation y = 4/3x + 7

Learn more about the equation of perpendicular line here:https://brainly.com/question/7098341

#SPJ4

The parents could have 3 boys and 3 girls in 400 ways

The given parameters are

Children, n = 6

Boys, r = 3

Girls, r =3

The number of combination is:

[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]

So, we have:

[tex]Ways = ^6C_3 *^6C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]

This gives

Ways = 400

Hence, the parents could have 3 boys and 3 girls in 400 ways

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

Answer:

[tex]y = -3x+4[/tex]

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

A linear equation means that the y value changes at a constant rate as x increases by 1.

To find the rate of change you need to plug 2 ordered pairs into the formula:
[tex]\frac{y1-y2}{x1-x2}[/tex]

(x1,y1) can be any data point on this table. To make it easy, we will make it (2,-2).

(x2,y2) can be any data point other than the previously chosen point. So, we will choose (-1,7).

If we substitute this into the formula, previously mentioned, we get:

[tex]\frac{-2-7}{2-(-1)}[/tex]

When we solve this, we get the rate of change as -3.

This will be the "m" value in the linear equation format:
"y = mx+b"

The b value is the y-value of the data when x = 0.

So to get the b-value, you need to plug in one ordered pair into the "y=mx +b" equation.

"m" was the rate of change, which we found in the previous step.

Let's use (2,-2) as the chosen ordered pair.

By substitution, we end up with:
[tex]-2=-3(2)+b[/tex]

If we solve this out, we get:
[tex]b = 4[/tex]

m was -3 and b is now 4.

So, putting this into the equation "y = mx+b"
We get our answer as [tex]y=-3x+4[/tex].

Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

Learn more about Perpendicular here: https://brainly.com/question/7098341

#SPJ4

Answer: B

Step-by-step explanation:

A) False. Rotations do not preserve parallelism.

B) True. Rotations are rigid motions and thus preserve angle measure.

C) False. A rotation that changes the location of every point except for the center of rotation.

The speed of light is 300,000 kilometers per hour. hence option c is correct.

According to the statement

we have to explain that the by how much speed the light travels.

So, Firstly

Light is the natural agent that stimulates sight and makes things visible.

and speed of light means that the distance covered by the light with respect to time.

So, it means those distance which is covered by the light with respect to time is called the speed of light.

The speed of light is measures in km, meters and in other units also.

And we can calculate the speed of light per hour or per minute or in other time measurements.

So, The speed of light is 300,000 kilometers per hour. hence option c is correct.

Learn more about speed of light here https://brainly.com/question/104425

#SPJ4

The probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

What is probability?

To find the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection:

Therefore, the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

Know more about probability here:

https://brainly.com/question/25870256

#SPJ4

The question you are looking for is given below.

Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?

(A) 0.05

(B) 0.10

(C) 0.45

(D) 0.55

Answer:

a) Height of the ledge is 1.6 m.

b) roots of the equation are: [tex]\bf d = 2[/tex] ,  [tex]\bf d = -1[/tex]

c) Maximum height reached = 1.8 m.

Step-by-step explanation:

a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:

[tex]h = -0.8(0)^2 + 0.8(0) + 1.6[/tex]

⇒ [tex]\bf h = 1.6 \space\ m[/tex]

∴ Height of the ledge is 1.6 m.

b) The x-intercepts occur where y = 0, that is when h = 0:

[tex]-0.8d^2 + 0.8d + 1.6 = 0[/tex]

Divide both sides of the equation by -0.8:

[tex]d^2 - d -2 = 0[/tex]

Factorizing:

⇒ [tex]d^2 -2d + d - 2 = 0[/tex]

⇒ [tex]d(d-2) +1 (d-2) = 0[/tex]

⇒ [tex](d-2)(d+1) = 0[/tex]

⇒ [tex]d - 2 = 0[/tex]    or    [tex]d + 1 = 0[/tex]

∴ roots are :  [tex]\bf d = 2[/tex]   ,   [tex]\bf d = -1[/tex]

c) To find the maximum value of a quadratic equation in the form

y = ax² + bx + c , use the formula:

max = c - (b² / 4a).

Using the formula for [tex]h = -0.8x^2 + 0.8x + 1.6[/tex] :

max h =  [tex]1.6 - ( \frac{0.8^2}{4(-0.8)} )[/tex]

       = 1.8

∴ Maximum height reached = 1.8 m.

Answer:

  a) 1.6 m

  b) -1, 2 meters

  c) 1.8 m

Step-by-step explanation:

Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.

The height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.

The height of the ledge is 1.6 meters.

The x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...

 d = -1

  d = 2 . . . . meters

The maximum height is the "h" coordinate of the vertex (d, h).

The maximum height is 1.8 meters.

__

Additional comment

"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".

Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.

Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

The roots of the polynomial equation are -1.73, 1.73 and 0

The polynomial equation is given as:

[tex]x^4 + x^2 = 4x^3 - 12x + 12[/tex]

Next, we split the equation as follows:

[tex]y = x^4 + x^2[/tex]

[tex]y= 4x^3 - 12x + 12[/tex]

Next, we plot the equations on a graphing calculator

From the graph, we have the x-coordinates of the intersection points to be:

x = -1.73, 1.73 and 0

Hence, the roots of the polynomial equation are -1.73, 1.73 and 0

Read more about polynomial equation at:

https://brainly.com/question/25958000

#SPJ1

A conclusion which can be derived from these random samples is that: E. Cars are faster than SUVs.

A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Based on the information provided for these random samples from the race, we can infer and logically conclude that Cars are faster than SUVs because a median speed of 132 is greater than a median speed of 115.

In conclusion, it is important to note that the Cars used in this survey (research) are faster than SUVs because the median for the SUVs in Sample 2 is equal to 115 while the median for the Cars in Sample 1 is equal to 132.

Read more on median here: brainly.com/question/9550536

#SPJ1

It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

Read more about  circles at:

brainly.com/question/15000795

#SPJ1