Suppose a golf ball bounces off a wall at a point P, and that
line mis perpendicular to the wall at point P.
What is the measure of the angle of reflection?
A. 50°
B. 40°
C. 140°
D. 90°

Answer:

u = 3

Step-by-step explanation:

Step 1: Distribute 5 in u - 5

[tex]\displaystyle{5\cdot u - 5\cdot 5 +6u=8}\\\\\displaystyle{5u-25+6u=8}[/tex]

Step 2: Add like terms together (u-term)

[tex]\displaystyle{11u-25=8}[/tex]

Step 3: Add both sides by 25

[tex]\displaystyle{11u-25+25=8+25}\\\\\displaystyle{11u=33}[/tex]

Step 4: Divide both sides by 11

[tex]\displaystyle{\dfrac{11u}{11}=\dfrac{33}{11}}\\\\\displaystyle{u=3}[/tex]

Answer Check

Step 1: Substitute u = 3 in the equation

[tex]\displaystyle{5(3-5)+6(3)=8}[/tex]

Step 2: Evaluate & Simplify

[tex]\displaystyle{5(-2)+18=8}\\\\\displaystyle{-10+18=8}\\\\\displaystyle{8=8}[/tex]

Since the equation is true after substituting u = 3. Therefore, the answer is u = 3.

Please let me know if you have any questions!

answer to the question that you have

2,048.0

2050 because

1-9 = ones place

10-99 = tenth place

100-999 = hundrends place

1000 - 999999 - thousands place

and you round to the nearest 0 if it is 5 or up and if it is 1 to 4 it stays the same

Note that:

Applying the addition formula given above to cos 150:

In the given figure : lines l and m are parallel and a, b are transversal

Since, the lines a and b are parallel and l act as a transversal.

Then,

x = 23

Answer : x = 23

The value of the unknown angle x is 22 degrees.

SV is a parallel to RU.

RV is a transversal line that cut across the parallel lines SV and RU.

Therefore,

x = ∠V(alternate angles)

Alternate angles are congruent.

Hence,

∠V + 44 + 5x + 4 = 180 (sum of angles in a triangle)

x + 44 + 5x + 4 = 180

x + 5x + 48  = 180

6x + 48 = 180

6x = 180 - 48

6x = 132

divide both sides by 6

x = 132  /6

x = 22 degrees

learn more on angles here: https://brainly.com/question/10254268

#SPJ1

The intervals to the given function are as follows:

This function is defined(values of x) for all real values and also assumes all real values(values of y), hence both the domain and the range are of the function are given by the interval (-∞,∞).

From the graph, the function is classified as decreasing or increasing according to the direction of movement in the graph, as follows:

Hence the intervals are given as follows:

The relative minimum is when the graph of the function changes from decreasing to increasing, hence it is at these two following points:

(-0.366, -5.848) and (2,-1).

The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:

(1.366, -0.652).

The end behavior of the function is given by the limits of the function when x go to infinity, looking to the left and to the right of the graph of the function, hence:

More can be learned about functions at https://brainly.com/question/28949511

#SPJ1

The formula for the given arithmetic series for the term aₙ will be aₙ=a₁+(n-1)d.

So, the possible sequence of -64, -16, 4:

So, the formula for the aₙ term will be:

Therefore, the formula for the given arithmetic series for the term aₙ will be aₙ = a₁ + (n - 1)d.

Know more about arithmetic series here:

https://brainly.com/question/6561461

#SPJ13

The correct question is given below:

Write an explicit formula for an, the nth term of the sequence

-64, -16, 4,....

Answer:

See below

Step-by-step explanation:

Length (L), volume (V), weight(W), or mass(M)

Mile     L

Cup           V

Pound   W

Centimeter L

Liter     V

Gram   M

Pint           V

Yard   L

Kilogram   M

Teaspoon  V

Milliliter    V

1. Mile

2. Cup

3. Pound

4. Centimeter

5. Liter

6. Gram

7. Pint

8. Yard

9. Kilogram

10. Teaspoon,

11. Milliliter

-24-68i is solution of complex number.

What is the best definition of a complex number?

(4-6i)(6-8i)

= 24-32i-36i+48i²

= 24 + -68i - 48

= -24-68i

Learn more about Complex numbers

brainly.com/question/20566728

#SPJ13

The complete question is -

Multiply the following complex numbers (4-6i)(6-8i)

The value of x in the vertical angles is 12.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Vertically opposite angles are congruent.

Therefore, the vertical angles measures 84 degrees and 8x - 12.

Let's find the value of x using the principle of vertically opposite angles.

Therefore,

84 = 8x - 12

add 12 to both sides of the equation

84 + 12 = 8x - 12 + 12

96 = 8x

divide both sides by 8

x = 96 / 8

x = 12

learn more on vertically opposite angles here: https://brainly.com/question/18045519

#SPJ1

A graph which best describes what the proportional relationship would be D. A line that passes through the point (0, 0) and continues through the point (12, 3).

In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Additionally, a graph which shows a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).

Since the graph represents a proportional relationship we will get;

Constant of proportionality, we get;

k = 12/3 = 8/2 = 24/6

k = 4

Ratio,

24:6

= 12:3.

Therefore, A line that passes through the point (0, 0) and continues through the point (12, 3).

Read more on graphs here:

brainly.com/question/4546414

#SPJ1

We will investigate the equal distribution of ribbon amoung her friends.

Isis has a ribbon for crafts for a certain length ( L ):

Isis has ( n ) number of friends amoung which she wants to equally distribute the length ( L ) of her ribbon:

Under the assumption of equal distribution we can divide the total length of ribbon ( L ) amoung Isis ( n ) of friends to determine what length ( l ) each friend got:

So each friend of Isis got a piece of 40 cm length of the ribbon. So the length of the ribbon accumulated for 5 friends would involves the direct multiplication of 5 number of friends and length of each piece ( l ):

Therefore, the answer to the question is:

Remember that

P(A or B)=P(A)+P(B)-P(A and B)

In this problem, we have that

Event A and Event B are not independent

we have

P(A)=0.68

P(B)=0.32

P(A and B)=0.11

substitute

P(A or B)=0.68+0.32-0.11

P(A or B)=0.89

EXPLANATION

We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:

Perimeter = 40 cm = 4x + 2x + 2 + x + 3

Adding like terms:

40 = 7x + 5

Subtracting 5 to both sides:

40 - 5 = 7x

Adding like terms:

35 = 7x

Dividing both sides by 7:

35/7 = x

Simplifying:

Then, by the obtuse triangle theorem, the following relationship should be fulfilled.

The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

What is factorization?

When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.

We are given a quadratic equation

[tex]4x^2+13x-15[/tex]

We use quadratic formula to compute the factor of the equation

[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]

Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

To learn more about factorization please refer

https://brainly.com/question/25829061

#SPJ13

The value of the function h(2) for h(t) = -16t2 + 32t + 5 is h(2) = 5

From the question, the function definition is given as

h(t) = -16t2 + 32t + 5

First, we express the exponent in the function properly

This is represented as

h(t) = -16t² + 32t + 5

The function value to calculate is given as

h(2)

This means that we calculate h(t) when t = 2

So, we have

h(2) = -16(2)² + 32(2) + 5

Evaluate the exponents

h(2) = -16(4) + 32(2) + 5

So, we have

h(2) = 5

Hence, the function value is 5

Read more about functions at

https://brainly.com/question/28532394

#SPJ1

the relation is 3x + y = 3

so,

y = 3x - 3

the domain is the values of x

so, substitute with each value of {-2,2,4} at the last equation of y

when x = -2 , y = 3*-2 - 3 = -6 - 3 = -9

when x = 2 , y = 3 * 2 - 3 = 6 - 3 = 3

when x = 4 , y = 3 * 4 - 3 = 12 - 3 = 9

so, the range will be {-9 , 3 , 9}

The correct answer is option a. (-9,3,9)x

Given

Two sets A = (-∞, - 5], B = [5, ∞)

Find

union, AUB

Explanation

Union of two sets A and B is the set of all elements that are present in A or in B

so , here A = (-∞, - 5], B = [5, ∞)

then union of set A and B is given by

Final Answer

Therefore., the union of A and B is (-∞, - 5] U [5, ∞)

Answer:

6.  Draw a vertical line that goes though points (4,7) and (4,9).  For a relation to be a function, each input has to have only one output.  The input 4 cannot have the output of 7 and 9.  This proves that this is not a function

7. The range is 91, 3, 6, 10 and 15)

Step-by-step explanation:

The range is the answer if you put in the x for range that they give you.

For example:

x ( x+ 1)/2  If I put in 1 for x, I will get

1(1+1)/2

2/2

1

When the input is 1, the output is one.  You that for each of the domains given and you will find the ranges (outputs) that I have written above.

Answer:

m = -5

n = -2

Step-by-step explanation:

5m + 6n = -37

10m + 4n = -58 multiply first equation by -2

-2 × 5m + 6n = -37

-10m + (-12n) = 74 now add two equations up

10m - 10m + 4n - 12n = 74 - 58 add/ subtract like terms

-8n = 16 divide both sides by -8

n = -2

to find the value of m, replace n with -2 in the first equation

5m + 6*(-2) = -37

5m - 12 = -37 add 12 to both sides

5m = -25 divide both sides by 5

m = -5

Answer:

Step-by-step explanation:

Find the amount of increase:

Find the percent value of the increase over the initial price:

To find the distance between two numbers on the number line, you have tu use absolute value

So, if I want to know the distance from -2 to 5, all I have to do is to substract 5 from -2 and then apply absolute value, like this:

And the number line should look like this:

In this problem, we are going to write and solve a system of equations based on a real world situation.

Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.

To begin, we need to create variables for the unknown cost of each chore.

Let x represent laundry, and let y represent dishes.

From the first equation, we can write the equation:

We can write the second equation as:

Together, we have the system:

Multiply the first equation by -1, then add it to the second equation:

We can divide the remaining equation by 2 on both sides:

Lada made $2 per load of laundry.

We can use the value of x in the first equation to find the value of y. Substitute x = 2:

Subtract 2 from both sides:

Divide by 8 on both sides:

Lada made $3 per load of dishes.

Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.

The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:

c² = a² + b² - 2 × a × b × Cos C.

Considering right triangle ABD,

BD = a

DC = b

BC = c

Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:

BD = √(7.5² + 5²)

BD = √(7.5² + 5²)

BD = 9.0 cm

Use the law of cosines to find the length of BC:

BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.

Substitute

BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38

BC² = 250 - 184.4

BC² = 65.6

BC = √65.6

BC = 8.1 cm

Learn more about the law of cosines on:

https://brainly.com/question/4372174

#SPJ1

If Tanya is training a turtle for a turtle race. For every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile. The  rate that  the turtle is crawling in miles per hour is:  0.2 miles /hour .

Given data:

1/2 of an hour  =  1/20 of a mile

Now let determine the unit rate

Unit rate that the turtle is crawling is: (1/20)/(1/2)

Hence,

Unit rate  = (1/20)×(2/1)

Unit rate  = 2/20 miles/hour

Unit rate = 0.2 miles /hour

Therefore the rate is 0.2 miles per hour.

Learn more about unit rate here: https://brainly.com/question/19493296

#SPJ1

If for every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile. then 0.1mile/ hour is the rate at which turtle travel per hour.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

A turtle is trained by Tanya,

For every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile.

We need to find at what rate the turtle is travelling per hour.

Let x be the distance travelled by turtle in hour.

1/20/1/2=x/1

Apply cross multiplication

x/2=1/20

x=2/20

x=0.1 miles / hour

Hence 0.1 miles per hour is the turtle travelling per hour.

To learn more on Ratios click:

https://brainly.com/question/1504221

#SPJ1

Answer:

1288 times greater

Step-by-step explanation:

(8.5x10^-2)/(6.6x10^-5)

(8.5/6.6)*(10^-2/10^-5)

(1.29)*(10^3)

1288 times greater

The value of x = 1/M-1 , x = -1/M+1

What is Graph?

The graph of a function f is the set of ordered pairs where "displaystyle f(x)=y" exists. In the common scenario when x and f(x) are real integers, these pairings represent Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane.

M(x) = |x + 1|

|x + 1| = M(x)

x + 1 = M(x)

x + 1 = -M(x)

Adding (-x) both side

x + 1 + (- x) = M(x) + (- x)

x + 1 + (- x) = -M(x) + (- x)

x + 1 - x = M(x) - x

x + 1 - x = -M(x) - x

1 = M(x) - x

1  = -M(x) - x

M(x) - x = 1

-M(x) - x  = 1

x(M-1)  = 1

x(-M-1)  = 1

Dividing both side with (M - 1) and (-M - 1)

x(M-1)/(M - 1)   = 1/(M - 1)

x(-M-1)/(-M - 1)  = 1 /(-M - 1)

x = 1/(M - 1)

x = 1/(-M - 1)

Hence, x = 1/M-1 , x = -1/M+1

To learn more about Graph click on the link

https://brainly.com/question/4025726

#SPJ9

Option C gives the graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Choice C provides a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

To know more about graph,

https://brainly.com/question/17267403?referrer=searchResults

#SPJ13

Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer: 0.125

Step-by-step explanation:

1 1/4 is equal to 5/4

5/4 is equal to 1.25

then you would do 1.25 divided by 10

once you do that you would get your answer of 0.125!

Answer:

11/4÷10 =

11/4 ×1/10=

11/40=

0.275

Step-by-step explanation:

you can ask questions for clarification

It took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.

The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.

Given is Davin who needs 1 3/4 hours to get to his aunt's house. However, due to the labor day traffic this year it took him 3 1/5 years.

We have to find the difference between the time span Davin took to reach his aunt's house.

Time taken by Davin without the labor day traffic = T[N] = 1 3/4 = 7/4 hours

Time taken by Davin with the labor day traffic = T[L] = 3 1/5 = 16/5 hours

Difference in time spans = T[D] = T[L] - T[N]

T[D] = 16/5 - 7/4

T[D] = 3.2 - 1.75

T[D] = 1.45 = 1 + 0.45

T[D] = 1 [tex]\frac{3}{4}[/tex] hours  

Davin took 1 [tex]\frac{3}{4}[/tex] hours more.

Therefore, it took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.

To solve more questions on unitary method, visit the link below-

https://brainly.com/question/13659834

#SPJ1