Classify the isometry.

a) glide reflection
b) reflection
c) rotation
d) translation

Classify The Isometry.a) Glide Reflectionb) Reflectionc) Rotationd) Translation

Answers

Answer 1

Answer:

A. glide reflection

Step-by-step explanation:

This is a glide reflection since the figure has been both reflected over a line and transported downwards.

Answer 2

Answer:

a) glide reflection

Step-by-step explanation:

An isometry is a transformation of a figure in the plane that preserves lenght, it could be reflections, rotations, or translations, in the figure you can se what is called a glide reflection, which is a reflection of the figure over a line, and then a translation of the same figure.


Related Questions

Find the area please

Answers

For this case we have that by definition, the area of a trapezoid is given by:[tex]A = \frac {(B + b) * h} {2}[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

According to the data we have:

[tex]B = 10ft\\b = 5ft\\h = 4ft[/tex]

Substituting:

[tex]A = \frac {(10 + 5) * 4} {2}\\A = \frac {15 * 4} {2}\\A = \frac {60} {2}\\A = 30[/tex]

So, the area of the figure is [tex]30 \ ft ^ 2[/tex]

ANswer:

Option D

Answer:

D 30 ft^2

Step-by-step explanation:

This figure is a trapezoid

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h  where b1 and b2 are the lengths of the top and bottom

A = 1/2( 10+5) * 4

   = 1/2 (15)*4

   = 1/2(60)

   = 30 ft^2

Find the slope of the line that passes through the points (2, 4) and (6, 9).

Answers

Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (6, 9)

m = [tex]\frac{9-4}{6-2}[/tex] = [tex]\frac{5}{4}[/tex]

Somebody help and explain!!!

Answers

Answer: The midpoint of segment PQ is the number 2.5

note: 2.5 as a fraction is 5/2; as a mixed number 2.5 converts to 2&1/2

============================================================

Explanation:

Apply the midpoint formula to get the midpoint of -8 and 6

We simply add up the values and divide by 2 and we get (-8+6)/2 = -2/2 = -1

So point Q is at -1 on the number line, which is exactly halfway from R to P

Focus on just points P and Q now. Apply the midpoint formula again

Q = -1

P = 6

(Q+P)/2 = (-1+6)/2 = 5/2 = 2.5

So the midpoint of segment PQ is 2.5

The decimal 2.5 can be written as the mixed number 2&1/2, showing that this new point is exactly halfway between 2 and 3.

Identify the "c" value of the following quadratic equation given below.
-8 = 2(x + 9)^2

Answers

[tex]\bf -8=2(x+9)^2\implies -8=2(\stackrel{\mathbb{F~O~I~L}}{x^2+18x+81})\implies \cfrac{-8}{2}=x^2+18x+81 \\\\\\ -4=x^2+18x+81\implies 0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{\boxed{+85}}[/tex]

48:15
The function f(x) = (x - 4)(x - 2) is shown
What is the range of the function?
O
O
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1

Answers

Answer:

all numbers greater than or equal to -1

Step-by-step explanation:

Let's find the vertex.

Since the function is in factored form, I'm going to find the zeros.

The average of the zeros will give me the x-coordinate of the vertex.

I can then find the y-coordinate of the vertex by using the equation

y=(x-4)(x-2).

Also the parabola is open up since the coefficient of x^2 is positive (or 1 in this case).

So the range has something to do with the y's. It is where the function exist for the y-values.

So the range for this one since the parabola is open up will be of the form

[y-coordinate of vertex , infinity).

So let's begin.

The zeros can found by solving (x-4)(x-2)=0.

This means we need to solve both x-4=0 and x-2=0.

x-4=0 gives us x=4

x-2=0 gives us x=2

Now the average of our x-intercepts (or zeros) is (4+2)/2=6/2=3.

So the x-coordinate of the vertex is 3. To find the y-coordinate of the vertex we are going to use y=(x-4)(x-2) where x=3.

Plug in:  y=(3-4)(3-2)=(-1)(1)=-1.

So the range is [tex][-1,\infty)[/tex]

or all numbers greater than or equal to -1

Answer:

all real numbers greater then or equal to -1

Step-by-step explanation:

X=2
X=5
X=2, x=5
No solution

Answers

Answer:

The answer is C. x=2, x=-5

Step-by-step explanation:

Edge 2021

The solutions are 2 and -5.

Option C is the correct answer.

What is a solution?

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

[tex]12^{x^2 + 5x - 4}[/tex] = [tex]12^{2x + 6}[/tex]

This means,

Since both sides' base is the same.

x² + 5x - 4 = 2x + 6

x² + 5x - 2x - 4 - 6 = 0

x² + 3x - 10 = 0

Solve for x.

x² + 3x - 10 = 0

x² + (5 - 2)x - 10 = 0

x² + 5x - 2x - 10 = 0

x(x + 5) - 2(x + 5) = 0

(x + 5)(x - 2) = 0

x - 2 = 0 and x + 5 = 0

x = 2 and x = -5

Now,

The solutions are 2 and -5.

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The school track has eight lanes. Each lane is 1.25 meters wide. The arc at each end of the track is 180. The distance of the home straight and the radii for the arcs in the 1st 4 lanes are given.

S=85m

r1=36.5m

r2=37.75m

r3=39m

r4=40.25m


Part one: Find the radii of lanes 5 through 8 of the track. Show your work.


Part two: If Max ran around lane one, how far did he run? Show your work and explain your solution.


Part three: Max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. Show your work and round to the hundredths.


Part 4: Based on your lane choices in part three, what was the total distance Max ran in the three laps around the track?

Answers

Answer:

Part one: r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25  

Part two: Max ran 399.34 m in lane one

Part three: The distance in lanes 3 and 7 are 415.04 m and 446.46 m

Part four: Max ran in the three laps 1260.84 m around the track

Step-by-step explanation:

* lets explain how to solve the problem

- The school track has eight lanes

- Each lane is 1.25 meters wide

- The arc at each end of the track is 180° , that means the arc at each

 end is a semi-circle

- The distance of the home straight for all lanes is 85 m

- The radius of the first lane is 36.5 m

∵ The width of each lane is 1.25

∴ The radius of the second lane = 36.5 + 1.25 = 37.75

- That means the radius of each lane increased by 1.25 then the

  previous lane

The radius of each lane = the radius of the previous lane + 1.25

# Part one:

∵ The radius of the 4 lane is 40.25

∴ The radius of the 5th lane = 40.25 + 1.25 = 41.5 m

∴ The radius of the  6th lane = 41.5 + 1.25 = 42.75 m

∴ The radius of the  7th lane = 42.75 + 1.25 = 44 m

∴ The radius of the  8th lane = 44 + 1.25 = 45.25 m

* r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25  

- The length of each lane is the lengths of the 2 end arcs and  2

   home straight distance

∵ The arc is a semi-circle

∵ The length of the semi-circle is πr

∴ The length of the 2 arcs is 2πr

∵ The length of the home straight distance is 85 m

∴ The length of each lane = 2πr + 2 × 85

The length of each lane = 2πr + 170

# Part two:

- Max ran around lane one

∵ The radius of lane one = 36.5 m

∵ The distance of each lane = 2πr + 170

∴ The distance of lane one = 2π(36.5) + 170 = 399.34 m

* Max ran 399.34 m in lane one

# Part three:

- We will chose lanes 3 and 7

∵ The distance of each lane = 2πr + 170

∵ The radius of lane 3 = 39

∵ The radius of lane 7 is 44

∴ The distance of lane 3 = 2π(39) + 170 = 415.04 m

∴ The distance of lane 7 = 2π(44) + 170 = 446.46 m

* The distance in lanes 3 and 7 are 415.04 m and 446.46 m

# Part four:

- To find the total distance that Max ran in the 3 laps ad the answers

  in part two and part three

∵ Max ran 399.34 m in lane one

∵ Max ran 415.04 m in lane three

∵ Max ran 446.46 m in lane seven

∴ The total distance of the 3 lanes = 399.34 + 415.04 + 446.46

∴ The total distance of the 3 lanes = 1260.84

* Max ran in the three laps 1260.84 m around the track

Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a
year. Jack opens his account with $1,000, and Susie opens her account with $800.
X = number of years
The following functions represent the value of the savings accounts in x years
Jack's savings account: f(x) = 1000(1.015)*
Susie's savings account: g(x) = 800(1.015)
Which function represents the total amount Jack and Susie will save in x years?
200(1.015)
1800(1.015)
1800(1.015)2
1800(1.030)

Answers

Answer:

[tex]1,800(1.015)^{x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=1,000(1.015)^{x}[/tex]

[tex]g(x)=800(1.015)^{x}[/tex]

we know that

To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)

so

[tex]f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}[/tex]

[tex]f(x)+g(x)=[1,000+800](1.015)^{x}[/tex]

[tex]f(x)+g(x)=1,800(1.015)^{x}[/tex]

Answer: 1,800(1.015)^{x}

Step-by-step explanation:

we have

f(x)=1,000(1.015)^{x}

g(x)=800(1.015)^{x}

we know that

To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)

so

f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}

f(x)+g(x)=[1,000+800](1.015)^{x}

f(x)+g(x)=1,800(1.015)^{x}

a direct variation function contains the points (2,14) and (4,28). which equation represents the function?​

Answers

[tex]\bf \begin{array}{ccll} x&y\\ \cline{1-2}\\ 2&\stackrel{2\cdot 7}{14}\\\\ 4&\stackrel{4\cdot 7}{28}\\\\ x&x\cdot 7 \end{array}~\hspace{7em}y=7x[/tex]

Answer:

y = 7x

Step-by-step explanation:

A direct variation is of the form

y = kx where k is the constant of variation

We have the point (2,14)

Substituting this in

14 = k*2

Divide each side by 2

14/2 =2k/2

7 =k

The direct variation equation is y = 7x

Find the value of m

Answers

Answer:

Option C. 32°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the measure of arc AB

we know that

The semi-inscribed angle measures half that of the arc comprising

so

74°=(1/2)[arc AB]

arc AB=(2)(74°)=148°

step 2

Find the measure of arc BCDA

we know that

arc BCDA+arc AB=360°

substitute the given value

arc BCDA+148°=360°

arc BCDA=360°-148°=212°

step 3

find the measure of angle m

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

m=(1/2)[arc BCDA-arc AB]

substitute

m=(1/2)[212°-148°]=32°

(2 3/4) to the second power

Answers

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 2^{\frac{3}{4}} \right)^2\implies 2^{\frac{3}{4}\cdot 2}\implies 2^{\frac{3}{2}}\implies \sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}[/tex]

a jar contains 30 red marbles 50 blue marbles and 20 white marbles if you select one marble from the jar at random what is the theoretical probability of getting a red marble

Answers

Answer:

3/10

Step-by-step explanation:

P(red) = red marbles / total marbles

We have 30 red marbles

total marbles = (20 white+ 50 blue+ 30 red) = 100 marbles

P(red) = 30/100 = 3/10

Answer:

0.30 or 30%.

Step-by-step explanation:

This = number of re marbles / total number of marbles

= 30 / (30+50+20)

= 30 / 100

= 0.30.

200 pills , 1 pill a day , how many months is this?​

Answers

Answer:

Around 6 - 7 months.

Step-by-step explanation:

Most months have varied number of days. If they were 30 days in each month, there would be a little less than 7 months that it would take to complete the pills.

Which function describes this graph?
Α. y = x^2 - 2x +6
Β. y = (x-2)(x – 6)
C. y = (x - 4)(x - 4)
D. y = x^2 + 8x + 12​

Answers

Answer:

D.  x^2 + 8x + 12.

Step-by-step explanation:

The zeroes of the graph ( the x -intercepts) are -2 and -6  so we can write the function as (x + 2)(x + 6) = x^2 + 8x + 12.

The function y = x² + 8x + 12​ describes this graph. This is obtained by using equation of parabola at the origin and transforming the graph to the required position as in the question by using rules of transformation of linear function.

What are the Rules of Transformation of Linear Function?

Rules of transformation of linear function are

f(x)+b - function is shifted b units upwardf(x)-b - function is shifted b units downwardf(x+b) - function is shifted b units to the leftf(x-b) - function is shifted b units to the right-f(x) - function is reflected over x-axisf(-x) - function is reflected over y-axis

What is the required function?

Equation of parabola at the origin is y = x²

First the graph is shifted left 4 units

By the transformation we can rewrite the function in f(x+b) form;

that is ⇒ y = (x+4)² ⇒ y = x² + 8x +16

Next the graph is shifted 4 units downward

By the transformation we can rewrite the function in f(x)-b form;

that is ⇒ y = x² + 8x +16 - 4 ⇒ y = x² + 8x +12

This is the required function.

Hence the function y = x² + 8x + 12​ describes this graph.

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what is y=2x^2-32x+56 rewritten in the form of y=a(x-h)^2+k ? and what is the x-coordianate of the mininum?​

Answers

Answer:

[tex]\large\boxed{y=2(x-8)^2-72}\\\boxed{minimum\ is\ -72\ for\ x=8}[/tex]

Step-by-step explanation:

[tex]y=a(x-h)^2+k[/tex]

It's the vertex form of a quadratic equation of [tex]y=ax^2+bx+c[/tex]

The vertex is at (h, k).

k is minimum or maximum for value of h.

[tex]h=\dfrac{-b}{2a}[/tex]

k - its value of y for x = h.

We have

[tex]y=2x^2-32x+56\\\\a=2,\ b=-32,\ c=56[/tex]

[tex]h=\dfrac{-(-32)}{2(2)}=\dfrac{32}{4}=8[/tex]

[tex]k=2(8^2)-32(8)+56=2(64)-256+56=128-256+56=-72[/tex

A rectangle is 9 ft long and 40 in. wide. What is its
area in square feet?

Answers

Answer:

29.97 square feet

Step-by-step explanation:

Given

The length of rectangle = 9 ft

The width of rectangle = 40 in

We have to bring the length and width in same unit. As the area is required in square feet so we will convert width in feet

The width will be divided by 12 to be onverted into feet

So,

Width = 40/12 = 3.33 feet

Now

Area = Length * width

= 9 * 3.33

= 29.97 square feet ..

Answer:

Area of rectangle = 30 square feet

Step-by-step explanation:

We are given that a rectangle is 9 feet long and 40 inches wide and we are to find its area in square feet.

For this, we will covert the width of the rectangle to feet and then find the area.

We know that:

[tex]\frac{1 foot}{x} =\frac{12 inches}{40}\\x=3.3 feet[/tex]

So width in feet is 3.3 feet.

Area of rectangle = [tex]9 \times 3.33[/tex] = 30 square feet

Mr. Ford drove 224 miles in 4 hours. At what rate of speed did he drive?

Mr. Liston bought lunch for $12.80. He gave the waiter a tip of 15%. How much money did the waiter receive?
A: $1.28
B: $1.92
C: $2.56
D: $3.84

PLEASE SHOW WORK!!

Answers

Part A) The rate of speed is 56 miles/ hour and

Part B) The money that waiter receive is $1.92.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Part A:

Distance traveled by Mr.Ford = 224 miles

Time taken by  Mr.Ford = 4 hours

Rate of speed can be found by

[tex]Speed = \frac{Distance}{time}[/tex]

⇒ [tex]Speed = \frac{224}{4}[/tex]

⇒ [tex]Speed = 56[/tex]

Thus the rate of speed is 56 miles/ hour

Part B:

Cost of lunch bought by Mr.Liston = $12.80

Mr.Liston gave the waiter a tip = 15%

⇒ [tex]15\% = 0.15[/tex]

Now, the money that waiter receive is

⇒ [tex]12.80(0.15)[/tex]

⇒ [tex]1.92[/tex]

Thus the money that waiter receive is $1.92.

Hence we conclude that A) the rate of speed is 56 miles/ hour and B) the money that waiter receive is $1.92.

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The system of equations y= 1/4x-5 and y= -1/2x-3 is shown on the graph below.

Which statement is true about the solution to the system of equations?
The x-value is between 2 and 3, and the y-value is between –4 and –5.
The x-value is between –4 and –5, and the y-value is between 2 and 3.
The x-value is between –2 and –3, and the y-value is between 4 and 5.
The x-value is between 4 and 5, and the y-value is between –2 and –3.

Answers

Answer:

the first one x value is between 2 and 3, and the y value is between -4 and -5

Step-by-step explanation:

Multiply the first equation for 4 and second equation by 3

y=1/4x-5 (x4) Then, 4y= x-20

y=-1/2x-3 (x3) Then, 2y=-x-6

From the fist equation we organize the equation as y= (x-20)/4

and we add this value of y on the second equation

2((x-20)/4)=-x-6  the number 4 goes to the other side multiply x-6 and number 2 on the other side multiply x-20

Then, 2x -40= -4x-24 then we put x in one side and numbers on the other

2x+4x = -24+40

Then. 6x = 16 then x= 2.66  => x is between 2 and 3

Then this value of X goes to the first equation y = (2.66-20 )/ 4

y= - 4.33 the value y is between -4 and -5

Answer:

A: The x-value is between 2 and 3, and the y-value is between –4 and –5.

Step-by-step explanation:

Abby has an exercise wheel with and 11 inches diameterFor her guinea pig. What is the circumference of the exercise wheel to the nearest whole number? Use 3.14 for

Answers

The formula for circumference of a circle is:

Circumference = PI x diameter.

Diameter is 11 inches.

Circumference = 11 x 3.14 = 34.54 inches.

.54 is greater then .5, so you would round up.

The answer would be 35 inches.

Island A is 160 miles from island B. A ship captain travels 220 miles from island A and then finds that he is off course and 200 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

Answers

Answer:

=135.53°

Step-by-step explanation:

The bearing that the captain should turn is the angle difference between the two islands from the position of the ship.

Let C be the position of the ship, then

AB is c=160

AC is b=220

BC is a=200

We use the cosine rule as follows:

c²=a²+b²-2ab Cos C

160²=200²+220²-2×200×220 Cos C

25600=88400-88000Cos C

88000 Cos C=88400-25600

88000Cos C=62800

Divide both sides by 88000.

Cos C=62800/88000

=0.7136

C=44.47°

He should turn (180°-44.47°)=135.53°

Answer:

135.53

Step-by-step explanation:

I got it correct on founders edtell

The odds against Carl beating his friend in a round of golf are 7:5. Find the probability that carl will beat his friend.

Answers

Final answer:

In a game, the odds against Carl winning are 7:5. For every 7 games he loses, there are 5 games he wins. Therefore, the probability of Carl winning is 5 divided by the total of possible outcomes (5+7), which equals to 5/12.

Explanation:

The subject of this question is Mathematics, specifically probability. The odds against Carl beating his friend in a round of golf are 7:5. To calculate the probability of Carl winning, we have to understand that the odds of an event occurring are the ratio of the possibility of the event happening to the possibility of the event not happening. If the odds are 7:5 against Carl winning, that means for every 7 games Carl loses, there are 5 games he wins.

To calculate the probability of Carl winning, we take the number of wins and divide it by the total number of outcomes. So the probability that Carl will beat his friend would be 5/(7+5) = 5/12.

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The area rectangle,a=1xw is represented by the expression 24x6y15. Which could be the dimensions of the rectangle

Answers

Final answer:

The dimensions of the rectangle are 24x and 90y.

Explanation:

The area of a rectangle is represented by the expression 24x6y15. To determine the dimensions of the rectangle, we need to factorize the expression. Factoring out the common factors, we have:

24x6y15 = 2 × 2 × 2 × 3 × x × (2 × 3) × y × (5 × 3)

From this, we can see that the dimensions of the rectangle are:

Length = 2 × 2 × 2 × x × 3 = 24x

Width = 2 × y × 3 × (5 × 3) = 90y

Before taxes and other deductions, your pay for last week was $230.40. You worked 30 hours. How much were you paid per hour?

Answers

Answer:

[tex]\large\boxed{7.68\,\text{per hour}}[/tex]

Step-by-step explanation:

In this question, we're trying to find how much you made per hour.

We can answer this question using the information given in the question.

Important information:

You were paid $230.40 last weekWorked for 30 hours

With the information above, we can solve the question.

We would simply divide 230.40 by 30 in order to find how much you made per hour.

Lets divide:

[tex]230.40\div30=7.68[/tex]

When you're done dividing, you should get 7.68

This means that you made 7.68 per hour.

I hope this helped you out.Good luck on your academics.Have a fantastic day!

For this case you must find the payment per hour, for this we must make a division. We divide the payment of the week between hours worked, then:

[tex]\frac {230.40} {30} = 7.68[/tex]

Thus, the hourly payment was $7.68

Asnwer:

$7.68

If Sarah is 24 years younger than her mother and if the um of their ages is 68, how old is Sarah? x best represents 1. Sarah's age 2. the mother's age. x-24 best represents 1.sarah's age 2. mother's age

Answers

Answer:

22

Sarah's age is best represented by M-24 or as the question used x-24 where the mother's age is best represented by M where the question used x.

Step-by-step explanation:

We are given that Sarah (S) is 24 years younger than her mother (M).

So S=M-24.

We are given that Sarah (S) and her mom's age adds up to 68.

So S+M=68.

We are going to solve this system by substitution since one of the variables is solved for. I'm going to plug first equation into second like so:

(M-24)+M=68   I replaced S with M-24.

M+M-24=68      Put like terms together.

2M-24  =68       Combined the like terms.

2M      =  92      Added 24 on both sides.

 M      = 92/2    Divided 2 on both sides.

 M      = 46        Simplified the 92/2.

So her mother's age is 46.

We know that S=M-24 so S=46-24=22.

Sarah is 22 years old.

Consider the following system of equations:
-1/3x^2 = -5/6 + 1/3y^2 and
5y^2 = 25/2 - 5x^2
How many solutions does the system have?

Answers

Answer:

The system has infinitely solutions

Step-by-step explanation:

we have

[tex]-\frac{1}{3}x^{2}=-\frac{5}{6}+\frac{1}{3}y^{2}[/tex]

[tex]\frac{1}{3}x^{2}+\frac{1}{3}y^{2}=\frac{5}{6}[/tex]

Multiply by 3 both sides

[tex]x^{2}+y^{2}=\frac{5}{2}[/tex] ----> equation A

The equation A is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]

and

[tex]5y^{2} =\frac{25}{2}-5x^{2}[/tex]

[tex]5x^{2}+5y^{2} =\frac{25}{2}[/tex]

Divide by 5 both sides

[tex]x^{2}+y^{2} =\frac{5}{2}[/tex] ----> equation B

The equation B is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]

Equation A and Equation B are the same

Therefore

The system has infinitely solutions

Answer:

infinitely many

Step-by-step explanation:

just took the assignment for

How can you find the magnitude of a vector , where the horizontal change is x and the vertical change is y?

Answers

Final answer:

The magnitude of a vector is found by applying the Pythagorean theorem to the horizontal and vertical changes. The formula to calculate the magnitude is given by A = sqrt(x^2 + y^2) where x and y are the vector’s horizontal and vertical displacements respectively.

Explanation:

The magnitude of a vector is calculated by forming a right triangle using the horizontal (x) and vertical (y) changes as the triangle's legs. The magnitude of the vector is the hypotenuse of this right triangle. This relationship is captured by the Pythagorean Theorem which states that the square of the hypotenuse (i.e. the magnitude of vector A) is equal to the sum of the squares of the other two sides (the vector's components or changes).

So, the formula for finding the magnitude of the vector (A) is:

A = sqrt(x^2 + y^2)

Where x is the horizontal displacement or change, and y is the vertical displacement or change.

For example, if you have a vector with an x component of 3 and y component of 4, you could compute the magnitude as follows:

A = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = 5

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Final answer:

To find the magnitude of a vector with horizontal change x and vertical change y, use the Pythagorean theorem: |v| = sqrt(x^2 + y^2).

Explanation:

To find the magnitude of a vector with horizontal change x and vertical change y, you can use the Pythagorean theorem. The magnitude (|v|) of the vector is given by the square root of the sum of the squares of the horizontal and vertical changes:

|v| = sqrt(x^2 + y^2)

For example, if x = 3 and y = 4, the magnitude of the vector would be:

|v| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

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13. For what value of b would the following system of equations have an infinite number of solutions?
9x + 12y = 21
6x + 8y = 7b


Please explain and show steps :)

Answers

Answer:

b=2

Step-by-step explanation:

we have

9x+12y=21 -----> equation A

6x+8y=7b ----> equation B

we know that

If the system of equations have an infinite number of solutions then the equation A must be equal to the equation B

Multiply equation B by 1.5 both sides

1.5*[6x+8y[=7b*1.5

9x+12y=10.5b ----> equation C

Compare equation A and equation C

9x+12y=21 -----> equation A

9x+12y=10.5b ----> equation C

For the equations to be equal it must be fulfilled that

21=10.5b

solve for b

b=21/10.5

b=2

A class of 25 students took a spelling test.

Two students scored 90 each
students scored 95 on each test, ten students scored 90 on each test, three students score
80 on each test and one student scored 70.

What is the average score of the spelling test rounded to one decimal place?​

Answers

Answer:

90.6

Step-by-step explanation:

I think you have the first line incorrect. You show below that 10 students scored 90, so the first line is that 2 students scored 100, not 90. The line with the score of 90 is missing the number of students, but we can find it out. Call that number x for now.

Two students scored 100 each                                2

x students scored 95 on each test                         x

ten students scored 90 on each test                    10

three students score  80 on each test                    3

and one student scored 70                                 +   1

                                                                            x + 16

There are x + 16 students accounted for. The total number of students is 25.

x + 16 = 25

x = 9

9 students scored 95 on each test.

Now add up all the points scored by all students.

Two students scored 100 each  (2 * 90)                200

9 students scored 95 on each test (9 * 95)          855

ten students scored 90 on each test (10 * 90)     900

three students score  80 on each test (3 * 80)      240

and one student scored 70 (1 * 70)                      +  70

Sum of all points:                                                  2245

Now we find the average grade by dividing the sum of the points by the number of students.

average = sum/number = 2265/25 = 90.6

Find the value of x if a linear function goes through the following points and has the following slope: (x,2), (-4,6), m=3

Answers

Answer:

X=-16/3 or 5.33

Step-by-step explanation:

The formula is y=mx+c

Substitute in values for gradient

6=-4×3+c

C=18

Y=3x+18

Substitute to find x

2=3x+18

-16=3x

X=-16/3

The slope of a line is the change in the y values over the corresponding x values.

The value of x, that makes the points a linear function is -16/3

Given that:

[tex]m = 3[/tex]

[tex](x_1,y_1) = (x,2)[/tex]

[tex](x_2,y_2) = (-4,6)[/tex]

The slope (m) of a line is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]3 = \frac{6-2}{-4-x}[/tex]

[tex]3 = \frac{4}{-4-x}[/tex]

Cross multiply

[tex]3 \times (-4 -x) = 4[/tex]

Divide by 3

[tex]-4 -x = \frac 43[/tex]

Add 4 to both sides

[tex]-x = \frac 43 + 4[/tex]

Take LCM

[tex]-x = \frac{4 + 12}3[/tex]

[tex]-x = \frac{16}3[/tex]

Divide by -1

[tex]x =-\frac{16}3[/tex]

Hence, the value of x is -16/3

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What is the solution to this equation?
X- 17 = -5

Answers

x-17=-5
Add 17 to both sides
x=12

Hey there!

Answer:

X = 12

Step-by-step explanation:

Given,

X - 17 = - 5

X = -5 + 17

X = 12

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