Red letters and blue letters are used in a game. Some of the letters are X. All the other letters are Y. X Y X Y The ratio of the number of red letters to the number of blue letters is 2:5 The ratio of the number of red Xs to the number of red Ys is 1: 3 The ratio of the number of blue Xs to the number of blue Ys is 3:1 Work out what fraction of all the letters are Xs.​

Answer:

[tex](x-5)^2=4(y+2)[/tex]

Please note that alternative forms of this equation (vertex and standard) are in the explanation.

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

Given:

Therefore:

Calculate p:

[tex]\implies -2+p=-1[/tex]

[tex]\implies p=-1+2[/tex]

[tex]\implies p=1[/tex]

Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:

[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]

[tex]\implies (x-5)^2=4(y+2)[/tex]

In vertex form:

[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]

In ax² + bx + c form:

[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]

This situation can be expressed by the equation [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.

What is an equation?

Let the weekly allowance of anna be = X

Allowance spent on movies= X/2

The extra money from the car wash = 8

Allowance retained with anna = 18

This situation can be expressed by the equation,

[tex]x-\frac{x}{2} +8=18[/tex]

Solving the above equation, we get,

[tex]\frac{x+16}{2} =18[/tex]

x+16=36

x=20

Therefore, her weekly allowance is $20.

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Answer: 43.47517

Step-by-step explanation:

Considering orders of magnitude, we see that Option 2 is the only reasonable answer.

Answer:

a = h/2 would be the answer.

Step;-

Find slope:-

m = rise/run = (16-8)/(8-4) = 8/4 = 2

Now,

y = mx + b

or, 8 = 2(4) + b

so, b = 0

So,

y = mx + b

or, h = 2a + 0

so, h = 2a

hence,a = h/2.

The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age [tex]a = \frac{h}{2}[/tex]

Hello!

First, let's analyze these two quadrilaterals:

• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.

Let's try to solve it using the lines AB and AB':

• The measurement of the ,line AB is 14 units,.

• The measurement of the ,line AB' is 7 units,.

Knowing it, let's write the scale factor as:

Answer: alternative D.

The corn's height when the fertilizer was applied is 13 centimeters and it grows at a rate of 13 centimeters each day.

The equation that is given is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

A linear equation increases or decreases at a constant rate. When a linear equation is drawn on a graph, it is a straight line that curves either upward or downward.

A linear equation usually has this form y = mx + b

Where:

H = 13 + 13t

Where:

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Graph f(x)=14.

Plot each graph on the same coordinate system.

f(x)=14x

image of graph

Rewriting the words mathematically:

Next we will write in standard decimal form:

The range of the function is -1 ≤ y ≤ 2

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The ordered pair is given as

{(−4,2), (−2,1), (0,0), (2,−1)}

Rewrite as

(x, y) = {(−4,2), (−2,1), (0,0), (2,−1)}

Remove the y values

So, we have

y = {2, 1, 0,−1}

Express as an inequality

-1 ≤ y ≤ 2

Hence, the range is -1 ≤ y ≤ 2

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The entrance fees is 13 dollars charges by the paintball court.

Let us assume that the entrance fees is $X and the actual cost of using one ball is $Y charged by the paintball court.

According to one situation,

Total cost of using to ball = Cost of entry fees + actual cost of using two ball.

So, we can write,

X + 2Y = 18

Let us say that this is our equation 1,

Also, it is provided,

Total cost of using 4 balls = cost of entry fees + actual cost of using four balls.

X + 4Y = 23

Let us say that this is our equation 2,

Both of our equations are linear equations with two variables,

Now, substracting equation 1 from equation 2,

X + 4Y -(X + 2Y) = 23 - 18

2Y = 5

Y = $2.5.

Putting the value of Y = 2.5 in equation 1,

X + 2(2.5) = 18

X = 18 - 5

X = $13.

So, the entry fees is 13 dollars.

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Step-by-step explanation:

(2x² + 3x+8) (x²-x-4)

= (2x² + 3x+8) (x² +-x²+-4)

= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)

= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32

=2x⁴ + x³ - 3x² - 20x - 32

The required value of x is -3.6 which is determined by the substitute that equals the vertical angles.

When two lines intersect at a location, vertical angles are generated. They are always equal to each other.

Since ∠A and ∠B are vertical angles then they are congruent, thus

⇒ (x - 29) = (6x - 11)

Subtract 6x from both sides of the above equation,

⇒ x - 29 - 6x = 6x - 11 -6x

⇒ -5x - 29 = - 11

Add 29 to both sides of the equation,

⇒ -5x - 29 + 29 = - 11 + 29

⇒ -5x = 18

Divided by 5 to both sides of the equation,

⇒ x = - 18/5

⇒ x = - 3.6

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Using it's concepts, the average speed and the average velocity are given as follows:

The average speed is given by the quotient between the total distance traveled and the time taken, that is:

Average speed = total distance/time

In this problem, the total distance is of 60 miles(30 miles west + 30 miles south), in a time of 1.5 hours(1 hour west and 0.5 hours south), hence the average speed is given as follows:

Average speed = 60/1.5 = 40 miles per hour.

The average velocity is given by the quotient between the displacement and the time taken, that is:

Average velocity = displacement/time

The displacement is the difference between the final position and the initial position. Since the person got back to the start, finish = start, hence the displacement is of zero, as is the average velocity.

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Answer:

16.4

Step-by-step explanation:

The time is irrelevant to the problem

fraction42 *20.5= 16.4

Hope this helps

1st step. Calculate the area of the parallelogram

We can use the following formula:

where,

base, b = 9 km

height, h = 5 km

Therefore,

The area of the parallelogram is 45 km^2

2nd step. Calculate the area of the triangle

Let's use this formula:

where,

base, b = 6 km

height, h = 3 km

Therefore,

The area of the triangle is 9 km^2

3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle

Answer: the area of the parallelogram is 5 times greater than the area of the triangle.

Answer:

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

Step-by-step explanation:

We have to find the GCF (Greatest common factor) of 135 , 225 and 315.

          135 = 5 * 3 * 3 * 3 = 45 * 3

          225 =  5 * 5 * 3 * 3 = 45 * 5

          315 =  5 * 3 * 3 * 7 =  45 * 7

GCF = 5 * 9 = 45

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

It's important to know that reciprocals are the multiplicative inverse of a numbers, for example, the reciprocal of 7 is 1/7.

As you can observe, using reciprocals would help to solve equations when we have to get rid off a factor. For example, if we have the equations 4x = 8, we would use the reciprocal of 4 to isolate the variable x: (4x)/4 = 8/4 then x = 2.

Samuel's order will ultimately cost $39.84.

One DVD Samuel purchased cost $9.96.

He purchased four DVDs in total.

as a result, his total outlay will be 4 * 9.96 = $39.84.

The 7.75% sales tax that must be paid is disclosed to us.

Adding 7.75% to $39.84 yields

39.84 x 7.75/(100) (100)

= $3.0876

Consequently, the total amount of tax due is $3.0876.

Using 25% of 39.84 to calculate a 25% discount,

39.84 x 25/100

= 996/100

=$9.96

Consequently, the total discount on the total of $39.84 will be $9.96.

as a result, the updated purchase price will be,

39.84-9.96

=$29.88

adding the tax to the updated price,

9.96+29.88

= $39.84

Consequently, Samuel's order will ultimately cost $39.84.

One must compute percentage in order to determine the proportion of a whole that is stated in terms of 100. A percentage can be determined using one of two methods:

using the unitary method.

by changing the fraction's denominator to 100.

It should be noted that the second method of percentage computation is not used when the denominator is not a factor of 100. In these circumstances, we make use of the unitary approach.

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All pairs of parallel segments are given below.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Given,

a) Line segment = AC and FD

Parallel = AC ║FD

b) Line segment = AE and BD

Parallel = AE ║BD

c) Line segment = EC and FB

Parallel = EC ║FB

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The probability of selecting two students has 10 ways

Total number of students = 5

Only two students can be selected for the conference who are equally qualified.

The probability that the first two students selected alphabetically is derived from the combinations.

Therefore, the final probability for selecting the students randomly is,

x = ⁵C₂

x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]

x = 10

Hence, the probability of selecting two students has 10 ways.

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Answer:

I would say its 4, the eighth to tenth hour.

Answer: 18: 18, 36, 54, 72, 90
20: 20, 40, 60, 80, 100
16: 16, 32, 48, 64, 80

32: 32, 64, 96, 128, 160

Step-by-step explanation:

multiply each number by 1 2 3 4 5 respectivly to get the answer.

The total distance from his highest point to his lowest point is 21.8 feet.

Height H climbed by Zack and Zane is 14.6 feet.

The depth D underwater that Zack got down to is 6.8 feet.

The distance between the highest and the lowest point can be found by assuming the coordinates axis.

Let us assume the origin is on the water surface,

So, going by this logic, highest point is at +14.6 feet.

The lowest point is at -6.8 feet.

The distance L between lowest and highest point is,

L = H - D

L = 14.6 -(-6.8) feet

L = (14.6 + 6.8) feet

L = 21.8 feet

So the distance L is 21.8 feets.

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Considering the definition of perpendicular line, the equation of a line perpendicular to 8x−5y=−9 that passes through the point ​(−8​,3​) is y=-5/8x-2 .

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 8x-5y= -9. Expressed in the form y = mx + b, you get:

-5y= -9 - 8x

y= (-8x -9)÷ (-5)

y= 8/5x +9/5

The line has a slope of 8/5. If you multiply the slopes of two perpendicular lines, you get –1. In this case:

8/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (8/5)

slope perpendicular line= -5/8

So, the perpendicular line has a form of: y= -5/8x + b

The line passes through the point (-8, 3). Replacing in the expression for perpendicular line, you get:

3= -5/8× (-8) + b

3= 5 + b

3- 5 = b

-2= b

Finally, the equation of the perpendicular line is y= -5/8x -2 .

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Answer:

Answer down below!

Step-by-step explanation:

The correct answers are as follows:

Answer: 2nd, 3rd, 5th

Step-by-step explanation:

Solve the problem

1/2*1/2*1/2 = 1/1/8

1 * 8/1

8

Check each answer

1) -(1/2)^3

-(1/2*1/2*1/2)

-(1/8)

-1/8

No

2) 2^3

2 * 2 * 2

8

Yes

3) 1/1/2^3

[tex]\frac{1}{\frac{1}{2} *\frac{1}{2} *\frac{1}{2} }\\ \frac{1}{\frac{1}{8} }\\1 * \frac{8}{1} \\8[/tex]

Note: Flip fraction when dividing a fraction.

Yes

4) 1/8

1/8

No

5) 8

8

Yes

Answer:

i don't know if this is fully correct but I believe that the answer is both because both elements are used it this piece of art. one the art is in color. two it uses both horizontal and vertical lines.

Megan spent 2 1/12 hours dancing both yesterday and today

Megan is involved in a musical production

Yesterday, she practiced for 2 3/4 hours

Today she practiced for 3 1/2 hours

The first step is to calculate the total number of hours she spent at the practice

2 3/4 + 3 1/2

= 11/4 + 7/2

The LCM between both fractions is 4

11/4 + 7/2

11 + 14/4

= 25/4

Megan spent 25/4 hours yesterday and today practicing

Out of this 25/4 hours, she spent 1/3 hours dancing

Therefore the hours she spent dancing can be calculated as follows

= 25/4 × 1/3

= 25/12

= 2 1/12

Hence Megan spent 2 1/12 hours dancing yesterday and today

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