express the ratio in its simpilest form

4:2:2

Answer:

2

Step-by-step explanation:

Average rate of change of a function between x=a and x=b is:

[ f(b) − f(a) ] / (b − a)

On the interval 3 ≤ x ≤ 5:

[ f(5) − f(3) ] / (5 − 3)

[ (5²/4 − 5) − (3²/4 − 5) ] / (5 − 3)

(25/4 − 5 − 9/4 + 5) / (5 − 3)

(25/4 − 9/4) / (5 − 3)

(16/4) / 2

2

Final answer:

To find the dimensions of Bill's sand box, use the given constraints and solve for the width and length using a simple equation.

Explanation:

Bill's sand box dimensions:

Let the width be x.

Length = x + 2.

Given 20 feet of boards, 2x + 2(x + 2) = 20.

Solving the equation, x = 4 feet (width) and length = 6 feet.

Answer:

(x, y ) → (x + 6, y + 12 )

Step-by-step explanation:

We require to determine the horizontal and vertical shift to go from one of the points on the line to the corresponding point on the image

Consider point V with x- coordinate - 8 and y- coordinate - 2

The corresponding point is V'

with x- coordinate - 2 and y- coordinate 10

Thus V → V' is 6 units right in the horizontal direction and 12 units up in the vertical direction.

These are the same shifts for W → W'

Thus the translation rule is

(x, y ) → (x + 6, y + 12 )

Answer:

27 miles

Step-by-step explanation:

Find the rate or speed that Shawn hikes at. Find this reduced to lowest terms.

speed = distance / time

speed = 12 miles / 4h

speed = 3miles / h

Every hour, Shawn hikes 3 miles.

Multiply speed by time to find distance.

3mph X 9h = 27 miles

Therefore Shawn could hikes 27 miles in 9 hours.

Answer:

y=4x-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-12-8)/(-1-4)

m=-20/-5

m=4

y-8=4(x-4)

y=4x-16+8

y=4x-8

Answer:

Step-by-step explanation:

Answer:6 of her counters are yellow.

9-3=6

The requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Mateo has 6.5 cups of sugar.
Each batch requires 3/4 cup of sugar,
Batches of cookies can he make,
= total cups of sugar/ 1 beach requires cups of sugar

= 6.5 / [3/4]
= 8.67 batches of cookies can be made.

Thus, the requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.

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Given number is 369. The number 3 is made of 5 match sticks, 6 is made of 6 match sticks and 9 is also made of 6 match sticks.

Let us try the possibilities of moving 1 match stick to make the biggest number.

(a) If the left upper match stick from 9 is moving to right upper position of 6, then the number will be 383.

(b) If the left bottom match stick from 6 is moving to left bottom position of 9, then the number will be 358.

(c) If the right upper match stick from 9 is moving to right upper position of 6, then the number will be 385.

(d) If the right upper match stick from 9 is moving to left upper position of 3, then the number will be 965.

The above four trials are shown in the below attachment.

Among these four possibilities, 965 is the biggest number.

Answer:

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

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [a, b ] = [ - 2, 2 ], thus

f(b) = f(2) = [tex]\frac{1}{8}[/tex] × 2³ - 2² = 1 - 4 = - 3

f(a) = [tex]\frac{1}{8}[/tex] × (- 2)³ - (- 2)² = - 1 - 4 = - 5

average rate of change = [tex]\frac{-3-(-5)}{2-(-2)}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

The average rate of change of h over the interval −2≤x≤2 is 1/2.

Here,

The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.

We have to find, the average rate of change of h over the interval −2≤x≤2.

What is Average rate?

The  Average rate of change of function f( x ) in the close interval [a, b ]

is, [tex]\frac{f(a)-f (b)}{b-a}[/tex]

Now,

The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.

Hence, [tex]h(-2) = \frac{1}{8} *(-2)^{3} -( -2)^{2} = -5[/tex]

And, [tex]h(2) = \frac{1}{8} *(2)^{3} -( 2)^{2} = -3[/tex]

So, Average rate of change of function h(x) = [tex]\frac{-3-(-5)}{2-(-2)} = \frac{2}{4} = \frac{1}{2}[/tex]

The average rate of change of h over the interval −2≤x≤2 is 1/2.

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Answer:

Therefore the value of x is 8 unit.

Step-by-step explanation:

Given:

In Right Angle Triangle ABC

angle B = 90°

angle C = 30°

AB = 4

To Find:

AC = Hypotenuse = ?

Solution:

In Right Angle Triangle ABC Sine Identity we have

[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\[/tex]

Substituting the given values we get

[tex]\sin 30 = \frac{AB}{AC}[/tex]

[tex]\dfrac{1}{2} =\dfrac{4}{x}\\\\\therefore x=4\times 2=8\\\\\therefore x =8[/tex]

Therefore the value of x is 8 unit.

Answer:

154 small cubes.

Step-by-step explanation:

We are given the dimensions of the cuboid as 72 cm × 66 cm × 56 cm.

So, length of the cuboid, l = 72 cm

Breadth of the cuboid, b = 66 cm

Height of the cuboid, h = 56 cm

Capacity of cuboid = l × b × h = 72 × 66 × 56 = 266112 cm³

Now, we have to find the number of small cubes of side 12 cm each that can be placed in the given cuboid.

Now, length of each side of each small cube, s = 12 cm

Volume of each small cube = s³ = (12)³ = 12 × 12 × 12 = 1728 cm³

For calculating the number of small cubes that can be placed in the given cuboid, we will divide the capacity of given cuboid by volume of each small cube.

Required number of cubes = [tex]\frac{Capacity\; of\; cuboid}{volume\; of\; each\; small\; cube}[/tex]

⇒ Number of cubes = [tex]\frac{266112}{1728}=154[/tex]

∴ 154 small cubes each of side 12 cm can be placed inside the given cuboid of dimensions 72 cm × 66 cm × 56 cm.

The two numbers are 30 and 11

Solution:

Given that we have to separate the number 41 into two parts

Let the second number be "x"

Given that first number is eight more than twice the second number

first number = eight more than twice the second number

first number = 8 + twice the "x"

first number = 8 + 2x

So we can say first number added with second number ends up in 41

first number + second number = 41

8 + 2x + x = 41

8 + 3x = 41

3x = 41 - 8

3x = 33

x = 11

first number = 8 + 2x = 8 + 2(11) = 8 + 22 = 30

Thus the two numbers are 30 and 11

Answer:

42. Graph a

43. Not possible.

44. Graph e

45. Graph c

46. Graph b.

Step-by-step explanation:

42. 7x + 13 ≥ 55

⇒ x ≥ 6

So, it matches graph a.

43. 12x - 8 > 4(3x + 2)

⇒ 12x - 8 > 12x + 8

Hence, d. not possible.

44. [tex]\frac{x}{- 4} - 3 < - 1[/tex]

⇒ [tex]\frac{x}{- 4} < 2[/tex]

⇒ x > - 8

Hence, graph e matches.

45. - 4(- 2x + 3) ≤ 5 + 8x

⇒ 8x - 12 ≤ 5 + 8x

⇒ - 12 ≤ 5

This is true for all values of x, hence that matches graph c.

46. - 4(x + 3) > 8(x + 3)

⇒ - 4x - 12 > 8x + 24

⇒ 12x < - 36

⇒ x < - 3

Hence, graph b matches the situation. (Answer)

Answer:

110°

Step-by-step explanation:

Angles of a quadrilateral add up to 360:

70 + 40 + ∠B + ∠O = 360

∠B + ∠O = 250

The central angle between A and C is double the angle B.  And, it plus angle O add up to 360.

Therefore:

2∠B + ∠O = 360

Solve the system of equations.  Subtracting the first equation from the second:

∠B = 110

Divide miles ran by speed to get time:

2 miles / 8 miles per hour = 0.25 hours = 15 minutes.

2 miles / 6 miles per hour = 0.33 hours = 20 minutes.

20 minutes - 15 minutes = 5 minutes longer.

Final answer:

After calculating the time taken by each runner to complete the 2-mile race, we find that Arif took 5 minutes longer than Sharif to finish.

Explanation:

To determine how many minutes longer Arif took to complete the race compared to Sharif, we need to calculate the time each runner took to complete the 2-mile race. First, we calculate Sharif's time. Since speed is distance divided by time, we can rearrange the formula to find time: time = distance/speed.

For Sharif:

Distance = 2 miles

Speed = 8 miles per hour

Time = 2 miles / 8 mph = 0.25 hours

Convert Sharif's time from hours to minutes by multiplying by 60 minutes per hour (0.25 hours * 60 minutes/hour = 15 minutes).

For Arif:

Distance = 2 miles

Speed = 6 miles per hour

Time = 2 miles / 6 mph = 0.333... hours

Convert Arif's time from hours to minutes (0.333... hours * 60 minutes/hour = 20 minutes).

Now, to find the difference in time, subtract Sharif's time from Arif's time:

Difference = Arif’s time - Sharif's time = 20 minutes - 15 minutes = 5 minutes

Arif took 5 minutes longer than Sharif to complete the race.

area of triangle = 1/2bh

area = 1/2(120)(252) = 15120 in²

answer: C

Answer:

C) 15,120 square inches

Step-by-step explanation:

To solve this problem we first need to convert both legs of the triangle to inches. 10 ft * 12 is 120 and 7 yards is roughly 21 ft and that times 12 is 252. All we have to do now is to plug these values into the formula for area of a triangle: 1/2(b x h) = 1/2(252 * 120) = 1/2(30240) = 15,120 square inches.

Answer: -2

Step-by-step explanation:

This is the greatest value for f(x).

1. I would multiply the dimensions of each room to find the area of each room. Then I can add up the areas to get the total area.

2. (24.5x16)+(15x12.75)+(10.5x10.5)

3. 392+191.25+110.25 = 693.5 ft²

Answer:

C) x2 + x = 306

Step-by-step explanation:

x2 + x = 306

x2 + x - 306  = 0

x2  + 18x - 17x + 18 * (-17) = 0

x ( x + 18) - 17 (x +18) =0

(x + 18) (x - 17 ) = 0

x = -18 or 17

Answer:

3m + 4

Step-by-step explanation:

4 is the starting number of stamps and 3m represents 3 stamps per month

Answer:

B

Step-by-step explanation:

9000-500 = 8500

8500 × (3/100) =255

8500 + 255 = 8755

8755 × (3/100) = 262.65

8755 + 262.65 = 9017.65

hence, the answer is B

*please correct me if im wrong ^^

Answer:

b) 2 years

Step-by-step explanation:

If you have $9000 in the saving account, and you take $500, you are left with:

$9000 - $500 = $8500

in one year you will have 3% more of the 8500 which is:

8500/100*3 = $255

so in one year the number on your savings account is:

8500 + 255 = $8755

and by the next year you will have 3% more of the 8755 which is:

8755/100*3 = $262.65

so in two years the number on your savings account is:

8755 + 262.65 = $9017.65

which is a little bit more than the $9000.

so it will take 2 years until the calance again reaches $9000

Answer:

3 it teaches them a lesson by dont judge someone by how he looks

everyone was judging her cause of her religious and looks and in the end they admired the wall that she had painted cause it teaches them a lesson dont judge a book by it cover

4 Was the painter an “outsider” or a part of the community? Why? she was an outsider she came for a purpose and its to paint the wall text from the story "The painter lady has come to town ostensibly with the purpose of painting a mural."

Answer:

73155

Step-by-step explanation:

To complete the sequence, we need to know the pattern.

88511= [tex]8+8, 8-5, 5\times 1, \frac{1}{1} = 16351[/tex]

16351= [tex]1+6, 6-3, 3\times 5, \frac{5}{1} = 73155[/tex]

73155= [tex]7+3, 3-1, 1\times 5, \frac{5}{5} = 10251[/tex]

10251

∴ The missing number is 73155 and complete sequence is 88511,16351,73155, 10251

Answer:

The segment is 6 units long.

Step-by-step explanation:

The points (–2, 4) and (–2, –2) are vertices of a heptagon. We have to explain how to find the length of the segment formed by these endpoints.

If two points at the ends of a straight line PQ are P([tex]x_{1},y_{1}[/tex]) and Q([tex]x_{2},y_{2}[/tex]), then the length of the segment PQ will be given by the formula  

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]

Now, in our case the two points are (-2,4) and (-2,-2) and the length of the segment will be  

[tex]\sqrt{(- 2 - (- 2))^{2} + (4 - (- 2))^{2}} = 6[/tex] units. (Answer)

The length of the segment is 6 units.

It is given that,

To find the length of the segment formed by these endpoints.

Explanation:

The distance formula is used to find the length of the segment formed by two endpoints.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(-2-(-2))^2+(-2-4)^2}[/tex]

[tex]d=\sqrt{(0)^2+(-6)^2}[/tex]

On further simplification, we get

[tex]d=\sqrt{36}[/tex]

[tex]d=6[/tex]

Thus, the length of the segment is 6 units.

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Answer:

two real solution

Step-by-step explanation:

x^2 + 10x − 25 = 0

we can solve this by finding out the value of x

lets assume the equation is   a\times x^{2}+b\times x+c=0

x=-b\pm \sqrt{(b^{2}-4ac)}\div 2a

x=-10\pm\sqrt{100+4*25}\div2

x=-5\pm5\sqrt2

then we get both real value of x

so two real solution

Answer:

[tex]P=\$9,174.31[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested  or present value

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=6\ years\\ P=?\\ A=\$10,000\\r=1.5\%=1.5/100=0.015[/tex]

substitute in the formula above

[tex]10,000=P(1+0.015*6)[/tex]

solve for P

[tex]10,000=P(1.09)[/tex]

[tex]P=10,000/(1.09)[/tex]

[tex]P=\$9,174.31[/tex]

Answer:

Step-by-step explanation:

In a figure like this, the largest angle is formed from the two outermost points, which are D and A. Since the vertex is X, the angle is DXA.

Answer:

55

Step-by-step explanation:

13+6*7=13+42=55