Which diagram BEST represents the relationship among integers, rational numbers, and whole numbers?

Answer:

[tex] KS = 12 [/tex]

Step-by-step explanation:

Given that ∆KLM ~ ∆RSK, [tex] \frac{KL}{KR} = \frac{KM}{KS} [/tex] (similarity theorem)

KL = 65

KR = 65 - 52 = 13

KM = 60

KS = ?

[tex] \frac{65}{13} = \frac{60}{KS} [/tex]

Cross multiply

[tex] 65*KS = 60*13 [/tex]

[tex] 65*KS = 780 [/tex]

[tex] \frac{65*KS}{65} = \frac{780}{65} [/tex]

[tex] KS = 12 [/tex]

Answer:

0.00432 km = 4320 mm

Step-by-step explanation:

There are 1000000 millimeters in a kilometer. To convert kilometers to millimeters, multiply the kilometer value by 1000000.

Quick check 0.00432 * 1000000 = 4320 mm

Answer:

4320

Step-by-step explanation:

Answer:

A model that shows a pitcher holding 8 times the amount of a glass

Step-by-step explanation:

I would need a picture of the models, but I think I can still help.

Any model that shows a pitcher holding 8 times as much as a glass is the correct model. Be sure to read carefully so you pick the right model.

The equation y = 8x shows the relationship between the holding capacity of the pitcher and glass, and x = 64/8 shows the total amount held by the glass.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the pitcher can hold x ounces

And the glass can hold y ounces

From the given problem:

y = 8x

The above equation modeled the relationship between the holding capacity of the pitcher and glass.

If y = 64

Then x = 64/8 = 8 ounces

Thus, the equation y = 8x shows the relationship between the holding capacity of the pitcher and glass, and x = 64/8 shows the total amount held by the glass.

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Work Shown:

We have two sequences, which we'll call A and B

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

467

Step-by-step explanation:

We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

10x² + -18

Step-by-step explanation:

g(f(x)) means you substitute 2x²-5 for every occurrance of x in g(x).

g(f(x)) = 5(2x²-5) + 7 = 10x² - 25 + 7 = 10x² - 18 =  10x² + -18

Answer:

[tex]\Large \boxed{k=2x + \frac{-7}{3}} \\ \\ \\ \Large \boxed{x=\frac{1}{2} k+\frac{7}{6}}[/tex]

Step-by-step explanation:

Solving for k:

[tex]\sf 3k+16=9+6x[/tex]

Subtracting 16 from both sides.

[tex]\sf 3k=6x-7[/tex]

Dividing both sides by 3.

[tex]\displaystyle \sf k=2x + \frac{-7}{3}[/tex]

Solving for x:

Flipping the original equation.

[tex]\sf 6x+9=3k+16[/tex]

Subtracting 9 from both sides.

[tex]\sf 6x=3k+7[/tex]

Dividing both sides by 6.

[tex]\sf \displaystyle x=\frac{1}{2} k+\frac{7}{6}[/tex]

Answer:

x = 5.98

Step-by-step explanation:

Step 1: Use tangent to solve for x

tan50.1 = [tex]\frac{x}{5}[/tex]

x = 5tan50.1

x = 5.98

Therefore x is equal to 5.98

Answer:

C or D

Step-by-step explanation:

It is a line segment but C and D are the exact same in the question you provided.

The part of a line that has two endpoints and includes all of the line segment

A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints

You can draw a line by locating any two point in space and then connecting them together.

Based on the explanation we can conclude that part of a line that has two endpoints and includes all of the line segment

Learn more on line segment here: https://brainly.com/question/18315903

Answer:

Step-by-step explanation:

[tex] \sf{9 - 4x = 17}[/tex]

Move 9 to right hand side and change it's sign

⇒[tex] \sf{ - 4x = 17 - 9}[/tex]

Subtract 9 from 17

⇒[tex] \sf{ - 4x = 8}[/tex]

Divide both sides of the equation by -4

⇒[tex] \sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}} [/tex]

Calculate

⇒[tex] \sf{x = - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

D. divide by -8

Step-by-step explanation:

Answer:

70 km/h

9 hr 22.5 min

Step-by-step explanation:

Given

Difference in time as equation:

Average speed was 70 km/h

Total time = 350/70 + 350/(70+10) = 5 + 4.375 = 9.375 hr = 9 hr 22.5 min

Answer:

a = 49

b = - 20√2

Step-by-step explanation:

5 - 2√6 / 5 + 2√6

We can rationalise the denominator as follow:

5 - 2√6 / 5 + 2√6

Multiply the numerator and the denominator by the conjugate of

5 + 2√6. The conjugate of 5 + 2√6 is

5 - 2√6

(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)

(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)

Expand

(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)

25 - 20√6 + 24 / 25 - 24

25 + 24 - 20√6 / 1

49 - 20√6

Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:

49 - 20√6 = a + b√3

From the above

a = 49

b√3 = - 20√6

Divide both side by √3

b = - 20√6/√3

Rationalise

b = - 20√6/√3 x √3/√3

b = - 20√(6×3)/ √3×√3

b = - 20√18 / 3

b = - 20√(9×2) / 3

b = - 20 × 3√2 / 3

b = - 20√2

Given info:- Rationalise the denominator and find out the value of "a" and "b"

Given expression: {(5-2√6)/(5+2√6)} = a+b√3

Explanation:-

{(5-2√6)/(5+2√6)} = a+b√3

We know that Rationalising factor of a+b√c is a-b√c.

Therefore, the rationalising factor of 5+2√6 is 5-2√6.

⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]

⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]

⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3

⇛{(5-2√6)²}/(25 - 4√6) = a+b√3

⇛{(5-2√6)²}/(25-24) = a+b√3

⇛{(5-2√6)²}/1 = a+b√3

⇛(5-2√6)² = a+b√3

⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3

⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3

⇛25 - 10 - 4√6 - 2√6 = a+b√3

⇛15 - 4√6 - 2√6 = a+b√3

⇛15 + 6√6 = a+b√3

∴ 15 + 6√6 = a+b√3

On, comparing with both RHS we notice that:

The value of a = 15 and b = 6.

Hope this helps!!

If you have any doubt, then you can ask me in the comments.

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Work Shown:

b = unknown number

2b = 2 times a number

2b+3 = the sum of 2 times a number and 3

2b+3 = 7, since the expression above is set equal to 7

The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

As per the given phrase,

The sum of 2 times a number and 3 equals 7.

2 times b = 2b

The Sum of 2b with 3 equal to 7 will be 2b + 3 = 7

2b = 7 - 3

2b = 4

b = 4/2 = 2

Hence"The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2".

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Answer:

25°

Step-by-step explanation:

180-130=50

50÷2=25°

Answer:8640 square inches

Step-by-step explanation:

Answer:

12 hours

Step-by-step explanation:

Let x hours be the time it will take you to mow the greens at the golf course.

Since Kim can mow twice as fast, it will take Kim x / 2 hours to mow the greens.

In 1 hour, you will mow 1 / x of the greens

in 1 hour, Kim will mow 1 / (x / 2) of the greens= 2 / x of the greens

In 4 hours, you will mow 4 * 1 / x of the course = 4 / x of the greens

In 4 hours, Kim will mow 4 * 1 / (x / 2) of the course = 4 / (x / 2) = 8 / x of the greens.

Since we are dealing in fraction, the sum of the amount of greens that they would individually mow in 4 hours should be 1. i.e

(4 / x) + (8 / x) = 1

12 / x = 1

Solve for x;

x = 12

Therefore, it will take you 12 hours to mow the greens alone.

Answer:8 weeks

Step-by-step explanation:

Answer:

Column 1 label:

✔ t

Column 2 label:

✔ 112 + 8t

Column 3 label:

✔ w

Column 4 label:

✔ (t, w)

Step-by-step explanation:

edge20

Stephen is tracking how many words per minute (wpm) he reads for reading class. He is now at 112 wpm, and each week he hopes to increase his speed by 8 words per minute.

Equation: w = 112 + 8t

t = time (weeks)

w = wpm

Label the columns for the table

Column 1 label:

✔ t

Column 2 label:

✔ 112 + 8t

Column 3 label:

✔ w

Column 4 label:

✔ (t, w)

Answer:

y = -5, 1

Step-by-step explanation:

2y² - 10y + 44 = (y - 7)²

expand (y - 7)²

(y - 7)² = y² - 14y + 49

move it to the left

(2y² - 10y + 44) - (y² - 14y + 49) = 0

distribute the (-)

2y² - 10 y + 44 - y² + 14y - 49 = 0

combine like terms

y² - 4y -5

factor with factoring X

y² + 5y - y - 5 = 0

factor by grouping ↓

factor out a y from first half of equation

y(y + 5) - y - 5 = 0

factor out a (-) from second half of equation

y(y +5) - (y + 5) = 0

(y +5)(y - 1) = 0

y = -5, 1

Answer: Yes it is possible to bisect the given segment

The compass width (9) is over half of the segment length (10), so we can form the arcs needed to get the perpendicular bisector.

Answer:

2.18

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Hello!

Since y varies directly with x what happens to y also happens to x

From y = -12 to y = -4 you divide by 3 so we do that to x

6 / 3 = 2

The answer is 2

Hope this helps!

Answer:

94

Step-by-step explanation:

PEDMAS

[tex]34 - 6 \times 3 + 78 \\ 34 - 18 + 78 \\ 34 + 60 \\ = 94[/tex]

Step 1 : Multiplication :

-6×3 =-18

Step 2: Addition: -18+78 = +60

Step 3: Addition : 35+60

= 94

Answer:

62

Step-by-step explanation:

Cause first is multiply 6x3 =18 so next you add 18+78 =96 then Subtract 96 -34 =62

Answer:

This will be -8x^3y^9.

Answer:

1.54 and 1.7 I believe

Step-by-step explanation:

Answer:

The full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Step-by-step explanation:

To find how many pounds each tire is, divide the weight in grams by 453.592

Full steel tire:

800/453.592 = 1.76 pounds

Lighter wheel:

700/453.592 = 1.54 pounds

So, the full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Hey there! I'm happy to help!

Squaring a number is when you multiply it by itself. You represent this with an exponent, which is a little number above the number that you multiply by itself. When you square a number, this exponent is two.

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

The square root is basically just doing this backwards. It is finding the number that can be multiplied by itself to equal that number. You represent this with the √ symbol.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=10

We know that 8 multiplied by itself is equal to 64. This means that the square root of 64 is 8.

I hope that this helps you out! Have a wonderful day! :D

Answer:

Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.

Step-by-step explanation:

The cost function of water bill is:

[tex]C = C_{f}+C_{v}[/tex]

Where:

[tex]C_{f}[/tex] - Fix costs, measured in USD.

[tex]C_{v}[/tex] - Variable costs, measured in USD.

The fix and variable costs are, respectively:

[tex]C_{f} = 24.60[/tex]

[tex]C_{v} =2\cdot \left(\frac{Q}{100} \right)[/tex]

Where [tex]Q[/tex] is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:

[tex]C = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

If [tex]C = 64\,USD[/tex], the maximum water capacity is:

[tex]64 = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]39.40 = 2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]Q = 1970\,ft^{3}[/tex]

Which is equivalent to 19.70 ccf.

Answer:

i)-240*a^4*b^3*c^2

ii)-15*x^2*y^2+3*x^3*y^2

iii)x^4*y^3*z^2-x^2*y^3*z^3+x^3*y^2*z^3

iv)p*q+6*q-7*p-42

v)2*x^3-3*x^2-23*x+42

vii)2*x^2-2*y^2+7*x-12*y-15

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{-x^2+2x}[/tex]

Step-by-step explanation:

2 times x subtracted by x².

[tex]\Rightarrow 2 \cdot x-x^2[/tex]

[tex]\Rightarrow 2x-x^2[/tex]

Rearranging the expression.

[tex]\Rightarrow -x^2+2x[/tex]

Answer:

2x -x^2

Step-by-step explanation:

[tex]2(x) - x^2\\= 2x-x^2[/tex]

Answer:

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

Simplified - r = 820

Step-by-step explanation:

I don't know how to explain it exactly, but I know you have to find out how much the carnations, tulips, and irises all cost,subtract that from how much money he has, and divide what left by the cost of the roses (by multiplying the 0.8 cents, because it's a decimal).

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

r = (5000 - [1500 + 2400 + 75])0.8

r = (5000 - 3975)0.8

r = 1025(0.8)

r = 820

Answer:

13.2

Step-by-step explanation:

We just divide 79/6 which is equal to 13.1666667 which we can round to 13.2

Answer:

13.166667 best describes the fraction 79/6