Which expression can be simplified to the form 3\y + 3, where y is a positive integer?

Which Expression Can Be Simplified To The Form 3\y + 3, Where Y Is A Positive Integer?

Answers

Answer 1

Answer: Choice B) [tex]\sqrt{63}[/tex]

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

Explanation:

Let's rewrite the given expression like so

[tex]3\sqrt{y+3}=\sqrt{3^2}\sqrt{y+3}\\\\3\sqrt{y+3}=\sqrt{9}\sqrt{y+3}\\\\3\sqrt{y+3}=\sqrt{9(y+3)}\\\\[/tex]

We can see that the radicand is a multiple of 9 since 9 is a factor.

This immediately rules out choices C and D because 75 and 84 are not multiples of 9.

-------------

Plug in the smallest positive integer (1) for y to get

[tex]\sqrt{9(1+3)}=\sqrt{9(4)} = \sqrt{36}\\\\[/tex]

The radicand 36 is larger than the radicand for choice A (18), meaning we can rule out choice A. There's no way to get a radicand of 18 since y = 1 is the smallest we can go for.

We can however get to 63 by using y = 4

[tex]\sqrt{9(4+3)}=\sqrt{9(7)} = \sqrt{63}\\\\[/tex]

Showing that choice B is of the form [tex]3\sqrt{y+3}[/tex] where y is a positive integer, specifically when y = 4.


Related Questions

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Find the exact value of the indicated trigonometric functions using the given information.


Given: tan a=2.4, and π/2Find the exact value of the indicated trigonometric functions using the given information.

Given: tan a=2.4, and π/2find sin a and cot a

Answers

Answer:

Viewed as a right angled triangle

tan

(

x

)

=

5

12

can be thought of as the ratio of opposite to adjacent sides in a triangle with sides

5

,

12

and

13

(where

13

is derived from the Pythagorean Theorem)

So

sin

(

x

)

=

5

13

and

cos

(

x

)

=

12

13

Step-by-step explanation:

Which statement correctly maps AB to A′B′
x,y)↦(x+7,y−8)(x,y)↦(x+7,y−8)

(x,y)↦(x+8,y−7)(x,y)↦(x+8,y−7)

(x,y)↦(x−8,y+7)(x,y)↦(x−8,y+7)

(x,y)↦(x−7,y+8)

Answers

Answer: ( x + 8, y -7)
x value is moved 8 units to the left. So add 8 to x value.
Y value is moved 7 units down. So subtract 7 from y value

Answer:x+8, y-7

Step-by-step explanation:

The mean of the values in a data set is c. If each of the values in the data set
a
were multiplied by 6, what would be the mean of the resulting data?
O A. 5c
O B. 6c
ос. 7с
D. C

Answers

Answer:

B 6c.

Step-by-step explanation:

The mean will be c multiplied by 6.

How many TRIANGLES can be constructed with sides measuring 8 cm, 9 cm, and 11
cm ?

Answers

Answer:

1 -- Triangle

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

During a sale at the electronics store​, movies sold for ​$3 and CDs sold for ​$2.50. Isla spent ​$24 and bought a total of 9 movies and CDs. How many of each did she ​buy?

Answers

6 CDS (2.5*6=$15)
3 Movies (3*3=$9)

I need help with this please

Answers

Answer:

4 and 7

2 and 5

Step-by-step explanation:

4 and 7 are co interior angles

2 and 5 are co interior angles

sum of co interior angles are 180° hence they are Supplementary

Write an equation of the line with a slope of -3 and y -intercept of 0 .

y=

Answers

Answer:

y=-3x

Step-by-step explanation:

An automotive website would like to estimate the percentage of drivers who own their cars, rather than lease their cars. Which of these survey methods would not provide a convenience sample to estimate the percentage who own their cars?

a survey of adults at an auto parts store
a survey of all adults attending a car show
a survey of people in a car dealership
an online survey for sharing data about their cars

Answers

The answer to your question is the last option. “An online survey for sharing data about their cars”. Have a great day

A survey of all adults attending a car show would not provide a convenience sample to estimate the percentage of drivers who own their cars, rather than lease their cars.

What is a survey?

A survey is a research method used to gather information from a sample of individuals about their opinions, behaviors, experiences, or demographic characteristics.

This is because a car show attracts a diverse group of people, including car enthusiasts, potential car buyers, and families looking for entertainment.

Therefore, a survey of all adults attending a car show would provide a more representative sample of the population, compared to the other options listed, which are more likely to provide a convenience sample.

A survey of adults at an auto parts store, a survey of people in a car dealership, and an online survey for sharing data about their cars are more likely to provide a convenience sample because they are only capturing the opinions of people who happen to be present at a particular place or who choose to participate in an online survey.

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in 1961 yuri gagarin became the first man to orbit the sun he traveled for 108 minutes at an average speed of 235 miles per minute how many miles did he travel

Answers

Answer:

25,380 miles

Step-by-step explanation:

108 minutes × 235 = 25,380

Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?

A. 95
B. 98
C. 80
D. 85

Answer: 98

Answers

To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

What is math average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics.

                 When calculating the average for a set of data, we first sum up all the values and divide the result by the total number of values.

Average = (sum of values) / (number of values)

The total of Laurence's marks on the first four biology exams can be calculated using the following formula

Sum of scores = 87 + 80 + 75 + 85

= 327

We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

Next score = (sum of all five scores) - (sum of first four scores)

= (85 x 5) - 327

= 25

Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

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Dylan has 58912 cookies he eats 34512 how much does he have now?

Answers

Answer:

24,400

Step-by-step explanation:

58912 minus 34512 equals 24400.

Hope this Helps.

BTW it's my birthday

Answer:

24400

Step-by-step explanation:

No explanations; 58912-34512=24400

Solve for X
Pls give your working out as well x

Answers

[tex]3^{x-2} = \left(\dfrac 13 \right)^{\sqrt x}\\ \\\implies 3^{x -2} = \left(3^{-1} \right)^{\sqrt x} \\\\\implies 3^{x-2} = 3^{-\sqrt x}\\\\\implies x -2 = -\sqrt x\\\\\implies (x-2)^2 = \left(-\sqrt x \right)^2\\\\\implies x^2 -4x +4 = x\\\\\implies x^2 -5x +4 =0\\\\\implies x^2 -4x-x+4=0\\\\\implies x(x-4) -(x-4)=0\\\\\implies (x-1)(x-4)=0\\\\\implies x = 1~~~~~~;[x = 4 ~ \text{Does not satisfy the original equation}]\\\\\text{Hence, x =1 is the solution.}[/tex]

x^2+6x+8÷x^2-16 simplify

Answers

Answer:

The answer is in the file below, I wasn't able to make it in text form.

8. A megaphone is formed by taking a cone with radius of 18 centimeters and an edge length of 60 centimeters from tip to base
and cutting off the tip. The
cut is made 12 centimeters along the edge from the tip and is parallel to the base. The cut produces
a new radius of 4 centimeters. Round your answers to the nearest tenth.
Hint: A megaphone is hollow, so do not include the base.
a. What is the surface area of the whole cone?
b. What is the surface area of the tip that is removed?

cone
megaphone
whole cone
C.
What is the surface area of only the megaphone?

Answers

The Surface area of the whole cone is 4408.56 cm²

The Surface area of the tips that is removed is  376.8 cm²

The Surface area of the megaphone(hollow) is  2712.96 cm²

What is surface area?

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

Therefore,

Surface area of the whole cone = πr² + πrl

Therefore,

Surface area of the whole cone = πr(r + l)

where

r = radius = 18 cml = edge length = 60 cm

Surface area of the whole cone = 3.14 × 18(18 + 60) = 4408.56 cm²

Surface area of the tips that is removed = 3.14 × 4 (18 + 12) = 376.8 cm²

Surface area of the megaphone(hollow) = πrl

Surface area of the megaphone(hollow) = 3.14 × 18 × (60 - 12) = 2712.96 cm²

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2root 3 + root 3 is equal to?

Answers

Answer:

i believe the answer is C

Step-by-step explanation:

Answer:

(C) 3√3

Step-by-step explanation:

Think of √3 as x.

Then 2x + x = 3x, so

2√3 + √3 = 3√3

When rounded to the ten thousands place, which of the
numbers below round to 110,000? Select all that apply.
A) 113,450
B) 95,678
C) 104,298
D) 94,560
E) 106,789

Answers

Answer:

e

Step-by-step explanation:

Answer:

a, e

Step-by-step explanation:

a would round to 110,000 because 113,450 rounded to the ten thousand round down to 110,000

95,678 would round up to 100,000 not 110,000

104,298 would round down to 100,000 not 110,000

94,560 would round down to 90,000

106,789 would round up to 110,000 because 6 rounds up because 5 and up is rounded up

Use the order of operations to find the value of the expression.

2
+
3
×
16

2
×
21

3
A.
5

B.
14

C.
35

D.
44

Answers

Using the order of operations to find the value of the expression, we have; A. 5

How to carry out order of operations?

We want to use order of operations to solve the problem;

2 + 3 × 16 − 2 × 21 − 3

Now, the order is called BODMAS which means;

Bracket, Of, Division, Multiplication, Addition, Subtraction.

From the order above and looking at our question, we will first carry out multiplication to get;

2 + 48 - 42 - 3

Next is addition to get;

50 - 42 - 3 = 5

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In the graph the horizontal axis says “proportion of heads”. Write a more accurate label for these values in terms of babies and toy preference.

Answers

The more accurate label for the x-axis of the Histogram should be the proportion of babies who love toys.

What is the  Chart Label of an Axis in Statistics?

A chart label is a name given to the factors represented by the axis of a chart.

Typically, a chart has two axes. In some cases, three.

Regardless of the number of axes that a chart has, it is important to properly label them for purposes of comprehension and accurate representation of the data on them.

The referrenced chart is attached.

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Drag each equation to its equivalent fact. DUE TODAY

Answers

Answer:

left left right

Step-by-step explanation:

rearange the formula as normal

Which lines are the directrices of the ellipse?

x = −4.25 and x = 8.25
x = −3.25 and x = 9.25
y = −4.25 and y = 8.25
y = −3.25 and y = 9.25

Answers

The lines that are the directrices of the ellipse is B. x = −3.25 and x = 9.25.

How to calculate the ellipse?

From the information given, the equation of parabola will be:

= (x - 3)²/5² + (y - 2)²/3² = 1

Hence, h = 3, k = 2, a = 5, b = 3

e = ✓1 - ✓3²/5²

E = 4/5 = 0.8

The directix will be:

x = 3 + 5/0.8

x = 9.25

x = 3 - 5/0.8

x = -3.25

Therefore, lines that are the directrices of the ellipse is x = −3.25 and x = 9.25.

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Porter drove due east 20 miles on Interstate 23, then due south 23 miles on Interstate 77. To the nearest hundredth of a mile, how far was he from his starting point?

A. 30.48 mi
B. 26 mi
C. 11.36 mi
D. 43 mi

Answers

Answer: D. 30.48 miles

Step-by-step explanation:

You basically use Pythagorean Theorem!

a2 + b2 = c2

Square root 20^2 +23^2

=√20^2 + 23^2

=20 x 2 + 23 x 2

= 929

And round it=

30.48 miles.

Hi my name is Leah and I need help with my homework that's on Ken Academy I'm in the 5th grade and I need help with this screenshot Can anybody give me an answer? it's due today!

Answers

Heyy, so the answer should be: 9.3

Hope this helps

Q9.
Solve the simultaneous equations
7x – 2y = 34
3x + 5y = -3
Show clear algebraic working.

Answers

After solving simultaneously we found the values for x and y are

2.76 and 5.65 respectively

Simultaneous Equations

We have the following two expressions

7x – 2y = 34 --------1

3x + 5y = -3 ---------2

Multiply 1 by eqn 5 and eqn 2 by 2

35x - 10y = 170-------3

6x + 10y = -6 ----------4

subtracting 4 from 3 we have

29 x= 164

divide both sides by 29

x = 164/29

x = 5.65

Put x = 5.65 in eqn 1 to find y

7*5.65 – 2y = 34

39.55 - 2y = 34

39.55-34 = 2y

5.55 = 2y

divide both sides by 2

x = 5.55/2

x = 2.76

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Use the distribution property to explain how 30 flowers in a bunch can be counted in groups of 2s and 3s.

Answers

The way 30 flowers in a bunch can be counted in groups of 2s and 3s is 2(3(3) + 3(2))

Prime factorization of numbers

From the question, the interpretation is that we are to write the prime factorization of 30

30 = 2 * 15

30 = 2{3 (3 + 2)}

Expand using the distribution property

30 = 2(3(3) + 3(2))

30 = 2(9 + 6)

Hence the way 30 flowers in a bunch can be counted in groups of 2s and 3s is 2(3(3) + 3(2))

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show complete solution​

Answers

Step-by-step explanation:

You can find the complete solution

You should use cross multiplication to solve

I hope it helped you

The expression below is a sum of cubes.

64x^3 + 125

A. True

B. False

Answers

Answer:

A True

Step-by-step explanation:

[tex]4^{3} x ^{3} + 5^{3} [/tex]

Factor x2 + 3x + 2 A) (x + 3)(x + 1) B) (x + 2)(x + 1) C) (x + 2)(x - 1) D) (x - 2)(x + 1) E) (x - 2)(x - 1)

Answers

Answer:

(x + 1) (x + 2)

Step-by-step explanation:

x² + 3x + 2

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like ax² + bx + c,

we need to think of 2 numbers such that:

N₁ · N₂ = a · c = 1 · 2 = 2

And,

N₁ + N₂ = b = 3

After trying out a few numbers we get N₁ = 2 and N₂ = 1

2 · 1 = 2 and 2 + 1 = 3

x² + 3x + 2 = x² + 2x + x + 2

x (x + 2) + 1 (x + 2)

(x + 1) (x + 2) , is the factorized form.

Answer:

(x+2)(x+1)

Step-by-step explanation:

[tex]x^{2} +3x+2[/tex]

→Multiply the first and last term's coefficient =1×2=2

Now,

→Factors of 2=2,1

→Using 2 and 1 we must add up to 3

Now we get,

[tex]\hookrightarrow x^{2} +3x+2\\\\\hookrightarrow x^{2} +2x+x+2[/tex]

Here when we add 2x and x we get 3x.

Now,

Take common x from x²+2x as well as 1 from x+2

Then we get,

[tex]\hookrightarrow x^{2} +2x+x+2\\\\\hookrightarrow x(x+2)+1(x+2)\\\\[/tex]

Here, x+2 is common. So we can write both of them as one.

[tex]\hookrightarrow (x+2)(x+1)[/tex]

And it is our final answer.

Hence, the final factors are (x+2)(x+1)

HELP PLEASE!!
Discuss the steps that you used
to create your tangent line.
What was the most important
step?
Give an example of tangents in
the real world that have not
been presented in this lesson.
Explain how you know the
tangent and the radius are
perpendicular.

Answers

Answer:

You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj

Step-by-step explanation:

Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.

The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.

PLEASE HELP ILL GIVE FIVE STARS AND GIVE BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray
What is the sum of their ages now?

Answers

Answer: The sum will be x+y because their ages are variables.

Step-by-step explanation:

De 17 estudiantes 4 hablan frances, si se seleccionan 3, ¿cuál es la probabilidad de que ninguna habla frances?

Answers

Esta es una cuestión de probabilidad condicional, y la resolución podría ser la siguiente:

Estudiantes seleccionados ÷ ninguno habla francés3 / (17 - 4) = 3/13¿Qué es la probabilidad condicional?

Corresponde a un concepto matemático que involucra la probabilidad de que ocurran dos eventos, es decir, la probabilidad de que ocurra el evento A, sabiendo que el evento B ya ocurrió.

Por lo tanto, la probabilidad de que ningún estudiante hable francés es 3/13 o 23%.

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