which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle ​

Parent function = √x

On stretching vertically by factor of 6

New function G(x) = 6√x

[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]

      [tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]

Calculates 2 to the power of 2 and gets 4.

      [tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]

      [tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]

      [tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]

Answer:

5+16x

Step-by-step explanation:

5+4x(8−6)

2

Subtract 6 from 8 to get 2.

5+4x×2

2

Calculate 2 to the power of 2 and get 4.

5+4x×4

Multiply 4 and 4 to get 16.

5+16x

Answer:

Arithmetic => each new term differs from the previous term by a fixed amount

an = a1 + d (n − 1)

Geometric => each element after the first is obtained by multiplying the previous number by a constant factor

an = a1 (r)^(n − 1)

4,8,16,32 the difference is not fixed so it is a geometric so it is ratio

the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64

To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.

if you also want the sum of them

arithmetic -> (n/2)(a1+an)

geometric -> (a1*(1-r^n))/(1-r) or

      when the sequence is infinite you can use a1/(1-r)

Step-by-step explanation:

Arithmetic => 1,3,5,7,9,11,13,15....

Geometric => 1,2,4,8,16,32,64....

Based on the information provided, the individuals in this study are: D. the students.

A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.

In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.

Based on the information provided, the individuals in this study are the students and these include the following subclasses:

Read more on variables here: https://brainly.com/question/523303

#SPJ1

The students are the individuals in this study and is therefore denoted as option D.

This refers to a group of people which are chosen or taken from a large population for measurement or surveys.

In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.

Read more about Sample study here https://brainly.com/question/20064039

#SPJ1

She will have $2118 in her account after five years

The given parameters about the compound interest are

Principal Amount, P = $1,900

Interest Rate, R = 2.2%

Time, t = 5

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R)^t - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

Substitute the known values in the above equation

A = 1900 * (1 + 2.2%)^5

Express 2.2% as decimal

A = 1900 * (1 + 0.022)^5

Evaluate the sum

A = 1900 * (1.022)^5

Evaluate the exponent

A = 1900 * 1.11495

Evaluate the product

A = 2118

Hence, she will have $2118 in her account after five years

Read more about compound interest at:

https://brainly.com/question/24924853

#SPJ1

Answer:

5

Step-by-step explanation:

You save ⅓ of entry fee, so you save 1.20 and you pay 2.40. We only really care about the 1.20 reduction. 5 / 1.2 = 4.16 so he must go 5 times to get the 5 back

Answer:

x = 3

Step-by-step explanation:

see image. Instead of distributive property, let's multiply by 2 to get rid of the fraction and also the parenthesis on the left. See image.

Then subtract 5 and finally, divide by 3 to solve. See image.

Answer:

So g(6) comes out to be 2.

Step-by-step explanation:

So f(6)=5 means when f acts on 6, the result is 5....so the inverse would take 5 back to 6...or g(5)=6

So f(2)=6 means that f reassigns 2 to 6....so the inverse would take 6 back to 2....or g(6)=2

hope this helps :)

Answer: 3

Step-by-step explanation:

If f(x) = y, then invf(y) = x
So, f(5) = invg(5) = 3

Answer:

6

Step-by-step explanation:

Solve for y:

[tex]y/8=9/12[/tex]

Multiply both sides by 8:

[tex]y=72/12[/tex]

Solve fraction

[tex]y=6[/tex]

Answer: 65.86 inches

Step-by-step explanation:

Length of the hypotenuse (length of diagonal) :  a^2 + b^2 = c^2

The length (a)= 57

The height (b) =33

57^2= 3,249

33^3= 1,089

3,249 + 1,089 = c^2

4,338 = c^2

We next square root both sides to find c by itself (length of the diagonal)

[tex]\sqrt{4,338} = c[/tex]

c= 65.8634952...

You can then round to however many decimals are required.

To the hundreds place: 65.86 inches

Answer:

[tex]x=1+\sqrt[n]{y}[/tex]

Step-by-step explanation:

Since: [tex](x-1)*(x-1)*(x-1)=y[/tex]

that would imply: [tex](x-1)=\sqrt[3]{y}[/tex]

This is a bit more clear, if you write the equation as:

[tex](x-1)^3=y[/tex]

and then take the cube root of both sides

[tex]\sqrt[3]{(x-1)^3}=\sqrt[3]{y}[/tex]

Which simplifies to

[tex]x-1=\sqrt[3]{y}[/tex]

Now add 1 to both sides, and you get the equation:

[tex]x=1+\sqrt[n]{y}[/tex]

Answer: 3(t-y)

Step-by-step explanation:

The term difference refers to subtraction, so that means t-y in parenthesis since you would have to solve that first.

Then after you'd solve that, then you would multiply it by 3

Hope I helped :)

Answer:

the correct answer is 25

Answer:

49°

Step-by-step explanation:

The circumference of a circle measures 360 degrees, so arc XW is 98°.

So, angle XWY is 49°.

The average number of pages she reads per hour is 19 pages per hour

The given parameters are:

Number of pages = 76 pages

Number of hours = 4 hours

The average number of pages she reads per hour is calculated using the following formula

Average = Number of pages/Number of hours

Substitute the known values in the above equation

Average = 76 pages/4 hours

Evaluate the quotient

Average = 19 pages per hours

Hence, the average number of pages she reads per hour is 19 pages per hours

Read more about average at:

https://brainly.com/question/20118982

#SPJ1

(a) The result of the long division is a - b + c.

(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:

(a) a² - b² + 2 · b · c - c² divided by a + b - c.

1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²

2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²

3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0

The result of the long division is a - b + c.

(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.

1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.

2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.

3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².

The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

To learn more on long divisions: https://brainly.com/question/12342242

#SPJ1

Step-by-step explanation:

First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]2 {x}^{2} + 7x - 9[/tex]

[tex]2 {x}^{2} - 2x + 9x - 9[/tex]

[tex]2x(x - 1) + 9(x - 1)[/tex]

[tex](2x + 9)(x - 1) = 0[/tex]

[tex]x = 1[/tex]

[tex]2x + 9 = 0[/tex]

[tex]x = - \frac{9}{2} [/tex]

Now, to find the gradient of the curve let take the derivative of both sides

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]0 = 4x + 7[/tex]

[tex]4x + 7[/tex]

Plug in -9/2, let call that point P

[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]

Plug in 1, let call that point Q

[tex]4(1) + 7 = 11[/tex]

So the gradient of the curve at point P (-9/2,5) is -11

The gradient of the curve at point Q (1,5) is 11.

The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.

If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.

The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.

Number of reams of paper in a box = 5 reams

1 ream = 500 sheets

500 sheets = 5.4 cm thick

The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}

Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

Learn more about measuring thickness at https://brainly.com/question/10473688

#SPJ1

Assume that one ream of paper is 5.4 cm thick.

Answer:

See below

Step-by-step explanation:

Here is HOW to solve this problem:

b = pounds of blue candy      then   r =  11-b = pounds of red candy

.79b = cost of blue candy             1.29 (11-b) = cost of red candy

   these two costs sum to   11.19  

.79b    + 1.29 ( 11-b)  = 11.19        Now you can solve for 'b'  the 'r' = 11-b

Answer:

Red candy =5

Blue candy = 6

Step-by-step explanation:

Let the pounds of red candy be x and blue candy y. Then y=11-x

Also 1.29x + 0.79y=11.19

1.29x+0.79(11-x)=11.19

0.5x=11.19–8.69

0.5x=2.5

X=5

Red candy =5

Blue candy = 6

a. Central angle: Angle BAC

b. Major arc: Arc BEC

c. Minor arc: Arc BC

d. m(BEC) = 260°

e. m(BC) = 100°

A major arc can be defined as an arc that has a measure that is greater than a semicircle (half a circle) or greater than 180 degrees.

A minor arc can be defined as an arc that has a measure that is less than a semicircle (half a circle) or less than 180 degrees.

An angle whose vertex is at the center of a circle and has two radii of as its  sides is called a central angle of a circle.

a. Central angle in the image given is: Angle BAC

b. Major arc of the circle is: Arc BEC

c. Arc BC is a minor arc.

d. m(BEC) = 360 - 100 [based on the central angle theorem]

m(BEC) = 260°

e. angle BAC = 100°

m(BC) = angle BAC [based on the central angle theorem]

m(BC) = 100°

Learn more about major and minor arcs on:

https://brainly.com/question/228276

#SPJ1

If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Given two equations x-2y=5 and 4x+12y=-20.

We are required to find the value of x and y through substitution method.

Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.

They can be solved as under:

x-2y=5---------------1

4x+12y=-20--------2

Finding value of variable x from equation 1.

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

Use the value of variable  x in equation 2.

4x+12y=-20

4(5+2y)+12y=-20

20+8y+12y=-20

20y=-20-20

20y=-40

y=-40/20

y=-2

Use the value of variable y in equation 3.

x=5+2y

x=5+2*(-2)

x=5-4

x=1

Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Question is incomplete as it should include one more equation x-2y=5.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

1 kilogram (kg) = 1000 grams (g)

as "kilo" means 1000.

b = a × c / 1000

it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.

and to get kg, we need to divide this number of grams by 1000.

that's it.

Answer:

[tex]x > 60[/tex]

Step-by-step explanation:

[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)

Answer:

v = -3w

Step-by-step explanation:

water level/volume = -3 x weeks

v = -3w

The statements that applies are;

The property of power function is known to be peculiar to the field of math. A power function is known to be one that is made up of a variable base that tends to be raised to a fixed power.

Note that the function is one that is made up of a constant base that is often raised to a variable power.

Following the property of power function, we can be able to obtain the information above.

Therefore, The statements that applies are;

Learn more about function from

https://brainly.com/question/15323484

#SPJ1

Answer:

soln,

write the question

=9x^2+1-6x-2×9x^2+25+9x^2+25

=9x^2+1-6x-18x^2+25+9x^2+25

=9x^2-18x^2+9x^2+1+25+25-6x

=51-6x

if(3x+1)^2 mean that (3x+1)has power of 2 and u don't have to use the formula this is the answer

Step-by-step explanation:

it's just BODMAS method

Answer:

25, 26, and 27 are the three consecutive integers.

Step-by-step explanation:

Let the numbers be represented as x, x + 1 and x + 2.

We can write the equation:

[tex]x+(x+1)+ (x+2)=78[/tex]

Opening the brackets and simplifying:

[tex]x+x+1+x+2=78[/tex]

[tex]3x+3=78[/tex]

Subtract 3 from both sides.

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=25[/tex]

Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.

∴ 25, 26 and 27 are the three consecutive integers.

Answer:

25 , 26 and 27

Step-by-step explanation:

Answer: one

Step-by-step explanation:

parallel faces are the ones that are opposite to each other.

Answer:

one

Step-by-step explanation:

there is only one pair of parallel faces.

Answer:

in case you don't understand feel free to ask bye.