will the square roots of perfect squares always be irrational numbers

Answer:

$6.80

Step-by-step explanation:

$8.16 ÷ 12 = $0.68

$0.68 x 10 = $6.80

Answer:

Infinitely many solutions

Step-by-step explanation:

Solve y = 3x+1 for y

y = 3x+1

Substitute 3x+1 for y in -6x+2y = 2

−6x+2y = 2

−6x+2(3x+1) = 2

2=2

2+−2=2+−2

0=0

Answer:

Domain: [-4, 4]

Range: [-3, 5]

Function? No

Step-by-step explanation:

Domain is all x-values that can be inputted in the graph that returns an output.

Range is all y-values that are outputted when x is inputted.

A function has to pass the Vertical Line Test.

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer:

144

Step-by-step explanation:

Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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Answer:

it's was helpful to you

second is the answer

правильный ответ В, тк -2 и 1 являются решением к иксу

Answer:-2 1m

Step-by-step explanation:

Answer:

  A.  1/4 gal/scoop

  B.  w = 1/4s

  C.  line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"

  D.  3 gallons

Step-by-step explanation:

Given 2 scoops of  powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.

A proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...

  w = ks

where k is the constant of proportionality.

Solving the equation for k, we get ...

  k = w/s

Using the given values, we find k to be ...

  k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop

The constant of proportionality is 1/4 gallon per scoop.

We show the equation in part A. Filling in the value of k gives ...

  w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water

The attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.

The equation tells you that 12 scoops will require ...

  w = 1/4·12 = 3 . . . . gallons

3 gallons of water are needed for 12 scoops of drink mix.

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Solution:

Given the cubic equation;

The roots of the equation are;

CORRECT OPTION: (D) 1 real; 2 complex

Answer:

1 pint is 4 dollar. you can get 5 pints for 20 dollars and 32 dollars for 8 pints.

Hope I can help

Happy Holidays and stay safe!

Step-by-step explanation:

Answer:1 pint is 4 dollars. you can get 5 pints for 20 dollars and 8 pints for 32 dollars.

Step-by-step explanation: stay safe and warm

Answer: 309 + n= k * 173 -232

Step-by-step explanation:

Translated:

309 + n= k * 173 -232

541 + n= 173k

I don't exactly know the answer to this question, but here is my thinking progress

Answer:

$7.25

Step-by-step explanation:

I'm pretty sure I'm correct. Hope this helps and have a nice day!

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

The minimum result (to 2 dp) of a / b is 38.66

Given:

a=460 rounded to the nearest 10

b=11.9

Now, substitute the values of a and b in a/b,

a/b = 460/11.9

Multiply the same integer(10) by both the numerator and denominator,

a/b = 4600/119

Round the number obtained

a/b ≅ 38.66

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Answer:

B. 9.7

Step-by-step explanation:

√12²-7²=√144-49=√95=9.7

The model is different because it has different denominator and numerator

a) The initial deposit in the account is given as follows: 1,287.39 euros.

b) The interest rate of the account is given as follows: 3%.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

Considering the balances after 5 and 6 years, the interest rate is obtained as follows:

r = 1524.60/1480.50 - 1

r = 0.03.

Considering the balance after 5 years, the initial deposit is obtained as follows:

P(1 + 0.03 x 5) = 1480.5

P = 1480.5/1.15

P = 1,287.39 euros.

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Answer:

yes

Step-by-step explanation:

Given:

You can rewrite it as follows:

You can graph it by following these steps:

1. Find the x-intercepts. By definition, the value of "y" is zero when the function intersects the x-axis. Then, you need to make:

Substitute this value into the equation:

Solving for "x", you get:

2. Identify the multiplicities:

- Notice that the first factor of the function is:

And has an exponent 2.

This means that:

Since it has an even Multiplicity, the graph touches the x-axis, at that point, but it does not intersect it.

- Having the other factor:

Its exponent is 1. Then:

That even Multiplicity indicates that the graph intersects the x-axis at that point.

3. Find the y-intercept. By definition, the value of "x" is zero when the function intersects the y-axis. Then, you need to make:

Substitute this value into the function and solve for "y":

4. By definition, the end behavior of a function can be determined knowing its Leading Coefficient and its degree. Then, you need to follow these steps to find the end behaviors of the function:

- Expand the right side of the equation. Remember this formula:

Then, you get:

Multiply the polynomials by applying the Distributive Property:

Add the like terms:

Knowing that the degree is the highest exponent and that the Leading Coefficient "a" is the number that multiplies the term with the highest exponent, you can identify that:

By definition, if:

The end behaviors of a function are:

Therefore, in this case, since the Leading Coefficient is positive, you can determine that as "x" approaches positive infinity, h(x) approaches positive infinity:

And as "x" approaches negative infinity, h(x) approaches negative infinity:

Knowing all the data found, you can graph the Cubic Function.

Hence, the answers are:

• x-intercepts:

• y-intercept:

• Multiplicity:

• End behaviors:

• Graph:

The difference in speed of the two cars is 72-60 = 12 km per hour.

The time they would be 8 km apart would be 8/12 = 2/3 of an hour

1 hour = 60 minutes

60 minutes x 2/3 = 40 minutes.

The cars will be 8 km apart in 40 minutes.

Answer:

After 40 min they will be 8km apart

Step-by-step explanation:

Car A is traveling 1km per minute Car B is traveling 1.2km per minute, so Car B will gain 1km on Car A every 5 min. To be 8km apart, you calculate 5min x 8 = 40 min

The calculated period of the function is 12

From the question, we have the following parameters that can be used in our computation:

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

d) 1/12

Step-by-step explanation:

Answer:

L.H.S. = \(\frac{1}{cosx} -\frac{sinx}{cosx}sinx\)

= \(\frac{1}{cosx} - \frac{sin^2x}{cosx}\)

= \(\frac{1-sin^x}{cosx} = \frac{cos^2x}{cos x}\)

= cos x = 1/secx

Step-by-step explanation:

Hey there!

Given;

sec x - tan x . sin x = 1/(sec x).

~ Taking LHS.

= sec x - tan x . sin x

= 1/(cos x) - (sin x/cos x) . sin x { Using formula sec x = 1/cos x and tan x = (sin x/cos x)}

~ Multiply (sin x) and (sin x).

\( = \frac{1 - { (\sin(x) )}^{2} }{ \cos(x) } \)

~ Use formula 1-sin²x= cos²x

\( = \frac{ {cos}^{2} x}{ \cos(x) } \)

~ Cancel cos x.

= cos x

= 1/sec x { cos x = 1/sec x}

→ RHS proved.

Hope it helps.....

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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