An arts academy requires there to be 4 teachers for every 68 students and for every 3 tutors for every 36 minutes. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has ​72 students?

The value of x that makes the equation true is 60/7.

The given equation is:-

4x - 2 + 3x - 7 = 51

The given equation is a linear equation in one variable.

Linear equation in one variable

A linear equation in one variable is of the form of ax + b = 0, where a and b are any two integers and x is an unknown variable having only one solution. Example : 5x + 3 = 10.

We have to find the value of x that makes the equation true.

Simplifying the given equation, we get

(4x + 3x) - (2 + 7) = 51

7x - 9 = 51

7x = 51 + 9

7x = 60

x = 60/7

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The equation of the line that passes through these coordinates is 3x-4y= 36

If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. m=(y2-y1)/(x2-x1), or the ratio of the change in the y values to the change in the x values, is the slope formula.

To find the equation of the line we first have to find the slope which is represented by m.

The slope or m is given by : y₂ - y₁ / x₂ - x₁

thus, m= 3-(-12)/ 16-(-4)

m= 3+12/ 16+4 = 15/20

m= 3/4

The equation of a slope is y-y₁=m (x-x₁)

y- (-12) = 3/4 (x- (-4))

y+12 = 3/4 (x+4)

On solving it further we get:

4y+48= 3x+12

3x-4y= 36

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The unknown length is 28. the values of the six trigonometric functions for angle b that is tan B = 7/24

From the question,

we are given

a = 96 and c = 100, to get the unknown side 'b',

we will substitute the given values into the formula above;

c² = a²+b²

100²  = 96² +b²

b²  = 100²  - 96²

b²  = 10,000 - 9216b²

= 784b = √784b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity.

According to TOA,

tan B = opposite/adjacenttan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given, b = 28 and a = 96tan B = 28/96tan B = 4*7/4*24

tan B = 7/24

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The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Answer:

128m²

Step-by-step explanation:

separate the two solids.The cube and the cuboid

find the volume of the cube i.e.5³=115m²

find the volume of the cuboid i.e 1×1×3=3m²

add the two volumes

Answer:

128m²

Explanation:

Add all volumes, 5+5+4+6+3, then times that by the volume below.

The best estimate of fraction is 131.445.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex]

Given Data

31[tex]\frac{3}{4}[/tex] × 4[tex]\frac{1}{7}[/tex]

Solving mixed fractions

[tex]\frac{127}{4}[/tex] × [tex]\frac{29}{7}[/tex]

31.75 × 4.14

Multiplying

131.445

The best estimate of fraction is 131.445.

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Answer:

Step-by-step explanation:

B

Answer: 8

Step-by-step explanation:

180 degrees in a triangle, so 180 - 92 - 48 = 40

So, the missing angle is 40, which is equal to 5t, so

40 = 5t

t = 8

For the given trigonometric function y =16sin1/2 x the graph shows the amplitude of 16 ,  graph of exactly one cycle is with period 4π , with no vertical and phase shift.

As given in the question,

Given trigonometric function :

y = 16sin 1/2 x

Attached graph of the given trigonometric function with

Amplitude = 16

Period = 4π

Vertical shift = None

Phase shift = none

Table for the required trigonometric function values which represent appropriate scale and graph exactly one cycle of the trigonometric function

x : 0        π        2π          3π         4π

y :  0       16        0            -16         0

Therefore,  graph of trigonometric function y =16sin1/2 x shows the amplitude of 16 ,  graph of exactly one cycle is with period 4π , with no vertical and phase shift.

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Answer:

12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]

Step-by-step explanation:

the second term should not be -8x, it should be -8[tex]x^{4}[/tex]

The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex])  is 8 but then we add the exponents 2 + 2 = 4

The coordinates of the vertex B' is (2,3)

Given,

The vertices of triangle ABC are

A = (-4,4)

B = (-2,3)

C = (-5,2)

and, reflected across the y-axis to produce the image of triangle A'B'C'

To find the coordinate of the vertex B'

Now, According to the question

For reflection across y-axis, the rule is:

(x, y) → (-x, y)

So, the image of B is:

(-2, 3) → (-(-2), 3)

(-2,3) → (2, 3)

Hence, The coordinates of the vertex B' is (2,3)

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Answer:

the value of x is -6

Step-by-step explanation:

1-3x= 3x+1

-3x -3x =1-1

-6x=0

-x=6

x= -6

Answer: Why it makes sense: When we compare or order decimals we need to compare place values just like we do with whole numbers. When the edges are “jagged” it makes it harder to compare each decimal place. Adding a zero in an empty place value makes it easier to compare the numbers.

Step-by-step explanation:

Answer:

you need to line them up to tell what place value each are in. if u don't the you won't known exactly what the product is equivalent to.

the leters c and d are correct for this equation

Answer: 94.2

Step-by-step explanation:

C = 2 πr

C = 2 x 3.14 x 15

C = 30 * 3.14

C = 94.2

The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.

The graph of the solution is shown below.

From the question, we are to solve the given inequalities

The given inequalities are

3 < 2p - 3 ≤ 12

We will solve  the inequalities separately

That is

3 < 2p - 3  and 2p - 3 ≤ 12

Solve 3 < 2p - 3

3 < 2p - 3

3 + 3 < 2p

6 < 2p

6/2 < p

3 < p

Solve 2p - 3 ≤ 12

2p ≤ 12 + 3

2p ≤ 15

p ≤ 15/2

p ≤ 7.5

Hence,

Joining the two solutions together, the solution is 3 < p ≤ 7.5.

The graph is shown below.

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Answer:

Obviously yes...

Step-by-step explanation:

Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.

Answer:

false

Step-by-step explanation:

From the given quadratic function, it is found that:

a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.

b) The number of bacteria will be minimal for a temperature of 0.5 ºC.

c) The minimum number of bacteria is of 115.

d) The graph that models the situation is sketched at the end of the answer.

The quadratic function is given as follows:

N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.

In which:

The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.

For a concave up quadratic function, the minimum value happens when the input is of:

Tm = -b/2a.

For this problem, the coefficients of the quadratic function are as follows:

b = -20, a = 20.

Hence the temperature in which the number of bacteria will be minimal is of:

Tm = 20/40 = 0.5 ºC.

The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:

N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.

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Answer:

B

Step-by-step explanation:

When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.

Answer:

b

Step-by-step explanation:

angle 3 and angle 6 are alternate interior angles which makes the congruent

The description of the intercepts of the Graph segments passing through the points (0, 4), (4, 8), (4, 8) and (8, 0) is given by the option;

A velocity time graph is a graph that shows how the velocity of an object changes with time

The given information on the graph are;

The coordinates of the points on the Graph of the first line segment = (0, 4) and (4, 8)

On Graph of the second line segment, the coordinates of the points = (4, 8), (8, 0)

The label of the axis of the graph are;

X–axis label = Time in seconds (s)

Y–axis label = Velocity in m/s

Required; The option that gives the description of the intercepts of the graph

Solution; The x and y–intercept are given as follows;

At the x–intercept the y–value is 0, which gives the x–intercept of the graph as the point (8, 0)

Given that the y–value which is the value of the velocity, is 0, it means that the runner stops at the point (8, 0), or after 8 seconds

At the y–intercept, the x–value is 0. The y–intercept is therefore the point (0, 4)

The 0 in the y–intercept means that the time is 0 seconds, which is the starting or initial time, while the 4 means that the velocity is 4 m/s.

Therefore, the y–intercept (0, 4) can be described as the initial velocity of the runner is 4 m/s

The description of the intercepts on the graph are therefore;

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Answer:

The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer

Step-by-step explanation:

The intercepts on the graph can be described as follows:- The y-intercept is the point at which the line intersects the y-axis, and it represents the initial velocity of the runner. In this case, the y-intercept is at (0, 4), which means that the initial velocity of the runner was 4 m/s.- The x-intercept is the point at which the line intersects the x-axis, and it represents the time at which the runner stopped. In this case, there are two x-intercepts: one at (4, 8) and another at (8, 0).
This means that the runner stopped twice, once after 4 seconds and again after 8 seconds.

Therefore, the correct description of the intercepts on the graph is: The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer.

Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

As given in the question,

Simple Interest:

The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.

Principal amount:

Principal amount is the money that is taken as loan or borrowed.

Formula of Simple Interest:

Simple interest = Principal amount × Rate × Time

Since,

Principal amount = $10,000

Rate = 4% per year

Time = 5 years

Then,

Simple interest = 10,000 × 4 × 5

Simple interest = $ 12000

Total value after 5 years = $ 12000

Principal amount = $ 10000

Interest Earned = (Total value) - (Principal amount)

Interest Earned = $ 12000 - $ 10000

Interest Earned = $ 2000

Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

The complete question is:

Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?

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This is the right response: T F- F.

What is the explanation:

If the answer to the following question is p, then 2 + 2 = 4.

which is accurate, meaning that this statement has a truth value of True.

The following assertion q illustrates q: 7 + 1 Equals 7.

This is untrue, making the statement's truth value Untrue

As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.

The truth table reveals that the truth value of pq will be False

So T F → F

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The number of years when Dylan would have over £3,600 in his account is 18 June, 2021.

The time that If the account earns interest every 3 months, it means that the value increases quarterly or 4 times a year. The account would increase at an exponential rate. This means that both the amount invested and the interest that has already been earned would increase in value 4 times a year.

The formula that can be used to determine the time is:

Time = In(FV / PV) / r

Where:

FV = future value

PV = present value

r = interest rate

t = In (£3,600 / £3,000) / 0.0102

t = In 1.2 / 0.0102 = 17.87 / 4 = 4.468 years

4 years = 2017 + 4 = 2021

0.468 x 12 = 5.616 months

January + 5 months = June

0.616 x 31 = 19 days

18 June, 2021

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Answer:

every number has a correlating value

Step-by-step explanation: