Write a linear(y =mx + b) quadratic (y = ax exponent 2) or exponential (y = a(b) x) function that models the data HELP

Answer:

A = 22.5 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2(5)(9)

A = 45/2

A = 22.5 cm^2

[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height}}}}}\end{gathered}[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 5 \: cm \: \times \: 9 \: cm[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 45 \: cm[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{45 \: {cm}^{2} }{2} \: \\ [/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \cancel\frac{45}{2} \: \: ^{22.5 \: {cm}^{2} } \: \\ [/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: 22.5 \: {cm}^{2} [/tex]

Hence , the area of triangle is 22.5 cm²

Answer:

D

Step-by-step explanation:

f(x)=-x(x-4)

f(x)=-x²+4x

-x²+4x=0

x(-x+4)=0

x=0, x=4

(2)

4x²-x-3=0

(4x²+3x)-(4x-3)=0

x(4x+3)-1(4x+3)=0

x=1, x=-3/4

From the formula R(300) - C(300) we understand that is loss of 7500 for the company.

The given functions are R(x) = 55x and C(x) = 15,000 + 30x.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is R(300) - C(300).

Now, R(300) = 55 × 300 = 16500

C(300) = 15,000 + 30 × 300

=15,000 + 9000

= 24,000

Now, R(300) - C(300) = 16500-24000

= -7,500

Therefore, from the formula R(300) - C(300) we understand that is loss of 7500 for the company.

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Answer:

2.5/ft per sec

Step-by-step explanation:

its vertica.

The height of the ladder is decreasing at a rate of 24 ft/sec.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's denote the distance between the base of the ladder and the wall by x.

The length of the ladder = L.

Now,

L = 10 ft

dx/dt = 4 ft/sec

x = 6 ft.

The rate of change of the height of the ladder with respect to time.

Using the Pythagorean theorem, we have:

L² = x² + y²

Differentiating both sides with respect to time t, we get:

2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)

Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.

20(dL/dt) = 12(4) + 2y(dy/dt)

Simplifying and solving for dy/dt.

dy/dt = (20/2y)(dL/dt) - 24

Now,

The height of the ladder.

Using the Pythagorean theorem again, we have:

y² = L² - x²

   = 100 - 36

   = 64

y = 8

Now,

Substituting y = 8 ft, dL/dt = 0

(since the length of the ladder is constant), and dx/dt = 4 ft/sec.

dy/dt

= (20/2(8))(0) - 24

= -24 ft/sec

Therefore,

The height of the ladder is decreasing at a rate of 24 ft/sec.

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Answer:

First one: 2.5

Second: -6

8.5+69.5(5) = 147.5

150 - 147.5 = 2.5

8.5 + 69.5(5) = 356

350 - 356 = -6

ED2021

The residual for 2 phone lines is $2.5.

The residual for 5 phone lines is -$6.

The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.

We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.

Thus for 2 phone lines:-

Actual Cost = $150.

Predicted Cost, y = 8.5 + 69.5*2 = 147.5.

Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.

Thus, the residual for 2 phone lines is $2.5.

Thus for 5 phone lines:-

Actual Cost = $350.

Predicted Cost, y = 8.5 + 69.5*2 = 356.

Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.

Thus, the residual for 2 phone lines is -$6.

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Answer:

[tex] = - \frac{1}{36(6x + 1) ^{6} } + c[/tex]

Answer:

[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]

Step-by-step explanation:

we're going to us u substitution

[tex]\int (6x+1)^-7 dx[/tex]

[tex]u=6x+1[/tex]

[tex]\int\frac{1}{6u^7} du[/tex]

take out the constant, [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{6}[/tex] · [tex]\int u^-7du[/tex]

next use the power rule, [tex]\int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]

[tex]\frac{1}{6}\cdot \frac{u^{-7+1}}{-7+1}[/tex]

simplify by substituting [tex]6x+1[/tex] for [tex]u[/tex]

[tex]\frac{1}{6}\cdot \frac{(6x+1)^{-7+1}}{-7+1} = -\frac{1}{36\left(6x+1\right)^6}[/tex]

add a constant, [tex]C[/tex]

[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]

Answer:

D. There is no x value as there is no solution to this system

Step-by-step explanation:

2x − 3y = 3                                  5x − 4y = 4

5x - 4y = 4               -4y = -5x + 4                         y = 5/4x - 1

2x - 3(5/4x - 1) = 3

2x - 15/4x + 3 = 3

-7/4x = 0

x = 0

9514 1404 393

Answer:

  a) CP = SP/1.1

  b) CP = $59.50

  c) GST = $5.95

Step-by-step explanation:

a) Divide by the coefficient of CP.

  SP = 1.1×CP

  CP = SP/1.1

__

b) Use the formula with the given value.

  CP = $65.45/1.1 = $59.50

__

c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.

  GST = SP -CP = $65.45 -59.50 = $5.95

  GST = CP×0.10 = $59.50 × 0.10 = $5.95

Answer:

(-14.8504 ; 0.5644)

Step-by-step explanation:

Given the data:

Population 1 : 30 35 23 22 28 39 21

Population 2: 45 49 15 34 20 49 36

The difference, d = population 1 - population 2

d = -15, -14, 8, -12, 8, -10, -15

The confidence interval, C. I ;

C.I = dbar ± tα/2 * Sd/√n

n = 7

dbar = Σd/ n = - 7.143

Sd = standard deviation of d = 10.495 (using calculator)

tα/2 ; df = 7 - 1 = 6

t(0.10/2,6) = 1.943

Hence,

C.I = - 7.143 ± 1.943 * (10.495/√7)

C.I = - 7.143 ± 7.7074

(-14.8504 ; 0.5644)

Answer:

Sin A = o/h

= 9/41

Step-by-step explanation:

since Sin is equal to opposite over hypotenuse, from the question, the opposite angle of A is 9 and hypotenuse angle of A is 41. Thus the answer for Sin A= 9/41

Answer:

∡A =41°

~~~~~~~~~~~~

BC=21

~~~~~~~~~~~~~~

sin(24)/AC=sin(41)/21

AC=13

~~~~~~~~~~~~~~

sin(115)/AB=sin(41)/21

AB=29

Step-by-step explanation:

Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

using the sine rule,

[tex]\frac{sin 60}{x} = \frac{sin 30}{6} \\x=\frac{sin60 * 6 }{sin30} \\x=6\sqrt{3}[/tex]

Answer:

[tex] { (\frac{3}{2} )}^{ - 2} \\ = { (\frac{2}{3}) }^{2} \\ = \frac{4}{9} \\ thank \: you[/tex]

Answer:

Option B.

Step-by-step explanation:

We can see that we have an asymptote at x = 2

Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.

So, the denominator is something like:

(x + a)

we have that the denominator is zero when x = 2

Then:

(2 + a) = 0

solving that for a, we get:

a = -2

Then the denominator of the rational function is:

(x - 2)

For the given options, the only one with this denominator is option B, then the correct option is B.

Answer:

B. f(x) = 1/x-2

Step-by-step explanation:

Math is ez bro.

Answer:

If the hypotenuse of the 30 60 90 triangle is 7 sqrt 3, then the length of the longer side is equal to 7 x 3, or 21.

Now going to the 45 45 90 triangle, we can see that x is equal to 21[tex]\sqrt{2}[/tex]. This is because the hypotenuse of a 45 45 90 triangle is equal to the side length times sqrt 2.

So our answer is, 21[tex]\sqrt{2}[/tex].

Let me know if this helps!

A = 10,00,000

P = 10,000

T = 2

1000000 = 10000(1+r/100)^2

1000000 = 10000((100 + r)/100)^2

1000000 = 10000× 100 + r/100 × 100 + r/100

1000000 = 10000 + r^2

1000000 - 10000 = r^2

990000 = r^2

√99000 = r

Quadratic Equation

10000(1+r/100)^2

Answer:

d. this graph

Step-by-step explanation:

(2/7)m - (1/7) = 3/14

2m/7 =(3/14) + (1/7)

2m/7 = (3/14) + 2(1/7)

here we are multiplying 2 with 1/7 to make the denominator same for addition.

2m/7 = (3/14) +(2/14)

2m/7 = (3 + 2)/14

2m/7 = 5/14

2m = (5 *7)/14

2m = 35/14

2m = 5/2

m = 5/4

m = 1.25

So the value of "m" is 1.25

[tex]\\ \large\sf\longmapsto -\dfrac{4x^3}{3y^2}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{4(3)^3}{3(4)^2}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{4(27)}{3(16)}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{108}{48}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{9}{4}[/tex]

Answer:

yes

Step-by-step explanation:

The complete sentence is,

A kite is a convex quadrilateral.

We have to given that,

To find a kite is which type of a quadrilateral.

We know that,

A quadrilateral known as a kite has four sides that may be divided into two pairs of neighboring, equal-length sides.

The two sets of equal-length sides of a parallelogram, however, are opposite one another as opposed to being contiguous.

Hence, The complete sentence is,

A kite is a convex quadrilateral.

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Answer:

Answer:

The probability that the average score of the 49 golfers exceeded 62 is 0.3897

Step-by-step explanation:

Answer:

how many times should u use the metal rod ??

Answer:

Step-by-step explanation:

Point-slope equation for line of slope m that passes through (x₀, y₀):

y-y₀ = m(x-x₀)

Slope =3 and (x₀, y₀)=(-3,0)

y = 3(x+3)

y = 3x+ 9

:::::

Slope-intercept equation for line of slope m and y-intercept b:

y = mx+b

m=1 and b= -4:

y = x-4

Answer:

28  and 38

Step-by-step explanation:

a+b = 66

a + 10 = b

using substitution, a + (a+10) = 66

2a = 56

a = 28

28 + 10 = 38

b = 38

Answer:

Sinx = 21/40

x = inverse of sin (21/40)

x= 31.6682

hope u got it

Answer:

31.6 degrees

Step-by-step explanation:

sin-¹(p/h) = 31.6

Answer:

0.99%

Step-by-step explanation:

Answer:

C - 136

(115+157)/2

Step-by-step explanation:

Answer:

(-2, 2)

Step-by-step explanation:

If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)

So, if the original point is (-8, 8)

And we do a dilation by a scale factor k = 1/4

Then the image of the point will be:

(-8*(1/4), 8*(1/4))

(-8/4, 8/4)

(-2, 2)