Write the equation of the graph shown below in factored form. a graph that starts at the top left and continues down through the x axis at negative four to a minimum around y equals negative two point eight and goes up to touch the x axis at negative two and then goes back down to a minimum around y equals negative zero point four and then goes back up to cross the x axis at negative one.

Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

Answer:

Option (3)

Step-by-step explanation:

By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.

From the figure attached,

Two tangents CD and DE are intersecting each other at point D outside the circle A.

Two intercepted arcs are minor arc CE and major arc CBE,

Measure of arc CE = 112°

Therefore, measure of major arc CBE = 360° - 112°

                                                               = 248°

m(∠CDE) = \(\frac{1}{2}(\text{arcCBE}-\text{arcCE})\)

                 = \(\frac{1}{2}(248-112)\)

                 = \(\frac{1}{2}\times 136\)

                 = 68°

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

To find the average, add up all the number and divide by the number of terms

(11+ 13+ 18 + 22)/4

64/4

16

Answer: 16

Step-by-step explanation:

To find the average, you want to take the sum of all the numbers and divide by the amount of numbers.

\(\frac{11+13+18+22}{4} =\frac{64}{4} =16\)

After we add 11, 13, 18, 22, we get 64. There are 4 total numbers. Therefore, we divide 64 by 4. We get the answer 16.

African Americans faced numerous challenges during the Civil Rights Movement.

The Civil Rights Movement, which spanned from the 1950s to the 1960s, aimed to secure equal rights and end racial segregation and discrimination in the United States. African Americans encountered significant challenges during this period. One of the key challenges was institutionalized racism, which permeated various aspects of society, including education, employment, housing, and voting rights. African Americans were subjected to Jim Crow laws, which enforced segregation and denied them equal treatment under the law. They faced violence, intimidation, and discrimination, particularly in the Southern states. Despite these obstacles, African Americans demonstrated resilience and determination in their pursuit of justice and equality. They organized peaceful protests, sit-ins, boycotts, and marches to demand their rights and challenge discriminatory practices. These efforts ultimately led to significant milestones in civil rights legislation, such as the Civil Rights Act of 1964 and the Voting Rights Act of 1965, which aimed to dismantle segregation and protect the voting rights of African Americans. The Civil Rights Movement remains an important chapter in American history, highlighting both the struggles and triumphs of African Americans in their fight for equality and justice.

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The value of the line integral is:

\((1/27) (49^{(3/2)} - 13^{(3/2)})\)

≈ 36.724

To evaluate the line integral:

\(\int C x^2/y^{(4/3)} ds\)

C is the curve given by x = t² and y = t^3, and ds is the element of arc length along the curve.

We can parameterize the curve as:

r(t) = (t², t³), 1 ≤ t ≤ ∛2

Then the tangent vector to the curve is:

r'(t) = (2t, 3t²)

The length of the tangent vector is:

|r'(t)| = √(4t² + 9t⁴ = t√(4 + 9t²)

So, the element of arc length ds is:

ds = |r'(t)| dt = t√(4 + 9t²) dt

The integral becomes:

\(\int C x^2/y^{(4/3)} ds\)

=\(\int(1 to 3\sqrt 2) (t^4)/(t^{(8/3)}) (t\sqrt{(4 + 9t^2)}) dt\)

= \(\int (1 to 3\sqrt 2) t^{(2/3)}\sqrt (4 + 9t^2) dt\)

To evaluate this integral, we can make the substitution u = 4 + 9t²:

u = 4 + 9t²

du/dt = 18t

dt = du/(18t)

The limits of integration become:

u(1) = 13

u(∛2) = 49

The integral becomes:

\(\int C x^2/y^{(4/3)} ds\)

= \((1/18) \int (13 to 49) u^{(1/2)} du\)

=\((1/27) (49^{(3/2)} - 13^{(3/2)})\)

So, the value of the line integral is:

\((1/27) (49^{(3/2)} - 13^{(3/2)})\)

≈ 36.724

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Answer:

see below

Step-by-step explanation:

The amount she withdrew is 45*4 =180

405 - 4*45=

405 -180 =225

There is 225 in the account

Answer: a) $225

Step-by-step explanation:

405 - 45 (4) = x

405 - 180 = x

225 = x

Answer:

i think its b

Step-by-step explanation:

True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.

The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.

The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.

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The system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

Carlos graphed the system of equations that can be used to solve the equation x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

To graph this system of equations, we need to set the equation equal to zero. So, the equation becomes:

x^3 - 2x^2 + 5x - 6 + 4x^2 - 14x - 12 = 0

Combining like terms, we get:

x^3 + 2x^2 - 9x - 18 = 0

To graph this equation, you can use a graphing calculator or plot points manually. Here are the steps to manually plot the graph:

1. Choose a range for x, for example, from -5 to 5.
2. Pick a few values for x within the chosen range and substitute them into the equation to find the corresponding y-values.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.

By following these steps, you can graph the system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

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Answer:

see explanation

Step-by-step explanation:

(a)

given the arithmetic series 5 + a + 14 + b

the difference between consecutive terms is constant , that is

a₂ - a₂ = a₃ - a₂ ( substitute values )

a - 5 = 14 - a ( add a to both sides )

2a - 5 = 14 ( add 5 to both sides )

2a = 19 ( divide both sides by 2 )

a = 9.5

then

a₄ - a₃ = a₂ - a₁

b - 14 = a - 5 = 9.5 - 5 = 4.5 ( add 14 to both sides )

b = 18.5

(b)

the sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 5 and d = a₂ - a₁ = 14 - a = 14 - 9.5 = 4.5 , then

S₁₀ = \(\frac{10}{2}\) [ (2 × 5) + (9 × 4.5) ]

     = 5(10 + 40.5)

     = 5 ×  50.5

     = 252.5

(c)

\(S_{n}\) > 500 , that is

\(\frac{n}{2}\) (50.5) > 500 ( multiply both sides by 2 )

50.5n > 1000 ( divide both sides by 50.5 )

n > 19.80198... , that is

n = 20

Therefore, the line integral ∫c F.dr is equal to -15π/4. To use Stokes' Theorem to evaluate the line integral ∫c F.dr, we need to find the curl of F and then evaluate the surface integral of that curl over the region bounded by the curve C.

First, let's find the curl of F:

curl(F) = <(dQ/dy - dP/dz), (dR/dz - dP/dx), (dP/dy - dQ/dx)>

where F = <P, Q, R> = <2yz, 5xz, In z>

So,

dP/dy = 2z

dQ/dz = 0

dQ/dx = 0

dR/dz = 1/z

dR/dx = 0

dP/dx = 0

dP/dy = 0

dQ/dy = 0

Therefore,

curl(F) = <2/z, 0, -5x>

Now, let's find the boundary curve C. The intersection of x² + y² + z² = 9 and x² + y² = 5 gives us the following system of equations:

x² + y² = 5

x² + y² + z² = 9

Subtracting the first equation from the second, we get:

z² = 4

Taking the square root of both sides and noting that we are only interested in the positive value of z, we get:

z = 2

Substituting this into the equation of the cylinder, we get:

x² + y² = 5

This is the equation of a circle with radius sqrt(5) centered at the origin in the xy-plane. Since we want the portion of this curve above the xy-plane, we add z = 2 to the equation, giving us the boundary curve C: x² + y² = 5, z = 2.

Now, let's evaluate the surface integral of curl(F) over the region bounded by C. The surface is the portion of the sphere x² + y² + z² = 9 above the xy-plane and below z = 2. This surface is a hemisphere with radius 3 centered at the origin in the xy-plane.

∬S curl(F) . dS

= ∫0^2π ∫0^π/2 <2/(3sinφ), 0, -15sinφcosφ> . ρ²sinφ dθ dφ

= ∫0^2π ∫0^π/2 (-30/3)sin²φ cosφ dθ dφ

= -15π/4

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Answer:

14-28

Step-by-step explanation:

The indefinite integral of (1 / 1+e^12x) is (1/12) ln|1+e^12x| + C, where C is the constant of integration.

To find the indefinite integral of (1 / 1+e^12x), we can use a table of integrals with forms involving eu. The form that matches our integral is ∫(1 / 1+e^u) du, where u=12x.

We can substitute u=12x and du/dx=12 to get ∫(1 / 1+e^12x) dx = (1/12) ∫(1 / 1+e^u) du.

Using the table of integrals, the integral of (1 / 1+e^u) du is ln|1+e^u| + C, where C is the constant of integration.

Substituting back in u=12x and multiplying by 1/12, we get the final answer: ∫(1 / 1+e^12x) dx = (1/12) ln|1+e^12x| + C.

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Answer:

 Slope = 0.667/2.000 = 0.333

 x-intercept = 6/1 = 6.00000

 y-intercept = 6/-3 = 2/-1 = -2.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x-12*y-(24)=0

Step 1: Pulling out like terms

Pull out like factors :

  4x - 12y - 24  =   4 • (x - 3y - 6)  

Equation at the end of step 1:

Step 2:

Equations which are never true:

Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

Solve   x-3y-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  x-3y-6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 2/-1 so this line "cuts" the y axis at y=-2.00000

 y-intercept = 6/-3 = 2/-1  = -2.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 6/1 Our line therefore "cuts" the x axis at x= 6.00000

 x-intercept = 6/1  =  6.00000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.000 and for x=2.000, the value of y is -1.333. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.333 - (-2.000) = 0.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.667/2.000 =  0.333  

Geometric figure: Straight Line

 Slope = 0.667/2.000 = 0.333

 x-intercept = 6/1 = 6.00000

 y-intercept = 6/-3 = 2/-1 = -2.00000

Degree of freedom for chi-square test for 10 categories will be 9.

What is chi- square test?

A test that evaluates how well a model matches real observed data is that the chi-square (χ²) statistic. A chi-square statistic can only be calculated with data that's random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a large enough sample.

The Formula for Chi-Square Is

χ(c)=²∑(Oₐ-Eₐ)₂/Eₐ²

where:

c=Degrees of freedom

O=Observed value(s)

E=Expected value(s)

​

Main Body:

Degree of freedom = total categories -1

so no. of categories= 10

Degree of freedom = 10 - 1

Hence degree of freedom = 9

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Answer:

the answer is

Step-by-step explanation:

if we take a and b as two pupil to share the money,then a gets

$15 and b gets $75

sum of the ratio is=6

a =1/6×$90

=$15

b=5/6×$90

=$75

Answer:

B.)58?

Step-by-step explanation:

Hope I helped..

Answer:

b: 58

Step-by-step explanation:

Answer:

dude im not so good in this compound interest stuff but lemme try dawg

So 2500*0.035=87.5 thats what he makes every year so times 9=787.5

Then add it to the initial and you got 2500+787.50= 3287.50

Might be wrong brooo but if its right the answer's $3,287.50

Answer:

25% of sophomores

Step-by-step explanation:

each quartile is 1/4 or 25% of the data set

Answer:

x = 2 pizzas

Step-by-step explanation:

Let

x = number of pizza ordered

Stella’s Pizza charges $16.00 room rental fee and an additional $8.00 for each pizza ordered.

cost for a party at Stella’s Pizza = 16 + 8x

Napoli’s Pizza charges $24 for the room rental fee and an additional $6.00 for each pizza ordered.

cost for a party at Napoli’s Pizza = 24 + 6x

Equate the cost for a party at Stella’s Pizza and cost for a party at Napoli’s Pizza

16 + 8x = 24 + 6x

8x - 6x = 24 - 16

2x = 8

x = 8/4

= 2

x = 2

Answer:

p = 913/670 or 1.3627

Step-by-step explanation:

\(p-\frac{3.1}{6.7}=\frac{4.5}{5}\\\\p=\frac{4.5}{5}+\frac{3.1}{6.7}\\\\p = \frac{913}{670}\)

That is the simplest form.

Answer:

i think x is 11

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

Hope it helps, sense it’s centered around 0.25 then the parameter would be 0.25

To It’s centered around 0.25 then the parameter would be 0.25.

We have given,

Suppose that many large samples were taken from a population and the sample proportion centered around 0.25

We have to determine which of the given is most likely the population parameter.

A sample means from any distribution. We could have a left-skewed or a right-skewed distribution.

To It’s centered around 0.25 then the parameter would be 0.25

Therefore option A(0.25) is correct

To It’s centered around 0.25 then the parameter would be 0.25.

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Answer:

third option

Step-by-step explanation:

Given

f(x) = 40x + 5x² ← express in standard form

f(x) = 5x² + 40x ← factor out 5 from each term

f(x) = 5(x² + 8x)

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 8x

f(x) = 5(x² + 2(4)x + 16 - 16)

f(x) = 5(x + 4)² + 5(- 16)

f(x) = 5(x + 4)² - 80

Answer:

3. f(x) = 5(x + 4)2 – 80

Step-by-step explanation:

Step-by-step explanation:

The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius. The circle centered at the origin with radius 1; its equation is x2+y2=1.

Hope it help!!!

The exponential function that represents this situation is given by y = 45000(1.05)ˣ

An exponential function is in the form:

\(y = a(1+r)^t\)

Where y= total amount, a= starting amount, r= the growth rate as a decimal, t= number of growth periods

The company wants to start you out at $45,000, hence a = 45000.

The raise is 5% (0.05), hence 1 + r = 1 + 0.05 = 1.05

The exponential function is given by:

y = 45000(1.05)ˣ

The exponential function that represents this situation is given by y = 45000(1.05)ˣ

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Answer:

total cost is $150 so the tip is $25

Step-by-step explanation:

125:100=1.25

1.25 x 20 = 25

125+25=150

Answer:

20/3

Step-by-step explanation:

By the property of equal intercepts made by transversals on parallel lines.

\( \frac{4x - 3}{x + 17} = \frac{1}{1} \\ \\ 4x - 3 = x + 17 \\ \\ 4x - x = 17 + 3 \\ \\ 3x = 20 \\ \\ x = \frac{20}{3} \\ \\ \)

The length of OP is √(3) and the Pythagorean Theorem is used to find it.

A theorem is a statement that has been proven to be true based on rigorous mathematical reasoning and evidence. It is a fundamental concept in mathematics and plays a central role in building the structure of mathematical knowledge. Theorems are often used as a basis for further mathematical analysis and the development of new theories and applications.

The length of OP can be found using the Pythagorean Theorem.

By the Pythagorean Theorem, we know that:

MN² + NO² = MO²

Since angle MNP is congruent to angle ONP, we know that triangles MNP and ONP are similar. Therefore, we can set up a proportion:

MN/NP = ON/NP

Simplifying this proportion, we get:

MN = ON

Substituting this into the equation for MO², we get:

MN²  + NO²  = MO²

2(MN² ) = MO²

Since MP is given as 2, we can use the Pythagorean Theorem in triangle MOP to find OP:

MO² = MP² + OP²

2(MN²) = MP² + OP²

2(MN²) - MP² = OP²

2(2²) - 1² = OP²

3 = OP²

OP = √3

Therefore,

The length of OP is √(3) and the Pythagorean Theorem is used to find it.

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