Clarissa has a budget of $1,200 a month to spend for rent and food. She has already spent $928 this month. Which
inequality represents the amount she can still spend this month and remain within her budget?

f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.

The first derivative of the function is:

\(f'(x) = 4x^3 - 3x^2\)

The second derivative of the function is:

\(f''(x) = 12x^2 - 6x\)

Setting f''(x) equal to zero and solving for x gives:

\(12x^2 - 6x = 0\)

6x(2x - 1) = 0

This equation has two solutions:

x = 0, or x = 1/2

To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.

When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.

Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.

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Given

The graph of the parent function f(x) is,

To find:

The graph representing the translation f(x+0.5) of f(x).

Explanation:

It is given that,

The graph of the parent function f(x) is,

That implies,

The equation of f(x) is,

Then,

Therefore, the graph of the translation f(x+0.5) is,

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

Answer: 62

Step-by-step explanation:

You do 112-19-31 and then it equal = 62

Answer:

-----------------------

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer:76 inches

Step-by-step explanation:

Answer:

76 inches

Step-by-step explanation:

Step-by-step explanation:

option number B.......

Answer:

A) Translating 20 units right

Step-by-step explanation:

The triangle is in the same orientation as it would be on the other side of n. It would be translated 20 units instead of 10 because you reflected the triangle twice so you would need to multiply 10 by 2. The 10 also represents the triangle only being reflected once. It would be to the right because the triangle moved to the right.

Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

ANSWER :

The answer is Option C.

EXPLANATION :

Using the quadratic formula in finding the values of x :

where a, b and c are the coefficients of the quadratic function.

a = -3, b = -4 and c = -4

Note that i = √-1

Answer:

-2x

Step-by-step explanation:

Step-by-step explanation:

4. because it's the highest number your can evenly divide both numbers by

Answer:

$102

Step-by-step explanation:

Answer:

64%

Step-by-step explanation:

16/25

Answer:

64%

Step-by-step explanation:

if they made 16/25 free-throws, you would multiply each side by 4 in order to get 100% on the right side, and if you multiply 16 by 4 it is 64

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

The value of a in Quadratic function ax^2 + bx + c is 1.

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

the polynomial function f(x)=Ax^2+Bx+C, where A 0 and A, B, and C R. A quadratic function is a second-degree polynomial function in which all the coefficients of the terms with a degree less than 2 are zeros.

Roots of the given equation are 4 and 7.

then the quadratic function whose roots are 4 and 7 is

x^2  - (4+11)x + (4*7)

x^2-11x+28

on comparing this to the Quadratic function ax^2+bx+c

the value of a is 1.

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Answer:

53 m^2

Step-by-step explanation:

53 m^2 is the area of the figure given!

So as given in the question that the sides meet at right angles.

we take the bottom of the upper rectangle as 5m, then the upper side of the lower rectangle will be 3+5+3= 11.

Now, by using the formula of the area of a rectangle that is Area = Height x width, we areas of the two rectangles. Then add both the areas.

Finally we get the area of the given figure!

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Answer:

A = 53 m²

Step-by-step explanation:

A = A1 + A2

= 4m×5m + 3m×(3m + 5m + 3m)

= 20m² + 3m×11m

= 20m² + 33m²

= 53 m²

The question is poorly formatted:

Example: Study the example on the right to help you complete the problem below.  

Solve the equation

\(A= \frac{1}{2}bh\) for h.  

Options:

\(h = \frac{2A}{b}\)    \(h = \frac{2b}{A}\)      \(h = \frac{b}{A}\)     \(h = 2Ab\)​

Example:  

\(8 = \frac{1}{3}6x\)

Multiplication property  

\((3)8 = (3)(\frac{1}{3})6x\)

\((3)8 = 6x\)

Simplify: \((3)\frac{8}{6} = \frac{6x}{6}\)  

Multiplication property: \((3)\frac{8}{6} = x\)

Simplify: \(\frac{8}{2} = x\)

Simplify : \(4 = x\)

Symmetric property : \(x = 4\)

Answer:

\(h = \frac{2A}{b}\)

Step-by-step explanation:

Given

\(A= \frac{1}{2}bh\)

Required

Solve for h

\(A= \frac{1}{2}bh\)

Multiplication property  

\(2 * A= \frac{1}{2}bh * 2\)

\(2A = bh\)

Simplify

\(\frac{2A}{b} = \frac{bh}{b}\)

\(\frac{2A}{b} = h\)

Symmetric property

\(h = \frac{2A}{b}\)

Hence, the expression for h is:

\(h = \frac{2A}{b}\)

Answer:

h = 2A/b

Step-by-step explanation:

that is the answer trust me. edge 2021

Answer:

Step-by-step explanation:

8.008.009

Answer:

2x-3/7x

Step-by-step explanation:

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

given that

they have 10 bags full of coins

in each bag are infinite coins.

but one bag is full of forgeries, and you can't remember which bag.

you know that genuine coins weigh= 1 gram

forgeries weight = 1.1 gram

now, we need to find which bag has  forgeries  in minimum readings

then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins

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Total weight=55gm ,then there is no forgeries coin bag

1 bag with forgeries = take 1 coin from first bag

from 2 bag = take 2 coin

and similarly with all 10 bags.....

from 10th bag = take 10 coin

if there is no forgeries ,then  total weight    = (1+2+3+4+5+6+7+8+9+10)

                                                                        =55gm

If bag weight 55.3 than we know that there are 3 forgeries.

So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.

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The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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Answer:

248 ounces

Step-by-step explanation:

I hope this helps :D

Answer:

248 ounces is the correct answer hope you will like it and Mark me as BRAINLIEST!!!!

Answer:

<A = 45°

<B = 110°

Step-by-step explanation:

Sum of the interior angles of a triangle = 180°

Therefore,

(x + 65)° + 25° + x° = 180°

Solve for x

x + 65 + 25 + x = 180

Add like terms

2x + 90 = 180

2x = 180 - 90

2x = 90

x = 90/2

x = 45°

✔️x + 65 = 45 + 65 = 110°

<A = x = 45°

<B = 110°

Answer:

its 3x9+13

Step-by-step explanation:

x

The expression 27+36 as be written as: 9(3+12)

An expression is a set of terms combined using the operations +, – , x or for example 4 x − 3 or x 2 – x y + 17 .

An equation states that two expressions are equal in value,

for example 4 b − 2 = 6 .

We have: 27+36

Prime factorise both the numbers:

27=3*3*3

36= 2*2*3*3

So,

27+36

=3*3*3+2*2*3*3

= 3*(3*3+2*2*3)

=9(3+12)

Hence, The expression 27+36 as be written as: 9(3+12)

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Answer:36in

Step-by-step explanation:

Answer: 36in

Step-by-step explanation: Its 36in because if you add them all up then you get 36. (hope it helps +)

Answer:

10/11

Step-by-step explanation:

Answer:

the answer is 2 2/7

Step-by-step explanation:

make them improper fractions

flip the second fraction

multiply the numerators

then multiply the denominators

then simplify your answer

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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