The graphs of the fuctions f and g are shown below, find all values of x for which f(x) < g(x). 30 points!!!

From the question, we are asked to find which is great between 12.5 or |-13|

recall:

|-13|

The absolute value is the distance between a number and zero. The distance between -13 and 0 is 13.

The absolute symbol makes any number positive.

So, |-13| is the greater because |-13| = 13.

So, between 12.5 and |-13|, |-13| is greater since it is same as 13.

Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.

The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:

c² = a² + b² - 2 × a × b × Cos C.

Considering right triangle ABD,

BD = a

DC = b

BC = c

Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:

BD = √(7.5² + 5²)

BD = √(7.5² + 5²)

BD = 9.0 cm

Use the law of cosines to find the length of BC:

BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.

Substitute

BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38

BC² = 250 - 184.4

BC² = 65.6

BC = √65.6

BC = 8.1 cm

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The fraction of oranges eaten by the family is 3/5

Given,

Number of oranges in a bag = 8 oranges

Number of bags sold to a family = 10 bags

Number of members in the family = 6 members

Number oranges ate by each member of the family = 6 oranges

We have to find the fraction of the oranges eaten by the family members;

Here,

8 oranges in 1 bag and 10 bags sold.

So, total number of oranges sold = 8 x 10 = 80 oranges

Each member ate 6 oranges and there are 8 members.

So, total number of oranges eaten by them = 6 x 8 = 48 oranges

Now,

The fraction of oranges eaten by the family = 48/80 = 6/10 = 3/5

That is,

3/5th of oranges were eaten by the family.

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Answer: 0.125

Step-by-step explanation:

1 1/4 is equal to 5/4

5/4 is equal to 1.25

then you would do 1.25 divided by 10

once you do that you would get your answer of 0.125!

Answer:

11/4÷10 =

11/4 ×1/10=

11/40=

0.275

Step-by-step explanation:

you can ask questions for clarification

we gotta know the conversion between cups and gallons

We know

1 cup (US) = 0.0625 gallons

So, 2 gallon would be 2/0.0625 = 32 cups

So, the problem in cups is:

32 cups = $23.36

17 cups = $20.06

Definitely 32 cups for 23.36 is better buy

2 gallons for $23.36 is the better buy

Note:

23.36/32 = $0.73 per cup

20.06/17 = $1.18 per cup

It took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.

The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.

Given is Davin who needs 1 3/4 hours to get to his aunt's house. However, due to the labor day traffic this year it took him 3 1/5 years.

We have to find the difference between the time span Davin took to reach his aunt's house.

Time taken by Davin without the labor day traffic = T[N] = 1 3/4 = 7/4 hours

Time taken by Davin with the labor day traffic = T[L] = 3 1/5 = 16/5 hours

Difference in time spans = T[D] = T[L] - T[N]

T[D] = 16/5 - 7/4

T[D] = 3.2 - 1.75

T[D] = 1.45 = 1 + 0.45

T[D] = 1 [tex]\frac{3}{4}[/tex] hours  

Davin took 1 [tex]\frac{3}{4}[/tex] hours more.

Therefore, it took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.

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-24-68i is solution of complex number.

What is the best definition of a complex number?

(4-6i)(6-8i)

= 24-32i-36i+48i²

= 24 + -68i - 48

= -24-68i

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The complete question is -

Multiply the following complex numbers (4-6i)(6-8i)

The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

What is factorization?

When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.

We are given a quadratic equation

[tex]4x^2+13x-15[/tex]

We use quadratic formula to compute the factor of the equation

[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]

Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

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Remember that

P(A or B)=P(A)+P(B)-P(A and B)

In this problem, we have that

Event A and Event B are not independent

we have

P(A)=0.68

P(B)=0.32

P(A and B)=0.11

substitute

P(A or B)=0.68+0.32-0.11

P(A or B)=0.89

To find the distance between two numbers on the number line, you have tu use absolute value

So, if I want to know the distance from -2 to 5, all I have to do is to substract 5 from -2 and then apply absolute value, like this:

And the number line should look like this:

the relation is 3x + y = 3

so,

y = 3x - 3

the domain is the values of x

so, substitute with each value of {-2,2,4} at the last equation of y

when x = -2 , y = 3*-2 - 3 = -6 - 3 = -9

when x = 2 , y = 3 * 2 - 3 = 6 - 3 = 3

when x = 4 , y = 3 * 4 - 3 = 12 - 3 = 9

so, the range will be {-9 , 3 , 9}

The correct answer is option a. (-9,3,9)x

In the given figure : lines l and m are parallel and a, b are transversal

Since, the lines a and b are parallel and l act as a transversal.

Then,

x = 23

Answer : x = 23

The value of the function h(2) for h(t) = -16t2 + 32t + 5 is h(2) = 5

From the question, the function definition is given as

h(t) = -16t2 + 32t + 5

First, we express the exponent in the function properly

This is represented as

h(t) = -16t² + 32t + 5

The function value to calculate is given as

h(2)

This means that we calculate h(t) when t = 2

So, we have

h(2) = -16(2)² + 32(2) + 5

Evaluate the exponents

h(2) = -16(4) + 32(2) + 5

So, we have

h(2) = 5

Hence, the function value is 5

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The image of the point (-4, -1) after the translation is:

(-3, 1)

A translation:

Tᵃ'ᵇ applied to a point (x, y) gives:

Tᵃ'ᵇ(x, y) = (x + a, y + b).

In this case, we know that:

Tᵃᵇ(1, 1) = (1 + a, 1 + b) = (0, 3)

Then:

1 + a = 0

1 + b = 3

Solving these we get:

a = 1

b = 3 - 1 = 2

The translation is:

T¹'²

Applying this to the point (-4, -1) gives:

T¹'²(-4, -1) = (-4 + 1, -1 + 2) = (-3, 1)

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Answer:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Explanation:

The symbol < means less than and the symbol > means greater than.

On the other hand, if we identify each number on a number line, we get:

Therefore, the true statements are:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Because, for example, -0.7 is on the left of -0.4 which means that -0.7 is less than -0.4.

0.5 in on the right of -0.6 which means that 0.5 is greater than -0.6.

In this problem, we are going to write and solve a system of equations based on a real world situation.

Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.

To begin, we need to create variables for the unknown cost of each chore.

Let x represent laundry, and let y represent dishes.

From the first equation, we can write the equation:

We can write the second equation as:

Together, we have the system:

Multiply the first equation by -1, then add it to the second equation:

We can divide the remaining equation by 2 on both sides:

Lada made $2 per load of laundry.

We can use the value of x in the first equation to find the value of y. Substitute x = 2:

Subtract 2 from both sides:

Divide by 8 on both sides:

Lada made $3 per load of dishes.

A graph which best describes what the proportional relationship would be D. A line that passes through the point (0, 0) and continues through the point (12, 3).

In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Additionally, a graph which shows a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).

Since the graph represents a proportional relationship we will get;

Constant of proportionality, we get;

k = 12/3 = 8/2 = 24/6

k = 4

Ratio,

24:6

= 12:3.

Therefore, A line that passes through the point (0, 0) and continues through the point (12, 3).

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The formula for the given arithmetic series for the term aₙ will be aₙ=a₁+(n-1)d.

So, the possible sequence of -64, -16, 4:

So, the formula for the aₙ term will be:

Therefore, the formula for the given arithmetic series for the term aₙ will be aₙ = a₁ + (n - 1)d.

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The correct question is given below:

Write an explicit formula for an, the nth term of the sequence

-64, -16, 4,....

Answer:

6.  Draw a vertical line that goes though points (4,7) and (4,9).  For a relation to be a function, each input has to have only one output.  The input 4 cannot have the output of 7 and 9.  This proves that this is not a function

7. The range is 91, 3, 6, 10 and 15)

Step-by-step explanation:

The range is the answer if you put in the x for range that they give you.

For example:

x ( x+ 1)/2  If I put in 1 for x, I will get

1(1+1)/2

2/2

1

When the input is 1, the output is one.  You that for each of the domains given and you will find the ranges (outputs) that I have written above.

The measure of the value of ∠j is 10°.

What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.

Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.

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Note that:

Applying the addition formula given above to cos 150:

Answer:

u = 3

Step-by-step explanation:

Step 1: Distribute 5 in u - 5

[tex]\displaystyle{5\cdot u - 5\cdot 5 +6u=8}\\\\\displaystyle{5u-25+6u=8}[/tex]

Step 2: Add like terms together (u-term)

[tex]\displaystyle{11u-25=8}[/tex]

Step 3: Add both sides by 25

[tex]\displaystyle{11u-25+25=8+25}\\\\\displaystyle{11u=33}[/tex]

Step 4: Divide both sides by 11

[tex]\displaystyle{\dfrac{11u}{11}=\dfrac{33}{11}}\\\\\displaystyle{u=3}[/tex]

Answer Check

Step 1: Substitute u = 3 in the equation

[tex]\displaystyle{5(3-5)+6(3)=8}[/tex]

Step 2: Evaluate & Simplify

[tex]\displaystyle{5(-2)+18=8}\\\\\displaystyle{-10+18=8}\\\\\displaystyle{8=8}[/tex]

Since the equation is true after substituting u = 3. Therefore, the answer is u = 3.

Please let me know if you have any questions!

Answer:

See below

Step-by-step explanation:

Length (L), volume (V), weight(W), or mass(M)

Mile     L

Cup           V

Pound   W

Centimeter L

Liter     V

Gram   M

Pint           V

Yard   L

Kilogram   M

Teaspoon  V

Milliliter    V

1. Mile

2. Cup

3. Pound

4. Centimeter

5. Liter

6. Gram

7. Pint

8. Yard

9. Kilogram

10. Teaspoon,

11. Milliliter

The value of the unknown angle x is 22 degrees.

SV is a parallel to RU.

RV is a transversal line that cut across the parallel lines SV and RU.

Therefore,

x = ∠V(alternate angles)

Alternate angles are congruent.

Hence,

∠V + 44 + 5x + 4 = 180 (sum of angles in a triangle)

x + 44 + 5x + 4 = 180

x + 5x + 48  = 180

6x + 48 = 180

6x = 180 - 48

6x = 132

divide both sides by 6

x = 132  /6

x = 22 degrees

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EXPLANATION

We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:

Perimeter = 40 cm = 4x + 2x + 2 + x + 3

Adding like terms:

40 = 7x + 5

Subtracting 5 to both sides:

40 - 5 = 7x

Adding like terms:

35 = 7x

Dividing both sides by 7:

35/7 = x

Simplifying:

Then, by the obtuse triangle theorem, the following relationship should be fulfilled.

The value of x = 1/M-1 , x = -1/M+1

What is Graph?

The graph of a function f is the set of ordered pairs where "displaystyle f(x)=y" exists. In the common scenario when x and f(x) are real integers, these pairings represent Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane.

M(x) = |x + 1|

|x + 1| = M(x)

x + 1 = M(x)

x + 1 = -M(x)

Adding (-x) both side

x + 1 + (- x) = M(x) + (- x)

x + 1 + (- x) = -M(x) + (- x)

x + 1 - x = M(x) - x

x + 1 - x = -M(x) - x

1 = M(x) - x

1  = -M(x) - x

M(x) - x = 1

-M(x) - x  = 1

x(M-1)  = 1

x(-M-1)  = 1

Dividing both side with (M - 1) and (-M - 1)

x(M-1)/(M - 1)   = 1/(M - 1)

x(-M-1)/(-M - 1)  = 1 /(-M - 1)

x = 1/(M - 1)

x = 1/(-M - 1)

Hence, x = 1/M-1 , x = -1/M+1

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Answer:

Step-by-step explanation:

Find the amount of increase:

Find the percent value of the increase over the initial price:

Option C gives the graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Choice C provides a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

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Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

Answer:

1288 times greater

Step-by-step explanation:

(8.5x10^-2)/(6.6x10^-5)

(8.5/6.6)*(10^-2/10^-5)

(1.29)*(10^3)

1288 times greater