Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

[tex]y \ \textgreater \ x^{2} -1[/tex]
[tex]y\leq -x^{2} +4[/tex]

Answer:

7x + 4,

8y - 3 > 13,

8a,

9 < 5x - 1

Step-by-step explanation:

Hello!

For this question it's important to know what form an expression takes, which is essentially a group of "things" (such as x, y, and numbers) that don't necessarily equal anything else, that would be an equation

In other words, an expression is a mathematical statement that does not include an = sign.

Explanation:

We can do cross multiplying through ratios:

310 feet / 10 secs = x feet / 12 secs

10x = 310 * 12

10x = 3720

x = 372 feet

OR

Divide 310 feet and 10 secs to get 31 feet in 1 sec

Multiply 31 ft and 1 sec to get 372 ft in 12 secs

Answer:

Slope = - 2

Explanation step by step:

Answer: [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

The two points found on the graph are:

The slope can be calculated as:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-4}{-1-2} =\frac{-7}{-3} =\frac{7}{3}[/tex]

Answer:

Step-by-step explanation:

define function fg(x) :

Fg(x)  = f(g(x))

         = [tex]\frac{5}{x}[/tex] (4-2x)-1

         = [tex]\frac{20}{x}[/tex] - [tex]\frac{10x}{x}[/tex] - 1

         = 20 - 10x -1

         = 20 - 1 - 10x

         = 19 - 10x

By the use of the law of conservation of mass, the mass of the aluminum chloride is  267 g.

We know that a chemical reaction occurs when there is the combination of two or more substances such that a new substances is formed. We have to put down the reaction equation in this case and we have;

[tex]4Al(s) + 3ZnCl_{2} (aq) ---- > 2Al_{2} Cl_{3}(aq) +3 Zn(s)[/tex]

Using the law of the combination of mass, the total mass of the reactants must be equal to the total mass of the products; Let the mass of the aluminum chloride formed be x

54 + 409.2 = 196.2 + x

x = (54 + 409.2) - 196.2

x = 267 g

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No, because it is plausible that she would make 3 or fewer shots by chance alone.

What is convincing evidence?

The proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent.

if our test statistic is: positive and greater than the critical value, then we have sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. positive and lower than or equal to the critical value, we must accept the null hypothesis.

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The amount after four years is £2649.79 .

Now we know that we need to obtain the rate for the compounding of the money and we need to recall that for the amount, we have;

A = P(1 +r/n)^nt

A = amount

P = principal

r = rate

n = number of times compounded

t = time

For one year in which the interest is compounded annually;

2496.96 = 2448(1 + r)^1

2496.96/ 2448 = (1 + r)

1.02 = 1 + r

r = 1.02 - 1

r = 0.02 or 2%

Now after four years;

A = 2448(1 +  0.02)^4

A = £2649.79

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The Fourier series representation of the output y(t) is;

(a) y(t) = 0.097 cos(3πt - 67)

(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

Given;

A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;

[tex]\frac{d}{dt}y(t) + 4y(t) = x(t)[/tex]

By taking Laplace's Transform;

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = H(s) = 1/(s + 4)

(a) When input x(t) = cos3πt

∵ ω = 3π

H(jω) = 1/(jω + 4)

H(jω₁) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.097

∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁

y(t) = H(jω₁)*cos(3πt + Ф₁)

→ y(t) = 0.097 cos(3πt - 67)

(b) When input x(t) = sin3πt + cos(6πt + π/4)

∵ ω = 6π

H(jω) = 1/(jω + 4)

H(jω₂) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.051

∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂

y(t) = H(jω₁) * sin(3πt + Ф₁) +  H(jω₂) * cos(6πt + π/4 + Ф₂)

→  y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

The Fourier series representation of the output y(t) is;

y(t) = 0.097 cos(3πt - 67)

y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

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No, this solution is not valid because of wrong concept and wrong calculations as he solved  [tex]\frac{10^{-7} }{10^{-2} }[/tex]  as [tex]10^{-7 + (-2)}[/tex]  but it should be solved as [tex]10^{-7-(-2)}[/tex] .

These exponents can be split since they all share the same base, x. You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).

So according to it,

As they have same the base i.e. 10, we will subtract their power which would be like  [tex]10^{-7-(-2)}[/tex]  = [tex]10^{-5}[/tex] not the [tex]10^{-9}[/tex].

Hence, the solution is not valid due to the wrong concept and wrong calculations.

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Answer:

5 whole laps + 1/4 of a lap. Or, 5.25 laps

Step-by-step explanation:

We can solve this 2 ways.
First, we can continuous add 4/3rds to itself until we reach 7 miles.

4/3 + 4/3 = 2 2/3
+ 4/3 = 4
+ 4/3 = 5 1/3
+ 4/3 = 6 2/3
Then you see that we are almost at 7. We have 1/3 left until we reach 7. 1/3 is 0.25% of 4/3, so its only 25% of a lap. That plsu the 5 other laps we did would equal 5.25 laps.

An easier way is 7 divided by (4/3), which is 5.25.

Good Luck! Hope this helps.

An equation to model this situation is M = t/3 + 3, which is shown in the graph attached below.

In order to solve this word problem, we would assign variables to the amount of time taken by Rick's bus ride and Matt's bus ride to school, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into an algebraic equation, we have the following;

M = 1/4(t) + 3

M = t/3 + 3

Based on the graph (see attachment) which models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can logically deduce that the slope of the graph is 1/4 and the y-intercept is equal to 3.

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The total bill that will be paid by the friends is $88.27.

Cost of meal = $72.50

Sales tax = 6.75%

The amount on tax will be:

= 6.75% × $72.50

= $4.89

Tip = 15% × $72.50

Tip = $10.88

The total bill will be:

= Cost of bill + Tax + Tip

= $72.50 + $4.89 + $10.88

= $88.27

The cost is $88.27.

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Answer:

1/2

Step-by-step explanation:

Because the y is going up by 0.5 which in a fraction form is 1/2 and it isn't negative 1/2 because the number is growing and is not decreasing.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

1) Find the difference between  and y

2) Find the pattern between the numbers

As we can see there is a pattern of subtract [tex]\frac{1}{2}[/tex] between every number

To find this just subtract each number by the other

As 0.5 is equal to [tex]\frac{1}{2}[/tex] the answer to the solution would be [tex]\frac{1}{2}[/tex]

Hope this helps, have a great day!!

Answer:

B. -x^2-2

Step-by-step explanation:

-x^2 would max out at 0, so you need to shift it down by 2 (hence the -2) to have the correct function.

Hope this helped!

The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

Given that,

p = $2,000, r = 3%, and t = 2 yr.

We have to find the i when i=prt.

Here,

i is interest amount.

p is principal amount.

r is rate of interest per year.

t is time period.

So,

Formula for finding interest amount is

i=prt

So,

i=2000(3/100)(2)

i=20×3×2

i=120

Therefore, The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

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Area of the base 'B' of a given rectangular prism is equal to 12 ft².

As given in the question,

For the given rectangular prism ,

Shape of the base is rectangle,

Length of the base of a rectangular prism = 4 ft

Width of the base of a rectangular prism = 3ft

Area of the base of a rectangular prism is given by

= ( length of the base ) × ( Width of the base)

Substitute the value of length and width of the base of the rectangular prism we get,

= ( 4 × 3 ) ft²

= 12 ft²

Therefore, area of the base 'B' of given rectangular prism is equal to 12 ft².

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Answer:

Step-by-step explanation:

As per given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

As given in the  question,

Number of copies of 26 pages article print by printing center is equal to 1,233 copies

Number of copies of 12 page article print by printing center is equal to 658 copies

Total number of pages print by printing center during this one week is equal to

= ( 1233 × 26 ) + ( 658 × 12 )

= 32,058 + 7896

=39,954 pages

Therefore, for the given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

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-691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.

An expression is combination of variables, numbers and operators.

The given expression is −||6c−16b||+1

The values of c is minus twenty three, the value a is minus twelve and the value of b is thirty four.

−||6c−16b||+1

-||6(-23)-16(34)||+1

-||-138--55||+1

-||-692||+1

-692+1

=-691

Hence -691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.

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the answer is 148 the reason is two angle interception

Step-by-step explanation:

The angle on top of x(x+4) is equal to 148.

The angle at x(x+4) = 180 -148 = 32

[tex]x(x + 4) = 32 \\ {x}^{2} + 4x = 32 \\ {x}^{2} + 4x - 32 = 0 \\ (x - 4)(x + 8) = 0[/tex]

x-4=0

x=4

x+8=0

x=-8

The required expression is

(4/3)π(7)³

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

We are given to select the correct expression that gives the volume of a sphere with a radius of 7 units.

We know that,

the VOLUME of a sphere with radius 'r' units is given by

V=(4/3)πr³

Here, the radius of the given sphere is

r = 7 units.

Therefore, the volume of the sphere will be

V=(4/3)π(7)³

Thus, the required expression is

(4/3)π(7)³

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The third congruent side is not included the side of angles thus it will be congruent by the AAS rule thus option (B) is correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given two triangles,

The two angles are congruent.

The sides which are congruent in both triangles are not the common side of angles or not included in the side of angles thus it will be AAS congruency.

Hence "The third congruent side is not included the side of angles thus it will be congruent by the AAS rule".

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Answer:

x= -3/5

Step-by-step explanation:

2x+21/5=3

2x+21/5-21/5=3-21/5           (subtract 21/5 from both sides)

2x=3-21/5                            (L.C.M=5)

2x= 15-21/5

2x= -6/5

2x/2=-6/5/2                        (divide both sides by 2)

x= -6/5x1/2                          (reciprocal)

x= -6/10

simplify:

x= -3/5

1. The number of sides of the polygon is of: 12 sides.

2. The missing exterior angles are of: α = 48.5º.

3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.

A regular polygon is a polygon in which all the sides have the same length.

The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:

Measure of each angle = 360º/number of sides.

For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:

24º = 360º/number of sides.

24n = 360

n = 360/24

n = 12 sides.

The sum of the measures of the external angles of a polygon is always of 360º.

Hence, for item 2, the missing angles are obtained as follows:

2α + 90 + 55 + 40 + 78 = 360

2α + 263 = 360

2α = 97

α = 97/2

α = 48.5º.

An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:

Exterior angle = 180º - 160º = 20º.

Then the number of sides of  the polygon is obtained as follows:

20n = 360

n = 360/20

n = 18 sides.

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The original price of the guitar is $120

From the question, we have

guitar is on sale for 3/4 of the original price (p).

3/4*p = $90

p = (90*4)/3

p= $120

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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