How can representing sentences and phrases with symbols help you determine whether to apply the Law of Detachment or the Law of Syllogism

the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

We know that if a parabola has x-intercepts a and b, and a leading coefficient A, then the equation is:

f(x) = A*(x - a)*(x - b)

In this case the x-intercepts are x = -4 and x = 5, then we have:

f(x) = A*(x + 4)*(x - 5)

Now we use the fact that the parabola passes through the point (1, -40), then we have that:

f(1) = -40 =  A*(1 + 4)*(1 - 5)

        -40 = A*(5)*(-4) = A*-20

       -40/-20 = A = 2

Then the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

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The best description of the given inequality is;

Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

Hence, Option B is true.

What is inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

The inequality is given as;

⇒ 120 ≤ 12 k + 29

It can be written as;

12k + 29 ≥ 120

Now, We have;

A constant term = 29

And, Variable with number = 12k

Which is multiple of the number of buttons collected and the number of years k.

The sign is ''greater than equal'' to with 120, that's mean 'at least 120'

So, The best description of the given inequality is;

Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

Hence, Option B is true.

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The complete question is this;

Which situation can be represented by this inequality? 120 ≤ 12 k + 29

(A)Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

(B)Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

(C)Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

(D)Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

Answer:

27

Step-by-step explanation:

Answer: Volume is calculated by lenght x width x height ,so you would say 6 x 4 x 4. Which is   96 cubic units !!!

Step-by-step explanation:

The value of x is 5 which is option (D) .

It is given that 25/20 = x/4

On simplifying , we get

          [tex]\frac{25}{20} =\frac{x}{4} \\\\x=\frac{25\times4}{20} \\\\x=\frac{100}{20} \\\\x=5[/tex]

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The complete question is mention below :

What value of x makes this proportion true? 25/20 = x/4

A.6

B.20

C.9

D.5

Answer:

(2, -3)

Step-by-step explanation:

x= -3y-7    

5x+6y=-8  

1. Substitute x= -3y-7 into 5x+6y=-8 which becomes

5(-3y-7)+6y=-8

2. expand the brackets

-15y-35+6y=-8

3. simplify the equation

 -9y-35=-8

4. from this we can find the value of y by adding 35 on each side and then dividing by -9 on each side

-9y=27

y=-3

5. so, the value of y is -3 to find the value of x we just substitute the value of y (-3) into the x=-3y-7

x= -3(-3)-7

expand the brackets and simplify the expression

x=9-7

x=2

6. so the value of x=2

7. your final answer will be (2, -3)

The length of the rectangle according to the task content where the length of a rectangle is twice its width whose perimeter is; 84 feet is; 31.33.

According to the task content, it follows that the length of the rectangle is twice its width, If the perimeter is 84 feet.

Since the perimeter of the rectangle in discuss can be determined as follows;

Perimeter = 2(l + w)

where l = 2w.

Therefore,

94 = 2(2w + w)

47 = 3w

w = 47/3

w = 15.667.

Ultimately, the length of the rectangle in discuss is; 2w = 2× 15.667

= 31.33 feet.

Therefore, the length of the rectangle according to the task content where the length of a rectangle is twice its width whose perimeter is; 84 feet is; 31.33.

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Based on Cameron's current music service fees, the number of songs that would make the new service a less expensive option is 101 songs

The expression for the new service assuming the number of songs is x is:

= 15 + 0.80x

The expression for Cameron's current service is:
= 0.95x

Equating them gives:

0.95x = 15 + 0.8x

0.95x - 0.8x = 15

0.15x = 15

x = 100 songs

The cost will be the same at 100 songs so the new service would be cheaper at 101 songs.

First part of question:

Cameron pays $0.95 per song with his current music service.

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Two or more expressions with equal sign in between is called as Equation. The value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.

Two or more expressions with equal sign in between is called as Equation.

The given equation is y=-2x2+4x+4

Where y=4

4=-2x2+4x+4

-2x^2+4x=0

x(-2x+4)=0

x=0 and -2x=-4

x=2

Therefore the value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.

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Since they're in arithmetic progression, the difference between consecutive terms is fixed.

[tex](x + 2) - (x - 1) = 3[/tex]

[tex]3x - (x + 2) = 2x - 2 = 3 \implies 2x = 5 \implies x = \dfrac52[/tex]

Then the first term is

[tex]x-1=\dfrac52 - 1 = \boxed{\dfrac32}[/tex]

and the fifth term is

[tex]3x + 3 + 3 = 3\cdot\dfrac32 + 3 + 3 = \boxed{\dfrac21}2[/tex]

The x-coordinate of the solution is -0.22

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

5x - 4y =8

10x + 3y = -9

Next, we graph the equations

From the graph, we have the x-coordinate of the intersection to be

x = -0.22

Hence, the x-coordinate of the solution is -0.22

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Answer:

for question a)

yes it is a function

Step-by-step explanation:

more hours studied = higher score

Answer:

r = 10 mph

Step-by-step explanation:

3 hr. x rate = 2.5 hr x (rate + 2

r = 10 mph

Answer:

r = 10 mph

Step-by-step explanation:

The slope of the line is -5 / 4.

The slope of a line is a measure of its steepness.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

Therefore,

slope = change in y / change in x

slope = y₂ - y₁ / x₂ - x₁

Using (1, -3)(-3, 2)

x₁ = 1

x₂ = -3

y₁ = -3

y₂ = 2

Therefore,

slope = 2 - (-3) / -3 - 1

slope = 2 + 3 / -4

slope = - 5 / 4

Therefore, the slope of the line is -5 / 4.

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Answer:

(0, -4)

Step-by-step explanation:

hope this helps!!! :))

Answer:

about 42%

Step-by-step explanation:

3/7 = 0.41857... =  42%

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

-x² + 7x + 5 is the domain of all real numbers.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².

we have to calculate (g - f)(x)

Which is equivalent to:

(g - f)(x) = g(x) - f(x)

Taking the two functions and substituting them into this expression, we get,

g(x) - f(x) = (7x + 5) - (x²)

simplifying the above function, we get

g(x) - f(x) = -x² + 7x + 5

Therefore, (g - f)(x) = -x² + 7x + 5.

We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.

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Answer:

- 4 < x < -1

Step-by-step explanation:

Answer: x=28/3=9.333

Step-by-step explanation:

Answer:

1/2 + 2/3 × 3/14

Step 1: you multiply first

= 2/3 × 3/14

= 6/42

= 7

Step 2: Now add

= 1/2 + 7

LCM = 14

= 1/2 + 7/1

= 1 + 14

2

= 15/2.

or 7.5

or 7½

Answer: B is correct answer

Answer:it’s 200 Oumou

Step-by-step explanation:203-3=200

The complete table is shown in the attachment.

1. 4.8 gallons of water

2. 25 mins

3. The constant of proportionality = 1.6

An example of a proportional relationship is the relationship between time taken and the number of gallons of water that fills the tank which is at a constant rate.

Constant rate is the same as constant of proportionality. It is calculated as, k = y/x.

The equation of a proportional relationship is expressed as y = kx.

Using the pair, (0.5, 0.8), find the constant rate/constant of proportionality (k):

k = y/x = 0.8/0.5

k = 1.6 gallon/min

Substitute k = 1.6 into y = kx

y = 1.6x

Fill the table using the equation, y = 1.6x

For 1 min (x):

y = 1.6(1) = 1.6

1.6 gallon

For 3 mins (x):

y = 1.6(3) = 4.8

4.8 gallons

For 40 gallons (y):

40 = 1.6x

40/1.6 = x

x = 25

25 mins.

The complete table is shown in the attachment.

1. 4.8 gallons of water will be in the tank after 3 mins

2. It will take 25 mins to fill the tank with 40 gallons of water.

3. The constant of proportionality = 1.6

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Comparing the price of a 50000 mercedes to the price of a 40000 lexus The absolute price difference is 10000 while the relative price difference is 20%

Absolute difference refers to the gap between the prices. This implies the amount one has more than the other.

This could be solved by subtraction an is solves as follows:

price of a mercedes -  price of a lexus

= 50 000 - 40 000

= 10 000

Here, the price difference is expressed in percentage of the reference price being checked with. This is achieved using the formula below:

( price of a mercedes -  price of a lexus ) / price of a mercedes * 100

= (( 50 000 - 40 000 ) / 50 000 ) * 100

= (( 10 000 ) / 50 000 ) * 100

= ( 0.2 ) * 100

= 20%

Hence the absolute price difference is 10 000 and the relative price difference is 20%

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Point Q will be located at 27 / 7.

We are given the points:

P = - 26

R = - 5

Let Q = x

Now, we also have the ratio as:

PQ : QR = 5 : 2

PQ = Q - P

PQ = x - ( - 26 )

PQ = x + 26

QR = R - Q

QR = - 5 - x

Now, we know that:

PQ / QR = 5 / 2

2 PQ = 5 QR

2 ( x + 26 ) = 5 ( - 5 - x )

2 x + 52 = - 25 - 5 x

2 x + 5 x = 52 - 25

7 x = 27

x = 27 / 7

Therefore, point Q will be located at 27 / 7.

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Solution of exponential equation 5²x=130 is , [tex]x = \frac{26}{5}[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa is also possible . The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

Mathematically, if  [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as    [tex]a^n = x[/tex] .

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

According to given statement,

5²x=130

divide both side by 5² , the equation becomes :

[tex]= > x = \frac{130}{(5^2)} \\\\= > x = \frac{26 (5)}{(5^2)}\\\\= > x = \frac{26}{5}\\\\[/tex]

Thus solution for this equation is  [tex]x = \frac{26}{5}[/tex]

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The growth factor for the annual rate of change of +12.5 % is 1.125.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 12.5 % = + 12.5 / 100 = + 0.125

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+ 0.125)

B = 1.125

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.125.

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Answer:

x<-27/4

​

Step-by-step explanation:

−4(2−x)1<−35

Multiply −4 and 1 to get −4.

−4(2−x) <−35

Use the distributive property to multiply −4 by 2−x.

−8+4x<−35

Add 8 to both sides.

4x<−35+8

Add −35 and 8 to get −27.

4x<−27

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

The values for 4f(x)+2 g(x) = 2x²- 2x + 24

Given :  f(x)=2x+5

           g(x)=x²-3x+2

Solution:

          4f(x) =  8x+20

           2g(x) = 2x²-6x+4

           4f(x) + 2g(x) = 8x+20 + 2x²-6x+4

          4f(x) + 2g(x) = 2x²- 2x + 24

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The cubic polynomial equation has three real roots. Simplify the expression to a linear factor and a quadratic expression. The linear factor is obtained by taking values for x and substituting in f(x) to get f(x) = 0. If a value of x gives f(p) = 0, then x-p is a linear factor. By algebraic long  division, obtain the quadratic equation and solve it to obtain the real roots.

f(x) = x³-7 x²+13 x-4

x = 4,

f(x) = 4³-7 (4)²+13 (4)-4 = 0

Thus, x-4 is a linear factor.  

x³-7 x²+13 x-4/ x-4.

(x³-7 x²+13 x-4)/ x-4 =  x²-3 x+1

x²-3 x+1  = 0

By quadratic formula: x = (-b±√(b²-4ac))/(2a)

x =  (--3±√((-3)²-4(1x1))/(2)

x = (3±√(9-4))/(2)

x  = (3±√5)/(2)  

x  = (3±2.24)/(2)  

x = (3+ 2.24)/2 = 2.62

x = (3- 2.24)/2 = 0.38

The real roots are x = 0.38, 2.62 and 4

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It should be noted that in order to measure the value, the measurement have to be in the same unit.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Measurement is crucial in establishing connections across different branches of mathematics. For instance, it gives the use of math abilities and spatial concepts a rich and meaningful context. Measurement also establishes connections between mathematics and other academic disciplines.

From the information, it was illustrated that the boys all had measurement of trees taken. Therefore, it should be noted that since they are in different units, it cannot be done.

In this case, the reason is that in order to measure the value, the measurement has to be in the same unit. This will make it easier to do the calculation.

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Answer:

1.) 3x + 7 = -x - 1

*collect like terms

3x + x = -1 - 7

4x = -8

x = -2

2.) 4x - 3 = 1 - 2x + 5

*collect like terms

4x + 2x = 1 + 5 + 3

6x = 9

x = 9/6

x = 3/2

3. 4x - 2 + x = 2x - 2

*collect like terms

4x + x - 2x = -2 + 2

3x = 0

x = 0/3

x = 0

4.) 3x - 4 + 1 = 5x - 5 - 2x

*collect like terms

3x - 5x + 2x = - 5 + 4 - 1

(this is a tricky one ... sorry I can't figure the answer)