The question is on the picture below

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of linear equations:

(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0    

- c + d = 1      (1)

3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0    

3 · c + d = 117       (2)

The solution of this system is c = 29 and d = 30.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

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Truth Value for p^ q when x is replaced by 2 is also true. (  p^q is True)

The prime numbers are those numbers that have only one factor namely 1 and the number itself.

Given that p = x is prime and q = x is even. If we replace x by 2 then we would get

p = 2 is prime

q = 2 is even

p^q will be held true only if p and q both are true.

The statement for p and q both are true because 2 only has two factors only 1 and 2 themselves.

2 is also considered an even number (2,4,6,8,...)

Since p = true and q = true then

p and q = p^q = true

Thus, p^q is True.

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Answer:

p^q is true

Step-by-step explanation:

If both p and q are true, the statement p^q is true. If both p and q are false, the statement p^q is still true. All other options yield a false result.

The factor by which the complex rational number be multiplied is; 2 -9i.

The expression given in the task is a fraction made up of complex numbers.

Hence in a bid to evaluate the quotient of the expression; -1 - 4i/ 2 + 9i.

The numerator and denominator must be multiplied by the conjugate of the denominator which in this case is; 2 -9i.

This is to help reduce the denominator to a real number.

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Answer:

$11.78

Step-by-step explanation:

14.89+9.33=24.22

36-24.22=11.78

Based on the given population function, the population of the town can be said to be increasing.

The population of the town is increasing because the value of "b" is positive and greater than one.

"b" which in this case is 0.87, is the rate at which the population is growing overtime. If it is a positive figure, then the population is expanding.

The question is:

Is the town's population increasing or decreasing?

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Answer:

domain of the sine and cosine functions is all real numbers

Step-by-step explanation:

range of both the sine and cosine functions is [−1,1]

graph can go left and right to infinity

graph goes up and down between 1 and -1

graph looks like a wave or

like U letters next to each other

UUUU

sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

mathlibretextsorg

Answer:

[tex]\sf C. - \dfrac{3}{4}[/tex]

Explanation:

[tex]\sf Given \ equation : 4x - 3y = 12[/tex]

Rewrite in slope intercept form "y = mx + b"

[tex]\rightarrow \sf 4x - 3y = 12[/tex]

[tex]\rightarrow \sf - 3y = 12 - 4x[/tex]

[tex]\rightarrow \sf y =\dfrac{ 12 - 4x}{-3}[/tex]

[tex]\rightarrow \sf y =\dfrac{ 4}{3}x - 4[/tex]

Here the slope is 4/3 and y-intercept is -4

Perpendicular lines has negatively inverse slope.

→ per. slope = -(slope)⁻¹ = -(4/3)⁻¹ = -3/4

Answer:

[tex]-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Given linear equation:

  [tex]4x-3y=12[/tex]

Find the slope of the given linear equation by rewriting the equation so that it is in slope-intercept form (i.e. make y the subject):

[tex]\implies 4x-3y=12[/tex]

[tex]\implies 4x-3y+3y=12+3y[/tex]

[tex]\implies 4x=12+3y[/tex]

[tex]\implies 4x-12=12+3y-12[/tex]

[tex]\implies 4x-12=3y[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{4}{3}x-\dfrac{12}{3}[/tex]

[tex]\implies y=\dfrac{4}{3}x-4[/tex]

Therefore, the slope of the given line is 4/3.

If two lines are perpendicular to each other, the product of their slopes will be -1.   Therefore, the slope (m) of the line perpendicular to the given line is:

[tex]\implies m \times \dfrac{4}{3}=-1[/tex]

[tex]\implies m=-\dfrac{3}{4}[/tex]

The value of 32 in the equation will serve as the time taken by the driver to travel

If Alice fills up the gas tank of her car before going for a long drive, and the equation that shows the amount of gas in gallons in Alice's car when she has driven m (miles). is given as:

g = 15 - m/32

The value of 32 in the equation will serve as the time taken by the driver to travel

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Answer:

-135689;456+((888888888

The magnitude of the resultant vector is 27 miles

Resultant vector = Distance of A - Distance of B

This is so because of the opposite direction of the car's movement

A = 87 miles

B = 114 miles

Resultant vector = 114 - 87

Resultant vector = 27 miles

Thus, the magnitude of the resultant vector is 27 miles

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By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.

In this question we have an application of direct proportionality model, whose form is shown below:

y = k · x     (1)

Where:

If we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:

y = (1/36.744 t/bu) · (45 bu)

y = 1.225 t

By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.

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Answer:

B

Step-by-step explanation:

i took the test

The answer choice in which case the equation has no solution are; Choice A ; 40x+40=40x+20 and Choice C; -20x+40=-20x+20.

A system of linear equations is determined to have no solutions when the variable coefficients diminish upon evaluation and hence, the value of the variable can not be determined.

Hence, Choices A and C; in which case; the coefficients of variable X amount to 0 upon evaluation are equations with no solution.

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Answer:

There are no solutions.

Step-by-step explanation:

Hope this helped! :D

Answer:

The graph increases.

Step-by-step explanation:

hope this helps!!

Answer: the graph increases

Step-by-step explanation: did test

The second statement is the inverse statement of the first conditional statement.

If x and y are two propositions, then:

x ⇒ y

Is a conditional statement:

"If x, then y".

The other statement is:

¬x ⇒ ¬y

Where:

¬x means "not x"

So the statement is:

"If not x, then not y".

That would be the inverse statement of the given conditional statement.

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The standard equation of a straight line is given by y = mx + b, where m is the slope (rate of change) and b is the y intercept of the line.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard equation of a straight line is given as:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept of the line.

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Answer:

dN)/(dt)=(rN(K-N))/K is the answer.

Step-by-step explanation:

The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst.

The continuous version of the logistic model is described by the differential equation is:

(dN)/(dt)=(rN(K-N))/K. (where r is the Malthusian parameter (rate of maximum population growth) and K is the so-called carrying capacity (i.e., the maximum sustainable population).

So, the correct option is ' (dN)/(dt)=(rN(K-N))/K'.

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By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists

[tex]$ 6(log _2(3) +3 log _2(n))[/tex].

A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.

From the definition of a logarithm, we get

aˣ = b exists the same as x = logₐb

Given: [tex]$3log _2(9n)[/tex]

Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]

[tex]$= 3(2log _2(3) + log _2(n))[/tex]

Expanding the equation, we get

[tex]$3(2log _2(3) + log _2(n))[/tex]

[tex]$= 6(log _2(3) +3 log _2(n))[/tex]

[tex]$= 6(log _2(3) +3 log _2(n))[/tex]

Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].

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The correlation is a negative correlation, because weights and city MPG do not increase at the same time

To graph of the table of values, we plot

See attachment for graph

The correlation is a negative correlation, because weights and city MPG do not increase at the same time

To do this, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

The line of best fit equation is

y = bx + a

Where

b = SP/SSX = -857.75/862.94 = -0.99

a = MY - bMX = 24.25 - (-0.99*28.94) = 53.0

So, we have:

y = -0.99x + 53

Hence, the equation of the line of best fit is y = -0.99x + 53

This means that y = 30

So, we have:

-0.99x + 53 = 30

Subtract 53 from both sides

-0.99x = -23

Divide by -0.99

x =23

Hence, the predicted weight is 23 pounds

This means that x = 1500

So, we have:

y = -0.99 * 1500 + 53

Evaluate

y = -1432

Hence, the city MPG for 1500 pounds is -1432

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The height of the building is 5.33m.

The question is to calculate the height of the building.

Based on the information given, the height will be:

Madeline eye height/Distance from X = Height of building/Building distance from X

1.55/2.75 = x/9.45

x = (1.55 × 9.45)/2.75

x = 5.33 m

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Answer:

x = 2

Step-by-step explanation:

1) If there is a number right next to a bracket, then it means that it should be multiplied. --> 4(5 -2x) = 25 - 10x

2) (20 - 8x) + 3 = 23 - 8x

3) 23 - 8x = 7

4) 16 = 8x

5) We divide both sides with 8 to leave x. --> 2 = x

6) x = 2

Answer: 13 vertices

Step-by-step explanation:

     We can use the following formula to find the number of vertices in the figure. V is the number of vertices, F is the number of faces, and E is the number of edges.

     V = 2 - F + E

     V = 2 - (13) + (24)

     V = 13

The equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2

The standard vertex of a function is given as shown below

y = a(x - h)² + k

where (h, k) is the vertex of the function

Given the vertex of a function at (-3, 2). On substituting, we will have:

y = a(x - (-3))² + 2

y = a(x + 3)² + 2

Hence the equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2

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The reciprocal relationship of the graph is graph (a)

The reciprocal relationship implies that:

The x and the y axes are swapped.

When the x and the y axes are swapped, the value on both axes swap their positions

For the given graph, the reciprocal relationship is graph (a)

This is shown in the attached graph

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Answer: 68

Step-by-step explanation:

By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.

Answer:

your answer please mark me as brainlist

Step-by-step explanation:

V

=

238

m³

Answer:

5610

Step-by-step explanation:

unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:

[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]

The result of the evaluation as demanded in the task content is; -40 - 80√3.

The expression; a² - b² can be evaluated by means of difference of two squares as follows;

a² - b² = (a+b)(a-b)

Therefore, we have;

= ((√3 +5√3 -5) + (√3 -5√3 -5)) ((√3 +5√3 -5) - (√3 -5√3 -5))

= (2√3 -10)(10√3 +10)

= 60 - 80√3 -100

= -40 - 80√3.

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