Need help with this geometry question.

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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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

When one is looking at a map of the united states, and it is assumed that you already know which direction is north, this illustrates a theorem.

It should be noted that a theorem simply means a statement that has been proved.

In this case, when one is looking at a map of the United States, and it is assumed that you already know which direction is north, this illustrates a theorem. This is because it's proven.

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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.

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:

1.5x = 7.5   (a)

Step-by-step explanation:

If Billy has $7.50 remaining, then he can buy x no. of boxes.

Each box costs $1.50

So, 1.5x = 7.5

According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).

This question is not valid because it specifies information that would surely change the answer of the respondent.

The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.

According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.

Note: This question is incomplete because the options are missing. Here are the options:

A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.

B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.

C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.

D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.

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11. The value of x is [tex]13\frac{3}{4}[/tex]

12. From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x

From the question, we are to solve the given equation

The given equation is

[tex]5 + \frac{1}{2}(4x +5) = 35[/tex]

This becomes

[tex]\frac{1}{2}(4x +5) = 35-5[/tex]

[tex]\frac{1}{2}(4x +5) = 30[/tex]

[tex]4x +5 = 2 \times 30[/tex]

[tex]4x +5 = 60\\[/tex]

[tex]4x= 60-5[/tex]

[tex]4x= 55[/tex]

[tex]x = \frac{55}{4}[/tex]

[tex]x = 13\frac{3}{4}[/tex]

Hence, the value of x is [tex]13\frac{3}{4}[/tex]

12.

From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x

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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]

Answer:

I did this quickly, so please check carefully.

d/a = -(11/12)

Step-by-step explanation:

a/(b+c+d)=4/3

3a = 4(b+c+d)    [Cross multiply]

3a = 4((b+c)+d)   [Note that b and c can be grouped as (b+c)]

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

We can see the second equation also has a (b+c) group.  Isolate it to one side:

a/(b+c)=3/5

5a = 3(b+c)

(b+c) = (5a/3)

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

Now use this definition of (b+c) in the first equation:

3a = 4((b+c)+d)

3a = 4((5a/3)+d)   [Use the new value of (b+c), which is (5a/3)]

3a = 4(5a/3+3d/3)

3a = 4((5a + 3d)/3)

3a = (4/3)(5a + 3d)

3a = (20/3)a + 4d

9/3a = (20/3)a + 4d

-(11/3)a = 4d

4d = -(11/3)a

d = -(11/12)a

d/a = -(11/12)

Answer:

$11.78

Step-by-step explanation:

14.89+9.33=24.22

36-24.22=11.78

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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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:

m = 1 and n = 10.

Step-by-step explanation:

I  am assuming you mean -8, m , n, 19.

If they are in AP the 4 terms will have a common difference.

19 - (-8) = 19 + 8 = 27.

So the increase over 3 terms (from -8 to 19) is 27 so we have:

27 / 3 = 9

Therefore the common difference is 9 and the A P is

-8, 1, 10, 19.

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 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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It is true that exponent laws apply all the time when simplifying variables

The laws of exponent state that:

[tex](ab)^m = a^m * b^m[/tex]

[tex](a+ b)^m \ne a^m + b^m[/tex]

[tex](a- b)^m \ne a^m - b^m[/tex]

[tex](a/b)^m \ne a^m / b^m[/tex]

The above laws must be followed in all variables.

When any of the law is misinterpreted, misrepresented or misused in simplifying variables, the result would be incorrect

Hence, it is true that exponent laws apply all the time when simplifying variables

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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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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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IfIf it forms interior <6 measuring70. The measure of <4 is: B. 110°.

Using this interior angle theorem

Measure of <4=180° - <6

Where:

<6 measure 70

Hence:

Measure of <4=180°-70°

Measure of <4=110°

Therefore the measure of <4 is: B. 110°.

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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:

-135689;456+((888888888

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]

Answer: That raw vegetables are better for the rabbit's growth than rabbit food.

Answer:

The rabbit food that was strictly a diet of raw vegetables is healthier for the rabbits.

Step-by-step explanation:

Answer: 68

Step-by-step explanation:

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

Answer:

The graph increases.

Step-by-step explanation:

hope this helps!!

Answer: the graph increases

Step-by-step explanation: did test

Answer:

x = -2

Step-by-step explanation:

Subtract 7 from both sides :

6x = -12

Divide both sides by 6 :

x = -2

Hope this helped and have a good day