what is the measure of

Answer:

a = 2

b = - 6

c = 0

Step-by-step explanation:

Since, -3,0 and 2 are the zeroes of the polynomial

[tex] Plug \:x = 0\: in \:p(X) \\

\implies p(0)= 0\\

\therefore 0= 0^3 +(a-1)(0)^2 +b(0)+c\\

\therefore 0= 0 +(a-1)\times 0 +b(0)+c\\

\therefore 0= 0 +0+0+c\\

\red{\bold{\therefore 0=c}}.....(1)\\\\

p(X)=x³+(a-1)x²+bx+c. \\

Plug \:x = -3\: in \:p(X) \\

[tex] \implies p(-3)= 0\\

\therefore 0= (-3)^3 +(a-1)(-3)^2 +b(-3)+c\\

\therefore 0= -27 +(a-1)\times 9 +b(-3)+c\\

\therefore 0= - 27 +9a-9 - 3b+c\\

\therefore 0= - 36+9a-3b+c\\

\therefore 36 =9a-3b+c... (2)\\

Plug \:c= 0\: in \:equation \: (2)\\

36= 9a - 3b + 0\\

36= 9a - 3b\\

36= 3(3a - b) \\

\purple {\bold{12 = 3a - b}} .... (3)\\\\

Plug \:x = 2\: in \:p(X) \\

\implies p(2)= 0\\

\therefore 0= 2^3 +(a-1)(2)^2 +b(2)+c\\

\therefore 0= 8 +(a-1)\times 4 +b(2)+c\\

\therefore 0= 8 +4a-4+2b+c\\

\therefore 0= 4 +4a+2b+c\\

\therefore - 4=4a+2b+c.....(4)\\

Plug \:c= 0\: in \:equation \: (4)\\

- 4 = 4a +2b+0\\

-4= 2(2a+b)\\

\orange{\bold{-2=2a + b}} .......(5)\\\\[/tex]

Adding equation (3) and (5), we find:

12 = 3a - b

-2 = 2a + b

_________

10 = 5a

10/5 = a

a = 2

Plug a = 2 in equation (5)

-2= 2(2) + b

-2 = 4 + b

-2 - 4 = b

-6 = b

b = - 6

Answer:

The absolute value of -4.5 is 4.5 so plot the point at 4.5

Step-by-step explanation:

absolute value= how far that number is from zero

-4.5 is 4.5 away from zero

so the absolute value of -4.5 is 4.5

Answer:

4.5

Step-by-step explanation:

I hope yout have a good day.

Answer:

b // f

c // e

Step-by-step explanation:

b // f

89.5 = 180 - 90.5

89.5 = 89.5       {corresponding angles are congruent.So b // f}

c//e

91.5 = 180 - 88.5

91.5 = 91.5    {corresponding angles are congruent.So b // f}

Answer:

About 4-5 miles at the most i rode a bike before to a store and it took me an hour to go there and get back so.... Ya i would say about 4-5 miles

Step-by-step explanation:

Because 22mph is pretty slow. And i was going faster then 22mph when i was on my bike.

Answer:

55 miles

Step-by-step explanation:

Subtract 9:30 & 7:00, it will give you 2.3...meaning 2.5 hours. If you are traveling 22 miles an hour for 2 hours & 30 minutes you will get 55 miles total. 22 + 22 + 11 = 55.

Answer:

The answer is

N+ 1 = 3+2/2

=3

Step-by-step explanation:

The answer is 3

This is a odd number

Answer:

N + 1 = 3+ 2/2 =3

Step-by-step explanation:

I'm pretty sure is odd because it has the number three(3) and the number three (3) is odd.

Answer:

i. y = 3(x)

ii. This implies that: hiker 1 has an altitude of 1500 m, while hiker 2 has a depth of 1500 m with respect to the surface of the earth after the 3 days.

Step-by-step explanation:

Let assume that the horizontal surface of the earth is taken to be zero. Thus any distance moved upward is positive, and any distance moved downward is negative. As compared to a number line.

Thus, after 3 days, the equation for each hiker is;

y = 3(x)

Where y is the total distance covered after 3 days, and x is the elevation of the hiker per day.

For Hiker 1, the elevation was upwards;

y = 3(500)

 = 1500 m

For Hiker 2, the elevation was downwards;

y = 3(-500)

  = -1500 m

This implies that: hiker 1 has an altitude of 1500 m, while hiker 2 has a depth of 1500 m with respect to the surface of the earth after the 3 days.

Understanding:

[Q4] Slope intercept form is [tex]y=mx+b[/tex], where m is slope and b is the y-intercept. We calculated the slope in the previous question which was -45. We can find b by using any point on the previous table and replacing it's x and y values, for this example, I'm going to use (0,1080).

[tex]y=mx+b\\1080=-45(0)+b\\b=1080[/tex]

Now, we can rewrite the equation as follows

[tex]y=-45x+1080[/tex]

[Q5] To find the y-intercept we simply replace every x value with a 0,

[tex]y=-45x+1080\\y=-45(0)+1080\\y=1080[/tex]

This means the y-intercept is at [tex](0,1080)[/tex].

For the x-intercept, you replace the y value with a 0 and solve for x,

[tex]y=-45x+1080\\0=-45x+1080\\-1080=-45x\\x=24[/tex]

This means the x-intercept is at [tex](24,0)[/tex].

Solutions:

[Q4] [tex]y=-45x+1080[/tex]

[Q5] x-intercept: [tex]x=24[/tex]; y-intercept: [tex]y=1080[/tex]

[Q6] The x-intercept represents the months it takes Philip to fully pay his friend for the car. The y-intercept represents the total amount Philip had to pay his friend.

Answer:

The baseball reached 9 feet high above the ground

Step-by-step explanation:

The given quadratic function representing the position of the baseball above ground is p(t) = 1/2·g·t² + v₀·t + p₀

Where;

t ≥ 0

g = -32 ft./sec²

v₀ = The initial velocity

p₀ = The initial position

Given that when the ball is thrown, we have;

The initial, straight up, velocity, v₀ = 16 ft./sec

The initial position, p₀ = 5 ft.

Substituting the above values in the quadratic function representing the position of the baseball above ground, we have;

p(t) = 1/2·(-32)·t² + 16·t + 5 = 16·t - 16·t² + 5

At the maximum point, the rate of change of the height with time = 0, therefore;

dp(t)/dt = 0 = d(16·t - 16·t² + 5)/dt = 16 - 32·t

16 - 32·t = 0

16 = 32·t

t = 16/32 = 0.5 seconds

Therefore, the time takes to reach the maximum height = 0.5 seconds

The height (maximum) reached in 0.5 seconds is given as follows;

h(t) = 16·t - 16·t² + 5, from which we have;

h(0.5) = 16 × 0.5 - 16 × (0.5)² + 5 = 9

Therefore, the height baseball reached = 9 ft. above ground

Answer:

The total cost will be equal to 25.6£

Step-by-step explanation:

In order to solve this question we will have to figure out the cost of the adult ticket and the children tickets when the railcard is used. For this we do the following.....

Let "a" be the cost of the adult ticket after using the railcard

Let "b" be the cost of the children ticket after using the railcard.

a = 24£ - (24£ x [tex]\frac{1}{3}[/tex]) = 24£ - 8£ = 16£

b = 12£ - (12£ x [tex]\frac{6}{10}[/tex]) = 12£ - 7.2£ = 4.8£

Now the total cost will be equal to the sum of an adult ticket and two children tickets after the railcard is used, so .....

Total cost = a + 2b = 16£ + 2(4.8£)= 16£ + 9.6£ = 25.6£

Answer:

Option (E)

Step-by-step explanation:

[tex]\frac{a}{b}=\frac{c}{d}=k[/tex]

[tex]\frac{a}{b}=k[/tex]

[tex]b=\frac{a}{k}[/tex] ------(1)

[tex]\frac{c}{d}=k[/tex]

[tex]d=\frac{c}{k}[/tex] -------(2)

Since, [tex]\frac{6a+24}{md+6b}=k[/tex]

By substituting the values of b and d from equation (1) and (2),

[tex]\frac{6a+24}{\frac{mc}{k}+\frac{6a}{k}}=k[/tex]

[tex]\frac{k(6a+24)}{6a+mc}=k[/tex]

[tex]\frac{6a+24}{6a+mc}=1[/tex]

6a + 24 = 6a + mc

mc = 24

m = [tex]\frac{24}{c}[/tex]

Therefore, Option (E) will be the correct option.

Answer:

d) No, it is not a proportional relationship because the graph does not go through the origin

Step-by-step explanation:

A proportional relationship has to pass through the origin (0,0)

Answer:

sir the picture is black

Step-by-step explanation:

Answer:

y=10

Step-by-step explanation:

If u need work just ask me in the comments!

Answer:

The highest point of y is 16, so the absolute maximum is y=16.

[tex]\huge\mathbb\purple{AnSwEr}[/tex]

[tex]\huge❤\bold\red{Hello}❤[/tex]

Hey mate 4 is your Answer

[tex]My \: pleasure \: to \: help \: you \: anytime.[/tex]

[tex]Mark \: me \: as \: brainliest .[/tex]

[tex] \huge \mathscr \pink \star\underline {Follow \: me } \red \star[/tex]

Answer:

4 friends

Step-by-step explanation:

so you do 5 1/4 minus 3/4 and then you get your awnser

Answer: 0.3

Step-by-step explanation: Because thats the answer

Answer:

0.3

Step-by-step explanation:

This is because, when you divide 3/9 it gives you 0.33333.. (Repeating, Irrational number) So you would round to the nearest tenths, which would give you 0.3 because the hundredths place isn't 5 or over. Hope this helps :)

Answer:

Nonlinear

Step-by-step explanation:

This is because the x^2. If there are any exponets, the equation would be considered nonlinear.

Hope this helps!

Step-by-step explanation:

2002 can be rounded to a compatible number such as 2000.

2000 / 2 = 1000.

They each received around 1000 marbles.

Answer: B.

Step-by-step explanation: (0, 2), (2, 0), and (1, -1) are the correct coordinates of the three vertices of the triangle.

Answer:

Yes

Step-by-step explanation:

I would say yes, x is multiplied by itself to get an answer for y.

Answer:

If an atom has the same number of protons and electrons then it is electrically neutral. Not all atoms have to have the same number of atoms because the number of electrons can be changed with the element remaining the same. Protons have a positive charge while electrons have a negative charge. The net charge is dependent on the number of protons and electrons. If it has more protons it would have a higher amount of positive charge therefore making it a positive net charge. The same thing applies with electrons just opposite.

If the atom has no charge (neutral) then there are the same number of protons and electrons. The positive protons cancel out with the negative electrons to produce this neutral state. We can say the net charge is 0 here.

Now if you take away one or more electrons, then there will be more positive protons to outnumber the negative electrons. Overall, the net charge will be positive. For example, if the atom loses 3 electrons, then you'll have a net charge of [tex]3^{+}[/tex]. These positively charged ions are known as cations. You pronounce this as "cat-ion" instead of "catshun".

On the flip side, if you add electrons to an atom, then you'll make the net charge overall to be negative. So let's say we add 4 electrons. We'll have the net charge be [tex]4^{-}[/tex] and this is an anion. To pronounce "anion" you would say "an ion" instead of "anyun".

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

In short, the number of protons and electrons are the same if the net charge is 0 and we're not dealing with ions. If you are dealing with ions, then the two counts will not be the same. Note how in the examples above, I didn't change the number of protons. Doing so would change the overall element entirely.

Answer:

a) 44[tex]\sqrt{3}[/tex]/3 feet

b) .3 minutes

Step-by-step explanation:

We know all three of the angles: 30 60 90. So we can divide 22 by [tex]\sqrt{3}[/tex], and then multiply that number by 2. We cannot have a radicand in the bottom, so multiply the denominator and numerator by

for b), simply divide a) by 75 ft/min, which is approximately  .3 minutes.

Answer:  5x +17

Step-by-step explanation:

2(x +7 )  + 3(x +1)  Apply the distributive property to break it down

2(x) + 2(7) + 3(x) + 3(1)

2x + 14 + 3x + 3      Now combine like terms

  5x + 17

Answer:

2x+14+3x+3

5x+17

Step-by-step explanation:

3 ft

Step-by-step explanation:

The amount of the school supply kit after the discounted price is $ 20

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of the school supply kit be A

The value of A is $ 25

The percentage discount of the school supply kit = 20 %

So , the value of the percentage amount is given by the equation

The cost of the school supply kit after discount = ( amount of the school supply kit - ( percentage discount of the school supply kit x amount of the school supply kit ) )

Substituting the values in the equation , we get

The cost of the school supply kit after discount = 25 - ( 20/100 x 25 )

The cost of the school supply kit after discount = 25 - ( 25 x 0.2 )

The cost of the school supply kit after discount = 25 - 5

The cost of the school supply kit after discount = $ 20

Therefore , the discounted price is $ 20

Hence ,

The amount of the school supply kit after the discounted price is $ 20

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Answer:

Yes it is

Step-by-step explanation:

The equation is proportional since as the value of x is increasing, y is also increasing

Equations can either be direct, inverse, or even joint. For instance, if y is directly proportional to x, this is expressed as:

y = kx

k is the variation constant

For a proportional equation, there an increase in a variable will lead to a decrease or increase in other variables

Given the expression y = 9x + 1/2,

when x = 1

y = 9(1) + 1/2

y = 9.5

when x = 2

y = 9(2) + 1/2

y = 18.5

We can see that the equation is proportional since as the value of x is increasing, y is also increasing

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Answer:

7.436 rounded to 7.44 hope this helps!

Step-by-step explanation:

7.7 + 6 2/3= 7.436

Answer:

- 8° per hour

Step-by-step explanation:

Given that:

Station A = - 6°

Station B = 2°

Rate of temperature change = x° / hour ; which is the same at both stations

Temperature at station A 3 hours after the recording is the same as the temperature in station B 4 hours after the recording ;

Temperature change in Station A:

-6 + 3x

Temperature change in station B:

2 + 4x

Temperature change in A = temperature change in B

-6 + 3x = 2 + 4x

Collect like terms

3x - 4x = 2 + 6

- x = 8

x = - 8

Hence, the rate of temperature change x in both stations is - 8° per hour