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Gregg has q quarters and p pennies. His brother has 4 times as many quarters and 8 times as many pennies as Gregg has. Write the sum of the number of coins they have, and then combine like terms.

Answer:

a([tex]b^{2}[/tex]+[tex]c^{2}[/tex]) = = -13

Step-by-step explanation:

Given that a = -1, b=2 and c= -3

find the value of a([tex]b^{2}[/tex]+[tex]c^{2}[/tex])

Just substitute the values given for each variable

a([tex]b^{2}[/tex]+[tex]c^{2}[/tex]) = (-1)([tex]2^{2}[/tex]+[tex](-3)^{2}[/tex]) ; do the exponents first

a([tex]b^{2}[/tex]+[tex]c^{2}[/tex]) = (-1)(4+9)=(-1)(13) ; now add inside the parenthesis;

a([tex]b^{2}[/tex]+[tex]c^{2}[/tex]) = -13 ; and multiply by -1

Answer:

In standard form -3x⁵ + x³ + 4x² - 8x

Step-by-step explanation:

=====================================================

Work Shown:

For now, let's assume they are equal. We'll show a contradiction happens.

5/6 = 2/3

5*3 = 6*2 ... cross multiply

15 = 12 ... here's the contradiction

If the original equation was true, then we would get the same thing on both sides in the final step shown above. However, we get a contradiction, so that means the original equation is false.

Furthermore, the left side is larger in the third step, so the left side is larger for each of the three steps. We can then say

5/6 > 2/3

5*3 > 6*2

15 > 12

Which helps show 5/6 is larger than 2/3.

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

Or you can use a calculator to see that

5/6 = 0.833 approximately

2/3 = 0.667 approximately

which shows the two fractions aren't equal and 5/6 is larger.

Answer:

because The perimeter of a rectangular playground can be no greater than 120 meters, The width of the playground cannot exceed 22 meters

=> the length of the playground cannot exceed: (120/2)-22= 38(meters)

Step-by-step explanation:

Answer:

x>12

Step-by-step explanation:

Answer:

These are = to........so =

Answer:

The rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]

Step-by-step explanation:

Given

[tex]25x - 4y = 50[/tex]

Required

Determine the rate of change of y w.r.t x

[tex]25x - 4y = 50[/tex]

First, make y subject of formula

[tex]4y = 25x- 50[/tex]

Divide through by 4

[tex]y = \frac{25x}{4} - \frac{50}{4}[/tex]

[tex]y = \frac{25x}{4} - 12.5[/tex]

Next, we differentiate the above w.r.t to x

The result of the differentiation is the solution to the question

[tex]y' = 1 * \frac{25x^{1-1}}{4} -0[/tex]

[tex]y' = 1 * \frac{25x^0}{4}[/tex]

[tex]y' = 1 * \frac{25*1}{4}[/tex]

[tex]y' = \frac{25}{4}[/tex]

Hence, the rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]

By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4

Rate of change of a function with respect to a variable is called derivative of that function with respect to that variable .

Here given relation is 25x-4y=0

[tex]\Rightarrow 4y=25x\\\\\Rightarrow y=\frac{25x}{4}[/tex]

We have to calculate rate of change of y with respect to x so we will calculate derivative of y with respect to x.

we can calculate derivative of y with respect to x as

[tex]\frac{dy}{dx}= \frac{d}{dx} (\frac{25x}{4})\\\\[/tex]

As 25/4 is constant we can take it out from derivative function as it is

[tex]\frac{dy}{dx}= (\frac{25}{4})\frac{dx}{dx}\\\\[/tex]

And we know derivative of a variable with respect to itself is 1

so

[tex]\frac{dy}{dx}= (\frac{25}{4})\times 1\\\\ \frac{dy}{dx}= \frac{25}{4}[/tex]

By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4

To learn more about derivative visit: https://brainly.com/question/25081524

Answer:

its not a straight line so what is the question ????????  maybe f(-3) = -3f

Step-by-step explanation:

i would love to help but i just need free points

Step-by-step explanation:

Answer:no

Step-by-step explanation:

Because there’s two number 9’s for the x values

Answer:

no because x = 9 has two y coordintates, and in a function every x value can only have one y value.

Step-by-step explanation:

Answer:

Slope = -7

y-intercept = -9

Step-by-step explanation:

The slope formula is y = mx + b where m is the slope value and b is the y-intercept value. In this case, since both values have a negative sign in front of them, they are both negative.

y = mx + b

y = -7x - 9

m = -7 which is the slope

b = -9 which is the y -intercept

Answer:

B.)

Step-by-step explanation:

A rational number is a number with no repeating decimals or decimals that go on “forever” like pi.  An expample of a rational number is 2 where 2.3333333... is not a rational number.  Pi isn’t a rational number either since forth there is no known end to that.  

So, when solved:

A.) = 1.58113883...  (irrational)

B.) = -8 (rational)

C.) = 8.94427191... (irrational)

D.) = 3.794733192... (irrational)

I hope you see the pattern.  Hope this helps!

Answer:

c(n) = 4n +20

let m = c(n)

m= 4n +20

make n the subject

m -20 =n

4.

inverse function of c(n)= n-20

4

It is a must that one replaces the m with the n in order to get the final answer

Answer:

x = - 1

Step-by-step explanation:

Given

f(x) = x³ + x² + x + 1

If x = 1 is a factor then f(1) = 0

f(1) = 1³ + 1² + 1 + 1 = 4 ≠ 0 , thus x = 1 is not a zero

f(- 1) = (- 1)³ + (- 1)² + (- 1) + 1 = - 1 + 1 - 1 + 1 = 0

Thus x = - 1 is the only zero

Answer:

72.5%

Step-by-step explanation:

Lets make his score a percentage: 58/80

Now covert it to a percentage: 58/80 = x/100

Cross multiply: 80x = 5800, x = 145/2

Divide 145 by 2: 72 1/2

Answer is 72.5%

I hope this helped, please mark Brainliest, thank you!

Answer:

4

Step-by-step explanation:

1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010

Answer:

The vertex is (3,1)

Step-by-step explanation:

Brainliest please

Answer:

y - 5 = -4(x + 1)

Step-by-step explanation:

The point-slope form is y - k = m(x - h).  The point is (h, k):  (-1, 5) and the slope is -4.

Here we have y - 5 = -4(x + 1)

The required point-slope form of the equation of the line is y - 5 = -4(x + 1).

Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-1, 5) and m=-4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - 5 = -4 (x - (-1))
y - 5 = -4 (x + 1)

Thus, the required point-slope form of the equation of the line is y - 5 = -4(x + 1).

Learn more about slopes here:
https://brainly.com/question/3605446

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Answer:

y=4

x=2

Step-by-step explanation:

y=4

x=2

I think it's right..

Hope I helped!

Answer:

x - intercept = 2

y - intercept = 4

Answer:

(2,5)

Step-by-step explanation:

it's (2,5) just to let you now

Answer:

111

I'm pretty sure

Step-by-step explanation:

Answer:

Kindly refer to explanation.

Step-by-step explanation:

Given that:

A,B and C are 3 points on circumference of circle with centre O.

AOB is diameter.

Kindly refer to the attached image.

To prove:

[tex]\angle ACB = 90^\circ[/tex]

Solution:

Let [tex]\angle A = x[/tex] and [tex]\angle B = y[/tex].

Construction: Join point  A with centre O.

Considering [tex]\triangle AOC[/tex]:

Side AO = OC because both are the radius.

Angles opposite to equal sides in a triangle are equal.

Therefore, [tex]\angle ACO=\angle A=x[/tex]

Considering [tex]\triangle BOC[/tex]:

Side BO = OC because both are the radius.

Angles opposite to equal sides in a triangle are equal.

Therefore, [tex]\angle BCO=\angle B=y[/tex]

[tex]\angle ACB = \angle ACO + \angle BCO = x+y[/tex] ...... (1)

Now, in [tex]\triangle ABC:[/tex]

Using angle sum property of triangle:

[tex]\angle A + \angle B + \angle ACB =180^\circ\\\Rightarrow x+y+x+y=180^\circ\\\Rightarrow 2(x+y)=180^\circ\\\Rightarrow x+y=90^\circ[/tex]

By equation (1):

[tex]\angle ACB = 90^\circ[/tex]

Hence proved.

Answer:

x = -5 , y = 2

Step-by-step explanation:

Solve the following system:

{y + 2 x = -8

-5 y + 3 x = -25

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{y + 2 x = -8

-5 y + 3 x = -25

Hint: | Solve for y.

Subtract 2 x from both sides:

{y = -2 x - 8

-5 y + 3 x = -25

Hint: | Perform a substitution.

Substitute y = -2 x - 8 into the second equation:

{y = -2 x - 8

3 x - 5 (-2 x - 8) = -25

Hint: | Expand the left hand side of the equation 3 x - 5 (-2 x - 8) = -25.

3 x - 5 (-2 x - 8) = (10 x + 40) + 3 x = 13 x + 40:

{y = -2 x - 8

13 x + 40 = -25

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{y = -2 x - 8

13 x + 40 = -25

Hint: | Isolate terms with x to the left hand side.

Subtract 40 from both sides:

{y = -2 x - 8

13 x = -65

Hint: | Solve for x.

Divide both sides by 13:

{y = -2 x - 8

x = -5

Hint: | Perform a back substitution.

Substitute x = -5 into the first equation:

{y = 2

x = -5

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = -5 , y = 2

Answer:

60.71

Step-by-step explanation:

Given that:

Consumption of poultry per capita is modeled by:

y=-.2125t^2 + 2.615t+56.33 ; t = 0 corresponds to 1990

Per capita poultry consumption in 1992;

1992 ; t = 2

y=-.2125t^2 + 2.615t+56.33

Put t = 2 in the equation

y=-.2125(2)^2 + 2.615(2) +56.33

y = -.2125(4) + 2.615(2) + 56.33

y = - 0.85 + 5.23 + 56.33

y = 60.71

Answer:

Step-by-step explanation:

Total cups of chocolate available = 7 1/3 cups

each batch uses 2/3 of a cup of chocolate

To get the number of batches of muffin Jim can bake, we will use the equality postulate.

1 batch = 2/3 cup of a chocolate

x batch = 7 1/3 cups of chocolate

Cross multiply

2/3 x = 7 1/3

2/3 x = 22/3

cross multiply

2x * 3 = 3 * 22

6x = 66

x = 66/6

x = 11

Hence Jim can bake at most 11 batches of muffins

Answer: B

Step-by-step explanation: You just multiplying 25 with 10 and w which can be simplified as 24(w+10) and adding with the 13.5 x 10 and 13.5 x w, which can be simplified as 13.5(10+w)

Answer/Step-by-step explanation:

Part A: The function that would best describe Option A is a linear function. This is because an increase in x would have a corresponding additive increase in y. With each increasing year, the value of Option A increases by $100. This is how we know Option A would be a linear function.

Part B: a(t) = y.

a(t) = a + 100t

Part C: The function that would best describe Option B is an exponential function. Unlike linear functions, an increase in x would have a corresponding multiplicative increase in y. Each value of Option B shares a common ratio of 1.1.

Part D: b(t) = y.

b(t) = b(1.1)^t

Part E: a(20) = a + 100(20)

1100 + 2000 = 3100

b(20) = b(1.1)^20

1100(1.1)^20

= 7400

There is definitely a significant difference between the value of Bridgette’s investment in both options. The difference between the values of each option after 20 years is 4300. Bridgette is better off using Option B if she wants more money at the end.

Hope this helps!

Answer:

85

Step-by-step explanation:

The range is defined as the difference between the highest observation and lower observation in a data.

Here,

The Highest observation in this data= 91

The Lowest observation in this data=6

Hence,

Range of the data= Highest observation - Lower observation

=91-6=85

Answer:

In arithmetic, variables look like letters.

Step-by-step explanation:

As we know that Mathematical arithmetic deals with numbers and certain properties with them.

Some of the main properties between numbers are as follows:

Variables do not remain constant, so we basically assign a number to a variable with an equal operator denoted by '='.

For example, let us assume a variable x being equal to 7. so it can written as:

[tex]x = 7[/tex]

Let suppose the value of the variable x=7 changes to x=10, then the new value will be:

[tex]x = 10[/tex]

Therefore, the correct answer is:

In arithmetic, variables look like letters.

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (5, 3)

m = [tex]\frac{3-3}{5+4}[/tex] = [tex]\frac{0}{9}[/tex] = 0