Use the graph on the right to locate points D, E, and G
5. Locate D so that ABCD is a rectangle.
6. Locate E so that ABCE is a trapezoid
7. Locate G so that ACBG is a parallelogram that is not a rectangle

The area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

For the given question;

Express the circle's area as a function of the its radius.

A = πr²

Determine the area's derivative with respect towards its radius.

dA/dr = 2πr

Using the chain rule, calculate the derivative of a area with respect to time.

dA/dt =  dA/dr . dr/dt

dA/dt = 2πr(9)

dA/dt = 18πr

When the radius is 32 cm, find the derivative of a area with respect to time.

dA/dt = 18π(32)

dA/dt = 576π

As a result, the area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

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The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.

what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.

Let y be the weight of the airplane and x be the amount of fuel

And we know that the general form of a linear

function is

(1) And given that the slope of the line is

y = mx + c

m = 5.9

Then (1) becomes

y = 5.9x + c

And given that for x = 53 , y = 2212.7

Then from (2), we have

2212.7 = 5.9 (53) + c

⇒ 2212.7 = 312.7 + c

c = 2212.7 - 312.7

c = 1900

Thus, (2) becomes

y = 5.9x + 1900

Then for x=22, from (3) y = 118 + 2100

= w = 2218

The weight of the plane with 20 gallons in its fuel tank is 2218 pounds

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Answer:

its {A} Hope gets some of a full chocolate bar

Step-by-step explanation:

she gets 7/8 of a chocolate bar the next day she gets 6/12       7+6=13 so she gets a full chocolate bar

The measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The figure is given in the picture:

From the property of interior angles:

x + 85 = 180

x = 95 degrees

6z - 85 + 85  = 180

z = 180/6

z = 30 degrees

Thus, the measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

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The single inequality:

y > |x + 2|

Can be rewritten into:

y > x + 2

y > -x - 2

So the second option is the correct one.

Remember that an absolute value equation like:

|x + a| = b

Can be rewritten as:

x + a = b

x + a = -b

So the inequality:

y > |x + 2|

Also can be rewritten into two equations, which are:

y > x + 2

-y < x + 2

The direction of the sign changes in the second one because the sign of the variable in the left changes.

Then if we multiply both sides by -1 of the second inequality, we get:

y > -x - 2

Then the two inequalities are:

y > x + 2

y > -x - 2

So the correct option is the second one.

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The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.

By expressing the given linear equation in slope-intercept form; it follows that we have;

x + y = 6

y = -x + 6

Hence, the slope of the equation by comparison with; y = mx + c is; -1.

Therefore, the slope of the required equation is same as the two lines are said to be parallel.

Therefore, the required equation from point-slope form of an equation is;

( y - 8) = -1 ( x - (-4))

y - 8 = -x - 4

x + y = -4 +8

x + y = 4.

Ultimately, the required equation is; x + y = 4.

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Answer: 6+1=7

Step-by-step explanation:

Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.

Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.

Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.

Converse of the statements will be as If two lines are parallel, then they have equal slopes.

Conditional statement will be; If two lines have same slopes, then the lines are parallel.

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x^2+ y^2-2x-2y = 0 has center (1,1) and radius sqrt 2 and the circle x^2+y^2 =1 has center (0,0) and radius 1

the unit circle has center

(1,1)  , ( 0,0)

and the unit circle has radius

1 , sqrt 2

for this the equation of the circle is

x^2 + y^2 = 1

if we take center as (0,0) then radius become 1

therefore equation of circle becomes x^2 +y^2 =1

similarly if we take center ( 1,1 ) and radius sqrt 2

then (x -1 )^2 + ( y-1 )^2 =2

x^2 +y^2 -2x- 2y +2 =2

this implies x^2 +y^2 -2x -2y =0

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Reason:

We look for two values that

Using trial and error, you should find those two values are 2 and 6

This is how we arrive at (x+2)(x+6)

Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.

Answer:

[tex]y = -\dfrac{1}{2}x + \dfrac{13}{2} \;\; \text{or}\\\\y = -0.5x + 6.5\\\\[/tex]

Step-by-step explanation:

The slope-intercept form of a straight line is

y = mx + b

where m = slope and b = y-intercept

A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through

Given
Line 1:  y = 2x - 6
Slope m = 2

Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5

So the equation would be y = (-1/2)x + b

We can solve for b given the info that the line passes through (5,4)

Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b

4 = -5/2 + b

4 + 5/2 = b

8/2 + 5/2 = b

13/2 = b

or b = 13/2

So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2

or
y = -0.5x + 6.5

Answer:

[tex]\textsf{Gradient\;$=-\dfrac{1}{3}$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope (gradient). \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]x+3y=13[/tex]

Rearrange the equation to make y the subject.

Subtract x from both sides of the equation:

[tex]\implies x+3y-x=13-x[/tex]

[tex]\implies 3y=-x+13[/tex]

Divide both sides of the equation by 3:

[tex]\implies \dfrac{3y}{3}=\dfrac{-x}{3}+\dfrac{13}{3}[/tex]

[tex]\implies y=-\dfrac{1}{3}x+\dfrac{13}{3}[/tex]

Compare the rearranged equation with the slope-intercept form.

Therefore, the gradient (slope) of the given equation is -¹/₃.

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Answer:

Step-by-step explanation:

y = mx + b

The gradient is slope "m" (coefficient by "x")

~~~~~~~~~~~~~~~~~

x + 3y = 13

Solve for "y" :

3y = - x + 13

[tex]\frac{3y}{3}[/tex] = - [tex]\frac{x}{3}[/tex] + [tex]\frac{13}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{13}{3}[/tex]

The gradient is ( - [tex]\frac{1}{3}[/tex] )

Answer:

f(x) = ax^2 + bx + c

I) f(1) = a + b + c = -2

II) f(2) = 4a + 2b + c = -2

III) f(3) = 9a + 3b + c = -4

II - I

IV) 3a + b = 0

III - I

V) 8a + 2b = -2

V - 2IV

2a = -2 --> a = -1

3(-1) + b = 0 --> b = 3

(-1) + (3) + c = -2 --> c = -4

f(x) = -x^2 + 3x - 4

The value of t after solving 2b+2.50t = 40 is t = (40-2b)/2.50.

According to the question,

We have the following expression:

2b+2.50t = 40

Now, in order to find the value of t, we will move other variables and numbers from the left hand side to the right hand side.

First, moving 2b from the left hand side to the right hand side will result in the change of the sign from plus to minus:

2.50t = 40-2b

Now, 2.50 is in multiplication on the left hand side. So, it will be in the division on the right hand side.

t = (40-2b)/2.50

Hence, the value of t after solving the given expression is t = (40-2b)/2.50.

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Hellow what grade of math is this?

The equation for the purchase of n number of notebooks by Caitlin is

4n = c , where c is representing the cost that Caitlin paid.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

the price for one notebook was = $4 each

n number of notebooks were purchased by caitlin

therefore the cost price of 4 notebooks will be = 4 * n

as per given in the question cost price = c

therefore the equation formed will be

4n = c

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x = milliliters of 40% alcohol

y = milliliters of 20% alcohol

so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]

(a) We have 13 possibilities that a five-card hand will contain four of a kind.

(b) We have 12 possibilities that a five-card hand will contain a full house.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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Answer: (-5, 8)

Step-by-step explanation:

       The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).

(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)

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We may be thinking about either of these choices depending on whether we are talking about immigration or emigration.

[tex]\frac{d P}{d t}=r_g \pm r[/tex]

This is further explained below.

Generally, The rates of births and deaths will be represented accordingly by the superscripts [tex]r_b[/tex] and [tex]r_d[/tex].

The model transforms into the following when subjected to the circumstances outlined in the problem:

[tex]\frac{d P}{d t}=r_b P-r_d P^2[/tex]

In conclusion, You need to submit model 1 in order to get more information.

In the event that the proportionality assumptions about birth and death be loosened up, the model that is necessary for issue 1 would become the following:

[tex]\frac{d P}{d t}=r_g \pm r[/tex]

Depending on whether we are discussing immigration or emigration, we may be contemplating either of these options.

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The final value of n is -7 for linear equation 3(n - 9) - 2(n + 4) = 6n.

3(n - 9) - 2(n + 4) = 6n

6n = 3n - 27 - 2n - 8

-6n + n - 35 = 0

-5n = 35

5n = -35

n = -7

Given equation is 3(n-9)-2(n+4)=6n.

Open the brackets for multiplication, 3n - 27 - 2n - 8 = 6n.

After shifting the variables to the left-hand side and constant to the right-hand side, 5n = -35.

As the value of the constant in the above step is negative the final constant value will be also negative, n = -7.

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Answer:

Assuming that this is referring to simple interest, your answer is C) 1,750.

Step-by-step explanation:

[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]

[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]

"An empty set is included in set N" is the translation of the mathematical sentence.

A set is defined as a collection of well-defined objects, numbers or things. In set theory, we use different symbols to represent statements.

To translate Ø⊆N, we need to know the meaning of the symbols we have:

Ø means empty set (A set that does not contain anything).

⊆ means subset (is included in)

N means set N

So we can translate  Ø⊆N as:

An empty set is included in set N or

Therefore, the mathematical sentence Ø⊆N can be translated as "an empty set is included in set N"

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Answer: 4x-9y=27 is this equation in standard form.

By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

12 × x + 2 × y = 90

6 × x + 2 × y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.

6x = 30

x = 5

Now we replace x in any of 2 equations to get y.

30 + 2y = 60

2y = 30

y=15

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The length of side AB after the dilation is 2 units.

Given that, ΔABC is dilated by a factor of 1/4.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

From the given figure, AB=8 units, BC=6 units and AC=10 units.

Let the x be the length of side AB after the dilation.

Now, using scale factor formula 1/4 = x ÷ 8

⇒x=2 units

Therefore, the length of side AB after the dilation is 2 units.

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