Because the dividend is the same for all three expressions the larger the divisor the__the quotient

The streets where Elmwood and Taylor drive are neither perpendicular nor parallel.

Elmwood Drive passes through R(4,-11) and S(0,-9)

Slope of this line is (y₁-y₂)/(x₁-x₂)

Here (x₁,y₁) is (4,-11) and (x₂,y₂) is (0,-9)

slope of this line is (-11 - (-9))/(4-0)

= (-11 + 9)/4

= -2/4 = -1/2

Taylor Road passes through J(6,-2) and K(4,-5)

Slope of this line is (y₁-y₂)/(x₁-x₂

Here (x₁,y₁) is (6,-2) and (x₂,y₂) is (4, -5)

slope of this line is (-2 - (-5))/(6 - 4)

= (5 - 2)/2

= 3/2

The slopes of both the line is not same, so they are not parallel.

The product of slopes of both the lines is equal to 1, then it can be said as perpendicular lines.

The product of slope of streets passed by Elmwood and Taylor is

- 1/2 x 3/2 = -3/4

The result is not equal to 1, so they are not perpendicular lines.

Therefore, the streets where Elmwood and Taylor drive are neither perpendicular nor parallel.

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The correct option D) Add 48 to 52 is the conjecture that describes for the  7th term in the sequence.

For the given question, the sequence is given as;

4, 20, 36, 52,

Where, the first term a₁ is 4.

Second term a₂ is 20 and,

Third term a₃ is 36

Common difference d for each case is;

d = a₂ - a₁

d = 20 - 4 = 16

d = a₃ - a₂

d = 36 - 20 = 16

as, common difference is same, the sequence is said to be in AP.

Then, the formula for finding the 7th term is -

a₇ = a₁ + 6d

a₇ = 4 + 6×16

a₇ = 100

Now, this 7th term from the options can be found as;

Add 48 to 52 = 100.

Thus, the conjecture that describes for the 7th term in the sequence is add 48 to 52.

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The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

As per the given,

Number of people who vote on their favorite fruit = 9

Number of people who vote for kiwi = 1

The fraction of person vote kiwi to vote on their favorite fruit = 1/9

In decimal form 1/9 =  0.1111111.

Hence "The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111".

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Answer:

1. Deductive reasoning, because it is testing the ecisting theory that odd numbers are not divisible by 2 and gives an example that 4 is an even number and is divisible by 2.

2. This statement would be deductive reasoning because the person stating this is establishing the truth that all photosynthetic organisms produce oxygen, they are not creating a theory, just stating facts.

3.  This would be inductive reasoning because they have given good reasons to base their theory however it is not simple fact.

Step-by-step explanation:

Hope i helped explain

The percentage discount for the pair of sneakers is 10%.

A percentage is a value per hundredth. Percentages can also be fractions and decimals by decimals by dividing by 100 and vice versa. To obtain a percentage of a given value we divide the given percentage by a hundred and multiply the value with it.

The percentage discount can be determined by putting the discounted value upon the price multiplied by a hundred and subtracting the obtained percentage from the hundred percentage.

∴ The percentage discount on the pair of sneakers is,

= (22.50/25)×100.

= 0.9×100.

= 90%.

So, the percentage discount is (100 - 90)% = 10%.

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Answer:x=7

Step-by-step explanation: 2(4x-2)=52

8x-4=52

8x=56

x=7

Answer:

slope of 1/2

Step-by-step explanation:

x-2y=-18

First, get the equation in slope intercept form

y = mx+b  where m is the slope and b is the y-intercept

-2y = -x -18

Divide each side by -2

y = 1/2 x + 9

The slope is 1/2

Parallel lines have the same slope, so lines that are parallel will have a slope of 1/2

Given:

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.

The volume of the trough will be as follows:

Answer:

225 lb

Step-by-step explanation:

Let x be Rashid's original weight.

If 16% of Rashid's original weight is 36 lb then:

[tex]\implies 0.16x=36[/tex]

To find Rashid's original weight solve for x:

[tex]\implies \dfrac{0.16x}{0.16}=\dfrac{36}{0.16}[/tex]

[tex]\implies x=225[/tex]

Therefore, Rashid's original weight is 225 lb.

Answer: Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?

$\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$

Solution

Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram.

[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("$A$",A,N); dot("$O$",O,NW); dot("$B$",B,W); dot("$C$",C,E); dot("$H$",H,S); label("$2$",O--(-.7,-.385),N); label("$1$",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]

We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.

See Also

The transformations that are needed to transform the graph of f(x) to the graph of g(x) include the following:

In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Given the following function:

Function, f(x) = 4^x

Next, we would translate f(x) 1 unit left based on this horizontal translation rule:

f'(x) = f(x + 1)

f'(x) = 4^{x + 1}

Now, we would apply a vertical translation 3 units down based on this horizontal translation rule:

f''(x) = f'(x) - 3

f''(x) = 4^{x + 1} - 3

Therefore, function g(x) = 4^{x + 1} - 3

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ANSWER

EXPLANATION

Given;

c) Hence;

In decimal form;

d)

Answer:

[tex]y=\dfrac{2}{7}x-12[/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. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given:

The y-intercept is the y-value when x = 0.

Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:

[tex]\implies y=\dfrac{2}{7}x-12[/tex]

Answer:

3 seconds

Step-by-step explanation:

We can solve this in either of two ways:  Graphing or taking the first derivative,  I'll use both,

Graphing

Plot the equation.  My DESMOS graph is attached.  One can find the vertex of this curve at 3 seconds.  Bonus:  It reaches a height of 144 units at this point.

Derivative

The first derivative of this function will produce an equation that returns the slope of the line at any point x.

S(t) = 96t - 16t^(2)

S'(t) = 96 - 2*16t

S'(t) = 96 - 32t

The slope of the curve will be 0 when the ball reaches it's maximum height and begins to fall.  Since we want the time it takes to reach a slope of zero, we can set S'(t) to 0 and solve:

S'(t) = 96 - 32t

0 = 96 - 32t

32t = 96

t = 3 seconds

Answer:

The height is 7 units the length is 12 units.

Step-by-step explanation:

It's 6 and 6 for the graph one.

The equation of the graphed function is  y = -f(x) +3​.

Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Only the object's location changes during translation; its size stays the same.

In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered.

Given:

f(x) = |x|

The graph given here is reflected over x- axis.

Now, to make it up- side down the parent function should be negative.

So, g(x)= -f(x)

then, the graph is also shifted 3 units up.

Thus, g(x)= -f(x) + 3

y = -f(x) +3​

Hence, the equation of the graphed function is  y = -f(x) +3​.

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The smallest height of the tower is 24 cm.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 44 + 3x + 4y = 7 is an expression.

We have,

Grace:

Blocks = 8 cm

Kian:

Blocks = 12 cm

Now,

Grace and Kian both have the same height.

This means,

The least common multiples of 8 and 12.

4 x 2 = 8

4 x 3 = 12

So,

4 x 2 x 3 = 24

Thus,

The smallest height of the tower is 24 cm.

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The unit price for a 5.15 pound bag is the better buy for Juan

Juan paid $13.36 for a 3.47 pound bag of shrimp:

So, cost of one pound bag of shrimp= [tex]\frac{1*13.46}{3.47}[/tex]

                                                            =$3.88

Hence, unit price for the 3.47 pound bag=$3.88

Following week, Juan paid $18.75 for a 5.15 pound bag at another store:

So, cost of one pound bag of another store= [tex]\frac{1*18.75}{5.15}[/tex]

                                                                        =$3.64

Hence, unit price for the 5.15 pound bag at another store=$3.64

It is clear from the above result that second buy (5.15-pound bag at another store) is the better buy for Juan because it cost less per pound.  

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The perimeter of the rectangle is  32 feet.

Perimeter of the rectangle:

The perimeter of a rectangle is stated that the sum of all the sides of a rectangle.

Through the definition, the perimeter of a rectangle,

P = 2 (a + b) units

where

“a” is the length of the rectangle

“b” is the width of the rectangle

Given,

Here we have the diagram of the rectangle and the measurements are given in it.

And we need to find the perimeter of the rectangle.

Through the given diagram, we know that, the values of

length = 12 feet

width = 4 feet

Now, we have to apply the values on the formula in order to solve it,

So, the perimeter is,

P = 2 ( 12 + 4)

When we simplify it then we get,

P = 2 (16)

After the multiplication we get the result as

P = 32 feet.

Therefore, the perimeter of the rectangle is 32 feet.

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The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

√9x^3/25y^2

Evaluate the square root of 9 in the expression

So, we have the following equation

√9x^3/25y^2 = 3x^3/25y^2

The above expression cannot be further simplified

Hence, the solution to the expression is 3x^3/25y^2

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Answer:

Step-by-step explanation:

It is assumed you are looking for the missing value of r.

Use the intersecting secants theorem:

Substitute known values and solve for r:

Answer:

(a) FB = 24 cm

(b)  r = 10

Step-by-step explanation:

Find the length, in cm, of FB.

Intersecting Secant and Tangent Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Given:

[tex]\begin{aligned}\implies FB^2 & =FE \cdot FD\\FB^2&=32 \cdot 18\\FB^2&=576\\\sqrt{FB^2}&=\sqrt{576}\\FB&=24\end{aligned}[/tex]

Therefore, the length of FB is 24 cm.

Find the value of r.

Triangle FBO is a right triangle with side lengths:

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

Therefore, substitute the side lengths of triangle FBO into Pythagoras Theorem and solve for r:

[tex]\begin{aligned}\implies BO^2+FB^2&=OF^2\\r^2+24^2&=(r+16)^2\\r^2+576&=r^2+32r+256\\576&=32r+256\\32r&=320\\r&=10\end{aligned}[/tex]

Therefore, the value of r is 10.