factorise 4y^2 – 4y + 1

To find the midpoint, add the two X values together and divide that by 2 and then add the two Y values together and divide by 2.

X = 8 +3 = 11 /2 = 5.5

Y = 5 +7 = 12 /2 = 6

Depending on how you need to answer the midpoint for X could stay the fraction 11/2, or you can divide it and get 5.5

The midpoint is (11/2,6) or (5.5,6)

Answer:

nope

Step-by-step explanation:

Answer:

The answer to this is 0.25

Step-by-step explanation:

7/12= 0.58333 repeating, and 1/3 is 0.3333 repeating. When you subtract 7/12 from 1/3 you get 0.25

Hope it helps

Answer:

0.25

Step-by-step explanation:

Answer: By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation: This is the sample response on Edge.

Both parallelograms are <L ≅ < T

Because, by the parallelogram angle theorem, opposite angles of a parallelogram are congruent.

Given parallelograms, GHLJ and GSTU such the parallelogram GSTU is inscribed inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Therefore, ∠L ≅ ∠T

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.

Parallelograms are shapes that have four sides with two pairs of sides that are parallel. The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.

Rectangles, rhombus, and squares are parallelograms. A trapezoid has at least one pair of parallel sides. The parallel sides are called the bases and the non-parallel sides are called the legs. There are three types of trapezoid - isosceles, right-angled, and scalene trapezoids.

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Answer:

B

Step-by-step explanation:

Note: The volume of a cylinder is:

radius² × π × height

First lets work out the volume of Cylinder A:

Volume = 1² × π × 4

             = 4π  m³

Now lets work out the volume of Cylinder B

Volume = 2² × π × 4

             = 16π  m³

__________________________________________

Now lets compare the volumes ( Cylinder A : Cylinder B)  :

4π : 16π

Lets simplify this by dividing both sides by 4π:

     4π : 16π            ( ÷ 4π)

----> 1 : 4        

_____________________________________________________

Answer:

Option b) 1 : 4

Answer:

1:4

Step-by-step explanation:

Answer:

B y=54 degrees

Step-by-step explanation:

Since a triangle's angles always add up to 180.

180-72=108

108/2=54

It must be divided by two because y is two angles not one.

Answer: FALSE

Step-by-step explanation:

The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:

[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]

Now, we need to calculate the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

We can identify in the given equation that:

[tex]a=3\\b=-6\\c=9[/tex]

Then, we only need to substitute these values into the formula:

 [tex]D=(-6)^2-4(3)(9)[/tex]

 [tex]D=-72[/tex]

Since [tex]D<0[/tex] then the equation has no real solutions.

The answer is:

She needs to buy 3 spindles of 60 CDS and 2 spindles of 25 CDs.

We know that the possibilities will depend always on how many CDs contain each type of spindles.

There is only one possible combination of spindles that can give the exact amount of CDs needed.

Let's try to find the combinations:

- First combination: With 1 spindle of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-60}{25}=\frac{170}{25}=6.8Spindles[/tex]

Since the result is not a whole number, we know that the first combination does not work.

- Second combination: With 2 spindles of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(2)*60}{25}=\frac{110}{25}=4.4Spindles[/tex]

Since the result is not a whole number, we know that the second combination does not work.

- Third combination: With 3 spindles of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(3)*60}{25}=\frac{230-180}=\frac{50}{25}=2Spindles[/tex]

Since the result is a whole number, we know that the third combination works.

Hence, the combination will be:

[tex]TotalCDs=3Spindles_{60}+2Spindles_{25}=3*60+2*25=180+50=230[/tex]

She needs to buy 3 spindles of 60 CDs and 2 spindles of 25 CDs.

Have a nice day!

Answer:2 of 25 cds 3 of 60 cds

Step-by-step explanation:

1. 3x60=180

2.2×25=50

3. So for science class she needs quality 2 of 25

4. Quality of 3 of 60

So there u go

Answer:

Step-by-step explanation:

note :

the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :

Δ = b² -4ac

1 )  Δ > 0  the equation has two reals solutions : x =  (-b±√Δ)/2a

2 ) Δ = 0 : one solution : x = -b/2a

3 ) Δ < 0 : no reals solutions

in this exercice : 4x²-30x+45=0

a= 4    b= -30  c=45

Δ = (-30)² - 4(4)(45) = 900 - 720 = 180.......continu

Answer:

Second choice

and the last 2 choices

Step-by-step explanation:

32m/16m=2 and our constant is 3 not 2 so not choice A

4m^2/2m=2m so possible 6m/2m=3 so choice B

4m/2m=2 and our constant is 3 not 2 so not choice C

10m/5m=2 same reason as A and C

10m^2/5m=2m possible...15m/5m=3 so choice E

32m^2/16m=2m and 48m/16m=3 so this last choice too

Answer:

y = (5/6)x - 7

is with

y = - (6/5)x + 1

y = - (5/6)x - 8

is with

y = (6/5)x - 5

y = - (7/4)x - 1

is with

y = (4/7)x + 9

y = (7/4)x - 2

is with

y = - (4/7)x + 2

Step-by-step explanation:

You can double check by dividing -1 by the number before x. The answer from that calculation will be the number before the x of the perpendicular line's equation

pair with their perpendicular equations are

y = - (6/5)x + 1

y = (6/5)x - 5

y = (4/7)x + 9

y = - (4/7)x + 2

The given line is perpendicular to the required line under the condition of perpendicular lines m1×m2=–1.

As, m1*m2=-1

m1= -1/m2

For first equation

y = (5/6)x - 7

m1= 5/6

So, m2= -1/m2= -6/5

Hence, the equation of perpendicular line is y = - (6/5)x + 1.

Similarly,

y = (5/6)x - 7

m1= 5/6

So, m2= -1/m2= -6/5

Hence, the equation of perpendicular line is y = (6/5)x - 5.

again,

y = - (7/4)x - 1

m1=-7/4

So, m2= -1/m2= 7/4

Hence, the equation of perpendicular line is y = (4/7)x + 9

again,

y = (7/4)x - 2

m1= 7/4

So, m2= -1/m2= -4/7

Hence, the equation of perpendicular line is y = - (4/7)x + 2.

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Answer:

$420

Step-by-step explanation:

Principal = $7000

Rate = 8%

Time = 9 months

9 months = 3/4 or 0.75 of a year

Simple Interest = Principal * Rate * Time ÷ 100

= $7000 * 8% * 0.75 ÷ 100

= $420

Answer:

Infinitely many solutions.

Step-by-step explanation:

2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.

2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)

2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.

6n - 2 = 6n - 2 Add 2n + 4n.

-6n        -6n Subtract 6n from both sides.

-2 = -2? Yes, -2 equals -2.

Therefore, the answer is infinitely many solutions, meaning that n can be any real number.

An equation can have no solution, one solution or infinitely many solutions.

The equation [tex]2(n -1) + 4n = 2(3n - 1)[/tex] has infinitely many solutions

Given that:

[tex]2(n -1) + 4n = 2(3n - 1)[/tex]

Open brackets

[tex]2n -2 + 4n = 6n - 2[/tex]

Collect like terms

[tex]2n + 4n - 6n= - 2+2[/tex]

[tex]0 = 0[/tex]

When the solution to an equation is 0 on both sides, the equation has infinitely many solutions

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Answer:

C. (-5,-4,-3,1,2,5) From the graph we can see the following points first come x-axis and Y-axis like (x, y). From graph we can see 6 points they are (-5,6),(-4,1),(-3,4),(2,4),(1,-2),(5,-3) Here the first no. is the domain like in (-5,6). -5 is domain and 6 is range so all the first no. of the points is in option C so it is the domain.

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

Plug x = -5 into f(x)

f(x) = 2x-20

f(-5) = 2(-5) - 20

f(-5) = -10-20

f(-5) = -30

Then plug x = -5 into g(x)

g(x) = x-1

g(-5) = -5-1

g(-5) = -6

Divide the two results

(f/g)(-5) = f(-5)/g(-5)

(f/g)(-5) = (-30)/(-6)

(f/g)(-5) = -5

For this case we have the following functions:

[tex]f (x) = 2x-20\\g (x) = x-1[/tex]

We must find [tex]\frac {f (-5)} {g (-5)}[/tex], then:

We have in mind that:

[tex]+ * - = -[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {f (-5)} {g (-5)} = \frac {2 (-5) -20} {- 5-1} = \frac {-10-20} {- 6} = \frac {-30} {- 6} = 5[/tex]

Answer:

5

To create a dot plot, you draw a number line from the smallest to the largest value in your dataset. Then, for each number in the dataset, mark a dot above the corresponding number on the line. If a number occurs more than once, stack the dots.

Creating a dot plot for a set of data on a number line involves the following steps:

Unfortunately, as this is a text-based platform, it's impossible to hover over the numbers and drag to create a dot plot interactively. This instruction seems to be meant for a specific interactive software or online tool.

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Answer:

The answer is both a and b

Answer:

both a and b is correct

Check the picture below.

notice the alternate interior angles in the picture.

[tex]\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill[/tex]

The width of the crater is 1.61 km.

Plane is flying at altitude of  1.5 km

The angle of depressions to point A = 68 degrees/

The angle of depression to point B = 56 degrees.

In the given diagram below, we can see:

Angle XPD is right angle and thus we have:

[tex]\angle APD + \angle APX = 90\\\angle APD = 180 - \angle APX = 90 - 68 = 22^\circ[/tex]

Similarly, Angle  YPD is right angle and thus:

[tex]\angle DPB + \angle BPY = 90\\\angle DPB = 90 - \angle BPY = 90 - 56 = 34^\circ[/tex]

Since the triangle ADP and triangle  PDB  are right angled triangles, thus we have by trigonometric ratios:

[tex]tan(22) = \dfrac{AD}{PD}\\\\0.404 \times 1.5 = AD\\\\AD = 0.606\: \rm km[/tex]

Similarly,

[tex]tan(34) = \dfrac{BD}{PD}\\\\0.674 \times 1.5 = BD\\\\BD = 1.01 \: \rm km[/tex]

The width of the crater = AD + DB = 1.01 km + 0.606 km  = 1.61 km

Thus, width of the crater is 1.61 km.

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Looking at the given points on the right side from (0,2) to (1,6) for 1 increase in X ( 1-0=1) the Y value increases by 3 ( 6/2 = 3)

This same increase happens for th other two points: 18/6 = 3

54 / 18 = 3

The rate of increase is 3.

Answer:

Answer = 3.14 * 40 = 125.6m^2

Step-by-step explanation:

Let R be the greater radius and r be the smaller radius

A) Area of the sidewalk =  \pi R^2 -  \pi r^2   - This can be the expression

B)  pi  = 3.14  

= pi (R^2-r^2)

= pi (11^2-9^2)

= pi (121-81)

= pi *40

That was the simplified expression

Answer = 3.14 * 40 = 125.6m^2

Answer:

Answer is 50 meters

Step-by-step explanation:

Solution:

Height of the building (h)= 90 meters.

Time taken by the ball to reach the ground (t) = 3 seconds

According to the statement;

h = kt²

90=k(3)²

90=k(9)

90=9k

Divide both the sides by 9

k=10

h=kt²

Put the value time (t)=2 in the equation

h=10(2)²

h=10(4)

h=40 meters

Distance from the ground = 90 - 40

=50 meters.

Thus the correct option is 50 meters....

Answer:

The answer is A) 50 meters

Step-by-step explanation:

Answer:

[tex]\large\boxed{6\sqrt[5]{x^2y}=6x^\frac{2}{5}y^\frac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\6\sqrt[5]{x^2y}=(6)(\sqrt[5]{x^2})(\sqrt[5]{y})=6x^\frac{2}{5}y^\frac{1}{5}[/tex]

Answer:

I'm pretty sure if you subtract 2 from eight you will find the answer of 6 i'm not sure if that question was implying this answer but I hope this helps

Step-by-step explanation:

For this case we must find the product of the following expression:

[tex](n ^ 3) ^ 2 * (n ^ 5) ^ 4[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Rewriting the expression we have:

[tex]n ^ 6 * n ^ {20} =[/tex]

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

[tex]n^{6 + 20} =\\n^{26}[/tex]

Answer:

[tex]n^{26}[/tex]

Answer:

n^26

Step-by-step explanation:

[tex]\sqrt[3]{b^{27}}=\sqrt[3]{(b^9)^3}=b^9[/tex]

Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

To obtain this form use the method of completing the square.

Given

x² + y² - 6x + 14y = 142

Collect the x and y terms together

x² - 6x + y² + 14y = 142

add (half the coefficient of both x and y terms )² to both sides

x² + 2(- 3)x + 9 + y² + 2(7)y + 49 = 142 + 9 + 49

(x - 3)² + (y + 7)² = 200 → A

Answer:

The total number of copy rooms in the building is 9.

Step-by-step explanation:

With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).

From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:

[tex]n = 6 \cdot r + 7[/tex]

From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:

[tex]n = 7 \cdot r - 2[/tex]

From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:

[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]

Puting known and unknowns on opposite sides, we get:

[tex]7+2 = (7-6) \cdot r [/tex]

Solving we get:

[tex]9 = r[/tex]

Therefor the total number of rooms is 9.

Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.

As a reference, the following link is useful:

https://en.wikipedia.org/wiki/System_of_linear_equations

The number of boxes of paper exists at 61.

The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).

Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:

[tex]$n=6 \cdot r+7$$[/tex]

Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:

[tex]$n=7 \cdot r-2$$[/tex]

From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.

From the 2 relations we can write:

[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]

Putting known and unknowns on opposite sides, we get:

[tex]$7+2=(7-6) \cdot r$$[/tex]

Solving we get:

[tex]$9=r$$[/tex]

Thus the total number of rooms exists at 9.

Plugging this solution into any of the 2 equations, then we get

The number of boxes of paper exists at 61.

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Answer:

horizontal line

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through.

Hence

y = - 1 is a horizontal line passing through all points with a y- coordinate - 1

The number line represents the solution to the inequality -2x + 7 > 8, and the solution is x < -0.5.

The filled circle and the arrow pointing left on the number line indicate that the solution to the inequality is to the left of -2.

The inequality that represents this solution is -2x + 7 > 8.

To solve this inequality, we can subtract 7 from both sides to isolate the x variable.

This gives us -2x > 1. Finally, we divide both sides of the inequality by -2, remembering that when we divide by a negative number, the inequality sign flips.

So, the solution to the inequality is x < -0.5.

Thus, Correct option for the given number line is F. -2x + 7 > 8.

Final answer:

The number line indicates the solution to the inequality H. 6x - 9 < -21, where x < -2, including -2 (since the circle is filled). The solution matches the given number line plot.

Explanation:

The number line given indicates the solution to an inequality that includes all numbers to the left of – the filled circle on –2, which means –2 is included in the solution set. This represents an inequality that is of the form x ≤ a where a is –2 in this case. Now let's analyze each of the provided inequalities.

F. -2x + 7 > 8: Solving this we get –x > 1 or x < –1, which does not match the plot.

G. 7x + 11 < 4: Solving this inequality we get x < –1, which also is not a match.

H. 6x - 9 < -21: Resolving this inequality leads to x < –2, which matches the number line.

J. -3x - 15 < -27: Solving this we get x > 4, which is incorrect as per the number line plot.

Therefore, the correct inequality is H. 6x - 9 < -21.

Answer:

Vertical angles must have the same vertex and be congruent as well.

Step-by-step explanation:

Answer:

Correct answer is B and C.

Step-by-step explanation:

Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.

When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.