The equation 3x2 = 6x – 9 has two real solutions
True
O False

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:

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: 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.

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.

To learn more about the system of linear equations

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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

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:

I am going to assume that you mean:

x² < 49

To solve this you must do the opposite of squaring, which would be taking the square root. What you do to one side you must do to the other.

√x² < √49

x < 7

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

To solve the inequality x^2 < 49, we take the square root of both sides resulting in the solution -7 < x < 7, which means x can be any real number between -7 and 7.

Explanation:

The student's question is about solving an inequality involving a square of a variable, specifically x^2 < 49. To solve this inequality, we will first take the square root of both sides, keeping in mind that when we take the square root of a square inequality, we must consider both the positive and negative roots. Therefore, we can express the inequality as -7 < x < 7, since both positive and negative square roots of 49 are 7 and -7, respectively. This represents the range of values for x where the original inequality holds true.

The solution implies that x can take on any real value that is less than 7 and greater than -7. There's no need for tools like completing the square or the quadratic formula here, as the inequality is already in a solvable form.

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:

$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:

The answer is both a and b

Answer:

both a and b is correct

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:

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

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.

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.

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:

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.

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

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:

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

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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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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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

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:

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:

Answer:

B

Step-by-step explanation:

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.

For this case we have a quadratic equation given by:

[tex]4x ^ 2 + 2x-1 = 0[/tex]

The roots are found by means of the quadratic formula below:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 4\\b = 2\\c = -1[/tex]

So, we have:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]

Or in an equivalent way we have:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2 + 4 (4) (1)}} {2 (4)}[/tex]

Answer:

The correct option will be:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]

Answer:

a = 4, b = 2 and c= -1

Step-by-step explanation:

Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a

Here quadratic equation is  4x2 + 2x – 1

a = 4, b = 2 and c= -1

x =[-b ± √(b² - 4ac)]/2a

 = [-2 ± √(2² - 4*4*-1)]/2*4

 = [-2 ± √(4  + 16)]/8

 = [-2 ± √20)]/8

 = [-2 ± 2√5)]/8

 =  [-1 ± √5)]/4

x = [-1 ± √5)]/4

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

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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