x^2 - 72 = 6x
how to complete the square?

Answer:

B

Step-by-step explanation:

Angle 1 and angle  3 are alternate interior angles.

Answer:

z = -1.8, y = 10.2

Step-by-step explanation:

- 2z -2y = -24 (EQ 1)

3z - 2y = -33 (EQ 2)

Change one of the equations to it's opposite (Turning a negative number to a positive/or the other way around)

Let's target the equation that can leave us with the simplest question to solve

-2z + -2y = -24

-3z + 2y = 33

-5z = 9

(Dividing and switching the negative sign over)

z = -1.8

Plug in Z to solve for y.

-2(-1.8) - 2y = -24

3.6 - 2y = -24

-2y = -20.4

y = 10.4

Answer:

They are neither,they intersect but not at a 90 degree angleStep-by-step

explanation: hope this helps :)

Answer: 25 inches

Step-by-step explanation:

24² + 7² = 625

Square root of 625 = 25

After the hurricane and the disease, 48% of the original population of rats is left.

We have,

After the hurricane, 40% of the rats were wiped out, which means

100% - 40% = 60% of the rats survived.

Then, after the disease spread through stagnant water, 20% of the remaining rats were killed.

This means 100% - 20% = 80% of the rats that survived the hurricane are still left.

To find the percentage of the original population of rats that is left after both events, we multiply the percentages:

Percentage left = 60% * 80% = 0.6 * 0.8 = 0.48

Finally, we convert the decimal value back to a percentage:

Percentage left = 0.48 * 100% = 48%

Therefore,

After the hurricane and the disease, 48% of the original population of rats is left.

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Answer:

a)  $8.80

b)  40%

Step-by-step explanation:

Part (a)

Given:

Original price - discounted price

= $22 - $13.20

= $8.80

Part (b)

percentage = (amount discounted ÷ original price) x 100

                    = (8.80 ÷ 22) x 100

                    = 40%

Answer:

100 degrees

Step-by-step explanation:

Answer:

x = 17, y = 28

Step-by-step explanation:

1. Isolate for x in "x - y = -3, -8":

x - y+y = -3, -8+y

x = -11 + y

2. Substitute "x = -11 + y" in for x in the second expression:

-11 + y + y = 45

3. Simplify:

-11 + 2y = 45

4. Isolate y:

-11+11 +2y = 45+11

2y = 56

[tex]\frac{2y}{2} = \frac{56}{2}[/tex]

y = 28

5. Substitute the new y-value into the first equation:

x = -11 + 28

x = 17

hope this helps!

Answer:

1/2, or around 9 times

Step-by-step explanation:

since a fair coin has 2 sides, that makes you have 2 possible outcomes. Heads and tails, 2 sides, makes it 50-50 so you would expect to get around 9 heads because 50% or 1/2 of 18 is 9. Hope this helps

Answer:

0.132

Step-by-step explanation:

Rolling a die is an independent event.

Chance of not rolling a 1 or 4 is 4/6 or 2/3

[tex]\frac{2}{3} ^5 = \frac{32}{243} = 0.13168[/tex]

Answer:

x ≈ 16.2

Step-by-step explanation:

tan56° = [tex]\frac{24}{x}[/tex] ( multiply both sides by x )

x × tan56° = 24 ( divide both sides by tan56° )

x = [tex]\frac{24}{tan56}[/tex] ≈ 16.2 ( to the nearest tenth )

Answer:

a) 2 ; b) 0; c) -2 ; d) -1

Step-by-step explanation:

a) f(-4)=2 ;

b) f(0)=0;

c) f(2)= -2 ;

d) f(5)= -1

the answer is 82 million

Answer:

Point C

Step-by-step explanation:

it is negative, so we can already eliminate points A and B so which leaves us with C and D. It is a fraction that is greater than -1 so that eliminates point D, so the remaining point is our final answer.

Answer:

Point C

Step-by-step explanation:

Step 1:  What point is located at -1/6

We can see that the arrow pointing up showcases us going positive and the arrow pointing down showcases us going negative.  0 gives us the middle point between negatives and positives. We can see that there are 6 ticks between each whole number.  Therefore, if we go 1/6 of a tick down in the negative direction we would get point C.

Answer: Point C

The maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, the height of the bullet from the ground is modeled by the equation:

[tex]h(t) = -16t^2 + 200t + 3[/tex]

where height is in meters and time is in seconds. And t is the time in seconds passed from the point of time when the bullet was fired.

Finding its first and second rate with respect to the variable 't', we get:

[tex]\dfrac{d(h(t))}{dt} = h'(t) = -32t + 200\\\\\dfrac{d^2(h(t))}{dt^2} = h''(t) = -32 < 0[/tex]

Thus, the second rate is negative no matter what the value of 't' is. So all the critical points would be corresponding to maxima.

Now, finding the critical points by equating the first rate = 0, we get:

[tex]h'(t) = 0\\\\-32t + 200 = 0\\\\t = \dfrac{200}{32} = 6.25 \: \rm sec.[/tex]

Due to only one critical point, and that each critical point is maxima, we have the value of h(t) globally maximum when t = 6.25

Putting t = 6.25 in the function h(t), we get the maximum height achieved by the bullet as:

[tex]h(t) = -16t^2 + 200t + 3\\h(6.5) = -16(6.5)^2 + 200(6.5) + 3 = 627 \: \rm ft[/tex]

When the bullet will fall on the ground, the value of h(t) would be 0.

Putting h(t) = 0, and finding the values of 't' for which this is true, we get:

[tex]h(t) = -16t^2 + 200t + 3\\0 = -16t^2 + 200t + 3\\\\16t^2 -200t -3 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(-3)}}{2(16)}\\\\t \approx \dfrac{200 \pm 200.479}{32}\\\\t \approx -0.0149 \: \rm sec., t \approx 12.51 \: sec.[/tex]

Bullet will fall only after it is shot, so time taken for the bullet to fall compared to the time when its shot would be greater, so time passed (t here) would be positive.

Thus, at approx t = 12.51 sec, the bullet will fall on the ground.

At  t = 0, bullet was at 3 ft, and therefore, whenever bullet will reach 400 ft, the time t would be > 0.

Putting h(t) = 400, we get:
[tex]h(t) = -16t^2 + 200t + 3\\400 = -16t^2 + 200t + 3\\\\16t^2 -200t +397 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(397)}}{2(16)}\\\\t \approx \dfrac{200 \pm 120.797}{32}\\\\t \approx 2.475\: \rm sec., t \approx 10.02\: sec.[/tex]

These both values are true. The time when t = 2.475 approx, the bullet would be going up, passing by 400 ft height, and when t = 10.02 approx, the bullet would be coming down, passing by 400 ft height.

Thus, the maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

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Answer:

The answer is y= -2

Step-by-step explanation:

(Arrange according to the like terms first)

5y-y+42= 34

4y+ 42-34= 0

4y+ 8= 0

4y= -8

∴ y= -8/4=-2

So, y= -2

Hope it will help.

Answer:

y = -2

Step-by-step explanation:

question : 5y + 42 − y = 34

⇒ 5y + 42 − y = 34

•shifting the +42 to the right side :

⇒ 5y - y = 34 - 42

⇒ 4y = -8

•shifting the 4 to the right side :

⇒ y = -8/4

⇒ y = -2 Answer...

hope that helps...

Answer:

[tex] \frac{4}{1} [/tex]

Step-by-step explanation:

[tex]writing \: as \: a \: fraction \: the \\ numerator = 28 \\ denominator = 7 \\ as \: a \: fraction \: it \: is \: \: \frac{28}{7} \\ dividing \: numerator \: and \: denominator \: by \: four \\ = \frac{4}{1} \\ hope \: this \: helps \\ please \: rate \: and \: mark \: brainliest[/tex]

Answer:

x=9

Step-by-step explanation:

9-6=3

Answer:

Step-by-step explanation:

Use the slope formula.

SLOPE FORMULA:

[tex]\Rightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]:\Longrightarrow \sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}}[/tex]

Solve.

[tex]\sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}=\dfrac{-6+4}{-4+3}=\dfrac{-2}{-1}=2}[/tex]

The slope is 2.

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:

[tex]\sf{y=mx+b}[/tex]

y=2x+2

I hope this helps, let me know if you have any questions.

[tex]\text{Given that,}\\\\(x_1,y_1) =(-3,-4)~~ \text{and}~~ (x_2,y_2) = (-4,-6)\\\\\text{Slope,}~m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-6+4}{-4+3} = \dfrac{-2}{-1} =2\\ \\\text{Equation of line,}\\\\~~~~~y-y_1 = m(x-x_1)\\\\\implies y+4=2(x+3)\\\\\implies y =2x+6-4\\ \\\implies y= 2x+2[/tex]

Answer:

8

Step-by-step explanation:

HOPE THIS HELPS! PLS GIVE ME BRAINILIEST PLSSSSSSSSSSSSSSSSSSS!

Answer:

76degrees

Step-by-step explanation:

Using the theorem which states that the vertex of the angle inside a circle is half the sum of the measured intercepted arcs. Hence;

Angle at the vertex = 53 degrees

Half the sum of intercepted arcs = 1/2(3x+3+10x-14)

Half the sum of intercepted arcs = 1/2(13x-11)

Equating to  the vertex to find x

1/2(13x-11) = 53

13x - 11 = 2 * 53

13x - 11 = 106

13x = 106 + 11

13x = 117

x = 117/13

x = 9

For the arc 3x + 3

= 3(9) + 3

= 27 + 3

= 30degrees

For the arc 10x - 14

= 10(9) - 14

= 90 - 14

= 76degrees

Hence the measure of the larger of the two arcs is 76degrees

[tex]\dfrac{\left(x^0 y^{\tfrac 23} z^{-2} \right)^{\tfrac 32}}{\left(x^2 z^{\tfrac 12} \right)^{-6}}\\\\\\=\dfrac{1\cdot \left( y^{\tfrac 23}\right)^{\tfrac 32} \cdot \left(z^{-2} \right)^{\tfrac 32}}{\left(x^2 \right)^{-6} \cdot \left( z^{\tfrac 12} \right)^{-6}}~~~~~~~~~~~~~~~~~~;\left[(ab)^m = a^m b^m\right]\\\\\\=\dfrac{y^{1} \cdot z^{-3}}{x^{-12} \cdot z^{-3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[(a^m)^n = a^{mn}\right]\\\\\\=\dfrac{y}{x^{-12}}\\\\\\[/tex]

[tex]=\dfrac{y}{\tfrac 1{x^{12}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m} } \right]\\\\\\=yx^{12}[/tex]

The volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

We have given that, the radius of the sphere is 9.1ft.

We have to determine the volume of the sphere

The volume of the sphere  is given by

[tex]V=\frac{4}{3}\pi r^3[/tex]

r is the radius of the sphere

V- is the volume of the sphere

So use the given value in the formula so that,

[tex]V=\frac{4}{3}\pi (9.1)^3[/tex]

[tex]V=3156.55082 ft^3[/tex]

Therefore the volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

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Answer:3156.6

Step-by-step explanation:

Answer:

With the area you can find the radius and then substitute the radius in the circumference formula

Answer:

B

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

this year's mean = [tex]\frac{7+3.3+2}{3}[/tex] = [tex]\frac{12.3}{3}[/tex] = 4.1

last year's mean = [tex]\frac{5.3+1.6+2.4}{3}[/tex] = [tex]\frac{9.3}{3}[/tex] = 3.1

difference = 4.1 - 3.1 = 1

To make a triangular prism we need cardboard, glue and scissors.

A triangular prism is a geometric shape characterized by:

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Answer:

∆The lateral surface area of cylinder =417.62 mm²

Step-by-step explanation:

Diameter = 7

Radius = 7/2

Lateral Surface Area of cylinder = 2πrh

=> 2× π × 7/2 × 19

=> 38 × 7/2 × π

=> 133 × π { taking π as 3.14}

=> 133× 3.14

=> 417.62 mm²