What is the value of "a" in the following quadratic? (Make sure the equation is in
standard form: ax² + bx+c=0)
x^2 + 28 = -11x

Answer:

a = -1/6

b = 7/6

c = 1

Step-by-step explanation:

[tex]f(x)=ax^3+2x^2+bx+c\\\\f(0)=a(0)^3+2(0)^2+b(0)+c\\\\1=c[/tex]

[tex]f(1)=a(1)^3+2(1)^2+b(1)+1\\\\4=a+2+b+1\\\\4=a+b+3\\\\1=a+b\\\\1-b=a[/tex]

[tex]f(-2)=(1-b)(-2)^3+2(-2)^2+b(-2)+1\\\\8=-8+8b+8-2b+1\\\\8=6b+1\\\\7=6b\\\\\frac{7}{6}=b[/tex]

[tex]1-b=a\\\\1-\frac{7}{6}=a\\ \\-\frac{1}{6}=a[/tex]

So, the true equation would be [tex]f(x)=-\frac{1}{6}x^3+2x^2+\frac{7}{6}x+1[/tex] if you substitute the coefficients and the constant.

Answer:

1. x= -1 & x= -13

2. x= -3 & x= -4

3. x= -3 & x= -5

4. x= -6 & x= -2

5. x= -5 & x= -2

8. x= -7 & x= -3

9. x= -8 & x= -2

10. x= -3 & x= -3

11. x= -5 & x= -4

12. x= -2 & x= -2

13. x= -6 & x= -7

14. x= -6 & x= -3

15. x= -10 & x= -7

Answer:

the solution of the equation.

Step-by-step explanation:

The variable(s) in each triangle below 9, 12 and 16.

The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle.

Let the base of the triangle be 15.

So, the area is:

Area= 1/2*b*h

       = 1/2*15*20

       = 150.

Let the base of the triangle be 25.

So, the area is:

Area= 1/2*b*h

  150= 1/2*25*h

       = 300/25

    h =12

Now, using Pythagoras Theorem

15²= h²+x²

15²=12²+x²

225-144= x²

x²= 81

x=±9

Now, x+y=25

            y=16

Thus , values are 9,12 and 16.

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Answer:

233km

Step-by-step explanation:

Answer:

  7 millicuries

Step-by-step explanation:

A period of 10 days is 2 times the half-life of 5 days.

In the first 5 days, the amount of the chemical decayed by half from 28 millicuries to 14 millicuries. In the next 5 days, it decayed by half again, from 14 millicuries to 7 millicuries.

10 days later, 7 millicuries of the chemical remains.

Answer:

2 hours and 5 minutes.

Step-by-step explanation:

2 hours is 60mins+60mins which is equal to 120mins and then the extra 5mins

Hilary studied for a total of 2 hours and 5 minutes this week.

If Hilary studied for 25 minutes each day for five days this week, we can calculate the total study time by multiplying the number of minutes studied per day (25) by the number of days (5):

25 minutes/day × 5 days = 125 minutes

To convert this to hours and minutes, we need to divide the total minutes by 60 (since there are 60 minutes in an hour) to get the number of hours and find the remainder as minutes.

125 minutes ÷ 60 = 2 hours and 5 minutes

Therefore, Hilary studied for a total of 2 hours and 5 minutes this week.

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Answer:

Step-by-step explanation:

The value of the given trigonometric function is 1.1547.

The main trigonometric ratios are: sinβ, cosβ and tg β. From these ratios, you can calculate other trigonometric ratios such as sec β, cossec β and cotg β.

These ratios help you find the angles and the sides of a rectangle triangle.

The question asks [tex]\frac{2 *sin(30)}{cos (30}[/tex], for the angle 30° you have sin=1/2 and cos= [tex]\frac{\sqrt{3} }{2}[/tex].

Thus,

[tex]\frac{2 *sin(30)}{cos (30}=\frac{2 *\frac{1}{2} }{\frac{\sqrt{3} }{2} }=\frac{1}{\frac{\sqrt{3} }{2} }= \frac{2}{\sqrt{3} } =\frac{2\sqrt{3} }{3}=1.1547[/tex]

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Answer:

1/3

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5x4=20 5 is one quarter of 20

Answer:

[tex] \frac{1}{4} \times 20 = 5 \\ [/tex]

Answer:

The radius is 8.

Step-by-step explanation:

Because OA is a radius and AB is a tangent, Angle A is a right angle. So you can use Pythagorean theorem (shortcut Pythagorean triple)

OA^2 + 15^2 = 17^2

OA^2 + 225 = 289

OA^2 = 64

OA = 8

OA is a radius, the radius = 8

Answer:

option d -1 is the answer

Answer:

I think C (19) might be wrong though

Answer:

x=7

Step-by-step explanation:

We know that in a parallelogram diagonals bisect each other

Therefore

x=7

Answer:

45 POINTS & BRAINLIST -- PLEASE HELP

Convert the following functions.

A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.

B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit

Step-by-step explanation:

45 POINTS & BRAINLIST -- PLEASE HELP

Convert the following functions.

A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.

B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit

Answer:

radius=2cm

because area =πr²

π2²=4π

hope this helps

please give me brainliest

Answer:

Step-by-step explanation:

(9-5+X)+ (39+211)

whats the Solution?

(9 - 5 + x) +  (39 + 211) =

4 + x + 39 + 211 =

254 + x

Answer:

254 + x

Step-by-step explanation:

(9 - 5 + x) +  (39 + 211) =

4 + x + 39 + 211 =

254 + x

Hope this helps

:)

Answer:

A. 120 cm²

Step-by-step explanation:

Area of figure :

Answer:

Step-by-step explanation:

1) a) r =  7 cm

 [tex]\sf \boxed{\text{Volume of sphere=$\dfrac{4}{3}\pi r^3$}}[/tex]

                             [tex]\sf =\dfrac{4}{3}*3.14*7*7*7\\\\= 1436 \ cm^3[/tex]

 [tex]\sf \boxed{\text{\bf Surface area of sphere = $4\pi r^2$}}[/tex]

                                           = 4*3.14 * 7 * 7

                                           = 615.44 cm²

b) r= 8.4 cm

     [tex]Volume = \dfrac{4}{3}\pi r^3[/tex]

                  [tex]\sf =\dfrac{4}{3}*\dfrac{22}{7}*8.4*8.4*8.4\\\\= 2483.7 \ cm^3[/tex]

   Surface area = 4*3.14*8.4*8.4

                         = 887.04 cm²

      a) r = 6 cm

     [tex]\sf \boxed{\text{\bf Volume of hemisphere =$\dfrac{2}{3} \pi r^3$}}[/tex]

                                                [tex]\sf =\dfrac{2}{3}*3.14*6*6*6\\\\= 452.16 \ cm^3[/tex]

        [tex]\sf \boxed{\text{\bf Surface area of hemisphere=3 \pi r^2}}[/tex][tex]\sf \boxed{\text{\bf Surface area of hemisphere = $3 \pi r^2$}}[/tex]

                                                            = 3 * 3.14 * 6 * 6

                                                             = 339.12 cm²

Answer:

125

Step-by-step explanation:

JIK is congruent to MIL so they both equal 55. 360-55=305-55=250. now MIJ and LIK are gonna be equal so you can divide 250 by 2 which gives you 125. if you add them up it equals 360, a full circle! pls give me brainliest!

The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

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Answer:577.35 square feet

Step-by-step explanation:

‍♀️

To Factorize Something:

 ⇒ means to put it into the simplest terms that when multiplied

     together transforms into the original form

Let's Solve:

  [tex]x^2-25=(x+5)(x-5)[/tex]

Let's Check:

  [tex](x+5)(x-5)=x*x+(-5)x+5x-25=x^2-5x+5x-25=x^2-25[/tex]

Answer: (x+5)(x-5)

Hope that helps!

Answer:

(x + 5)(x - 5)

Step-by-step explanation:

[tex]x^2-25[/tex]

[tex]=x^2-5^2[/tex]

[tex]x^2-5^2=\left(x+5\right)\left(x-5\right)[/tex]

[tex]=\left(x+5\right)\left(x-5\right)[/tex]

[tex]base \: area = 44.3 \: {units}^{2} [/tex]

[tex]volume = 221.5 \: {units}^{3} [/tex]

the height of the given rectangular prism.

[tex]volume= base \: area \times height[/tex]

[tex]height = \frac{volume}{base \: area} [/tex]

[tex]height = \frac{221.5}{44.3} [/tex]

[tex]height = 5 \: units[/tex]

Therefore, the height of the given rectangular prism is 5 units.

The value of height of rectangular prism is,

⇒ h = 5 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The rectangular prism below has a base area of 44.3 units² and a volume of 221.5 units³.

Since, The volume of rectangular prism is,

⇒ V = Base area x height

⇒ 221.5 = 44.3 × h

⇒ h = 221.5 / 44.3

⇒ h = 5 units

Thus, The value of height of rectangular prism is,

⇒ h = 5 units

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Answer:

Step-by-step explanation:

Slope of f(x) :

Y-intercept of g(x) :

The 1st option is correct.

The new coordinates of A is (-12,8)

To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping.

For any dilation the mapping will be (x,y) → (kx,ky).

Convert the point (x, y) to (-y, x) in order to rotate 90 degrees counter clockwise.

The given point is A(-4 ,6) ,after it has been rotated the new coordinates are A(-6,-4)

After reflecting it over x axis the new coordinated will be (-6,4)

Then dilating it with a scale factor of 2

The new coordinates of A is (-12,8)

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Answer: -3.125

Step-by-step explanation: -1 divided by 8 = .125

Answer:

0.940

Step-by-step explanation:

100 = 36 x pi x r^2

now divide both sides by 36pi

r^2 = 0.88419412...

then square root both sides

r = 0.94031597...

The magnitude of the force per unit length between the wires is [tex]3 \times 10^{-5} N/m[/tex].

In a wire carrying a current I 2, the force that each wire feels due to the presence of the other depends on the distance between them and the magnitude of the currents.

Force per unit length = magnetic permeability * (current 1) * (current 2) / (2 π distance between the wires).

The below expression for the force per unit length.

Moreover, before using the below formula we have to change the unit centimeter into a meter. So, we just divide the centimeter by 100.

[tex]\rm \dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\\dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\Where; \ \mu_0 = 4\pi \times 10^{-7} , i_13 . \ i_2 = 3 \ d=0.06[/tex]

Substitute all the values in the formula

[tex]\rm\dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\Where; \ \mu_0 = 4\pi \times 10^{-7} , i_13 . \ i_2 = 3 \ d=0.06\\\\ \dfrac{Force}{length}=\dfrac{4\pi \times 10^{-7} \times 3 \times3}{2\pi \times 0.06}\\\\ \dfrac{Force}{length}= 3 \times 10^{-5} N/m[/tex]

Hence, the magnitude of the force per unit length between the wires is [tex]3 \times 10^{-5} N/m[/tex].

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Answer:

Step-by-step explanation: