Could you guys plesssse help me with 3
and 4

Rewrite the given number as

[tex]\dfrac{a+ib}{c+id}=\dfrac{(a+ib)(c-id)}{(c+id)(c-id)}=\dfrac{ac+bd+i(bc-ad)}{c^2+d^2}[/tex]

If it's purely real, then the complex part should be 0, so that

[tex]\dfrac{bc-ad}{c^2+d^2}=0\implies bc-ad=0\implies\boxed{ad-bc}[/tex]

as required.

Answer:

Option B

Step-by-step explanation:

we know that

To find the reciprocal of a fraction, flip the fraction.

Remember that

A number multiplied by its reciprocal is equal to 1

In this problem we have

[tex]\frac{10b}{2b+8}[/tex]

Flip the fraction

[tex]\frac{2b+8}{10b}[/tex] -----> reciprocal

therefore

The reciprocal is

The quantity 2 multiplied by b plus 8 end of quantity divided by the quantity 10 multiplied by b end of quantity.

Step-by-step explanation:

Length of arc = (Central Angle/360) × 2

[tex]\pi[/tex]

r

= 21/360 × 2 × 3.14 × 3

Length = 1.099 feet

Please mark Brainliest if this helps!

Answer:

Your answer is [tex]\frac{7\pi}{20}[/tex].

If you prefer an answer rounded to nearest hundredths you would have 1.10 or just 1.1.

Step-by-step explanation:

The formula for finding the arc length s is given by:

[tex]s=r \cdot \frac{\theta \pi}{180^\circ}[/tex]

where [tex]\theta[/tex] is in degrees.

Plug in 3 for r and 21 for [tex]theta[/tex]:

[tex]s=3 \cdot \frac{21 \pi}{180}[/tex]

I'm going to reduce 21/180 by dividing top and bottom by 3:

[tex]s=3 \cdot \frac{7 \pi}{60}{/tex]

I'm going to multiply 3 and 7:

[tex]s=\frac{21 \pi}{60}[/tex]

I'm going to reduce 21/60 by dividing top and bottom by 3:

[tex]s=\frac{7\pi}{20}[/tex]

Your answer is [tex]\frac{7\pi}{20}[/tex].

If you prefer an answer rounded to nearest hundredths you would have 1.10 or just 1.1.

Answer:

Speed of the boat in still water = 6.125 miles/hour

Step-by-step explanation:

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming [tex]S_b[/tex] to be the speed of the boat in still water and [tex]S_w[/tex] to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

[tex]Speed = \frac{distance}{time}[/tex]

[tex]S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours} [/tex]

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

[tex]S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours} [/tex]

Adding the two equations to get:

   [tex]S_b+S_w=\frac{d}{t_1}[/tex]

+  [tex]S_b-S_w=\frac{d}{t_2} [/tex]

___________________________

[tex]2S_b=\frac{d}{t_1} +\frac{d}{t_2}[/tex]

Solving this equation for [tex]S_b[/tex] and substituting the given values for [tex]d,t_1, t_2[/tex]:

[tex]S_b=\frac{(t_1+t_2)d}{2t_1t_2}[/tex]

[tex]S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}[/tex]

[tex]S_b=\frac{(11 hour)(33mi)}{56hour^2}[/tex]

[tex]S_b=6.125 mi/hr[/tex]

Therefore, the speed of the boat in still water is 6.125 miles/hour.

Answer:

[tex]6.48\frac{mi}{h}[/tex]

Step-by-step explanation:

Let' call "b" the speed of the boat and "c" the speed of the river.

We know that:

[tex]V=\frac{d}{t}[/tex]

Where "V" is the speed, "d" is the distance and "t" is the time.

Then:

[tex]d=V*t[/tex]

We know that distance traveled downstream is 33 miles and the time is 4 hours. Then, we set up the folllowing equation:

[tex]4(b+c)=33[/tex]

For the return trip:

 [tex]7(b-c)=33[/tex]  (Remember that in the return trip the speed of the river is opposite to the boat)

By solving thr system of equations, we get:

- Make both equations equal to each other and solve for "c".

[tex]4(b+c)=7(b-c)\\\\4b+4c=7b-7c\\\\4c+7c=7b-4b\\\\11c=3b\\\\c=\frac{3b}{11}[/tex]

- Substitute "c" into any original equation and solve for "b":

[tex]4b+\frac{3b}{11} =33\\\\4b+\frac{12b}{11}=33\\\\\frac{56b}{11}=33\\\\b=6.48\frac{mi}{h}[/tex]

Answer:

b) −8x+6

Step-by-step explanation:

-3x+4 - (5x-2)

Distribute the minus sign

-3x+4 -5x+2

Combine like terms

-3x-5x +4+2

-8x+6

Answer:

the answer is b -8x+6

Step-by-step explanation:

Answer:

788.13  to the nearest hundredth.

Step-by-step explanation:

Let A be the total amount in the account after 3 years.

The formula is A = P(1 + x/100)^t .

Here P = 5000, x = 5 %  and the time t = 3. years.  

Amount after 3 years = 5000(1 + 5/100)^3

=  5788.13

So the Interest is 5788.13 - 5000

= 788.13.

Answer:

Compound interest = 788.125

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 + R/100]^N

Were A - Amount

P - Principle

R - Rate of interest

N - Number of years

To find the compound interest

Here P - 5,000

R = 5%

N - 3 years

A = P[1 + R/100]^N

 = 5000[1 + 5/100]^3

 = 5000[1 + 0.05]^3

 = 5788.125

Compound interest  = A - P

 = 5788.125 - 5000

 = 788.125

Answer:

1,779.33 ft³

Step-by-step explanation:

volume of cone = 1/3(pi)r²h (r=radius, h=height)

= 1/3 x 3.14 x (10)² x 17,

= 1/3 x 314 x 17

= 1/3 x 5338

= 1779.33 ft³

Answer:

just answering so this guy can get brainiest

Answer:

B) 28.53 unit²

Step-by-step explanation:

The diagonal AD divides the quadrilateral in two triangles:

Area of Quadrilateral will be equal to the sum of Areas of both triangles.

i.e.

Area of ABCD = Area of ABD + Area of ACD

Area of Triangle ABD:

Area of a triangle is given as:

[tex]Area = \frac{1}{2} \times base \times height[/tex]

Base = AB = 2.89

Height = AD = 8.6

Using these values, we get:

[tex]Area = \frac{1}{2} \times 2.89 \times 8.6 = 12.43[/tex]

Thus, Area of Triangle ABD is 12.43 square units

Area of Triangle ACD:

Base = AC = 4.3

Height = CD = 7.58

Using the values in formula of area, we get:

[tex]Area = \frac{1}{2} \times 4.3 \times 7.58 = 16.30[/tex]

Thus, Area of Triangle ACD is 16.30 square units

Area of Quadrilateral ABCD:

The Area of the quadrilateral will be = 12.43 + 16.30 = 28.73 units²

None of the option gives the exact answer, however, option B gives the closest most answer. So I'll go with option B) 28.53 unit²

Answer:

k = 2

Step-by-step explanation:

If the roots are real and equal then the condition for the discriminant is

b² - 4ac = 0

For 2x² - (k + 2)x + k = 0 ← in standard form

with a = 2, b = - (k + 2) and c = k, then

(- (k + 2))² - (4 × 2 × k ) = 0

k² + 4k + 4 - 8k = 0

k² - 4k + 4 = 0

(k - 2)² = 0

Equate factor to zero and solve for k

(k - 2)² = 0 ⇒ k - 2 = 0 ⇒ k = 2

Answer:

Step-by-step explanation:

A quadratic equation has two equal real roots if a discriminant is equal 0.

[tex]ax^2+bx+c=0[/tex]

Discriminant [tex]b^2-4ac[/tex]

We have the equation

[tex]2x^2-(k+2)x+k=0\to a=2,\ b=-(k+2),\ c=k[/tex]

Substitute:

[tex]b^2-4ac=\bigg(-(k+2)\bigg)^2-4(2)(k)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=k^2+2(k)(2)+2^2-8k=k^2+4k+4-8k=k^2-4k+4\\\\b^2-4ac=0\iff k^2-4k+4=0\\\\k^2-2k-2k+4=0\\\\k(k-2)-2(k-2)=0\\\\(k-2)(k-2)=0\\\\(k-2)^2=0\iff k-2=0\qquad\text{add 2 to both sides}\\\\k=2[/tex]

For this case we must represent the following expression algebraically, in addition to indicating its result:

"2 plus 9"

So, we have:

[tex]2 + 9 =[/tex]

By law of the signs of the sum, we have that equal signs are added and the same sign is placed:

[tex]2 + 9 = 11[/tex]

ANswer:

11

Answer:

She has 9 5 cent stamps and 6 7 cent stamps.

Step-by-step explanation:

Let the number of five cent stamps be represented by F and the number of seven cent stamps be represented by S.

The difference between the number of five cent and seven cent stamps is 3

F-S=3

The sum of the collection from each type of stamp is 87 cents

5F+7S=87

Let us solve the equations simultaneously.

F-S=3

5F+7S=87

Using substitution method,

F= 3+S

5(3+S)+7S=87

15+5S+7S=87

12S=87-15

12S=72

S=6

F=3+S

=3+6=9

Therefore the number of five cent stamps is 9 and seven cent stamps is 6.

Answer:

Number of 5 cent stamps = 9

Number of 7 cent stamps = 6

Step-by-step explanation:

We are given that Bianca has a stamp collection of 5 cent stamps and 7 cent stamps in which there are 3 less 7 cent stamps as 5 cent stamps.

If the total face value of stamps is 87 cents, we are to find the number of stamps of each value.

Assuming [tex]t[/tex] to be the number of 5 cent stamps and [tex]s[/tex] to be the 7 cent stamps so we can write it as:

[tex]0.05t+0.07s=0.87[/tex] --- (1)

[tex]s=t-3[/tex] --- (2)

Substituting this value of [tex]s[/tex] from (2) in (1):

[tex]0.05t+0.07(t-3)=0.87[/tex]

[tex]0.05s+0.07t-0.21=0.87[/tex]

[tex]0.12t=1.08[/tex]

[tex]t=9[/tex]

Number of 5 cent stamps = 9

Number of 7 cent stamps = 9 - 3 = 6

Answer:

-12 <p <12

Step-by-step explanation:

|p|<12

We can write this without the absolute values

Take the equation with the positive value on the right hand side  and take the equation with a negative value on the right side remembering to flip the inequality.  Since this is less than we use and in between

p < 12 and p >-12

-12 <p <12

Step-by-step explanation:

[tex]For\ a>0\\\\|x|<a\Rightarrow x<a\ \wedge\ x>-a\\\\|x|>a\Rightarrow x>a\ \wedge\ x<-a\\\\===============================\\\\|p|<12\Rightarrow p<-12\ \wedge\ p>-12\Rightarrow-12<p<12[/tex]

Answer: The quotient of powers was used because 25=5^2 which means that 5^4/25 is the same as 5^4/5^2. 5^4/5^2= 5^2. You can check your answer by simplifying 5^4 which is 625 and 5^2 which is 25, then divide the two which is 625/25 which equals 25 (or 5^2)

Step-by-step explanation:

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{5^4}{25}\implies \cfrac{5^4}{5^2}\implies \cfrac{5^4}{1}\cdot \cfrac{1}{5^2}\implies 5^4\cdot 5^{-2}\implies 5^{4-2}\implies 5^2[/tex]

The length of the edge of the cube whose net area is 24 in sq is calculated as: 2 inches.

What is the length of a cube?

The net of a cube consists of six identical square faces. Let's denote the length of one side of the square as s.

The total surface area of the cube is the sum of the areas of its six faces. Since each face has an area of s², the total surface area (A) is given by:

[tex]\[ A = 6s^2 \][/tex]

You mentioned that the net has an area of 24 square inches. Therefore, we can set up the equation:

6s² = 24

Now, solve for s:

[tex]s^2 = \frac{24}{6}[/tex]

s² = 4

Take the square root of both sides:

[tex]s = \sqrt{4}[/tex]

s = 2

So, the length of each edge of the cube is 2 inches.

Answer:

26

Step-by-step explanation:

The formula is a half the positive difference of the measurements of the intercepted arcs.

That is you do .5(66-14) here.

I'm going to distribute first and instead of find the difference first.

.5(66)-.5(14)

   33-  7

   26

Or.... you could do the difference first which gives us .5(66-14)=.5(52)=26.

So that angle is 26 degrees.

Answer:

x = 26°

Step-by-step explanation:

A secant- secant angle is an angle whose vertex is outside the circle and whose sides are 2 secants of the circle. It's measure is

x = 0.5(66 - 14)° = 0.5 × 52° = 26°

Answer:

Probability = 5/6

Step-by-step explanation:

Step 1: Write the formula of probability

Probability = number of possible outcomes/total number of outcomes

There is only one 28 so the chance of getting a 28 is 1/6.

Not getting a 28 would mean getting any one number from 23, 24, 25, 26 and 27.

Step 2: Apply the probability formula

Probability = number of possible outcomes/total number of outcomes

Probability of not getting 28 = 5/6

!!

Answer:

7/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first choice describes the right way to find the length of an arc in a circle.

The length of an arc is defined as

[tex]L=2\pi r (\frac{\theta}{360\°} )[/tex]

Where [tex]2\pi r[/tex] represents the circumference of the circle and [tex]\theta[/tex] represents the arc's degree measure.

So, as you can observe through this formula, we need to divide the arc's degree measure by 360°, and then multiply this result with the circumference of the circle, that's the right way based on the definition of arc length.

Therefore, the right answer is A.

The length of an arc in the circle is L = Divide the arc's degree measure by 360°, then multiply by the circumference of the circle

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the length of the arc of the circle be L

Now , Central Angle = ( L x 360° ) / 2πr

where s is the length of the arc

On simplifying the equation , we get

Divide by 360° on both sides , we get

L / 2πr = Central Angle θ / 360°

Multiply by 2πr ( circumference ) on both sides , we get

L = ( θ / 360° ) x 2πr

Hence , the length of an arc is L = ( θ / 360° ) x 2πr

To learn more about central angle click :

https://brainly.com/question/11877137

#SPJ5

Answer:

m=-2/3  (slope)

b=3        (y-intercept)

Step-by-step explanation:

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

You have 3y+2x=9.

We need to solve this for y to get it into y=mx+b form.

3y+2x=9

Subtract 2x on both sides:

3y     =-2x+9

Divide both sides by 3:

[tex]y=\frac{-2}{3}x+\frac{9}{3}[/tex]

[tex]y=\frac{-2}{3}x+3[/tex]

Now compare this to:

y=mx+b

m=-2/3  

b=3

Answer:

-a^2 +2ab + b^2

Step-by-step explanation:

b (a+b) - a (a-b)

Distribute

ab +b^2 -a^2 +ab

Combine like terms

b^2 -a^2 +2ab

-a^2 +2ab + b^2

Answer:

[tex]\frac{147}{100}[/tex]

Step-by-step explanation:

This is the answer because 147 ÷ 100 = 1.47

Answer:

110

Step-by-step explanation:

He said he had atleast 1 of each. Hope it helps.

The smallest possible total weight of Tom's toys​ is:

                          210 grams

It is given that:

Tom has 8 toys each toy weighs either 20 grams or 40 grams or 50 grams.

Also, he  has a different number of toys (at least one) of each weight.

Now, the smallest possible weight of Tom's toy is such that:

He has one toy of 50 grams , one of 40 grams and the other's are of smallest weight i.e. 20 grams.

This means he has 6 toys of 20 grams.

One of 40 grams.

One of 50 grams.

Hence,

Total weight= 20×6+40+50

i.e.

Total weight= 120+90

i.e.

Total weight= 210 grams.

Answer:

y=(x-3)^2 -2

Step-by-step explanation:

when the number to the power of two is positive the graph will aslo go up, (both ends go up as shown in the graph. the parabula of the graph is -2.

Answer:

Step-by-step explanation:

sin=y/r

cos=x/r

sin=21/29

cos=x/29

x^2+y^2=r^2

x^2+21^2=29^2

x^2+441=841

x=sqrt(841-441)

x=20

cos=20/29

  Only              |

   sin +             |     All Positive

---------------------|-------------------

           only      |    Only cos +

            tan +    |

Answer:

C

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex]

Given

sinx = [tex]\frac{21}{29}[/tex], then

cosx = [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex] ( positive since 0 < x < 90 )

       = [tex]\sqrt{1-\frac{441}{841} }[/tex]

       = [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{20}{29}[/tex]

Answer:

The correct answer is second option

78°

Step-by-step explanation:

Points to remember

The measure of arc BC = 2 * measure of angle BDC

To find the measure of arc BC

From the figure we can see the BD is the diameter of the given circle.

Therefore the ΔBDC is right angled triangle. m<C = 90°

m<CBD = 51°   (given)

m<CBD + m<BDC = 90

m<BDC = 90 - m<CBD

 = 90 - 51 = 39

Therefore measure of arc BC = 2 *m<BDC

  = 2 * 39

 = 78°

The correct answer is second option

78°

there's a scale factor of two!

five times two is ten.

hope this helps! :) xx

Answer:

"The maximum number of solutions is one."

Step-by-step explanation:

Hopefully the drawing helps visualize the problem.

The circle has a radius of 9 because the vertex is 9 units above the center of the circle.

The circle the parabola intersect only once and cannot intercept more than once.  

The solution is "The maximum number of solutions is one."

Let's see if we can find an algebraic way:

The equation for the circle given as we know from the problem without further analysis is so far [tex]x^2+y^2=r^2[/tex].

The equation for the parabola without further analysis is [tex]y=ax^2+9[/tex].

We are going to plug [tex]ax^2+9[/tex] into [tex]x^2+y^2=r^2[/tex] for [tex]y[/tex].

[tex]x^2+y^2=r^2[/tex]

[tex]x^2+(ax^2+9)^2=r^2[/tex]

To expand [tex](ax^2+9)^2[/tex], I'm going to use the following formula:

[tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](ax^2+9)^2=a^2x^4+18ax^2+81[/tex].

[tex]x^2+y^2=r^2[/tex]

[tex]x^2+(ax^2+9)^2=r^2[/tex]

[tex]x^2+a^2x^4+18ax^2+81=r^2[/tex]

So this is a quadratic in terms of [tex]x^2[/tex]

Let's put everything to one side.

Subtract [tex]r^2[/tex] on both sides.

[tex]x^2+a^2x^4+18ax^2+81-r^2=0[/tex]

Reorder in standard form in terms of x:

[tex]a^2x^4+(18a+1)x^2+(81-r^2)=0[/tex]

The discriminant of the left hand side will tell us how many solutions we will have to the equation in terms of [tex]x^2[/tex].

The discriminant is [tex]B^2-4AC[/tex].

If you compare our equation to [tex]Au^2+Bu+C[/tex], you should determine [tex]A=a^2[/tex]

[tex]B=(18a+1)[/tex]

[tex]C=(81-r^2)[/tex]

The discriminant is

[tex]B^2-4AC[/tex]

[tex](18a+1)^2-4(a^2)(81-r^2)[/tex]

Multiply the (18a+1)^2 out using the formula I mentioned earlier which was:

[tex](u+v)^2=u^2+2uv+v^2[/tex]

[tex](324a^2+36a+1)-4a^2(81-r^2)[/tex]

Distribute the 4a^2 to the terms in the ( ) next to it:

[tex]324a^2+36a+1-324a^2+4a^2r^2[/tex]

[tex]36a+1+4a^2r^2[/tex]

We know that [tex]a>0[/tex] because the parabola is open up.

We know that [tex]r>0[/tex] because in order it to be a circle a radius has to exist.

So our discriminat is positive which means we have two solutions for [tex]x^2[/tex].

But how many do we have for just [tex]x[/tex].

We have to go further to see.

So the quadratic formula is:

[tex]\frac{-B \pm \sqrt{B^2-4AC}}{2A}[/tex]

We already have [tex]B^2-4AC}[/tex]

[tex]\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}[/tex]

This is t he solution for [tex]x^2[/tex].

To find [tex]x[/tex] we must square root both sides.

[tex]x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]

So there is only that one real solution (it actually includes 2 because of the plus or minus outside) here for x since the other one is square root of a negative number.

That is,

[tex]x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]

means you have:

[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]

or

[tex]x=\pm \sqrt{\frac{-(18a+1)-\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex].

The second one is definitely includes a negative result in the square root.

18a+1 is positive since a is positive so -(18a+1) is negative

2a^2 is positive (a is not 0).

So you have (negative number-positive number)/positive which is a negative since the top is negative and you are dividing by a positive.

We have confirmed are max of one solution algebraically. (It is definitely not 3 solutions.)

If r=9, then there is one solution.

If r>9, then there is two solutions as this shows:

[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]

r=9 since our circle intersects the parabola at (0,9).

Also if (0,9) is intersection, then

[tex]0^2+9^2=r^2[/tex] which implies r=9.

Plugging in 9 for r we get:

[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2(9)^2}}{2a^2}}[/tex]

[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+324a^2}}{2a^2}}[/tex]

[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{(18a+1)^2}}{2a^2}}[/tex]

[tex]x=\pm \sqrt{\frac{-(18a+1)+18a+1}{2a^2}}[/tex]

[tex]x=\pm \sqrt{\frac{0}{2a^2}}[/tex]

[tex]x=\pm 0[/tex]

[tex]x=0[/tex]

The equations intersect at x=0. Plugging into [tex]y=ax^2+9[/tex] we do get [tex]y=a(0)^2+9=9[/tex].  

After this confirmation it would be interesting to see what happens with assume algebraically the solution should be (0,9).

This means we should have got x=0.

[tex]0=\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}[/tex]

A fraction is only 0 when it's top is 0.

[tex]0=-(18a+1)+\sqrt{36a+1+4a^2r^2}[/tex]

Add 18a+1 on both sides:

[tex]18a+1=\sqrt{36a+1+4a^2r^2[/tex]

Square both sides:

[tex]324a^2+36a+1=36a+1+4a^2r^2[/tex]

Subtract 36a and 1 on both sides:

[tex]324a^2=4a^2r^2[/tex]

Divide both sides by [tex]4a^2[/tex]:

[tex]81=r^2[/tex]

Square root both sides:

[tex]9=r[/tex]

The radius is 9 as we stated earlier.

Let's go through the radius choices.

If the radius of the circle with center (0,0) is less than 9 then the circle wouldn't intersect the parabola.  So It definitely couldn't be the last two choices.

Answer:

Option A.

Step-by-step explanation:

A circle was drawn with the center at origin (0, 0) and a point (0, 9) on the circle.

So the radius will be r = [tex]\sqrt{(0-0)+(0-9)^{2}}=9[/tex]

Equation of this circle will be in the form of x² + y² = r²

Here r represents radius.

So the equation of the circle will be x² + y² = 9²

Or x² + y² = 81

Now we will form the equation of the parabola having vertex at (0, 9)

y² = (x - h)² + k

where (h, k) is the vertex.

Equation of the parabola will be y² = (x - 0)² + 9

y² = x² + 9

Now we will replace the value of y² from this equation in the equation of circle to get the solution of this system of the equations.

x² + x² + 9 = 81

2x² = 81 - 9

2x² = 72

x²= 36

x = ±√36

x = ±6

Since circle and parabola both touch on a single point (0, 9) therefore, there will be only one solution that is x = 6.

For x = 6,

6² + y² = 9²

36 + y² = 81

y² = 81 - 36 = 45

y = √45 = 3√5  

Option A. will be the answer.

Answer:

=70$

Step-by-step explanation:

The total in her account at day zero =85$

Lunch for five days= 3$×5

=15$

Total in her account= Initial amount - Expenditure on lunch

=85$-15$

=70$

The balance in Latesha's Lunch Account after having lunch for five day=70$

Answer:

Step-by-step explanation:

We only need two points to plot the graph of each equation.

[tex]y=-3x+2\\\\for\ x=0\to y=-3(0)+2=0+2=2\to(0,\ 2)\\for\ x=1\to y=-3(1)+3=-3+2=-1\to(1,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)[/tex]

Look at the picture.

Read the coordinates of the intersection of the line (solution).

Answer:

regular

Step-by-step explanation:

1. look at table

Answer:

The correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Step-by-step explanation:

Consider the provided table.

We need to find which strategy is better.

If team play regular defense then they win 38 matches out of 50.

[tex]Probability=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

[tex]P(Win|Regular)=\frac{38}{50}[/tex]

[tex]P(Win|Regular)=0.76[/tex]

If team play prevent defense then they win 29 matches out of 50.

Thus, the probability of win is:

[tex]P(Win|Prevent )=\frac{29}{50}[/tex]

[tex]P(Win|Prevent )=0.58[/tex]

Since, 0.76 is greater than 0.58

That means the probability of winning the game by playing regular defense is more as compare to playing prevent defense.

Hence, the conclusion is: You are more likely to win by playing regular defense.

Thus, the correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Answer:

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Step-by-step explanation:

It is given that the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. Using Pythagoras theorem, the third side of the base is

[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]

[tex]hypotenuse^2=(9)^2+(12)^2[/tex]

[tex]hypotenuse^2=225[/tex]

[tex]hypotenuse=\sqrt{225}[/tex]

[tex]hypotenuse=15[/tex]

The area of a triangle is

[tex]A=\frac{1}{2}\times base \times height[/tex]

Area of the base is

[tex]A_1=\frac{1}{2}\times 9\times 12=54[/tex]

The curved surface area of triangular prism is

[tex]A_2=\text{perimeter of base}\times height[/tex]

[tex]A_2=(9+12+15)\times 10[/tex]

[tex]A_2=9\times 10+12\times 10+15\times 10[/tex]

[tex]A_2=360[/tex]

The surface area of the triangular prism is

[tex]A=2A_1+A_2[/tex]

[tex]A=2(54)+360[/tex]

[tex]A=108+360[/tex]

[tex]A=468[/tex]

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Answer:

468 square centimeters

Step-by-step explanation: