Define the axis of symmetry, vertex, focus and directrix for

16(y-4)= (x-3)^2

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2b + 21 < 22

b is the unknown number so multiply it by 2 to get 2b then add 21, bring the less than sign and write the 22 after the less than sign

Answer:

-1, 3, 7, 11

Step-by-step explanation:

First, let's find term 1. To find this term, we need to replace n with 1 - what is 4(1) - 5? Well, that's just 4 - 5, or -1. So, our first term is -1. Next, we'll find our second term. To do this, we'll replace n with 2. 4(2) = 8, and then 8 - 5 is equal to 3, so our second term is 3. Let's now find the third term by replacing n with the number 3. 4(3) - 5 is equal to 12 - 5, or 7. So, 7 is our third term. Finally, we'll find the fourth term. 4(4) is equal to 16, and 16 - 5 is equal to 11. So, the fourth and final term is equal to 11.

Hopefully that's helpful! :)

Step-by-step explanation:

Term 1: - 1

Term 2: 3

Term 3: 7

Term 4: 11

The rule is, where you see n, substitute with the position/term requested

First 4 terms are: - 1,3,7, 11

Answer:

[tex]\boxed{(0, 0), (\sqrt{6}, -12-3\sqrt{6}), (-\sqrt{6}, -12+3\sqrt{6})}[/tex]

Step-by-step explanation:

Step 1: Take the derivative of the function with respect to x

[tex]\frac{d}{dx} (\frac{1}{3}x^4-4x^2-3x)\\=\frac{d}{dx} (\frac{1}{3}x^4)-\frac{d}{dx}(4x^2)-\frac{d}{dx}(3x)\\=\frac{4}{3}x^3-8x-3[/tex]

Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,

Step 2: Set the derivative of the function equal to -3 and solve for x

[tex]\frac{4}{3}x^3-8x-3=-3\\\frac{4}{3}x^3-8x=0\\4x(\frac{1}{3}x^2-2)=0\\[/tex]

We can see that one solution is x=0.

The other 2 solutions are:

[tex]\frac{1}{3}x^2-2=0\\\frac{1}{3}x^2=2\\x^2=6\\x=\sqrt{6}, x=-\sqrt{6}[/tex]

Now that we found out the x value, we can plug it in back to the equation to find their respective y value:

x=0: y=0

x=sqrt(6): y=-12-3sqrt(6)

x=-sqrt(6): y=-12+3sqrt(6)

Hence we have our answer.

Let [tex]f^{-1}(x)[/tex] be the inverse of

[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]

Then by definition of inverse function,

[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

Solve for the inverse :

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]

[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]

[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]

nCx⋅px⋅(1−p)n−x

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Answer:

200% increase

Step-by-step explanation:

Answer is below in the picture:-

(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')

I hope it helps.

It is proved that the ray BC is the angle bisector of angle ABA'.

Angle bisectors are lines who bisect the considered angle. Bisect refers to splitting in two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if it in a mirror.

We will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

From the given problem, we know Triangle A'B'C' is a reflection of triangle ABC across line BC.

Therefore, <A'B'C' = <ABC

By the properties of congruent triangles. Means if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Hence, the ray BC is the angle, bisector of angle ABA'.

Learn more about reflection here;

https://brainly.com/question/28186407

#SPJ5

Answer:

4a(3a+5)

We take H.C.F of both number and the variables then we compare the HCF number and variable with our question and equate and write the answer about how much should be multiplied from the H.C.F answer to get the question.

Answer:

The solution is x = 3, y = 2.

Step-by-step explanation:

4x + 6y = 24

15x – 6y = 33    Add these 2 equations:

19x = 57

x = 57/19

x = 3.          Now Substitute for x in the original equation:

2(3) + 3y = 12

3y = 12 - 6

2y = 6

y = 2.

Answer:

Step-by-step explanation:

1. Pythagorean theorem: a^2+b^2=c^2

Note that the hypotenuse is 11 (for the second right triangle).

Find the length of the dotted line by doing 7^2+b^2=11^2

49+b^2=121, b=[tex]\sqrt{72\\}[/tex].

Now you can the area of the second right triangle: ([tex]\sqrt{72\\}[/tex](7))/2=29.7.

Find the length of the first right triangle:

Note that 9 is the hypotenuse; ([tex]\sqrt{72\\}[/tex])^2+b^2=9^2

=72+b^2=81

b=3.

([tex]\sqrt{72}[/tex])(3))/2=12.7

Th e correct equation will be y = 5x

Ratios is a way dividing two integers. For instance, the ratio of a to b is written as a:b.

Given the ratios expressed as x:y = 1:5

Since ratio means division hence;

x:y = 1:5

x/y = 1/5

Cross multiply

1 * y = 5 * x

y = 5x

Hence the correct equation will be y = 5x

Learn more on ratios here: https://brainly.com/question/2914376

Answer:

i think x = -5, y = -7 is a other solution set

Answer:

elga is 32 and alvin is 49

You see here, there are too many people in the government and all of this gets us no where. So, too many is the answer.

Answer:

204

Step-by-step explanation:

90-5 (9-5 (9- (14-12) 3 ) ÷5

▪︎ First we have to solve the ones in the brackets ___ ( 14-12 ) which is e equal to 2

90-5 (9-5 (9- 2×3 ) ÷5 "the 3 comes inside the bracket coz we solved the previous one"

▪︎then we have to solve ( 9-2×3 ) which is equal to 3 _____ is 3 because if we go in the BODMAS way it will be

( 2×3 =6) , then... (9-6=3)

▪︎at the same time we can subtract 9-5 because we are done with the first bracket ( 9-5=4 )

90-5 (4×3)÷5

▪︎at the same time we can subtract 90-5 as well coz we are done with the first bracket ( 90-5=85)

▪︎then we can multiply (4×3) coz it's in the brackets (4×3=12)

85×12÷5

▪︎so then we hv to multiply 85 by 12 , then the answer is 1020

1020÷5

▪︎then divide (1020÷5=204)

☆90-5 (9-5 (9- (14-12) 3 ) ÷5

=90-5(9-5(9-2×3)÷5

=90-5(4×3)÷5

=85×12÷5

=1020÷5

=204

hope this helps☆☆☆

( sorry fr the long answer )

Answer:

5 weeks

Step-by-step explanation:

75 w + 55 ≥ 400

75 w ≥ 345

15 w ≥ 69

w ≥ [tex]\frac{23}{5}[/tex] = 4.6 weeks ⇒ the minimum number of weeks Jordan must work is 5 weeks

Answer:

Step-by-step explanation:

To find the number of yard, divide the number of feet by the unit rate 3 feet per yard.

[tex]\cfrac{\underline{4}}{5}-\cfrac{1}{4}\implies \cfrac{(4)(\underline{4})~~ - ~~(5)(1)}{\underset{\textit{using this LCD}}{20}}\implies \cfrac{16-5}{20}\implies \cfrac{11}{20}[/tex]

Answer:

The blogger needs at least 189subscribers to break even

Answer:

6x +4=10

I think this is answer

Answer:

night.....

Step-by-step explanation:

..............

Answer:

1.

m= 1; b= 4

m= -4; b= 2

m= 1; b= 0

m= 3/2; b= -9

m= -7; b= 4/5

2. C

Step-by-step explanation:

Question 1.

Your slope equation is

y=mx+b

The number before the x is your slope. The number added or subtracted after is your b.

Question 2.

Slope is rise over run.

Answer:

104-5/9

Step-by-step explanation:

just divided ND SUBTRACT

Answer:

b. 9

Step-by-step explanation:

2+9=11

11+11=22

22+6=28

Answer:

Step-by-step explanation:

RSB is a right angle

12. RSB is 90 degrees

13. A right angle is 90 degrees

H is between P and S

14. PS + PH = HS

15. Deductive Reasoning

Answer:

yes you are correct

Step-by-step explanation:

Answer:

i think the perimeter is 60

Step-by-step explanation:

9²+12² = x²

15 = x

perimeter = 15×4 = 60

Answer:

10,485,760

Step-by-step explanation:

Multiply -4