The third term in a sequence is 25. The fifth term is 225. What are the possible values of the 4th term of the sequence if it is arithmetic? If it is geometric?

Answer:

[tex](x +10)^2 + (y+6)^2 = 121[/tex]

Step-by-step explanation:

Given equation :

                        [tex]x^2 + y^2 + 20x +12y + 15 = 0[/tex]

Standard equation of circle :

                                            [tex](x - a)^2 + (y-b)^2 = r^2[/tex]

We will consider the x terms in the equation first to find a.

[tex](x-a)^2 = x^2 - 2ax + a^2[/tex]

-2ax = 20x

a = -20x/2x = -10

a = -10

Next consider the y terms to find b.

[tex](y - b)^2 = y^2 -2by + b^2[/tex]

-2by = 12y

b = -12y /2y = -6

b = -6

[tex](x+10)^2 + (y-6)^2 = x^2 +20x +100 + y^2 +12y + 36[/tex]

                             [tex]=x^2 + y^2 + 20x +12y + 136\\[/tex]

But the given equation constant is 15. So find the difference between 136 and 15 to find the radius : 136 - 15 = 121

Therefore, radius = √121 = 11

Equation in standard form :

                                         [tex](x +10)^2 + (y+6)^2 = 121[/tex]

Answer:

69.47%

Step-by-step explanation:

Calculation to determine Find the percent of markup

Using this formula

Percent of markup=New price-Old price/Old price

Let plug in the formula

Percent of markup=$15.95-$4.87/$15.95

Percent of markup=$11.08/$15.95

Percent of markup=0.6947*100

Percent of markup=69.47%

Therefore the percent of markup is 69.47%

Answer:

3x - 4

Step-by-step explanation:

(6x^2 − 8x) ÷ (2x) =

(6x^2)/2x - 8x/2x =                 

3x - 4

Answer:

(C). 3x - 4

Step-by-step explanation:

It will be easily to break this down so,

6/2=3

x^2/x=x

therefore, 6x^2/2x = 3x

Minus stay minus

8/2 = 4

x/x=1

therefore, 8x/2x=4

If we put it all together,

3x - 4

if this helps you, please give brainliest!

Answer:

16 and 56

Step-by-step explanation:

gcf of 24 and 48 is 24

gcf of 14 and 32 is 2

gcf of 16 and 28 is 4

Let's find one by one

#1

24 and 48

No

#2

14 and 32

No

#3

GCF is 4

No

#4

16 and 56

Yes

= 5-³ -³

= 5-⁶

= 1/5⁶

= 5⁷+³

= 5¹⁰

= 5⁶ - ⁴

= 5²

= 5-⁴ + ⁴ × 1

= 5⁰

Answer:

answser  in picturew

Step-by-step explanation:

Answer:

x=-14

Step-by-step explanation:

because -2(-14)=-26

Answer:

This is the ans i think this is right

Answer:

Step-by-step explanation:

for y

take 30 degree as reference angle using sin rule

sin 30=opposite/hypotenuse

1/2=9/y (do cross multiplication)

2*9=y

18=y

for x

using pythagoras theorem

a^2+b^2=c^2

9^2+x^2=18^2

81+x^2=324

x^2=324-81

x^2=243

x=[tex]\sqrt{243[/tex]

x=9[tex]\sqrt{3[/tex]

d = 17.3 m

Step-by-step explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

[tex] {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} [/tex]

or

[tex]d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } [/tex]

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

[tex]d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } [/tex]

or

[tex]d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m[/tex]

This becomes

d = 17.3 m

Answer

Ok i will help

Step-by-step explanation:

Yay!

Answer:

the missing side is 6

Step-by-step explanation:

Using the Pythagorean theorem, ([tex]a^{2} + b^{2} = c^{2}[/tex]), for right triangles, you get [tex]4^{2} + (2\sqrt{5}) ^{2} = c^{2}[/tex].  Since the square cancels the square root for side b you get [tex](2^{2})*(5)[/tex] which equals 20. This makes your equation go to 16+20 = [tex]c^{2}[/tex]. Then add the numbers to make [tex]36=c^{2}[/tex]  solve for c by taking the square root of both sides to get c = 6.

Answer:

x=46 degree

Step-by-step explanation:

32 +x=Angle ABC

32 + x =78 degree

x=78 - 32

x=46 degree

Answer: 3rd

Answer: 3rd

25/15

Answer:

A. 52

Step-by-step explanation:

Find how many months are in 4 years, since there are 4 years between her 13th and 17th birthdays.

There are 12 months in a year, so multiply 12 by 4:

12(4)

= 48

So, there are 48 months in 4 years. Since she buys a new teacup every month, this means she will have bought 48 more teacups.

Add this to the 4 teacups she got on her 13th birthday:

48 + 4

= 52

So, on her 17th birthday, she will have A. 52 teacups

Answer:

-10

Step-by-step explanation:

i think this is the answer

Answer:

Surds. Note: a root we can't simplify further is called a Surd. So √3 is a surd.

Answer:

y = -3

Step-by-step explanation:

y = -0.5(6)

y = -3

Step-by-step explanation:

The formula for the lateral area of a right cone is :

LA = rs

Where

r is the radius of the base and s is the slant height of the cone

Equivalent expression,

[tex]r=\dfrac{LA}{s}[/tex]

or

[tex]s=\dfrac{LA}{r}[/tex]

Hence, this is the required solution.

Answer:

The answers are C & E

Answer: 160 chicken sandwiches were sold.

To convert a percentage into a decimal, move the decimal two places back.

40%=0.40, or 0.4

This means that 0.4 is still equivalent to 40%

Remember that "of" means multiplication.

So 0.4*400=160

160 chicken sandwiches were sold

Answer:

Side-Side-Side (SSS) Congruence - if three sides of one triangle are congruent to three sides of  another triangle, then the triangles are congruent.

Side-Angle-Side (SAS) Congruence - If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Side-Angle (ASA) Congruence - If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Angle-Side (AAS) Congruence - If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

u see which one fits

Answer:  SAS

Step-by-step explanation: because there are Two sides and the angle between them are congruent.

Answer:

b = x - y

Step-by-step explanation:

Given the expression x - y = b

We are to rewrite the value of b;

We can simply do this by swapping both sides that are putting b at the Left hand side and x - y at the right as shown

b = x - y

Hence the correct expression will be b = x - y

Answer:

a. i. sinθ = +0.941

ii. cosθ = +0.339

b. i. sinθ = -0.842

ii.  cosθ = +0.540

Step-by-step explanation:

a. Given that tanθ almost equal to≈ 2.773 where 0<θ<π/2, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = 2.773, cotθ = 1/tanθ = 1/2.773 = 0.3606

So, 1 + cot²θ = cosec²θ

1 + (0.3606)² = cosec²θ

1 + 0.13 = cosec²θ

1.13 = cosec²θ

cosec²θ = 1.13

cosecθ = ±√1.13

cosecθ = ±1.063

1/sinθ = ±1.063

sinθ = ±1/1.063

sinθ = ±0.9407

sinθ ≅ ±0.941

Since we have 0<θ<π/2, sinθ is in the first quadrant, so we choose the positive value.

So, sinθ = +0.941 where 0<θ<π/2

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = 2.773,

So, 1 + tan²θ = sec²θ

1 + (2.773)² = sec²θ

1 + 7.6895 = sec²θ

8.6895 = sec²θ

sec²θ = 8.6895

secθ = ±√8.6895

secθ = ±2.9478

1/cosθ = ±2.9478

cosθ = ±1/2.9478

cosθ = ±0.3392

cosθ ≈ ±0.339

Since we have 0<θ<π/2, cosθ is in the first quadrant, so we choose the positive value.

So, cosθ = +0.339 where 0<θ<π/2

b. Given that tanθ ≈ -1.559 where 3π/2<θ<2π, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = -1.559, cotθ = 1/tanθ = 1/-1.559 = -0.6414

So, 1 + cot²θ = cosec²θ

1 + (-0.6414)² = cosec²θ

1 + 0.4114 = cosec²θ

1.4114 = cosec²θ

cosec²θ = 1.4114

cosecθ = ±√1.4114

cosecθ = ±1.1880

1/sinθ = ±1.1880

sinθ = ±1/1.1880

sinθ = ±0.8417

sinθ ≈ ±0.842

Since we have 3π/2<θ<2π, sinθ is in the fourth quadrant, so we choose the negative value.

So, sinθ = -0.842 where 3π/2<θ<2π

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = -1.559,

So, 1 + tan²θ = sec²θ

1 + (-1.559)² = sec²θ

1 + 2.4305 = sec²θ

3.4305 = sec²θ

sec²θ = 3.4305

secθ = ±√3.4305

secθ = ±1.8522

1/cosθ = ±1.8522

cosθ = ±1/1.8522

cosθ = ±0.5399

cosθ ≈ ±0.540

Since we have 3π/2<θ<2π, cosθ is in the fourth quadrant, so we choose the positive value.

So, cosθ = +0.540 where 3π/2<θ<2π

Answer:

No

Yes

Step-by-step explanation:

Let's find the inclination of the 3 lines.

m:

((-4) -3)/(0 - (-4))

-7/4

n:

((-2) -2)/(3 - 1)

-4/2

-2

k:

(1 -(-3)/(4 -(-3)

(1 +3)/4 +3

4/7

Okay, we find the inclination of all the three lines. For two lines be parallel, they have to have the same inclination. The inclination of m = -7/4 and the inclination of n = -2, so they're not parallel. And now, to know if m is perpendicular to k, they inclination have to be the opposite of the inverse of each other, so it means that they have to have opposite signals, and they need to be inverted fractions (for example a/b are inverted to b/a), and they are these two things: m = -7/4 and n = 4/7, so they're perpendicular

Answer:

No, the slopes are not equal.

Yes, the slopes are negative reciprocals.

Step-by-step explanation:

Just did it on edge.

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant [tex]b^2-4ac[/tex] applies to quadratic equations when they are organised in standard form: [tex]ax^2+bx+c=0[/tex].

All quadratic equations can be solved with the quadratic formula: [tex]x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex].

When [tex]b^2-4ac[/tex] is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

[tex]3x^2+5x=-1[/tex]

We're given the above equation. It hasn't been organised completely in [tex]ax^2+bx+c=0[/tex], but we can change that by adding 1 to both sides to make the right side equal to 0:

[tex]3x^2+5x+1=0[/tex]

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

[tex]D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13[/tex]

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

Answer:

ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm   and i Oop

Step-by-step explanation:

answer:

N(t)=2×[tex]1.7^{t}[/tex]

17

15

step by step explain:

before lesson (t=0), she knows 2 words.

after a week (t=1), she knows

2×(1+70%)=3.4 words

after one more week (t=2), she knows

3.4×(1+70%)=5.78 words

one more week later (t=3), she knows

5.78×(1+70%)=9.826 words

and so on ...

from pattern shown above, we know that she knows

2×[tex]1.7^{t}[/tex] words after t weeks

so N(t)=2×[tex]1.7^{t}[/tex]

after 4 weeks (t=4), she knows 2×[tex]1.7^{4}[/tex]=16.7042≈17 words

for learning 5000 words, she need:

2×[tex]1.7^{t}[/tex]=5000

   [tex]1.7^{t}[/tex]=2500

t log(1.7)=log(2500)

         t=[tex]\frac{log(2500)}{log(1.7)}[/tex]

          =14.7448727

          ≈15 (round up)

Answer:

(a) N(t) = 2(1.7)^t

(b) 17

(c) 15

Step-by-step explanation:

(a) N(t) = 2(1.7)^t

There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)

(b) Just plug in the equation

N(4) = 2(1.7)^4

N(4) = 2(8.3521)

N(4) = 16.7042

Round, so it is 17

(c) Once again, plug in the equation

5000 = 2(1.7)^t

2500 = (1.7)^t

use a calculator for the part below

log1.7(2500) = log1.7(1.7)*t

t = log1.7(2500)

t = 14.7448

Round, so it is 15

Answer:

B.6

Step-by-step explanation:

3 + 2x + 22 = x + 17

Combine like terms

25 + 2x = x + 17

Subtract 17 from both sides

8 + 2x = x

Subtract 2x from both sides

8 = -x

Divide both sides by -1

x = -8

Substitute -8 for x in 2x + 22 to find value of QR

2(-8) + 22

Multiply

-16 + 22

Add

QR = 6

The length of QR in the given figure by combining like terms and applying the substitution method, QR = 6

Used the concept of addition and combining like terms in the mathmatical expression.

Given that,

The length of line segments is,

PQ = 3

QR = (2x + 22)

PR = (x + 17)

Now, from the figure,

PQ = QP + QR

Substitute the given values,

x + 17 = 3 + 2x + 22

Combine like terms

x + 17 = 25 + 2x

Subtract 17 from both sides

x = 8 + 2x

Subtract 2x from both sides

x - 2x = 8

- x = 8

Divide both sides by -1

x = -8

So, for the length of QR,

Substitute - 8 for x in the length of QR,

QR = 2x + 22

= 2(-8) + 22

= -16 + 22

= 6

Learn more about the line segment visit:

https://brainly.com/question/280216

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