Please solve 3^(x+3) + 3^(x+4)/3 = 162​

Answer:

Step-by-step explanation:

These angles will be equal when each of them measures 45 degrees. On the unit circle, 45 degrees and reference angles of 45 degrees are the only places where sin and cos are the same. This means that

sin(4x + 10) = 45 and cos(6x) = 45

If we add the angles together (the angles being 4x+10 and 6x) we get a 90 degree angle. Thus,

4x + 10 + 6x = 90 and

10x = 80 so

x = 8. Let's try it out:

sin(4(8) + 10) = sin(42) = .6691306064 and

cos(6(8)) = cos(48) = .6691306064

Yay!!!!!

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]

SIMPLIFY THE EXPRESSION [tex] \blue{\frac{m^{ \frac{2}{3} } }{m {}^{ \frac{1}{5} } } }[/tex]

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \pink{ \frac{m^{ \frac{2}{3} } }{m {}^{ \frac{1}{5} } }} \\ m^{ \frac{2}{3} - \frac{1}{5} } \\ m^{ \frac{(2 \times 5) - (1 \times 3)}{3 \times 5} } \\ m^{ \frac{10 - 3}{15} } \\ m^{ \frac{7}{15} } [/tex]

[tex] \green{SECOND \: \: OPTION->}\purple{ m^{ \frac{7}{15} } }[/tex]

Answer:

See answers to parts a and b below.

Step-by-step explanation:

A. Value: y=20+.20x

Best Rent y=30+.10x

B. 20+.20x=30+.10x make equations equal each other by subbing y values.

.10x=10 simplify equation

x=100

check answers by subbing 100 for x in each equation.

y=20+.20(100)

y=20+20

y=40

y=30+.10(100)

y=30+10

y=40

Both equations equal 40, so 100 is the correct number of miles for when Value equals Best Rent.

Answer:

6 days

Step-by-step explanation:

Hi there!

Let d be equal to the number of days that pass.

1) Form expressions

We're told that our sister earns $30 a day, but needs to pay $60 at first:

[tex]30d-60[/tex]

We're also told that we earn $20 a day:

[tex]20d[/tex]

2) Form an equation

We're solving for the number of days that pass (d) in order for both our and our sister's income to equal each other.

For our income and our sister's income to equal each other, the following must be true:

[tex]30d-60=20d[/tex]

Because the only variable here is d, we can simply isolate it to determine the number of days that would pass.

3) Solve for d

[tex]30d-60=20d[/tex]

Subtract 30d from both sides to isolate d on one side

[tex]30d-60-30d=20d-30d\\-60=-10d[/tex]

Divide both sides by -10 to isolate d

[tex]6=d[/tex]

Therefore, for both our income and our sister's income to become equal, 6 days would pass.

I hope this helps!

Answer:

24 in^2

Step-by-step explanation:

To get the area of a triangle, multiply the base and height, then divide by 2.

Base=6

Height=8

6*8/2=48/2=24

24 in^2

Answer:

24 inch^2

Step-by-step explanation:

6 times 8 equals 48

Divide that by 2 and get 24

Area of Triangle is A=1/2bh

Can I get Brainliest, please!

Answer:

La primera es la respuesta la segunda parte es la

Step-by-step explanation:

La que te muestra como va el procedimiento

Answer:

-57x^2-10x+8

Step-by-step explanation:

i just did the test on edmentum

Answer:

[tex]5[/tex]

Step-by-step explanation:

Segments are named by their endpoints. Therefore, segment PQ will have endpoints P and Q. The length of the segment is equal to the distance between these points.

To find the distance between P and Q given their coordinates, use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let:

[tex]P(-2, 7)\implies (x_1, y_1),\\Q(1, 3)\implies (x_2, y_2)[/tex]

The distance between these points is equal to:

[tex]d=\sqrt{(1-(-2))^2+(3-7)^2},\\d=\sqrt{3^2+(-4)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=\boxed{5}[/tex]

Answer:

[tex]5[/tex]

Step-by-step explanation:

This problem gives one the following points on a line: ([tex]P(-2,7)[/tex]), and ([tex]Q(1,3)[/tex]). The problem asks one to find the distance between the two points. The formula to find the distance between two points on a coordinate point is the following,

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the given values in and solve for the distance;

[tex]D=\sqrt{(-2)-(1))^2+((7)-(3))^2}[/tex]

Simplify,

[tex]D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\\\\D=\sqrt{(-3)^2+(4)^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D = 5[/tex]

Answer:

(A). F(x) = (x+1)^2

Step-by-step explanation:

If you replace x with the values of the axis, you get all the coordinates of the graph.

If this helps you, please give brainliest!

Answer:

N(2,3)

Step-by-step explanation:

According to the Question,

Thus, M(x,y) = (-1+7)/2 , (3-3)/2 ⇒ M(3,0)

Thus. N(a,b) = (1+3)/2 , (6+0)/2  ⇒ N(2,3)

Answer:

the answer is 101.

Step-by-step explanation:

it is the smallest three-digit number whose value does not change on reversing its digits.

Answer:

X=-1

Step-by-step explanation:

X=-1 is just a vertical line since it only tells where the x point is.

Answer:

$45.07

Step-by-step explanation:

46.91-1.84= 45.07

Answer:

[tex]34^{\circ}[/tex]

Step-by-step explanation:

The incenter of a triangle can be defined as the intersection of three angle bisectors that bisect all angles of the triangle.

By definition, an angle bisector divides an angle into two equal smaller angles.

Therefore:

[tex]\angle KJN=\angle LJN,\\\angle KLM=\angle JLM, \\\angle JKP=\angke LKP[/tex]

What we're given:

The sum of the interior angles of a triangle always add up to be 180 degrees. Since these six angles make up the total sum of the interior angles, we have the following equation:

[tex]\angle KJN+\angle LJN+\angle KLM +\angle KLM +\angle JKP+ \angle LKP=180^{\circ}[/tex]

Substituting given values:

[tex]30+30+26+26+\angle JKP+\angle LKP=180[/tex]

Since [tex]\angle JKP=\angle LKP[/tex],

[tex]30+30+26+26+2(\angle JKP)=180,\\112+2(\angle JKP)=180,\\2(\angle JKP)=180-112,\\2(\angle JKP)=68,\\\angle JKP=\frac{68}{2}=\boxed{34^{\circ}}[/tex]

Given:

Growth rate = 30% decrease

To find:

The growth factor associated with the given growth rate.

Solution:

The general exponential function is:

[tex]y=a(1+r)^x[/tex]

[tex]y=a(b)^x[/tex]

Where, a is the initial value, r is the growth rate in decimal and [tex]b=1+r[/tex] is the growth factor.

It is given that the growth rate is 30% decrease. So,

[tex]r=-30\%[/tex]

[tex]r=-\dfrac{30}{100}[/tex]

[tex]r=-0.3[/tex]

Now,

[tex]b=1+r[/tex]

[tex]b=1+(-0.3)[/tex]

[tex]b=1-0.3[/tex]

[tex]b=0.7[/tex]

Therefore, the growth factor is 0.7.

Answer:

12600 (ZAR)

Step-by-step explanation:

4.2*3000

Answer:

100 degrees

Step-by-step explanation:

This is because AED And CED ARE supplimetary.

80+<CED=180

-80           -80

<Ced=100

Answer:

4pi/15=θ  - i think

Step-by-step explanation:

S = r*θ

r=9

s=12pi/5

12pi/5=9*θ

12pi/45=θ

4pi/15=θ

Answer:

Option B  

(B) 2880   Hope this helps <3

Step-by-step explanation: the total number of people affected by flu during  

the 2nd and 3rd week of January, 1200 + 1680  = 2880

Answer:

1,200

Step-by-step explanation:

40%=.4

(3,000)x(.4)=1,200

1,200 more people were more affected in the third week then the first week

=====================================================

Work Shown:

36 inches = 3 feet

Divide by 12 to go from inches to feet

The block has the dimensions

Use the formula below to calculate the surface area

SA = 2*(LW+LH+WH)

SA = 2*(5*8+5*3+8*3)

SA = 2*(40+15+24)

SA = 2*(79)

SA = 158 square feet

So if you had 158 square feet of wrapping paper, then you can cover this entire 3D box without any gaps or overlaps. The paper can be folded over the box, or you can cut/glue the pieces on, but make sure there isn't any leftover scraps of paper.

Answer:

r = 9.61 cm

Step-by-step explanation:

Volume of a rectangular box = length × width × height

= 21.5 cm × 13.5 cm × 6 cm

= 1,741.5 cm³

Volume of a rectangular box = 1,741.5 cm³

Since,

Volume of a rectangular box = Volume of a circular box

Then,

1,741.5 cm³ = Volume of a circular box

Volume of a circular box = πr²h

1,741.5 cm³ = 3.14 * r² * 6 cm

1,741.5 = 18.84r²

r² = 1,741.5/18.84

r² = 92.436305732484

r = √92.436305732484

r = 9.6143801533163

Approximately,

r = 9.61 cm

9514 1404 393

Answer:

  4.  n = 4

  5.  P(A|B) = 0.75

Step-by-step explanation:

4. The coefficient of x will depend on n. The expansion is ...

  (5 +nx)^2(1 +3/5x)^n = (25 +10nx +n^2·x^2)(1 +3/5nx +...)

So, the x-term of the expansion is ...

  25(3/5nx) +(10nx)(1) = 25nx

The problem statement tells us that is 100x, so we have ...

  25nx = 100x

  n = 100x/(25x) = 4 . . . . . divide by the coefficient of n

The value of n is 4.

__

5. For the conditional probability formula, we need to know P(A∩B).

  P(A∩B) = P(A) +P(B) -P(A∪B)

  P(A∩B) = 0.5 +0.4 -0.6 = 0.3

Then the conditional probability is ...

  P(A|B) = P(A∩B)/P(B) = 0.3/0.4

  P(A|B) = 0.75

Answer:

B 5/6 * -11/-7

Step-by-step explanation:

-5 / -7 = 5/7

-11/-6 = 11/6

Multiply

5/7 * 11/6

Rewriting

5/6 * 11/7

We can make  the 11 and the 7 negative (-11/ -7 = 11/7)

5/6 * -11/-7

Answer:

ok so the equation would look like this

B=1.5A

so b is 1.5 times more then a