3.
If 9x = 27, what is the value of x?

Answer:

[tex]a_n = 4.5 * 3^{n-1}[/tex]

Step-by-step explanation:

Given

[tex]a_4 = 121.5[/tex]

[tex]r = 3[/tex]

Required

[tex]a_n = a_1 * r^{n -1}[/tex]

Substitute 4 for n in [tex]a_n = a_1 * r^{n -1}[/tex]

[tex]a_4 = a_1 * r^{4 -1}[/tex]

[tex]a_4 = a_1 * r^3[/tex]

Substitute 121.5 for [tex]a_4[/tex]

[tex]121.5 = a_1 * 3^3[/tex]

[tex]121.5 = a_1 * 27[/tex]

Solve for a1

[tex]a_1 = \frac{121.5}{27}[/tex]

[tex]a_1 = 4.5[/tex]

So, we have:

[tex]a_n = a_1 * r^{n -1}[/tex]

[tex]a_n = 4.5 * 3^{n-1}[/tex]

Answer:

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Step-by-step explanation:

sample answer on edge ;)

Answer with Step-by-step explanation:

Complete question:

The coordinates  of the vertices of the triangle are (-8,8),(-8,-4), and. Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = units. The area of triangle PQR is square units.

Let

P=(-8,8)

Q=(-8,-4)

QR=b=18 units

Height of triangle, h=Length of PQ

Distance formula

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

Using the formula

Height of triangle, h=[tex]\sqrt{(-8+8)^2+(-4-8)^2}=12units[/tex]

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

Area of triangle PQR=[tex]\frac{1}{2}\times 18\times 12[/tex]

Area of triangle PQR=108 square units

Length of QR=18units

Let the coordinates of R(x,y)

[tex]\sqrt{(x+8)^2+(y+4)^2}=18[/tex]

[tex](x+8)^2+(y+4)^2=324[/tex]

[tex]x^2+64+16x+y^2+8y+16=324[/tex]

[tex]x^2+y^2+16x+8y=324-64-16[/tex]

[tex]x^2+y^2+16x+8y=244[/tex]   ......(1)

Using Pythagoras theorem

[tex]H=\sqrt{P^2+B^2}[/tex]

[tex]H=\sqrt{(18)^2+(12)^2}[/tex]

[tex]H=6\sqrt{13}[/tex]units

[tex](6\sqrt{13})^2=(x+8)^2+(y-8)^2[/tex]

[tex]x^2+64+16x+y^2+64-16y=468[/tex]

[tex]x^2+y^2+16x-16y=468-64-64=340[/tex]

[tex]x^2+y^2+16x-16y=340[/tex] .....(2)

Subtract equation (2) from (1) we get

[tex]24y=-96[/tex]

[tex]y=-96/24=-4[/tex]

Using the value of y in equation (1)

[tex]x^2+16x+16-32=244[/tex]

[tex]x^2+16x=244-16+32[/tex]

[tex]x^2+16x=260[/tex]

[tex]x^2+16x-260=0[/tex]

[tex]x^2+26x-10x-260=0[/tex]

[tex]x(x+26)-10(x+26)=0[/tex]

[tex](x+26)(x-10)=0[/tex]

[tex]x=-26, x=10[/tex]

Hence, the coordinate of R (10,-4) or (-26,-4).

Answer:

D is the correct answer.

Step-by-step explanation:

You can get every y value by multiplying the x value by 3/2. This value never changes and there are no extra limitations.

Answer:

Step-by-step explanation:

Answer:

Cluster sample

Step-by-step explanation:

i did it before

Answer:

Total no. of students =175

percent of students athletes who attend a preseason meeting =84

No. of students who attend the meeting

= 84% of 175

=147

9514 1404 393

Answer:

  the function has no finite limit at the left end of the interval (5, ∞)

Step-by-step explanation:

In order for the function to be piecewise continuous, it must have finite limits at the endpoints of each of the subintervals. Here, the function goes to infinity as x → 5+, so has no finite limit there.

Answer:

y = 0.9143x - 0.8

Step-by-step explanation:

Given the data :

Region Temperature Yield (in bushes per acre)

4 ______ 3

8 ______ 7

10 _____ 8

12 _____ 10

9 ______ 8

6 ______ 4

Using technology, the least square regression equation obtained by fitting the data is :

y = 0.9143x - 0.8

Where ;

y = predicted Bush yield, predicted variable

x = Average temperature, dependent variable

The slope Coefficient = 0.9143

The intercept = - 0.8

Answer:

11

Step-by-step explanation:

I'm assuming that [.] fldenote absolute value even tho the absolute value function is represented by (|.|)

value of [-7] will be positive that us 7.

= 7 + 4

= 11

Answer:

18%

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Simple Interest Rate Formula: A = P(1 + rt)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 12600

A = 23940

t = 5

Step 2: Solve for r

Answer:

69.14% probability that the diameter of a selected bearing is greater than 84 millimeters

Step-by-step explanation:

According to the Question,

Given That, The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 millimeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters.

we have μ=87 , σ=6 & X=84

This is 1 subtracted by the p-value of Z when X = 84.

So, Z = (84-87)/6

Z = -3/6

Z = -0.5 has a p-value of 0.30854.

⇒1 - 0.30854 = 0.69146

Note- (The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X)

Answer:

37.94

Step-by-step explanation:

the 9th percentile is equal to a zscore of -1.34

-1.34=(x-50)/9

x=37.94

hope it helps.

Answer: look below

Step-by-step explanation:

A straight angle is 180

180-50=130

the opposite is also the same angle which is the same

180-50-50=80 and 80 + 2x =180

x=50

the angles are 50, 50, 50, 50, 80, 130 and 130 degrees respectively

Answer:

$138.72

Step-by-step explanation:

(1-0.999578)*$240,000 = $101.28

$240 - $101.28 = $138.72

Answer:

0.015

Step-by-step explanation:

1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015

Solution :

1). The cost of the formula is given as :

   $ 19,350 + $12 x

2). 95% [tex]\text{confidence interval}[/tex] for the prediction is :

    [tex]$21430 - 1.96 \times 220 < \text{Yf} < 21430+1.96 \times 220$[/tex]

     [tex]$20998.8 < \text{Yf} < 21861.2$[/tex]

     [tex]$20999 < \text{Yf} < 21861$[/tex]    (rounding off)

3). r = 0.92

Therefore, [tex]$r^2 = 0.8464$[/tex]

That is 84.64 % of the variability in the moving cost is best explained by the number of moves.

Answer:

Step-by-step explanation:

It is a  28×12 rectangle, minus a 5×6 cutout.

area of 28×12 rectangle = 336 ft²

area of 5×6 cutout = 30 ft²

area of carpet = 336-30 = 330 ft²

Answer: 440 cm^3

Step-by-step explanati

Answer:

5000 km

Step-by-step explanation:

We are given that

3 cm represents on a map of  a town=150 m

Distance between two points=1 km

We have to find the distance between two points on the map.

3 cm represents on a map of  a town=150 m

1 cm represents on a map of  a town=150/3 m

1 km=1000 m

1 m=100 cm

[tex]1km=1000\times 100=100000 cm[/tex]

100000 cm  represents on a map of  a town

=[tex]\frac{150}{3}\times 100000[/tex] m

100000 cm  represents on a map of  a town=5000000 m

100000 cm  represents on a map of  a town

=[tex]\frac{5000000}{1000} km[/tex]

100000 cm  represents on a map of  a town=5000 km

Hence, two points are separated by 5000 km on the map.

Hello,

In a diginacci sequence, all term is the sum off digits of the 2 terms before.

Answer: 2,3

[tex]u_{-2}=1\\u_{-1}=1\\u_0=digit(u_{-2})+digit(u_{-1})=1+1=2\\u_1=1+2=3\\u_2=2+3=5\\u_3=3+5=8\\u_4=5+8=13\\u_5=8+1+3=12\\...\\u_{18}=11\\u_{19}=8\\u_{20}=10\\u_{21}=9\\u_{22}=10\\u_{23}=10\\u_{24}=2**********\\u_{25}=3**********\\2020=24*84+4\\u_{2020}=u_{4}=13\\[/tex]

We must begin with 13 , 10

Proof:

Dim a As Long, b As Long, c As Long, nb As Integer

a = 13

b = 10

nb = 1

Print nb, a

While nb < 2021

   nb = nb + 1

   c = somme&(a, b)

   a = b

   b = c

   '    Print nb, a

Wend

Print nb, a

End

Function somme& (a1 As Long, b1 As Long)

   Dim strA As String, strB As String, n As Long

   strA = LTrim$(Str$(a1))

   strB = LTrim$(Str$(b1))

   n = 0

   For i = 1 To Len(strA)

       n = n + Val(Mid$(strA, i, 1))

   Next i

   For i = 1 To Len(strB)

       n = n + Val(Mid$(strB, i, 1))

   Next i

   somme& = n

End Function

Answer:

The distance between the campsites was 70 miles.

Step-by-step explanation:

Since two groups were moving from one campsite to another, and the first group traveled the distance in 5 hours while the second group finished in 7 hours, to find the distance between the campsites if the first group was going 4mph faster than the second group, the following calculation must be performed:

X + 4 = 5

X = 7

4 x 7 = 28

(4 + 4) x 5 = 40

10 x 7 = 70

(10 + 4) x 5 = 70

Therefore, the distance between the campsites was 70 miles.

Answer:

the terms in the expression are p squared, negative 3,3p, negative 8,p,p cubed

Step-by-step explanation:

hope that helps

[tex]\\\\\\[/tex]

Therefore

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]

Answer:

-8x² -6x + 35

Step-by-step explanation:

A expression is given to us and we need to find out the quadratic equation . For that Multiply the two terms of the quadratic equation. The given expression is ,

Given expression :-

[tex]\rm\implies ( 2x +5)( 7 - 4x ) [/tex]

Multiply the terms :-

[tex]\rm\implies 2x ( 7 - 4x )+5(7-4x) [/tex]

Simplifying the brackets :-

[tex]\rm\implies 14x - 8x^2 + 35 - 20x [/tex]

Rearrange and simplify :-

[tex]\rm\implies -8x^2 -6x + 35 [/tex]

Therefore :-

[tex]\rm\implies\boxed{ \rm Quadratic\ Equation \ = -8x^2 -6x + 35} [/tex]

Answer:

x=70

y=30

z=20

Step-by-step explanation:

x=180-110 (angles on a straight line)

y=180-110-40 (angle sum of triangle)

z= 180-90-70 (angle sum of triangle)

Answer:

x=70°

y=30°

z=20°

Step-by-step explanation:

x=180°-110°(anlges on a straight line)

x=70°

y+110°+40°=180°(sum of angles of triangle)

y+150°=180°

y=180°-150°

y=30°

z+x+90°=180°(sum of angles of triangle)

z+70°+90°=180°

z+160°=180°

z=180°-160°

z=20°

Answer:

1.504

Step-by-step explanation:

0.47×100 = 47

3.2×100 = 320

47×320 = 15040

15040÷10000 = 1.504

Answer:

2x + 2y = 4 and 4x + 4y = 16

Step-by-step explanation:

For two lines to be parallel, they must have the same slope.

To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:

1st option:

3x + 2y = 45 and 8x + 4y = 135

We shall rearrange the above equations to look like y = mx + c

NOTE: m is the slope.

3x + 2y = 45

rearrange

2y = –3x + 45

Divide both side by 2

y = –3x/2 + 45/2

Slope (m) = –3/2

8x + 4y = 135

Rearrange

4y = –8x + 135

Divide both side by 4

y = –8x/4 + 135/4

Slope (m) = –8/4 = –2

The two equation has different slopes. Thus, they are not parallel.

2nd option:

x + y = 25 and 2x + y = 15

x + y = 25

Rearrange

y = –x + 25

Slope (m) = –1

2x + y = 15

Rearrange

y = –2x + 15

Slope (m) = –2

The two equations has different slopes. Thus, they are not parallel.

3rd option:

2x + 2y = 50 and 4x + 2y = 90

2x + 2y = 50

Rearrange

2y = –2x + 50

Divide both side by 2

y = –2x/2 + 50/2

Slope (m) = –2/2 = –1

4x + 2y = 90

Rearrange

2y = –4x + 90

Divide both side by 2

y = –4x/2 + 90/2

Slope (m) = –4/2 = –2

The two equations has different slopes. Thus, they are not parallel.

4th option:

2x + 2y = 4 and 4x + 4y = 16

2x + 2y = 4

Rearrange

2y = –2x + 4

Divide both side by 2

y = –2x/2 + 4/2

Slope (m) = –2/2 = –1

4x + 4y = 16

Rearrange

4y = –4x + 16

Divide both side by 4

y = –4x/4 + 16/4

Slope (m) = –4/4 = –1

The two equations have the same slopes. Thus, they are parallel.

Answer: …

Step-by-step explanation: you need an image

Answer:

what expression?

Step-by-step explanation:

Answer:

It should be 8.6 yards, as 238.64÷3.14 = 74.

√74 = 8.60, or 8.6 :)