Please select the best answer.

Answer:

r = ±1/√7

a₁ = 7 − √7

Step-by-step explanation:

The first term is a₁ and the second term is a₁ r.

a₁ + a₁ r = 48/7

The sum of an infinite geometric series is S = a₁ / (1 − r)

a₁ / (1 − r) = 7

Start by solving for a₁ in either equation.

a₁ = 7 (1 − r)

Substitute into the other equation:

7 (1 − r) + 7 (1 − r) r = 48/7

1 − r + (1 − r) r = 48/49

1 − r + r − r² = 48/49

1 − r² = 48/49

r² = 1/49

r = ±1/√7

When r is positive, the first term is:

a₁ = 7 (1 − r)

a₁ = 7 (1 − 1/√7)

a₁ = 7 − 7/√7

a₁ = 7 − √7

The value of the common ratio r is 1/√7 and the first term is 7 − √7 in the geometry progression.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

The first term is a

So the second term is a r.

a + ar = 48/7

The sum of an infinite geometric series is :

S = a / (1 − r)

a / (1 − r) = 7

Solve for a,

a = 7 (1 − r)

Substitute value into the equation:

7 (1 − r) + 7 (1 − r) r = 48/7

1 − r + (1 − r) r = 48/49

1 − r + r − r² = 48/49

1 − r² = 48/49

r² = 1/49

r = ±1/√7

When r is positive, the first term will be:

a = 7 (1 − r)

a = 7 (1 − 1/√7)

a = 7 − 7/√7

a = 7 − √7

Thus, the value of the common ratio r is 1/√7 and the first term is 7 − √7 in the geometry progression.

Learn more about geometric series here:

brainly.com/question/21087466

#SPJ2

Answer:

first choice

Step-by-step explanation:

The volume of a rectangular prism is L*H*B.

So the volume of the rectangular prism pictured here is 24*10*8

The volume of a triangle prism is 1/2 *H*L*B.

So the volume of the triangle prism pictured here is 1/2 *6*24*8

The volume of the whole figure is the sum of the volume of the rectangular prism and volume of the triangular prism which is in this case:

24*10*8 + 1/2 *6*24*8.

Answer is the first choice.

(It wouldn't be third because 10 has nothing to with the triangular prism part)

Answer:

parallelogram

Step-by-step explanation:

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

The best name for a trapezoid with congruent legs and congruent bases is Option (B) parallelogram .

A quadrilateral with at least one pair of parallel sides is called, a trapezoid. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles trapezoid).

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Therefore, a trapezoid having parallel sides with congruent legs and bases have the opposite adjacent sides of equal lengths. The shape thus will form a parallelogram satisfying each and every property.

Thus, the best name for a trapezoid with congruent legs and congruent bases is Option (B) parallelogram .

To learn more about trapezoid, refer -

https://brainly.com/question/1463152

#SPJ2

No Solution

Brainliest Please :)

Answer:

[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]

The number pi occurs when calculating the surface area or volume of the rotational solids.

Cylinder:

[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]

Cone:

[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]

Sphere:

[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]

The number pi occurs when calculating the area and the circumference of a circle.

[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]

It is also used to convert angle measure in degrees to radians.

[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]

The meaning of pi is when you calculate the volume for cylinders, cone, and spheres. A cone volume shows [tex]\frac{1}{3}[/tex][tex]\pi[/tex][tex]r^2h[/tex]. You see, it shows pi. Also, pi means 3.14 in approximation, but if it was not in approximation, it would have been 3.141592654. Pi is a irrational number, since it goes on forever. For the circumference to the diameter (of a circle) formula would be [tex]\pi[/tex] = C/D. And there more about the definition of pi, it is also the sixteenth letter of the Greek alphabet, considering to be the letter P.

Hope this helped!

Nate

Answer:

[tex]\frac{25}{2}[/tex] or 12.5

Step-by-step explanation:

So if 25 - x items are sold, and they each cost x, we can write an equation for the revenue to be

y = (25 - x)x

The vertex of this equation will represent the maximum revenue.  So we need to write this equation in vertex form so we can find the vertex.

Vertex from is

y = a(x - h)^2+ k,

where (h,k) represent the vertex.

the vertex form of this equation would be

[tex]y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}[/tex]

And the vertex would be

[tex](\frac{25}{2} ,\frac{625}{4})[/tex]

This means the maximum revenue will occur when x = 25/2

The maximum revenue is at a price of $11.5 each for a certain lamp

The revenue is the total amount of money that can be made from selling a number of goods.

Revenue = price * total number of items

Since the price per item is x dollars and the total number of items is 25 - x, hence:

Revenue (R) = x * (25 - x) = 25x - x²

R = 25x - x²

The maximum revenue is at dR/dx = 0, hence:

dR/dx = 25 - 2x

25 - 2x = 0

2x = 25

x = $11.5

Hence, The maximum revenue is at a price of $11.5 each for a certain lamp.

Find out more at: https://brainly.com/question/16872607

Answer:

c=-5

d=1

Step-by-step explanation:

[tex](cy^2)(4y^d)=-20y^3[/tex]

I'm going to reorder the left-hand side.  Multiplication is commutative.

[tex](4c)(y^2y^d)=-20y^3[/tex]

Since the bases are the same in [tex]y^2y^d[/tex] and the operation is multiplication, I'm going to add the exponents giving me:

[tex]4cy^{2+d}=-20y^3[/tex]

So this implies we have two equations to solve:

[tex]4c=-20[/tex] and [tex]2+d=3[/tex]

So the first equation can be solved by dividing both sides by 4 giving you [tex]c=-5[/tex].

The second equation can be solved by subtracting 2 on both sides giving you [tex]d=1[/tex].

Answer:

a. Arithmetic

b. [tex]a_{n} = a_{n-1} + 15[/tex]

c. [tex]a_{n} = 15n + 125[/tex]

Step-by-step explanation:

A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.

In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️

The recursive formula will be the following: [tex]a_{n} = a_{n-1} + 15[/tex]

The explicit formula is the following: [tex]a_{n} = 15n + 125[/tex]

Answer:

720

Step-by-step explanation:

The mean of a set of credit scores is u=690 and o=14.

mean = 690  and standard deviation SD = 14

We use z- score formula

z= 3.3 given

Plug in the values and find out x

Multiply 14 on both sides

46.2 = x- 690

Now add 690 on both sides

x= 736.2

Credit score is 720 that comes under 736.2

Answer:

Step-by-step explanation:

[tex]x+6y=18\\\\x-intercept\ for\ y=0:\\\\x+6(0)=18\\x+0=18\\x=18\\\\y-intercept\ for\ x=0:\\\\0+6y=18\\6y=18\qquad\text{divide both sides by 6}\\y=3[/tex]

Step-by-step explanation:

An exponential function has the form:

y = a · b^x

Are you sure you copied the problem correctly?  Perhaps instead of minus, you meant multiplication:

f(x) = 620 · 7.8^x

If so, then a = 620 and b = 7.8.

Answer:

sqrt(545)

Step-by-step explanation:

The distance between 2 points can be found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (6--10)^2 + (8--9)^2)

      sqrt( (6+10)^2 + (8+9)^2)

        sqrt( (16)^2 + (17)^2)

      sqrt( 256+289)

    sqrt(545)

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[6-(-10)]^2+[8-(-9)]^2}\implies d=\sqrt{(6+10)^2+(8+9)^2} \\\\\\ d=\sqrt{256+289}\implies d=\sqrt{545}\implies d\approx 23.35[/tex]

Answer: -2x+10

Step-by-step explanation:

you just multiply x and -5 by -2

Answer: what equations did they provide

Step-by-step explanation:

Carla skateboarded 28/15 miles farther than Alex.

To find out how much farther Carla skateboarded than Alex, we first calculate the total distance each student skateboarded:

Next, we find the difference:

Carla - Alex = 21/5 - 7/3 = 63/15 - 35/15 = 28/15 miles.

Therefore, Carla skateboarded 28/15 miles farther than Alex.

Answer:

(- 5, 3 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Hence

C(5, 3 ) → C'(- 5, 3 )

If ABC is reflected across the y-axis then the coordinates of c is (-5,3).

The coordinates refers to a point on the graph which are used to draw a line, a shape on the graph by plotting these points.

The coordinates of ABC presently are (1,3),(3,6),(5,3). If we just reflect ABC cross y-axis then on the second quadrant only the value of x changes, the value of y remains same. So we have to just put a negative sign in front of the value of x and it becomes -5 with the value of y=3.

Hence the coordinates of C is (-5,3).

Learn more about coordinates at https://brainly.com/question/17206319

#SPJ2

Let d = discriminant

d = b^2 - 4ac

Let a = 2, b = 4 and c = -9

We now plug and chug.

d = (4)^2 - 4(2)(-9)

d = 16 - 8(-9)

d = 16 + 72

d = 88

Answer:

А. 88

Step-by-step explanation:

2х^2 + 4x - 9

This is in the form

ax^2 +bx +c

where a=2 b=4 and c=-9

The discriminant is

b^2 -4ac

Substituting into the equation

4^2 -4(2) (-9)

16 - (-72)

16+72

88

[tex]-a^2b\left(8+a^4b^3\right)[/tex]

When we factor out a expression, we seek the terms that are common and then take it away. This is the opposite of applying distributive. In this exercise, we need to factor the following expression:

[tex]-8a^2b-a^6b^4[/tex], so:

STEP 1: Applying exponent rules:

We know that:

[tex]a^{m+n}=a^mb^n[/tex]

So:

[tex]a^6b^4=a^2a^4bb^3[/tex]

Then, our expression remains:

[tex]-8a^2b-a^2a^4bb^3[/tex]

STEP 2: Taking common factor [tex]-a^2b[/tex], we finally get:

[tex]\boxed{-a^2b\left(8+a^4b^3\right)}[/tex]

Answer:

189ish

Step-by-step explanation:

use a calculator

and I think that this is right...

Answer:

(4,5)

Step-by-step explanation:

The vertex is written in vertex form.

y = a(x - b)^2 + c

Vertex: (b,c)  Notice the sign change on b.

So for your equation, you get (4,5) No sign change on the 5.

Answer: (4, 5)

Proof of validity is shown below.

Answer:

2 2/3 or

2.666667 inches rainfall or

8/3 inches of rainfall.

Step-by-step explanation:

Set up a proportion. Since you are going to be looking for inches of rainfall, it should go in the numerator.

2 in rainfall/9 hours = x / 12 inches.               Multiply both sides by 12

2*12 /9 = x

8/3 inches = x

2 2/3 inches should fall in 12 hours.

Answer:

2.67 in

Step-by-step explanation:

∵ In 9 hours amount of rainfall = 2 in

∴ In 1 hours amount of rainfall = 2/9 in

∴ in 12 hours amount of rainfall = (2/9) × 12

                                                  =  [tex]\frac{24}{9}[/tex] =  [tex]\frac{8}{3}[/tex]

                                                 ≈  [tex]2\frac{2}{3}[/tex] in or 2.67 in.

In 12 hours 2.67 in. rain fell.

Answer:

Step-by-step explanation:

Given that Jacob surveyed members of three different gyms and recorded the number of hours they exercised last week.

Table is as follows:

Gym     Mean       Std dev

  A            7            2.9

  B            8            4.2

  C            6            3.2

We know that std deviation is a measure of variation of the data set from the mean.  

Hence if std deviation is the least the data would be more consistent.

Here A has the least sd

Hence The members of gym show the most consistency in the number of hours they exercised last week, because the

of this data set is the one which has lowest std deviation

Final answer:

Gym A's members show the most consistency in their exercise habits because it has the lowest standard deviation (2.9) compared to Gyms B and C.

Explanation:

The members of Gym A show the most consistency in the number of hours they exercised last week, because standard deviation of this data set is the lowest. To assess consistency among data sets, we look at the standard deviation, which measures the spread of data around the mean. A lower standard deviation indicates that the data points tend to be closer to the mean. Looking at the given data for the three gyms:

Gym A has the lowest standard deviation of 2.9, which suggests the members' weekly exercise hours vary less from the mean compared to Gyms B and C, indicating more consistency.

Answer:

(-9,9) is the correct answer

Answer:

A

Step-by-step explanation:

Since the dilatation is centred at the origin, then each of the coordinates of B are multiplied by the scale factor of 3

B(- 3, 3 ) → B'( 3 × - 3, 3 × 3 ) → B'(- 9, 9 ) → A

Answer:

D. 2

Step-by-step explanation:

Since midpoints will be involved, use multiples of 2 to name the coordinates for M and N.

Let

Then the midpoint P coordinates are

[tex]P\left(\dfrac{2a+0}{2},\dfrac{0+2b}{2}\right)\Rightarrow P(a,b)[/tex]

Use distance formula to find OP and MN:

[tex]OP=\sqrt{(a-0)^2+(b-0)^2}=\sqrt{a^2+b^2}\\ \\MN=\sqrt{(2a-0)^2+(2b-0)^2}=\sqrt{4a^2+4b^2}=2\sqrt{a^2+b^2}[/tex]

So,

MN=2OP

or

OP=1/2 MN

Answer:

The correct option is D.

Step-by-step explanation:

Given: ΔMNO is a right angled triangle with right angle ∠MON, P is midpoint of MN.

To prove: [tex]OP=\frac{1}{2}MN[/tex]

Since midpoints will be involved, use multiples of _2_ to name the coordinates for M and N.

Let the coordinates for M and N are (0,2m) and (2n,0) receptively.

Midpoint formula:

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

The coordinates of P are

[tex]Midpoint=(\frac{2n+0}{2},\frac{2m+0}{2})[/tex]

[tex]Midpoint=(n,m)[/tex]

The coordinates of P are (n,m).

Distance formula:

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

Using distance formula, the distance between O(0,0) and P(n,m) is

[tex]OP=\sqrt{(n-0)^2+(m-0)^2}=\sqrt{n^2+m^2}[/tex]

Using distance formula, the distance between M(0,2m) and N(2n,0) is

[tex]MN=\sqrt{(2n-0)^2+(0-2m)^2}[/tex]

[tex]MN=\sqrt{4n^2+4m^2}[/tex]

On further simplification we get

[tex]MN=\sqrt{4(n^2+m^2)}[/tex]

[tex]MN=2\sqrt{(n^2+m^2)}[/tex]

[tex]MN=2(OP)[/tex]

Divide both sides by 2.

[tex]\frac{1}{2}MN=OP[/tex]

Interchange the sides.

[tex]OP=\frac{1}{2}MN[/tex]

Hence proved.

Therefore, the correct option is D.

Answer:

Option D, 34.5 cm

Step-by-step explanation:

Length of arc is represented by (rθ)

Where r = radius and θ = angle at the center formed by arc in radians.

length of arc = [tex]33\times (\frac{\Theta}{180})\pi[/tex]

                     = [tex]33\times (\frac{60\pi}{180})[/tex]

                      = (33 × π/3)

                      = (11π)

                      = 11 × 3.14

                      = 34.5 cm

Option D, 34.5 cm is the answer.

Answer:

A = 72 ft^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

A = 1/2 (9)*16

A = 72 ft^2

A = 72ft².

We have to use the area of a triangle equation A = (b*h)/2.

A triangle with a base b = 9ft and a height h = 16ft:

A = (9ft*16ft)/2 = 144ft²/2

A = 72ft²

Answer:

James=x=15 points

Matt=4x=4×15=60 points

Emily=4x+20= (4×15)+20= 60+20=80points

Step-by-step explanation:

You should breakdown the question by writing an expression to represent the points for each person

Lets assume James had x points

So Matt had 4 times as many points as James= 4x points

Emily had 20 points more than Matt= 4x+20 points

Total number of points all together was =155

Write an expression for the total number of points all together

[tex]x+4x+4x+20=155[/tex]

Solve for x in the equation

[tex]x+4x+4x+20=155\\\\9x+20=155\\\\\\9x=155-20\\\\\\9x=135\\\\\\x=15[/tex]

Substitute values in expressions

James=x=15 points

Matt=4x=4×15=60 points

Emily=4x+20= (4×15)+20= 60+20=80points

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped.

Let y be the depth of a toy and x is time, in seconds.

In the given graph a solid horizontal line passes through the point (0,-1) and shaded region is above the line. So, the inequality of red line is

[tex]y\geq -1[/tex]

The depth of a toy can be less than -1. It means the pool is 1 meter deep.

The blue line is a dashed line which passes through (0,0) and (2,-1).

So the slope of line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{2-0}=-\frac{1}{2}[/tex]

The equation of blue line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

[tex]y=-\frac{1}{2}x+0[/tex]

[tex]y=-\frac{1}{2}x[/tex]

The shaded region is below the line so the required inequality is

[tex]y< -\frac{1}{2}x[/tex]

it means the toy sinks at a rate of less than 1/2 meter per second.

Therefore the correct option is 1.

Answer:The Answer is A

Step-by-step explanation: I took the test on edge

Answer:

[tex]4,320\pi\ ft^{3}[/tex]  or  [tex]13,564.8\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder (well) is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]h=30\ ft[/tex]

[tex]r=24/2=12\ ft[/tex]

substitute

[tex]V=\pi (12)^{2}(30)[/tex]

[tex]V=4,320\pi\ ft^{3}[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=4,320(3.14)=13,564.8\ ft^{3}[/tex]