The formula for any arithmetic sequence is an = a1 + d(n - 1), where an represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence -15, -11, -7, ...? an = -15 + (-4)(n - 1) an = -15 + (n - 1) an = 4 + (-15)(n - 1) an = -15 + 4(n - 1)

Answers

Answer 1

Answer:

4th choice

Step-by-step explanation:

First we would just solve the equation since that is the easiest way. So 15 would be our a1 or first term and each time the number is being added by  4 so we would get an = -15 + 4(n - 1) for our final answer or the 4th choice

Answer 2

Answer:

option 4

Step-by-step explanation:

-15, -11 , -7 ,......

First term = [tex]a_{1}[/tex] = -15

Common difference = d = 2nd term -  1st term

                                 = -11 - [-15]

                                 = -11 + 15 = 4

Plug in the values of [tex]a_{1}[/tex] & d in the formula

[tex]a_{n} = a_{1} + d (n-1)\\\\a_{n} = -15 + 4*(n-1)[/tex]


Related Questions

Complete the point-slope equation of the line through ( − 1 , − 10 )and (5 , 2) y-2 =?

Answers

Answer:

y - 2 = 3(x - 5).

Step-by-step explanation:

We need to find the slope of the line.

[2 - (-10)] / [5 - (-1)] = (2 + 10) / (5 + 1) = 12 / 6 = 2 / 1 = 2

So, y1 = 2, x1 = 5, and m = 2.

y - 2 = 3(x - 5)

Hope this helps!

The formula for point slope is written as y - y1 = m(x -x1)

You are given y - 2 = ?

Since the 2 form the point (5,2) is the y1 value, then the 5 is equal to x1

The formula becomes: y-2 = m(x-5)

Now solve for the slope, which is the change in y over the change in x:

Slope = -10 - 2 / -1 - 5 = -12/-4 = 3

Now replace m to get y-2 = 3(x-5)

b Given: m AB =m BC , m∠x=60°, m∠y=15° Find: m AC

Answers

Answer:

105

Step-by-step explanation:

because all the angles added up have to = 180

60+15=75

75-180=105

Tyler needs to get the windows in his new home cleaned. The cleaning company needs to know the total number of window panes before it can tell him how much the job will cost. There are 12 windows, each with four window panes across, and four window panes down. Tyler can find the total number of window panes by multiplying the number of windows by the number of panes in each window. The total number of window panes is an expression with a whole-number exponent. Part A Write an expression with exponents to find the total number of panes in 12 windows.

Answers

Answer:

I'm not completely sure but I believe it's (4^2)*12

Step-by-step explanation:

To find the amount of window panes there are, we have to find how much window pains are in each window. So we have a 4 by 4 so that's 16. Since 4 and 4 are the same numbers, we can raise 4 to the power of two to get 16. Then we have to do 16*12 to get the total amount of panes since Panes Per Window multiplied by Number Of Windows equals Total Number Of Panes

Answer:

(4^2)*12

Step-by-step explanation:

PLEASE HELP ME FAST, PLEASE

Answers

Answer:

The temperature order are;

(b) 96.62 K = (d) 96.62 K > (a) 48.31 K = (c) 48.31 K = (e) 48.31 K =  (f) 48.31 K

Arrangement in order from highest to lowest and alphabetically gives;

(b) ↔ (d) → (a)↔ (c)↔ (e)↔ (f)

Step-by-step explanation:

From the universal gas equation

P×V = N×k×T

Where:

P = Pressure

V = Volume

N = Number of molecules

k = Boltzmann constant = 1.38 × 10⁻²³ J/K

T = temperature

Therefore;

[tex]T =\dfrac{P \times V}{k \times N}[/tex]

Which gives;

(a) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have

100000*0.004/(6*10^(23)*1.38*10^(-23)) = 48.31 K

(b) When P = 200 kPa = 200,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have

200000*0.004/(6*10^(23)*1.38*10^(-23)) = 96.62 K

(c) When P = 50 kPa = 50,000 Pa, V = 8 L = 0.008 m³, N = 6 × 10²³, we have

50000*0.008/(6*10^(23)*1.38*10^(-23)) = 48.31 K

(d) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have

100000*0.004/(3*10^(23)*1.38*10^(-23)) = 96.62 K

(e) When P = 100 kPa = 100,000 Pa, V = 2 L = 0.002 m³, N = 3 × 10²³, we have

100000*0.002/(3*10^(23)*1.38*10^(-23)) = 48.31 K

(f) When P = 50 kPa = 50,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have

50000*0.004/(3*10^(23)*1.38*10^(-23)) = 48.31 K

15 POINTS!!!!!!!
How is a linear function affected by a horizontal shift?

Answers

Answer:

horizontal shift can affect the linear function, because it is impossible to distinguish which transformation was applied by looking at the resulting graph.

Step-by-step explanation:

a horizontal shift is a movement left to right along the x-axis, and in equation of a function it's change in the value of x before it's multiplied by the slope.

Answer:

I agree with Lambina and added this answer so she could get brainliest

Step-by-step explanation:

Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of r and u, 13, 14, 15, 16. How many angles are alternate exterior angles with angle 5?

Answers

Answer:

Step-by-step explanation:

The alternate exterior angles with angle 11 are angle 13 and angle 5.Step-by-step explanation: Two angles are called Alternate exterior angles if1. They are on the exterior side of parallel lines and2.  Lie on the opposite sides of the transversal line.It is given that r\\ s andt\\ u. From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.Therefore  alternate exterior angles with angle 11 are angle 13 and angle 5.

Answer:

<5=<16

Step-by-step explanation:

Define - An angle is said to be another angles exterior angle if

           1) It on either side of transversal

          2) Both the angles r exterior angle

Here <16 is the one and only exterior angle of <5 as it satisfies the rules for the same.

Therefore....

<16 is the exterior angle of <5

there is only 1 exterior angle

Sry dude....but the ans of above guy is wrong

Hope this helps.....

PLS PLS PLS mark my ans as brainliest :)

Amanda is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 1 flavor, and 6 toppings to choose from. How many different ice cream desserts could she order?

Answers

Answer: 12

Step-by-step explanation:

Order requirement:

Size ; flavor and topping

Available variety:

Size = 2

Flavor = 1

Toppings = 6

Number of different ice-cream desserts which can be ordered :

Since one of each of size, topping and flavor must be selected :

(Number of available flavors * number of Toppings available * number of sizes available)

1 * 6 different Toppings = 6 varieties

6 varieties * 2 different sizes = 12 varieties

Therefore, there are 12 different variety of ice-cream dessert she can order.

QUESTION 8
Simplify the expression
(5-4 (25)2
expressing the answer as a power of 5

Answers

The answer is -195
EXPLANATION:
5-(4)(25)(2)
=5-(100)(2)
=5-200
=-195
The answer is negative 195 ( -195 )

please help i'm doing summer school and i have 2 days

Answers

Answer:

a. y < -4x + 4

Step-by-step explanation:

(0, 4) (2, -4)

find the equation of the line.

1. slope: (y² - y¹) / (x² - x¹)

a. (-4 - 4) / (2 - 0) = -8 / 2 = -4

2. y-intercept

a. from the graph, we see it is 4

3. plug it in

a. y = -4x + 4

since this is an equality, we use < > ≤ or ≥

the shaded region is below a dashed line, therefore we use <

y < -4x + 4

Can you pleease help ill mark as brainliest

Answers

Answer:

Step-by-step explanation:

to reflect an object in given line , measure the distance perpendicular to the line from each point and to the other side by line


Now let reflect

Here a picture

Hope this help you

im badd i kinda understand but not really understanding it

Answers

Answer:

40

Step-by-step explanation:

if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails

Answer:

If they are proportional we can expect 40

lol iready

Please help me find x!!!!

Answers

Answer:

x = 56

Step-by-step explanation:

Well if both lines are straight that means that 118 is on both sides,

180 - 118 = 62

So angle E and F are both 62.

So we do 62 *2 = 124.

180 - 124 = 56

x = 56

Thus,

angle x is 56.

Hope this helps :)

X= 56
A line is 180 so do 180- 118 to find the angle same for the other side and from there you should be able to figure it out easy

HELPPPP HURRYYYYYYY A bag contains 150 marbles which are red, green, and blue. Suppose a student randomly selects a marble without looking, records the color, and then places the marble back in the bag. The student has recorded 9 red marbles, 15 green marbles, and 6 blue marbles. Predict how many green marbles are in the bag.

Answers

Answer:

75 green marbles

Step-by-step explanation:

From the information given in the question, we can create a ratio representing all the marbles in the bag.

9 red:15 green:6 blue

We need to find the total number of times the student drew a marble by finding the sum

9+15+6= 30

The sample size is 30

150 is 5x the amount of 30, that means we need to multiply the given information by 5 to predict the number of green marbles

9x5=45

15x5=75

6x5=30

Now we have 45 red: 75 green: 30 blue

Based on the given information, we can predict that the bag contains 75 green marbles

The following data points represent the number of points scored by each player on the Wildcats basketball team last game. ____________________________ 4, 5, 6, 8, 9, 10, 11, 13 (Find the interquartile range (IQR) of the data set.)

Answers

Answer:

The answer is 5,  TRUST ME

Step-by-step explanation:

I tried the other answer but i got it WRONG.

The interquartile range (IQR) of the data represents the number of points scored by each player is 7.

What is the interquartile range (IQR)?

The interquartile range is a measure of variability which can be calculated by dividing data into quartiles.

The formula of IQR = [tex]\rm Q_{3} -Q_{1}[/tex]

The given data is as follows

4, 5, 6, 8, 9, 10, 11, 13

To find the first quartile

[tex]\rm Q_{1}[/tex] = (n + 1)/4 term

   = (8+1)/4

    = 9/4

To find the Third quartile

[tex]\rm Q_{3}[/tex] = 3(n + 1)/4 term

    = 3 (9)/4

    = 27/4

The formula of IQR = [tex]\rm Q_{3} -Q_{1}[/tex]

                                = 27/4 - 9/4

                                = 28/4

                                = 7

The interquartile range (IQR) of the data represents the number of points scored by each player on the Wildcats basketball team last game is 7.

Learn more about the interquartile range:

https://brainly.com/question/4135956

QUESTION 10
What is the slope of a line that is parallel to the line
2y = 3x - 5

Answers

Answer:

Slope: 1.5

Step-by-step explanation:

We first have to find what y is equal to. That means we take 3x - 5 and divide it by 2. We get 1.5x - 2.5. Since the lines are parallel and they have the same slope and different y - intercepts, we know that the slope will be equal.

Answer:

m = 3/2

Step-by-step explanation:

2y = 3x - 5

First find the slope of this line

Divide by 2

2y/2 = 3x/2 - 5/2

y = 3/2 x - 5/2

This is in slope intercept form  y= mx+b where m is the slope and b is the y intercept

The slope is 3/2

Parallel lines have the same slope

m = 3/2

write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step

Answers

Answer:

w = 40 miles per hour

r = 300 miles per hour

Step-by-step explanation:

We add w with the wind and subtract w against the wind

r+w = 340 miles per hour

r - w = 260 miles per hour

Add the two equations together to eliminate w

r+w = 340 miles per hour

r - w = 260 miles per hour

----------------------------------------

2r = 600

Divide by 2

r = 300 miles per hour without the wind

Now find w

r+w = 340

300 + w = 340

Subtract 300

w = 340-300

w = 40 miles per hour

The figure shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4. What set of transformations is performed on triangle ABC to form triangle A'B'C'? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin

Answers

Answer:

A 180 degree counterclockwise rotation about the origin followed by a translation 5 units to the right

Step-by-step explanation:

Answer:

translation down 5, rotation 180°

Step-by-step explanation:

A woman bought some large frames for ​$10 each and some small frames for ​$5 each at a closeout sale. If she bought 27 frames for ​$​180, find how many of each type she bought. She bought ____ large frames.

Answers

Answer:

Step-by-step explanation:

This is a guessing game. You assume how much there is, and then you check. I was led to the conclusion that there are 9 large frames and 18 small frames.

Answer:

She bought 9 large frames

Step-by-step explanation:

Create a system of two equations and two unknowns (the number of small frames that we call S, and the number of large frames that we call L).

The two equations become:

(a)    L + S = 27    (since she bought 27 frames total)

(b)   10 L + 5 S = 180

Now, let's solve for S in the first equation:  S = 27 - L

ad use it to replace for S in equation (b):

10 L + 5 (27 - L) = 180

10 L  - 5 L + 135 = 180

5 L = 180 - 135

5 L = 45

L = 9

Therefore she bought 9 large frames

A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box? Enter the correct answer in the box by replacing the values of m and n.

Answers

Answer:

  26.8 in

Step-by-step explanation:

The red dashed line is the hypotenuse of the right triangle with one leg equal to 24 inches and the other leg equal to 12 inches. Its length is given by the Pythagorean theorem:

  space diagonal = √(24^2 +12^2) = √(720) = 12√5

  space diagonal ≈ 26.83 . . . inches

The length of the longest item that will fit in the box is about 26.83 inches.

An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?

Answers

Answer:

48.28 cm

Step-by-step explanation:

The shortest distance would be to travel diagonally to the top-right corner, and then travel along the edge to B,

Diagonal = 20^2+20^2=c^2

400+400=c^2

800=c^2

square root of 800=c

c=28.28

Edge = 20

Total: 20+20.28=48.28 cm

Which of the following can prove that figure ABCD is a square?

Answers

Answer:

A

Step-by-step explanation:

all sides of square is 90degrees

Since AC and BD is the same, when you join the lines together, it will definitely be a square

Sid is packing crushed ice into a cone-shaped cup. The cone has a height of 5 in. Its base has a diameter of 4 in. What is the volume of the cone? StartFraction 20 Over 3 EndFraction pi inches cubed 20 pi inches cubed StartFraction 80 Over 3 EndFraction pi inches cubed 80 pi inches cubed

Answers

Answer:

20 over 3 pi inches cubed

Step-by-step explanation:

The formula for the volume of a cone is 1/3πr² · h

1. Set up the equation

1/3π2² · 5

2. Solve

1/3π(4)(5)

20/3π in.³

Answer:

20 over 3 pi inches cubed

Step-by-step explanation:

height - 5 in

diameter - 4 in

radius - 2 in (half of diameter)

V = [tex]\pi r^{2} \frac{h}{3}[/tex]

V = [tex]\pi (2)^{2} \frac{5}{3}[/tex]

V = [tex]\pi (4)\frac{5}{3}[/tex]

V = [tex]\pi (\frac{20}{3} )[/tex]

V = [tex]\frac{20}{3} \pi[/tex] in³

The volume of the cone is 20 over 3 pi inches cubed.

Hope that helps.

The number of members of an online community increases each month. The
function M(t) = N(1 + ) represents the number of members at month t, where
Nis the initial number of members and ris the rate of increase. Select the
correct statement.
O A. Nincreases each month.
B. The initial value is (1 + r).
C. The function is linear.
D. The value of Mis a product of Nand a factor that does not depend
on N.

Answers

Answer:

Option D.

Step-by-step explanation:

Note: The given function is incomplete. Consider the given function as [tex]M(t)=N(1+r)^t[/tex].

The number of members at month t is  

[tex]M(t)=N(1+r)^t[/tex]

where,

N is the initial number of members.

r is the rate of increase.

t is number of months

Here, N is constant. So, option A is incorrect.

N is initial value and (1+r) is growth factor. So, option B is incorrect.

The given function is an exponential function.

The value of M is a product of N and a factor that does not depend on N.

Therefore, the correct option is D.

Max and Sven bike away from home in the same direction starting at noon. They bike at constant speeds. Max bikes at xmph and he is ymph faster than Sven. By 4pm, how far ahead of Sven would Max be? Translate into an algebraic expression and simplify if possible.

Answers

Answer:

4y miles

Step-by-step explanation:

Max : x miles per hour

Sven: y miles per hour  slower

        x-y is the speed for Sven

We know that distance = speed * time

Distance for Max = x*t

Distance for Sven = (x-y) * t = xt - yt

The difference in distance is Max's distance minus Sven's distance

xt - ( xt-yt)

xt - xt +yt

yt

Max is yt miles ahead where t is the time

The time is noon to 4  which is 4 hours

Changing t to 4

The distance ahead is 4y miles

Can someone help me please

Answers

Answer:

No more than ≥

Not under ≤

No less than ≤

maximum ≥

Greater than or equal to ≥

Less than or equal to ≤

Does not exceed ≥

At most ≥

At least ≤

Minimum ≤

15 POINTS!!!!!!!! How is a linear function affected when a constant is multiplied by x?

Answers

Answer:

The Y-intercept changes .

Step-by-step explanation:

Answer:

The y-intercept changes

Step-by-step explanation:

Please answer both questions

Answers

Answer:

36 and 24

Step-by-step explanation:

Answer:

Part a : 20 units², Part d : 12 units²

Step-by-step explanation:

We are given that the side lengths of each square is 6 units. In this case we can calculate the area of the triangles, subtracting from the area of the outer square, such that we calculate the remaining, area of the shaded region / inscribed square.

Area of Outer Square ( Same in all Cases ) = 6 [tex]*[/tex] 6 = 36 units²,

Area of Common Triangles ( 4 Triangles ) = 1 / 2 [tex]*[/tex] Base [tex]*[/tex] Height = 1 / 2 [tex]*[/tex] 2 [tex]*[/tex] ( 6 - 2 ) = 1 / 2 [tex]*[/tex] 2 [tex]*[/tex] 4 = 4,

4 [tex]*[/tex] 4 = 16 units²

Area of inscribed Square = 36 units² - 16 units² = 20 units²

For this second case the inscribed shape is not a square, but it can be calculated through a similar approach,

Area of Outer Square ( Same in all Cases ) = 6 [tex]*[/tex] 6 = 36 units²,

Area of Common Triangles ( 2 Triangles ) = 1 / 2 [tex]*[/tex] Base [tex]*[/tex] Height = 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 6 = 2 [tex]*[/tex] 6 = 12,

12 [tex]*[/tex] 2 = 24 units²

Area of inscribed shape = 36 units² - 24 units² = 12 units²

Does coordinate c or coordinate d represent a greater number?

Answers

Answer:

Coordinate D

Step-by-step explanation:

Perform all indicated operations, and express each answer in simplest form with positive exponents. Assume that all variables represent positive real numbers. Have to show all work.

Answers

Answer:

a. [tex]-( 4\sqrt{3} + 3)[/tex]

b.  [tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]

c.  [tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]

d. [tex]45 + 12\sqrt{5y} + 4 y[/tex]

e. [tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]

Step-by-step explanation:

a.

[tex]\sqrt{12} - \sqrt{108} - \sqrt[3]{27}[/tex]

Expand each expression

[tex]\sqrt{4*3} - \sqrt{36 * 3} - \sqrt[3]{3*3*3}[/tex]

Split the first two surds

[tex]\sqrt{4}*\sqrt{3} - \sqrt{36} * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]

Apply law of indices

[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3^3}[/tex]

Apply law of indices

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{3*\frac{1}{3}}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{1}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3[/tex]

[tex]2\sqrt{3} - 6\sqrt{3} - 3[/tex]

[tex]- 4\sqrt{3} - 3[/tex]

Factorize

[tex]-( 4\sqrt{3} + 3)[/tex]

The expression cannot be further simplified

b.

[tex](\frac{x^{\frac{-3}{4}}y^{\frac{2}{3}}}{x^{\frac{-1}{3}}y^{\frac{-5}{8}}})[/tex]

Expand the expression

[tex](\frac{x^{\frac{-3}{4}} * y^{\frac{2}{3}}}{x^{\frac{-1}{3}} * y^{\frac{-5}{8}}})[/tex]

Apply the following law of indices;

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

[tex]x^{{\frac{-3}{4} - \frac{-1}{3}}} * y^{{\frac{2}{3} - \frac{-5}{8}}}}[/tex]

[tex]x^{{\frac{-3}{4} + \frac{1}{3}}} * y^{{\frac{2}{3} + \frac{5}{8}}}}[/tex]

Add the exponents

[tex]x^{\frac{-9+4}{12}} * y^{{\frac{16+15}{24}}}}[/tex]

[tex]x^{\frac{-5}{12}} * y^{{\frac{31}{24}}}}[/tex]

[tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]

The expression cannot be further simplified

c.

[tex]\frac{8}{\sqrt{x} - \sqrt{5}}[/tex]

Rationalize the denominator

[tex]\frac{8}{\sqrt{x} - \sqrt{5}} * \frac{\sqrt{x} + \sqrt{5}}{\sqrt{x} + \sqrt{5}}[/tex]

[tex]\frac{8(\sqrt{x} + \sqrt{5})}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]

Simplify the numerator

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]

Simplify the denominator by difference of two squares

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{\sqrt{x}^2 - \sqrt{5}^2}[/tex]

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]

The expression cannot be further simplified

d.

[tex](3\sqrt{5} + 2\sqrt{y})^2[/tex]

Expand the expression

[tex](3\sqrt{5} + 2\sqrt{y})(3\sqrt{5} + 2\sqrt{y})[/tex]

Open the bracket

[tex]3\sqrt{5} (3\sqrt{5} + 2\sqrt{y})+ 2\sqrt{y}(3\sqrt{5} + 2\sqrt{y})[/tex]

Open both brackets

[tex]3\sqrt{5} *3\sqrt{5} + 3\sqrt{5}*2\sqrt{y}+ 2\sqrt{y}*3\sqrt{5} + 2\sqrt{y}*2\sqrt{y}[/tex]

[tex](3\sqrt{5} *3\sqrt{5}) + (3\sqrt{5}*2\sqrt{y})+ (2\sqrt{y}*3\sqrt{5}) + (2\sqrt{y}*2\sqrt{y})[/tex]

Multiply each expression in the bracket

[tex](3*3\sqrt{5*5}) + (3*2\sqrt{5*y})+ (2*3\sqrt{5*y}) + (2*2\sqrt{y*y})[/tex]

[tex](9\sqrt{25}) + (6\sqrt{5y})+ (6\sqrt{5y}) + (4\sqrt{y^2})[/tex]

Solve like terms

[tex](9\sqrt{25}) + (12\sqrt{5y}) + (4\sqrt{y^2})[/tex]

Take square root of 25 and y²

[tex](9 * 5) + (12\sqrt{5y}) + (4 * y)[/tex]

[tex](45) + (12\sqrt{5y}) + (4 y)[/tex]

Remove the brackets

[tex]45 + 12\sqrt{5y} + 4 y[/tex]

The expression cannot be further simplified

e.

[tex]-\sqrt{\frac{3}{5x}}[/tex]

This expression can not be simplified; However, it can be rewritten, by applying law of indices as

[tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]

Murray’s father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account? x + y = 6,000. 0.025 x + 0.015 y = 110. x + y = 6,000. 0.25 x + 0.15 y = 110. x + y = 6,000. 0.025 x minus 0.015 y = 110. x + y = 6,000. 2.5 x minus 1.5 y = 110.

Answers

Answer:

x+y=6000

Step-by-step explanation:

0.025x-,0.015y=110

Answer:

x+y=6000

0.025x-,0.015y=110

Step-by-step explanation:

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