Keisha, Miguel, and Pablo sent a total of 69 text messages during the weekend. Miguel sent 5 more messages than Keisha. Pablo sent 2 times as many
messages as Keisha. How many messages did they each send?
Number of text messages Kelsha sent:
Number of text messages Miguel sent:
N
aftavt mes Pablo sent:

Answer:

The number is -84.

Step-by-step explanation:

-x/7-2=10

-x/7=10+2

-x/7=12

-x=12*7

-x=84

x=-84

Answer:

Kelan gets 135 Euros.

Step-by-step explanation:

First of all you add up the ratio getting 10, with 10 you divide it from 450 getting 45. Then you multiply 3 (Kelan's Part) by 45 getting your answer. Tell me if this helped, i'd appreciate knowing.

This question is based on simple mathematics. Therefore, the answer is £135.

Given:

Harry, regan and kelan share £450 in the ratio 2 : 5 : 3.

We have to determined the money would kelan get.

According to questions,

First of all, adding  up the ratios.

We get,

2+5+3 = 10

Regan and kelan share £450. So divided £450  by 10, and solve it further.

We get,

[tex]\dfrac{450}{10} = 45[/tex]

Now, multiplying 45 by 3 (Kelan's part).

We get,

[tex]45\times3= 135[/tex]

Therefore, the money that kelan get is £135.

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Answer:

what is the question

Step-by-step explanation:

You will pay 5% sales tax.

Step-by-step explanation:

Given,

Cost of item = $40

Sales tax = $2

Percent of sales tax = [tex]\frac{Sales\ tax}{Cost\ of\ item}*100[/tex]

[tex]Percent\ of\ sales\ tax=\frac{2}{40}*100\\Percent\ of\ sales\ tax=\frac{200}{40}\\Percent\ of\ sales\ tax=5\%[/tex]

You will pay 5% sales tax.

Keywords: sales tax, division

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line

m = [tex]\frac{6-7}{4-2}[/tex] = - [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, 8) ⇒ c = 8

y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of line

Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex]  and [tex]y=\frac{-1}{2}x+8[/tex] respectively.

Step-by-step explanation :

The general form for the formation of a linear equation is:

[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)

where,

x and y are the coordinates of x-axis and y-axis respectively.

m is slope of line.

First we have to calculate the slope of line.

Formula used :

[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

Here,

[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]

[tex]m=\frac{(6-7)}{4-2)}[/tex]

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

Now put the value of slope in equation 1, we get the linear equation.

[tex](y-y_1)=m\times (x-x_1)[/tex]

[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]

[tex]y-7=\frac{-1}{2}x+1[/tex]

[tex]y=\frac{-1}{2}x+1+7[/tex]

[tex]y=\frac{-1}{2}x+8[/tex]

Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex]  and [tex]y=\frac{-1}{2}x+8[/tex] respectively.

The cost of slippers is $10.5 after discount.

Step-by-step explanation:

Given,

Price of slippers = $15

Sale = 30%

Amount of discount = 30% of price of slippers

[tex]Amount\ of\ discount=\frac{30}{100}*15\\Amount\ of\ discount=\frac{450}{100}\\Amount\ of\ discount=\$4.5[/tex]

Sale price = Price of slippers - amount of discount

[tex]Sale\ price=15-4.5\\Sale\ price=\$10.5[/tex]

The cost of slippers is $10.5 after discount.

Keywords: percentage, subtraction

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To find the cost of the slippers after the 30% discount, multiply the original price by 30% and subtract the discount from the original price. The cost of the slippers after the discount is $10.50.

To find the cost of the slippers after the 30% discount, first calculate the amount of the discount by multiplying the original price by 30% (or 0.30).

Discount = $15 × 0.30 = $4.50

Next, subtract the discount from the original price to find the sale price:

Sale Price = $15 - $4.50 = $10.50

Therefore, the cost of the slippers after the discount is $10.50.

a) 5000 represents the initial amount that Sue invested in a money market account

b) The annual percentage rate is 7%

c) Sue will have $7012.76 after 5 years

Step-by-step explanation:

The exponential growth function is [tex]f(t)=P(1+r)^{t}[/tex] , where

Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function [tex]5000(1.07)^{t}=B[/tex]

∵ The function is [tex]5000(1.07)^{t}=B[/tex]

∵ The form of the exponential growth function is tex]f(t)=P(1+r)^{t}[/tex]

- By comparing the two functions

∴ P = 5000

∵ P is the initial amount

∴ The initial amount is 5000

a) 5000 represents the initial amount that Sue invested in a money market account

∵ [tex](1+r)^{t}=(1.07)^{t}[/tex]

∴ 1 + r = 1.07

- Subtract 1 from both sides

∴ r = 0.07

∵ r is the annual rate in decimal

∵ 0.07 × 100% = 7%

∴ The annual rate is 7%

b) The annual percentage rate is 7%

∵ t = 5

- Substitute the value of t in the function

∴ [tex]5000(1.07)^{5}=B[/tex]

∴ B = 7012.76

c) Sue will have $7012.76 after 5 years

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The value of z is zero

Step-by-step explanation:

The slope is the steepness of the line.

The formula for slope is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]

Here

(x1,y1) = (1,z)

(x2,y2) = (2,8)

So,

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]

The value of z is zero

Keywords: slope, Line

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Answer:

2x-2+3x

Step-by-step explanation:

2x-2+3x

combine like terms (2x + 3x = 5x)

So 2x-2+3x = 5x-2

Answer:

$ 929

Step-by-step explanation:

Given: Original price of stay in hotel= $240 per night

           Discount= 25%

           Total taxes and fee = 29%

Now, finding the price of stay for four night.

Using unitary method to solve:

As we know original price of hotel stay per night is $240

∴ Price of four night stay at original price is [tex]240\times 4 = \$ 960[/tex]

Next, 25% discount given on the price of four night stay.

∴ [tex]960 - \frac{25}{100} \times 960 = 960 - 240[/tex]

= [tex]\$ 720[/tex]

∴Price of four night hotel stay after discount is [tex]\$ 720[/tex]

Now, 29% taxes and fees been added to the price.

Price of hotel stay after discount + Taxes paid.

[tex]720 + ( \frac{29}{100} \times 720) = 720 + 209[/tex]

= [tex]\$ 929[/tex]

∴ [tex]\$ 929[/tex] is the price to be paid for four night stay at hotel after discount and taxes.

Answer:

B. 10.2

Step-by-step explanation:

Answer : The value of chord XY is, 10.2 units

Step-by-step explanation :

As we are given that, XY and YZ are congruent.

XY and YZ are congruent by SSA.

The ΔXOY and ΔZOY are congruent triangles.

Side OX = Side OZ           (side)

Side OY = Side OY     (common side)

∠XOY = ∠ZOY                   (angle)

That means, in this two sides and one angle of a triangle are equal to another triangle then the triangles are congruent.

So, Side XY = Side YZ

As we are given :

Chord YZ = 10.2

So, Chord YZ = Chord XY = 10.2

Hence, the value of chord XY is, 10.2 units

Answer:

(1, -2).

Step-by-step explanation:

y=-4x+2

y=6x-8

Substitute y = 6x - 8 in the first equation

6x - 8 = -4x + 2

10x = 10

x = 1

So y = 6x - 8

= 6(1) - 8

= -2.

The pair should be (1, -2).

The equation is y=-4x+2 and y=6x-8

here we Substitute y = 6x - 8 in the first equation

So,

6x - 8 = -4x + 2

10x = 10

x = 1

Now

y = 6x - 8

= 6(1) - 8

= -2.

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Answer:

5

Step-by-step explanation:

We have: [tex]$ \frac{18}{4} \times \frac{20}{7} $[/tex]

Simplifying we get: [tex]$ 18 \times \frac{5}{7} $[/tex]

⇒ [tex]$ \frac{90}{17} $[/tex]

This is equal to 5.2 ≅ 5.

So, Option C - 5 is the answer.

The contractor bought 2 small boxes and 6 large boxes of nails. This was determined by setting up and solving a system of equations based on the given conditions.

To solve the problem of determining the number of small and large boxes of nails purchased by the contractor, we can set up a system of equations based on the information given:

Let's denote the number of small boxes as S, and the number of large boxes as L. The equations then are:

Substituting the value of L from equation (1) into equation (2):

150S + 400(3S) = 2700

Solving for S:

150S + 1200S = 2700

1350S = 2700

S = 2

Then, substituting S = 2 into the first equation to find L:

L = 3(2) = 6

Therefore, the contractor bought 2 small boxes and 6 large boxes of nails.

The contractor bought 2 small boxes and 6 large boxes, totaling 2700 nails, with each small box containing 150 nails.

Let's denote:

- x as the number of small boxes purchased.

- y as the number of large boxes purchased.

We're given the following information:

1. Each small box contains 150 nails.

2. Each large box contains 400 nails.

3. The total number of nails purchased is 2700.

4. The contractor bought 3 times as many large boxes as small boxes, so y = 3x.

We can set up two equations to represent the given information:

1. Total number of nails equation:

150x + 400y = 2700

2. Relationship between the number of small and large boxes:

y = 3x

Now, let's substitute the value of y from the second equation into the first equation:

150x + 400(3x) = 2700

150x + 1200x = 2700

1350x = 2700

Now, let's solve for x:

[tex]\[ x = \frac{2700}{1350} \][/tex]

x = 2

So, the number of small boxes purchased [tex](\( x \))[/tex] is 2.

Now, let's find the number of large boxes [tex](\( y \))[/tex]:

y = 3x

y = 3(2)

y = 6

So, the number of large boxes purchased [tex](\( y \))[/tex] is 6.

To summarize:

- The contractor purchased 2 small boxes.

- The contractor purchased 6 large boxes.

Answer:

-3

Step-by-step explanation:

Given, f(x)=-4log2(x+3)-6

      So, for domain of f(x) ,we have to find the domain of log2(x+3) as all other things are just numbers which do not affect the domain.

For domain of f(x),    2(x+3) > 0

                    Thus,      x + 3 > 0

                                    x > -3.

So, all real numbers greater than -3 are in the domain of f(x).

Answer:

The student is expected to spend 15.4 hours doing homework

Step-by-step explanation:

The scattered plot shows there is a close correlation between the variables. A line of best fit will go through the 'center' of the points. Since we are not required to find an exact line, we'll draw it in red color as shown below

To know the equation of that line, we must take two clear points of it from the graph. We'll pick (28,4) and (4,25)

The equation of a line, given two points (a,b) and (c,d) is

[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]

Using the selected points

[tex]\displaystyle y-4=\frac{25-4}{4-28}(x-28)[/tex]

Simplifying and computing results, the equation is

[tex]\displaystyle y=-\frac{7}{8}x+\frac{57}{2}[/tex]

Using that equation, we can predict how many hours the students will spend doing homework if they spend 15 hours watching TV

[tex]\displaystyle y=-\frac{7}{8}(15)+\frac{57}{2}[/tex]=15.4 hours

So the student is expected to spend 15.4 hours doing homework

Answer:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Step-by-step explanation:

Given:

Center of the ellipse is, [tex](h,k)=(-4,-3)[/tex]

Minor axis length is, [tex]2b=6[/tex]

A vertex of the ellipse is at (1, -3)

Now, distance between the center and the vertex is half of the length of the major axis.

Using distance formula for (-4, -3) and (1, -3), we get:

[tex]a=\sqrt{(1+4)^2+(-3+3)^2}=5[/tex]

Therefore, the value of half of major axis is, [tex]a=5[/tex]. Also,

[tex]2b=6\\b=\frac{6}{2}=3[/tex]

Now, equation of an ellipse with center [tex](h,k)[/tex] is given as:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Plug in [tex]h=-4,k=-3,a=5,b=3[/tex] and determine the equation.

[tex]\frac{(x-(-4))^2}{5^2}+\frac{(y-(-3))^2}{3^2}=1\\\\\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Therefore, the equation of the ellipse is:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

75100 > 34

75100 is greater than 34

Answer:

its <

Step-by-step explanation:

Answer:

September 17th will be the first date that she has to choose between cheerleading and play practice.

Step-by-step explanation:

Least Common Multiple for 4 and 6 is 12 that is LCM(4, 6) = 12

12 days after September 5th is September 17th

Patsy would need to choose between cheerleading and play practice on September 29th, as this is the next date when both practices fall on the same day, calculated by finding the least common multiple of the practice schedules.

To determine when Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of the two practice schedules, since she has cheerleading every fourth day and play practice every sixth day.

First, list the multiples of both 4 and 6 until we find a common one:

The lowest common multiple of 4 and 6 is 12, but since our sequence started on September 5th and 12 is not a multiple of both 4 and 6, we need to keep going. Continuing our list, 24 is the next common multiple but still not satisfying both conditions. At 24 days, the cycle would repeat itself, and Patsy would again have both practices on the same day.

If these practices both start on September 5th, to find the next date she has both practices, we add 24 days to September 5th. Because September has 30 days, adding 24 days to September 5th results in September 29th. Hence, Patsy would need to choose between cheerleading and play practice on September 29th.

Answer:

multiply both 3.25 and 10 by 100

or

multiple 3.25 by 10 then multiply by 10

Answer:

2 transformations

Step-by-step explanation:

1)Reflection

2) Rotation 180 degrees clockwise

Answer:

4x-14

Step-by-step explanation:

8x-(14+4x)

8x-14-4x

8x-4x-14

4x-14

Answer: 12:40

Step-by-step explanation:

Answer:

12:40 PM

Step-by-step explanation:

By the time the plane arrives in Minnesota, the time is already 13:40 or 1:40 PM (eastern time). From eastern time to central time, the time decreases by 1 hour. 1:40 PM - 1 hour is 12:40 PM.

Answer:

[tex]\frac{11}{20}[/tex]

Step-by-step explanation:

Total no. of possible outcome= 100  (from 1 to 100)

total no. of favorable outcome= 60 (50 even and 5 odd perfect square)

Hence PROBABILITY=[tex]\\\frac{55}{100}[/tex]

                                    =[tex]\frac{11}{20}[/tex]

Answer:

[tex]x-2x-6=8x+12-x-4\\-x-6=7x+8[/tex]

Step-by-step explanation:

Given:

The equation is;

[tex]x-2(x+3)=4(2x+3)-(x+4)[/tex]

Now we need to simplify this equation we get;

Step 1: We need to simplify all the terms which are in brackets we get,

[tex]x-2x-6=8x+12-x-4[/tex]

Step 2: Now we need to simplify all variable term and non variable term we get:

[tex]-x-6=7x+8[/tex]

Answer:

These two equivalent equations Katrina has used

[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]

Step-by-step explanation:

Given :

[tex]x - 2(x + 3) = 4(2x + 3) - (x + 4)\\[/tex]

Applying distributive property that is [tex]A\times (B +C) = A\times B + A\times C[/tex] we get

[tex]x - 2x + 3\times -2 = 4\times 2x + 4\times 3 - x - 4\\[/tex]

[tex]x - 2x - 6 = 8x + 12 - x - 4\\-x - 6 = 7x + 8\\[/tex]

Answer:

The number of textbooks of each type were sold is 134 math and 268 psychology books.

Step-by-step explanation:

Given:

Total number of math and psychology textbooks sold in a week is 402.

Now, let the number of math textbooks sold be [tex]x[/tex].

And, the number of psychology textbooks be [tex]2x[/tex].

According to question:

[tex]x+2x=402[/tex]

[tex]3x=402[/tex]

Dividing both sides by 3 we get:

[tex]x=134[/tex]

So, total number of math textbooks were 134 .

And, total number of psychology textbooks were [tex]2x=2\times 134[/tex]

                                                                                 [tex]=268[/tex].

Therefore, the number of textbooks of each type were sold is 134 math and 268 psychology books.

(a) The recursive rule for the sequence is:

     [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]

Step-by-step explanation:

The form of the recursive rule of an arithmetic sequence sequence is

[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where

The form of the explicit rule of nth term of an arithmetic sequence is

[tex]a_{n}=a+(n-1)d[/tex] , where

∵ The sequence is 5, 20, 35, 50, ….......

∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15

∴ The sequence is an arithmetic sequence with a common

   difference 15

∵ The form of the recursive rule of the arithmetic sequence is

   [tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]

∵ First term = 5

∵ d = 15

∴ [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

(a) The recursive rule for the sequence is:

     [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

∵ The form of the explicit rule of nth term of an arithmetic

   sequence is [tex]a_{n}=a+(n-1)d[/tex]

∵ a = 5 and d = 15

- Substitute these values in the rule

∴ [tex]a_{n}=5+(n-1)15[/tex]

- Simplify the right hand side

∴ [tex]a_{n}=5+15n-15[/tex]

- Add like terms

∴ [tex]a_{n}=15n-10[/tex]

(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]

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Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

[tex]\sin (x+y) = 3\sin (x-y)[/tex]

Using the identities

[tex]\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\[/tex]

we get

[tex]\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y[/tex]

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

[tex]3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}[/tex]

Answer:

Explanation:

The diagram provides the proportion of the heights to the shadows:

From that you are asked (i) to simplify the fraction of the right side to one with whole numbers.

You can do that in two steps by multiplying both numerator and denominator by 10:

You can simplify that fraction if you divide by the greatest common factor of 180 and 150, which is 30:

The second part (ii) asks to find the height of the tree, that is x. To solve for x you can multiply both sides by the denominator of the fraction on the left and then simplify:

[tex]\frac{x}{33}=\frac{6}{5}\\ \\ x=\frac{6\times 33}{5}\\  \\ x=\frac{198}{5}=39.6[/tex]

Thus, the height of the three is 39.6 feet.