It costs $0.05 to send a text message and $0.10 to send a picture on your cell phone. You spend $4 and send five more text messages than pictures. How many text messages, x, and pictures, y, did you send?

Answers

Answer 1

The first thing we must do for this case is to define variables:
x: text messages
Y: pictures
We write the system of equations:
0.05x + 0.10y = 4
x = y + 5
Solving the system we have:
x = 30
y = 25
Answer:
you send:
30 text messages
25 pictures

Answer 2

Final answer:

This is a problem of system of linear equations. We form two equations from the conditions given in the problem, and solve the system of equations to find the number of text messages and pictures sent.

Explanation:

This is a problem of system of linear equations. Here are two conditions mentioned: The total cost and difference of number of text messages and pictures.

Let's denote the number of text messages as x and pictures as y as per your question.

From the cost, we have the equation: $0.05x + $0.10y = $4.

From the difference of the number of sent messages and pictures, we have: x = y + 5.

Now we can substitute x from the second equation into the first one, get the value for y, and calculate the value for x after. Here you have step-by-step solution for your problem.

Learn more about system of linear equations here:

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Related Questions

identify the slope and Y- intercept of the graph of the equation.Then graph the equation, Y = - 5/4X + 1

Answers

The solution is as shown in the figure.

The slope = -5/4

8x+6=5x+9
[tex]8x + 6 = 5x + 9[/tex]

Answers

First step is to get variables on one side and constants on the other so that we can combine like terms. To do so, subtract 5x from both sides and subtract 6 from both sides. This gives you:

8x - 5x = 9 - 6

Now combine like terms:

3x = 3

Divide by 3 to isolate the variable x.

x = 1

Final answer:

To solve the equation 8x + 6 = 5x + 9, subtract 5x from both sides to get 3x + 6 = 9, then subtract 6 from both sides to get 3x = 3. Finally, divide by 3 to find x = 1.

Explanation:

The equation given is 8x + 6 = 5x + 9. To solve for x, you first want to get all terms containing x on one side and the constants on the other. This is achieved through the use of addition or subtraction. From LibreTexts™, we know that addition or subtraction of the same number on both sides of an equation maintains equality. So, subtract 5x from both sides:

8x + 6 - 5x = 5x + 9 - 5x

3x + 6 = 9

Next, you subtract 6 from both sides to isolate the x term:

3x + 6 - 6 = 9 - 6

3x = 3

Now, you divide both sides by 3, a step also indicated by LibreTexts™ as multiplication or division by the same number maintains the equation's balance:

3x / 3 = 3 / 3

x = 1

The solution to the equation is x = 1.

which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))

Answers

Answer: x = 5π/6

Explanation:

1) Given function:

[tex]y=tan(x- \frac{5 \pi }{6} )[/tex]

2) x-intercept are the roots of the function, i.e. the solution to y = 0

3) to find when y = 0, you can either solve the equation or look at the graph.

4) Solving the equation you get:

y = 0 ⇒ tan(x - 5π/6) = 0 ⇒ x - 5π/6 = arctan(0)

arctan(0) is the angle whose tangent is zero,so this is 0

⇒ x - 5π/6 = 0 ⇒ x = 5π/6.

Then, one example of an x-intercept is x = 5π/6, which means that when x = 5π/6, the value of the function is 0.

Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.

You can verify by replacing the value x = 5π/6 in the given function:

y = tan (5π/6 - 5π/6) = tan(0) = 0.

Answer:

Step-by-step explanation:

what is sqrt p^5 q^10 expressed in simplified form?

Answers

The simplified form of the expression [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p, obtained by separating and simplifying the square roots of the individual factors.

The expression [tex]\sqrt{p^5q^{10}}[/tex] can be simplified by separating the square roots of the individual factors and simplifying each one individually.

First, let's rewrite the square root of the entire expression:

[tex]\sqrt{p^5}[/tex] = p²√p because we are taking the square root of p to the fifth power which results in p squared and the square root of p remaining.[tex]\sqrt{q^{10}}[/tex] = q⁵ because q to the tenth power is a perfect square, and taking the square root gives us q to the fifth power.

Therefore, the simplified form of [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p.

Ken started saving for retirement at age 35 with plans to retire at age 70. He invested an average of $600 per month in various securities, with an average annual return of 5% adjusted for inflation. Assuming monthly compounding, how much has Kent saved at the start of retirement

A: $54,192.18
B: $825,655.45
C: $499,355.18
D: $681,655.46

Answers

The answer is C $499,355.18

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?
A) 28 77/125 feet
B) 49 1/25 feet
C) 57 29/125 feet
D) 59 29/125 feet

Answers

Answer:

The answer is 57 29/125 feet ⇒ answer (C)

Step-by-step explanation:

∵ The ball dropped from a height 10 feet

∴ The vertical distance = 10 feet

∵ It bounces 4/5 as high as the preceding one

∴ 1st bounce = 10 × 4/5 = 8 (move down another 8)

∴ The vertical distance = 8 + 8 = 16 feet

∴ 2nd bounce = 8 × 4/5 = 6.4 (move down another 6.4)

∴ The vertical distance = 6.4 + 6.4 = 12.8 feet

∴ 3rd bounce = 6.4 × 4/5 = 5.12 (move down another 5.12)

∴ The vertical distance = 5.12 + 5.12 = 10.24 feet

∴ 4th bounce = 5.12 × 4/5 = 4.096 (move down another 4.096)

∴ The vertical distance = 4.096 + 4.096 = 8.192 feet

∵ The ball will hit the surface to make the 5th bounce

∴ The total vertical distance is :

10 + 16 + 12.8 + 10.24 + 8.192 = 57.232 = 57 29/125

Another way:

* We can use the formula of geometric sequence with

1st bounce distance (a) = 8 + 8 = 16 and ratio (r) = 4/5

and number of bounces (n) = 4 (hit the surface for its 5th bounce)

∵ [tex]S_{n}=\frac{a(1-(r^{n}))}{1-r}[/tex]

∴ [tex]S_{4}=\frac{16(1-(\frac{4}{5})^{4})}{1-\frac{4}{5}}=47\frac{29}{125}[/tex]

* Then we must to add the 10 feet

(the ball dropped from height 10 feet)

∴ The total vertical distance = 10 + 47 29/125 = 57 29/125 feet

Jordan worked out at a gym for 2 hours. His workout consisted of stretching for 21 minutes, jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Jordan’s workout was spent lifting weights?

Answers

2 hours is equivalent to 120 minutes. 21+45 is 66. So he spent 66 minutes not lifting weights, and 54 minutes lifting weights. 54/120 would be equivalent to 45%. So he spent 45% of his workout lifting weights. Hope this helps!!

the slope of the line below is -3. which of the following is the point-slope form of the line? A.) y+2=3(x-2) B.) y+2=-3(x-2) C.) y-2=-3(x+2) D.) y-2=3(x+2)

Answers

The "point-slope" form of the equation of a straight line is:

[tex]y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line[/tex]

We have:

[tex]m=-3;\ (x_1;\ y_1)=(2;-2)[/tex]

Substitute

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

Answer: B. y + 2 = -3(x - 2)

Answer:

B) y + 2 = -3(x - 2)

Step-by-step explanation:

it's what I got

what is the median number for the numbers 4,8,10,5,9?

Answers

Hey there!

The median is the number in the middle when the numbers go from least to greatest. This would be 4, 5, 8, 9, 10. The middle number would be 8. A way to find the middle number is to mark off the end number on the right and left side until you are left with 1 number. If you are left with 2, add the numbers up and divide. The answer to this is 8.

I hope this helps!

Hello There!

Median: The middle number when all the numbers are listed in oder from least to greatest.

To find the median, place the numbers in order from least to greatest.

In this case, the numbers would be 4, 5, 8, 9, 10

The middle number would be 8 so the median for this set of numbers is 8.

The sum of two numbers is 43 . The larger number is 11 more than the smaller number. What are the numbers

Answers

a- one number
b- second number

a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)

so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16

now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27

that is:
a = 16
b = 27

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

checking:

b - a = 11
27 - 16 = 11 (TRUE)

2,5,11,20 32,47 what is the next number in the series

Answers

it is easy 2, 5, 11, 20, 32, 47, 65
+3,+6, +9,+12,+15,+18, +21,

The next number in the series is 65. To identify the pattern in the given series and find the next number, let's look at the differences between consecutive terms.

5 - 2 = 3

11 - 5 = 6

20 - 11 = 9

32 - 20 = 12

47 - 32 = 15

As we observe, the differences between consecutive terms are increasing by 3 each time. So, to find the next difference, we add 3 to the last difference:

15 + 3 = 18

Now, to find the next number in the series, we add this difference to the last number in the series:

47 + 18 = 65

Therefore, the next number in the series is 65.

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The table below shows a correct representation that 15 pounds (lb) of sugar cost $3: lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1

Answers

by the way you are saying it the answer would be 0.20

Answer:

true

Step-by-step explanation:

an organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%. What does the margin of error imply?

Answers

Margin of error implies that the number of those who rated the vacation as delightful ranges between 81% (that is, 83-2) and 85% (that is, 83+2) of the population at a 95% confidence interval.

Answer:

Given is:

Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.

±2% means plus 2% from 83% and minus 2% from 83%, making the interval between 81% and 85%.

In general the margin of error tells that, how many percentage points the results will differ from the real population value. A small margin of error shows trustworthy results whereas a large margin of error means the results are not accurate.

Therefore, it can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

If you roll a fair six-sided die and a fair four-sided die, what is the probability that neither die shows a 1?

Answers

Answer in fraction form: 5/8
Answer in decimal form: 0.625

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

Explanation:

There are 5 sides that aren't labeled "1" out of 6 total. So the probability of not rolling a "1" on the six-sided die is 5/6

Similarly, there are 3 sides that aren't labeled "1" out of 4 sides on the four-sided die. The probability of not rolling a "1" for this die is 3/4

Multiply the fractions
(5/6)*(3/4) = (5*3)/(6*4) = 15/24 = 5/8

The answer in fraction form is 5/8 which converts to 0.625 (use long division or a calculator)

Note: the multiplication of probabilities works because the two events (of rolling each die) are independent

#1. if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then what is the central angle, what is the measure of the arc that 2 pieces together would intercept, and the equation that represents as well as the circumference?

I also need the same answers for these:

#2. radius 10 inches, 14 equal pieces, and points of (3, 7)

#3. radius 25 cm, 16 pieces and 14 and 53

#4. radius 12 inches, 8 pieces and points of (2, 5)

#5. radius 4 inches, 12 equal pieces, and points of (3, 6)

Answers

part 1)
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²

b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in

the measure of the arc that 2 pieces together would intercept is 9.42 in

c)  The central angle of one slice is 45 degrees

Part 2)
coordinates of the center (3,7)
radius=10 in
is cut into 14 equal slices-----> 360°/14-----> 25.71° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-7)²=10²

b) circumference=2*pi*r-----> 2*pi*10---> 62.8 in
if 360° (full circle) has a length of---------> 62.8 in
51.42° (2 pieces together)---------> x
x=51.42*62.8/360-----> x=8.97 in

the measure of the arc that 2 pieces together would intercept is 8.97 in

c)  The central angle of one slice is 25.71 degrees

Part 3)
coordinates of the center (14,53)
radius=25 cm
is cut into 16 equal slices-----> 360°/16-----> 22.5° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-14)²+(y-53)²=25²

b) circumference=2*pi*r-----> 2*pi*25---> 157 cm
if 360° (full circle) has a length of---------> 157 cm
45° (2 pieces together)---------> x
x=45*157/360-----> x=19.63 cm

the measure of the arc that 2 pieces together would intercept is 19.63 cm

c)  The central angle of one slice is 22.5 degrees

Part 4)
coordinates of the center (2,5)
radius=12 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-2)²+(y-5)²=12²

b) circumference=2*pi*r-----> 2*pi*12---> 75.36 in
if 360° (full circle) has a length of---------> 75.36 in
90° (2 pieces together)---------> x
x=90*75.36/360-----> x=18.84 in

the measure of the arc that 2 pieces together would intercept is 18.84 in

c)  The central angle of one slice is 45 degrees

Part 5)
coordinates of the center (3,6)
radius=4 in
is cut into 12 equal slices-----> 360°/12-----> 30° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-6)²=4²

b) circumference=2*pi*r-----> 2*pi*4---> 25.12 in
if 360° (full circle) has a length of---------> 25.12 in
60° (2 pieces together)---------> x
x=60*25.12/360-----> x=4.19 in

the measure of the arc that 2 pieces together would intercept is 4.19 in

c)  The central angle of one slice is 30 degrees

Q9 Q6.) Write an equation for intersection l₂ that keeps traffic moving.

Answers

The numbers of cars entering the intersection are z and 7. The numbers of cars exiting the intersection are x and 5. To keep traffic moving, ...
number entering = number exiting
z + 7 = x + 5

The appropriate selection is ...
A. z +7 = x +5

A rectangular prism has a volume of 96ft3. The area of the base is 24ft2. What is thw height of the prism? answer soon please

Answers

96/24=4
The height is 4ft.

hey can you please help me posted picture of question

Answers

The discriminant can be determined from the number of roots of the graph.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

Since the given graph has no real root, i.e. it does not cross x-axis at any point, so we can say that the discriminant of the given function is negative.

So the answer to this question is option C

Choose the correct factorization for the polynomial 21xy+15x+35ry+25r

Answers

(21xy +15x )+ (35ry +25r)
3x(7y+5)+ 5r(7y+5)
(3x+5r)(7y+5)

Please rate

In a survey conducted in an Office, 60% of the sample respondents agreed that employees should have flexible working hours.
If the margin of error is +-2%, the expected population proportion that wanted flexible working hours is between -------% and------%

Answers

The % margin of error means that the real value is in the range between the mean less the margin error and the mean plus the margin error. This is [ mean - % of error, mean + % of error]. Then, in this case the error of +/- 2% means that the expected population proportion that wants flexible working hours is between 60% - 2% and 60% + 2%, which is between 58% and 62%.

Answer:

Yes, the answer is between 58% and 62%

Step-by-step explanation:

I just did it on Edmentum

At a school for performance art students
2/5

of the girls study music,
3/5

of the girls study dance and
1/6

of the girls study music and dance. What fraction of those who study music also study dance?

Answers

the to the girls studying music and dance the factions is 55

Solve the system using the substituiton method
branliest offered
3x-7y=10
x-4y=5

Answers

Hi there!

To solve this problem using substitution, we need to set x equal to a value and substitute it into the other equation.

Since
x - 4y = 5,
x = 5 + 4y

3x - 7y = 10
3(5 + 4y) - 7y = 10
15 + 12y - 7y = 10
15 + 5y = 10
5y = -5
y = -1

Now that we know y is -1, we can substitute it back into the equation to find x:

y = -1
x - 4y = 5
x - 4(-1) = 5
x - (-4) = 5
x + 4 = 5
x = 1

So, your answers are x = 1 and y = -1.

Hope this helps!

hey can you please help me posted picture of question

Answers

The correct answer is option B

(5 + 3i)(4+ 2i)

= 5(4+2i) + 3i(4+2i)

= 20 +10i + 12i +6i²

= 20 +22i +6(-1)

= 20 + 22i - 6

= 14 + 22i

A bookstore costs $75 a day to keep open, and it spends $11 for each book that it sells. If each book sells for $16, what is the break-even point for this bookstore?

Answers

In order for the bookstore to continue its business, it should sell at least 15 books to meet its $75 cost. For the computation:The formula for solving the breakeven point (BEP) is:Fixed Cost / (Selling Price - Variable Cost) = BEPFixed Cost is the cost that remains constant whether the services provided or products sold increases or decreases.Variable Cost is the cost that varies or differs in proportion to the products or services produced, whether they increased or decreased. In the problem, the Fixed cost is 75 and the variable cost is 11, and lastly, the selling price is 16.To substitute the given to the problem:75 / (16 - 11) = 15

Answer:c=11n+75

Step-by-step explanation:

What are a) the ratio of the perimeter’s b) and the ratio of areas of the larger figure to the smaller figure?

Answers

did you get the answers?

a) We have been given two similar figures and we have to find ratio of perimeters of these figures.

Let a be given side of larger figure and b be the given side of smaller figure. Let [tex]p_{1} \text{ and } p_{2}[/tex] be the perimeters of two figures and [tex]A_{1} \text{ and } A_{2}[/tex] be the areas of the two figures.

We know that perimeters of two similar figures are in the ratio of corresponding sides.

[tex]\frac{p_{1}}{p_{2}}=\frac{a}{b}[/tex]

We have been given, [tex]a=26\text{ and }b=6[/tex]

Therefore, upon substituting these values in the above equation, we get

[tex]\frac{p_{1}}{p_{2}}=\frac{26}{6}[/tex]

[tex]\frac{p_{1}}{p_{2}}=\frac{13}{3}[/tex]

(b)

Further we know that areas of two similar figures are in the ratio of squares of corresponding sides.

[tex]\frac{A_{1}}{A_{2}}=\frac{a^{2}}{b^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{26^{2}}{6^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{676}{36}\\ \frac{A_{1}}{A_{2}}=\frac{169}{9}\\[/tex]

Therefore, first option is the correct answer.

Hey can you please help me posted picture of question

Answers

The correct option is: Option (D) 7

Explanation:
These type of questions can easily be solved using the Venn diagram. Below is the image attached that shows the Venn diagram and the solution.

THere are seven patrons that dont like any of these coffee drinks

so the answer for your question is D.7

I hope I can show the solution but I cant post the picture right now :(

Hope Ihelped

suppose you toss a fair coin and roll a fair six-sided die. What is the probability your actions result in tails on the coin and 3 on the die

Answers

mines 3 to 6 and use 2 power

write in short; × + 2× + 13×

Answers

The distributive property applies.
x + 2x + 13x = (1 + 2 + 13)x = 16x

A marble is drawn at random first from a jar containing four black and four white marbles, and then from a jar containing six black and two white marbles. What is the probability of drawing two black marbles?

Answers

[tex] |\Omega|=8\cdot8=64\\
|A|=4\cdot6=24\\\\
P(A)=\dfrac{24}{64}=\dfrac{3}{8}=37.5\% [/tex]

Answer:

the answer is 37.5% Hope this helps!

Q # 17 , Find the slope

Answers

In order to find the slope we need to find two points on the line.

From the above graph we can see that the points (-4,-1) and (0, -3) lie on the line. So using these two points we can find the slope.

[tex]Slope=m= \frac{-3-(-1)}{0-(-4)} \\ \\ m= \frac{-3+1}{0+4} \\ \\ m= \frac{-2}{4} \\ \\ m= \frac{-1}{2} [/tex]

So, first option is the correct answer

The slope is given by:
m = (y2-y1) / (x2-x1)
Substituting values we have:
m = (- 4 - (- 3)) / (2-0)
Rewriting we have:
m = (- 4 + 3) / (2-0)
m = (- 1) / (2)
m = -1 / 2
Answer:
The slope is given by:
m = -1 / 2
option 1

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