We are given an inequality proble. Our approach is to test our options.
We begin with the second option.
[tex]\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}[/tex]We'll solve it in parts and compare to our number line
[tex]\begin{gathered} -5<(x-a-5) \\ \text{Adding 5 to both sides gives us:} \\ -5+5On the other hand, we have:[tex]\begin{gathered} (x-a-5)<5 \\ \text{Adding 5 to both sides} \\ x-a<5+5 \\ x-a<10 \\ \text{Adding a to both sides} \\ x<10+a \end{gathered}[/tex]The range of x is therefore: a < x < 10 + a
SECOND OPTION
An uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. Write an equation to find the number of miles m for which uber and lyft would cost the same amount.
A merchant is bagging potatoes that he will sell for 5 a bag he want to take 400 for then how many bags should he prepare
The number of bags that the merchant should prepare if he wants to make 400 is; 80 bags
How to solve Algebra Word Problems?The method to solve algebra word problems is as follows;
1. Carefully read through the problem thoroughly, and try to know the meaning.
2. Use variables to denote unknown numbers.
3. Translate the remaining part of the problem into a mathematical expression.
4. Solve the problem.
We are told that the merchant sells 5 for a bag. Now, he wants to make 400. This means if the number of bags is x, then;
x = 400/5
x = 80 bags
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48.06 ÷ 6 what is the anwser
Answer:
8.01 is the answer
Answer:
8.01
Step-by-step explanation:
A pottery factory kept track of the number of broken plates per shipment Number of broken plates Number of shipments 2 376 2 380 6 567 5 737 2 928 964 3 X is the number of broken plates that a randomly chosen shipment had. What is the expected value of X? Write your answer as a decimal.
Answer: The expected value of X is 672.75
Expected value can be calculated using the below formula
[tex]\begin{gathered} \text{Expected value = }\frac{\Sigma fx}{\Sigma f} \\ \Sigma fx\text{ = 376 x 2 + 380 x 2 + 567 x 6 + 737 x 5 + 928 x 2 + 964 x 3} \\ \Sigma fx\text{ = 752 + 760 + 3, 402 + 3, 685 + 1, 964 + 2, 892} \\ \Sigma fx\text{ = 13, 455} \\ \Sigma f\text{ = 2 + 2 + 6 + 5 + 2 + 3} \\ \Sigma f\text{ = 20} \\ \text{Expected value = }\frac{13,\text{ 455}}{20} \\ \text{Expected value = 672.75} \end{gathered}[/tex]Therefore, the expected value of X is 672.75
The buyer purchased 48 lounge pants to be priced at $39. There were already 10 pair of lounge pants in stock but they were repriced from $34 to $39 for consistency. All of the lounge pants sold. (a) What was the additional markup percent earned on the lounge pants already in inventory? (b) What was the total net sales on all pants during the event?
Solution
Question A:
- The lounge pants already in stock are 10.
- The price of the pants was moved from $34 to $39. Thus, the markup percent is:
[tex]\begin{gathered} \frac{39-34}{34}\times100\% \\ \\ =\frac{5}{34}\times100\% \\ \\ =14.70588\% \end{gathered}[/tex]We have two fractions, 3/4 and 7/6, and we want to rewrite them so that they have a common denominator (and whole number numerators).
What numbers could we use for the denominator?
Choose 2 answers:
(Choice A)
A
8
(Choice B)
B
12
(Choice C)
C
18
(Choice D)
D
24
Answer:
B
Step-by-step explanation:
Katie’s hair is 4 ½ x + 1 inches long. She decides to get a haircut. The barber cuts ¼ x – 2 inches off her hair. Write an expression that would represent how long Katie’s hair is when she leaves the barbershop, if simplified.
Katie's hair is (17x/4 +3) inches long when she leaves the barber shop.
According to the question,
We have the following information:
Katie’s hair is 4 ½ x + 1 inches long.
The barber cuts ¼ x – 2 inches off her hair.
Now, the remaining length of her hair will be obtained by subtracting the length of hair cut from the original length.
So, we have the following expression:
([tex]4\frac{1}{2} x+1[/tex])-(x/4-2)
9x/2+1-x/4+2
9x/2-x/4+3
Taking 4 as the least common factor:
18x-x+12/4
17x+12/4
17x/4 + 12/4
17x/4 + 3 inches
Hence, Katie's hair is (17x/4 +3) inches long when she leaves the barber shop.
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Estimate the sum by rounding each number to the nearest hundredth: 0.087+0.043 that's my question
To round each number to the nearest hundredth, you need to look th
x/7=2
2x/3=8
7x-10=11
9x+2=20
pls give a step-by-step answer
ITS URGENT
Answer:
x=14
Step-by-step explanation:
x/7=2
7 x x/7 = 7x2
A car's velocity is modeled by v(t) = 0.5t2 – 10.5t + 45 for 0 ≤ t ≤ 10.5, where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?
2.5 seconds
6 seconds
10.5 seconds
15 seconds
Answer:
6 Seconds
Step-by-step explanation:
The car come to a complete stop after the time of 6 seconds.
What is defined as the velocity?Velocity is a vector assertion of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also recognized as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s).For the given question;
A car's velocity is modeled by v(t) = 0.5t² – 10.5t + 45.
The time inequality is given as; 0 ≤ t ≤ 10.5.
To calculate the time for which velocity becomes zero.
Put v(t) = 0.
v(t) = 0.5t² – 10.5t + 45 = 0
0.5t² – 10.5t + 45 = 0
Divide equation by 0.5.
t² – 21t + 90 = 0
factorize the values.
(t - 15)(t - 6) = 0
t = 15 and t = 6 seconds
As, 0 ≤ t ≤ 10.5.
Thus, t = 6 seconds.
Therefore, the car come to a complete stop after the time of 6 seconds.
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Japanese adults eat about 79 pounds of fruit each year. How many years will it take for a Japanese adult to eat 1,100 pounds of fruit?
the length and width of a rectangular soccer field can be representedby 5x - y and x 3y. find the polynomial expression that represents thearea of the soccer field. write your answer in descending order. please use the palette below to enter your answer.
the polynomial expression that represents the area of the soccer field is
5x^2 -16xy +3y^2
given length of a rectangular soccer is 5x -y
and width of a rectangular soccer is x- 3y
find the polynomial expression that represents the area of the soccer field.
we know that the formula for the area of a rectangle is
area= length * width
=( 5x-y)*( x-3y)
= 5x^2 -15xy-xy +3y^2
= 5x^2 -16xy +3y^2
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Joanne cannot decide which of two washing machines to buy. The selling price of each is $390. The first is marked down by 40%. The second is marked down by 10% with an additional 30% off. Find the sale price of each washing machine. Use pencil and paper. Explain why Joanne should buy the first washing machine rather than the second if the machines are the same except for the selling price.
Answer:
Joanne should definitely purchase the first one because it is much cheaper.
Step-by-step explanation:
So, to find the cost of each washing machine, we can simply turn the percentages into decimals and multiply to get our answer. Let's start with 40%. We bring the decimal back to spaces to get: 0.40. Then, we multiply it from the $390, because 40% 'of' means multiply:
0.40 x 390 = $156.
390 - 156 = $234
Now, the next one:
0.10 x 390 = $39
390 - 39 = $351
Then, we take 351 dollars and find the 30% off difference.
0.30 x 351 = 105.30
390 - 105.3 = $284.70
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
17. P(-6, 16), Q(2, -4), R(-6, 14), S(-2, 4)Slope of PQ Slope of RSTypes of Lines
The formula for finding slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y2 and y1 are final and initial values of the y coordinates respectively
x2 and x1 are final and initial values of the x coordinates respectively
Considering line PQ,
x1 = - 6, y1 = 16
x2 = 2, y2 = - 4
Slope = (- 4 - 16)/(2 - - 6) = - 20/8
Slope = - 2.5
Considering line RS,
x1 = - 6, y1 = 14
x2 = - 2, y2 = 4
Slope = (4 - 14)/(- 2 - - 6) = - 10/4
Slope = - 2.5
If the slope of two lines are equal, it means that they are parallel. We can see that the slopes of PQ and RS are equal. Thus,
Line PQ is parallel to line RS
2
4.An image of a book shown on a website is 1.5
inches wide and 3 inches tall on a computer monitor.
The actual book is 9 inches wide.
5.
be
di
a) What scale is being used for the image? Explain or
show your reasoning.
b) How tall is the actual book? Show your
calculations.
S
a. The scale that is being used for the image is: 1 inches to 6 inches or 1 inches = 6 inches.
b. The actual book is 18 inches tall.
What is an Image?An image is the new figure formed when an original figure is dilated, either by enlargement or by reduction. The image is a similar figure to the preimage (original figure).
Given the following:
Width of the image = 1.5 inchesHeight of the image = 3 inchesActual book width (preimage) = 9 inchesa. The scale being used = width of image : width of preimage (actual book)
Scale = 1.5 : 9
Scale = 1 : 6
This is, 1 inches to 6 inches or 1 inches = 6 inches.
b. Height of image = 3 inches
Height of actual book (preimage) = 3 × 6 = 18 inches.
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Solve the quadratic equation. Show all of your steps.
x² + 3x - 5 = 0
Ma
Rel
Gea
Gro
Trig
▸ Stat
What is the measure of BOC I couldn’t figure this out.
The arc length formula is :
[tex]\text{arc}=r\theta[/tex]where r = radius and the angle is in radians
From the problem, the arc length is 21π units and the radius is 15 units.
Using the formula above :
[tex]\begin{gathered} 21\pi=15\theta \\ \theta=\frac{21\pi}{15} \\ \theta=\frac{7}{5}\pi \end{gathered}[/tex]ANSWER :
A.
suppose there is a 1.2°F drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 56.9°F, what will be the temperature when the plane reaches an altitude of 8,000 ft?
We have a linear model, that relates temperature with altitude.
The first senctence gives us a clue about tha rate of change (the slope) of temperature in function of the altitude.
We can write the slope, in °F/1000 ft, as:
[tex]m=-1.2[/tex]The temperature on the ground, where h=0, is 56.9 °F, so we can write the equation of the line as:
[tex]T(h)=-1.2h+56.9[/tex]When the altitude is 8,000 ft, h=8 and T is:
[tex]T(8)=-1.2\cdot8+56.9=-9.6+56.9=47.3[/tex]The temperature at 8,000 ft will be 47.3 °F.
At work one day, Erica Franz received 11 packages. Speedy Delivery delivered four times as many as Ralph's Express, while Ralph's Express delivered one more than SendQuick Package Service. How many packages did each service deliver to Erica?
She received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery
What is a word problem?A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.
Let SQPS represent SendQuick Package Service
SD represent Speedy Delivery
RE represent Ralph's Express, then:
Let the number of packages from SQPS be x
The number of packages from RE will be x+1
The number of packages from SD will be 4(x+1)
Given that the total number of packages received is 11, then:
x + x+1 + 4(x+1) = 11
x + x+1 + 4x + 4 = 11
6x + 5 = 11
6x = 11-5
6x = 6
x = 1
x = 1 package from SQPS
x + 1 = 2 packages from RE
4(x+1) = 8 packages from SD
Therefore, Erica Franz received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $30456. The variable costs will be $10 per book. The publisher will sell the finished product to bookstores at aprice of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:
[tex]30456+10x=21.75x\text{.}[/tex]Subtracting 10x from both sides of the equation we get:
[tex]30456=21.75x-10x,[/tex]adding like terms we get:
[tex]30456=11.75x\text{.}[/tex]Dividing by 11.75 we get:
[tex]x=2592.[/tex]Then the producer must sell 2592 books.
Answer: 2592.
Determine if the triangles are congruent. If so, state which reason proves the triangles are congruent.
Group of answer choices
Not congruent
SAS
HL
SSA
The △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.
What do we mean by the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
You can move, flip, twist, and turn these triangles to produce the same effect.
So, first label the two triangles as △ABC and △ADE.
Now, to prove that △ABC ≅ △ADE:
BA = DA (Given)
AC = ED (Given)
∠BAC = ∠ADE (Since, both lines are similar, so the angle between them will also be soililar and congruent.
So, we can say that △ABC ≅ △ADE is under SAS conditions.
Therefore, the △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.
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Complete question:
Determine if the triangles are congruent. If so, a state which reason proves the triangles are congruent.
Group of answer choices
a. Not congruent
b. SAS
c. HL
d. SSA
Rosalia went on a long bike ride. The table shows how long she biked and the distance she traveled. Determine whether the relationship between hours biked and miles traveled is proportional.
The rate of change is not the same for all the cases so,
The relationship between hours biked and the miles traveled is not proportional.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the table, we need to find the rate of change between two given hours and the miles traveled at that time.
Now,
Between 1 hour and 2 hours.
The rate of change.
= (26 - 12) / (2 -1)
= 14 / 1
= 14
Between 2 hours and 3 hours.
The rate of change.
= (30 - 26) / (3 - 2)
= 4 / 1
= 4
Between 3 hours and 4 hours.
The rate of change.
= (48 - 30) / (4 - 3)
= 18 / 1
= 18
We see that,
The rate of change is not the same for all the cases so,
The relationship between hours biked and the miles traveled is not proportional.
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Five friends together earned $165 raking leaves. they divided the money evenly among the 5 of them. maria earned another $10 walking a neighbor's dog. how much money did maria earn in all?
Answer:
Maria earns $43
Step-by-step explanation:
$165 divided by 5 = $33 + $10 = $43
if a= -3, find the value of a²
Answer:
a = 9
Step-by-step explanation:
[tex]a^{2}[/tex] = a*a
a = -3
-3 * -3 = 9
NOTE: 2 negative numbers multiplied by each other always equals a positive
So.... a = 9
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 70 people. The drama club must make no less than $400 from ticket sales to cover the show's costs. Also, they can sell at most 50 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities for the given situation is
x +y ≤ 70.
$4x + $8x ≤ $400.
y ≤ 50.
And one possible solution is (40,30) and the graph of the inequality is attached below.
Inequality:
Inequality refers the non equal comparison of the expressions.
Given,
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 70 people. The drama club must make no less than $400 from ticket sales to cover the show's costs. Also, they can sell at most 50 adult tickets.
Here we need to find the system of inequalities graphically and also determine one possible solution for it.
Let us consider x represents the number of student tickets sold and y represents the number of adult tickets sold.
Therefore, in here we know that, they can sell at most 50 adult tickets.
Which means that the value of y can't be greater than 50.
So, in inequality it can be written as,
y ≤ 50.
And the total number of seats in the auditorium is 70.
Therefore,
x + y ≤ 70
And we also know that, they sells the ticket at the cost not less than $400.
So,
$4x + $8x ≤ $400.
Now, we have to plot those inequality on the graph, the we get he following graph.
In the graph, the blue line represents the inequality x + y ≤ 70 and the red line represents the inequality $4x + $8x ≤ $400.
While we looking into the graph we have identified that the solution of the graph is (40,30).
Which means there are 40 number of students and 30 number of adults.
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WILL GIVE BRAINLIEST write your answer as a simplified mixed number please show your work
Answer:
Step-by-step explanation:
Given equation...
[tex]-2\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex] =
Step One...
= [tex]\frac{-5}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex]
Step Two...
= [tex]\frac{-10}{3}[/tex]
Step Three...
= -3[tex]\frac{1}{3}[/tex]
Hope this helps!
The parent function of the graph of F(x) is the square root function, whichwas reflected across the x-axis. Which of the following is the equation of F(x)2O A. F(x) = -1O B. F(x) - Vx+1O C. F(x) -O D. F(X) ---
The rule of a reflection about the x-axis is given by
[tex]f(x)\longrightarrow-f(x)[/tex]in our case,
[tex]f(x)=\sqrt[]{x}[/tex]then, by reflecting this function about the x-axis, we get
[tex]f(x)=\sqrt[]{x}\longrightarrow F(x)=-\sqrt[]{x}[/tex]therefore, the answer is option D.
x = 3y + 18
5x+4y = -5
X =
y = 0
010
X
5
Answer:
Step-by-step explanation:
x = 3y + 18
5x+4y = -5
X =
y = 0
010
X
5
help meeeeeeeeeeeeeeeeeeeeee
Answer:
To the nearest tenth, the length is 6.4 meters, and the width is 3.4 meters.
Step-by-step explanation:
Let w be the width of the rectangle. Then l = w + 3, and we have:
[tex] w(w + 3) = 22[/tex]
[tex] {w}^{2} + 3w = 22[/tex]
[tex] {w}^{2} + 3w - 22 = 0[/tex]
Calculating the discriminant:
[tex] \sqrt{ {3}^{2} - 4(1)( - 22)} = \sqrt{9 + 88} = \sqrt{97} [/tex]
So by the quadratic formula, and discarding the negative solution, we then obtain:
[tex]w = \frac{ - 3 + \sqrt{97} }{2} = 3.4[/tex]
[tex]l = w + 3 = 3.4 + 3 = 6.4[/tex]
The English teachers at Baker High School added a new class in creative writing. The teachers
expected 20 students to sign up, so they were very surprised when 45 students actually
enrolled. What is the percent error for their estimate?