The area A of a rectangle with dimensions 4x and 5 is described with the inequality 100 ≤ A ≤ 1,000 Select the compound inequality for the area written in terms of x. A 100 ≤ 10+8x ≤ 1,000 B. 100 ≤18x ≤ 1,000 C. 100 ≤ 9x ≤ 1.000 D. 100 ≤20x ≤ 1.000 The solution to the compound inequality is _____ ≤x≤ ________ Are all of your solutions viable? ________
Someone help me on this question, please. I don't understand!!
Answers
The compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000, the solution is 5 ≤ x ≤ 50 and all the solutions are viable
How to select the compound inequality for the area written in terms of x?The given parameters are
Dimensions = 4x and 5
Area: 100 ≤ A ≤ 1,000
The area is calculated as
A = Product of dimensions
So, we have
A = 4x * 5
Evaluate
A =20x
Substitute A =20x in 100 ≤ A ≤ 1,000
100 ≤ 20x ≤ 1,000
So, the compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000
Divide through 100 ≤ 20x ≤ 1,000 by 20
5 ≤ x ≤ 50
Hence, the solution is 5 ≤ x ≤ 50 and all the solutions are viable
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Related Questions
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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3 ⅕ -⅔ divided by 2 ⅘
Answers
Can I have some help? What is LCM for 5 and 14
Answers
Answer:
70
Step-by-step explanation:
Least common multiple (LCM) of 5 and 14 is 70.
=70
1. An isosceles triangle has a base with a length of 14 inches and base angles that measure 68° each. Which
expression below correctly calculates the area of this isosceles triangle?
(1) 7²-tan (68°)
(2) 14²-sin (68°)
(3) 7²-cos (68°)
(4) 14-7-sin (68°)
Answers
None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).
To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.
However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.
We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.
tan(44°) = height/7, where 7 represents half of the base length.
Rearranging the equation, we have: height = 7 * tan(44°).
Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).
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I need the answers for the table below.
Answers
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
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Points A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a square ABCD. The square ABCD is reflected about the line through (0, 0) and (-2, 2). Find the vertices of the image of the square ABCD and present both the figures on the same graph.
Answers
The vertices of the reflected square.
Let's calculate them:
A' = (-0.914, 3.914)
B' = (-2.828, 5.828)
C' = (-0.086, 7.086)
D' = (1.828, 5.172)
The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:
Find the equation of the reflection line:
The reflection line passes through (0, 0) and (-2, 2).
We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):
m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.
Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:
y - 0 = -1(x - 0)
y = -x.
Find the midpoint of each side of the square:
The midpoints of the sides of a square are also the midpoints of its diagonals.
The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).
The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).
The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).
The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).
Reflect the midpoints about the line:
To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.
The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:
d = (y + x) / √(2).
The coordinates of the reflected points can be found using the formula for reflection across a line:
x' = x - 2d / √(2)
y' = y - 2d / √(2).
Calculate the reflected vertices:
The coordinates of the reflected vertices are as follows:
A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))
B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))
C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))
D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))
Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.
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if a fair coin is flipped 1600 times, what is the probability of getting more than 800 heads? a.: less than 0.01. b.: more than 0.01, but less than 0.05. c.: more than 0.05, but less than 0.10. d.: more than 0.10, but less than 0.25. e.: none of the above solution: e.
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E. None of the above solutions
The probability of 800 or more heads out of 1600 tosses of a fair coin falls into none of the specified ranges. To compute exact probabilities, we can use the normal distribution to approximate the binomial distribution of the numbers.
The average number of heads in 1600 flips is 800, with a standard deviation of about 25.8. Using the normal distribution, we can compute the probability of more than 800 tables as follows:
P(X > 800) = 1 - P(X <= 800)
Using a standard regular table or calculator, we find that P(X <= 800) is approximately 0.5. So the probability of getting more than 800 heads is 1 - 0.5 = 0.5 or 50%. Since this is not in any given range, the correct answer is
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Solve for x.Leave your answer I simplest radical form
Answers
Answer:
x=sqrt(28)
Step-by-step explanation:
x^2+2^2=9^2-7^2
x^2=28
x=sqrt(28)
A square with side length 5.5 mm is increased by a factor of 11. What will be the perimeter of the square after dilation?
22 mm
60.5 mm
242 mm
2,662 mm
Answers
Answer:
The perimeter of the square after dilation will be 242 mm
Step-by-step explanation:
\(5.5*11 = 66.5\\P = 4s\\P = 4(66.5mm)\\P = 242mm\)
Answer:
its c
Step-by-step explanation:
got it right on edge
Please helped me
Please I need help ^_^:-{^_^:-{^_^:-{^_^:-{^_^:-{^_^
Answers
Answer:
A. 8
Step-by-step explanation:
This is just an educated guess
If a0=10 and an+1=-5an then find the value of a4
Answers
The value of a4 would be equal to -666.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that \(a_0=10\) and \(a_n+1=-5a_n\)
This is a recursive formula. So we can simply substitute in each value. For instance, a₂
Use the recursive definition repeatedly.
a2 = -5(6) +4 = -26
a3 = -5(-26) +4 = 134
a4 = -5(134) +4 = -666
Therefore, the value of a4 is -666
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please help image attached! x=?
Answers
Answer:
90°
Step-by-step explanation:
from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.
I am very confused on this topic, it would mean the world to me if you can explain it thoroughly with understandable words for a kidPlease do number 5 and if you can number 6 so I can comprehend more. Thanks
Answers
The first step in solving the exercise is to replace the given value of b into the equation:
\(\begin{gathered} 65\div b+8\cdot4=20 \\ \frac{65}{b}+8\cdot4=20 \\ \frac{65}{5}+8\cdot4=20 \end{gathered}\)Now, we follow the PEMDAS order, that is, first multiplications and divisions and then the addition:
\(\begin{gathered} \frac{65}{5}+8\cdot4=20 \\ 13+32=20 \\ \boldsymbol{45\neq20}\text{ }\Rightarrow\text{ "}\ne\text{" reads "different"} \end{gathered}\)Finally, since 45 is different from 20, then the given value of the variable is not a solution to the equation.
PLEASE HELP WITH THESE QUESTIONS
1) What are the three forms of quadratic functions?
2) For each of the three forms, when would it be most convenient to have the function in that form?
3) Create a quadratic function in one of the forms and show how to convert it to another one of the three forms.
Answers
Answer:
I only know number 1
vertex form, standard form and factored form
write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
1. What would the slope of a line that is parallel to the line in the graph be?
(4,3)
X
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}\)
answer for brainliest
Answers
What is 1/2 of some number?
(By the way this is translating to an algebraic expression)
Answers
Answer:
1/2(x)
Step-by-step explanation:
Let's break down the question.
1/2 = 1/2, of course
of = multiplied by
some number = x
Given the information above, we multiplying 1/2 by x. This can be algebraically written as 1/2(x).
Have a lovely rest of your day/night, and good luck with your assignments! ♡
HOMEWORK iwiwieiwieieie
Answers
Step-by-step explanation:
Hello
According to fithaghores law:
\( {a}^{2} + {b}^{2} = {c}^{2} \)
So
\( {5}^{2} + {12}^{2} = 25 + 144 = 169 \\ {c}^{2} = 169 \\ c = \sqrt{169 } = 13\)
Let's continue
Tan A = a/b= 5/12
So A is about 22 or 23 degrees.
You know sum of the triangle angles are 180
So sum 90 +23
Then 180-(90+23)=180-113=67
B is about 67 degrees.
I hope this help you.
The price structure in a store is such that, for every $100 of sales, $40 is the cost of the goods sold and $45 goes to overhead costs.
For an item with a wholesale cost of $119, determine:
a. Its selling price. (Round your answer to the nearest cent.)
Selling price $
b. The rate of markup on cost. (Round your answer to one decimal place.)
Rate
%
c. The rate of markup on selling price. (Round your answer to one decimal place.)
1%
Rate
d. The operating profit on the item. (Round your answer to the nearest cent.)
Profit
$
Answers
9514 1404 393
Answer:
a. $297.50
b. 150%
c. 60%
d. $14.88
Step-by-step explanation:
We are given that $100 of selling price breaks down to ...
cost: $40
operating profit: $100 -40 -45 - $5
markup: $100 -40 = $60
__
a. The selling price is $100/$40 = 2.5 times the cost.
selling price = 2.5 × $119 = $297.50
__
b. The ratio of markup to cost is ...
markup/cost = $60/40 = 1.5 = 150%
__
c. The ratio of markup to selling price is ...
markup/selling price = $60/$100 = 0.60 = 60%
__
d. The ratio of profit to cost is ...
profit/cost = $5/$40 = 1/8
Then the operating profit on this item is ...
$119 × 1/8 = $14.875 ≈ $14.88
The least common denominator is: (x − 4)(x + __ )(x −__ )
Answers
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answers
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
According to this diagram, what is tan 62 degrees ?
Answers
Answer:
According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.
What is the right angle triangle property?
In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.
Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.
The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.
Re-draw, the Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.
In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.
The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,
Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.
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You and your friends bought some movie tickets. Each movie ticket cost $6.32 per person. You also spent $14.00 on popcorn. If you and your friends spent a total of $45.60, how many total tickets were purchased?
Answers
Answer:
Step-by-step explanation:
10
What is the slope of the line?
Answers
Answer:
2
Step-by-step explanation:
Rise over run.
The line goes up two and over one. So you get 2/1. Then you can just get rid of the denominator. 'Cause that's how fractions work. You can get rid and add 1 as a denominator.
Answer:
The slope is 2.
Step-by-step explanation:
Let me know if you need an explanation.
hope this helps and is right :)
A bag contains n cards, each having numbers (1,2,3...,n) written on it. If all numbers are used, the probability of drawing a card with a number less than or equal to 4 is 1/6. How many cards are in the bag?
Answers
Step-by-step explanation:
There are 4 cards less than or equal to 4.
1/6 = 4/n
n = 24
What is the solution of the inequality x3 + 3x2 > 7x + 6?
Answers
Answer:
Inequality form : - 5 + squareroot13 / 2 < x < - 5- squareroot13 / 2 or x > 2
Step-by-step explanation: Solve the inequality by finding the roots and creating test intervals.
I hope this helps you out! :)
The solution to the inequality is \(\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2\).
The Interval Notation is \(\rm \left (\dfrac{-5+\sqrt{13} }{2} , \dfrac{-5-\sqrt{13} }{2} \right ) \cup (2, \infty)\).
What is inequality?In Mathematics, the relationship between two values that are not equal is defined by inequalities.
The given inequality is;
\(\rm x^3 + 3x^2 > 7x + 6\)
The solution to the inequality is determined in the following steps given below.
\(\rm x^3 + 3x^2 > 7x + 6\\\\\rm x^3 + 3x^2-7x-6 > 7x + 6-7x-6\\\\ x^3 + 3x^2-7x-6 > 0\\\rm \\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\ \rm x^3+5x^2+3x-2x^2-10x-6 > 0\\\\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\\rm (x-2)(x^2+5x+3) > 0\)
Now finding the roots of the inequality;
\(\rm (x-2)(x^2+5x+3) > 0 \\\\(x-2) \left (\dfrac{-5\pm\sqrt{25-12} }{2} \right )\\\\(x-2)\left (\dfrac{-5+\sqrt{13} }{2} \right )\left (\dfrac{-5-\sqrt{13} }{2} \right )\)
Hence, the solution to the inequality is \(\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2\).
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Wanda pays $19.50 per month for her gym membership. She can take yoga classes at her gym that
cost an additional $8 per class. At the end of January, she paid $43.50 in total. How many yoga classes
did Wanda take in January? Write and solve an equation.
Answers
Answer: She took 6 yoga classes
Step-by-step explanation: So first
Subtract
$43.50 - $19.50 = $24
Carry then Divide
$24 / 8 = 6 Classes
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Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
Answers
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
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Solve the system of linear equations using substitution. Use a pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning.
x=4y-9
x+4y=3
Answers
Answer:
(- 3, 1.5)
--------------------------
Given system:
x = 4y - 9x + 4y = 3The first expression is ready to be substituted as no further operation is required to simplify it.
4y - 9 + 4y = 38y - 9 = 38y = 12y = 12/8y = 1.5Find x:
x = 4*1.5 - 9x = 6 - 9x = - 3