Write and solve an inequality:
Total(t) = $5.42 + ($1.08/therm)(t) ≤ $87.50.
First, subtract $5.42 from $87.50: then ($1.08/therm)(t) ≤ $82.08
Next, divide both sides by $1.08 per therm:
t ≤ ($82.08) / ($1.08/therm) = 76 therms (maximum). Thus, Rameen's usage could be [0,76] (therms).
Answer:
[0,76]
Step-by-step explanation:
Step 1. Read the problem.
Step 2. Identify what you are looking for.
the number of therms Rameen can buy
Step 3. Name what you are looking for. Choose a variable to represent that quantity.
Let t= the number of therms.
Step 4. Translate. Write a sentence that gives the information to find it. Translate into an inequality.
$5.42 plus $1.08 times the number of therms is less than or equal to $87.50.
5.42+1.08t≤87.50
Step 5. Solve the inequality.
1.08tt≤82.08≤76
Step 6. Check the answer in the problem and make sure it makes sense.
Yes, 5.42+1.08(76)=87.50.
Step 7. Answer the question with a complete sentence.
Rameen can buy no more than 76 therms if he wants his heating bill to be a maximum of $87.50.
Since it is not possible to buy a negative number of therms, the lest number of therms Rameen can buy is 0.
In interval notation, the amount of therms Rameen can buy is [0,76].
Which value for the number makes this statement true? The quotient of a number and five is eight
Answer: The answer is 40
Step-by-step explanation:
Jake and erica were solving a system of equations. They both noticed that the two lines had the same slope. Jake said that because each line in the system had the same slope, the two lines had to be the same, which meant there were infinitely as many solutions to the solutions to the system. Erica disagreed, and said they ahould also look at the y-intercepts before determining how many solutions there were. Who is correct?
Answer:
Erica
Step-by-step explanation:
Two lines with the same (defined) slope will only have infinite solutions if their y-intercepts are the same. Otherwise, the number of solutions (points on both lines) is zero.
Since the 2 lines have the same slope, then the lines are parallel and never intersect. Thus there is no solution to the system of equations
Neither Jake nor Erica are correct.
What is the median of this set of values? 6, 8, 10, 8, 4, 2, 12
The median is the middle number in order of the set of values:
2, 4, 8, 10, 12
8 is the median in the set of values!
Answer:
its 8
Step-by-step explanation:
No
Maria is applying for a summer job. Six employees who do various jobs at the company earn $8.00, $8.50, $9.00, $9.50, $10.00, and $23.50 per hour. In the interview, the boss tells Maria that the median of the hourly wages is $9.25. Is the boss’s statement misleading? Why or why not?
Find the first fourth and tenth terms of the arithmetic sequence described by the givin rule a (n) = -3 + (n -1) (-2.2)
- 3, - 9.6 and - 22.8
to generate the first, fourth and tenth term substitute n = 1, 4, 10 into the rule
a(1) = - 3 + 0 = - 3
a(4) = - 3 - 6.6 = - 9.6
a(10) = - 3 - 19.8 = - 22.8
The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?
a reflection over the x-axis and then a reflection over the y-axis
a reflection over the y-axis and then a 90 degree clockwise rotation about the origin
a 90 degree clockwise rotation about the origin and then a reflection over the y-axis
a 90 degree counterclockwise rotation about the origin and then a reflection over the x-axis
In the attachment, the original parallelogram is shown in red. Its image is shown in blue. The purple parallelogram is the original reflected across the y-axis. You can see that it becomes the blue parallelogram if rotated 90° clockwise around the origin.
The appropriate choice is ...
... a reflection over the y-axis and then a 90 degree clockwise rotation about the origin
Answer:
B. a reflection over the y-axis and then a 90degree clockwise rotation about the origin
Step-by-step explanation:
I just did it, and all was well! :) :) :)
Please help. Question in photo
Answer:
1/8
Step-by-step explanation:
The relations can be written as ...
... blue = (3/5)×shirt
... sale = (5/8)×blue
... medium = (1/3)×sale
Substituting, we get
... medium = (1/3)×((5/8)×((3/5)×shirt)) = (1·5·3)/(3·8·5) × shirt = (1/8)×shirt
_____
1/8 of the shirts in the shop are medium blue T-shirts on sale.
find the equation of the line parallel to y=5x+1 that contains the point (4,8)
The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.
... y = 5x + ___
... 8 = 5·4 + ___
... 8 - 20 = -12 = ___
Your equation is ...
... y = 5x -12
Viete's Formulas - what are they used for?
If we have a quadratic equation 2X^2 + 4X -6 = 0, whose roots are x1=1 and x2=-3 and where a = 2 b=4 and c=-6 then according to Viete's formulas (x1 + x2) = (-b/a) and (x1 • x2) = (c/a).
I suppose these formulas could be used as a double check for calculating the roots but do they serve any other purpose? (I also know there are other Viete's formulas for cubic, quartic, etc. equations).
For quadratics, these formulas are used mainly for factoring.
Your equation can be written as ...
... 2(x² +2x -3) = 0
You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...
... 2(x -1)(x +3) = 0
The roots are then 1 and -3, which sum to -b = -2.
(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)
How do I get this form?
Short answer: you don't.
The linear term in the numerator of the integral means the form shown is not applicable. Rather, you perform the integration using partial fraction expansion.
[tex]\displaystyle\int{\frac{5x+1}{25x^2+60x-13}}\,dx=\int{\frac{5x+1}{(5x-1)(5x+13)}}\,dx\\\\=\frac{1}{35}\int{\frac{5}{5x-1}}\,dx+\frac{6}{35}\int{\frac{5}{5x+13}}\,dx[/tex]
The integral is ...
... (1/35)ln|5x-1| +(6/35)ln|5x+13| +C
_____
If the numerator of your integral were a constant, then the fractions multiplying the separate partial fraction integrals would have the same magnitude and opposite signs. You would end with the difference of logarithms, which could be expressed as the log of a ratio as shown in your problem statement.
adam is three years younger than twice bobs age. in 5 years adams age will be 8 years more than bobs age. what are their 2 ages
Adam will be 14, and it is 8 more than 6.
We have given that,
Adam is three years younger than twice bobs age. in 5 years Adams's age will be 8 years more than bobs age.
We have to determine the what are their 2 ages.
What is the age?The age of majority is the age when children legally become adults.
Adam is 9 years old and Bob is 6.
Twice Bob’s age is 12, and three years younger than that is 9.
If Adam is 9 now then in five years, Adam will be 14, which is 8 more than 6.
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Which of the following is a solution to 2cos x + 1 = 0?
A.
60°
B.
120°
C.
210°
D.
300°
Answer:
B. 120
Step-by-step explanation:
2cos x + 1 = 0
2 cos x = -1
cos x = -1/2
x = cos^1(-1/2)
(cos inverse (-1/2))
x = 120°
5.1(3+2.2x)>-14.25-6(1.7x+4)
Answer:
(-2.5, ∞)
Step-by-step explanation:
You can add the opposite of the right side.
5.1(3 +2.2x) +14.25 +6(1.7x +4) > 0
15.3 +11.22x +14.25 + 10.2x +24 > 0 . . . eliminate parentheses
21.42x +53.55 > 0 . . . . . . . . . . . . . . . . . . collect terms
x + 2.5 > 0 . . . . . . . . . . . . . . . . . . . . . . . . .divide by the coefficient of x
x > -2.5 . . . . . . add the opposite of the constant
(- 2.5, ∞ )
distribute parenthesis on both sides of inequality and simplify
15.3 + 11.2x > - 14.25 - 10.2x - 24
15.3 + 11.2x > - 38.25 - 10.2x ( add 10.2x to both sides )
15.3 + 21.42x > - 38.25 ( subtract 15.3 from both sides )
21.42x > - 53.55 ( divide both sides by 21.42 )
x > - 2.5
solution x ∈ (- 2.5, ∞ )
In this figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠6=75°.
What is m∠3?
m∠3 + m<6 = 180
Given: m∠6 = 75°
so
m<3 + 75°= 180°
m<3 = 105°
Answer:
Here is the answer! Hope I helped! Have a nice day! Really helpful for k12 users! And sorry I am late!!!!
Step-by-step explanation:
Given the graph of a line y=−x. Write an equation of a line which is parallel and goes through the point (8,2).
The slope of y = -x is m = -1. Thus, starting with the slope-intercept form y = mx + b, we substitute -1 for m, 8 for x and 2 for y, to determine the vaue of b:
2 = -1(8) + b, or 10 = b. Then the equation of the line parallel to y = -x and passing thru (8,2) is:
y = -x + 10.
Jacksons rectangular bedroom has an area of 90 ft.². The area of his bedroom is nine times that of his rectangular closet. If the closet is 2 feet wide, what is its links?
The closet area is 1/9 of the bedroom area, so is (1/9)·(90 ft²) = 10 ft².
The width of the closet multiplied by the length is the area.
... length×(2 ft) = 10 ft²
... length = (10 ft²)/(2 ft) = 5 ft
The length of Jackson's closet is 5 ft.
Given any linear equation, explain how to find the slope for a line that is perpendicular to the given equation. please help i suck in math :(
given a linear equation in slope- intercept form y = mx + c
where m is the slope and c the y -intercept
the slope of a line perpendicular to it is - [tex]\frac{1}{m}[/tex]
If equation is y = 2x + 3 ( with slope m = 2 )
then the perpendicular slope = - [tex]\frac{1}{2}[/tex]
Factor. 8a2−2ac+12ab−3bc
A. (2a+3b)(c-4a)
B. (2a+3b)(4a-c)
C. (2a-3b)(4a+c)
D. (2a-3b)(c-4a)
Answer:
B. (2a +3b)(4a -c)
Step-by-step explanation:
Group the terms pairwise, then factor each pair.
... (8a² -2ac) +(12ab -3bc)
2a is a common factor in the first pair of terms; 3b is a common factor in the second pair of terms. We can factor those out.
... = 2a(4a -c) +3b(4a -c)
Then we see that (4a-c) is a common factor in the result. We can factor that out.
... = (2a +3b)(4a -c) . . . . matches selection B
Find absolute value of the following numbers -37, 2.987, 53, -2/3, -45
Drop all the minus signs (change them to +) to get your answers:
37, 2.987, 54, 2/3, 45
I need help with this problem, please help!!!
Answer:
Yes. (See below for explanation.)
Step-by-step explanation:
The number of servings is found by dividing the quantity available by the size of a serving. The quantity of punch is the sum of the quantities of the juices that go into the punch. The serving size of 3/4 cup is the same as 6 ounces, since a cup is 8 ounces. (3/4 × 8 oz = 6 oz)
The quantity available is (64 oz + 28 oz + 76 oz). The serving size is 6 oz. Since the units of numerator and denominator are the same, they cancel, leaving ...
... number of servings = (quantity available)/(serving size)
... = (64 +28 +76)/6 . . . . as shown in the problem statement
_____
It might not be obvious that the above ratio gives the number of servings. However, if you look at the real units, you see how it happens.
[tex]\dfrac{oz}{(\frac{oz}{serving})}= oz\dfrac{serving}{oz}=\dfrac{oz}{oz}serving=serving[/tex]
Raise to the power: (–am)^3
- a³m³
each term inside the parenthesis is raised to the power of 3
note that (- 1 )³ = - 1, thus
(-am)³ = - a³m³
What is the median of the box-and-whisker plot?
A) 36
B) 38
C) 42
D) 43
The median on any box plot is the little dot in the middle of the box so the answer is C)42. So where the line is in the middle of the box it is always going to be the median. The median is in the middle. You can also remember it like this Hey Diddle diddle the medians the middle you add and divide for the mean and the mode is the most.
Answer:
B) 38
Step-by-step explanation:
38 is the first (lower) quartile of the box-and-whisker plot.
I need help with this question
The only factorial expression that is shown properly evaluated is that of selection A.
_____
If you number the terms starting from 0 on the left, you find that 20 is term #3 on the row that has 6 as term #1. In combination notation, this would be
... 6C3 or C(6, 3)
It is computed as
... 6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 20
help asap! will mark brainlyst
Answer:
The answer will be 3.55
Step-by-step explanation:
Answer:
3.55
Step-by-step explanation:
26.30 - 22.75 = 3.55
So, you got it right.
[tex]Echy[/tex]
Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate of the intersection point of the lines in terms of m and b.
The x-coordinate of the intersection point of two perpendicular lines, one with equation y = mx + b and the other with equation y = -x/m - b, is given by x = 2b/(m + 1/m).
Explanation:Given two perpendicular lines, one has the equation y = mx + b. The y-intercept of this line is b, and the slope is m. The equation of the second line, which is perpendicular to the first, will have a negative reciprocal slope, -1/m, and for opposite y-intercepts, we'll assume its y-intercept to be -b. Thus the equation of the second line is y = -x/m - b.
For the intersection point, equal the y-values of the two equations: mx + b = -x/m - b. Simplify to obtain the x-coordinate of the intersection point:
mx + x/m = 2b or x(m + 1/m) = 2b. Therefore, the x-coordinate of the intersection point is x = 2b/(m + 1/m).
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To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, set the equations of the lines equal to each other and solve for x.
Explanation:To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, we need to find the equations of both lines. Let's assume the equation of one line is y = mx + b. Since the lines are perpendicular, the slope of the other line will be the negative reciprocal of m. Let's call the slope of the other line n. Therefore, the equation of the other line will be y = -nx + c, where c is the y-intercept of the second line. To find the x-coordinate of the intersection point, we can set the two equations equal to each other and solve for x:
mx + b = -nx + c
x(m + n) = c - b
x = (c - b)/(m + n)
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What describes a rational number? please be specific and show examples of the number ASAP!! XD
6th Grade Line Graph-will give brainliest
At a basketball game, student tickets are sold for $4.50 each.
a) Write an equation that models the income y from the sale of x student tickets.
b) How many student tickets must be sold to have $1125 in student ticket sales?
Show all work
what is the equation of a line, in point-slope form, that passes through (5, -3) and has a slope of 2/3? please help me
y + 3 = [tex]\frac{2}{3}[/tex] (x - 5)
the equation of a line in point- slope form is
y - b = m ( x - a )
where m is the slope and (a, b) a point on the line
here m =[tex]\frac{2}{3}[/tex] and (a,b) = (5 , - 3 )
y + 3 = [tex]\frac{2}{3}[/tex] (x - 5 ) ← in point-slope form
The equation of the line that passes through the point (5, -3) and has a slope of 2/3 is y = 2/3x - 19/3, using the point-slope form for the equation of a line.
Explanation:
The line that you're looking for can be represented using the point-slope form of a linear equation. This form is written as y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and 'm' is the slope of the line. For a line that passes through the point (5, -3) and has a slope of 2/3, you replace x1 with 5, y1 with -3, and m with 2/3. So, the equation of the line becomes y - (-3) = 2/3(x - 5), which simplifies to y + 3 = 2/3x - 10/3. Further simplifying, we get y = 2/3x - 10/3 - 3, or y = 2/3x - 19/3.
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7/10=x/100 Show work please
First you had to switch sides of equation form.
[tex]\frac{x}{100}= \frac{7}{10}[/tex]
Then you multiply by one-hundred from both sides of equation form.
[tex]\frac{x}{100}*100= \frac{7}{10}*100[/tex]
And finally, simplify by equation.
[tex]\frac{x}{100}*100=x[/tex]
[tex]\frac{7}{10}*100=70[/tex]
[tex]70*1=70[/tex]
[tex]x=70[/tex]
Final answer: [tex]\boxed{x=70}[/tex]
[tex]70/10=7[/tex]
[tex]70/7=10[/tex]
[tex]10*7=70[/tex]
[tex]7*10=70[/tex]
Hope this helps!
And thank you for posting your question at here on brainly, and have a great day.
-Charlie
x = 70
given [tex]\frac{7}{10}[/tex] = [tex]\frac{x}{100}[/tex] ( cross-multiply )
10x = 7 × 100 = 700 ( divide both sides by 10 )
x = [tex]\frac{700}{10}[/tex] = 70