Answer:
a=0.41
Step-by-step explanation:
7(a-10)=13-202a+3
7a-70=13+3-202a
7a-(-202a)-70=16
7a+202a=16+70
209a=86
a=86/209
a=0.41
To solve the equation 7(a - 10) = 13 - 202a + 3, begin by simplifying both sides of the equation and combining like terms. Then isolate the variable 'a' to one side and the constant terms to the other. Finally, divide both sides by the coefficient of 'a' to solve for 'a'.
Explanation:To solve the equation 7(a - 10) = 13 - 202a + 3, you can start by simplifying both sides of the equation. Expand the terms on the left side by distributing the 7 to the terms inside the parentheses. Combine like terms on both sides of the equation. Then, isolate the variable by moving all the terms with 'a' to one side of the equation and all the constant terms to the other side. Finally, divide both sides of the equation by the coefficient of 'a' to solve for 'a'.
Step-by-step solution:
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write an integer for $50 withdrawal
Answer: -50
Step-by-step explanation: A withdrawal means that you're decreasing the amount of money you have.
So a withdrawal of $50 can be written as -50.
The price of a train ticket consists of an initial fee plus a constant fee per stop.
The table compares the number of stops and the price of a ticket (in dollars).
Stops Price (dollars)
3 6.50
7 12.50
11 18.50
What is the initial fee?
The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.
Explanation:To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.
To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.
Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).
By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.
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Hector spent three force of this money the day after he cashed his paycheck of $50 let him represent the amount of money Hector spent
Answer:
Hector has spent $37.5.
Step-by-step explanation:
Given:
Total money he cashed = $50
Also Given:
Hector spent [tex]\frac{3}{4}[/tex] of his money the day after he cashed his paycheck of $50.
Let 'm' be the amount of money hector spent.
Now according to question;
amount of money hector spent is equal to [tex]\frac{3}{4}[/tex] times the amount of money he cashed his paycheck.
framing in equation form we get;
[tex]m =\frac{3}{4}\times 50 = \$37.5[/tex]
Hence hector has spent $37.5.
The coordinates of the vertices of triangle ABC are A (1,-1),B (1,4), and C (8,4). what is the length in units of the line segment that connects vertex A and vertex B
The length of the line segment that connects vertex A and vertex B is 5 units
Step-by-step explanation:
Let us revise some facts about the horizontal and vertical segments
The segment is horizontal if the y-coordinates of all points on the segment are equalThe length of the horizontal segment whose endpoints are [tex](x_{1},y)[/tex] and [tex](x_{2},y)[/tex] is [tex]x_{2}-x_{1}[/tex]The segment is vertical if the x-coordinates of all points on the segment are equalThe length of the vertical segment whose endpoints are [tex](x,y_{1})[/tex] and [tex](x,y_{2})[/tex] is [tex]y_{2}-y_{1}[/tex]In Δ ABC
∵ A = (1 , -1)
∵ B = (1 , 4)
∵ C = (8 , 4)
∵ The x-coordinate of point A = 1
∵ The x-coordinate of point B = 1
∴ The x-coordinates of points A and B are equal
- The x-coordinates of A and B are equal, then the line AB is a
vertical segment
∴ The length of AB is the difference between the y-coordinates
of points A and B
∵ The y-coordinate of point A = -1
∵ The y-coordinate ob point B = 4
∴ The length of AB = 4 - (-1)
∴ The length of AB = 4 + 1
∴ The length of AB = 5 units
The length of the line segment that connects vertex A and vertex B is 5 units
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Answer:
5 units
Step-by-step explanation:
What is 6x+4x-3x the x's are variables so can someone please help me please help me
Answer:
[tex]6x + 4x - 3x = 10x - 3x = 7x[/tex]
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)? The graph of y = f(x) will shift up 6 units. The graph of y = f(x) will shift down 6 units. The graph of y = f(x) will shift left 6 units. The graph of y = f(x) will shift right 6 units.
Answer:
The graph of y = f(x) will shift left 6 units, as shown in figure a.
Step-by-step explanation:
A translation means we are able to move the graph of a function up or down - normally called Vertical Translation - and right or left - commonly called Horizontal Translation.
If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the x, so it is f(x + 6).
For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.
So, the graph of y = f(x) will shift left 6 units.
Keywords: graph shift, translation
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The graph of y = f(x) will shift left 6 units. The correct option is the third one.
Which is the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)?For any function y = f(x), we define an horizontal translation of N units as:
y = f(x + N)
Where if:
N > 0, the translation is to the left.
N < 0, the translation is to the right.
Here we have:
y = f(x + 6)
So this is a translation of 6 units to the left.
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20% tip on a bill of 31.60
Answer:
6.32
Step-by-step explanation:
There's an easy trick for this. Move the decimal point once to the left, and then multiply by 2.
31.60 turns into 3.16 (which is 10% btw)
Multiply 3.16 by 2 and you get 6.32, or 20% of 31.60. Hope this helped!
an object travels along a horizontal straight path at a constant rate the object travels 1/20 of the length of the path in 3/4 seconds at that rate how many seconds does it take the object to travel the entire length of the path
Answer:
15 sec.
Step-by-step explanation:
Given: Object travels 1/20 of the length of the path in 3/4 seconds.
Let the entire length of the path be "x".
Now, solving to find the total time taken to travel entire length.
First step, Object travel= [tex]\frac{1}{20}\times x = \frac{x}{20}[/tex]
Next putting the value in the ratio of Length: time.
[tex]\frac{\frac{x}{20} }{\frac{3}{4} }[/tex]
And another ratio of entire length and total time
[tex]\frac{x}{Total\ time}[/tex]
Now, using scissor method fractioning to solve the ratio or fraction
⇒[tex]\frac{\frac{x}{20} }{\frac{3}{4} }= \frac{x}{Total\ time}[/tex]
To divide fraction, take reciprocal of the divisor and multiply the dividend.
⇒ [tex]\frac{x}{20} \times \frac{4}{3} = \frac{x}{Total\ time}[/tex]
⇒[tex]\frac{4x}{20\times 3} = \frac{x}{Total\ time}[/tex]
Cross multiplying both side.
⇒ [tex]Total\ time= \frac{20x\times 3}{4x}[/tex]
⇒ [tex]Total\ time= \frac{20\times 3}{4}[/tex]
⇒[tex]Total\ time= 5\times 3= 15\ sec[/tex]
∴ Total time taken by Object to travel entire length is 15 sec.
an = 12 – 5(n − 1)
What is the 30th term of the sequence?
Answer:
- 133
Step-by-step explanation:
To find the 30 th term substitute n = 30 into the formula, that is
[tex]a_{30}[/tex] = 12 - 5(30 - 1) = 12 - (5 × 29) = 12 - 145 = - 133
Final answer:
The 30th term of the sequence defined by an = 12 – 5(n – 1) is – 133.
Explanation:
To calculate the 30th term of the sequence given by an = 12 – 5(n – 1), we start by substituting the value of n with 30.
[tex]a_{30}[/tex] = 12 – 5(30 – 1)
[tex]a_{30}[/tex] = 12 – 5(29)
[tex]a_{30}[/tex] = 12 – 145
[tex]a_{30}[/tex] = – 133
The 30th term of the sequence is – 133.
Practice 0.4+y_>7 answer plssss
For this case we have the following inequality:
[tex]0.4 + y\geq 7[/tex]
If we subtract 0.4 from both sides of the inequality we have:
[tex]y \geq7-0.4\\y \geq6.6[/tex]
Thus, the solution is given by all the values of "y" greater than or equal to 6.6.
The graph of the solution is attached.
Answer:
[tex]y\geq6.6[/tex]
1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct
variation.
Answer:
Yes, y varies directly with x.
[tex]y=\frac{11}{8} x[/tex]
Step-by-step explanation:
[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]
Hence [tex]y[/tex] varies directly with [tex]x[/tex].
[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]
Question 2 (6 points)
You invest $15,000 in a savings account with an annual interest rate of 2.5% in
which the interest is compounded quarterly. How much money should you expect to
have in the account after 5 years? Show your work to receive full credit!
Answer:
$16,991
Step-by-step explanation:
Rate = r = 2.5%
Times = b = 4
A = P [1 + (r / b)]ⁿᵇ
A = $15,000 [1 + (0.025 / 4]⁵ ˣ ⁴
A = $15,000 [1 + 0.00625]²⁰
A = $15,000 [1.00625]²⁰
A = $15,000 x 1.132708
A = $16,991
Suppose that y varies inversely with x, and y=2 when x=10.
(A) write an inverse variation equation that relates x and y
(b) find y when x= 4
Answer:
see explanation
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
(A)
To find k use the given condition y = 2 when x = 10
k = yx = 2 × 10 = 20, thus
y = [tex]\frac{20}{x}[/tex] ← equation of variation
(B)
When x = 4, then
y = [tex]\frac{20}{4}[/tex] = 5
5. Find the sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4
Answer:
The sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4 is 2555.
Step-by-step explanation:
Given:
a = 5
d = 4
To Find :
The sum of first 35 terms of the arithmetic sequence = ?
Solution:
Step 1 : finding the 35th term
[tex]a_n = a_1 +(n-1)d[/tex]
[tex]a_35 = 5 +(35-1)4[/tex]
[tex]a_35 = 5 +(34)4[/tex]
[tex]a_35 = 5 +136[/tex]
[tex]a_35 = 141[/tex]
Step 2: Finding the sum of first 35 terms
[tex]S_n = \frac{n(a_1 +a_n)}{2}[/tex]
Substituting the values
[tex]S_n = \frac{35(5+141)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{5110)}{2}[/tex]
[tex]S_n = 2555[/tex]
how many times dose 10 go into 450
Answer:
10 go into 450 45 times
Step-by-step explanation:
Mr. Jones took a survey of college students and found that 60 out of 65 students are liberal arts majors. If a college has 8,943 students, what is the expected number of students who are liberal arts majors? answer fast
Should be 5812.95 Students
helppppppppppp me pleaseeee
Answer:
Step-by-step explanation:
8) a) No: of sides of a regular polygon = 360° / exterior angle
= 360°/18° = 20 sides
b) Sum of interior angles of regular polygon = (n-2) * 180° {n-no:of sides}
= (20-2)*180° = 18*180° = 32400°
9) Let the exterior angle be x.
So, interior angle = 140° + x
Interior angle + exterior angle = 180°
140° +x + x = 180°
140° +2x = 180°
2x = 180° - 140°
2x =40°
x = 40°/2 = 20°
Exterior angle = 20°
Interior angle = 160°
No: of sides of a regular polygon = 360° / exterior angle
= 360°/20° = 18 sides
Hint: Always sum of exterior angles of regular polygon is 360°
Andrew's rotation maps point M(9, -1) to M'(-9, 1). Which describes the rotation?
180° rotation
270° clockwise rotation
90° counterclockwise rotation
90° clockwise rotation
Answer:
180° rotation
Step-by-step explanation:
sign changes when we rotate a point to 180 degrees. so 9 became -9 and -1 became 1, which gave us the clue that it's 180° rotation
The given situation described 180° rotation
Given information:Andrew's rotation maps point M(9, -1) to M'(-9, 1).
Rotation:Since signing is changed when we rotate a point to 180 degrees. So here 9 became -9 and -1 became 1, which provides us the clue that its 180° rotation.
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Find the value of x in each case. Give reasons to justify your solutions!
B, C ∈ AD
Step-by-step explanation:
DCF is 90°
so to find BCE
BCE+64+90=180
BCE=26°
CBE is (180-3x)
taking triangle BEC
(180-3x)+x+26=180
180-3x+x+26=180
-2x+26=0
-2x=-26
x=13
X-4y=-18
Graphing linear equations
Answer:
as illustrated
Step-by-step explanation:
X-4y= - 18
find 2 points on the line
x = 0 y = 4.5 (0, 4.5)
x = 4 y = 5.5 (4, 5.5)
Answer:
Please Check the image for the answer to your question hope this helps!
4. What is the equation of the midline of the sinusoidal function?
The midline equation for the sinusoidal function is y = 4 sin(ωx + ∅) - 3, derived by calculating the amplitude and vertical shift within the general function equation.
A function is a mathematical expression, rule, or law that defines the relationship between one variable and another. In mathematics, functions play a crucial role in representing physical relationships and various mathematical concepts. One specific type of function is the sinusoidal function, characterized by its repetitive pattern within a specific time interval.
The general form of a sinusoidal function is given by the equation:
y = A sin(ωx + ∅) + c
Here, A represents the amplitude, ω is the argument, ∅ is the phase difference, and c is the vertical shift known as the midline.
To find the equation of the midline, we use the formula:
A = (Maximum value - Minimum value) / 2
Given that the maximum value is 1 and the minimum value is -7, the amplitude (A) is calculated as:
A = (1 - (-7)) / 2 = 4
The vertical shift (c) is determined to be -3. Substituting these values into the general equation, we obtain the equation of the midline for the sinusoidal function:
y = 4 sin(ωx + ∅) - 3
In summary, the equation of the midline for the sinusoidal function is y = 4 sin(ωx + ∅) - 3.
The amplitude and vertical shift inside the general function equation are used to obtain the midline equation for the sinusoidal function, which is y = 4 sin(ωx + ∅) - 3.
A mathematical phrase, rule, or law that establishes the connection between two variables is called a function.
Functions are essential to the representation of both mathematical concepts and physical relationships in mathematics.
The sinusoidal function is one particular kind of function that is distinguished by its repeating pattern inside a predetermined time frame.
The following formula provides the generic form of a sinusoidal function:
sin(ωx + ∅) + c = A
In this case, amplitude is denoted by A, argument by ω, phase difference by ∅, and vertical shift, or midline, by c.
We utilise the to determine the midline's equation.
A is equal to (Maximum - Minimum) / 2.
A = (1 - (-7)) / 2 = 4 is the formula for calculating the amplitude (A), given that the maximum value is 1 and the minimum value is -7.
It is found that the vertical shift (c) is -3. The equation of the midline for the sinusoidal function is obtained by substituting these values into the general equation: y = 4 sin(ωx + ∅) - 3
In conclusion, y = 4 sin(ωx + ∅) - 3 is the equation of the midline for the sinusoidal function.
1. 4/5 - (-3/10)=
2. 5.5 - 8.1=
3. -5 - 5/3=
4. -8 3/8 - 10 1/6=
5. -4.62 - 3.51=
Answer:
Step-by-step explanation:
4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10
5.5-8.1=-2.6
-5-5/3=-15/3-5/3=-20/3
-8 3/8-10 1/6=-67/8-61/6=-445/24
-4.62-3.51=-8.13
Ryan has $40 in the bank. He writes
a check for $64.75 and then uses his
check card to buy gas for $40. What is
his new balance?
Show work and explain clearly
Susie and jack are on a basketball team. The total amount of points scored was 86. If Susie has 5 more than as many points as jack then how many points do they each have
Answer:
The points each have scored are Susie 45.5 points and jack 40.5 points.
Step-by-step explanation:
Given:
Susie and jack are on a basketball team.
The total amount of points scored was 86.
Susie has 5 more than as many points as jack.
Now, to find the points they each have:
Let the points of jack be [tex]x[/tex].
Then the points of Susie be [tex]5+x[/tex].
There total points scored = 86.
According to question:
[tex]x+(x+5)=86.[/tex]
⇒ [tex]x+x+5=86.[/tex]
⇒ [tex]2x+5=86.[/tex]
Subtracting both sides by 5 we get:
⇒ [tex]2x=81.[/tex]
Dividing both sides by 2 we get:
⇒ [tex]x=40.5.[/tex]
Jack scored = 40.5 points.
Putting the value of [tex]x[/tex] to get the points of Susie:
[tex]x+5[/tex]
⇒ [tex]40.5+5 = 45.5[/tex]
Susie scored = 45.5 points.
Therefore, the points each have scored are Susie 45.5 points and jack 40.5 points.
Rewrite the following linear equation in slope-intercept form. Write youk
answer with no spaces.
y+4= -2(x - 1)
Answer:
y=-2x-2
Step-by-step explanation:
y+4=-2(x-1)
y+4=-2x+2
y=-2x+2-4
y=-2x-2
the slope of y+4=3/5(x-7
Answer:
3/5
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
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
y + 4 = [tex]\frac{3}{5}[/tex](x - 7) ← is in point- slope form
with slope m = [tex]\frac{3}{5}[/tex]
Write 2x^2+7x -3 in the form of a(x+m)^2 +n
Answer: Search it up
Step-by-step explanation:
It shows you all the steps and will help you
Luke sells you cars for $12 each. His expenses are $3.50 per car, plus $34 for tools. How many cars must he sell for his revenue to equal his expenses?
Answer:
Step-by-step explanation:
x = number of cars
12x = 3.50x + 34
12x - 3.50x = 34
8.5x = 34
x = 34/8.5
x = 4 <=====he would have to sell 4 cars
In this case, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
To determine how many cars Luke must sell for his revenue to equal his expenses, let's define the variables and set up the equation.
Let x be the number of cars Luke sells.
Revenue:
Luke sells each car for $12, so his revenue for selling x cars is:
[tex]\[ \text{Revenue} = 12x \][/tex]
Expenses:
Luke's expenses include $3.50 per car and a fixed cost of $34 for tools. So his total expenses for x cars are:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
We need to find the number of cars x such that his revenue equals his expenses:
12x = 3.50x + 34
To solve for x subtract 3.50x from both sides:
12x - 3.50x = 34
8.50x = 34
Now, divide both sides by 8.50:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
x = 4
Therefore, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
william drives 55 mph to abilene. How many miles will we have driven after driving for 3 hours
Answer:
165
Step-by-step explanation:
55* 3 = = 165
Isabel will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an additional $0.13 per mile driven.
The second plan has an initial fee of $55 and costs an additional $0.11 per mile driven.
For what amount of driving do the two plans cost the
To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.
Explanation:To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:
Total cost = $46 + $0.13x
The total cost for Plan 2 can be calculated as:
Total cost = $55 + $0.11x
We can set the two equations equal to each other and solve for x:
$46 + $0.13x = $55 + $0.11x
$0.02x = $9
x = $9 / $0.02 = 450
Therefore, the two plans cost the same for 450 miles of driving.