Answers
Domain:
[tex]v+12\neq0\\\\\boxed{v\neq-12}[/tex]
[tex]9=\dfrac{v+4}{v+12}\quad|\cdot(v+12)\\\\\\9(v+12)=v+4\\\\9v+108=v+4\\\\9v-v=4-108\\\\8v=-104\quad|:8\\\\\boxed{v=-13}[/tex]
4)
[tex]7-(5t-13)=-25\\\\7-5t+13=-25\\\\-5t=-25-7-13\\\\-5t=-45\quad|:(-5)\\\\\boxed{t=9}[/tex]
5)
[tex]-3(7p+5)=27\\\\-21p-15=27\\\\-21p=27+15\\\\-21p=42\quad|:(-21)\\\\\boxed{p=-2}[/tex]
6)
[tex]14+13y=20y-21\\\\13y-20y=-21-14\\\\-7y=-35\quad|:(-7)\\\\\boxed{y=5}[/tex]
7)
[tex]\dfrac{-8-3k}{2}=11\quad|\cdot2\\\\-8-3k=22\\\\-3k=22+8\\\\-3k=30\quad|:(-3)\\\\\boxed{k=-10}[/tex]
8)
[tex]-15b+21+5b=-19\\\\-15b+5b=-19-21\\\\-10b=-40\quad|:(-10)\\\\\boxed{b=4}[/tex]
Related Questions
The length of rectangle is 6 feet greater than the width. the perimeter is 40 ft. find the dimensions of the rectangle.
Answers
if L is 6 great than W
L=6+W
and P=40
subsitute 40 for P and 6+W for l
40=2(6+W+W)
40=2(6+2W)
divide both sides by 2
20=6+2W
minus 6 both sides
14=2W
divide both sides by 2
7=W
W=7
sub back
L=6+W
L=6+7
L=13
the rectangle has a length of 13ft and width of 7ft
If the length of a rectangle is 6 ft greater than the width and the perimeter is 40 ft , then the dimensions of the rectangle will be 6ft x 7ft.
What is the Area of Rectangle?
The area of the rectangle is length times of width.
Let the Length and Width of the rectangle be 'L' and 'B' , then the dimensions of the rectangle will be L x B
Given data , we have L = 6 + B
The perimeter of the rectangle = 40 ft
= 2 x ( L + B ) = 40 ft
= 2 x ( 6 + B + B ) = 40 ft
= ( 6 + 2B ) = 20 ft
Substract both sides by 6
2B = 14 ft
Divide both sides by 2
B = 7 ft
Now , Length of the rectangle will be L = 6 + 7 = 13 ft
Hence, the dimensions of the rectangle is Length x Width = 13 ft x 7 ft
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Last year, 1300 procedures were performed on 3900 patient visits. 33% of your patient visits involved a procedure. If you are able to increase that percentage to 45%, what is the number of procedures you will do this year?
Answers
y = number of patient visits
n = % (in decimal form)
Note:
Percentage form = 33%
Decimal form = 0.33
Conversion factor: 1 = 100%
Considering the first statement that 33% or 0.33 is derived from dividing 1300 procedures with 3900 patient visits.Then, our working formula is x/y = n.
If we are ask to increase the percentage to 45% or 0.45, then substitute this value to n in the formula. We subsequently get,
x/y = 0.45
Assuming the patient visits remains the same and substitute it in the formula. We subsequently get,
x/3900 = 0.45
Solving for x. We arrive at an answer of x = 1755 procedures.
if the square of a number decreased by the number is 12 then what is the number
Answers
The difference of two supplementary angles is 32 degrees. what are the angles
Answers
180-32=148 hope this helps
Let x and y define the two angles, and let's say x is the larger of the two angles
We can write two equations:
x+y = 180 (definition of supplementary angles)
x-y = 32 (given)
Add the equations together to eliminate y:
------------
2x = 212 [divide both sides by 2]
x=106
The other angle is 180-106 = 74
Find the distance between the given points. A(5, 3) and B(7, -4) Distance =
Answers
d=sqrt(2^2+(-7)^2)
d=sqrt(4+49)
d=sqrt(53)
d=7.28 units
For A(5, 3) and B(7, -4), the distance is is mathematically given as
What is the distance between the given points?Generally, the equation for distance is mathematically given as
[tex]D=\sqrt{(x')^2+(y')^2)}[/tex]
Therefore
[tex]D=\sqrt((7-5)^2+(-4-3)^2)[/tex]
[tex]D=\sqrt{2^2+(-7)^2) }[/tex]
[tex]D=\sqrt(53)[/tex]
D=7.28 units
In conclusion, the distance is
D=7.28 units
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find the measure of an angle between 0 and 360 coterminal with an angle of -271 in standard position. a. 181 b. 271 c. 89 d. 91
Answers
360° - 271° = 89° (answer c)
Answer:
C) 89 degrees
Step-by-step explanation:
Given:
The given angle is -271. which is standard position
We have to subtract 271 from 360 to find the required angle.
= 360 -271
= 89 degrees.
The answer is C) 89 degrees
Hope this will helpful.
Thank you.
A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B. What objective function can be used to maximize the profit?
Answers
Let b = units of B produced
At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.
Therefore
a ≥ 30
b ≥ 10
a + b ≤ 80
Product A yields a profit of $15 and product B yields a profit of $8.
Therefore the objectve profit function is
P(a,b) = 15a + 8b
Answer:
The objective function is
P(a,b) = 15a + 8b, subject to
a >= 30; b>= 10; a+b <= 80
Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.
The maximum profit occurs when a=70 and b=10.
is the answer
Perform the indicated operation. 5 1/6 – 2 2/3
2 1/3
2 1/2
2 1/6
Answers
5 1/6 - 2 2/3
convert to improper fractions:
5 1/6 = 31/6
2 2/3 = 8/3
find common denominator:
8/3 = 16/6
31/6 - 16/6 = 15/6
15/6 = 2 3/6 = 2 1/2
= 5 1/6 - 2 4/6
= 4 7/6 - 2 4/6
= 2 3/6
= 2 1/2
answer
2 1/2
please help me thanks!!
Answers
for the first one, you are adding angles, and for the second, i believe it was suppose to be subtraction
hope this helps
Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir?
Answers
Answer: After 24 minutes Chris begins riding so, he catch up to Samir.
Step-by-step explanation:
Since we have given that
Speed of Samir riding his bike = 6mph
Speed of Chris riding his bike = 9 mph
Time taken by Chris be x
Time taken by Samir be x+12
AS we have given that at any given time ,t, the distance traveled can be using the formula " d=rt "
where d means distance and r represents rate.
So, our equation becomes,
[tex]9x=6(x+12)\\\\9x=6x+72\\\\9x-6x=72\\\\3x=72\\\\x=\frac{72}{3}=24\ minutes[/tex]
As there is no need to change mph into miles per minutes as applying both will nullify the effect.
Hence, after 24 minutes Chris begins riding so, he catch up to Samir.
Anybody know this one?
Answers
Which is correct regarding the statement: “If x is an odd integer, then the median of x , x + 2, x + 6, and x + 10 is an odd number”
A.) the statement is sometimes true
B.) the statement is always false
C.) the statement is always true
D.) there is not enough information provided to answer the question
Answers
x+2 is also odd (consider the example x = 3 so x+2 = 3+2 = 5). Adding 2 to any odd number is always odd
Similarly, so is x+6 (since we have x+2+2+2).
And so is x+10 (x+2+2+2+2+2).
So every value in this list is an odd number. The middle most values are x+2 and x+6 which are both odd.
Adding any two odd numbers together yields an even number. For example 3+5 = 8. Divide this even number in half and we may or may not get an odd number (eg: 8/2 = 4 and 6/2 = 3)
So this statement is sometimes true
the median will be the middle number, if there are 2, then it is the average of the 2 middle numbers when they are arranged in increasing order
we can see that there are 4 numbers, the middle 2 are x+2 and x+6
the average of those is (2x+8)/2=x+4
if x is odd, then we can replace x with 2n+1
2n+1+4=2n+4+1=2(n+4)+1, and n+4 is an integer so that is an odd result, bein 2(n+4)+1 is the same as 2m+1 where m is an integer
the statement is always true
C is answer
Thad and his four family members are going to the fair. admission to the fair costs $8. books of ride tickets are $15. thad has $200. how much money will he have for food and souvenirs?
Answers
And then 5*15=75
And add them together and you get
75+40=115
200-115=85
And you got 85 for food and souvenirs
A total of 518 tickets were sold for the school play. they were either adult tickets or student tickets. there were 68 more student tickets sold than adult tickets. how many adult tickets were sold?
Answers
By setting up two equations based on the total number of tickets and the difference in the number of student and adult tickets, we find that 225 adult tickets were sold for the school play.
To determine the number of adult tickets sold, we can set up two equations based on the information provided. Let A represent the number of adult tickets and S represent the number of student tickets.
The first equation comes from the total number of tickets sold: A + S = 518.
The second equation comes from the additional information about the number of student tickets being greater than adult tickets: S = A + 68.
We can substitute the second equation into the first to solve for A:
A + (A + 68) = 5182A + 68 = 5182A = 518 - 682A = 450A = 450 / 2A = 225Therefore, 225 adult tickets were sold for the school play.
Just wanna check my answers...find (f+g)(x) if f(x)=3x-7 and g(x)=x^2+3x-4
Answers
3x-7+x^2+3x-4
x^2+6x-11
Final answer: x^2+6x-11
I gave 3 packs of baseball cards to my friends. Each friend got 1/3 of a pack. How many friends got baseball cards
Answers
(3/1)*(3/1)=9 friends
In the circle shown below T is the center of the circle, and segments PN and SQ are diameters, and segment PR is tangent to the circle. The measure of angle SQN is 66 degrees
33 degrees
42 degrees
66 degrees
48 degrees
Answers
----------------------------
Use the inscribed angle theorem to get
Minor Arc SN = 2*(angle SQN)
Minor Arc SN = 2*(66)
Minor Arc SN = 132 degrees
----------------------------
Arc PSN is a semicircle so it is 180 degrees, meaning that...
Arc PSN = (minor arc PS) + (minor arc SN)
180 degrees = (minor arc PS) + (132 degrees)
180 = (minor arc PS) + 132
180 - 132 = (minor arc PS) + 132 - 132
48 = minor arc PS
minor arc PS = 48 degrees
central angle RTP = minor arc PS = 48 degrees
----------------------------
Focus on triangle PTR; isolate angle PRT
(angle TPR) + (angle PRT) + (angle RTP) = 180
(90) + (angle PRT) + (48) = 180
(90+48) + (angle PRT) = 180
138 + (angle PRT) = 180
138 + (angle PRT) - 138 = 180 - 138
angle PRT = 42 degrees
----------------------------
----------------------------
Final Answer:
The measure of angle PRT is 42 degrees
What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 in? (round to nearest tenth)
Answers
Area of triangle = 1/2 base x height
15.588 = 1/2 * base x 5.196
15.588 = base x 2.598
base = 15.588 / 2.598 = 6
equi center of triangle = 1/3*5.196 = 1.732
radius of circle = Sqrt(1.732^2 + 3^2) =
sqrt (2.999824 +9) =
sqrt(11.999824) = 3.464
rounded to nearest tenth = 3.5 inches
The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches
Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;
Centroid distance to vertex = ²/₃h
Where h is the altitude of the triangle.
We are given altitude = 5.196 in
Thus;
Centroid distance to vertex = ²/₃(5.196)
⇒ 3.464 inches
Approximating to the nearest tenth gives;
Centroid distance to vertex = 3.5 inches
Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.
Thus; radius = 3.5 inches
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An appliance company uses the function f(h) = 40h + 120 to calculate the total repair bill, f(h), for h number of hours worked. Find h if f(h) = $200.
8,120 hours
8,000 hours
5 hours
2 hours
Answers
200 = 40h + 120
200 - 120 = 40h
80 = 40h
80/40 = h
2 = h <=== 2 hrs
You have a coordinate grid that is 96 x 96. assuming that you encode the x and y coordinate as separate numbers, what is the minimum number of bits that you will need to encode a coordinate in that space?
Answers
To encode a separate x and y coordinate on a 96 x 96 grid, you would need a minimum of 7 bits to represent each coordinate. This is because the nearest power of 2 above 96 is 128, which is 2^7.
Explanation:The subject of this question deals with using binary numbers, or bits, to store data in two-dimensional space, such as with a coordinate grid or a digital image. In this specific case, a coordinate grid with a size of 96 by 96. When encoding the x and y coordinate as separate numbers, we are trying to represent numbers from 0 to 96, so we have 97 different values to represent.
To calculate how many bits you need to store an integer, the question becomes: how many powers of 2 (bits) does it take to store that many different values? The closest power of 2 greater than 96 is 128, which is 2 to the seventh power (2^7). Therefore, you would need a minimum of 7 bits to store a coordinate in that space.
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Find the sum of (x+5)and(2x+3)
Answers
Answer:
3x + 8
Step-by-step explanation:
We have to find the sum of (x+5)and(2x+3).
Write it in sum form
x+5+2x+3
Group the like terms first.
(x+2x)+(5+3)
Combine the like terms
(1+2)x+8
= 3x +8
Therefore, the sum is 3x + 8
The sum of (x+5) and (2x+3) is calculated by adding the coefficients of like terms, which results in 3x + 8.
Explanation:To find the sum of (x+5) and (2x+3), you simply need to add the like terms. The first step is to add the terms that contain the variable x, and then add the constant terms.
Step 1: Add the x terms together: x + 2x = 3x.
Step 2: Add the constant terms together: 5 + 3 = 8.
Step 3: Combine the results from step 1 and step 2 to get the final sum: 3x + 8.
Therefore, the sum of (x+5) and (2x+3) is 3x + 8.
Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. Write these numbers in scientific notation.
Answers
150,000 Hz = 1.5 × 10^5 Hz
Humans can hear up to 20,000 Hz, written as 2.0 x 10⁴ Hz in scientific notation, while dolphins can hear up to 150,000 Hz, written as 1.5 x 10⁵ Hz.
Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. These numbers can be written in scientific notation as follows:
20,000 Hz = 2.0 x 10⁴ Hz
150,000 Hz = 1.5 x 10⁵ Hz
Writing these frequencies in scientific notation helps simplify and understand large numbers easily.
I need help on number 97 please
Answers
since gecko is 1/ the length of an iguana,
that would mean iguanas are twice as long as geckos
so 4*2 = 8 inches for iguanas
|+2|=4 Solve the equation step by step
Answers
2 = 4
Not true.
Find a number such that one-half of the number is 2 less than two-thirds of the number
Answers
Half of the number (x), is equal to 2 less than 2/3rds of the number:
0.5x = (2/3)x -2
1.5x = 2x - 6
-0.5x = -6
0.5x = 6
x = 12
So a number that such that statement is true is 12.
Two or more expressions with an Equal sign is called as Equation. The number is 16 in sentence one-half of the number is 2 less than two-thirds of the number
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
We x be the unknown number which we have to find.
Given,
one-half of the number is 2 less than two-thirds of the number
Which is one-half of the number is x/2
2 less than two-thirds of the number is 2/3 x-2
So let us form a equation
x/2 = 2x/3-2
x/2=(2x-6)/3
Apply cross multiplication
3x=2(2x-6)
Use distributive law on RHS
3x=4x-16
16=4x-3x
16=x
Hence the number is 16 in sentence one-half of the number is 2 less than two-thirds of the number
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John has 305 and he spending 3 each day which algebraic expression describes this situation where d represents the number of days
Answers
d = number of days
hope this helps
Solve 1/r =1/r1+1/r2 for R
Answers
---------
r1r2
r = r1r2
-----------
r2 + r1
The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We have been given a equation as
1/r = 1/r1 + 1/r2
Let r1 = x and r2 = y for an instance, then solve for equivalent r.
Therefore,
1/r = 1/x + 1/y
Solving further;
1/r = (y + x)/xy
Or
r = xy/(x +y)
Now substitute the real values of x and y, we get;
r = xy/(x +y)
r = r1 r2/(r1 + r2)
Hence, The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).
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Evaluate the expression 8√8.41 +1.8
Answers
The value of the expression is 25
What is an expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, 8√8.41 +1.8
8√8.41 +1.8
= 8×2.9 + 1.8
= 23.2 + 1.8
= 25
Hence, the value of the expression is 25
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The approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.
To evaluate the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex], follow these steps:
1. First, approximate the square root of 8.41. The square root of 8.41 is approximately 2.902, because [tex]\( 2.902^2 \approx 8.41 \)[/tex].
2. Now, multiply this approximate square root by 8:
[tex]\[ 8 \times 2.902 \approx 23.216 \][/tex]
3. Finally, add 1.8 to this result:
[tex]\[ 23.216 + 1.8 \approx 25.016 \][/tex]
Therefore, the approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.
The answer is: 25.016.
Circle the letters of the parallel lines.
a. y = - 2/3 x +2
b. y = 2/3 x + 2
c. y =
Answers
----------------------------------------------
Parallel lines have equal slopes. Each answer choice is in the form y = mx+b which is slope intercept form. For choices B and D, we see the slope is m = 2/3. This is why these lines are parallel. The other choices have different slopes (m = -2/3 for choice A; m = 3/2 for choice C)
If g(x) = 3x is graphed on a coordinate plane, what is the y-intercept of the graph?
A. 0
B. 1
C. 2
D. 3
Answers
The y - intercept of the line is 0.
We have f(x) = 3x
We have to find the y - intercept of this function f(x).
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to question, we have -
f(x) = 3x
or
f(x) = 3x + 0
Comparing it with the general equation of a straight line, we get -
y = f(x)
m = 3
c = 0
Here, c is the y - intercept of the line f(x) = 3x.
Hence, the y - intercept of the line is 0.
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