Answers
Answer:
[tex]\textsf{a.} \quad b=\dfrac{120}{23}-\dfrac{17}{23}h[/tex]
[tex]\textsf{b.} \quad h=\dfrac{120}{17}-\dfrac{23}{17}b[/tex]
Step-by-step explanation:
Given equation:
[tex]5.75b + 4.25h = 30[/tex]
Part aTo solve the equation for b, subtract 4.25h from both sides:
[tex]\implies 5.75b + 4.25h -4.25h= 30-4.25h[/tex]
[tex]\implies 5.75b = 30-4.25h[/tex]
Divide both sides by 5.75:
[tex]\implies \dfrac{5.75b}{5.75} = \dfrac{30-4.25h}{5.75}[/tex]
[tex]\implies b= \dfrac{30-4.25h}{5.75}[/tex]
[tex]\implies b= \dfrac{30}{5.75}-\dfrac{4.25h}{5.75}[/tex]
[tex]\implies b=\dfrac{120}{23}-\dfrac{17}{23}h[/tex]
Part bTo solve the equation for h, subtract 5.75b from both sides:
[tex]\implies 5.75b + 4.25h -5.75b= 30-5.75b[/tex]
[tex]\implies 4.25h = 30-5.75b[/tex]
Divide both sides by 4.25:
[tex]\implies \dfrac{4.25h}{4.25} = \dfrac{30-5.75b}{4.25}[/tex]
[tex]\implies h= \dfrac{30-5.75b}{4.25}[/tex]
[tex]\implies h= \dfrac{30}{4.25}-\dfrac{5.75b}{4.25}[/tex]
[tex]\implies h=\dfrac{120}{17}-\dfrac{23}{17}b[/tex]
Related Questions
5. The box plot represents the distribution of the number of children in 30 different
familes.
After further examination, the value of 12 is removed for having been recorded in
error. The box plot represents the distribution of the same data set, but with the
maximum, 12, removed.
The median is 2 children for both plots.
a. Explain why the median remains the same when 12 was removed from the data
set.
b. When 12 is removed from the data set, does mean remain the same? Explain
your reasoning
Answers
It should be noted that the median remains the same because removing an extreme value from a data set will not have much effect on the median.
What is meant by Statistical data?Statistical data established on the minimum, first quartile, median, third quartile, and maximum exist shown graphically in a box plot.
The box plot represents the number of kids in 30 distinct households in accordance with the families, and the value of 12 is subtracted for inaccuracy.
Therefore, if there exist two kids in the median for both plots when 12 stood eliminated from the data set, it remained unchanged.
In conclusion, the median stays exact because removing an extreme value from a data set will not have much effect on the median.
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Help me!
It is due tonight!
Answers
9 is a coefficient of u in mathematical expression.
What does a math expression mean?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used.What does an example of a math expression mean?
Mathematical expressions are sentences having a minimum of two numbers or variables, at least one arithmetic operation, and a mathematical concept. Let's examine the writing of expressions. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, the sentence is represented as x/2 + 6.= 7 ( 9u + 2 ) ( 1 + 3 )
In this expression statement 1 is correct and statement 2,3,4,5,6 are false.
9u, 9 is a coefficient of u.
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Nakeisha and Katherine work at a dry cleaners ironing shirts. Nakeisha can iron 20
shirts per hour, and Katherine can iron 10 shirts per hour. Nakeisha and Katherine
worked a combined 10 hours and ironed 140 shirts. Graphically solve a system of
equations in order to determine the number of hours Nakeisha worked, x, and the
number hours Katherine worked, y.
Answers
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an endless number of solutions.
The equations that can be used to calculate how many hours Caleb and Landon work are as follows:Eq. 1: 20c + 10l = 320
Equation 2: c - l = 10
where x = total hours Caleb puts in y hours of work. Landon has a job
The total number of shirts that Caleb and Landon iron in an hour depends on how many hours each of them works overall.
The total number of shirts they can both iron is equal to the product of the number of shirts Caleb can iron in an hour and the number of hours he worked (shirts that Landon can iron in an hour x number of hours Landon worked)
Eq. 1: 20c + 10l = 320
Equations 1 and 2 must be solved jointly because they are simultaneous equations, and doing so will yield the solution.
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If the measure of ZCBD is equal to (5x)° and
the measure of ZDBE is 40°, write an equation
involving x. Then solve it.
=[
+
X =
Answers
The value of x in the angle ∠BCE is 10 so the measure of ∠BCE is 50°.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. Based on the measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.So, the value of x will be:
∠BCE = 5x° and ∠ECD = 40°, and we can see in the diagram that the ∠BCD = 90°.Then, the equation formed will be:
∠BCE + ∠ECD = ∠BCD 5x° + 40° = 90°5x° = 90 - 405x° = 50x = 50/5x = 10So, ∠BCE = 5x° ⇒ 5(10) = 50°.
Therefore, the value of x in the angle ∠BCE is 10 so the measure of ∠BCE is 50°.
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The correct question is given below:
If the measure of ∠BCE is 5x° and the measure of ∠ECD is 40°, write an equation involving x and find the value of x.
In AJKL, m/J = (8x + 6)°, mZK = (2x + 2)°, and m≤L = (4x + 4)°. Find
m/L.
Answers
The angel L in the triangle JKL is measured as 52 degree.
What is triangle?
A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given in the question,
∠J = (8x+6)°
∠K = (2x+2)°
∠L = (4x+4)°
We know that, the sum of the all angles in triangle is 180°
So, in triangle JKL
∠J + ∠K + ∠L = 180
Putting the values from the question. we get,
(8x+6) + (2x+2) + (4x+4) = 180
14x + 12 = 180
(180 - 12)/14 = x
x = 12
Putting the value of x in given value of angle L.
∠L = 4x+4
∠L = 4(12)+4
∠L = 48 + 4
∠L = 52°
Hence the angle L is measured as 52 degrees.
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Find the distance between the pair of parallel lines with the given equations.
y=−5x
y=−5x+26
Answers
The distance between the two parallel lines is 26 units
What is are parallel lines?Parallel lines are lines that do not meet or intersect.
If y = mx +c as the equation of a straight line
For the line y = -5x
comparing with the standard equation of a line,
y = -5x has no y-intercept, so the coordinates of the point is (0,0)
For the second line y = -5x + 26
comparing with the standard equation
The y-intercept is 26, which means the coordinates of the point is (0, 26)
The distance between these two points is the distance between the two lines.
Formula for distance between two point,
D = [tex]\sqrt{(y_{2} -y_{1}) ^{2} + (x_{2} - x_{1}) ^{2} }[/tex]
D = [tex]\sqrt{(26-0)^{2} + (0-0)^{2} }[/tex]
D = 26 units
In conclusion, the distance between the two parallel lines is 26 units
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The telephone company purchased 95 yards of wire for $1,235 in September. They plan on making a purchase of 285 yards in October. How much will the October purchase cost?
Answers
285 yards of wire purchased in October will cost $3705.
We will use unitary method for calculation.
The cost of one yard of wire = total cost ÷ length of wire × unit length
Cost of one yard of wire = 1235 ÷ 95 × 1
Performing division on Right Hand Side of the equation
Cost of one yard of wire = $13
Now calculating the cost for purchase of 285 yards of wire in October.
Cost of wire in October = 285 × 13
Performing multiplication on Right Hand Side of the equation
Cost of wire in October = $3705
Thus, the cost of purchase in October is $3705.
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The numbers 15 and 35 have been
written as the product of their prime
factors.
15
3 × 5
35 = 5 x 7
=
Which of the following represents the
lowest common multiple (LCM) of 15 and
35?
2×3×5
2×5×7
3x5x5×7 3x5x7
Answers
LCM of 15 and 35 = 105
3x5x7 = 105
Answer:
3x5x7
Use the graph to find the value of f (x) when x = 1 for the function f (x) = -x2 - 4.
Answers
Answer: The value of f (1) is -6
Step-by-step explanation:
Substitute the 1 into the equation: f (1) = -(1)2 - 4
f (1) = -2 - 4
f (1) = -6
What is the value of this expression when c = -4 and d = 10? (c²³ +ď²)
Answers
The value of the given expression [tex]\frac{1}{4}(c^{3}+d^{2} )[/tex], when c = -4 and d = 10 is 9
The expression is
[tex]\frac{1}{4}(c^{3}+d^{2} )[/tex]
The expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication.
The expression is
[tex]\frac{1}{4}(c^{3}+d^{2} )[/tex]
The values are
c = -4
d = 10
Substitute the values in the expression
[tex]\frac{1}{4}((-4)^{3}+10^{2})[/tex] = 1/4(-64+100)
Do the arithmetic operation in bracket
= (1/4)×36
Multiply the numbers
= 36/4
Divide the numbers
= 9
Hence, the value of the given expression [tex]\frac{1}{4}(c^{3}+d^{2} )[/tex], when c = -4 and d = 10 is 9
The complete question is
What is the value of this expression when c = -4 and d = 10?
[tex]\frac{1}{4}(c^{3}+d^{2} )[/tex]
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The students in Tammy's class got to choose whether to visit the zoo or the aquarium. 11 students went to the zoo and 9 students went to the aquarium. What is the ratio of the number of students who went to the aquarium to the total number of students?
Answers
Answer:
11 to 20
Step-by-step explanation:
first you get the number 11
second you add 11 and 9 which equals 20
third you make it a ratio which is 11:20 or (11 to 20) and that's your final answer.
How many solutions can be found for the equation 4x = 4x?
a Zero
b One
c Two
d Infinitely many
Answers
Answer:
I think its infinitely many because:
4x=4x
x=4x\4
x=x
--HELP FAST!!! -BRAINLY-
Click ALL the boxes for which each number is classified.
a: −3 3/4 - Integer or Rational Number
b 7/9 - Integer or Rational Number
c -0.75 - Integer or Rational Number
d 3 - Integer or Rational Number
e -3 - Integer or Rational Number
f 2.25 - Integer or Rational Number
- Integer | Rational Number..
HELP FAST!!!
Answers
Each number should be classified as follows:
−3 3/4: rational number.7/9: rational number.-0.75: rational number.3: integer and rational number.-3: integer and rational number.2.25: rational number.The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbers.Real numbersIntegersWhole numbersRational numbersIrrational numbersWhat is a rational number?A rational number simply refers to a type of number which consist of integers, fractions, terminating or repeating decimals such as -3, 3, 1/2, -3 3/4, etc.
Additionally, an integer is a whole number that may either be positive, negative, or zero such as, -3, -2, -1, 0, 1, 2, 3, 4 etc.
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What part of the quadratic formula is the discriminate ?
Answers
Answer:
The discriminant of the quadratic formula is given by
[tex] {b}^{2} - 4ac[/tex]
-57 + 57 I really need the answer
Answers
Answer:
The answer is 0
Step-by-step explanation:
-57 cancels out 57 making it 0.
(03.01 LC)
A theater company charges $5.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets? (1 point)
Answers
Answer: 5.50 (c + a)
Step-by-step explanation:
Solve the following inequality algebraically. [tex] |x - 5| \leqslant 8[/tex]
Answers
The inequality to solve is:
[tex]|x-5|\leq8[/tex]Whenever we have absolute value inequality, we solve it in:
[tex]\begin{gathered} |x|Thus, we can write the problem as:[tex]-8\leq x-5\leq8[/tex]Now, solving it:
[tex]\begin{gathered} -8+5\leq x-5+5\leq8+5 \\ -3\leq x\leq13 \end{gathered}[/tex]
Marlee's job pays her $13.80 per hour plus overtime pay for any additional hours worked above her normal 40 hour work week. Last week, Marlee worked for 68 hours. For each hour of overtime Marlee works,
she earns____.
Her gross pay for the week was____.
Answers
Answer:
938.4 normal time
Step-by-step explanation:
13.8 times 68.also what is overtime pay that no answer
Answer: $20.7 per hour of overtime
$1131.6 gross pay for the week
Step-by-step explanation: traditional overtime pay is 1.5 times regular pay meaning that she earns 13.8•1.5 for her overtime
multiply 13.8 times her regular 40 hour work week plus 28 hours of overtime pay
(13.8•40)+(13.8•1.5)•(hours of overtime)=gross pay
this is all subjective depending on your states overtime laws and if they count overtime as double for hours worked in excess of 48 hours in a week.
I would look at your states overtime laws and work on a conclusion.
if this is the case then the answer would be
(13.8•40)+(20.7•8)+(27.6•20)=gross pay
The graph represents a quadratic function. Write an equation of the function in standard form
Answers
The quadratic quadratic equation represented in the graph has the equation y = 2x² + 7x + 4 .
The values of x that satisfy the equation are the roots or zeros of the expressions on the left side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double origin if there is only one solution. One real double root, two complex solutions that are complicated conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options. A quadratic equation will always have two roots if complex roots are taken into account; a double root counts as two. A quadratic equation can be factored into an equivalent equation.The graph of the function which is quadratic can be represented by the equation in the standard form of
y=ax²+bx+c
The graph passes through the points (-4,0) , (-0.5,0) and (0,4)
Putting the values in the equation we get:
0 = 16a - 4b + c
4 = c
0 = 0.25 a +0.5b + c
Solving the equations we get :
16 a - 4 b = -4
0.25a -0.5 b = -4
a =2 and b = 7
The required quadratic equation is y = 2x² + 7x + 4
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Hey I really need help with this :(
Answers
After Simplification, The final answer is 5.26923077
What is simplification?Reducing a mathematical expression to a simpler version is known as simplification. To simplify, utilize the BODMAS rule.
The letters B, O, D, M, A, and S stand for bracket, of, division, multiplication, and addition, respectively. Simplifying occurs when you explain a difficult mathematical concept to a young child in terms they can grasp. You have streamlined when you do away with many of the activities that were keeping you busy and stressed out.
Here,
[tex]\frac{2.5 \times 13.7}{4.9 + 1.6}\\\\\frac{34.25}{6.5}\\\\5.26923077[/tex]
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The image of point (4,4)under a translation is (6,0). Find the coordinates of the image of the point (1,-4) under the same translation
Answers
The coordinates of the point's image (1,-4) under the same translation are (2, 0)
What is translation?A translation is a geometric transformation that moves all points of a figure, shape, or space by the same amount in the same direction. A translation can also be thought of as adding a constant vector to each point or shifting the coordinate system's origin. A translation is a type of transformation that involves sliding each point in a figure the same distance in the same direction. A translation is a transformation that moves every point in a figure in the same direction by the same amount. For example, this transformation shifts the parallelogram 5 units to the right and 3 units up. It is written as ( x , y ) → ( x + 5 , y + 3 ) .
Therefore,
The coordinates of the point's image (1,-4) under the same translation are (2, 0)
The x coordinate increased by 1, and the y coordinate increased by 4.
Now, do these same transformations to the other point, (1, -4)
x coordinate: 1 + 1 = 2
y coordinate: -4 + 4 = 0
So, the new point is (2, 0)
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Question 10 of 10
Which value of x is in the domain of f(x) = √x – 11?
-
A. X=0
B. x= -4
C. x= 13
D. x = 10
Answers
Answer:
C: x = 13
Step-by-step explanation:
It looks like the question is f(x) = sqrt(x - 11)
DOMAIN
The domain of a function refers to values of x that the function can graph and give a definite y value for. Functions can graph x values that do not result in undefined or complex numbers.
If that is the case then x would have to be greater than or equal to 11 because you can not get the square root of negative numbers unless you want to deal with complex numbers.
13 - 11 >= 0 so it is the answer.
Brad buys a pack of 12 bottles of energy drink for £9.25
He then sells the 12 bottle for £1 each
Work out Brads percentage profit
Give your answer correct to 2 significant figures
Answers
Answer:
That would be a 30% profit.
Step-by-step explanation:
if you add a ten thousands digit that is 3 times the thousands digit to the number 3,721, what is the new number
Answers
Answer:
the answer is 93,721
the sum of an integer and five times the next consecutive odd integer is -32. Find the value of the lesser integer
Answers
The value of the lesser integer is a = -7
How to find the value of the lesser integer?
Let an integer be = a
Let the next consecutive odd integer (b) = a+2
a + 5( b) = -32
a +5(a+2)= -32
a+ 5a +10 = - 32
6a = -32 -10
6a = -42
a = - 42 /6
a = - 7
The integer a = -7
The next consecutive odd integer (b) = a+2
= -7 + 2
b = -5
So, the value of the lesser integer is a = -7
What is an integer?
The integers are the smallest group and ring of natural numbers. In algebraic number theory, the integers are occasionally designated as rational integers to distinguish them from the algebraic integers, which are more broadly defined. Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The corresponding positive numbers' additive inverses are the negative numbers.To learn more about integers, refer:
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Find the values of x and y
Answers
This is an equilateral triangle since 2 angles are already 60 degrees
one of the sides is 10 so that means all other sides must also equal 10
For x, you make the equation equal to 10, since that’s the value it must equal to
10x-14=10
Add 14 to both sides to leave the x alone
10x=24
Divide both sides by 10 to leave x alone
x=2.4
For Y, you also make the y equal to 10
2y-2=10
Add 2 to both sides to leave the y alone
2y=12
Divide both sides by 2 to leave y alone
y=6
in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds.shifow,removedb8d80da1d80dbeab33a3b645b3904854d9277daeadeae8d9774eb5c43aba0e6aremoved
Answers
in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds . The distance is 2.664 km.
D = distance of marathon = 42.195 km = 42195 m
tw = time taken by winner = 2 h 17 min = 2 (60) + 17 = 137 min = 137 (60) = 8220 sec
Vw = speed of winner
speed of winner is given as
Vw = D /tw = 42195/8220
ts = time taken by second place = 2 h 26 min 14 sec = 2 (60)(60) + (26)(60) + 14 = 8774 s
Vs = speed of second place
speed of second place is given as
Vs = D /ts = 42195/8774
distance of the second place holder from the finish line is given as
D' = Vs (ts - tw)
D' = (42195/8774 )(8774 - 8220)
D' = 2664.24 m
D'= 2.664 km
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Help please guys thanks
Answers
From the figure of the triangle, the length of LK is calculated to be 10
How to calculate the length of LK from the triangleThe knowledge used here is that of similar triangles.
In similar triangles the sizes of the triangles are not equal however the ratio of the sizes are equal
The formula for the similar triangle used here is:
JR / JL = SR / LK
from the given figure
JL = 2JR, SR = 5
plugging the values into the equation gives
JR / 2JR = 5 / LK
1 / 2 = 5 / LK
LK = 10
The length of KL = 10 units
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There are 36 green, 22 white, 30 purple and 14 blue gumballs in the gumball machine. Jon wants to get a white or green gumball.
What is the probability of getting a green gumball?
What is the probability of getting a white gumball?
What is the probability that she will get a white or green gumball?
Answers
Answer: Look below
Step-by-step explanation:
1. Number of green gumballs/ The total amount of gumballs
= 36/102 = 18/51 = 6/17
2. Same formula: 22/102 = 11/51
3. (Green gumballs+ White gumballs) / total
= ( 36 + 22) / 102
= 58/102
= 29/51
4 x + 2 + x = Blank x – 19
Answers
[tex]x = \frac{5 +\sqrt{109} }{2} \text{ or }\\\\ x = \frac{5-\sqrt{109} }{2}[/tex]
How to find x?
4 x + 2 + x = ___ x – 19
⇒ 4 x + 2 + x = x(x) – 19
⇒ 5x+ 2 = [tex]x^{2}[/tex] - 19
⇒ 5x +2 - [tex]x^{2}[/tex] + 19 = 0
⇒ 5x - [tex]x^{2}[/tex] + 21 =0
⇒ -[tex]x^{2}[/tex] + 5x + 21 = 0
[tex]x^{2}[/tex] - 5x - 21 = 0 ----(1)
(1) is of the form [tex]ax^{2} +bx+c=0[/tex]
In (1) a = 1, b = - 5 , c = -21
Applying quadratic formula,
[tex]x = \frac{-b\pm\sqrt{b^{2} -4ac } }{2a} \\\\x = \frac{-(-5)\pm\sqrt{(-5)^{2} -4(-21)} }{2(1)} \\\\x = \frac{(5)\pm\sqrt{25 +84} }{2}\\\\x = \frac{5\pm\sqrt{109} }{2}\\\\x = \frac{5 +\sqrt{109} }{2} \text{ or } \frac{5-\sqrt{109} }{2}[/tex]
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