Solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).
How to Solve an Equation?To solve an equation for a given variable is to make the variable the subject of the formula. To do this, isolate the variable to one side of the equation using appropriate properties of equality.
Given the equation,
y = x(ab/a - b)
Multiply both sides by 1/x
y/x = ab/(a - b)
Multiply both sides by (a - b)
y/x × (a - b) = ab/(a - b) × (a - b)
y(a - b)/x = ab
(ay - by)/x = ab
ay - by = abx
ay - by + by = abx + by
ay = abx + by
ay - abx = abx + by - abx
ay - abx = by
a(y - bx) = by
Divide both sides by (y - bx):
a(y - bx)/(y - bx) = by/(y - bx) [division property of equality]
a = by/(y - bx)
Thus, solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).
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Question 1 (Multiple Choice Worth 5 points)
(01.08 MC)
When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic
145-6t if 0≤t≤5
pressure, S(t), can be measured by the following piecewise defined function: S(t)
115 if 5
52+7t if 9≤t≤12
where t is the time, in hours, since taking the medication. Based on the graph of the piecewise function, if the patient
takes the blood pressure medication at 7 a.m., in which interval will their systolic pressure be lowest?
O1 p.m. to 3 p.m.
4 p.m. to 6 p.m.
07 a.m. to 9 a.m.
10 am to 12 p.m.
P
The interval will their systolic pressure be lowest is 4p.m. to 6p.m.
Given that
the effects on the systolic
145-6t if 0≤t≤5
function: S(t)
115 if 5 52+7t if 9≤t≤12
where t= time
the blood pressure medication takes at 7 a.m.
first of all we have to nknow about the Interval.
What is interval?
An interval is a distinct measure of time or the physical or temporal distance between two things.
From the function given above, the lowest systolic pression can be seen from 5 and 8 hours after taken the medication.
Therefore, this will fall into or between the interval of 2pm to 5pm.
And as such, looking at the question, the option that best fit into this time range is 4pm to 6pm.
Therefore, Based on the above, the interval will their systolic pressure be lowest is 4pm to 6pm.
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Identify the location of the values square root of 10, square root of 13, and twenty two ninths on the number line.
Number line with points plotted at two and four tenths labeled point A, three and two tenths labeled point B, and three and six tenths labeled Point C.
Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
Point A is square root of 10, point B is square root of 13, and point C is twenty two ninths.
Point A is twenty two ninths, point B is square root of 13, and point C is square root of 10.
Point A is square root of 10, point B is twenty two ninths, and point C is square root of 13.
The location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be A. Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
How to calculate the square root?The square root of 10 will be 3.16
The square root of 13 will be 3.6
Twenty two ninths will be 22/9 = 2.44
Therefore, the location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
In conclusion, the correct option is A.
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Solve: 1 4/5 x 5/6 =
Group of answer choices
1 3/11
15/30
1 2/3
1 1/2
The multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
In this question, we have been given an expression 1 4/5 x 5/6
We need solve given mathematical expression.
First we write improper fraction 1 4/5 as proper fraction.
1 4/5 = 9/5
So, given expression becomes,
1 4/5 x 5/6
= 9/5 x 5/6
= 9/6
= 3/2
Now we write 3/2 as improper fraction.
If we divide the 3 by 2,then we will get 1 as quotient and 1 as remainder.
3/2 = 1 1/2
Therefore, the multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
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need answers for each question asap
All the questions have been solved in the above pictures 7,8,9,10,11,12 & 13
What is the equation of the line?
y = 4/3x
y = 3/4x
y = - 4/3x
y = - 3/4x
Answer:
y=-4/3x
Step-by-step explanation:
ans would be c y=-4/3x
What is the value of the median? 8, 12, 14, 20
Answer: 14 ==> 3rd option
Step-by-step explanation:
The median is the middle value of a set of ordered numbers. Since this set of numbers from 8 to 20 are already ordered, the median would be the average number between 8 and 20.
(8+20)/2=
28/2=14 ==> 3rd option
Find the least common denominator (LCD) of 5/9 and 6/5.
Please help ASAP!!
Thanks in advance
Answer:
45
Step-by-step explanation:
5/9 = 24/45
6/5 = 54/45
5/9= 5/9× 5/5 = 25/45
6/5 = 6/5 × 9/9 = 54/45
can you guys evaluate this function? I seem to be confused , thank you in advance.
k(z) = 7z^2 + 7 , find k(8z - 2)
z(q) = -10q^2 - 5 , find z(q^2)
Answer: k(8z - 2)=448z^2-224z+35
z(q^2)=-10q^4 - 5
Step-by-step explanation:
k(z) = 7z^2 + 7
k(8z - 2)=7(8z - 2)^2 + 7
k(8z - 2)=7(8z - 2)(8z - 2) + 7
k(8z - 2)=7(64z^2-16z-16z+4) + 7
k(8z - 2)=7(64z^2-32z+4) + 7
k(8z - 2)=7(64z^2-32z+4+1) ==> 7*1=7, so +1 is added in parentheses while +7 is removed outside of parentheses.
k(8z - 2)=7(64z^2-32z+5)
k(8z - 2)=448z^2-224z+35
z(q) = -10q^2 - 5
z(q^2)=-10(q^2)^2 - 5
z(q^2)=-10(q^(2*2)) - 5
z(q^2)=-10q^4 - 5
The length of a rectangular playground is 3x−2 feet while the width is 5x +12 feet. The perimeter of the playground is
The perimeter of the playground is 16x + 20
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l+w)
Given the following
l = 3x-2
w = 5x+12
Substitute to have:
P = 2(3x-2+5x+12)
P = 2(8x + 10)
p = 16x + 20
Hence the perimeter of the playground is 16x + 20
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you find a treasure map Angle is 55 A to B 7 A to C 12
Answer:
55 A
Step-by-step explanation:
Find the value of x in each case
Answer: x = 23
Step-by-step explanation:
Angle in a X shape, the two 'opposite' eachother must be the same so angle HGC is 14
Angle in a Z shape where the lines of the Z are parralell, the two innercorner angles of the Z must be the same os angle GCE must be 14
In triangle GEC we now know two out of the three angles 78 and 14 and we know that angles in a trianlge add up to 180 so the missing angle GEC must be 180-78-14=88
Angles on a straight line must add up to 180 so 4x+88=180
Then this can be used to figure out x
4x+88=180
4x = 92
x = 23
(−x
2
−2x−2)(x
2
+x−3)
The expression is simplified -x^4 -3x³ -x² + 4x + 6
What are algebraic expressions?
Algebraic expressions are expressions consisting of variables, constants, factors and coefficients.
They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc
Given the expression:
(-x² - 2x - 2) (x² + x - 3)
expand the bracket
-x^4 - x³ + 3x² -2x³ - 2x² +6x - 2x² - 2x + 6
collect like terms
-x^4 - x³ - 2x³ + 3x² - 2x² - 2x² + 6x - 2x + 6
Add or subtract like terms
-x^4 -3x³ -x² + 4x + 6
The expansion of the expression is -x^4 -3x³ -x² + 4x + 6
Hence, the expression is simplified -x^4 -3x³ -x² + 4x + 6
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Cant answer this question
give the reason
75% of 210 =
Answer: 157.5
"Of" means to multiply. When multiplying percentages by whole numbers, the percentage becomes smaller. The commonly asked question in scenarios just like this is, "what is x% of y?" where x is the percentage and y is your number you want a percentage out of. This question requires you to use multiplication, because it uses the word, "of".
[tex]\bold{Step-by-step}[/tex]
[tex]\mathrm{"What}[/tex] [tex]\mathrm{is}[/tex] [tex]\mathrm{x\%}[/tex] [tex]\mathrm{of}[/tex] [tex]\mathrm{y?"}[/tex]
[tex]P = (x\% \times y)\\P = (75\% \times 210)\\p = 75\% = 0.75\\P = (0.75 \times 210)\\P = 157.5[/tex]
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The volume of dry goods, like apples or peaches, can be measured usings bushels, pecks, and quarts. A bushel contains 4 pecks, and a peck contains 8 quarts.
What is the relationship between number of bushels, b, and the number of quarts, q? If you get stuck, try creating a table.
The relationship between the number of bushels and the number of quarts is b = 32q.
What is the relationship?The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of a number. The sign used to represent multiplication is x.
The equation that represents the relationship between bushel and pecks is: b = 4p
The equation that represents the relationship between a peck and quarts is: p = 8q
In order to determine the relationship between bushels and quarts, substitute for p in the first equation
b = 4(8q)
Expand the bracket : b = 4 x 8q
b = 32q
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A traffic helicopter flew directly from Point A to Point B in 8 minutes. Did the helicopter travel faster or slower than the driver? Explain or show your reasoning.
The time it takes the driver to travel from Point A to Point B is 8 minutes, the same as the helicopter but through a more longer path, such that, we have;
The helicopter travels slower than the driverHow can the speed of the helicopter and the car be compared?Based on a similar question, the first part required to determine if a driver that drives from Point A to Point B in 8 minutes obeyed the speed limit of 55 miles per hour.
The path of the driver consists of a short path, a bend changing the direction, then a long straight path.
The path of the helicopter is directly from Point A to Point B.
Therefore;
The length of the path of the driver, d1, is longer than that the helicopter, d2, which gives;
d1 > d2
From kinematics, we have;
[tex]Speed = \frac{Distance}{Time} [/tex]
The time taken by the helicopter and the and the driver are equal to 8 minutes, therefore;
[tex] Speed \: of \: the\: driver = \frac{d_1}{8} [/tex]
[tex] Speed \: of \: the \: helicopter = \frac{d_2}{8} [/tex]
[tex] d_1 > d_2 [/tex]
According to the division property of equality, we have;
[tex] \frac{d_1}{8} > \frac{d_2}{8} [/tex]
[tex] \frac{d_2}{8} < \frac{d_1}{8} [/tex]
Therefore;
The speed of the helicopter is lesser than the speed of the driver, which gives;
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Angle A and angle B are complementary.
The measure of angle A = 3x+7. The measure of angle B=6x+11. Determine the measure of each angle.
The measure of angle A and angle B are 31° and 59° respectively.
What are complementary angles?Complementary angles that sum up to 90 degrees.
Given the angles as;
angle A = 3x+7angle B =6x+11We have that;
Angle A + Angle B= 90
Substitute the values
3x + 7 + 6x + 11 = 90
collect like terms
9x = 90 - 18
9x = 72
Make 'x the subject
x = 72/ 9
x = 8
Angle A = 3x + 7 = 3(8) + 7 = 31°
Angle B = 6x +11 = 6(8) + 11 = 59°
Thus, the measure of angle A and angle B are 31° and 59° respectively.
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Given Angle A and angle B are complementary, the measure of Angle A and angle B are 31° and 59° respectively.
What is the measure of each angle?complementary angles are angles that sum up to 90 degrees.
Given the data in the question;
Angle A and angle B are complementaryMeasure of angle A = 3x + 7measure of angle B = 6x + 11Numerical measure of each angle = ?Since complementary angles sum up to 90 degrees.
Measure of angle A + Measure of angle B = 90°
Plug in the given values and solve for x.
(3x + 7) + (6x + 11) = 90
Collect like terms
3x + 6x + 11 + 7 = 90
9x + 18 = 90
Subtract 18 from both sides
9x + 18 - 18 = 90 - 18
9x = 72
x = 72/9
x = 8
Hence;
Measure of angle A = 3x + 7 = 3(8) + 7 = 24 + 7 = 31°
Measure of angle B = 6x + 11 = 6(8) + 11 = 48 + 11 = 59°
Given Angle A and angle B are complementary, the measure of Angle A and angle B are 31° and 59° respectively.
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I need help solving x. photo is attached below.
Write the equation of the line parallel to the line and passing through
the point. Y=-2x-1, (4, 3)
Answer:
y = - 2x + 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x - 1 ← is in slope- intercept form
with slope m = - 2
• Parallel lines have equal slopes , then
y = - 2x + c ← is the partial equation of the parallel line
to find c substitute (4, 3 ) into the partial equation
3 = - 8 + c ⇒ c = 3 + 8 = 11
y = - 2x + 11 ← equation of parallel line
the cuboid below is placed on a table.it exerts a pressure f 40 N/cm2. calculate the force exerted on the table.
Answer:
40 multiply by area of the table
Step-by-step explanation:
force = pressure * area of the table
The weight of the items in a truck is ton.
How many pounds do the items in the
truck weigh?
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line in the given graph = rise/run = 3.
How to Find the Slope of a Line?To determine the value of the slope of a line on a coordinate plane, we can find the ratio of the rise of the line to that of its run. This means that, the formula for calculating the slope of a line would be:
Slope = rise/run.
Vertical distance across the line is the rise of the line
Horizontal distance across the line is the run of the line
In the graph given, we have:
The rise is labelled as the blue line = 9 units
The run is labelled as the red line = 3 units
Slope of the line (m) = 9 units/3 units
Slope (m) of the given line = 9/3 = 3
Therefore, the slope of the line in the given graph = rise/run = 3.
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What is the slope of the line that passes through the points (2, 8) and (12, 20)?
Write your answer in simplest form.
Answer:
6/5
Step-by-step explanation:
m = (y_2 - y_1)/(x_2 - x_1) = (20 - 8)/(12 - 2) = 12/10 = 6/5
What is the measurement of this angle?
Answer:
80 degrees
Step-by-step explanation:
80 degrees because part of it is on zero and the other part is on 80 so 80-0=80 degrees,
Which statement does not belong with the other three?
Responses ⬇️
If today is Tuesday, then tomorrow is Wednesday.
If today is Tuesday, then tomorrow is Wednesday.
If it is Independence Day, then it is July.
If it is Independence Day, then it is July.
If an angle is acute, then its measure is less than 90°.
If an angle is acute, then its measure is less than 90°.
If you are an athlete, then you play soccer.
If you are an athlete, then you play soccer.
Question 2
Explain your reasoning.
This statement does not belong with the other three because it is ⬇️.
True
False
Conditional statement
Not a conditional statement
Answer:
If you are an athlete, then you play soccer
Step-by-step explanation:
This statement is not true as you can be an athlete and play football, run, etc. You could play soccer but this sentence is implying that you do play soccer. It is also not a conditional statement. A conditional statement is "If A then B".
Find the slope of the following lines
Explain how you got the answer
[tex]-\displaystyle\frac{4}{3}[/tex]
Step-by-step explanation:Slope describes the change in y divided by the change in x.
Solving Using Slope Formula
One way to find slope when you are given 2 points is the slope formula.
Slope = [tex]\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex]To solve, plug in the x and y-values and simplify. For this question, let (-2, 3) represent the (x₂, y₂) and (1, -1) represent (x₁, y₁).
[tex]\displaystyle\frac{3-(-1)}{-2-1}=-\frac{4}{3}[/tex]This shows that the slope of this line is -4/3.
Solving Through Counting
When given the graph of a function, you can also count out the slope. Starting from the left point, count the change in y-values and the change in x-values. Remember, when the y-values decrease, the change should be negative. The y-value changes by -4 and the x-value changes by +3.
Since the slope is change in y over change in x, the slope is -4/3.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line shown is -2/5
Slope of a lineThe formula for calculating the slope of a line is expressed according to the formula
Slope = Rise/Run
Slope = y₂-y₁/x₂-x₁
Using the coordinate point (0,7) and (5, 5)
Slope = 5-7/5-0
Slope = -2/5
Hence the slope of the line shown is -2/5
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41. find the odds against selecting an ace when a card is drawn from a standard deck of cards. odds against
The odds against selecting an ace when a card is drawn from a standard deck of cards is 12:1.
The total number of cards in a deck is 52.The number of suits in the deck is 4.Each suit has its own ace card.So, the number of aces in the deck is 4.The probability (p) of selecting an ace card from the deck is the number of ace cards divided by the total number of cards.p = 4/52p = 1/13The probability (p') of not selecting an ace card from the deck is the number of non-ace cards divided by the total number of cards.p' = 48/52p' = 12/13The odds against selecting an ace card are equal to the probability (p') of not selecting an ace card divided by the probability (p) of selecting an ace card.The odds against selecting an ace card are p'/p.The odds against selecting an ace card are (12/13)/(1/13).The odds against selecting an ace card are 12/1.The odds against selecting an ace card are 12.To learn more about probability, visit :
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The perimeter of the entire garden.
all combinations from 0-9 that equals 0
D. 153 Jenny bought 3/4 kg of margarine. She will use 2/3
of it for her hotcake recipe. How much of Margarine
did she use?
Answer:
1/2
Step-by-step explanation:
2/3 x 3/4 = 6/12 =1/2