The expression (A) $20 – (9)($1.10) will correctly represents the given situation.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression that represents the given situation will be:
The total bill is 20$.The number of pens purchased is 9.Each pen cost $1.10.Then, the expression will be:
20 - 9(1.10)Therefore, the expression (A) $20 – (9)($1.10) will correctly represents the given situation.
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find rates in context
To find out the rate of change, divided 110,400 miles by 24 hours
so
110,400/24=4,600 miles per hour
Assume the base unit of water is 555 gallons and the cost per unit is $1.74. How much money will be saved in a month by a family who conserves 8000 gallons of water per month?
1) Gathering the data
555 gallons ----- $ 1.74
2) If 8000 gallons could be spent
If a Family conserves 8000 gallons this family would not have an expense of?
Let's set a proportion for that:
555 g-----$1.74
8000g ---x
555x =13920 Dividing both sides by 555
x=25.08
If a family conserves 8000 gallons of water. They save $25.08 per month assuming that $1.74 is equal to 555 gallons of water.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
If the speed of pulley A is 600 r.p.m., find the speed of the other pulleys.
Speed of pulleys B and C: ___r.p.m.
Speed of pulley D: ___ r.p.m
The corresponding speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm
How to find the rpm speed of the pulleys?
The speed of the pulleys can be determined by using the formula that relates the speed and diameters of the pulleys
N1/N2 = D2/D1
Where: D1 is the diameter of the driven pulley, D2 is the diameter of the drive pulley, N1 is the speed of the driven pulley and N2 is the speed of the drive pulley
Given: Da = 2'', Db =4'' Dc = 1'', Dd =5'' and Na = 600rpm
Na/Nb = Db/Da
600/Nb = 4/2
2Nb = 600
Nb = 600/2 = 300 rpm
Nb/Nc = Dc/Db
300/Nc = 1/4
Nc = 300 x 4 = 1200rpm
Nc/Nd = Dd/Dc
1200/Nd = 5/1
5Nd = 1200
Nd = 1200/5 = 240 rpm
Therefore, the speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm respectively
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(12-√-8)/2
solve as a complex number?
The solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.
What is expression?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots.
The expression (12-√-8)/2 involves a square root of a negative number, which cannot be represented by a real number. Therefore, we need to extend the real numbers to the complex numbers to solve this expression.
To evaluate the square root of a negative number, we can use the imaginary unit, denoted by i, which is defined as the square root of -1. Then, we have:
√-8 = √(8) √(-1) = 2i√2
Substituting this value back into the original expression, we get:
(12-√-8)/2 = (12 - 2i√2)/2
Simplifying the expression by dividing both the numerator and denominator by 2, we get:
(12 - 2i√2)/2 = 6 - i√2
Therefore, the solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.
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Use<, >, or = to compare each pair of
expressions.
(-5)², -5² (-5)³, -53
Using <, >, or = to compare each pair of expressions, we get:
(A) (-5)² > -5² (-5)³(B) -5² (-5)³ < -53(C) (-5)² > -53What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
So, using <, >, or = to compare each pair of expression:
Given expressions: (-5)², -5² (-5)³, -53
Then,
(A) (-5)²__-5² (-5)³
(B) -5² (-5)³ __ -53
(C) (-5)² __ -53
Now calculate as follows:
(A) (-5)²__-5² (-5)³
25 __ 25(-125)
25 > -3,125
(B) -5² (-5)³ __ -53
-3,125 < -53
(C) (-5)² __ -53
25 > -53
Therefore, using <, >, or = to compare each pair of expressions, we get:
(A) (-5)² > -5² (-5)³(B) -5² (-5)³ < -53(C) (-5)² > -53Know more about expressions here:
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i really need help with this math question
(7, -3) are the coordinates of R' after dilation with center (0, 0) and with the scale factor of 2.
What is meant by graph and coordinates?A graph's basic relationship is represented by a point.
A pair of numbers containing two coordinates define each point.
A coordinate is one of a set of numbers used to locate a point on a graph.
Each point is assigned an x and a y coordinate.
Each point is identified by an ordered pair of numbers: an x-coordinate on the x-axis and a y-coordinate on the y-axis.
Parentheses indicate ordered pairs (x-coordinate, y-coordinate).
The starting point is at (0,0).
The horizontal and vertical distances from the two reference axes are used to describe the position of a point on a coordinate plane.
So, after dilation with center (0, 0) and with the scale factor of 2, the coordinates will be:
R' are (7, -3)
P' are (4,-3)
Q' is (4,4)
Hence, the coordinates of R are (7, -3).
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1. The volume of a 3-D shape is 27 cubic inches. The shape is scaled up by a factor of 3. What is the
volume of the new shape?
Answer:
81
Step-by-step explanation:
27 * 3 = 81
What does the y-intercept on this graph represent? a.At 0 days, there are 400 pages remaining b. At 0 days, there are 16 pages remaining c. At 16 days, there are no pages remaining d. At 16 days, there are 400 pages remaining,
Explanation:
The y-intercept is the point where the line crosses the y-axis. This always happens when x = 0.
In this case x = 0 represents 0 days. The y-intercept is 400 pages remaining
Answer:
The answer is option a. At 0 days there are 400 pages remaining
Nicolas drinks 2/3 liters of water in the morning and three 1/2 liters of water at lunch . during basketball practice, he drinks another 2/5 liter of water. what is the total amount of water in liters, that Nicolas drinks.
The total amount of water Nicholas drank is 47/ 30 liters of water.
Given : Amount of water Nicholas drinks in the morning = 2/3 liters
Amount of water he drinks at lunch = 1/2 liters
Amount of water he drinks during his basketball practice = 2/5 liters
Thus to calculate the total amount of water he drank in the whole we would you the operation of addition in which we will add all the above mentioned value.
The value which comes after adding all of the above mentioned numbers is called sum .
Thus the total amount of water Nicholas drank = 2/3 + 1/2 + 2/5
On taking the LCM we will get
= [tex]\frac{20 + 15 + 12}{30}[/tex]
= 47 / 30
Thus the total amount of water Nicholas drank is 47/ 30 liters of water.
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how do you ?????????????????????????
what???
any question?????
Or watch a video leroy is a citizen scientist for a monarch butterfly project. every week, he visits a local patch of milkweed and counts the number of monarch larvae on the plants. last week, leroy didn't count many larvae. this week, he counts 29 larvae on the milkweed. for both weeks, leroy's total count is 41 larvae.
Leroy's count for last week is 21 larvae.
Define subtractionThe process of determining the difference between two integers is called subtraction, which is a fundamental arithmetic operation and is represented by the symbol (-). To determine the difference between two numbers, perform the subtraction process. When you remove a few items from a group of things, the group gets smaller.
Given, total count for both week is 41 larvae
Count for this week is 29 larvae.
Now, find the count for last week,
count = 41 - 29
= 12
Therefore, Leroy's count for last week is 12 larvae.
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The complete question is:
Leroy is a citizen scientist for a monarch butterfly project. Every week, he visits a local patch of milkweed and counts the number of monarch larvae on the plants. Last week, Leroy didn't count many larvae. This week, he counts 29 larvae on the milkweed. For both weeks, Leroy's total count is 41 larvae. Find Leroy's count for last week.
what does 7m- m equal
7m-m is equal to 6m.
Mr. Newman packed 16 large - size ornaments and 29 medium - size ornaments into a box. He packed 13 boxers like this. Mr.Newman used this this equation to find x, the number of ornaments he packed into all the boxes x = (16+29)13how many ornaments did Mr.Newman pack into the boxes
We were told that Mr. Newman packed 16 large - size ornaments and 29 medium - size ornaments into a box. This means that the number of large and medium ornaments in each box is 16 + 29. Given that there were 13 boxes and x represents the total number of ornaments, the equation would be
x = (16 + 29)13
x = 45 * 13
x = 585
Option F is correct
8. Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 jars of jelly and 5 jars
of peanut butter for $15.67.
Find the cost of a jar of peanut butter using substitution.
The cost of a jar of peanut butter is $2.36.
Let cost of one jar of jelly be x and the cost of jar of peanut butter be y.
According to question, total cost of 4 jars of jelly and 6 jars of peanut butter is $19.32.
So, 4x+6y = 19.32 ..............(i)
According to question again, the cost of 3 jars of jelly and 5 jars of peanut butter is $15.67.
So, 3x+5y = 15.67 ...........(ii)
4*(ii) - 3*(i) we get,
12x+20y - (12x+18y) = 62.68 - 57.96
2y = 4.72
y = 4.72/2 = 2.36
Substituting the value of y in (i) we get,
4x+6*2.36 = 19.32
4x+14.16 = 19.32
4x = 19.32-14.16
4x = 5.16
x = 5.16/4
x = 1.29
Hence the cost of jar of peanut butter is $2.36.
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complete the identitysin 2x - cot x
Let's complete the identity:
[tex]\begin{gathered} \sin 2x-\cot x=2\sin x\cos x-\frac{\cos x}{\sin x} \\ =\frac{2\sin^2x\cos x-\cos x}{\sin x} \\ =\frac{\cos x(2\sin^2x-1)}{\sin x} \\ =\frac{\cos x}{\sin x}(2\sin ^2x-1) \\ =\frac{\cos x}{\sin x}(2(1-\cos ^2x)-1) \\ =\frac{\cos x}{\sin x}(2-2\cos ^2x-1) \\ =\frac{\cos x}{\sin x}(1-2\cos ^2x) \\ =\frac{\cos x}{\sin x}(-\cos 2x) \\ =-\cot x\cos 2x \end{gathered}[/tex]1 divided by 4/9 lowest term
The number obtained 9/4 is the reciprocal of the number 4/9.
What is defined as the reciprocal of a number?The multiplicative inverse of the a number is defined as the reciprocal. In other words, a number's reciprocal is described as 1 divided by such a number. The product of a specific number and its reciprocal always equals one.The reciprocal of the a fraction can be calculated by swapping the numerator as well as denominator values.For the given number.
Divide 1 by 4/9
This can be written as;
= 1/(4/9)
= 9/4
Then, the number obtained 9/4 is the reciprocal of the number 4/9.
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find an equation of a line with a slope of 6 and having the point (3,5) on the line
Given:
The point (3,5)
The slope is 6.
To find the equation of the line:
Using the point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]Substituting the point and slope, we get
[tex]\begin{gathered} y-5=6(x-3) \\ y-5=6x-18 \\ y=6x-18+5 \\ y=6x-13 \\ y-6x+13=0 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y-6x+13=0[/tex]evaluate the polynomial -x^4-3+4x^2+2 when x=-1
the given expression is,
[tex]=-x^4-3+4x^2+2[/tex]put x = -1 in the above expression
[tex]\begin{gathered} =-(-1)^4-3+4(-1)^2+2 \\ =-1-3+4+2 \\ =2 \end{gathered}[/tex]so the answer is 2
what is the zero of f(x)=-2x+6
Answer:
Step-by-step explanation:
the answer is x=25
What is the x-coordinate of the point in the stan- dard (x, y) coordinate plane at which the two lines y = - 2x + 7 and y = 3x - 3 intersect? A. 10B. 5 C. 3D. 2 E. 1
we can equalize the equations and solve x
[tex]-2x+7=3x-3[/tex][tex]\begin{gathered} 7+3=3x+2x \\ 10=5x \\ x=2 \end{gathered}[/tex]the option is D
una persona olvido su paraguas en un autobuses pero se acordó que la suma de los digitos del l camion eran 11 si su producto son 24 que numeros eran del camion
Ecuaciones
Llamemos x al primer número del camión y y al segundo número.
Tenemos que su suma es 11, así que:
x+y=11
También sabemos que su producto es 24:
xy=24
De esta forma, tenemos un sistema de ecuaciones. Vamos a despejar la x de la primera ecuación:
x=11-y
Y la reemplazamos en la segunda:
(11-y)y=24
Operamos y ordenamos el poninomio para formar la ecuación cuadrática:
[tex]\begin{gathered} 11y-y^2=24 \\ y^2-11y+24=0 \end{gathered}[/tex]Para hallar las soluciones de esta ecuación, tomemos los coeficientes de la ecuación de segundo grado:
a=1, b=-11, c=24
Y aplicamos la fórmula resolvente
[tex]\begin{gathered} y=\frac{-\text{b}\pm\sqrt[]{b^2-4ac}\text{ }}{2a} \\ y=\frac{11\pm\sqrt[]{(-11)^2-4(1)(24)}\text{ }}{2(1)} \\ y=\frac{11\pm\sqrt[]{121-96}\text{ }}{2} \\ y=\frac{11\pm\sqrt[]{25}\text{ }}{2} \\ y=\frac{11\pm5\text{ }}{2} \end{gathered}[/tex]Tenemos dos posibles respuetas:
y=16/2=8
y=6/2=3
Sustituimos ambas respuestas para hallar x:
x=11-y
x=11-8=3
x=11-3=8
En cualquier orden que los tomemos, los números del camón eran 3 y 8
Is 4/21 and 16/84 proportional
Answer:
True. They are both 4/21 and 4/21.
Step-by-step explanation:
You know they are proportional if they can be reduced any smaller. 4/21 cannot be reduced, but 16/84 can. 16 divided by 4 = 4. 84 divided by 4 = 21.
So, we are left with the answers 4/21 and 4/21. So, this answer is True.
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find the counterexample to show that the statement is incorrect the difference of any two counting numbers will be a counting numbera: 7-4=3 which is not a counting number b: 10-2=8 which is a counting numberc: 3-5= -2 which is not a counting number d: there is no counterexample they statement is correct.
The right answer to your question is b: 10-2=8 which is a counting number
Find the midpoint of the segment with endpoints of (-1, 7) and (3, -3) andenter its coordinates as an ordered pair. If necessary, express coordinates asfractions, using the slash mark (7) for the fraction bar.
The two endpoints we have are (-1,7) and (3,-3).
And we need to find the midpoint.
Step 1. Label the given coorfinates as (x1,y1) and (x2,y2):
[tex]\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=3 \\ y_2=-3 \end{gathered}[/tex]Step 2. Use the midpoint formula:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Substituting the values for x1, x2, y1, and y2 that we found in step 1:
[tex](\frac{-1+3}{2},\frac{7-3}{2})[/tex]Step 3. Solve the resulting operations to find the coordinates of the midpoint:
[tex](\frac{2}{2},\frac{4}{2})[/tex]Solving the divisions:
[tex](1,2)[/tex]The midpoint is (1,2).
Answer: (1,2)
what's the answer
find m<2ifm
The m∠2 is m∠2 = 14°.
What is degree measure?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
As given in the figure,
m ∠WHI = 160°,
m ∠EHI = 104°
m ∠THE = 42°
We have to find the m ∠2
From figure,
m ∠WHI = m ∠WHT + m ∠THE + m ∠EHI
m ∠WHT = m ∠WHI - m ∠THE - m ∠EHI
m ∠WHT = 160° - 42° - 104°
m ∠WHT = 14°
Hence the measure of angle 2 is, m ∠2 = 14°.
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a farmer keeps cows,pigs and sheep on his farm. the ratio of cows to pigs to sheep on the farm is 2:7:16. work out the percentage of the animals that are sheep
Using percentages, we know that there are 64% of sheep in the total of all the animals, which is the ratio [Cows:pigs:sheep = 2:7:16].
What are percentages?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, the decimal 0.35, or the fraction, represents 35%. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage of sheep in the given ratio:
Cows:pigs:sheep = 2:7:16So, the total number of animals:
2+7+16 = 25Now, calculate 16 as what percentage of 25 as follows:
25/100 × x = 1625x = 1600x = 1600/25x = 64%
Therefore, using percentages, we know that there are 64% of sheep in the total of all the animals, which is the ratio [Cows:pigs:sheep = 2:7:16].
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What is the probability that a student‘s favorite hobby is roller skating ?Theoretical =Experimental =
The theoretical probability is given by 1 over the number of hobbies.
If there is a total of 8 hobbies, the probability of a student having a specific hobby is:
[tex]P=\frac{1}{8}[/tex]The experimental probability is given by the number of students with that hobby over the total number of students. If 3 students have the hobby roller skating among the 24 students surveyed, the probability is:
[tex]P=\frac{3}{24}=\frac{1}{8}[/tex]Proportions: Aubrey's car used 2 gallons to travel 90 miles. How far can she travel on 11 gallons?
Answer:
495 gallons
Step-by-step explanation:
2= 90
11=?
90×11÷2
= 495 gallons
Math To Do, -ReadyHome Jefferson County School X+/student/dashboard/homeWhich unit would you most likely use to measure the capacity of a mug?
Although both fluid ounces and quarts are measurements for volume, the mug would be a very small fraction of a quart.
Thereby, the most likely unit of measurement used for the capacity of a mug would be fluid ounces.