Determine which property of real numbers is used to simplify the expression.4 minus 5 plus 6 minus 7 plus 8 minus 9equals open parentheses 4 minus 5 close parentheses plus open parentheses 6 minus 7 close parentheses plus open parentheses 8 minus 9 close parentheses
Answers
In this case, in order to obtain the right hand side of our equation, we applied the associative property, which leads to
[tex]\begin{gathered} 4-5=(4-5) \\ 6-7=(6-7) \\ 8-9=(8-9) \end{gathered}[/tex]then, the answer is option A
Related Questions
A company sells one of its products for $32 each. The monthly fixed costs are $3800. The marginal cost of the produce is $12. Let q = quantity and C(q) = cost.a) Express the total monthly costs, C, as a function of q, the quantity produced each monthC(q) = b) Express the total monthly revenue, R, as a function of the quantity, q, sold each monch.R(q) =c) Find the quantity, q, produced and sold each month at which this company will break even. Round your answer to a whole number.
Answers
a)
The monthly cost is composed by the fixed cost of $3800 plus the cost of production, which is $12 per unit.
If the company produced q products, the cost C(q) is:
[tex]C(q)=3800+12q[/tex]b)
The revenue is given by the products sold, which are worth $32 per unit.
Since the number of products is q, the revenue is:
[tex]R(q)=32q[/tex]c)
To find the quantity q so the company will break even (that is, profit = 0), let's equate the revenue and the cost and then calculate the value of q:
[tex]\begin{gathered} \text{profit}=\text{revenue}-\text{cost} \\ 0=\text{revenue}-\text{cost} \\ \text{revenue}=\text{cost} \\ R(q)=C(q) \\ 32q=3800+12q \\ 32q-12q=3800 \\ 20q=3800 \\ q=190 \end{gathered}[/tex]Therefore the quantity q is equal to 190 units.
find two functions f and g such that f(g(x)=h(x).h(x)=2÷(x-4)^3Find the inverse Function of g(x)= x-1÷ x+5
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h(x) =
[tex]h(x)=\frac{2}{(x-4)^3}[/tex]Let f(x) =
[tex]f(x)=\frac{2}{x^3}[/tex]And
[tex]g(x)=(x-4)[/tex]Then h(x) = f(g(x)) =
[tex]h(x)=\frac{2}{(x-4)^3}[/tex]Translate the following sentence to an inequality.A number is no less than seven.On<7Ons7On27On>7
Answers
Here, we want to translate the sentence into an inequality
The sentence is that a number n is no less than 7
What this mean is that although the number can be equal to 7, it is not less than 7
The inequality is thus;
[tex]n\text{ }\ge\text{ 7 or 7 }\leq\text{ n}[/tex]Which equation represents a line that is perpendicular to y=-5x+4?
Answers
Recall that given a line with equation
[tex]y=mx+b[/tex]A line perpendicular to that equation can be determined by getting the negative reciprocal of the equation
[tex]y=-\frac{1}{m}+b[/tex]Given the equation y = -5x + 4, the slope of the line is -5, get the negative reciprocal and we have
[tex]-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5}[/tex]We should have an equation with a slope of 1/5, this is represented therefore by the equation
[tex]y=\frac{1}{5}x-1\text{ \lparen final answer\rparen}[/tex]If set A = {3,4,7,9}, set B = {8,9,10,11}, and set C = {4,9,11,14,15}, then An(BuC) =
Answers
SOLUTION
From the question, we have
A = {3, 4, 7, 9}
B = {8, 9, 10, 11}
C = {4, 9, 11, 13, 15}
To get this lets first find B union C. This is all the items found in B or C or both, but not repeated. So B union C is
[tex]B\cup C=\lbrace4,8,9,10,11,13,15\rbrace[/tex]Now A intersection B union C are the elements common to set A and set B union C. We have
[tex]A\cap(B\cup C)=\lbrace4,9\rbrace[/tex]Hence the first option is the answer
Consider two rectangular medicine boxes labeled as B1 and B2. For box B1, theratio of the length to the width to the height is 5:2:1. For box B2, the ratio of thelength to the width to the height is 6:2:1. If the widths of the two boxes are equal,what is the ratio of the volume of B1 to the volume of B2?
Answers
Volume of a rectangular box is
[tex]v=\text{lbh}[/tex]for B1, the ratio is 5:2:1
For B2, the ratio is 6:2:1
Given,
2x=2x
x=2
thus,
the volume of B1 is
[tex]10\times4\times2=80[/tex]the volume of B2 is
[tex]12\times4\times2=96[/tex]Thus the ratio is
[tex]\frac{80}{96}=\frac{5}{6}[/tex]Which number line shows the solution of - 4x + 6 > 18?O A.-10 -9 -8 -7 -6 -5 -4e-3 -2 -1012345678co910B.0-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 234ch6 7 8 9 10C. +-10-9-8-7 -6 -5 -4 -3-2 -1 0 1 2 3 4 5 6 78 9 10O D.3-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 24 5 6 7 8 9 10
Answers
Start by solving the inequality,
[tex]\begin{gathered} -4x+6>18; \\ \text{ subtract 6 on both sides} \\ -4x>18-6; \\ \text{ simplify} \\ -4x>12;\text{ } \\ \text{ divide both sides by -4 and invert the sign } \\ x<\frac{12}{-4};\text{ } \\ \text{ simplify} \\ x<-3 \end{gathered}[/tex]then, all numbers less than -3 are solutions to the inequality.
Answer:
how do I identify the proper steps and evaluating log 7 to the power of 2
Answers
1) To evaluate the following logarithm:
[tex]\log _72[/tex]Given:
[tex]\log _74\approx0.712\text{ and }\log _78\approx1.069[/tex]2) Notice that we can rewrite that log of 4 this way, using the quotient property of logarithms:
[tex]\begin{gathered} \log _7(\frac{8}{4})=\log _78-\log _74=\log _72 \\ 1.069\text{ -}0.712\text{ = }0.357 \\ \log _72\approx0.3567 \end{gathered}[/tex]As we know that 8/4 =2, we could rewrite that as above.
3) Hence, the answer is:
[tex]\begin{gathered} 1)\text{ }\log _72\text{ =}\log _7(\frac{8}{4}) \\ 2)\text{ }\log _72=\log _78-\log _74 \\ \end{gathered}[/tex]the total cost in dollars of a monthly gym membership can be represented by the expression 42x+50 where x is the number of months. what information does the term 42x give the expression
Answers
In the given expression, the term 42x refers to the ratio of change of the situation. In other words, that term is telling that the cost per month is $42.
QUESTION IS IN IMAGE! DO NOT NEED TO SHOW WORK UNLESS YOU NEED OR WANT TO!
Answers
Given:
Find-:
The value of "x"
Explanation-:
Use the property of circle:
The angle is always the same, no matter where it is on the same arc between endpoints:
Apply the property,
[tex]x+14=41[/tex]The value of "x" is:
[tex]\begin{gathered} x+14=41 \\ \\ x=41-14 \\ \\ x=27 \end{gathered}[/tex]So,
The value of "x" is 27.
Tammy got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13
cents per yard. If after that purchase there was $9.41 left on the card, how many yards of ribbon did Tammy buy?
Answers
initial amount in debit card = $15
price of ribbon = 13 cents/yard
after purchase,
amount on card = $9.41
To calculate the yard of ribbon Tommy bought:
amount Tommy spent = initial amount in card - amount after purchase
= $15 - $9.41 = $5.59
amount spent is $5.59.
We need to convert $3.61 into cents:
[tex]\since\\[/tex][tex]\because\\[/tex] $1 = 100cent
[tex]\therefore\\[/tex] $5.59 = 100 x 5.59 = 559 cents
if 13cents gives one yard of ribbon
then 13cents ⇒ 1yard
559cents ⇒ x
after cross multiplying :
13x = 559
[tex]x= \frac{559}{13}[/tex]
[tex]x = 43[/tex]
[tex]\therefore \\[/tex] Tommy bought 43 yards of ribbon.
Find out more about conversion of dollar into cents:
https://brainly.com/question/20145274
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if the expression 4 (3x + 5) is expanded, what is the coefficient of x?
Answers
4 (3x +5) =4(3x) +4(5) =12x +20
thus the coefficient of x is 12
Answer:
12
Step-by-step explanation:
4 (3x + 5)
Distribute
4*3x + 4*5
12x + 20
The coefficient of x is 12
point Given the information belowhat is the value of x? Be careful identifying each angle.
Answers
6
Explanation
Step 1
Let
[tex]\begin{gathered} \measuredangle QRS=7x-2(\text{blue)} \\ \measuredangle QRT=9x+1(\text{red)} \\ \measuredangle SRT=15\text{ (green)} \end{gathered}[/tex]then
blue +green = red
[tex]\measuredangle QRS+\measuredangle SRT=\measuredangle\text{QRT}[/tex]Step 2
replace and solve for x
[tex]\begin{gathered} \measuredangle QRS+\measuredangle SRT=\measuredangle\text{QRT} \\ (7x-2)+15=9x+1 \\ 7x-2+15=9x+1 \\ 7x+13=9x+1 \\ 7x-9x=1-13 \\ -2x=-12 \\ x=\frac{-12}{-2} \\ x=6 \end{gathered}[/tex]I hope this helps you
Which letter on the number line corresponds to each square root?
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To solve this problem, the first step is to recall the squares of numbers 1 to 10.
The square root of 56:
[tex]\begin{gathered} 7^2=49\text{ and 8}^2=64 \\ \sqrt{56}\text{ must be in between 7 and 8.} \\ T\text{he letter E is the letter which corresponds to the }\sqrt{56} \end{gathered}[/tex]The square root of 10:
[tex]\begin{gathered} 3^2=9\text{ and 4}^2=16 \\ \sqrt{10}\text{ must be in between 3 and 4.} \\ T\text{he letter C is the letter which corresponds to the }\sqrt{10} \end{gathered}[/tex]The square root of 39:
[tex]\begin{gathered} 6^2=36\text{ and 7}^2=49 \\ \sqrt{39}\text{ must be in between 6 and 7.} \\ T\text{he letter A is the letter which corresponds to the }\sqrt{39} \end{gathered}[/tex]The square root of 7:
[tex]\begin{gathered} 2^2=4\text{ and 3}^2=9 \\ \sqrt{7}\text{ must be in between 2 and 3.} \\ T\text{he letter D is the letter which corresponds to the }\sqrt{7} \end{gathered}[/tex]The square root of 32:
[tex]\begin{gathered} 5^2=25\text{ and 6}^2=36 \\ \sqrt{32}\text{ must be in between 5 and 6.} \\ T\text{he letter F is the letter which corresponds to the }\sqrt{32} \end{gathered}[/tex]The square root of 98:
[tex]\begin{gathered} 9^2=81\text{ and 10}^2=100 \\ \sqrt{98}\text{ must be in between 9 and 10.} \\ T\text{he letter B is the letter which corresponds to the }\sqrt{98} \end{gathered}[/tex]Is (3, 1) a solution to the equation y = 3x? yes no
Answers
the point (3, 1) means that x=3 and y=1
so in the equation y = 3x
if we put x= 3
y= 3 x 3 =9
y =9 which does not correspond to y = 1
so (3,1) IS NOT A SOLUTION
Given right triangle ABC with right angle at C, find sin A if a=8 and b=15
Answers
we know that
In the right triangle ABC
Applying Pythagorean Theorem
Find the length of the hypotenuse c
so
c^2=a^2+b^2
c^2=8^2+15^2
c^2=64+225
c^2=289
c=17
Find sin(A)
we have that
sin(A)=BC/AB
we have
BC=a=8
AB=c=17
so
sin(A)=8/17the variable, y, varies directly with x. if y = 18 when x = 13, what is y when x = 63?
Answers
When we talk about direct variation we mean the following relationship between variables:
[tex]y=kx[/tex]where "k" is a constant. We must determine the value of this constant. To do that, we use the fact that when y = 18, x = 13, we replace that in the relationship:
[tex]18=k(13)[/tex]Now we solve for "k", dividing both sides by 13, like this:
[tex]\frac{18}{13}=k[/tex]solving we get;
[tex]k=1.38[/tex]We replace this value in the relationship:
[tex]y=1.38x[/tex]Now we are asked the value of "y", when "x = 63", we replace x = 63 in the relationship, we get:
[tex]\begin{gathered} y=1.38x \\ y=1.38(63) \end{gathered}[/tex]solving we get;
[tex]y=87.23[/tex]Therefore, y = 87.23 when x = 63
Rectangle ABCD with vertices A(-8, 6), B(-2, 8), C(-1,5), and D(-7, 3); reflected in the y-axis,
Answers
ANSWER
[tex]\begin{gathered} A^{\prime}(8,6) \\ B^{\prime}(2,8) \\ C^{\prime}(1,5) \\ D^{\prime}(7,3) \end{gathered}[/tex]EXPLANATION
When a point is reflected across the y axis, the y coordinate stays the same but the x coordinates become the negative inverse.
The point changes as follows:
[tex]X(x,y)\Rightarrow X^{\prime}(-x,y)[/tex]Therefore, the points change as follows:
[tex]\begin{gathered} A(-8,6)\Rightarrow A^{\prime}(8,6) \\ B(-2,8)\Rightarrow B^{\prime}(2,8) \\ C(-1,5)\Rightarrow C^{\prime}(1,5) \\ D(-7,3)\Rightarrow D^{\prime}(7,3) \end{gathered}[/tex]That's the answer
If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. Using the above technique, find the equation of the line containing the points (-2,7) and (4,-2).
Answers
The general slope - intercept form of the line is ;
[tex]y=mx+b[/tex]where m is the slope, b is y-intercept
We need to find the equation of the line containing the points ( -2 , 7 ) and ( 4 , -2 )
The slope will be calculated as following:
[tex]m=\frac{-2-7}{4-(-2)}=\frac{-9}{6}=-\frac{3}{2}[/tex]So, the equation of the line will be :
[tex]y=-\frac{3}{2}x+b[/tex]using the point ( -2 , 7 ) to find b:
So, when x = -2 , y = 7
so,
[tex]\begin{gathered} 7=-\frac{3}{2}\cdot-2+b \\ 7=3+b \\ b=7-3=4 \end{gathered}[/tex]so, the equation of the line is:
[tex]y=-\frac{3}{2}x+4[/tex]HELP ME PLEASE I JUST WANT TO GET THE CREDIT I DIDNT GET TO GRADUATE PLEASE HELP ME
Answers
Given the parent function;
[tex]y=x^3[/tex]When reflected over the y-axis, this becomes;
[tex]y=-x^3[/tex]Note that reflecting over the y axis can be explained like folding over the graph page along the vertical line (y-axis is the vertical line), which means all values would flip over from negative to positive and positive to negative depending on the original equation.
Next we are told that that the function is horizontally stretched by a factor of 1/5.
This means the x-value of the function is multiplied by 1/5.
We now have the following;
[tex]\begin{gathered} y=x^3\Rightarrow y=-x^3 \\ y=-x^3\times\frac{1}{5} \\ y=-\frac{1}{5}x^3 \end{gathered}[/tex]ANSWER:
The parent function
[tex]y=x^3[/tex]After a horizontal stretch by a factor of 1/5 and a reflection over the y-axis now becomes;
[tex]y=(-\frac{1}{5}x)^3[/tex]The last option is the correct answer.
For the linear function ƒ(x) = 7x – 4, find the value of ƒ(x) at x = –2, 0, and 2.Question 3 options:A) ƒ(–2) = 10, ƒ(0) = –4, ƒ(2) = –18B) ƒ(–2) = –18, ƒ(0) = 4, ƒ(2) = 10C) ƒ(–2) = 18, ƒ(0) = –4, ƒ(2) = 10D) ƒ(–2) = –18, ƒ(0) = –4, ƒ(2) = 10
Answers
From the question,
We are given the function
[tex]f(x)=7x-4[/tex]We are to find the value of f(x) at
[tex]x=-2,x=0,x=2[/tex]When x = - 2 then
[tex]\begin{gathered} f(-2)=7(-2)-4 \\ f(-2)=-14-4 \\ f(-2)=-18 \end{gathered}[/tex]When x = 0, then
[tex]\begin{gathered} f(0)=7(0)-4 \\ f(0)=0-4 \\ f(0)=-4 \end{gathered}[/tex]when x = 2, then
[tex]\begin{gathered} f(2)=7(2)-4 \\ f(2)=14-4 \\ f(2)=10 \end{gathered}[/tex]Therefore, the values of f(x) at x = -2, x = 0, x = 2 are
f(-2) = -18
f(0) = -4
f(2) = 10
Hence the correct option is D
Senora Cruz will use four triangles on the door decoration. How many square centimeters of paper will Senora Cruz used to create the triangles?
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We have the following triangle:
the area of this triangle is the following:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \Rightarrow A=\frac{3.5\cdot7}{2}=\frac{24.5}{2}=12.25 \\ A=12.25\operatorname{cm}^2 \end{gathered}[/tex]Since Senora Cruz sill use four triangles on the door decoration, we have that the area of the original triangle will be multiplied by 4:
[tex]4\cdot A=4\cdot12.25=49\operatorname{cm}^2[/tex]Thus, senora Cruz will use 49 square centimeters for the triangles
Find the domain and range in interval notation and intercepts of the function f(x)=2x+7.
Answers
We have a linear function.
In linear function we have a domain and range of ALL real numbers. So the domain and range is equal to:
[tex](\text{ -}\infty,\infty)[/tex]The x-intercept is when y is 0
[tex]\begin{gathered} 0=2x+7 \\ \text{ -}7=2x \\ x=\text{ -}\frac{7}{2} \end{gathered}[/tex]And the y-intercept when x is 0
[tex]\begin{gathered} f(x)=2(0)+7 \\ f(x)=7 \end{gathered}[/tex]Anyway, the graph is the following:
See that the x axis and the y axis are infinite, they will never end
find the slope of the lineI really need help with these two
Answers
Given a graph.
let us consider points,
[tex]\begin{gathered} (4,0) \\ (0,-2) \end{gathered}[/tex]The formula to find the slope m is,
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{-2-0}{0-4} \\ m=\frac{-2}{-4} \\ m=\frac{1}{2} \end{gathered}[/tex]The slope of the given graph is 1/2.
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(2, -3). (4, 5)
Answers
The equation in slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
To find it for the given points, we can use this equation to find the slope first:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Since we have the points (2, -3) and (4, 5):
[tex]\begin{gathered} x_1=2_{}_{}_{} \\ y_1=-3 \\ x_2=4 \\ y_2=5 \\ m=\frac{5-(-3)}{4-2}=\frac{5+3}{2}=\frac{8}{2}=4 \end{gathered}[/tex]To get to the slope-intercept, we can first use the slope and one of the point to write it in the slope-point form:
[tex]\begin{gathered} y-y_1_{}=m(x-x_1) \\ y+3=4(x-2) \end{gathered}[/tex]And solve for y to get to the answer:
[tex]\begin{gathered} y+3=4x-8 \\ y=4x-11 \end{gathered}[/tex]what must x equal is a parallel b
Answers
Let'sThe general equation of line is
y = mx + b
Where m is the slope and b is y-intercept.
Lets say,
The equation of the line a is
y1 = m1x1 + b1
line b:
y2 = m2x2 + b2
Now, both the lines are parallel if they have the same slope value, that is the difference of y values over x values.
If both lines are parallel.
m1 = m2 = m
Hence, the slope must be equal if the line a is parallel to line b.
Several prefixes often used with units of measurement are shown below. each prefix has a specific value in the metric system. what is the correct order of the prefixes, from largest value to smallest value?1.Kilo- milli- deci- unit deca- centi- hecto2.Kilo- hecto- deca- unit deci- centi- mill- 3.Kilo- hecto- deca- centi- deci-unit milli4.unit kilo- hecto- deca- deci- centi- milli
Answers
If g(x) is the f(x)=x after a vertical compression by 35 , a shift left by 2, and a shift up by 3,a) write an equation for g(x) : g(x) = b) The slope of this line is: c) The vertical intercept of this line is:
Answers
we have the parent function
f(x)=x
step 1
vertical compression by 3/5
so
x ---------> (3/5)x
step 2
shift left by 2
(3/5)x ------------> (3/5)(x+2)
step 3
shift up by 3
(3/5)(x+2) --------> (3/5)(x+2)+3
so
g(x)= (3/5)(x+2)+3Part 2
The slope is 3/5part 3
Vertical intercept
The y-intercept is the value of y when the value of x=0
For x=0
g(x)= (3/5)(0+2)+3
g(x)=(6/5)+3
g(x)=21/5
the y-intercept is the point (0,21/5)Without multiplying, find the sign of the product. Explain your thinking -27 x 14 x (-10) x (-72) x 45
Answers
ANSWER
Negative sign (-)
EXPLANATION
We want to find the sign of the product of those numbers without carrying out athe multiplication of those numbers.
To do this, we have to arrange the negatve numbers close to one another:
(-27) * (-10) * (-72) * 14 * 45
We know that the product of an even number of negative signs will produce a positive sign and vice versa. That is:
- => negative
- * - => positive (+)
- * - * - => negative (-)
- * - * - * - => positive (+)
If we continue in that pattern, we see that the product of an odd number of negative signs gives a negative sign (-) and the product of an even number of negative signs gives a positive sign (+).
Since there are 3 negative signs, the product will have a negative sign.
The total amount of money in an account with P dollars invested in it is given by the formulaA = P + Prt.where r is the rate expressed as a decimal and t is time (in years).If $1862 is invested at 5 %, how much money will be in the account after 6 months? Round your answer to the nearest cent.
Answers
Given the formula:
[tex]A=P+Prt[/tex]You know that "A" is the amount, "P" is the number of dollars invested" r" is the rate (as a decimal), and "t" is time in years.
In this case, you can identify that:
[tex]\begin{gathered} P=1862 \\ \\ r=\frac{5}{100}=0.05 \end{gathered}[/tex]Remember that a percent can be converted to a Decimal Number by dividing it by 100.
Knowing that 1 year has 12 months, you can determine that 6 months is a half of a year:
[tex]t=\frac{1}{2}[/tex]Then, substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} A=P+Prt \\ A=1862+(1862)(0.05)(\frac{1}{2}) \end{gathered}[/tex][tex]\begin{gathered} A=1862+46.55 \\ A=1908.55 \end{gathered}[/tex]Therefore, the answer is: $1908.55