r > -1
Explanations:Negative eighty times r is less than 80 is expressed mathematically as;
[tex]-80r<80[/tex]Divide both sides by -80.
[tex]\begin{gathered} \frac{-80r}{-80}<-\frac{80}{80} \\ r>-1 \end{gathered}[/tex]Note the change in sign when divided by a negative value
Solve for b
-73 = b/7- 81
Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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If the equation be -73 = b/7- 81 then the value of b is 56.
What is meant by Linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
Hence,
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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ax^2 + bx + c (a in not equal to 0) is a ____?____Select one:a. Quadraticb. Vertexc. Domaind. None of the above
We have the following expression
[tex]ax^2+bx+c[/tex]This can't be a vertex, since, in geometry, a vertex is a point where two or more elements meet.
A domain is not either, since, in mathematics, the domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
The Standard Form of a Quadratic Equation looks something like this:
[tex]ax^2+bx+c=0[/tex]Where a, b, and c are known values and a cannot be 0.
In conclusion, the answer is that is a Quadratic
Solve the inequality b+ 5 ≥ -12
The solution of the inequality is b ≥ -17.
Given inequality:-
b + 5 ≥ -12
We have to find the solution of the inequality.
Subtracting 5 from the given inequality, we get
b + 5 - 5 ≥ -12 - 5
b + (5 - 5) ≥ -17
b + 0 ≥ -17
b ≥ -17
Hence, b can be equal to or greater than -17.
Inequality
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
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Select the correct answer.
Find the inverse of function f.
f (x) = 9x + 7
A. f^{\small -1}(x)\ =\ 7x\ +\ 9
B. f^{\small -1}(x)\ =\ -9x\ -\ 7
C. f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}
D. f^{\small -1}(x)\ =\ \frac{7}{9}x\ -\ \frac{1}{9}
Answer:
[tex]\dfrac{x-7}{9}[/tex]
which corresponds to choice
C : [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]
Step-by-step explanation:
The inverse of a function y = f(x) can be found by interchanging x and y and solving for y
Let y = f(x)
y = 9x + 7
Interchange x and y:
x = 9y + 7
9y + 7 = x (switch sides)
subtract 7 both sides
→ 9y + 7 - 7 = x - 9
→ 9y = x - 9
Divide both sides by 9
→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]
which corresponds to choice C
Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan’s train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be?
The time when the two trains reach each other is
.
The trains are
away from the city when they reach each other.
Answer:
1.25 hours.
68.75 miles from the city
Step-by-step explanation:
Eltan's train (E) is travelling 65mph west.
Dmitri's train (D) is travelling 55mph west.
In terms of vectors, we can write E as 65E and D as 55W
The miles travelled by each is a function of time, T, in hours.
Each train's distance is:
E: T*65E
D: T*55W
They are 150 miles apart. They will meet with the combined miles travelled is 150 miles.
150 miles = T*65E + T*55W
150 miles = T(120 miles/hour)
T = (150 miles/120 miles/hour)
T = 1.25 hours
Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.
They will have travelled the following miles in 1.25 hours:
Demitri: (1.25hr)(55 m/hr) = 68.75 miles
Eitan: (1.25hr)(65 m/hr) = 81.25 miles
Total = 150 miles
Dimitri is headed away from the city. After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city. They meet 68.75 miles from the city.
Answer:
question one is B and question 2 is C
Step-by-step explanation:
Which expression is equivalent to
09
O
15
8h6
O
2h²
15
2h6
g8
(295)³
(44²) ³²
8h
The equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].
What is inequality?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Consider the given expression, [tex]\frac{(2g^5)^3}{(4h^2)^3}[/tex]
Using the rule, [tex](a^m)^n = a^m^n[/tex]
So, [tex]\frac{(2g^5)^3}{(4h^2)^3} = \frac{8g^1^5}{64h^6}[/tex]
After simplifying we get, [tex]\frac{g^1^5}{8h^6}[/tex]
Therefore, the equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].
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Use the Product Property for Exponents: thoroughly explain why x · x = x^2.
1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.
2) So we can write out the following steps to get that product as x²:
[tex]\begin{gathered} x=x^1 \\ x^1\cdot x^1=x^{1+1}=x^2 \end{gathered}[/tex]That's why we can write that, applying the property of exponents.
5. suppose waiting time until the next failure of oil pump system is exponentially dis tributed, with mean of 37 hours. the pump is continuously in operation. what is the probability that the system does not fail for 2 days?
The Probability that the system does not fail for 2 days is 0. 053
Given ,
Mean (u) = 37 hours .
Step 1 : Calculate the rate parameter, λ.
λ = 1/ mean
λ = 1/ 37 = 0.02703
Step 2 : Find the probability that the system does not
fall for two days, P ( x[tex]\leq[/tex]2 )
P ( x[tex]\leq[/tex]2 ) .= 1 - e power (lamda(x))
= 1 - e - 2(lamda)
= 1 - e power -2(0. 02703 )
By solving,
P ( x[tex]\leq[/tex]2 ) = 0.05263
P ( x[tex]\leq[/tex]2 ) = 0. 053 [ upto three decimals]
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Which function is the inverse of f(x) = 8x + 4?A. 5-18) = —841 – 4)B. 7-14x) = 554OC. 5-11%) = 8.1 – 4)OD. 1x) = -1
ANSWER:
[tex]f^{-1}(x)=\frac{x-4}{8}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=8x+4[/tex]We calculate the inverse function as follows:
[tex]\begin{gathered} x=8\cdot f^{-1}(x)+4 \\ 8\cdot f^{-1}(x)=x-4 \\ f^{-1}(x)=\frac{x-4}{8} \end{gathered}[/tex]Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16
two lines are perpendicular when their slope is inverted and have the opposite sign
the general form of the equation line is-3,1
[tex]y=mx+b[/tex]where m is the slope
rewrite
[tex]\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=\frac{3x-16}{8} \\ y=\frac{3}{8}x-2 \end{gathered}[/tex]so, the slope 3/8
the slope of the other line is
[tex]\frac{3}{8}\longrightarrow-\frac{8}{3}[/tex]to write the new equation of the line we use the slope and replace the point (-3,1)
[tex]\begin{gathered} (1)=(-\frac{8}{3})(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}[/tex]now, replace b and the slope to create the line
[tex]y=-\frac{8}{3}x-7[/tex]Question 5
The equation 2x² - 8x = 10 is rewritten in the form of 2(x-p)²+ q = 0. What is the value of q?
-18
2
-2
18
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation -2x²-8x = 10 consists of the two equations is rewritten in the form of 2(x-p)²+ q = 0. , which are separated by the 'equal' sign.
What are two illustrations of equations?Answer :q = -2
-2x²-8x = 10 (divide both sides by -2)
x² + 4x = -5 (Apply completing the square method)
x² + 4x + (4/2)²= -5 + (4/2)²
x² + 4x + 2²= -5 + 2² (reduce left hand side using a²+2ab+b² = (a+b)² )
(x+2)² = -5 +4
(x+2)² = -1
(x+2)² + 1 = 0 (multiply both sides by -2)
(-2)(x+2)² + 1 (-2) = 0
-2[x - (-2)]² + (-2) = 0 ---> compare this with -2(x-p)² + q = 0
We can see that p = 2 and q = -2
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REINFORCEMENT #1 IN MATHEMATICS 10Please draw and fill the table :)
A set of data is given. It is required to find the first, second, and third quartile.
The given data is:
[tex]2,8,9,10,14,15,16,16,17,17,20[/tex]Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.
The lower half is:
[tex]2,8,9,10,14[/tex]Find the median of the lower half to get the first quartile, Q₁:
Hence, Q₁=9.
Recall that the second quartile Q₂ is the same as the median of the data.
The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Notice that the middle number is 15.
Hence, second quartile Q₂=15.
The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.
The upper half of the data is:
[tex]16,16,17,17,20[/tex]Calculate the median to find the third quartile, Q₃:
It follows that Q₃=17
The complete table is shown below:
What is the perimeter of this rectangle?
The perimeter of the rectangle is 6.89
Perimeter of the rectangle:
The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.
The formula for the perimeter of the rectangle is
P = 2(l + w)
The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.
Given,
Here we have the graph with the following points:
(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)
Now we need to find the perimeter of the rectangle.
To calculate the perimeter, first we have to find the length and width of the rectangle.
To calculate the length, we have to use the values of x axis,
That is,
=> -3/2 + 7/2
=> (-3+7)/2
=> 4/2
=> 2
Therefore, the length of the rectangle is 2.
Now, we have to find the width of the rectangle using the y axis coordinates,
=> -1 7/9 + 3 2/9
Convert the mixed fraction into normal form, then we get,
=> -16/9 + 29/9
=> (-16 + 29)/9
=> 13/9
Therefore, the width of the rectangle is 13/9
Now, we have to use this to calculate the perimeter of the triangle,
P = 2 (2 + 13/9)
P = 2 ((18+13)/9)
P = 2 (31/9)
P = 62/9
P = 6.89
Therefore, the perimeter of the rectangle is 6.89.
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The base of this right prism is a rectangle. What is the surface area of the prism? Height = 10 ft
Surface area of a rectangular prism formula
[tex]SA=2(wl+hl+hw)[/tex]where w is width, l is length, and h is height.
Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get:
[tex]\begin{gathered} SA=2(4\cdot6+10\cdot6+10\cdot4) \\ SA=2(24+60+40) \\ SA=2\cdot124 \\ SA=248\text{ ft}^2 \end{gathered}[/tex]
8g - 7 = 18 + 3g
SOLVE EQUATION PLEASE
Answer:
g = 5
Step-by-step explanation:
8g - 7 = 18 + 3g
add 7 to both sides:
8g - 7 + 7 = 18 + 3g + 7
8g = 25 + 3g
subtract 3g from both sides:
8g - 3g = 25 + 3g - 3g
5g = 25
divide both sides by 5:
5g/5 = 25/5
g = 5
100pts. find the area of these questions below
Answer:
20 feet²Step-by-step explanation:
triangle area formula: A = 1/2 × b × h
Find the base7 +3 = 10 ft
Find Area1/2 10 × 4 =
5 × 4 =
20 feet²
The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Area of circle A is 113.04 in²
Area of circle B is 200.96 in²
Area of circle C is 452.16 in²
Area of circle B is 254.34 in²
The number of times that the area of Circle D greater than Circle A is 2.25
What are the areas of the circles?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 3.14R = radiusArea of circle A = 3.14 x 6² = 113.04 in²
Area of circle B = 3.14 x (6 + 2)² = 200.96 in²
Area of circle C = 3.14 x (8 + 4)² = 452.16 in²
Area of circle B = 3.14 x (12 - 3)² = 254.34 in²
Number of time that is the area of Circle D greater than Circle A = 254.34 in² / 113.04 in² = 2.25
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Please help! I’ve tried this a couple times now and still don’t understand it! Math is not my thing.
The function f(z) is graphed below. (Picture below)
a) What is f(0)?
b) What is f(3)?
c) What is f(1)?
Answer:
Step-by-step explanation:
Please explain how you got your answer.
Answer:
4th option
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 = - [tex]\frac{2}{3}[/tex] x + 8 ← is in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 6, 2 ) into the partial equation
2 = - 9 + c ⇒ c = 2 + 9 = 11
y = [tex]\frac{3}{2}[/tex] x + 11 ← equation of perpendicular line
Answer:
I miss you
Step-by-step explanation:
What is the equation of the line in slope-intercept form? 1,6 and 2,-6
The equation of the line in slope-intercept form would be; y = -12x + 18
How to get the slope-intercept form of a straight-line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = MX +c
To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
We have been given the point (1,6) and (2,-6)
y-y₁ = m(x-x₁)
m = (-6-6)/(2 -1)
m = -12/1
Now substitute;
y-y₁ = m(x-x₁)
y- 6 = -12(x- 1)
y- 6 = -12x + 12
y = -12x + 18
Hence, the equation of the line in slope-intercept form would be; y = -12x + 18
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Lydia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $2.50 per mile. The total fare was $36.60, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.
Answer:
4.10 + 2.50x = 36.60
x = 13 miles
Step-by-step explanation:
I hope this helped
have a good day ^^
What is the value of q − 7 if q = −17? 24 10 −10 −24
PLEASE HELP!!!
When q = -17, the value of the equation, q - 7 would be: d. -24.
How to Evaluate an Equation?If we are given an equation to evaluate for a given value of a variable, we are to substitute the value of the variable into the equation and solve or simplify.
For example, if an equation is given as 3x + 4, and we are told that the x = 3, to determine the value of the equation, 3x + 4, substitute x = 3 into the equation as:
3(3) + 4
= 9 + 4
= 13
Here, we can now conclude that the value of the equation is 13.
Given the equation, q - 7, to find the value of the equation when q = -17, substitute the value of q into q - 7.
Therefore:
q - 7 = -17 - 7
= -24.
The value of the equation is: d. -24.
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The value of q - 7, when q = - 17 is - 24.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, q = - 17.
∴ q - 7.
To solve our expression we'll substitute the numerical value of q in the given expression.
= (-17) - 7.
= - 17 - 7.
= - 24.
We can also take negative sign common in the second step and distribute them later.
- 17 - 7.
= - (17 + 7).
= - (24).
= -24.
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1.
Rule/Equation: y = slope (x) +/- y-intercept
OR y = m(x) +/- b
X
2
6
10
14
18
y
12
8
4
0
TABLES TO EQUATIONS #2
-4
Slope (growth rate):
y-intercept (starting value):
2
Equation:
Answer:
Step-by-step explanation:
x y
2 12
6 8
10 4
14 0
18 -4
The slope is the Rise/Run, or change in y over the change in x. Pick any two points. I'll choose (2,12) and (18,-4),
Rise = (-4 - 12) = -16
Run = (18 - 2) = 16
Slope = Rise/Run = -16/15, or -1
The equation becomes y = -1x + b
To find b, use any of the points in the equation and solve for b. I'll use (14,0):
y = -1x + b
0 = -1(14) + b
b = 14
The equation is y = -x + 14
See the attached graph.
Graph the linear equations 65 points
Answer:
Step-by-step explanation:
A single piecewise-defined function f(x) has been
graphed for you on the display to the left.
At how many values c on the interval x€[−6, 4) is it
true that the limx→cf(x) = 1?
Answer: 1
Step-by-step explanation:
[tex]\lim_{x \to -6} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
[tex]\lim_{x \to -1} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.
Mrs. Smith runs a dessert parlor. Her top-selling items are mixed berry smoothies and milkshakes. She sells mixed berry smoothies for $5 each and milksh
for $3 each. Mrs. Smith wants to sell at least 60 mixed berry smoothies and milkshakes in all and wants to earn at least $210. Each mixed berry smoothie ta
7 minutes to make, and each milkshake takes 3 minutes to make.
O
New folder
How many mixed berry smoothies and milkshakes should Mrs. Smith make to minimize the time she spends making the desserts, also selling at least the
minimum total number and earning at least the minimum amount of money?
Answer:
Step-by-step explanation:
0 mixed berry smoothies and 70 milkshakes
Solve using elimination.–10x − 10y = –1010x + 8y = –8
The question asks us to solve the following system of equations by elimination:
[tex]\begin{gathered} -10x-10y=-10 \\ 10x+8y=-8 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -10x-10y=-10\text{ (Equation 1)} \\ 10x+8y=-8\text{ (Equation 2)} \\ \\ \text{Add Equation 1 and 2 together.} \\ \\ -10x-10y+(10x+8y)=-10+(-8) \\ -10x-10y+10x+8y=-10-8 \\ -10x+10x+8y-10y=-18 \\ -2y=-18 \\ \text{Divide both sides by -2} \\ -\frac{2y}{-2}=-\frac{18}{-2} \\ \\ \therefore y=9 \\ \\ \text{Substitute the value of y into equation 1.} \\ -10x-10y=-10 \\ -10x-10(9)=-10 \\ -10x-90=-10 \\ Add\text{ 90 to both sides} \\ -10x=-10+90 \\ -10x=80 \\ \text{Divide both sides by -10} \\ -\frac{10x}{-10}=\frac{80}{-10} \\ \\ \therefore x=-8 \end{gathered}[/tex]
Answer
The solution to the system of equation is:
x = -8
y = 9
Select all rational numbers.
All of the rational numbers that we have in the question that we have here are:
-√25√100√0.36√0.0144What is a rational number?This is the term that is used to refer to the ratio of two numbers that when they are expressed as a ratio of two different numbers, the denominator does not have to be 0.
The rational numbers when they are solved would not give us terminating decimals. That is they would be able to be expressed as fractions.
-√25 = -5
√0.0144 = 0.12
√0.36 = 0.6
√100 = 10
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-√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.
As of the given data, numbers are given we have to determine which of the number are rational numbers.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
Here,
All the numbers are irrational numbers except -√25, √100, √0.36, and √0.0144 because the number picked out is required rational number.
Thus, -√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.
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Use the graph or table to find the equation that represents the relationship.
Answer:
1) y = 3x + 5
2) y = -12x + 2
3) y = 5/4 - 5
4) y = -6x + 3
Step-by-step explanation:
jane wants to know what percentage of freshmen at her college purchase clothing with college logos. she decides to randomly interview 10 freshmen from each of the dorms. these people are her
Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.
What is Sample?
Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.
Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.
Therefore, by the above information, these people are her Sample.
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