Step-by-step explanation:
the domain is the interval of the x (input) values.
in other words, is g(x) invalid for certain x ?
it does not look like it. it looks like g(x) is valid for every possible value of x from -infinite to +infinite.
the range is the interval of possible y (functional) values.
and that is clearly valid for every y between -1 and +infinity.
Can someone please help me?
1.Modeling with mathematics: The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.
a. Solve the equation for x.
b. How many ski trips do you take if you spend a total of $315 and $485?
Part (a)
We have some unknown number x which is a placeholder for a positive whole number (eg: x = 4).
What's happening to x are these two things, in this exact order
Multiply by 85Add 60We multiply first, then add. The order is important. We're following the order of operations PEMDAS here. If we knew what x was, then we'd go forward in the PEMDAS chain; however, we don't know what x is. So we go backwards in the chain to isolate x. This will undo every operation applied to x.
So,
C = 85x+60
C-60 = 85x
85x = C-60
x = (C-60)/85
In the second step, I subtracted 60 from both sides to undo the "plus 60" operation. Then in the last step, I divided both sides by 85 to undo the multiplication.
Answer: x = (C-60)/85===============================================================
Part (b)
How many ski trips can we take if we spend $315? We simply plug in C = 315 into that equation we just found at the end of part (a).
Doing so gets us...
x = (C-60)/85
x = (315-60)/85
x = 255/85
x = 3
We can take 3 ski trips if we spent a total of $315
Repeat the same steps for C = 485
x = (C-60)/85
x = (485-60)/85
x = 425/85
x = 5
We can take 5 ski trips if we spent a total of $485
Note how plugging something like x = 5 into the original equation yields:
C = 85x+60
C = 85*5+60
C = 425+60
C = 485
Showing that x = 5 leads to C = 485. This helps confirm the second answer. I'll let you check the first answer.
Answers: 3 trips and 5 trips respectivelyA businessman marks the price of a washing machine 30% above the cost price and provided 15% discount. Find the profit percentage.
Answer:
10.5 percents
Step-by-step explanation:
1)100+30=130 percents;
2) 130/100*15=19.5percents of discount from the first price
3) 130-19.5=110.5 percents- new price from the initial price
4)110.5-100=10.5 percents - the percentage of profit
what is a vertical line ?
Step-by-step explanation:
A line perpendicular to a surface or to another line considered as a base.
please help due soonA credit card company surveys 125 of its customers to ask about satisfaction with customer service. The results of the survey, divided by gender, are shown below.
Males Females
Extremely Satisfied 25 7
Satisfied 21 13
Neutral 13 16
Dissatisfied 9 14
Extremely Dissatisfied 2 5
If you were to choose a female from the group, what is the probability that she is satisfied with the company's customer service? Answer choices are rounded to the hundredths place.
0.13
0.24
0.62
0.38
If a female is chosen, then the probability that she is satisfied with the company's customer service is 0.24.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, A credit card company surveys 125 of its customers to ask about satisfaction with customer service. The results of the survey, divided by gender, are shown below.
Males Females
Extremely Satisfied 25 7
Satisfied 21 13
Neutral 13 16
Dissatisfied 9 14
Extremely Dissatisfied 2 5
Here, the total number of customers is 125. (N=125).
If a female is chosen, find the probability that she is satisfied with the company's customer service. Here, conditional probability is used.
[tex]P(satisfied|female) = \frac{P(satisfied and female)}{P(females)} \\Here\\P(satisfied|female) = \frac{n(satisfied and female)}{N} \\= \frac{13}{125} \\= 0.104\\P(female) = \frac{n(female)}{N} \\= \frac{55}{125} \\= 0.44\\Now, \\P(satisfied|female) = \frac{n(satisfied and female)}{P(female)} \\= \frac{0.104}{0.44}\\= 0.24[/tex]
Hence, if a female is chosen, then the probability that she is satisfied with the company's customer service is 0.24.
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9x=10 please help…….
Let's solve your equation step-by-step.
9x=10
Step 1: Divide both sides by 9.
9x / 9 = 10 /9
x = 10 / 9
Answer:
x = 10 / 9
HELP PLEASE 17 POINTS
Step-by-step explanation:
1000ml =1 L150m> 1500 cm4000g > 3kgAbraham has visited 10 states already. He has a goal of visiting all 50 states. He plans to achieve this goal by visiting 5 new states per year (y) for the next several years.
Which equation and solution shows the number of years that it will take for Abraham to meet his goal?
A
5y+10=50; y=12 years
B
10y+5=50; y=5.5 years
C
5y+10=50; y=8 years
D
10y+5=50; y=4.5 years
Answer:
C
Step-by-step explanation:
5 states per year = 5y
Already visited 10 states = +10
5y + 10 = 50
To find y
5y = 50 - 10
5y = 40
y = 40/5
y = 8 years
Help please, question in picture
Answer:
option A is right answer
Find the product of 3 1 11 and 5 1 2 .
Answer:
16896
Step-by-step explanation:
3×1×11×512
=16896
Step-by-step explanation:
3×1×11×5×1×2=330
please mark my answer as BRAINLIEST if you liked it..The lengths of the sides of a triangle are consecutive even integers. The perimeter is 174 feet.
Answer:
56,58,60
Step-by-step explanation:
x = 1st side of triangle
x+2 = 2nd side
x+4 = 3rd side
P = side1 + side 2 + side 3
174 = x+ x+2 + x+4
Combine like terms
174 = 3x+6
Subtract 6 from each side
174 -6 = 3x+6-6
168 = 3x
Divide by 3
168/3 = 3x/3
56 =x
1st side = 56
2nd side = 58
3rd side = 60
True or False: The correct answer to a numeric entry field will automatically be populated in the correct field after you open the explanations.
Although your question is vague a general answer within the concept of your of your question is provided. The correct answer to a numeric entry field will be automatically populated after the explanation is open ( i.e. True is the correct answer )
When you open up the explanations to a correct answer the entry field for the answer will automatically be populated with the correct answer, because by selecting/clicking on the explanation you will be granted access to the answer behind the explanation as well. also another way to access the correct answer is to simply select the entry field
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Study the pattern of numbers given below and write the rule that describes the pattern 1,3,9,27,81
Dose anyone know how to solve this?
Answer:
Derivative of any constant is zero
you can solve it by first derivative rule
Answer:
Derivative of any constant is zero
Step-by-step explanation:
Which is not a rational number?
someone pls answer- will give brainliest
Hello there!
Formulas
[tex] \displaystyle \large{ \sin (2 \theta) = 2 \sin \theta \cos \theta} \\ \displaystyle \large{ \cos (2 \theta) = \begin{cases} 2 { \cos}^{2} \theta - 1 \\ 1 - 2 { \sin}^{2} \theta \\ { \cos}^{2} \theta - { \sin}^{2} \theta \end{cases}}[/tex]
First, we have to find cos(theta). We know that the theta lies in Q3 which is negative for both sin and cos. To find cos, you can use the identity or Pythagoras.
Recall
[tex] \displaystyle \large \tt{ \sin \theta = \frac{opposite}{hypotenuse} } \\ \displaystyle \large \tt{ \cos \theta = \frac{adjacent}{hypotenuse} }[/tex]
Finding cos, I will use Pythagoras.
Recall Pythagorean
Define a or b = adjacent or oppositeDefine c = hypotenuse[tex] \displaystyle \large{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]
From sin = -1/6
opposite = 1hypotenuse = 6adjacent = x[tex] \displaystyle \large{ {1}^{2} + {b}^{2} = {6}^{2} } \\ \displaystyle \large{1 + {b}^{2} = 36 } \\ \displaystyle \large{ {b}^{2} = 36 - 1 } \\ \displaystyle \large{ {b}^{2} = 35 } \\ \displaystyle \large{ {b} = \sqrt{35} }[/tex]
b is our adjacent. Hence,
[tex] \displaystyle \large{ \cos \theta = \frac{ \sqrt{35} }{6} }[/tex]
Since theta is in Q3, cos < 0 or in negative.
[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]
Finding sin(2theta)
[tex] \displaystyle \large{ \sin \theta = - \frac{ 1 }{6} }[/tex]
Hence,
[tex] \displaystyle \large{ \sin 2 \theta = 2( - \frac{ 1 }{6} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = ( - \frac{ 1 }{3} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = \frac{ \sqrt{35} }{18} }[/tex]
Recall
Negative × Negative = PositiveFinding cos(2theta)
The cos of 2theta has multiple formulas. All of them are same and also identity to each others.
I will be using the first one as it only involves cos, not sin.
[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]
Therefore,
[tex] \displaystyle \large{ \cos2 \theta = 2 { ( - \frac{ \sqrt{35} }{6} )}^{2} - 1 } \\ \displaystyle \large{ \cos2 \theta = 2 (\frac{ 35}{36}) - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - \frac{18}{18} \longrightarrow \boxed{\frac{17}{18} }}[/tex]
Answer
sin(2theta) = √35/18cos(2theta) = 17/18The last choice.
Let me know if you have any questions!
How do you solve this?9=8x+15/x
8x=15+9
8x÷8=24÷8
x=3
you are going to divide 8 by 8 which will cancel each other and you will left with x and divide 24by 8 which will give you 3
Write an equation for the nth term of the arithmetic sequence 6,3,0,-3,...?
Answer:
the answer is 3-3n
Step-by-step explanation:
6-(n-1)x3
=3-3n
An equation for the nth term of the arithmetic sequence is aₙ=9-3n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is 6,3,0,-3,...
Here, first term a=6 and common difference is 3-6=-3
Substitute a=6 and d=-3 in aₙ=a+(n-1)d, we get
aₙ=6+(n-1)(-3)
aₙ=6-3n+3
aₙ=9-3n
Therefore, an equation for the nth term of the arithmetic sequence is aₙ=9-3n.
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is -16/-2 an integer?
Answer:
yes
Step-by-step explanation:
because -16 and -2 is a whole number. and it doesnt have neither fractions nor decimals.
hope this helps. have a good day
If x2 + y2 = 14 and xy = 5, find the value of
(x + y)2
and
(X-y)2
Answer:
3x(7-3)y2=21
Step-by-step explanation:
hope it is write
25 points !Can you find the cube root of a negative number? If so, is it positive or negative? Complete the explanation. (select) ; the cube root of a negative number is (select) , because a negative number cubed is always (select) , and a nonnegative number cubed is always nonnegative.
for the drop downs!
For the first one Yes or no for the second one positive or negative and the last one is also positive or negative
Answer:
true, negative, negative
The value of the expression 2x² + x(100- 15 x) when x = 5 is X
a 119
b 129
c 135
d 145
[tex]\text{x}=5\\\\2\text{x}^2+\text{x}(100-15\text{x})=2\cdot5^2+5\cdot(100-15\cdot5)=\\\\=2\cdot25+5\cdot(100-75)=50+5\cdot25=\\\\=50+125=\boxed{175}[/tex]
[tex] \boxed{ \boxed{ \mathrm{ \: \: \: \: \: \: \: \: \: 175 \: \: \: \: \: \: \: \: \: }}}[/tex]
Solution :Plugging the value of x as 5 in the given expression we get,
[tex] \hookrightarrow \: 2 {x}^{2} +x (100 - 15x)[/tex]
[tex] \hookrightarrow \: 2(5) {}^{2} + 5(100 - (15 \times 5))[/tex]
[tex] \hookrightarrow \: (2 \times 25) + 5(100 - 75)[/tex]
[tex] \hookrightarrow \: 50 + 5(25)[/tex]
[tex] \hookrightarrow \: 50 + 125[/tex]
[tex] \hookrightarrow \: 175[/tex]
how do you write 9/11 as a decimal
Answer:
0.81
Step-by-step explanation:
Answer:
0.81818181818181....
Step-by-step explanation:
It is irrational
Can someone please solve this ..word by word or by number
-7x+4=39
Answer:
x = -5
Step-by-step explanation:
-7x + 4 = 39
-7x (+ 4 - 4) = 39 - 4
-7x = 35
-7x/-7 = 35/-7
x = -5
Can someone help provide the steps?
9514 1404 393
Answer:
r = 2
Step-by-step explanation:
"A varies inversely with r cubed" means the relation is of the form ...
A = k/r³
We can find the value of k as ...
k = Ar³ = 72·5³ = 9000 . . . . . . . multiply the above relation by r³
And we can solve this for r to get ...
r³ = 9000/A . . . . . . divide by A
r = ∛(9000/A) . . . . . take the cube root
So, for A = 1125, we have ...
r = ∛(9000/1125) = ∛8
r = 2
A. Explain why a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.
The statement "a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions" is true .
What is linear equation?A linear equation is an algebraic equation of the form [tex]y= mx+b.[/tex]involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
What is quadratic equation?We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is , [tex]y = ax^2 + bx + c[/tex]
where a, b, and c are numbers and a cannot be 0.
According to the question
A system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.
This statement is true as
if we see graphically
A quadratic equation is a parabola and a linear equation is a straight line.
There could be 3 situations of intersection of line and parabola
1. straight line never crosses the parabola
i.e line passing above or below parabola without touching
it is called zero solution
2. where the straight line is a tangent to the parabola, 'touching' it at only one point.
i.e single point lies in both line and parabola
it is called one solution
3. the line cuts across the parabola, it will cut the parabola at 2 points
it is called two solution .
Hence, The statement " a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions "is true .
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Answer: The intersections of the graphs of a system of equation correspond to the solutions of the system. Since we saw that a line can intersect a parabola zero, one, or two times, a linear-quadratic system can have zero, one, or two solutions.
Step-by-step explanation:PLATO
Michael bought four packs of pens. Each pack contains 12 pens. Mark bought twice as many pens as Michael. How many pens did mark buy?
Answer:
96
Step-by-step explanation:
12×4=48
mark bought twice as many pens so 48×2=96
Step-by-step explanation:
Mark bought 96 pens , 12 multiply by 8 is equal to 96
Round to the nearest cent:
32% of $1,275
Answer:
408
Step-by-step explanation:
1275 times .32=408.
Answer:
The answer would be $408
Pls help quickly I really need help no spam pls
what help you want
can u tell
Maya made a playlist with 20 songs. The playlist includes 3
rap songs, 12 pop songs, and 5 R&B songs. If she plays the
playlist on shuffle, what is the probability an R&B song will
play first?
Answer:
0Step-by-step explanation:
The probability an R&B song will play is 0 because 20 - 3 = 17 and 17 - 12 = 5, leaving 5 - 5 to be 0.
Write the number 0.0000031 in scientific notation.
Answer:
[tex]3.1 \times {}^{ - 6} [/tex]
Step-by-step explanation:
[tex]3.1 \times 10 {}^{ - 6} [/tex]