Answer:
g(f(x)) = 6x -9
Step-by-step explanation:
Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).
Function evaluationA function is evaluated by simplifying the result of substituting the argument for the function's variable.
g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1
g(f(x)) = 6x -9
In the final round of a singing competition, the audience voted for one of the two finalists, Luke or Sean. Luke received 25% more votes than Sean received. Altogether, the two finalists received 5175 votes. How many votes did Luke receive?
Based on the number of votes that the two finalists received, the number of votes that Luke received was 2,875 votes
What number of votes did Luke receive?Assuming that the number of Sean's votes could be shown as x, the expression for the votes would be:
x + (x + 25%) = 5,175
2.25x = 5,175
x = 5,175 / 2.25
= 2,300 votes
Luke's votes were:
= 2,300 x (1 + 25%)
= 2,875 votes
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Why is the opposite of the reciprocal of 5 the same as the reciprocal of the opposite of 5 ?
Yes, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5 ,both are equals to (-1/5).
As given in the question,
Given number is 5
Case 1 : First find reciprocal of 5
Reciprocal of 5 =1/5
Then, opposite of the reciprocal of 5 =(-1/5)
Case 2. First find the opposite of 5
Opposite of 5 =-5
Reciprocal of the opposite of 5 =(1/ -5)
=(1/-5) × (-1/-1)
=(-1/5)
Therefore, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5 ,both are equals to (-1/5).
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Escalators consist of steps on a continuous loop that is driven by a motor. At the top and bottom of the platform, the steps collapse to provide a level surface for entrance and exit.
a. What is the relationship between the treads of the ascending stairs?
The climbing steps have parallel planes for the treads. Although each step may appear to be a line, it is actually a plane.
Considering it as a staircase; a moving stairway that transports people between levels of a building or structure is known as an escalator. It is made up of a motor-driven chain of individually connected steps on a track that cycles along a pair of tracks that maintain them horizontal.
The climbing stair treads are parallel planes. Each step appears to be a line, but it is actually a plane.
The top two steps of the inclination are on the same plane. They are parallel.
These tires are twisted. They are neither parallel, nor do they share the same plane.
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How are previously decided court cases similar to theorems?
Question 7: Luna has consumed 900 calories so far today. She has also burned 500 calories in dance class. She wants to keep her daily calorie total to 1,500 calories per day. How many calories does she have left to consume for the day? Is 1,200 a viable solution to this problem?
No; 1,200 is more than the 500 she burned dancing.
No; 1,200 will cause her to exceed 1,500.
Yes; 1,200 is less than 1,500.
Yes; 1,100 is less than 1,500.
1,200 is not a viable solution to this problem as B.
No; 1,200 will cause her to exceed 1,500
How to calculate the value?It should be noted that Luna has consumed 900 calories so far today and has also burned 500 calories in dance class.
Therefore, the amount left will be:
= 1500 - (900 - 500)
= 1500 - 400
= 1100
Therefore, 1,200 is not a viable solution to this problem
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The difference between two numbers is 30. The sum of two-third of the first number and one-eleventh of the second number is 5. Find the product of the two numbers.
Answer:
26 and 32 are the two numbers, the product is 832
Step-by-step explanation:
h(t) = 2t^{2}[/tex] − t; t = 2, t = 9 Determine the net change between the given values of the variable. Determine the average rate of change between the given values of the variable.
The average rate of change between the given values of the variable is 21
What is a function?A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.
Given the function;
h(t) = 2t^{2}[/tex] − t
For t =2
Substitute the value of t as 2 in the function, we have;
h(2) = 2 (2)² - (2)
Find the square
h(2) = 2(4) - 2
h(2) = 8 - 2
h(2) = 6
For t = 9
Substitute the value of t as 9 in the function, we have;
h(9) = 2(9)² - 9
Find the square
h(9) = 2(81) - 9
h(9) = 153
The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21
Thus, the average rate of change between the given values of the variable is 21
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A spinner numbered 1 through 6 is spun. Find the probability that the number spun is a 3 given that it was less than 4 .
The probability that the number spun is a 3 given that it was less than 4 is 1/6.
Let A is the event of a number less than 4.
P(A) is the probability of getting a number less than 4.
The total number less than 4 is 3
Here, the total numbers in the game are 6.
By the Formula for the probability of an event E can be observed as:
P(A)= no of favorable cases/total no. of cases = 3/6 = 1/2
B is the event of getting the number 3
P(B) be the probability of getting 3
The total possible cases is 1
Therefore , P(B)= 1/6
Now, P(B/A) is the probability of getting 3 which is an odd number.
P(B/A)= P(A ∩ B) / P(A)
=1/6 / 1/2
= 1/3
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Please give me the answer for a) and b)
Answer: a) y=x²+6x+2 b) x=-3-√7, -3+√7
Step-by-step explanation:
(0,2) (-6,2) (-3,-7)
a)
y=ax²+bx+c
(0,2)
x=0 y=2
⇒ 2=a(0²)+b(0)+c
⇒ 2=0+0+c
⇒ 2=c
(-6,2)
x=-6 y=2
⇒ 2=a(-6)²+b(-6)+2
⇒ 2=36a-6b+2
⇒ 2-2=36a-6b+2-2
⇒ 0=36a-6b
⇒ 0+6b=36a-6b+6b
⇒ 6b=36a
Divide both parts of the equation by 6:
b=6
(-3,-7)
⇒ -7=a(-3)²+6(-3)+2
⇒ -7=9a-18+2
⇒ -7=9a-16
⇒ -7+16=9a-16+16
⇒ 9=9a
Divide both parts of the equation by 9:
1=a
Hence,
y=x²+6x+2
b)
x²+6x+2=0
D=(-6)²-4*1*2
D=36-8
D=28
√D=√28
√D=√(4*7)
√D=2√7
x=(-6±2√7)/2
x=-3-√7
x=-3+√7
Evaluate each expression for the given values of the variables.
-5(x + 2y) + 15(x + 2y) ; x=7 and y=-7
The result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70
Given,
The expression = -5(x+2y)+15(x+2y)
The value of the variables
x=7 and y= -7
Substitute the values in the expression
-5(7+2(-7))+15(7+2(-7))= -5(7-14)+15(7-14)
=-5(-7)+15(-7)
=35-105
=-70
Hence, the result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70
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If (3/5 - 1/8 i ) - (7/10 + 1/6 i )
Answer:
-1/10 - 7i/24
Step-by-step explanation:
solve the equation v3 = 12
Answer: v= root[3] {12}=2.2894
Step-by-step explanation:
Answer:Your answer is V=4
Step-by-step explanation:Need brainliest award
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Which describes the range of the parent absolute value function?
{y | y is a real number}
{y | y is an integer}
{y|y > 0}
{y|y < 0}
Answer:
{y|y≥0}
Step-by-step explanation:
The parent absolute value function is
This is a V-shaped function whose vertex is at the origin.
This means that, the least y-value is 0 and there is no highest y-value.
The range refers to all y-values for which the function exists.
Therefore the range is
Or
{y|y≥0}
Answer:
{y | y is a real number}
Step-by-step explanation:
because yxy=y=2
10. Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and
occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of
88mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered
potentially dangerous.
We get the absolute value inequality as | x - 88 | > 38.
We are given that:
Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and can occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88mg. We need to write an inequality for it.
We know that the blood sugar level should not be less than:
88 mg - 38 mg = 50 mg
Also, the blood sugar level should not be higher than:
88 mg + 38 mg = 126 mg
The inequality then will become:
50 mg ≤ Blood sugar level ≤ 126 mg.
The absolute value inequality will be:
| x - 88 | > 38
Therefore, we get the absolute value inequality as | x - 88 | > 38.
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Organic hotdogs at the grocery store cost $2.00 each. at a major league baseball game, an organic hotdog cost $6.50. by what percent does the baseball field mark up its organic hotdogs?
The baseball field mark up its organic hotdogs from $2.00 to $6.50 each by 225%.
The markup on cost is defined as the amount added to the original cost of a product or service to arrive at the new selling price. It can also be a percentage of the original cost.
mark up = selling price - original price
If organic hotdogs at the grocery store cost $2.00 each and at a major league baseball game, an organic hotdog cost $6.50, then the mark up price is the difference between the two.
mark up = selling price - original price
mark up = $6.50 - $2.00
mark up = $4.50
To get the percentage of the mark up from the original price, divide the mark up price by the original selling price and multiply by 100%.
percent mark up = (mark up price/original price) x 100%
percent mark up = ($4.50/$2.00) x 100%
percent mark up = 2.25 x 100%
percent mark up = 225%
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Kelsey used 2 identical stones to form a path that was 1.7 meters long. How long was each of the stones?
Point N is the midpoint of FG. If FN = 2x, what expression represents FG?
The line segment FG can be represented as expression 4x whose midpoint is N
We are provided with that Point N is the midpoint of FG and FN = 2x and We need to find expression that represents FG
As N is the midpoint of line segment FG than FN = NG
Also it could be written as FG = FN + NG because FG is the broken into two different line segment FN and NG because of the midpoint N
Therefore, FN = 2x which means FN= NG=2x
So, we can write an expression that could represent FG
FG = FN + NG
FG = 2x + 2x
FG = 4x
Hence, The line segment FG can be represented as expression 4x
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Identify the pattern and find the next three terms. 5/7, 8/7, 11/7, 2, ...........
The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are 17/7, 20/7, 23/7.
What is defined as the arithmetic progression AP?An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.
The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-
Common difference 'd' = a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = ....= an - a(n-1).nth term : an = a + (n - 1) dSum of nth terms; Sn = n/2(2a+(n-1)d) = n/2(a + l), where 'l' is the last term of an AP.Now, as per the stated question;
The AP given as; 5/7, 8/7, 11/7, 2, ...........
The series consists of four given terms.
Consider the initial term be 'a₁' = 5/7.
Then, the second term be 'a₂' = 8/7.
And, the third term be 'a₃' = 11/7.
And, the fourth term is 'a₄' = 2.
The AP have the same common difference. so,
d = a₃ - a₂
Substitute the values.
d = 11/7 - 8/7
d = 3/7
Thus, the common difference is 3/7.
or d = a₄ - a₃ (Put the values)
d = 2 - 11/7
d = 3/7
As, a₃ - a₂ = a₄ - a₃
Thus, we can conclude that the given sequence is in AP.
The fifth term will be; a₅ = a₄ + d = 2 + 3/7
a₅ = 17/7
Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7
a₆ = 20/7
Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7
a₇ = 23/7
Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.
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hi can someone help me here
Answer:
[tex]\textsf{1.} \quad x^2-2x-1[/tex]
[tex]\textsf{2.} \quad -3x^4-5x^3+14x^2+20x-8[/tex]
[tex]\textsf{3.} \quad -\dfrac{5}{2}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x) = x^2 - 4\\g(x) = x + 2\\h(x) = -3x + 1\end{cases}[/tex]
Question 1
The composite function (f + g - h)(x) means to add functions f(x) and g(x) then subtract function h(x):
[tex]\begin{aligned}(f+g-h)(x) & = f(x)+g(x)-h(x)\\& = (x^2-4)+(x+2)-(-3x+1)\\& = x^2-4+x+2+3x-1\\& = x^2+3x+x-4+2-1\\& = x^2+4x-3\end{aligned}[/tex]
Question 2
The composite function (fgh)(x) means to multiply functions f(x), g(x) and h(x):
[tex]\begin{aligned}(fgh)(x) & = f(x)\cdot g(x) \cdot h(x)\\& = (x^2-4)(x+2)(-3x+1)\\& = (x^2-4)(-3x^2-5x+2)\\& = -3x^4-5x^3+2x^2+12x^2+20x-8\\& = -3x^4-5x^3+14x^2+20x-8\end{aligned}[/tex]
Question 3
The composite function (f/g)(h)(1/2) means to substitute the value of function h(x) when x = 1/2 into function f(x) and function g(x) and divide the former by the latter:
[tex]\begin{aligned}\left(\dfrac{f}{g}\right)(h)\left(\dfrac{1}{2}\right) & = \dfrac{f\left(h\left(\dfrac{1}{2}\right)\right)}{g\left(h\left(\dfrac{1}{2}\right)\right)}\\\\& = \dfrac{f\left(-3\left(\dfrac{1}{2}\right)+1\right)}{g\left(-3\left(\dfrac{1}{2}\right)+1\right)}\\\\& = \dfrac{f\left(-\dfrac{1}{2}\right)}{g\left(-\dfrac{1}{2}\right)}\\\\& = \dfrac{\left(-\dfrac{1}{2}\right)^2-4}{\left(-\dfrac{1}{2}\right)+2}\\\\& = \dfrac{-\dfrac{15}{4}}{\dfrac{3}{2}}\\\\& = -\dfrac{5}{2}\end{aligned}[/tex]
Find the sum.
(3x² + x + 5) + (2x² + x - 2)
Answer:
5X2 + 2X + 3 orr 10x + 2
Step-by-step explanation:
What is the value of Σ⁵n=1 (2 n-3) ?
What is the value of Σ⁵n=1 (2 n-3) ? 15
[tex]\sum_{n=1}^{5} (2 n-3)\\\\ (2 (1)-3)+ (2 (2)-3)+ (2 (3)-3)+ (2 (4)-3)+ (2 (5)-3)\\\\ -1+1+3+5+7=15[/tex]
The sum of the given expression is 15
What is summation?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.To learn more about summation, refer:
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The midpoint M of FG has coordinates (8, 5). Point F has coordinates (6, 8). Find the
coordinates of point G.
Write the coordinates as decimals or integers.
Coordinates of point G is ( 10 , 2) in this equation.
What do mathematical point coordinates mean?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.M is the mid points of FG.
coordinates of M is ( 8,5)
coordinates of F is ( 6,8 )
Let coordinates of G point is ( x₂, y₂)
[tex]x = \frac{x_{1} + y_{1} }{2} , y = \frac{x_{2}+ y_{2} }{2}[/tex]
[tex]8 = \frac{6 + x_{2} }{2} , 5 = \frac{8 + y_{2} }{2}[/tex]
[tex]16 = 6 + x_{2} , 10 = 8 + y_{2}[/tex]
x₂ = 10 , y₂ = 2
So, coordinates of point G is ( 10 , 2)
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3. If pencils cost 15 cents each, and notebooks cost 85 cents each, find the number of pencils
purchased if 50 items cost $18.00.
Answer:
Pencils = 35
Notebooks = 15
Step-by-step explanation:
15 cents = 15/100 = $0.15
85 cents = 85/100 = $0.85
p + n = 50 Eq. 1
0.15p + 0.85n = 18 Eq. 2
p = number of pencils
n = number of notebooks
From Eq. 1
p = 50 - n Eq. 3
Replacing Eq. 3 in Eq. 2:
0.15(50-n) + 0.85n = 18
(0.15*50 + 0.15*-n) + 0.85n = 18
(7.5 - 0.15n) + 0.85n = 18
7.5 + 0.7n = 18
0.7n = 18 - 7.5
0.7n = 10.5
n = 10.5 / 0.7
n = 15
From Eq. 3:
p = 50 - n
p = 50 - 15
p = 35
Check:
From Eq. 2
0.15p + 0.85n = 18
0.15*35 + 0.85*15 = 18
5.25 + 12.75 = 18
e
Solve for y;
7(3y - x) = -21
Solve each equation. -y+13=-67
The solution of the given linear equation is y = 80.
According to the given question.
We have an equation.
-y + 13 = -67
Since, we have to solve the above linear equation in variable.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable -y + 13 = -67 is given by
-y + 13 = -67
⇒ - y = -67 -13 (subtractting 13 from both the sides)
⇒ -y = -80
⇒ y = 80
Hence, the solution of the given linear equation is y = 80.
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Solve the equation
|x/7|=3
Answer:
x = 21, -21
Step-by-step explanation:
Let's solve the problem,
→ |x/7| = 3
→ x/7 = 3 ll -x/7 = 3
→ x = 3 × 7 ll -x = 3 × 7
→ [ x = 21 ] ll [ x = -21 ]
So, the value of x is 21, -21.
-4>y+2>-10
qwdasdasddddddddddddddddddddddddddddddd
If you are looking to solve the inequality for y:
_____________________________________
Inequality Form:
[tex]-12 < y < -6[/tex]
Interval Notation:
[tex](-12, -6)[/tex]
Hope this helps!
Please help with problem 18, Algebra 1, in the attachment
Answer:
r=2
Step-by-step explanation:
To find the slope, we take the difference in the y values over the difference in the x values
m = ( y2-y1)/(x2-x1)
2 = ( 9-3)/ (5-r)
2 = (6)/(5-r)
Multiply each side by (5-r)
2 ( 5-r) = 6
Divide each side by 2
5-r = 6/2
5-r = 3
Subtract 5 from each side
5-r-5 = 3-5
-r = -2
r = 2
Answer:
r = 2
Step-by-step explanation:
To solve this problem, we have to use the following formula for slope:
[tex]\boxed{m= \frac{y_2 - y_1}{x_2 - x_1}}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points.
We are given the coordinates [tex](r, 3)[/tex] and [tex](5, 9)[/tex], and told that [tex]m = 2[/tex]. To find the value of r, we have to substitute the given values into the formula and then solve for r :
[tex]2 = \frac{9 - 3}{5-r}[/tex]
⇒ [tex]2 = \frac{6}{5-r}[/tex]
⇒ [tex]2\times (5-r) = \frac{6}{5-r} \times (5 - r)[/tex] [Multiplying both sides by (5 - r)
⇒ [tex]2(5-r) = 6[/tex]
⇒ [tex]\frac{2}{2}(5-r) = \frac{6}{2}[/tex] [Dividing both sides by 2]
⇒ [tex]5- r = 3[/tex]
⇒ [tex]5 - r - 5 = 3 - 5[/tex] [Subtracting 5 from both sides]
⇒ [tex]-r = -2[/tex]
⇒ [tex]\frac{-r}{-1}= \frac{-2}{-1}[/tex] [Dividing both sides by -1]
⇒ [tex]r = \bf 2[/tex]
What are the solutions of x² + 6x - 16 = 0?
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}\\\sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}\\\sqrt{6^2+64}\\\sqrt{36+64}\\\sqrt{100}\\\sqrt{10^2}\\=10\\x_1=\frac{-6+10}{2\cdot \:1},\:x_2=\frac{-6-10}{2\cdot \:1}\\\\\bold{x_1:2}\\\frac{-6+10}{2\cdot \:1}\\\frac{4}{2\cdot \:1}\\\frac{4}{2}\\=2\\\\\bold{x_2:-8}\\\frac{-6-10}{2\cdot \:1}\\\frac{-16}{2\cdot \:1}\\\frac{-16}{2}\\-\frac{16}{2}\\=-8[/tex]
Answer:
x₁ = 2
x₂ = -8
what’s the midpoint of C(-3,-8) and D(-6.5, -4.5)
Answer: M(-4.75,-6.25)
Step-by-step explanation:
C(-3,-8) D(-6.5,-4,5)
Let the midpoint of C(-3,-8) and D(-6.5, -4.5) is M(x,y)
[tex]\displaystyle\\M(x,y)=(\frac{-3+(-6.5)}{2} ,\frac{-8+(-4.5)}{y} )\\\\M(x,y)=(\frac{-9.5}{2},\frac{-12.5}{2})\\\\M(x,y)=(-4.75,-6.25)\\\\Thus, \ M(-4.75,-6.25)[/tex]
