The value of x is when the value of the function f(x) = 7 is x= -24 and x = 16
Function:
A correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to output is known as the function of the relation.
Given,
Here we have the function f(x) = 0.5|x - 4| - 3.
Now, we have to find the value of x when the value of f(x) = 7.
In order to find the value of x as have to equate the give function with the value of f(x), that is 7,
So, when we apply these on the function then we get,
=> 7 = 0.5|x - 4|-3
Now, we have to move all the numbers instead of x, then we get,
=> 7 + 3 = 0.5|x - 4|
=> 10 = 0.5 |x - 4|
=> 10/0.5 = |x - 4|
=> 20 = |x - 4|
So in this place we can get the following forms,
=> x - 4 = 20 and
=> x - 4 = - 20
Because we get two values being an absolute value function.
Now, we have to add 4 on both sides
Then we get
=> x - 4 + 4 = 20 + 4 and
=> x - 4 + 4 = - 20 + 4
So, the value of x is
=> x = 24 and x = - 16
Therefore, for the given function the values of x are 24 and - 16.
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Express 25p as a percentage of £2
Answer:
0.5
Step-by-step explanation:
If 50% of £2 is £1
and 25% of £1 is 25p
we can workout that 25% of £2 is 0.5
Write the equation of the function in point-slope form.
A line with a slope of 2 and passes through (5,-2)
Find equivalent expressions for 2y + 7 - 5y + 6y - 3 + y
Answer:
4y + 4
Step-by-step explanation:
Place similar together: 2y - 5y + 6y + 1y + 7 -3
Solve: (2-5+6+1)y + 4
4y + 4
Susan Asked her father for a no-interest loan of $8,000 so she could purchase a used car. She told her father that she would repay the loan at a rate of $250 per month.
The amount remaining on her after one year is $5000 .
In the question ,
it is given that ,
amount taken by Susan from her father = $8000 ,
interest rate charged by Susan father = 0%
amount that Susan will repay her loan per month = $250 .
So , the amount that Susan will repay in 12 months = 12×250
= $3000
So , in 1 year Susan will pay $3000 ,
the amount of loan remaining after 1 year = (loan amount) - (amount paid in 1 year)
the amount of loan remaining after 1 year = 8000 - 3000
= $5000
Therefore , The amount remaining on her after one year is $5000 .
The given question is incomplete , the complete question is
Susan Asked her father for a no-interest loan of $8,000 so she could purchase a used car. She told her father that she would repay the loan at a rate of $250 per month . How much will be remaining on her loan after one year ?
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Which of the following is the correct formula for the margin of error in the interval estimation of p?
Multiple Choice
zα / 2p ( 1 − p )n− 1−−−−−−√zα / 2p ( 1 − p )n− 1
zα / 2p¯ ( 1 − p¯ )n − 1 −−−−−−−√zα / 2p¯ ( 1 − p¯ )n − 1
zα / 2p ( 1 − p )n−−−−−−√zα / 2p ( 1 − p )n
zα / 2p¯ ( 1 − p¯ )n−−−−−−−√
The correct formula for the margin of error in the interval estimation of p is Za/2 √p(1-p)/n.
Interval estimation:
Interval estimation refers the evaluation of a parameter—for example, the mean (average)—of a population by computing an interval, or range of values, within which the parameter is most likely to be located.
Given,
Here we need to find the correct formula for the margin of error in the interval estimation of p.
In order to find the correct formula for the margin of error, we have to know the definition of the margin of error,
Margin of error states that "a statistical measurement that accounts for the difference between actual and projected results in a random survey sample."
According to this definition, we have identified that the correct formula, for the margin of error in the interval estimation P is written as,
=> Za/2 √p(1-p)/n.
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Given f(x) = 3x + 5, describe how the graph of g compares with the graph of f. g(x) = 3(0.1x) + 5
The following data is gotten from comparing the graph of f(x) = 3x + 5 to graph of g(x) = 3(0.1x) + 5
Both has y intercept of 5
g(x) is a vertical compression of f(x) by a factor of 0.1
How to make the comparisonThe graph of the both linear equation is plotted and attached
solving for y intercept by substituting x = 0 into f(x) = 3x + 5 shows that
f(x) = 5
solving for y intercept by substituting x = 0 into g(x) = 3(0.1x) + 5 shows that
g(x) = 5
examining the both equations, it can show that the slope of f(x) is multiplied by a factor 0.1 this results to vertical shrink
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Find the slope of the line \mathrm{y}=5\mathrm{x}+4y=5x+4.
The slope of the line y = 5x + 4 is 5.
Slope i.e. m = 5.
Given, a line of equation
y = 5x + 4
We have to find the slope of the given line,
Now, as we know the slope-intercept form of a line i.e.
y = mx + c
where, m is the slope of the line and c is the y-intercept of the line.
So, using the same form in the line, we get
y = 5x + 4
the slope of the line is 5.
Hence, the slope of the line y = 5x + 4 is 5.
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Emmy bought 53.6 ounces of cat food and 4.7 ounces of dog food. How much pet food did
she buy in all?
Answer:
Step-by-step explanation:
53.6 oz + 4.7 oz
= 58.3 oz in total
Answer:
58.3 ounces
Step-by-step explanation:
53.6 + 4.7 = 58.3
what direction does this parabola open? (x-4)2=-15(y+18)
The parabola with the equation (x-4)²=-15(y+18) opens downwards.
The equation of the parabola is (x-4)²=-15(y+18)
From the equation we can infer that the parabola has the vertex at (4,-18) and the axis of symmetry is the line x = 4 .
(x-4)²=-15(y+18)
or, x² -8x + 16 = -15y -270
or, 15y = -x² + 8x - 286
The equation is of the general form : y = ax² + bx + c therefore the parabola will have two x values for every y value. So either the parabola will open upwards or downwards.
Now the general form of the parabola we find that the coefficient of the highest power of x is -1 (negative value)
Therefore the graph of the parabola opens downwards as illustrated by the graph of the parabola attached below.
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Jordan i working two ummer job, making $13 per hour lifeguarding and $10 per hour walking dog. Lat week Jordan earned a total of $177 and worked 3 more hour lifeguarding than hour walking dog. Determine the number of hour Jordan worked lifeguarding lat week and the number of hour he worked walking dog lat week
Jordan worked 9 hours as lifeguarding
Jordan worked 6 hours walking dog
given that
Jordan making $13 per hour lifeguarding and $10 per hour walking the dog
last week Jordan earned a total of $177
let x be the number of hours she worked walking the dog
let y be the number of hours she worked as a lifeguard
13y+10x=177 -------- (1)
worked 3 more hour lifeguarding than an hour walking dog
y = 3 + x --------(2)
substitute equation 2 in 1
13(3+x) +10x =177
39+13x+10x = 177
39 + 23x = 177
23x = 177 -39
23x = 138
x = 138/23
x = 6
now substitute x=6 in equation 2
y = 3 + 6
y = 9
9 number of hours he worked lifeguarding last week
6 number of hours he worked walking dog last week
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Question 4(Multiple Choice Worth 2 points) (Evaluating Algebraic Expressions LC) What is the value of 12x if x = -5? O-60 O-17 O-125 O-47 please help
The value of 12x is -60, if x = -5.
Given expression is 12x, if x = -5
To solve the expression we have to compute the x value in the given expression:
= 12x
= 12(-5)
Now we have to simplify 12(-5) by multiplying negatives
= -12*5
Multiplying an odd number of negative numbers gives a negative number.
So, Now we have to multiply the constants, that equals to
= -60
Hence the answer is the value of 12x is -60, if x = -5.
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The equation of line line a gis y = (startfraction b over a c endfraction)x. the midpoint of bc is (a c, b). does the midpoint of bc lie on line a g? why or why not? no, because (startfraction b over a c endfraction)b does not equal a c no, because (startfraction b over a c endfraction)(a c) does not equal b yes, because (startfraction b over a c endfraction)b = a c yes, because (startfraction b over a c endfraction)(a c) = b
yes, because the midpoints (a+c) = b
Given that the line's equation is y=x.
B and C are the two points on this line.
( a+ c, b) is the midpoint of B and C.
We can see from this that using the midpoint formula
a + c = [tex]\frac{x1+x2}{2}[/tex]
b=[tex]\frac{y1+y2}{2}[/tex]
Because both points are on y=x, we get
x1=y1, x2=y2.
As a result, x1 = a+c and 2y1 = 2b or y1 =b.
Because x1=y1, we have a+c =b.
In other words, the coordinates of the midpoint satisfy the equation y=x.
Thus, the answer is
because (a+c) = b
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Find the Error A student found the slope of one segment on a line to be 4 and the slope of another segment on the same line to be 8/2. He concludes that the slope is different at different points on the line. Correct his thinking
If we simplify the fraction we will see that the slope is equal in the two segments of the line.
How to correct the student?
A linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept, both of these are constants.
In this case the student found the slope on one part to be 4, and on other part to be 8/2.
But if you solve that second quotient:
8/2 = 4
The slope is still 4, so in both segments the slope is the same, which means that the slope is equal at different parts of the line.
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which function represents g(x), a reflection of f(x) = 6
H
across the y-axis?
) = −6(-3)*
O g(x) =
©_g(x) = −6[³]*
O g(x) = 6(3)*
O g(x) = 6(3)*
Step-by-step explanation:
Answer: D.) g(x) = 6(3)^{-x}g(x)=6(3)
−x
Step-by-step explanation: We are given an exponential function f(x).
g(x) is an exponential function that is being reflected across y-axis.
According to rules of transformations y=f(-x).
That is variable x is being multiplied by a negative sign.
In the given options g(x) = 6(3)^{-x}g(x)=6(3)
−x
, the variable x is being multiplied by a negative sign.
Therefore, correct option is D option.
The function represents the reflection is g(x) = 6 (3[tex])^{-x[/tex].
What is Function?A function is a type of rule that produces one output for a single input.
a mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependent variable (the dependent variable).
We are given an exponential function f(x).
Also, g(x) is an exponential function that is being reflected across y-axis.
Here the rule of transformations y=f(-x).
The x-coordinate and y-coordinate swap places and the signs if you deflect across the line y = -x.
Reflections: By multiplying by -1, a function can be mirrored about an axis.
So, the function after reflection is
g(x) = 6 (3[tex])^{-x[/tex]
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The graph f (x) = x is shifted down 6 and to the right 3 and reflected over the x-axis. Which of the following is the function of the resulting transformation?
The function of the resulting transformation is f(x) = -x - 3 + 6.
Given:
The graph f (x) = x is shifted down 6 and to the right 3 and reflected over the x-axis.
The first transformation:
shifted down 6 units
f(x) = x - 6
second transformation:
x = x + 3.
f(x) = x + 3 - 6
Third transformation:
reflected over the x-axis.
f(x) = -1(x+3-6)
f(x) = -x - 3 + 6.
Therefore the function of the resulting transformation is f(x) = -x - 3 + 6.
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04.02 Comparing Functions
i need help asap yall
The values of the function when x = 3 are -10. -1 and -3, respectively
The values of the functionFunction 1
The equation of the function is given as
y = -4x + 2
We have the value of x to be 3
So, we have
y = -4 x 3 + 2
Evaluate
y = -10
Function 2
The graph represents the notation of the function
On the graph, we have the value of y to be -1, when x = 3
This means that
y = -1
Function 3
The table represents the notation of the function
On the table, we have the value of y to be -3, when x = 3
This means that
y = -3
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Y+6=7(c-4) in slop intercept form
y = 7c - 34 is slop intercept form of equation .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form. A line has the equation 3x + 4y + 5 = 0. The slope intercept form can be used to calculate the line's slope and y-intercept.slop intercept form of equation
y = mx + c
Y+6=7(c-4)
y + 6 = 7c - 28
y = 7c - 28 - 6
y = 7c - 34
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(9x 10^-2 )- (3x 10^-2
a.6 x 10^-4
b.12 x 10^-2
c.6 x 10^0
d.6 x 10^-2
Answer:
Step-by-step explanation: i'm not one hundred percent sure but i think its B
The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A
The rate for Printer B is greater than the rate for Printer A because the rate of 25 pages per minute is greater than the rate of 15 pages per minute for Printer A.
How to compare graph rates?From the attached graph of the printing rate of Printer A, we can see that;
At 1 minute, number of pages printed = 15
At 2 minutes, number of pages printed = 30 minutes
At 3 minutes, number of pages printed = 45
Thus printing rate for printer A is; 15/1 = 30/2 = 45/3 = 15 pages per minutes
Since printer B can print 25 pages per minute, we can conclude that;
The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A
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Complete question is;
The graph shows the printing rate of printer A. Printer B can print at the rate of 25 pages per minute. How does the printing rate of printer B compare to the printing rate for printer A.
Match the numbers with the correct label.
Answer:
a = [tex]\frac{1}{7}[/tex]
b = .2
c= [tex]\frac{3}{9}[/tex]
Step-by-step explanation:
You could change all of the numbers to decimals and then order
[tex]\frac{1}{7}[/tex] ≈ .1428
.2 =.2
[tex]\frac{3}{9}[/tex] ≈ .3
Type the correct answer in each box. Use numerals instead of words.
The table below shows the cost for certain number of truck loads of fruit. Fill in the missing costs.
Truck
Load Cost ($)
1 2,530
2
3 7,590
8
Based on the pattern in the table, 11 truck loads of fruit would cost $
.
Based on the pattern in the table (see attachment), 11 truck loads of fruit would cost $27,830.
What is a direct proportion?Mathematically, a direct proportion or direct variation can be represented the following mathematical expression:
y = kx
Where:
y represents the truck load.x represents the cost in dollars.k represents the constant of proportionality.By applying direct proportion, we have the following mathematical expressions:
1 truck load of fruit = 2,530 dollars.
11 truck load of fruit = X dollars.
Cross-multiplying, we have the following:
Cost, X dollars = 11 truck load of fruit × 2,530 dollars.
Cost, X dollars = 27,830 dollars.
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if the probability that the islanders will beat the rangers in a game is 0.62 what is the probability that the islanders will win exactly one out of three games in a series against the rangers?
Answer : The chance that the Islanders will win n games out of 6 is:
0.47 ^ n + (1 - 0.47) ^ (6 - n) * 6! / n! / (6 - n!)So, the chance of winning 4 games is 0.205605
the chance of winning 5 games is 0.072932
the chance of winning all 6 games is 0.010779
Adding these together we get 0.289316
Rounding to the nearest thousandth we get 0.289 (or 28.9%)891 viewsRelated questions (More answers below)
Step-by-step explanation:
how to solve percent change and percent error problem
The way to calculate the percentage change will be:
Step 1: Take one value and subtract it from another.
Step 2: Subtract the error from the exact or ideal value (not your experimental or measured value). This will result in a decimal number.
Step 3: Multiply the decimal number by 100 to get the percentage.
Step 4: To report your percent error value, use the percent or % symbol.
What is percentage error?The difference between an approximate or measured value and an exact or known value is expressed as a percentage in percent error.
It is a scientific term that describes the difference between a measured or experimental value and a true or exact value.
It's important to divide the new value by the old value to get the percentage change.
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find the value of w. round to the nearest tenth
Answer:
[tex]\pmb {w=13.11}[/tex]Step-by-step explanation:
[tex]\pmb {sin(22)^o=\cfrac{x}{35} }[/tex]
[tex]\pmb {35sin(22)=w}[/tex]
[tex]\pmb {w=13.11}[/tex]
_________________
Hope this helps!
Have a great day! :)
i really need help with
Given: Circle O, and RO bisects MP
prove: MR is congruent to PR
Answer:
Step-by-step explanation:
Statements: Reasons:
RO bisects MP Given
MO is congruent to PO Definition of a bisector
RO is congruent to RO Reflexive property
That is all i know so far and what I have learned. I'm in 9th grade so i don't know much. Sorry! Wish i could help more
The position of the squirrel can be calculated using the function p (t) = at² + bt + c.
What is the value of a?
What is the value of b?
What is the value of c?
The value of a is 5/19
The value of b is -160/19
The value of c is 960/19
Given,
The quadratic function formula;
p(t) = at² + bt + c
We have to interpret quadratic graphs;
Thus, the equation is now;
p(t) = at² + bt + 0
p(t) = at² + bt
From the graph, we see that when x = 8, y = 0. Thus;
p(8) = a(8²) + 8b + c = 0
64a + 8b + c = 0 ------(1)
From the graph, we know that the axis of symmetry is;
x = -b/2a
Thus;
16 = -b/2a
b = -32a -----(2)
From the graph, we see that when x = 5, y = 15. Thus;
p(8) = a(5²) + 5b + c = 0
25a + 5b + c = 15 ------(3)
Put -32a for b in eq 1 and 3 to get;
64a + 8(-32a) + c = 0
-192a + c = 0 ------(4)
25a + 5(-32a) + c = 15
-135a + c = 15 ------(5)
Subtract eq 4 from eq 5 to get;
192a - 135a = 15
57a = 15
a = 15/57
a = 5/19
Thus;
b = -32(5/19) = -160/19
-135(5/19) + c = 15
15 + (675/19) = c
c = 960/19
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Find the slope (6,-10),(-15,15)
Answer:
-25/21
Step-by-step explanation:
Slope Formula:
m=(y1-y2)/(x1-x2) where m is the slope
m=(-10 - 15)/(6 - (-15))
m=(-(10+15)/(6+15))
m=-25/21
Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 3/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should be 5/2 equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.
Now, use opposite operations on the equation from part B to move one of the terms so they are both on the same side of the equal sign.
Please it worth 43 points
The equation that represents this situation while the variable s representing the amount of dough needed , for a small pizza is (5/2)S = (3/2)S + S .
In the question ,
it is given that
amount of dough for a medium pizza is 3/2 times the amount of dough for small pizza ,
let the amount of dough required for small pizza = S
let the amount of dough required for large pizza = L
let the amount of dough required for medium pizza = M
So , M [tex]=[/tex] (3/2)S
and amount of dough for a large pizza is 5/2 times the amount of dough for small pizza ,
that is
L [tex]=[/tex] (5/2)S
amount of dough used for one large pizza is equal to the amount of dough used for one medium and one small pizza ,
that is L [tex]=[/tex] M [tex]+[/tex] S .
Substituting the value of L and S , we get
(5/2)S [tex]=[/tex] (3/2)S + S
We have a linear equation that is true for all S , there is no unique solution to this equation .
Therefore , The equation that represents this situation is (5/2)S = (3/2)S + S .
The given question is incomplete , the complete question is
Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be 3/2 times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 5/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should to be equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.
Write an equation to represent this situation while the variable s representing the amount of dough needed , for a small pizza .
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