Answer:
Step-by-step explanation:
[tex]f(x)=g(x) \implies \frac{1}{x+1}=\frac{1}{x^{2}}[/tex]
This means the denominators cannot equal to (because then the fractions would be undefined) so the domain is [tex]x \in \mathbb{R} -\{-1,0\}[/tex]
please help me quick!
Answer:
transition 1 would be 5 to the right
transition 2 would be 1 down
Step-by-step explanation:
Every variable has a coefficient. That’s the number it is multiplied by. According to mathematical convention, coefficients always go in front of their variable. If there is no number in front of a variable in an expression, the coefficient is 1 since the product of any number and 1 is that number. In expressions, operations can be applied directly to a variable. Here are some examples: What is the coefficient of the variable in the expression ½ + v - 3?
Answer:
1
Step-by-step explanation:
Answer:
There is only 1 variable and it is v.
There is no coefficient.
That means the coefficient is 1.
The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]
What is the coefficientIn mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b, and c). When the coefficients are themselves variables, they may also be called parameters.
Given that,
[tex]\frac{1}{2}[/tex] is the coefficient
[tex]v[/tex] is the variable
[tex]3[/tex] is the constant
Therefore, The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]
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Isabel works for a company that makes toys. She is trying to figure out what types of toys kids enjoy playing with most. She started with a survey asking whether kids liked dolls or trains. She surveyed 80 kids. Of the kids who don't like dolls, 30% more kids like trains than don't like trains. Fill out the rest of his table.
The table that represents the survey conducted by Isabel is:
Like Dolls Don't like Dolls Total
Like Trains 40 15 55
Don't like Trains 17 8 25
Total 57 23 80
How can the table be filled?The total number of kids that like dolls = total number kids - total number of kids that don't like dolls
80 - 23 = 57
Number of kids that don't like Trains but like dolls = total number kids that like dolls - Number of kids that like Trains and dolls
57 - 40 = 17
Number of kids that don't like dolls and but like trains :
30% x 23 = 7
(23 - 7) /2 + 7 = 15
Number of kids that don't like dolls and trains = (23 - 7) / 2 = 8
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HELP!!! The box plots compare the speeds of cars traveling on a highway
Answer:
See below ~
Step-by-step explanation:
The statements which are true :
The interquartile range for the cars going South is 9The maximum speed for the cars going North is higher than the maximum speed for the cars going SouthThe interquartile range for the cars going North is higher than the interquartile range for the cars going SouthThe late fees for a school library are represented by the function
c=0.25d, where c is the total cost and d is the number of days.
a book is late. The fees charged by a city library are shown in the
table.
Answer:
Rates of change:
school library: $0.25 per day;
city library: $0.35 per day
| Snapsolve. ... where \(c\) is the total cost and \(d\) is the number of days a book is late. The fees charged by a city library are shown in the table
Step-by-step explanation:
Does this app offer tutoring for college algebra?
What is the mean absolute deviation of 4,6,7,10,13
Answer:
2.8
Step-by-step explanation:
To find the mean aboslute deviation, you first need to find the mean:
(4 + 6 + 7 + 10 + 13)/5 = 8
Then, subtract the mean from each value, and take the abosulte value. Absolute value is essentially the same number, but if it is negative, make it positive.
4 - 8 = -4 = 4
6 - 8 = -2 = 2
7 - 8 = -1 = 1
10 - 8 = 2 = 2
13 - 8 = 5 = 5
Then, take the mean of all of these values:
(4 + 2 + 1 + 2 + 5)/5 = 2.8
hi can anyone solve my math problem
Answer:
The solutions to this equation are x = -8/9 and x = -16/3.
Step-by-step explanation:
We have this equation here:
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+\frac{6}{3} |[/tex]First, let's simplify the right sight of the equation by simplifying 6/3 to 2.
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+2 |[/tex]Multiply both sides of the equation by 3 in order to get rid of the fractions.
[tex]|x-4|=2x+6|x+2|[/tex]Move the terms on either side of the equation to set them equal to 0.
[tex]|x-4|-2x-6|x+2|=0[/tex]Now, we can split this equation up into 4 possible cases. In each case, we make the absolute values negative or positive.
Case #1 (first absolute value: positive; second absolute value: positive)[tex](x-4)-2x-6(x+2)=0[/tex]Simplify this equation by distributing -6 inside the parentheses.
[tex]x-4-2x-6x-12=0[/tex]Combine like terms.
[tex]-7x-16=0[/tex]Add 16 to both sides of the equation and divide by -7.
[tex]\displaystyle \boxed{x=-\frac{16}{7}}[/tex]Case #2 (first absolute value: negative; second absolute value: positive)[tex]-(x-4)-2x-6(x+2)=0[/tex]Distribute the negative sign and -6 inside of their respective parentheses.
[tex]-x+4-2x-6x-12=0[/tex]Combine like terms.
[tex]-9x-8=0[/tex]Add 8 to both sides of the equation and divide by -9.
[tex]\displaystyle \boxed{x=-\frac{8}{9}}[/tex]Case #3 (first absolute value: positive; second absolute value: negative)[tex](x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative sign inside the parentheses first.
[tex]x-4-2x-6(-x-2)=0[/tex]Now, distribute -6 inside the parentheses.
[tex]x-4-2x+6x+12=0[/tex]Combine like terms.
[tex]5x+8=0[/tex]Subtract 8 from both sides of the equation and divide by 5.
[tex]\displaystyle \boxed{ x=-\frac{8}{5}}[/tex]Case #4 (first absolute value: negative; second absolute value: negative)[tex]-(x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative signs inside the parentheses first.
[tex]-x+4-2x-6(-x-2)=0[/tex]Distribute -6 inside the parentheses.
[tex]-x+4-2x+6x+12=0[/tex]Combine like terms.
[tex]3x+16=0[/tex]Subtract 16 from both sides of the equation and divide by 3.
[tex]\displaystyle \boxed{x=-\frac{16}{3}}[/tex]Extraneous SolutionsWhenever we solve problems with absolute values, we will always need to check for extraneous solutions.
Definition: These are solutions that may come up while solving but do not actually fit in the domain of the original problem.
Checking for these is tedious, but it will help eliminate wrong answers, so let's plug every "solution" for x that we found back into the original equation.
1) x = -16/7Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{7}) -4|=\frac{2}{3} (-\frac{16}{7}) +2|(-\frac{16}{7}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{21} =-\frac{20}{21}[/tex]Since this equation is NOT true, this means that x = -16/7 is NOT A SOLUTION.
2) x = -8/9Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{9}) -4|=\frac{2}{3} (-\frac{8}{9}) +2|(-\frac{8}{9}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{27} =\frac{44}{27}[/tex]Since this equation IS true, this means that x = -8/9 IS A SOLUTION.
3) x = -8/5Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{5}) -4|=\frac{2}{3} (-\frac{8}{5}) +2|(-\frac{8}{5}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{15} =-\frac{4}{15}[/tex]Since this equation is NOT true, this means that x = -8/5 is NOT A SOLUTION.
4) x = -16/3Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{3}) -4|=\frac{2}{3} (-\frac{16}{3}) +2|(-\frac{16}{3}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{9} =\frac{28}{9}[/tex]Since this equation IS true, this means that x = -16/3 IS A SOLUTION.
Final AnswerThe two true solutions of the double absolute value equation, shown above, are:
[tex]\displaystyle \boxed{-\frac{8}{9} } \ \ \& \ \ \boxed{-\frac{16}{3}}[/tex]Answer:
x = -16/3 or -8/9
Step-by-step explanation:
The equation can be rewritten as a piecewise linear function with two breakpoints, or three domain regions. Each breakpoint is at the value of x where the argument of the absolute value function is zero: at x=4 and x=-2.
For each absolute value, we have ...
|q| = -q for q < 0
|q| = q for q ≥ 0
Then the three parts of the domain are ...
x < -2 . . . . . . . . where |x +2| has its vertex-2 ≤ x < 4 . . . . . between the vertices4 ≤ x . . . . . . . . . where |x -4| has its vertex__
Subtracting the right side, the equation becomes ...
1/3|x -4| -2/3x -2|x +2| = 0
Then the three piecewise functions are ...
x < -2Both absolute value arguments are negated.
1/3(-(x -4)) -2/3x -2(-(x +2)) = 0
x(-1/3 -2/3 +2) +4/3 +4 = 0 . . . . . collect terms
x +5 1/3 = 0 . . . . . . . simplify
x = -5 1/3 . . . . . . . . . subtract 5 1/3. This result is in the domain
__
-2 ≤ x < 4Only the argument of |x -4| is negated.
1/3(-(x -4)) -2/3x -2(x +2) = 0
x(-1/3 -2/3 -2) +4/3 -4 = 0 . . . . collect terms
-3x -8/3 = 0 . . . . . . . simplify
-3x = 8/3 . . . . . . . add 8/3
x = -8/9 . . . . . divide by -3. This result is in the domain
__
4 ≤ xNeither absolute value function argument is negated.
1/3(x -4) -2/3x -2(x +2) = 0
x(1/3 -2/3 -2) -4/3 -4 = 0 . . . . . collect terms
-7/3x -8/3 = 0 . . . . . . . . . simplify
-7/3x = 8/3 . . . . . . . . add 8/3
x = -8/7 . . . . . . . . . divide by -7/3. This result is not in the domain.
There is no solution in this region.
__
The solutions are ...
x = -5 1/3x = -8/9how many circular tiles are needed for pattern 20
Which of the following graphs matches the equation y=−4x+3?
CLEAR CHECK
On a coordinate plane, a line goes through (0, 3) and (3, negative 3).
On a coordinate plane, a line goes through (negative 2, 5) and (0, negative 3).
On a coordinate plane, a line goes through (0, 3) and (3, negative 1).
Answer:
On a coordinate plane, a line goes through (0, 3) and (3, negative 1).
Answer: the bottom left
Step-by-step explanation:
you will find it or just look it up if im wrong
Select the statement that describes this expression: fraction 1 over 2 x (734 − 246).
Half the sum of 734 and 246
fraction 1 over 2 the difference between 734 and 246
fraction 1 over 2 the quotient of 734 and 246
2 times the difference between 734 and 246
Help me with the 2 problems
Answer:
9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.
10a) 310,000 + x = 465,000; so x = 155,000
10b) 930,000/310,000 = 3 times more
Step-by-step explanation:
Based on the data in the two-way table, what is the probability that a person consumes 1,500 to 2,000 calories in a day? A. 0.22 B. 0.28 C. 0.35 D. 0.50
Using it's concept, it is found that the probability that a person consumes 1,500 to 2,000 calories in a day is given by:
D. 0.50
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching the problem on the internet, it is found that out of 500 people, 250 consume 1,500 to 2,000 calories in a day, hence the probability is given by:
p = 250/500 = 0.5.
Which means that option D is correct.
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rewrite! Write an new and equivalent equation that is easier to solve
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - an equation in a standard formTo do - simplify the equation so as to obtain an easier oneSince the equation provided isn't in it's general form , let's first convert it ~
General form of a Linear equation -
[tex]\bold{ax + b = 0}[/tex]
The equation after getting converted will be as follows ~
[tex] - 7 + ( \frac{4x + 2}{2} ) = 8 \\ \\ \implies \: \frac{ - 14 + 4x + 2}{2} = 8 \\ \\ \implies \: - 14 + 4x + 2 = 16 \\ \\ \implies \: 4x = 16 + 14 - 2 \\ \\ \implies \: 4x = 28 \\ \\\bold{ General \: form \: \dashrightarrow \: 4x - 28 = 0}[/tex]
hope helpful ~
At a baseball game, a vender sold a combined total of 183 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.
Answer:
61 hot dogs
122 sodas
Step-by-step explanation:
x+x2=183
3x=183
183÷3=
61
Please help pethagriem entherum
Hey ! there
Answer:
13 is the answer .Step-by-step explanation:
In this question we are provided with right angle triangle having hypotenuse ( longest side ) = c , perpendicular = 5 and base = 12 . And we are asked to find the length of missing side i.e. hypotenuse and if necessary we have to round it off to 2 decimal places.
We can find the missing side by using Pythagorean Theorem . It states that sum of squares of perpendicular and base is equal to square in a right angle triangle that is ,
[tex] \: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^{2} = P {}^{2} + B {}^{2} }}}[/tex]
Where ,
H refers to HypotenuseP refers to PerpendicularB r refers to BaseSOLUTION : -
Substituting value of hypotenuse as c , perpendicular as 5 and base as 12 in formula :
[tex] \quad \longmapsto \qquad \: (c) {}^{2} = (5) {}^{2} + (12) {}^{2} [/tex]
Squaring 5 and 12 :
[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 25 + 144[/tex]
Adding 25 and 144 :
[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 169[/tex]
Applying square root to both sides :
[tex] \quad \longmapsto \qquad \: \sqrt{(c) {}^{2} } = \sqrt{169} [/tex]
On simplifying , We get :
[tex] \quad \longmapsto \qquad \orange{\underline{\boxed{\frak{c = 13}}}} \quad \bigstar[/tex]
Henceforth , ❝ 13 ❞ is the length of missing side .Verifying : -
Now we are checking our answer by putting all values in formula . So ,
( 13 )² = ( 5 )² + ( 12 )²169 = 25 + 144169 = 169L.H.S = R.H.SHence, Verified .Therefore , our answer is correct .
#Keep LearningAnswer :
13[tex] \: [/tex]
Step-by-step explanation :
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]
Here,
The Base is 12The Perpendicular is 5The Hypotenuse is c.[tex] \: [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= (12) {}^{2} + (5 {)}^{2} }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 144 + 25 }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 169 }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad c = \sqrt{169} }}} \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad c= 13 }}}\\ \\[/tex]
Therefore,
The measure of the third side (c) is 13Answer for x?
Helppp
Answer:
x = 7
The length of the side is 18
Step-by-step explanation:
40 / 16 = 2.5
meaning the shape is dilated by 2.5
45 / (2x + 4) = 2.5
→ multiply both side by the denominator
45 / (2x + 4) * (2x + 4) = 2.5 * (2x + 4)
→ simplify
45 = 2.5 * (2x + 4)
→ divided both side by 2.5
45 / 2.5 = 2.5 * (2x + 4) / 2.5
18 = 2x + 4
→ subtract 4 from both sides (want x alone)
18 - 4 = 2x + 4 - 4
14 = 2x
→ divid both side by 2
14 / 2 = 2x / 2
7 = x
Plug in x:
2x + 4 = 2(7) + 4
14 + 4 = 18
Evaluate the expression below for x = 2.
3x+4 x-81-14
Answer:
I think that the answer is -81
Step-by-step explanation:
We have 3x+4x-81-14 x is given as 2.So we'll have 3*2+4*2-81-14= -81 per my calculations. TRY THIS
Which is a statistical question that you can ask to learn about your classmates' pets?
How many students in my class have a dog for a pet?
How many pets are in each student's household?
O How many classmates have a reptile for a pet?
How many pets does Mrs. Bruckner have?
Answer:
Answer "A" is correct
Step-by-step explanation:
I got it right on edge test
What is the volume of the bookend?
“See image” I CANT FIGURE THIS OUT
(Hint: The volume of a rectangular prism is the product of its length, width, and height.)
A.
B.
C.
D.
Answer:
(573+9/2 cubic inches
Step-by-step explanation:
the answer is A
va rog, dau coroana + 20 de puncte (doar exercitiul 2)
Step-by-step explanation:
a) 1*7=7 (Litres);
b) 1*2*5=10 (Litres);
c) 10*0.5*1/0.5=10 (bottles)
Your Assignment
210 students were asked whether they want to go to a water park or a roller skating rink for a class party.
50 students are girls who want to go to the water park.
45 students are girls who want to go skating.
60 students are boys who want to go to the water park.
Water park
Skating
Total
Boys
Girls
Total
Answer the questions to analyze the data.
1. Use the given information to fill in the two-way table.
if a+b=10 and a-b=6,then find the value of (a²+b²)
Answer:
68
Explanation:
Sets of equations:
1) a + b = 10
2) a - b = 6
Make 'a' the subject:
1) a = 10 - b --- equation 1
2) a = 6 + b --- equation 2
Solve them by substituting:
⇒ 10 - b = 6 + b
⇒ -b - b = 6 - 10
⇒ -2b = -4
⇒ b = 2
Find value of 'a', a = 10 - b, a = 10 - 2 = 8
Then find (a²+b²), by inserting a = 8, b = 2,
⇒ ((8)²+(2)²) = 64 + 4 = 68
Step-by-step explanation:
given,
a+b=10.............( eqn 1)
a-b=6................(eqn 2)
adding eqn1 and eqn2
a+b=10
a-b=6
______
2a=16
a=16/2
a=8
putting the value of a in eqn 1
a+b=10
8+b=10
b=10-8
b=2
now,
(a²+b²)= 64+4=68
find the domain and range with a vertex of (1,-2)
Answer:
see explanation
Step-by-step explanation:
the domain ( values of x ) that a quadratic can have is all real numbers
domain : - ∞ < x < ∞
the range ( values of y ) are from the vertex upwards , that is
range : y ≥ - 2
A line passes through the point (-2, -9) and has a slope of 8
Step-by-step explanation:
[tex]y - y_1 = m.(x - x_1)[/tex]
[tex]y - ( - 9) = 8.(x - ( - 2))[/tex]
[tex]y = 8x + 16 - 9[/tex]
[tex]y = 8x + 7[/tex]
Answer:
y = 8x + 7
Step-by-step explanation:
We are given that a line contains the point (-2, -9), and a slope of 8
We want to write the equation of this line
There are multiple ways to write the equation of the line:
Slope-intercept form, written as y=mx+b where m is the slope and b is the y interceptStandard form, written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero and a cannot be negativePoint-slope form, written as [tex]y-y_1=m(x-x_1)[/tex], where m is a slope and [tex](x_1, y_1)[/tex] is a pointThe most common of these 3 methods is slope-intercept form, so let's write our equation this way
As we are already given the slope, we can immediately plug that into our formula for m
Replace m with 8:
y=8x+b
Now we need to find b
As the equation passes through (-2, -9), we can use its values to help solve for b
Substitute -2 as x and -9 as y:
-9 = 8(-2) + b
Multiply
-9 = -16 + b
Add 16 to both sides
7 = b
Substitute 7 as b.
y = 8x + 7
Topic: finding the equation of the line
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What is the slope of the line through (-4,2) and (−4,2)
Answer:
Step-by-step explanation:
there is no slope. they have the same coordinates
find the volume of this figure. round your answer to the nearest hundredth. if necessary
#8
Answer:
30 miles²
Step-by-step explanation:
To solve the area of the prism we have to multiply the area of the base * the height of the prism. The base of the prism is a right triangle.
(b*h)÷2 = Area of a triangle
Base = 4
Height = 3
Now:
(4*3)/2 = 6 miles²
Now we have to multiply 6 miles² by 5 as our height.
We get 30 miles² as the volume of the figure.
EXTREMELY URGENT Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function h because the graphs of ƒ and h are symmetrical about the x-axis
the function g because the graphs of ƒ and g are symmetrical about the x-axis
Answer:
The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
What is the area of the pizza? Explain how you know and the formulas that you used.
Answer:
90.24 in²
Step-by-step explanation:
Area of the pizza :
⇒ Area (rectangle) + Area (semicircle)
⇒ length × width + π × (radius)²
⇒ 8 x 5 + 3.14 x 4²
⇒ 40 + 3.14 × 16
⇒ 40 + 50.24
⇒ 90.24 in²
The area of a 2D form is the amount of space within its perimeter. The area of the pizza is 65.1327 in².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the pizza = Area of semi-circle + Area of Rectangle
= (π/2)r² + (d×h)
= [(π/2)×4²] + (8×5)
= 25.1327 in² + 40 in²
= 65.1327 in²
Hence, the area of the pizza is 65.1327 in².
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Find the area of the shapes below. Make sure to label your answers with units.
Figure a: The area of the triangle is 13.3 sq. km.
Figure b: The area of the rectangle is 57.4 sq. cm.
Figure c: The area of the parallelogram is 45.5 sq. km.
Figure d: The area of the trapezoid is 24.36 sq. m.
What is the area of a two-dimensional figure?The area of a two-dimensional closed figure is the total space within its boundary.
How to solve the question?In the question, we are asked to find the area of the given shapes.
Figure a:-
It is showing a triangle.
The area of a triangle is calculated using the formula:
Area = (1/2)*Base*Height.
Thus, the area of the triangle
= (1/2)*7*3.8 sq. km
= 13.3 sq. km.
Figure b:-
It is showing a rectangle.
The area of a rectangle is calculated using the formula:
Area = Length*Width.
Thus, the area of the rectangle
= 8.2*7 sq. cm
= 57.4 sq. cm.
Figure c:-
It is showing a parallelogram.
The area of a parallelogram is calculated using the formula:
Area = Base*Height.
Thus, the area of the parallelogram
= 9.1 * 5 sq. km
= 45.5 sq. km.
Figure d:-
It is showing a trapezoid.
The area of a trapezoid is calculated using the formula:
Area = (1/2)*(Sum of parallel sides)*(height).
Thus, the area of the trapezoid
= (1/2)*(2.7 + 8.9)*4.2 sq. m.
= 11.6 * 2.1 sq. m.
= 24.36 sq. m.
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