To find the inverse of the function f(x) = 2x - 5/3x + 4, swap x and y and solve for y. The inverse function is f-1(x) = (x - 4) / (2 - 5/3).
Explanation:To find the inverse of a function, we need to swap the variables x and y and solve for y. Let's start:
f(x) = 2x - 5/3x + 4
Replace f(x) with y:
y = 2x - 5/3x + 4
To find the inverse, solve for x:
x = (y - 4) / (2 - 5/3)
Now, swap x and y to find the inverse function:
y = (x - 4) / (2 - 5/3)
Therefore, the inverse of f(x) = 2x - 5/3x + 4 is f-1(x) = (x - 4) / (2 - 5/3).
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What percent of 14 is 35
Answer:
250%
Step-by-step explanation:
First, set the equation.
35/14 x 100% = answer
Simplify.
2.5 x 100 = answer
250 = answer
250% is your answer
~
Answer:
The answer is 2.5
Step-by-step explanation:
14*2.5%=35
Refer to the table of long distance rates. Write an expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes.
Answer:
a(n) = 0.55 + (n -5)0.07
Step-by-step explanation:
The cost goes up $0.07 for each additional minute, so that is the slope of the linear function. In point-slope form the equation can be written ...
... a(n) - 0.55 = 0.07(n -5)
adding 0.55, and rearranging slightly, this becomes ...
... a(n) = 0.55 +(n -5)0.07
is -4.2778 rational or irrational?
Answer:
Rational
Step-by-step explanation:
A rational number would be a number or a fraction that has a repeating decimal, or as ones say it ... "terminating decimal".
A polynomial function has -5√3i as a root. Which of the following must also be a root of the function?
-5-√3i
-5+√3i
5-√3i
5+√3i
Answer:
-5+√3i is the given root so -5-√3i must be the other root
Step-by-step explanation:
We know that complex roots must come in pairs. The pairs are complex conjugates. (a+bi) and (a-bi)
You are missing a sign between -5 and the square root
So if - 5+ sqrt(3) i is a root, then -5 - sqrt(3) i must be a root
if -5 - sqrt(3)i is a root, then -5 + sqrt(3)i must be a root.
I will assume you missed a + sign
-5+√3i is the given root so -5-√3i must be the other root
Answer: is A
Step-by-step explanation:
(1) Tom took a trip of 1,020 miles. He traveled by train at 55 miles an hour and the same number of hours by plane at 285 mph.
How many hours did the trip take?
A) 3 hours
B) 6 hours
C) 8 hours
B) 6 hours
Step-by-step explanation:Let h represent the total trip time. Then h/2 is the time spent traveling at each speed. The distance covered is ...
... distance = speed · time
The sum of the distances in each mode is the total distance.
... 1020 = 55·h/2 +285·h/2
... 2040 = h·(55+285) . . . . multiply by 2
... 2040/340 = h = 6 . . . . . . . divide by the coefficient of h
The trip took a total of 6 hours.
After m months the height of a plant is 10 + 3m millimeters. How tall is the plant after 8 months? Three years?
Answer:
A. 34 millimeters.
B. 118 millimeters.
Step-by-step explanation:
We have been given that after m months the height of a plant is [tex]10+3m[/tex] millimeters.
To find the height of plant after 8 months we will substitute m=8 in our given expression.
[tex]\text{The height of plant after 8 months}=10+3\times 8[/tex]
[tex]\text{The height of plant after 8 months}=10+24[/tex]
[tex]\text{The height of plant after 8 months}=34[/tex]
Therefore, the height of plant after 8 months will be 34 millimeters.
B. Now let us find height of plant after 3 years.
First of all we will convert 3 years into months by multiplying 3 by 12 as 1 year equals to 12 months.
[tex]\text{3 years}=3*12\text{ months}=36\text{ months}[/tex]
Now let us substitute m=36 in our given expression.
[tex]\text{The height of plant after 36 months}=10+3\times 36[/tex]
[tex]\text{The height of plant after 36 months}=10+108[/tex]
[tex]\text{The height of plant after 36 months}=118[/tex]
Therefore, the height of plant after 3 years (36 months) will be 118 millimeters.
Look at the model to the right. 3/5 of the whole is shaded. Divide the model into a different number of equal parts to find an equivalent fraction. Complete the equation
Solution:
[tex]\frac{3}{5}=\frac{6}{10}=\frac{9}{15}[/tex]
Two or more fractions are said to be equivalent , if reduced in lowest terms that is numerator and denominator are co-prime, they are equal.
[tex]\frac{3}{5}[/tex] Three out of five is shaded.
Equivalent fraction of
[tex]\frac{3\times 6}{5\times 6}=\frac{18}{30} \\\\ \frac{3\times 8}{5\times 8}=\frac{24}{40}[/tex]
Answer:
Step-by-step explanation:
A rectangular field is 115 meters long and 70 meters wide. Give the length and width of another rectangular field that has the same perimeter but a larger area
To find a rectangular field with the same perimeter but a larger area than the original field (115m x 70m), we should search for dimensions that sum up to half of the perimeter (185m) and form a shape closer to a square. An example would be a field measuring 92.5m by 92.5m, which has the same 370m perimeter but a larger area.
Explanation:You have asked about the length and width of another rectangular field that has the same perimeter but a larger area than a field measuring 115 meters in length and 70 meters in width. To find the dimensions of such a field, we must first calculate the perimeter of the original field.
The formula for the perimeter (P) of a rectangle is P = 2(length + width). Plugging in the given dimensions, we get P = 2(115m + 70m) = 2(185m) = 370 meters. Now we need to find dimensions that add up to half this perimeter, since length + width = P/2, which is 185 meters, but form a rectangle with a larger area.
Area (A) is calculated by the formula A = length x width. To maximize the area for a given perimeter, the rectangle should be closer to a square because a square has the largest area for a given perimeter. Hence, the dimensions we are looking for should be closer to each other compared to the original dimensions of 115m x 70m.
An example of dimensions that meet these criteria would be 92.5 meters by 92.5 meters. Although this results in a square, it fulfills the condition of having the same perimeter (since 2(92.5m + 92.5m) = 370m) but a larger area (92.5m x 92.5m = 8556.25 square meters) than the original rectangular field (115m x 70m = 8050 square meters).
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Answer:
<C =120
Step-by-step explanation:
Since the figure in inscribed in the circle, <A = <C and <B = <D
<B= <D
2x-1=3x-59
Subtract 2x from each side
2x-2x-1=3x-2x-59
-1= x-59
Add 59 to each side
-1+59 = x-59+59
58 =x
<A = 2x+4
<A= 2(58) +4
= 116+4
<A =120
<C = <A
<C =120
NEED ANSWER ASAP PLEASE!
Answer:
(-4,-1)
Step-by-step explanation:
The solution to the system of equations is where the two lines cross.
The x coordinate is -4
The y coordinate is -1
Olivia took half a gallon of water on a hike. During the hike, she drank .75 of the water, How much water did she drink
Olivia drinks 0.375 gallons of water.
What is problem-solving?
Problem-solving is defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. For example, a trainer may need to figure out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Quantity of water Olivia took = half a gallon i.e 0.5 gallons.
Quantity of water Olivia drank =0.75 of 0.5
∴ 75% of 0.5 gallons
= 75/100 × 0.5
= 0.375 gallons.
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A store is having a 15% off sale on all shirts. When Suri checks out, the clerk takes $4.50 off the original price of the shirt. What was the original cost of the shirt? Use the formula to find the answer.
Answer:
30
Step-by-step explanation:
4.50=15%
30=100%
check;
30*0.85=25.5
30-25.5=4.50
The summer youth camp is going on an excursion to atlantis Amusement Park. 50% of the 78 students that are going want to go to the Sinking Of Atlantis first.How many students want to visit the sinking of Atlantis first?
Answer:
78*50/100= 78/2 ( half of 78) = 39
Step-by-step explanation:
By which matrix should you multiply vector [1 3] to rotate it 180°?
Answer:
B
Step-by-step explanation:
Rotation 180° is accomplished by negating both the x- and y-coordinates. That is, you multiply each of them by -1. You want the opposite of the identity matrix, so matrix B.
We have that the Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]
Option D is correct
From the Question we are given
[tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex]
it is important to note that the rotation of the identity matrix [tex]\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}[/tex] rotating across the Cartesian co-ordinate is a [tex]180 \textdegree[/tex] is going to give a matrix [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]
Therefore
The Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]
Option D is correct
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Lucy and Ethel’s favorite store was having a sale. Lucy bought 10 shirts and 4 pairs of jeans and spent $280. Sabrina bought 12 shirts and 5 pairs of jeans and spent $344.
Assuming that each shirt was the same price, and each pair of jeans was the same price, how much did each shirt and each pair of jeans cost? Write a system of equations to represent this situation. Then solve for the solution using the elimination method.
Final answer:
By defining variables for the prices and setting up a system of equations, we determine that each shirt costs $12 and each pair of jeans costs $40 after solving the system using the elimination method.
Explanation:
The subject of this question is a problem involving systems of equations, which falls under the category of Mathematics. We are given a scenario where Lucy and Ethel are buying clothing at the same prices, but in different quantities and we need to determine the cost of each item. First, let's define variables: let s be the price of a shirt and j be the price of a pair of jeans. We then have two equations based on the purchases:
10s + 4j = $280 (Lucy's purchase)12s + 5j = $344 (Sabrina's purchase)To solve these equations using the elimination method, we will multiply the first equation by 5 and the second by 4 to eliminate the jeans variable:
50s + 20j = $140048s + 20j = $1376Subtract the second equation from the first:
2s = $24Now divide by 2 to find the price of one shirt:
s = $12 (price of a shirt)We can substitute s = $12 into the first original equation to find the price of a pair of jeans:
10(12) + 4j = $280120 + 4j = $2804j = $160j = $40 (price of a pair of jeans)What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negative four. y = − (x − 3)2 + 1 y = − (x + 3)2 + 1 y = (x − 3)2 − 1 y = (x + 3)2 − 1
Answer:
[tex]y=(x+3)^{2} -1[/tex]
Step-by-step explanation:
General equation of a parabola that opens up is [tex]y=a(x-h)^{2} +k[/tex] , a>0
So equation becomes [tex]y=(x-h)^{2} +k[/tex] which implies option A and option B can never be true for this parabola.
Also this parabola's vertex lies in 3rd quadrant where coordinates of both x and y will be negative.
So, the equation of parabola will be of the form [tex]y=(x+h)^{2} - k[/tex]
Hence, option 4 that is [tex]y=(x+3)^{2} -1[/tex] is correct.
The correct equation of the graph is: x² + 6x - 35y + 8 = 0.
The equation of the graph shown, which is a parabola that opens upwards and crosses the x-axis at -2 and -4, can be determined by examining its key features.
The fact that the parabola opens upward indicates that the coefficient of the squared term (x²) in the equation must be positive.
The parabola crosses the x-axis at -2 and -4. This means that the two x-intercepts are -2 and -4.
Putting this information together, we can form the equation:
y = a * (x - r1) * (x - r2)
where 'a' is a positive constant (coefficient of x²), and r1 and r2 are the x-intercepts.
Since the x-intercepts are -2 and -4, the equation becomes:
y = a * (x - (-2)) * (x - (-4))
y = a * (x + 2) * (x + 4)
Now, let's find the value of 'a.' We are given that the parabola passes through the point (3, 1). We can substitute these coordinates into the equation to find 'a':
1 = a * (3 + 2) * (3 + 4)
1 = a * 5 * 7
a = 1 / (5 * 7)
a = 1 / 35
Now that we have the value of 'a,' we can finalize the equation:
y = (1/35) * (x + 2) * (x + 4)
Expanding the equation:
y = (1/35) * (x² + 6x + 8)
To put the equation in standard form, we can multiply both sides by 35 to eliminate the fraction:
35y = x^2 + 6x + 8
Finally, rearrange to get the equation in standard form:
x² + 6x - 35y + 8 = 0
So, the correct equation of the graph is: x² + 6x - 35y + 8 = 0.
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The lengths of two sides of a triangle are 26 meters and 46 meters. What is the range of possible lengths for the third side, x of the triangle.
What is an equation of the line that is perpendicular to y=−23x+5 and passes through the point (2, 11) ?
Answer:
The equation would be y = 1/23x - 251/23
Step-by-step explanation:
To start, you need to locate the slope of the first equation. Since the slope is the coefficient of x, we know it to be -23. Now, the perpendicular slope is the opposite and reciprocal of that, which makes the new slope 1/23.
Now that we have this, we can use the point and the slope in point-slope form to get the equation.
y - y1 = m(x - x1)
y - 11 = 1/23(x - 2)
y - 11 = 1/23x - 2/23
y = 1/23x - 251/23
Answer:
Step-by-step explanation:
I know your smart !!! Who knows this answer ? ❤️
Answer:
The range is { -1,3,7,11,15}
Step-by-step explanation:
The range is just the output values
f(-2) = 4(-2) +7 = -8+7 =-1
f(-1) = 4(-1) +7 = -4+7 = 3
f(0)= 4(0) +7 = 7
f(1) = 4(1) + 7 = 11
f(2) = 4(2) +7 = 8+7 = 15
Answer:
The answer is B
Step-by-step explanation:
First you should make a table to explain it better to yourself. Make 2 columns named Domain(Input) and Range(Output). Now put your ordered pair in the range area. Now calculated the function by replacing X with the range. Calculate.
I've been struggling with this. I need help asap.
(Anyone that's good in math.)
The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.
Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.
Answer:
y = 3500(3/7 ) ^ 1/3
y = 239.23
Step-by-step explanation:
For exponential decay
y =a b^x
a = 3500
b<1
We can use the point (3, 1500)
1500 = 3500 * b^3
Divide each by 3500
1500/3500 = 3500/3500 b^3
15/35 = b^3
3/7 = b^3
Take the cube root of each side
(3/7) ^ 1/3 = b^3 ^ 1/3
b = (3/7 ) ^ 1/3
The function is
y = 3500 (3/7) ^ 1/3 x
We want to find y when x=9.5
y = 3500 (3/7) ^ (9.5 /3)
y = 3500 ( 3/7) ^ 3. 166666666
y = 3500 (.06835)
y = 239.23
Lets check a point and see if we a close
(7,500)
y = 3500 (3/7)^ (1/3*7)
y = 3500 (3/7) ^ (7/3)
y = 484.68
That is pretty close. We do not know the exact value since we are reading from a graph.
LE _____ VO
Choose the relationship symbol to make a true statement.
<
=
>
Answer:
LE > VO
Step-by-step explanation:
This is a short answer, but I assure you that it is 100% correct.
Hope it helps.
There are 7 people on a bus each person has 7 backpacks in each backpack there are 7 dogs for every dog there are 7 puppies how many legs are on the bus
Since a math school opened the girls basketball team had the same record every season the team won a total of 182 games while losing only 13 games find the constant of proportionality of wins to loses
Answer:
11
Step-by-step explanation:
I guess
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply. For any value of x, g(x) will always be greater than h(x). For any value of x, h(x) will always be greater than g(x). g(x) > h(x) for x = -1. g(x) < h(x) for x = 3. For positive values of x, g(x) > h(x). For negative values of x, g(x) > h(x).
ANSWER
g(x) > h(x) for x = -1 is TRUE
For positive values of x, g(x) > h(x) is TRUE
For negative values of x, g(x) > h(x) is also TRUE
EXPLANATION
The given functions are
[tex]g(x)={x}^{2}[/tex]
and
[tex]h(x)=-{x}^{2} [/tex]
If
[tex]x=0[/tex]
[tex]g(0)={0}^{2}=0[/tex]
[tex]h(0)=-({0})^{2}=0[/tex]
Based on this options A and B are FALSE.
When
[tex]x=-1[/tex]
[tex]g(-1)={( - 1)}^{2}=1[/tex]
[tex]h(-1)=-{(-1)}^{2}=-1[/tex]
[tex]g( - 1)>\:h(-1)[/tex]
for x=-1 is True.
When x=3,
[tex]g(3)={3}^{2}=9[/tex]
and
[tex]h(3)=-{3}^{2}=-9[/tex]
[tex]g(3)>\: h( 3)[/tex]
g(x) < h(x) for x = 3 is a FALSE statement.
For positive values of x, g(x) > h(x) is TRUE
See graph.
For negative values of x, g(x) > h(x) is also TRUE
See graph
The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are: h(x) will always be greater than g(x), g(x) < h(x) for x = 3, and for positive values of x, g(x) > h(x).
Explanation:The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are:
For any value of x, h(x) will always be greater than g(x).g(x) < h(x) for x = 3.For positive values of x, g(x) > h(x).These statements can be verified by plugging in values for x and comparing the outputs of the functions.
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Kelley ate 3/5 of her brownies on Monday and 6/8 of her brownies Tuesday. If Kelley originally had 2 brownies, what fraction brownie is left over? Simplifty your answer
Answer:
[tex]\frac{13}{20}[/tex]
Step-by-step explanation:
First, we need to add the two fractions together. To do this we need to make the denominator a factor of both 8 and 5. Easy way to do this is to multiply each fraction by the denominator of the other fraction:
[tex]\frac{3}{5} * 8 = \frac{24}{40}[/tex]
[tex]\frac{6}{8} * 5 = \frac{30}{40}[/tex]
[tex]\frac{24}{40} + \frac{30}{40} = \frac{54}{40}[/tex]
We can also show 2 brownies as [tex]\frac{2}{1}[/tex] or [tex]\frac{80}{40}[/tex]
Now we can subtract the two:
[tex]\frac{80}{40} - \frac{54}{40} = \frac{26}{40}[/tex]
Simplify the fraction down by dividing by two:
[tex]\frac{13}{20}[/tex]
Which is the fraction of brownie left!
Which equation represents a line that has a slope of 4 and passes through the point (3,-8)?
Answer:
The equation of this line would be y + 8 = 4(x - 3)
Step-by-step explanation:
In order to get this we can start with the base form of point-slope.
y - y1 = m(x - x1)
Now that we've got this, we can plug in the slope for m. We can also plug in the point for (x1, y1).
y + 8 = 4(x - 3)
A board is leaning against a vertical wall.
Answer:
C) 68 in
Step-by-step explanation:
We use sine ratio
= 68 inches
Thank you.
please help me with.
image attached.
m<1 is 90 degrees
m<2 is 121 degrees
m<3 is 42 degrees
m<4 is 42 degrees
m<5 is 35 degrees
m<6 is 90 degrees
m<7 is 48 degrees
m<8 is 35 degrees
m<9 is 35 degrees
To play bingo,there is a $10 cover charge plus $2 per bingo card.Write an expression to represent this.
Answer:
An expression y = 10+ 2x
Step-by-step explanation:
As per the statement: To play bingo,there is a $10 cover charge plus $2 per bingo card.
Let x represents the number of bingo card and y represents cost .
"$2 per bingo card" means 2x
"$10 cover charge plus $2 per bingo card" means 10 + 2x
then,
an expression to represents this statement;
y = 10 + 2x
There are 90 girls and 60 boys in the sixth grade at a middle school. Of these students, 19 girls and 11 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed?
Answer:
The percentage of left-handed 6th graders is 20%.
Step-by-step explanation:
To find this, start by finding the total number of lefties.
19 girls + 11 boys = 30 students.
Next find the total number of students
90 girls + 60 boys = 150 students
Now divide the lefties by the total number.
30/150 = 20%