Which function has an asymptote at x= 39
Answer:
option B : [tex]f(x)= log_7(x-39)[/tex]
Step-by-step explanation:
(a) [tex]f(x) = 7^{x-39}[/tex]
For exponential function , there is no vertical asymptotes
General form of exponential function is
[tex]f(x) = n^{ax-b}+k[/tex]
[tex]f(x) = 7^{x-39}[/tex]
In the given f(x) the value of k =0
So horizontal asymptote is y=0
(b) lets check with option
[tex]f(x)= log_7(x-39)[/tex]
To find vertical asymptote we set the argument of log =0 and solve for x
Argument of log is x-39
x-39=0 so x=39
Hence vertical asymptote at x=39
Answer:
The correct answer is b. f(x) = log7(x-39)
Write the equation of a line that is perpendicular to the given line and that passes through the given point. Y-2=-1/4(x+3); (-3,5)
A. Y= -3x - 5
B. Y=1/4x-6
C. Y=4x+17
D. Y =4x+5
Answer:
A
Step-by-step explanation:
The equation of the line perpendicular to the given line and passing through the point (-3, 5) is option C. y = 4x + 17.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Given the equation of a line in point slope form as,
y - 2 = -1/4 (x + 3)
We have to calculate the equation of a line perpendicular to the given line.
Slope of a line perpendicular to another line is the reciprocal of the given line with opposite sign.
Slope of the given line = -1/4
Slope of the perpendicular line = - (1 ÷ -1/4) = 4
Given a point (-3, 5).
Equation of the required line in point slope form is,
y - 5 = 4 (x - -3)
y - 5 = 4 (x + 3)
y - 5 = 4x + 12
y = 4x + 12 + 5
y = 4x + 17
Hence the equation of the required line perpendicular to the given line is y = 4x + 17.
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Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
The line is -2,1 and 4,3
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
Answer:
Correct choice is C
Step-by-step explanation:
Consider segment AB with endpoints A(-2,1) and B(4,3).
1. Rotation counterclockwise of 90° has a rule
(x,y)→(-y,x),
then
A(-2,1)→C(-1,-2);B(4,3)→D(-3,4).2. x-axis reflection has a rule
(x,y)→(x,-y),
then
C(-1,-2)→E(-1,2);D(-3,4)→F(-3,-4).3. Rotation counterclockwise of 270° has a rule
(x,y)→(y,-x),
then
E(-1,2)→G(2,1);F(-3,-4)→H(-4,3).4. y-axis reflection has a rule
(x,y)→(-x,y),
then
G(2,1)→A(-2,1);H(-4,3)→B(4,3).Answer:
C) Rotation counter-clockwise of 90 degree → x-axis reflection → rotation counter-clockwise of 270 degree → y-axis reflection
Step-by-step explanation:
We are given the line segment AB with end points (-2,1) and (4,3).
It is provided that after applying rigid transformations the line segment AB maps onto itself.
So, according to the options,
1. Rotation counter-clockwise by 90 degree changes (x, y) into (-y, x)
i.e. (-2,1) → (-1,-2) and (4,3) → (-3,4)
2. X-axis reflection changes (x, y) into (x, -y)
i.e. (-1,-2) → (-1,2) and (-3,4) → (-3,-4)
3. Rotation counter-clockwise by 270 degree changes (x,y) into (y, -x)
i.e. (-1,2) → (2,1) and (-3,-4) → (-4,3)
4. Y-axis reflection changes (x,y) into (-x,y)
i.e. (2,1) → (-2,1) and (-4,3) → (4,3)
Hence, we see that after applying transformations to AB we are again obtaining the line AB as seen below in the figure.
So, option C is correct.
April sold 75 tickets to a school play and collected a total of $495. If adult cost $8 each and child tickets cost $5 each, how many adult and how many child tickets did she sell?
April sold 40 adult tickets and 35 child tickets.
Explanation:To find the number of adult and child tickets sold, we can set up a system of equations based on the given information:
Let x be the number of adult tickets sold and y be the number of child tickets sold.
We can establish two equations:
x + y = 75 (equation 1, representing the total number of tickets sold)8x + 5y = 495 (equation 2, representing the total amount collected)To solve this system, we can use the method of substitution or elimination. Let's use the elimination method:
By multiplying equation 1 by 5, we get:
5x + 5y = 375 (equation 3)
Subtracting equation 3 from equation 2:
(8x + 5y) - (5x + 5y) = 495 - 375
Simplifying:
3x = 120
Dividing both sides by 3:
x = 40
Substituting the value of x into equation 1:
40 + y = 75
Solving for y:
y = 75 - 40
y = 35
Therefore, April sold 40 adult tickets and 35 child tickets.
Train A departs station one traveling at 75 mph. Train N departs station two 30 minutes later traveling at 45 mph. The stations are 300 miles apart. The equation below gives the distance between the trains, D, in miles as a function of, T, the time after Train B departs. D=|262.5-120T| For which two values of T will D=50? Round to the nearest tenth.
A)1.8 and 2.6
B)0.2 and 0.3
C)-17.8 and 26.0
D)-1.8 and 1.8
Answer:B
Step-by-step explanation:
Explain why all circles must be similar. That is, describe a sequence of transformations that will always carries one circle onto another.
All circles are similar because they can be transformed into each other through a series of transformations without changing their core properties. These transformations include translation (shifting the position) and scaling (resizing).
Explanation:All circles are similar because they maintain the same shape and can be scaled up or down without changing their properties. A sequence of transformations such as scaling (resizing) can carry one circle onto another. Here is how:
Identify the centres of the two circles. Let's say the centre of Circle A is at point a, and the centre of Circle B is at point b. Translate Circle A such that its centre aligns with Circle B. Translation is a transformation that shifts the position of a shape, without changing its size, shape, or orientation. If the radius of Circle A differs from Circle B, apply a scaling transform to Circle A such that its radius becomes equal to the radius of Circle B. Scaling is a process that enlarges or shrinks a shape but keeps its shape intact.
By performing these transformations, Circle A transforms into Circle B. This holds true for any two circles, thus all circles are always similar.
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state of each triangle is acute, obtuse, or right
Answer:
5 is right 6 is right 7 is right ....
Step-by-step explanation:
actually they are all right triangles
Each of the triangle should be classified as follows;
5. Acute triangle.
6. Right triangle.
7. Obtuse triangle.
8. Obtuse triangle.
9. Obtuse triangle.
10. Acute triangle.
11. Right triangle.
12. Right triangle.
How to determine and classify each of the triangles?A triangle is classified as an acute triangle if the square of its longest side (c) is less than the sum of the squares of the two smaller sides (a + b).
Also, a triangle is classified as an obtuse triangle if the square of its longest side (c) is greater than the sum of the squares of the two smaller sides (a + b).
A triangle is classified as a right triangle if the square of its longest side (c) is equal to than the sum of the squares of the two smaller sides (a + b).
Part 5.
c² > a² + b²
15² > 11² + 12²
225 > 265 (False, it's an acute triangle).
Part 6.
c² > a² + b²
13² > 5² + 12²
169 > 169 (False, it's a right triangle).
Part 7.
c² > a² + b²
10² > 3² + 8²
100 > 73 (True, it's an obtuse triangle).
Part 8.
c² > a² + b²
20² > 9² + 12²
400 > 225 (True, it's an obtuse triangle).
Part 9.
c² > a² + b²
15² > 7² + 12²
225 > 193 (True, it's an obtuse triangle).
Part 10.
c² > a² + b²
10² > 8² + 7²
100 > 113 (False, it's an acute triangle).
Part 11.
c² > a² + b²
15² > 9² + 12²
225 > 225 (False, it's a right triangle).
Part 12.
c² > a² + b²
13² > 5² + 12²
169 > 169 (False, it's a right triangle).
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How many variable terms are in the expression 3x^3y+5x^2-4y+z+9
Answer:
5
Step-by-step explanation:
x + y + x + y + z = 5
9^-5/9^3 single positive exponent
Answer: 9^-8
Step-by-step explanation:
To get single positive exponent,
9^-5 / 9^3
Since the exponent is same
So we can solve the coefficient like this
9^-5-3
So
9^-8
The problem 9⁻⁵ /9³ simplifies to -8 by subtracting the exponent in the denominator (3) from the exponent in the numerator (-5). To achieve a single positive exponent, take the reciprocal of the base, then the final answer becomes 1/9⁸.
Explanation:The question pertains to the laws of exponents in mathematics. To be specific, you are asked to simplify the expression 9⁻⁵ /9³ into a single positive exponent. In this case, you should remember that division of the same base translates to subtraction of exponents, according to the exponent laws. Therefore, you simply subtract the exponent of the denominator (3) from the exponent of the numerator (-5).
Following the rule, -5 - 3 results in -8. So the expression simplifies to 9^-8. But, since we need a single positive exponent, we take the reciprocal of 9. Remember that changing the sign of an exponent is equivalent to taking the reciprocal of the base. Hence, the final answer = 9⁻⁸ becomes 1/9⁸.
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Use the formula F = 9/5c + 32 to convert -3 degrees Celsius to degrees Fahrenheit
[tex]\text{Put c = -3 to the equation}\ F=\dfrac{9}{5}c+32.\\\\F=\dfrac{9}{5}(-3)+32=-\dfrac{27}{5}+32=-5.4+32=26.6\\\\Answer:\ \boxed{-3^oC=26.6^oF}[/tex]
1/2x + 1/3y = 0
1/4x -1/2 y = 8
What is the solution of the system shown?
(-8, 12)
(8, -12)
(8, 12)
Answer:
[tex](8,-12)[/tex]
Step-by-step explanation:
The two equations are:
[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{4}x-\frac{1}{2}y=8[/tex]
We can solve the first equation for [tex]x[/tex] and then substitute into second equation to find the value of [tex]y[/tex].
[tex]\frac{1}{2}x+\frac{1}{3}y=0\\\frac{1}{2}x=-\frac{1}{3}y\\x=\frac{-\frac{1}{3}y}{\frac{1}{2}}\\x=-\frac{2}{3}y[/tex]
Now,
[tex]\frac{1}{4}x-\frac{1}{2}y=8\\\frac{1}{4}(-\frac{2}{3}y)-\frac{1}{2}y=8\\-\frac{2}{12}y-\frac{1}{2}y=8\\-\frac{2}{3}y=8\\y=\frac{8}{-\frac{2}{3}}\\y=-12[/tex]
Substituting [tex]y=-12[/tex] into the "solved for [tex]x[/tex]" version of first equation, we get the value of [tex]x[/tex]. So,
[tex]x=-\frac{2}{3}y\\x=-\frac{2}{3}(-12)\\x=8[/tex]
Hence the ordered pair is [tex](8,-12)[/tex] and this is the solution to the system of equations shown.
Answer:
(8,-12) the second option :)
Step-by-step explanation:
Lee is making cookies. she needs 3/4 cup white sugar and 1 2/4 cups brown sugar for each batch. she makes 2 batches. how many total cups of brown and white sugar does she need
The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar
What is a fraction?
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
Lee needs 3/4 cup of white sugar for each batch of cookies, and she is making 2 batches, so she needs:
= 3/4 cup/batch x 2 batches
= 6/4 = 3/2 cups of white sugar
Lee needs 1 2/4 cups of brown sugar for each batch of cookies, and she is making 2 batches, so she needs:
= 1(2/4) cups/batch x 2 batches
= 3 cups of brown sugar
Therefore,
The total amount of brown and white sugar that Lee needs is:
= 3/2 cups of white sugar + 3 cups of brown sugar
= 4 1/2 cups of sugar
Thus,
The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar
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Chang spent $16
on fruit at the grocery store. He spent a total of $80
at the store. What percentage of the total did he spend on fruit?
Chang spent $16 on fruit out of a total of $80 at the grocery store. In terms of percentages, this equals 20% of his total grocery bill spent on fruit.
Explanation:The subject is about finding out what percentage of the total Chang spent on fruit at the grocery store. In order to solve this problem, we first need to know the total amount spent and how much was spent on one part, in this case, fruit.
Chang spent $16 on fruit and a total of $80 at the store. So, to find out the percentage spent on fruit, we divide the amount spent on fruit by the total amount spent, and then multiply by 100 to change the decimal to a percentage.
Here is the math: (16 ÷ 80) x 100 = 20%
So, Chang spent 20% of his total grocery bill on fruit.
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write the equation in slope intercept form what are the slope and y intercept? -12+11y=-8
To write the equation in slope-intercept form, rearrange the equation to isolate the y variable. Then, divide both sides by the coefficient of y to solve for y. The equation is y = 4/11, with a slope of 0 and y-intercept of 4/11.
Explanation:To write the equation in slope-intercept form, we need to isolate the y variable on one side of the equation.
Start by rearranging the equation to get the y variable alone:
-12 + 11y = -8
Next, add 12 to both sides to move the constant term to the other side:
11y = 4
Then, divide both sides by 11 to solve for y:
y = 4/11
The equation in slope-intercept form is y = 4/11. The slope is 0 and the y-intercept is 4/11.
Final answer:
The equation -12 + 11y = -8 in slope-intercept form is y = 4/11. There's no x term in the equation, indicating that the slope is 0, and the y-intercept is 4/11.
Explanation:
To write the equation -12 + 11y = -8 in slope-intercept form, we start by isolating the y-variable on one side of the equation. Here's how you can do it:
Add 12 to both sides of the equation to get 11y = 4.
Divide both sides of the equation by 11 to solve for y, resulting in y = 4/11.
The equation in slope-intercept form is y = 4/11. In this form, y = a + bx, the slope (b) is the coefficient of x, and the y-intercept (a) is the constant term. Since our equation has no x term, the slope is 0 and the y-intercept is 4/11.
Therefore, the slope of the line is 0, and the y-intercept is the point (0, 4/11).
Find the surface area of the figure below.
We have two equilateral triangles and three rectangles.
The formula of an area of an equilateral triangle:
[tex]A_{\triangle}=\dfrac{a^2\sqrt3}{4}[/tex]
a - length of side
We have a = 14 ft. Substitute:
[tex]A_{\triangle}=\dfrac{14^2\sqrt3}{4}=\dfrac{196\sqrt3}{4}=49\sqrt3\ in^2[/tex]
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=lw[/tex]
l - length
w - width
We have l = 10ft and w = 14 ft. Substitute:
[tex]A_{\boxed{\ }}=(10)(14)=140\ ft^2[/tex]
The Surface Area of the figure:
[tex]S.A.=3A_{\boxed{\ }}+2A_{\triangle}\\\\S.A.=3\cdot140+2\cdot49\sqrt3=(420+98\sqrt3)\ ft^2[/tex]
what is 25.9 billion times 20 and then divided by 100? will mark brainliest.
Answer:
five hundred seventeen billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred
Step-by-step explanation:
25.9 billion times 20=five hundred eighteen billion
then subtract one hundred from that to get the answer
Answer:
Step-by-step explanation:
5180000000
what is the sum in degrees of the measures of the interior angles of the polygon
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° ( n - 2) ← n is the number of sides of the polygon
Solve for x.
.
Simplify your answer as much as possible.
Answer:
[tex]x=25[/tex]
Step-by-step explanation:
The given linear equation is
[tex]30=\frac{6}{5}x[/tex]
We multiply both sides by the reciprocal of [tex]\frac{6}{5}[/tex] which is [tex]\frac{5}{6}[/tex].
This will give us,
[tex]30\times \frac{5}{6} =\frac{5}{6}\times \frac{6}{5}x[/tex]
We cancel out common factors to get;
[tex]5\times \frac{5}{1} =x[/tex]
This implies that;
[tex]x=25[/tex]
Solve the equation for x. 3/ 5 (5x + 10) = −24
Solve the equation for x.
A) −8
B) −10
C) −15
D) −18
Answer:
B
Step-by-step explanation:
−10
3 /5 (5x + 10) = −24
3x + 6 = −24
3x = −30
x = −10
Rewrite the set E by listing its elements. Make sure to use the appropriate set notation. E= { x | x is an interger and -5 ≤ x < -2
Answer:
E = {-5, -4, -3}
Raul used this method to find tje sum 229+313
Answer:
possible answrs addition, expanded form
Step-by-step explanation:
So I copied this off from my teacher she was showing this on the board but I need help showing my work on this so that she doesn’t know I copied it which I think she wouldn’t but you never know
Answer:
x < 3 or x > 9
Step-by-step explanation:
given 6| x - 6 | + 7 > 25 ( subtract 7 from both sides )
6| x - 6 | > 18 ( divide both sides by 6 )
| x - 6 | > 3
Inequalities of the form | x | > a always have solutions of the form
x < - a OR x > a, hence
x - 6 < - 3 or x - 6 > 3 ( add 6 to both sides in both inequalities )
x < 3 or x > 9
Answer: x > 9 or x < 3
Step-by-step explanation:
Step 1: Isolate the absolute value expression.
6 | x - 6 | + 7 > 25
6 | x - 6 | > 18 subtracted 7 from both sides
| x - 6 | > 3 divided both sides by 3
Step 2: Solve for x.
Note: the absolute value symbol makes the value positive, so the value inside could be positive or negative. We need to find both solutions.
If inside is negative
-(x - 6) > 3
x - 6 < -3 divided both sides by -1 which flipped the inequality
x < 3 added 6 to both sides
If inside is positive
+(x - 6) > 3
x - 6 > 3 distributed +1, which didn't change the inequality
x > 9 added 6 to both sides
Step 3: Graph the solution
←-------------o -3 9 o--------------→
Teresa bought a 50 pound bag of flour for her bakery. She used 13.65 pounds of flour.
How many pounds of flour are left in the bag?
You have 4 cups of raisins. A recipe calls for 3/8 cup of raisins per serving. How many full servings can you make
Answer:
10 servings
Step-by-step explanation:
not very hard at all, all you have to do is do 4/(3/8) to get you 10.66, but since you need full servings, you leave out the decimal (logic) to get the answer
You can make 10 full servings of the recipe with 4 cups of raisins and have some leftover.
To determine how many full servings you can make with 4 cups of raisins when a recipe calls for 3/8 cup of raisins per serving, you can set up a division problem.
Divide the total amount of raisins, which is 4 cups, by the amount of raisins per serving, which is 3/8 cup.
You can convert 3/8 to a decimal by dividing the numerator (3) by the denominator (8).
This gives you 0.375.
Then, divide 4 by 0.375 to find the number of full servings.
The result is 10.67, which means you can make 10 full servings and have a little bit of raisins leftover.
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You have 4 cups of raisins. A recipe calls for 3/8 cup of raisins per serving. How many full servings can you make?
At 10:00 AM, Gavin rented a mountain bike. He returned the bike at 3:00 PM, having gone 30 miles. He paid $33 for the rental. Find the rental rate, in dollars per mile.
$6.60/mile
$1.10/mile
$6.00/mile
$0.92/mile
Answer:
$1.10 per mile PLEASE GIVE BRAINLIEST
Step-by-step explanation:
30 miles ÷ $33 = $1.10 per mile
Find the midpoint between the points A(-2,5) and B(4,-7)
Answer:
(1, - 1 )
Step-by-step explanation:
using the midpoint formula
midpoint = [ [tex]\frac{1}{2}[/tex](- 2 + 4), [tex]\frac{1}{2}[/tex](5 - 7) = (1, - 1 )
What value correctly fills in the blank in the equation 16 + 12 = 4 ´ ( __ + 3) to show the sum of the two areas of flowers?
Answer:
4
Step-by-step explanation:
what is the equation of a line that passes through the point (6,1) and perpendicular to the line whose equation is 2x+y= - 6 ?
Answer:
y = [tex]\frac{1}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + y = - 6 into this form
subtract 2x from both sides
y = - 2x - 6 ← in slope-intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (6, 1) into the partial equation
1 = 3 + c ⇒ c = 1 - 3 = - 2
y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of perpendicular line
Find the distance between (-3,7) and (2,9). Use an exact answer in radical form.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 7) and (2, 9). Substitute:
[tex]d=\sqrt{(2-(-3))^2+(9-7)^2}=\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}[/tex]
Answer:
sqrt(29)
Step-by-step explanation:
To find the distance between two points, we use the formula
d =sqrt((x2-x1)^2 + (y2-y1)^2 )
= sqrt( (2--3)^2 + (9-7)^2)
= sqrt( 2+3)^2 + (2)^2)
= sqrt( 5^2 + 4)
= sqrt( 25+4)
= sqrt(29)
The distance is the sqrt(29)
if a line includes the points (8,0) and (20,12). What is its equation in slope-intercept form?
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
substitute the coordinates of the points (8, 0) and (20, 12) to the formula:
[tex]m=\dfrac{12-0}{20-8}=\dfrac{12}{12}=1[/tex]
y = 1x + b = x + b
Put the coordinates of the point (8, 0) to the equation of a line:
0 = 8 + b subtract 8 from both sides
-8 = b
Answer: y = x - 8