Answers
Using the functions, we can find the graphs for each function as follows:
Graph 3 is: g (x) = [tex]4^{x}[/tex]
Graph 4 is: h (x) = [tex]-4^{x}[/tex]
Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]
Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]
Define functions?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|
Based on elements like the domain and range of a function, as well as the function expression, the function y = f(x) is categorised into many categories of functions. The domain x value is referred to as input for the functions. The domain value can be a fraction, decimal, angle, integer, or decimal. The range is also represented by the y value or the f(x) value.
Graph 3 is: g (x) = [tex]4^{x}[/tex]
Graph 4 is: h (x) = [tex]-4^{x}[/tex]
Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]
Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]
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Related Questions
HELLLLLLP!!! I WILL GIVE BRAINLIEST!!!
Answers
The expression that is equivalent to 6x2y + 2xy^5 include:
2(3x²y + xy^5).
2xy(3x + y⁴)
xy(6x + 2y⁴)
What is an expression?An expression can refer to a variety of things depending on the context in which it is used.
In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"
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A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar. At this rate, how many cups of sugar should be used if 5 cups of flour included?
Answers
According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product
According to the given information:If the recipe requires 2 cups of flour for every 2/3 cups of sugar, we can write this relationship as:
2 cups of flour : 2/3 cups of sugar
To find out how many cups of sugar should be used if 5 cups of flour are included, we can set up a proportion:
2 cups of flour / 2/3 cups of sugar = 5 cups of flour / x cups of sugar
where x is the number of cups of sugar we want to find.
To solve for x, we can cross-multiply:
2 cups of flour * x cups of sugar = 2/3 cups of sugar * 5 cups of flour
2x = (2/3) * 5
2x = 10/3
x = 5/3
Therefore, According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
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Which equation is correct for the circle shown on the graph?
(x+3)²+ (y-6)² = 4
(x-3)² + (y+6)² = 4
(x+3)² + (y-6)² = 2
(x-3)² + (y-6)² = 4
Answers
Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.
What is a distance formula?The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.
To answer this we need to know the equation of a circle.
Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:
(x - a)² + (y - b)² = r²
We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.
We can now substitute these information in the circle equation,
(x - -3)² + (y - 6)² = 2²
(x+3)² + (y - 6)² = 4
That is the equation of the given circle is (x+3)² + (y - 6)² = 4.
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The piecewise function g(x) is shown in the graph.
Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma negative 1. The second piece is curved with a solid point at negative 1 comma 0, which ends at 1 comma 1. The last piece starts with a solid circle at 0 comma 1 and increases to the right as it passes through 4 comma 5.
Which of the following represents g(x)?
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than or equal to x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than or equal to x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
Answers
The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).
What represents g (x)?Looking at the graph, we can see that:
g(x) is equal to -2 for x ≤ -1.g(x) is a quadratic function that passes through the point (-1,0) and (1,1), with a vertex at (0,1), for -1 < x ≤ 0.g(x) is a linear function that passes through the point (0,1) and (4,5), for x > 0.Thus, the correct piecewise function that represents g(x) is:
g(x) = {-2 if x ≤ -1
{ (x-1)^2 if -1 < x ≤ 0
{ -x+1 if x > 0
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1. The relationship between distance
measured on a map and the actual
distance on the ground
A. A sketch
B. A statement
C. Layout
D. Scale
What if the correct answer
Answers
Answer: A Map Scale.
Step-by-step explanation:
A Map Scale is the relationship with the ground.
The definition given in the question is referring to the concept of "scale" in cartography. Scale is the ratio between the distance on a map and the actual distance on the ground, and it is an important consideration when creating and using maps. Therefore, the correct answer is D. Scale.
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
co
5
H
The mapping diagram above|
Set B
✓in
-2
3
O
7
શ function since
where there
Answers
Answer:
It is not a function
Step-by-step explanation:
A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.
Here, element "1" has two images 3 and 7. Therefore it's not a function.
Write an equation of the line below.
Answers
Find the slope of the line that contains these points.
(1, -3) (2, -5)
Answers
use slope equation -5 - (-3)/(2-1) then solve
Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
a picture of a snow flake
Answers
Answer:
Yes, the figure is line symmetric.
A snowflake has six lines of symmetry. Therefore, the correct answer is: 6.
What expression is equivalent to 4- 1/3-7/8+1/6?
A. 6/24-8/24-21/24+4/24?
Answer for brainliest. Don't care if its wrong.
Answers
The simplified form of the expression is 71/24.
What is the simplified form?
To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.
Here's the step-by-step solution:
Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.
Convert the fractions to have the same denominator, which is 24:
4 - 1/3 - 7/8 + 1/6
= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)
= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)
Combine the numerators over the common denominator:
= (96 - 8 - 21 + 4)/24 (Combining numerators)
= 71/24 (Performing the subtraction)
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Description of the circumscribed angle
Answers
A circumscribed angle is an angle that has its vertex on the circumference of a circle and whose sides are chords of the circle. The measure of a circumscribed angle is equal to half the measure of the intercepted arc. Circumscribed angles are important in geometry because they are used to prove theorems about angles, chords, and arcs in circles. The opposite angles of a cyclic quadrilateral are always supplementary, and the sum of the angles in a cyclic polygon is always equal to (n-2)180 degrees, where n is the number of sides of the polygon.
Choose the scatterplot(s) that DO NOT suggest a linear relationship between x and y.
O a
Ob
Oc
Od
y
y
*
y
LOVE
y
X
Answers
The scatter plots that do not show a linear relationship are B and C
How can a scatter plot show a linear relationship?The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.
The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.
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Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Answers
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
What is the opposite of 12 written in simplest terms?
Answers
Answer:
Step-by-step explanation:
It is -12.
The opposite of a positive number would be its negative.
A car is purchased for $19,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
Answers
The resale value of the car after 3 years is $9,984.
How to find the resale value after 3 years?Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.
After the first year, the resale value of the car will be 80% of its original value:
Resale value after 1 year = 80/100 * $19,500 = $15,600
After the second year, the resale value of the car will be 80% of its value after the first year:
Resale value after 2 years = 80/100 * $15,600 = $12,480
After the third year, the resale value of the car will be 80% of its value after the second year:
Resale value after 3 years = 80/100 * $12,480 = $9,984
Therefore, the resale value of the car after 3 years will be $9,984.
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NO LINKS!! URGENT HELP PLEASE!!!
Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB.
A(-6, 4), B(14, -12)
Answers
Answer:
The perpendicular bisector of a line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.
To find the equation of the perpendicular bisector of segment AB, we can follow these steps:
Find the midpoint M of AB. The coordinates of M are:M = ( (x1 + x2)/2, (y1 + y2)/2 )
where A = (x1, y1) and B = (x2, y2).
In this case, A = (-6, 4) and B = (14, -12), so the coordinates of M are:M = ( (-6 + 14)/2, (4 - 12)/2 ) = (4, -4)
Find the slope m of AB. The slope of AB is:m = (y2 - y1) / (x2 - x1)
In this case, the slope of AB is:m = (-12 - 4) / (14 - (-6)) = -16/20 = -4/5
Find the slope of the line that is perpendicular to AB. The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So, the slope of the line that is perpendicular to AB is:m_perp = -1/m
In this case, the slope of the line that is perpendicular to AB is:m_perp = -1/(-4/5) = 5/4
Use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. The point-slope form of the equation of a line is:y - y1 = m(x - x1)
We can use the midpoint M as the point (x1, y1) and the slope m_perp as the slope m:y - (-4) = (5/4)(x - 4)
Simplifying, we get:
y + 4 = (5/4)x - 5
Moving terms around, we get:(5/4)x - y - 9 = 0
So, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB is:
(5/4)x - y - 9 = 0
a recipe for sugar cookies calls for 3 cups of sugar and 6 cups of flour so how many cups of sugar are there for each cup of flour?
Answers
The number of cups of sugar that are there for each cup of flour would be = 1/2 cup of sugar.
How to calculate the number of cups of sugar for each cup of flour?The recipe contains sugar of = 3 cups
The recipe contains flour of = 6 cups
If 3cups sugar = 6 cups of flour
X cups sugar = 1 cup of flour
make X the subject of formula;
X = 3×1/6
X = 3/6 = 1/2
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Help please i dont remeber how to do this
Answers
Answer:
-20
Step-by-step explanation:
[tex]\frac{5}{3}x +\frac{1}{3} x=13\frac{1}{3}+\frac{8}{3}x\\\\\frac{6}{3} x = 13 \frac{1}{3} +\frac{8}{3} x\\\\\frac{-40}{3} =\frac{2}{3} x\\\\\frac{3}{2} *(\frac{-40}{3} )\\\\\frac{3}{2} *\frac{2}{3} x\\\\-20 = x[/tex]
what is the answer (x+80)(x-20)
Answers
Answer:
Using the FOIL method to multiply (x + 80)(x - 20), we get:
(x + 80)(x - 20) = x^2 - 20x + 80x - 1600
Simplifying the expression, we get:
(x + 80)(x - 20) = x^2 + 60x - 1600
Therefore, the answer is x^2 + 60x - 1600.
If the point (1,5) lies on a circle with center (0,0), determine which point in quadrant 2 that also lies on the circle.
Answers
Answer:
If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:
r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)
So the equation of the circle is:
x^2 + y^2 = 26
To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.
Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:
For point (a) (-5,1):
x^2 + y^2 = 26
(-5)^2 + 1^2 = 26
25 + 1 = 26
This point does not lie on the circle.
For point (e) (-2,3):
x^2 + y^2 = 26
(-2)^2 + 3^2 = 26
4 + 9 = 26
This point also does not lie on the circle.
Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.
Step-by-step explanation:
since the center of the circle is at the origin, that means that the circle is evenly going through all four quadrants - one quarter arc after the other.
the point (1, 5) is in the first quadrant (upper right one, positive x, positive y).
the circle arc in the second quadrant (upper left one, negative x, positive y) is the mirrored image of the arc in the first quadrant across the y-axis.
so, the point on it gets mirrored too.
that means, it's coordinates are then the same y and the x is converted to its negative value :
(-1, 5)
that is the easily identifiable point in the second quadrant that has to be on the circle.
A carpenter has two different-sized circular saws. The smaller saw has the radius shown. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
.
Answers
If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.
The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;
The diameter of the smaller saw can be calculated as:
⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;
The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,
⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,
⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;
So, Circumference of circle is = 2 × π × radius;
The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,
⇒ circumference of smaller saw = 7.85 inches;
circumference of "larger-saw" = 2 × 3.14 × 2 inches
⇒ circumference of larger saw = 12.56 inches;
The difference in circumference between the two saws is:
⇒ circumference of larger saw - circumference of smaller saw
⇒ 12.56 inches - 7.85 inches = 4.71 inches;
Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.
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The given question is incomplete, the complete question is
A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
Select all the expressions that have the same value. a \large 3^3 b \large 3^4 c \large 6^2 d \large 6^3 e \large 9^2 f \large 9^3
Answers
The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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Choose the tool or tools you can use to
measure the object. Then measure the length.
string and straws
art.
non
7. straws
about
Company LLC. All Rights Reserved.
straws
00
Topic 12 Reteaching
Answers
The tools you can use to measure the object is Ruler
What is the technique to determine the size of a string using ruler?First you need to Indicate the starting and ending points of the curved line on the string. To determine the distance between the two markings on the string, lay the string flat on a ruler, or a stretched-out measuring tape if the line is curved, and measure the length in between.
Commonly found in bars and restaurants, disposable straws intended for one-time use have a common size of 8.5 inches in length and width. The typical size of a drinking straw is one that is having a width of 24 inches. At times, you may need a lengthier or broader straw to suit yourself.
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The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?
Answers
Answer:
If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the values given in the problem:
y = kx
12 = k(8)
Solving for k, we get:
k = 12/8 = 3/2
Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:
y = kx
30 = (3/2)x
Solving for x, we get:
x = (30)/(3/2) = 20
Therefore, when y = 30, x = 20
Evander Holyfield (the champion boxer who had part of his ear bitten off by Mike Tyson) made $290 million during his boxing career but declared bankruptcy because of poor financial choices. His July interest at 18% was $248. What was Evander’s principal at the beginning of July? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest whole dollar.)
Answers
Evander's principal at the beginning of July was approximately $16,533. Rounded to the nearest whole dollar, this is $16,533.
How do we calculate?Applying the formula for simple interest:
Interest = Principal x Rate x Time
Here, we know the interest ($248), the rate (18%), and the time (1/12 of a year for one month, since we're using a 360-day year).
Let the principal = "P":
$248 = P x 0.18 x (1/12)
$248 = P x 0.015
P = $248 / 0.015
P ≈ $16,533.33
Simple interest is described as an interest charge that borrowers pay lenders for a loan.
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The distance of 15 miles on a map is represented by 2 inches.
If the distance between two cities on the map is 8 inches, what is the actual distance
between them?
A 60 miles
B 75 miles
C 90 miles
D 120 miles
awing of an airplane. The airplane has a 100-foot wings
Answers
Answer:
A. 60 miles
Step-by-step explanation:
2 in. = 15mi or like 2in+2in+2in+2in = 8in
15mi+15mi+15mi+15mi = 60mi
2×4 =8
/
/
v
4 × 15mi = 60mi
1 1 Jemima has three boxes with a total weight of 51 kg. Box B weighs 5 kg more than box A and box C weighs 3 kg more than box B. Ch the correct statement. Select one: a. Box C weighs 21 O b. O c. kg. 30 1 Box A weighs 42 kg. 1 Box B weighs 12 kg. O d. 5 Box A weighs 17 kg.
Answers
On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
Let's use "x" to symbolise box A's weight. Then, we could type:
Given that box B weighs 5 kg more than box A, its weight is "x + 5".
Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".
We can write: Since we are aware that the combined weight of the three boxes is 51 kg:
[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]
Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:
17.67 kg (x + 5) is the estimated weight of Box B.
The approximate weight of Box C is 25.67 kg (x + 8).
Therefore, none of the answers to the question's assertions are true.
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50 points! Multiple choice algebra question. Gilda used the formula f(x) = x/144 to convert square inches to square feet. Find the inverse of f(x). Photo attached. Thank you,
Answers
To find the inverse of f(x), we need to switch x and f(x) and solve for x:
x = f(f^(-1)(x))
In this case, f(x) = x/144, so we have:
x = f(f^(-1)(x))
x = (f^(-1)(x))/144
Simplifying for f^(-1)(x), we multiply each side by 144:
144x = f^(-1)(x)
Therefore, the inverse of f(x) is:
f^(-1)(x) = 144x
Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
Answers
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
4/7 of the length of a car ride is 8 miles. How many miles is the whole car ride ?
Answers
hi
4/7 = 8
7/7 = ?
so ? = 7/7 * 8 /4/7 = 8/4/7 = 8 *7/4 = 4*2*7 /4 = 2*7 = 14
so whole thing is 14
let's check : 14 * 4/7 = 56/7 = 8
Match initial data. answer is correct.