Answer: To find the answer, I first understood that the first number is a product of two factors and the second number is the sum of those two factors.
So, I started by listing out all the factors of the first number which is 16. The factors of 16 are 1, 2, 4, 8, 16.
Then I looked for a pair of factors from the list whose product is 16 and sum is 10.
I found the pair (4, 6) which satisfies the condition.
So, I confirmed that 4 x 6 = 16 and 4 + 6 = 10.
Step-by-step explanation:
Write an exponential decay function to model the situation. Compare the average rates of change over the given intervals.
initial value: 42
decay factor: 0.7
1
Answer: An exponential decay function models a situation in which a value decreases over time at a rate that is proportional to its current value. The function has the form:
y = A*e^(-kt)
Where y is the final value, A is the initial value, e is the base of the natural logarithm (approximately 2.718), k is the decay factor, and t is the time.
In this case, the initial value is 42 and the decay factor is 0.7. So the exponential decay function that models the situation is:
y = 42 * e^(-0.7t)
To compare the average rates of change over the given intervals, we need to find the derivative of the function, which represents the instantaneous rate of change of the function at any given point in time.
The derivative of this function is:
dy/dt = -0.742e^(-0.7t)
The negative sign indicates that the value is decreasing over time. The absolute value of the derivative will be the rate of decay.
So, the average rate of change over the given intervals is -0.7*42 which is -29.4
The rate of decay is always -29.4 for this function.
Step-by-step explanation:
6
Select the correct answer from each drop-down menu.
Point A is the center of this circle.
The ratio of the lengths of
and
is 2:1.
The ratio of the lengths of ( AD, IH ) is 2:1
What is chord?A chord that passes through the center of the circle is known as diameter of he circle. Chords IH and EF are diameters of our given circle.
Point A is the center of this circle.
In the given diagram we have EF is the diameter of the circle.
BC is the chord of the circle and Diameter and chord length will vary.
AD is the radius of the circle and IH is the diameter of the circle.
Diameter of the circle IH is 2 times the radius AD
So,
The Answer is option B
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If the numerator of a fraction is increased by 2 and the denominator by 5 it becomes 1/2. Again if the numerator is decreased by 4 and the denominator by 1 it becomes 1/3, find the fraction.
The original fraction is 10/19
Let the fraction be [tex]\frac{x}{y}[/tex]
Now , according to question
[tex]\frac{x+2}{y+5}[/tex] =[tex]\frac{1}{2}[/tex]
⇒ 2(x+2)=y+5
⇒2x-y-1=0-------(1)
and [tex]\frac{x-4}{y-1}[/tex]=[tex]\frac{1}{3}[/tex]
⇒3(x-4)=y-1
⇒3x-y-11=0------(2)
subtracting 1 from 2 we get
2x-y-1
3x-y-11
- + +
⇒ x=10
putting in (1)
20-y-1=0
y=19
∴ The actual fraction was 10/19
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a palindrome is a number that has the same value when read from left to right or from right to left.
T/F?
Answer:
True
Step-by-step explanation:
7.4x+3-9= 6 + 7.4x
with solution please
Answer:
6
Step-by-step explanation:
Solution for 7.4x+3-9=6+7.4x equation:
Simplifying
7.4x + 3 + -9 = 6 + 7.4x
Reorder the terms:
3 + -9 + 7.4x = 6 + 7.4x
Combine like terms: 3 + -9 = -6
-6 + 7.4x = 6 + 7.4x
Add '-7.4x' to each side of the equation.
-6 + 7.4x + -7.4x = 6 + 7.4x + -7.4x
Combine like terms: 7.4x + -7.4x = 0.0
-6 + 0.0 = 6 + 7.4x + -7.4x
-6 = 6 + 7.4x + -7.4x
Combine like terms: 7.4x + -7.4x = 0.0
-6 = 6 + 0.0
-6 = 6
Solving
-6 = 6
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
Question 5 of 11
Write an equation of the form y = mx for the line shown below.
(-3,6)
(-2,4)
Answer here
I
5
SUBMIT
Answer:
y = -2x
Step-by-step explanation:
Slope = change in y/ change in x
Points: -3, 6 / -2 4
x, y
-3 - -2 = -1
6 - 4 = 2
2/-1 = -2
y = mx
y = -2x
In the middle school band, there are 5 flutes for every 2 tubas. Write the ratio of flutes to tubas in three different ways. Group of answer choices
Answer:
5:2
2/5
5 to 2
Step-by-step explanation:
Find the slope of the line graphed below.
Answer:
-1
Step-by-step explanation:
:)
1) write slope formula:
rise y2-y1
m= ------- =-----------
run x2-x1
put your problem in the y and x your problem
1 - 2 -1
m=---------= -----------=-1
2 - 1 1
Also you don't even need need to do this entire you can just see what it is decreasing or increasing by it it is a whole number
a.-3x+12 - 6x + 21
b. 12- 9x + 21
which property of equality is demonstrated
-3x +12 -6x +21 = 12 - 9x + 21
Here the Additive property of the Equality was demonastrated.
What are properties of Equality ?Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality. Algebraic equations involving real numbers can be resolved with the aid of the addition, subtraction, multiplication, and division characteristics of equality.
When the same quantity is added to both sides of an equation, the equation still holds true, according to the definition of the addition property of equality. This condition may be formally expressed as follows: for real numbers a, b, and c, if a = b, then a + c = b + c. Equations involving algebra and arithmetic can both leverage this characteristic.
-3x +12 -6x +21 = 12 - 9x + 21
Here the Additive property of the Equality was demonastrated.
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what is the inverse of the function f(x) = 3(c+5)^2-4 such as x < -5
for the figures below
e they are made of semi circles,quater circles and square for each shape fins area and perimeter .give your answer as a completely simplified
The the area and perimeter of the shapes in terms of pi are 36pi - 72.
What is Perimeter?You should understand that the perimeter of the object is the distance round the object.
A circle's area is calculated as pi*r², so a semicircle is pi*r² / 2, and a quarter circle is pi*r² / 4.
A triangle's area is 0.5*base*height.
We have a quarter circle of radius 12, of which the area is pi*(12² / 4) = 36pi.
The area of the triangle ABC is 0.5*12*12 = 72,
This means that the shaded area is 36pi - 72.
Rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of AD is actually identical in area to the blank semicircle-shaped space to the left of BC.
So if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. The area of a square is s² = 24² = 676 cm².
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Correct question:
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Luke is going to plant 54 cucumber plants and 72 carrot plants. Luke would like to plant the plants in rows where each row has the same number of cucumber plants and each row has the same number of carrot plants. What is the greatest number of rows Luke can plant?
Answer: He will have to plant 14 rows
Step-by-step explanation:
Identify two angles that are marked congruent to each other on the diagram
below. (Diagram is not to scale.)
The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In triangles ΔIHD and ΔFGE, we have
∠IHD ≅ ∠FGE (Given)
The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.
Congruent means equal. Then The measure of the angle ∠IHD is equal to the measure of the angle ∠FGE.
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what's the answer to this?
The slope of the line made by these given coordinates is 7/6.
What is proportionality?In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.
Given coordinates of a graph. Since the coordinates are proportional thus, these coordinates represent the graph of the line as shown in the figure below.
From the general formula of the slope of the line (m) = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
The slope of the line = (14-7) / (12- 6)
The slope of the line = 7/6
Equation of the line id y = 7/6x + c
Since, the line passes through the point (18, 21)
21 = 7 /6 * 18 + c
c = 0
thus, the equation of the line is 6y = 7x
therefore, the slope of the line made by these given coordinates is 7/6 and this line passes through the origin.
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11/22 of the 4 Carla read of the pocketbook yesterday and pocketbook today. What part of the pocketbook did she read already?
Answer: The question states that Carla read 11/22 of the pocketbook yesterday and today. The phrase "of the pocketbook" is referring to the entire book, so 11/22 of the entire book has been read by Carla. This fraction represents the proportion or part of the book that has been read, and can be visualized as 11 out of 22 equal parts of the book have been read.
Final Answer = 11/22 of the pocketbook has been read by Carla.
Step-by-step explanation:
In WXY, if x y, WX = 9x - 11, XY =4x - 1, and WY =7x - 3, find x and the measure of each side.
The value of x is given as follows:
x = 1.5.
The measure of each segment is given as follows:
WX = 2.5.XY = 5.WY = 7.5.What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
For this problem, we have that segment WY is divided into two smaller segments, WX and XY.
This means that the equation to find the value of x is presented as follows:
WY = WX + XY
7x - 3 = 9x - 11 + 4x - 1
13x - 12 = 7x - 3
6x = 9
x = 1.5.
Hence the segment lengths are given as follows:
WX = 9x - 11 = 9(1.5) - 11 = 2.5.XY = 4x - 1 = 4(1.5) - 1 = 6 - 1 = 5.WY = 7x - 3 = 7(1.5) - 3 = 10.5 - 3 = 7.5.More can be learned about the segment addition postulate at https://brainly.com/question/2134445
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I’ll give BRAINLIEST if correct
Which of the following inequalities matches the graph ?
Option A is correct.
The given line has a slope of 5 which can be calculated by counting the change in the y-direction with respect to the change in the x-direction from the graph. And the y-intercept is -1
The equation of the line is,
y=5x-1 or
5x-y=1
Checking the point (0,0) into the equation we can see that 0<1, hence, the correct inequality is,
[tex]5x-y\leq 1[/tex]
Hence, the correct inequality is not listed.
evaluate the following expression by substituting -2 for x. Expression: 3x + 4
Answer:
-2
Step-by-step explanation:
3(x)+4
3(-2)+4
-6+4
-2
HELP
A particular hybrid car travels approximately168 miLe on 4 gal of gas. Find the amount of gas required for 714 -miLe trip.
The car needs____ gallons of gas for 714 -miLe trip.
(Type an integer or a decimal.)
The hybrid car needs 17 gallons of gas for 714 -mile trip.
How to find the number of gallons of gas the hybrid car will requireThe problem is solved using the unit rate.
Where unit rate refers to an item's consumption or price for one of it. This is expressed as a ratio with one as the denominator.
In the problem, we have that 4 gallons travels 168 miles the unit rate is solved as follows
unit rate = number of gallons / number of miles
unit rate = 4 gallons / 168 miles
unit rate = 1/42 gallons per mile
solving for 714 miles trip
= unit rate * number of miles
= 1/42 * 714
= 17 gallons
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Answer:
17 gallons
Step-by-step explanation:
714 * 4 / 168 = 17 gallons
a sceintist conducts an invenstigation she mixes 4/5 ounce of one chemical with 13/20 ounce of another chemical how many ounces are in the mixture?
There are an improper fraction of 29/20 ounces or a mixed fraction of one whole number and a fraction of 1/20 ounces in the mixture.
How to calculate for the fraction of ouncesWe shall add the two fractions 4/5 and 13/20, but firstly we find the lowest common multiple (LCM) of their denominators to enable us get a single denominator before simplifying the numerator.
LCM of 2 and 20 is equal to 20
20/5 = 4 and 20/20 = 1
4/5 + 13/20 = (4×4 + 1×13)/20
4/5 + 13/20 = (16 + 13)/20
(4/5 + 13/20) ounces = 29/20 ounces
Therefore, 29/20 is an improper fraction gotten by adding the fraction of ounces, but when expressed as mixed fraction is one whole number, and a fraction 1/20 ounces in the mixture.
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List the types of angles from smallest angle measurement (at the top) to the largest angle measurement (at the bottom)
Acute
Reflective
Obtuse
Right
Straight
Circle
The list of types of angles from the smallest angle to the largest angle measurement is listed below:
Acute --> right angle--> Obtuse angle --> Straight angle --> Reflective angle and circle.
What are the types of angles?The types of angles that are commonly used in mathematics include the following from the least angle to the largest:
Acute angle: This is an angle that is less than 90 degrees.Right angle: This is an angle that is exactly 90°Obtuse angle: This is an angle that is more than 90° but less than 180°Straight angle : This is an angle that is exactly 180°Reflective angle and circle.
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help!!!!!!!!!!!!!!!!!!!!!
Answer:
J is a function
K is not a function
Step-by-step explanation:
A function is when every input (x) has only one output (y).
J
The ordered pairs are:
(-4,2) ( -8,2) (4, 1) ( 5,1) Every x has only 1 y.
K
The ordered pairs are:
(4,-3) (3, -5) (2, -5) (2, -4)
the input (x) 2 has two outputs (-5, and -4) This is why this is not a function.
Solve for brainliest
Answer:
Step-by-step explanation:
In this equation, 500 is the coefficient of the variable h, 4,000 is the constant, and E and h are both variables. Therefore, the equation should be written as:
E = 500h + 4000
Is y=10/x a non liner or liner
The equation y = 10/x is a nonlinear equation
How to determine the equation typeFrom the question, we have the following parameters that can be used in our computation:
y = 10/x
As a general rule, a linear equation can be represented using any of the following forms
y = mx + c
y = mx
y = c
x = c
Ax + By = c
y - y1 = m(x - x1)
Any form other than the above is a nonlinear equation
The equation y = 10/x does not take any of the forms
Hence, the equation is nonlinear
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Solve for a. a+1−2=4 Select the number from the drop-down menu to correctly complete the statement.
Answer:
5
Step-by-step explanation:
set everything equal to a to solve for a.
a + 1 - 2 = 4
a + 1 = 6
a = 5
so your answee would be 5.
we can check this by plugging back in.
5+1-2=4
the points given in the table below represent a function. What is the rate of change in the function?
The points given represent a function. The rate of change in the function is 5. The correct option is C.
What is the average rate of change of a function?It is the average amount by which the function is modified per unit throughout that time period. The specified points' coordinates should be found. The choice to label them is yours. The difference between the output values should be found. The difference between the input values should be found.
It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
Therefore, the correct option is C, 5.
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Which equation has the solution x = 5? Select each correct answer. Responses x5+5=6 x over 5 end fraction plus 5 equals 6 25x+4=9 25 over x end fraction plus 4 equals 9 32−4x=12 32 minus 4 x equals 12 11 + 6x = 22 11 + 6, x, = 22 3x + 1 = 9 3, x , + 1 = 9 18−2x=9
The equations that have the solution x = 5 are 25/x + 4 = 9 and 32 − 4x = 12
How to determine the equationFrom the question, we have the following parameters that can be used in our computation:
x⁵ + 5 = 6
25/x + 4 = 9
32 − 4x = 12
11 + 6x = 22
3x + 1 = 9
18 − 2x = 9
Solving each equation, we have
Equation 1: x⁵ + 5 = 6
Evaluate the like terms
x⁵ = 1
Take the fifth-root
x = 1
Equation 2: 25/x + 4 = 9
Evaluate the like terms
25/x = 5
So, we have
5x = 25
Divide by 5
x = 5
Equation 3: 32 − 4x = 12
Evaluate the like terms
4x = 20
Divide by 4
x = 5
Equation 4: 11 + 6x = 22
Evaluate the like terms
6x = 11
Divide by 4
x = 11/6
Equation 5: 3x + 1 = 9
Evaluate the like terms
3x = 8
Divide by 3
x = 8/4
Equation 6: 18 − 2x = 9
Evaluate the like terms
2x = 9
Divide by 2
x = 9/2
Hence, the equations are 25/x + 4 = 9 and 32 − 4x = 12
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Part b: if a = 10 b = -4 have would you find the r number of solutions in the equation.
10x -12 = 10x + 4
Part a: For what values would the equation have infinite amounts of solutions.
Answer I got: a = 10 b = -12
The number of solutions of the system of equations 10x - 12 = 10x + 4 is given as follows:
Zero.
The system of equations 10x - 12 = ax + b would have an infinite number of solutions when:
a = 10.b = -12.How to define the number of solutions of the system of equations?The systems in this problem are defined by linear functions, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.The slope and the y-intercept are used to determine the number of solutions of the system, as follows:
Different slope: One solution.Same slope and different intercept: No solutions, as the lines are paralle.Same slope and same intercept: Infinite solutions, as the lines are equal.The system of equations 10x - 12 = 10x + 4 falls in the second case, while for a system to have an infinity number of solutions, it must fall on the third case.
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What three properties hold to the congruence of angels?
Answer:
The three properties of congruence are reflexivity, symmetry, and transitivity. These properties can be applied to segments, angles, triangles, or any other shape.
The owner of the theater in
Item 18 wants to make at least
$400 at each performance. Let x be
the number of adult tickets and y
be the number of child tickets sold.
Write an inequality to show the
number of tickets that need to
be sold
An inequality to show the number of tickets that need to be sold is;
x + y ≥ $400
How to solve Inequality Word Problems?
Inequality is simply defined as the comparison and boundary for two non equal values. Thus, we can easily say that inequality compares the values that are non equal.
We are told that the owner wants to make $400 and sets boundary that;
The least amount to make = $400
The highest amount to make = infinite
This introduces relation in inequality as $400 or greater than $400.
Therefore the money made is counted as a combination from child tickets and adult tickets. If x is the amount that is made made through child tickets and y is the amount made from the adults, then we have;
x + y ≥ $400
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