When Kenneth opened her account, her account balance was 30.
A function is an expression that assigns each input value, say x, a unique output value, say y. Mathematically, a function can be represented as-
F(x) = x + a
Here, we are given that Kenneth's bank account is modeled by the following equation-
f(x) = 13x + 30
here, x = number of weeks
and f(x) = total amount
When Kenneth must've opened his account, the number of weeks would've been zero.
⇒ x = 0
Substituting the value of x = 0 in f(x), we get-
f(0) = 13(0) + 30
f(0) = 0 + 30
f(0) = 30
Thus, when Kenneth opened her account, her account balance was 30.
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Error Analysis A worker in a silver mine descends 78 feet. Use an integer to represent the change in the worker's position.
An integer to represent the change in the worker position is -78
If the worker is descending, he is going down.The change in his position could be marked on a graph by translating the original point down by 60 units. Integers are a set of numbers that include the positive whole numbers (1,2,3,4,5,....), their opposites (-1,-2,-3,-4,-5,...) are zero. This number line shows the integers from -5 to 5 .You can use integers to help represent many real - world situations, such as:Increase and decreases in temperature.Profits and losses of moneyLocations above and below sea level.Hence, An integer to represent the change in the worker position is -78
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There were approximately 3.3 * 10 8 people in the united states of america in 2010 the average person ate 1.5 * 10 2 lb of sugar that year approximately how many pounds of sugar were eaten in the us in 2010
Amount of sugar eaten in the US in 2010 = 4.95 x 10¹⁰ lb
Approximate number of people in the United States of America in 2010 = 3.3 x 10⁸
Amount of sugar ate by an average person in US = 1.5 x 10² lb
We have to find an approximate amount of sugar eaten in US in 2010.
It will be the product of the number of people in US and the sugar ate by a person in US.
So, Amount of sugar eaten in the US in 2010 approximately = 3.3 x 10⁸ x1.5 x 10²
= 4.95 x 10¹⁰ lb
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Im doing geometry, I forgot how to do this.
Answer:
12
Step-by-step explanation:
You have a right triangle, so use the Pythagorean theorem.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12
a charity benefit is attended by 25 people and three gift certificates are given away as door prizes: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10. assuming that no person receives more than one prize, how many different ways can the three gift certificates be awarded?
Number of ways that the three gift certificates can be awarded = 13800 ways
There are a total of 25 people attended the charity benefit. There are three gift certificates: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10.
Assume that no person receives more than one prize.
One of the 25 people can get gift certificate of $100.
⇒ 25 ways for $100 gift certificate.
Then remaining 24 people are considered for further counting.
One of the 24 people can get gift certificate of $25.
⇒ 24 ways for $25 gift certificate.
Now there are 23 people remained.
One of the 23 people can get the $10 gift certificate.
⇒ 23 ways for $10 gift certificate.
Therefore, Number of ways that the three gift certificates can be awarded = 25 x 24 x 23 = 13800 ways.
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how can i solve literal equations?
Literal equations are equations containing two or more variables. Our goal is to solve for just one variable with respect to others. If it is known to us that how to solve regular equations, then literal equations are very easy to solve.
Literal equation is also termed as simultaneous equation ,
where more than 1 variable is present and can be solved by inputting value entirely into 1 variable form
For example,
x+ y=6
x-y=2
now putting x=y+2 from the second equation,
y+2+y=6
2y+2=6
y+1=3
y=2
x=y+2=2+2=4
To solve a literal equation means to express one variable with respect to the other variables in the equation.
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Equations that have two or more variables are considered literal equations. Our aim is to solve for a single variable in relation to other variables. Literal equations are fairly simple to solve if we know how to solve regular equations.
Simultaneous equation is another name for a literal equation.
where a problem with more than one variable can be handled by entering all of the values into a single variable form.
For Example :
x + y = 6
x - y = 2
Now putting x = y + 2 from the equation
y + 2 +y = 6
2y + 2 = 6
2y = 6-2
2y = 4
y = 2
Hence,
x = y + 2 = 2 + 2 = 4
To express one variable in relation to the other variables in an equation is to solve it literally.
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50 points mathamatics please help
Answer:
Option B: 6342
Step-by-step explanation:
Answer: 6342
Step-by-step explanation:
906 x 7 = 6342
The cost of one pound of grapes, g, is 15 cents more than one pound of apples, a. The cost of one pound of
bananas, b, is twice as much as one pound of grapes. Write an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples
An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Cost of one pound of grapes = g
Cost of one pound of apples = a
Cost of one pound of banana = b
Since, The cost of one pound of grapes is 15 cents more than one pound of apples.
It can be written as;
g = a + 15 .... (i)
And, The cost of one pound of bananas is twice as much as one pound of grapes.
It can be written as;
b = 2g ..... (ii)
To find an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples as,
Put the value of g from (i) in (ii) we get,
b = 2 ( a + 15 )
b = 2a + 30
Hence, An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
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(-125) power -1/3
Evaluate this with step by step
Hello I will AWard Brainlist !!! Help its A Math Question Please Help I will AWard Brainlist thanls so much !!!
The lengths 9, 9 / 2 and 9√3 are not part of a 30 - 60 - 90 right triangles. (Correct choice: A)
What set of measures are associated with a 30 - 60 - 90 right triangles?
Herein we must find what set of lengths are part of a 30 - 60 - 90 right triangle. In accordance with the Euclidean geometry, there are the following relationships for the sides of the 30 - 60 - 90 right triangle:
The longest leg is √3 times the length of the shortest leg.The hypotenuse is 2 times the length of the shortest leg.The hypotenuse is 2√3 / 3 times the length of the longest leg.Now we proceed to check if each set of sides belongs to a 30 - 60 - 90 right triangle:
Case 1
The length of the shortest leg of the triangle is 9 / 2, then the lengths of the longest leg and the hypotenuse are 9√3 / 2 and 9, respectively. (False)
Case 2
The length of the shortest leg of the triangle is 4, then the lengths of the longest leg and the hypotenuse are 4√3 and 8, respectively. (True)
Case 3
The length of the shortest leg of the triangle is 7, then the lengths of the longest leg and the hypotenuse are 7√3 and 14, respectively. (True)
Case 4
The length of the shortest leg of the triangle is 5 / 3, then the lengths of the longest leg and the hypotenuse are 5√3 / 3 and 10 / 3, respectively. (True)
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HELP PLEASE I DON'T UNDERSTAND :[
Answer: the first option i believe
Step-by-step explanation:
The altitude a (in feet) of a plain t minutes after liftoff is given by a= 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet?
The number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
What is a function?A function can be defined as an expression or law that shows the relationship between a dependent and independent variable.
Given the function;
a= 3400 t + 600
Where;
a is the altitude in feett is the time in minutesIf the altitude is 21000 feet, let's determine the time
Substitute the value into the function
21000 = 3400t + 600
collect like terms
21000 - 600 = 3400t
20400 = 3400t
Make 't' the subject
t = 20400/ 3400
t = 6 minutes
Thus, the number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
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please help me with this Qestion
Answer: 5.5 inches
Step-by-step explanation:
Using the formula for the area of a square, we can plug the known values in and solve.
a = x²
30 = x²
[tex]\sqrt{30 } =\sqrt{x^2}[/tex]
[tex]\sqrt{30 }[/tex] = x
5.477 ≈ x
Now, we will round to the nearest tenth.
5.477 ≈ 5.5 inches
work out the surface area of the prism
The surface area of the prism is 200 cm².
The surface area of the prism is given by the formula:
Surface area (S) = 2 B + p h
where B is the area of base of prism
p = perimeter of base
h = height of the prism.
Perimeter = 2(5 + 3) cm
p = 16 cm
B = 5 cm × 4 cm = 20 cm²
h = 10 cm
Substituting it in the formula, we get that:
S = 2 B + p h
S = 2 (20) + (16) (10)
S = 40 + 160
S = 200 cm²
Therefore, we get that, the surface area of the prism is 200 cm².
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How can u determine whether a relation represented as an equation is a function
It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.
which also signifies that for each value of x , there is a value of y which exists and is real.
A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.
Or in simple words if there is no corresponding value of y for any x, then that is not a function.
For example,
[tex]x^{2} +y^{2}[/tex]=1
when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.
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At the end of 1994 Walters Was half as old as his grandmother. The sum of the years in which they were born in 3838. How old will Walter be at the end of 1999?
The age of Walter at the end of year 1999 will be equal to 55 years.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
Let's assume respective age of Walter and Walter's grandmother is x and y years respectively.
In 1994 , age of Walter was :
x = y / 2
or y = 2x
It is also given that the sum of years they were born is 3838.
The year Walter was born = (1994 - x)
The year Walter's grandmother was born :
= (1994 - y)
= 1994 - 2x (∵ y = 2x)
So , we can write an equation to find out Walter's age which is :
1994 - x + 1994 - 2x = 3838
3988 - 3x = 3838
3x = 3988 - 3838
x = 150 / 3
x = 50 years
or the age of Walter in 1994 is 50 years.
At end of 1999 Walter's age will be:
= 50 + 5.
= 55 years
Therefore , the age of Walter at the end of year 1999 will be equal to 55 years.
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researchers are investigating whether taking aspirin regularly reduces the risk of heart attacks. four hundred men participate in the study. the men are divided randomly into two groups: one group takes aspirin pills, and the other group takes placebo pills (a pill with no aspirin in it). the men each take one pill a day, and they do not know which group they are in. at the end of the study, researchers will count the number of men in each group who have had heart attacks. identify the explanatory and response variables in this situation.
Explanatory variable: The type of pill the men took each day.
Response variable: Whether a subject had a heart attack.
We have been given that :
Participated candidates are 400
Men are divided randomly so we find out explanatory and response variable.
The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.
Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.
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which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?vertical translationhorizontal translationreflection over the x-axisreflection over the y-axis
The type of transformation that preserves the symmetry is Vertical translation.
For instance, a parabola is still symmetric about the y-axis if you move it up. It loses its symmetry if you move it to the left or right. Reflection keeps both even and odd functions symmetrical.
What is the difference between even and odd function ?The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin [tex](0, 0)[/tex]. This means that if you rotate an odd function 180 degrees around the origin, the function you started with will still exist.
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to determine whether or not number of complaints influences accidents occurring in an area, charles has designed a survey. what is the explanatory variable?
In the survey study, the explanatory variable is: number of complaints .
What is an Explanatory Variable?An explanatory variable can be described as a type of independent variable that is manipulated by the researcher which explains the or predict the differences that occurs in a response variable.
For example, number of complaints is the independent variable that the dependent variable, "accidents that occurs in an area" depends on. That is, it explains or predicts the accidents that occurs in an area.
Therefore, we can conclude that, in the survey study, the explanatory variable is: number of complaints .
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Use the Distributive Property to rewrite each expression.
4(x + 2y - 3)
Answer:4x + 8 y -12
Step-by-step explanation:
If segment RS has endpoint R(5,1) and midpoint M(1,4), what will be point S?
Answer:
S(-3,7)
Step-by-step explanation:
Rise/Run
M(1,4) R(5,1)
1+run=5 4+rise=1
run=4 rise= -3
1-4= -3 4+3=7
A skin on skin 63 photos in a minute if it’s skins photos at a consistent rate it can scan bring photos in 21 minutes
When it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
How to calculate the value?From the information, it should be noted that the skin on skin 63 photos in a minute.
Therefore, the number of photos that can be skinned at a particular minutes will be illustrated as:
p = 63m
where p = number of photos
m = number of minutes
Therefore, it should be noted that using p = 63m. The appropriate number of photos will be:
p = 63m
p = 63 × 21
p = 1323 photos
Therefore, when it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.
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What is 7+7?
Easy Brainly and points if 2 ppl answer :)
The answer to this question is 14
Solve for the value of x in the diagram below.
an equilateral triangle has three congruent sides that measure 1.5 inches on each side. what is the perimeter of the triangle?
The perimeter of the triangle is 4.5inches.
Equilateral Triangle : can be defined as a triangle having all three sides equal.
Perimeter of triangle is defined as the sum of the lengths of the three side.
Perimeter of triangle is denoted by 3x(side).
Given that the side of the triangle is 1.5 inches
Perimeter = 3x(1.5)
Perimeter=4.5 inches
Therefore , The Perimeter of the triangle is 4.5 inches .
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A leather recliner with a regular price of $795.00 is on sale for 15% off. What is the sale price of the recliner?
Answer:
$675.75
Step-by-step explanation:
To find the sale price of the recliner, we can multiply 15% by the regular price.
15% = 0.15
(0.15)(795.00) = $119.25
This gives us the amount that the sale takes off from the regular price. We can subtract that from the regular price to find the sale price.
795.00 - 119.25 = $675.75
A bonus shortcut way to get our answer would be to subtract 15% from 100%.
100% = 1.00
1.00 - 0.15 = 0.85
This tells us that the sale price is 85% of the regular price. Using this information, we can multiply 85% by the regular price to also get our sale price.
85% = 0.85
(0.85)(795.00) = $675.75
use the given conditions to write an equation for the line. passing through (−9,2) and parallel to the line whose equation is
The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.
What is an equation?There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
[tex]$$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$[/tex]
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(-7,10) perpendicular to 2x - 3y= -3 using slope-intercept form
y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3
In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that 2x - 3y= -3
can also be written as
y = 2/3x + 1
Here 2/3 is the slope and 1 is the y-intercept
To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = -3/2, x₁ = -7 and y₁ = 10
y - 10 = -3/2(x - (-7))
y - 10 = -3/2(x + 7)
y - 10 = -3/2x - 21/2
y = -3/2x - 21/2 + 10
y = -3/2x - 20.5
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Describe in words where cube root of 70 would be plotted on a number line.
A Between 3 and 4, but closer to 3
B Between 3 and 4, but closer to 4
C Between 4 and 5, but closer to 4
D Between 4 and 5, but closer to 5
Answer:
C Between 4 and 5, but closer to 4
Step-by-step explanation:
cube root of 70 is 4.1212
An angle measures 84.2° less than the measure of its supplementary angle. What is the measure of each angle?
The measure of the supplementary angles are 48° and 132°.
Let the measure angle be x.
Its supplementary angle will be x + 84
We know that the sum of supplementary angles is 180°.
So, we get the equation as:
x + x + 84 = 180
Combining the like terms, we get that:
2 x + 84 = 180
Subtract 84 from both sides, we get that:
2 x = 180 - 84
2 x = 96
Divide both sides by 2, we get that:
x = 96 / 2
x = 48°
x + 84 = 48+ 84 = 132°
Therefore, we get that, the measure of the supplementary angles are 48° and 132°.
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An electrician charges $24 per hour and $36 for each hour of overtime. For a job, the electrician works 8 regular hours and overtime hours. He also charges $202 for materials. The total amount of the bill for the job is $538. How many overtime hours did the electrician work?
Fill in the blanks to create an equation that represents the situation.
Blanks-
24( )+ x+202=538
Answer:
hindi kasi ka nag aaral hhahhaha