Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Trey has 49 miles
to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving. How many miles will he have to his
destination after 57 minutes of driving?
distance (in miles)
Driving time(in minutes)
As per the linear function, the destination after 57 minutes of driving is 1055 miles.
Linear function:
The linear equation is defined as an algebraic equation of the form
y = mx + b.
involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given,
Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes).
Trey has 49 miles to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving.
Here we need to find his destination after 57 minutes of driving.
In this one, first we have to find the linear equation for the situation.
For that, we need the slope and the intercept.
So, here we consider the distance as y axis and the corresponding time as x axis. then we get the points as,
(x1. y1) => (37, 49)
(x2, y2) => (51,37.8)
Then the slope of the line is calculated as,
m = (37.8 - 49) / (51 - 37)
m = -11.2/14
Now, the intercept is calculated using the point (37,49) and the slope m = -11.2/14 is,
49 = -11.2/14(37) + b
686 = -414.4 + b
b = 1100.4
So, the linear equation of the function is
y = -11.2/14x + 1100.4
Here we need to find the distance when the time is 57 minutes,
For that, we have to apply the value of x as 57, to get the value of y,
Therefore,
y = -11.2/14 (57) + 1100.4
y = -45.6 + 1100.4
y = 1055
Therefore, the destination after 57 minutes of driving is 1055 miles.
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suppose f(x) = 3x + 10 and g(x) = 17x + 4
find (f+g) (x)
Suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14
The function is an expression the show the relationship between one variable and another variable. If one variable is dependent variable another variable will be independent variable. We can also says that the function shows the relationship between set of inputs and set of out puts
The function f(x) = 3x+10
g(x) = 17x+4
We have to find the value of (f+g)(x)
We know,
(f+g)(x) = f(x) + g(x)
Substitute the values in the equation
(f+g)(x) = 3x+10 + 17x+4
Add the like terms
(f+g)(x) = 20x+14
Hence, suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14
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If f(x)= x³+4x² - 15-18 and a + 1 is a factor of f(x), then find all of the
zeros of f(x) algebraically?
Answer:
I believe you typed that wrong.
The third term should be -15X
And the 3 answers are 3 -6 -1
Step-by-step explanation:
Answer: x=-1 x=-6 x=3
Step-by-step explanation:
[tex]f(x)=x^3+4x^2-15x-18[/tex]
Let's isolate the multiplier (x+1) from the expression x³+4x²-15x-18 :
[tex]x^3+4x^2-15x-18=\\\\x^3+x^2+3x^2-15x-18=\\\\x^2(x+1)+3(x^2-5x-6)=\\\\x^2(x+1)+3(x^2+x-6x-6)=\\\\x^2(x+1)+3(x(x+1)-6(x+1))=\\\\x^2(x+1)+3(x+1)(x-6)=\\\\(x+1)(x^2+3(x-6))=\\\\(x+1)(x^2+3x-18)[/tex]
Decompose the polynomial х²+3х-18 into factors:
[tex]x^2+3x-18=\\\\x^2+6x-3x-18=\\\\x(x+6)-3(x+6)=\\\\(x+6)(x-3)[/tex]
[tex]Thus,\\\\x^3+4x^2-15x-18=(x+1)(x+6)(x-3)\\\\[/tex]
[tex](x+1)(x+6)(x-3)=0\\\\x+1=0\\x+1-1=0-1\\x=-1\\\\x+6=0\\x+6-6=0-6\\x=-6\\\\x-3=0\\x-3+3=0+3\\x=3[/tex]
Dividing polynomials
(12x5+4x4-24x²-8x) + (3x + 1)
Answer:
Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1).
9th term of 25,150,900
Answer: The 9th term is 41990400
Step-by-step explanation:
As we can see here 25, 150, 900 to find the common ratio i'll divide 150 by 25 which gives me 6
to 25 times 6 is 150
150 times 6 is 900
T=Term
1t=25 2t=150 3t=900 4t=5400 5t=32400 6t=194400 7t=1166400 8t=6998400 9t= 41990400
900*6= 5400
5400*6=32400
32400*6= 194400
194400*6= 1166400
1166400*6= 6998400
6998400*6=41990400
Name the property illustrated.
(7 + 8) + 9 = 7 + (8 + 9)
answer: associative property
Step-by-step explanation:
7y - 14 factor please ..
Answer:
2
Step-by-step explanation:
7y-14=0
7y=14
7y/7=14/7
y=2
e function.
f(x) = -4x² + 3x − 11
Find f(-4)
Answer:
-87
Step-by-step explanation:
-4x^2 + 3x - 11
-4(-4)^2 + 3(-4) - 11
-4 * 16 + 3(-4) - 11
-4 * 16 - 12 - 11
-64 - 12 - 11
-76 - 11
-87
Hope this helps! :)
a solid cube has side length 3 inches. a 2-inch by 2-inch square hole is cut into the center of each face. the edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. what is the volume, in cubic inches, of the remaining solid?
The volume of remaining solid is 7 in³.
What is volume of cube?The whole three-dimensional area occupied by a cube is its volume.
A cube is a solid 3-D object with six square faces and equal-length sides.
The cube is one of the five platonic solid shapes and is also referred to as a regular hexahedron.
The cubic units are used to represent the cube's volume.
Imagine performing each cut individually.
A box 2*2*3 is eliminated in the initial cut. Two boxes with dimensions of 2*2*0.5 are removed during the second cut, and the third cut eliminates the same number of boxes on the final two faces.
Therefore, the sum of all cuts is 12 + 4 + 4 = 20.
∴Volume of rest of cube = 3³-20
= 7 in³
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ignore the 7. Appreciate if its done quickly. No need to graph. Just solve inequality
Answer:
[tex]x \leq -1[/tex]
Step-by-step explanation:
divide both sides by -4
-2 >= x - 1
(FLIP THE INEQUALITY!!!)
now add 1 to both sides
-1 >= x
flip the equation
x <= -1
that is your answer
Need help with math question
Answer:
3/2
Step-by-step explanation:
XY/Z
-2×-3/4
6/4
3/2
I need help doing this, I dont really know how. show work
Check the picture below.
Given the line segment AB with endpoints (-10,0) and (6,8). Find the approximate value of AB, round the answer to the nearest tenth if necessary. Then find the exact coordinates of its midpoint.
The line segment AB with endpoints (-10,0) and (6,8). The equation of the line segment is x-2y+10=0.
Given that,
The line segment AB with endpoints (-10,0) and (6,8).
We have to find the equation of the line segment.
The equation of the line formula is y-y₁=m(x-x₁).
Here we don't know the m value that is nothing but slope of the line.
First we have to find the slope of the line segment.
Slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(8-0)/(6+10)
m=8/16
m=1/2
Now,
We know the equation of line is y-y₁=m(x-x₁)
y-0=1/2(x+10)
2y=x+10
x-2y+10=0
Therefore, The equation of the line segment is x-2y+10=0.
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What is an equation of the line that passes through the point (-1, 5) and is parallel
to the line x - y = 6?
Answer:
Step-by-step explanation:
An equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .What is the Point-slope form?The equation of the straight line has its slope and given point.If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equationy-y₁ = m(x-x₁)Which is the required equation of a line in a point-slope form.WE havex + y = 6y = - x + 6Slope= -1Now, Use the same slope since the two lines are parallel to each other.Point-slope formula:y - 8 = -1 (x - - 4)y - 8 = -1 (x + 4)y - 8 + 8 = -x - 4 + 8y = - x + 4 (Slope-intercept form)Hence, an equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .Learn more about slope here: brainly.com/question/2503591#SPJ2
⇒Parallel lines have equal gradients . It means that to obtain the gradient of the new equation we should first find the gradient of the given equation by writing the given equation in the form y=mx+c
[tex]x-y=6\\y=x-6[/tex]
⇒The gradient of the given equation is 1 as we know that the gradient of the equation is the coefficient of the variable x
This means the equation of the new equation is also going to be 1 since I explained above why. to find the value of c in the new equation we will substitute the known values in the general equation including the point.
[tex]5=1(-1)+c\\6=-1+c\\c=5+1\\c=6[/tex]
This means that the new equation is going to be:
[tex]y=x+6[/tex]
suppose that a certain college class contains students. of these, are juniors, are chemistry majors, and are neither. a student is selected at random from the class. (a) what is the probability that the student is both a junior and a chemistry major? (b) given that the student selected is a junior, what is the probability that she is also a chemistry major?
The answer will be .25 and .25 for both set of question. using probablity.
What is Probability ?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.
Total number of students =1-juniors+chemistry+neither+both
(a) For both a junior and chemistry major =1/4 =. 25
(b) probability that she is also a chemistry major will be 1/4 =. 25
Hence The answer for the above two set of qustion will be .25 and .25.
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If X=[tex]\frac{2a+3}{3a-2}[/tex] ,express [tex]\frac{x-1}{2x+1}[/tex] in terms of a
Expressing [tex]\frac{x-1}{2x+1}[/tex] in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]
How to write the given expression in terms of aGiven that:
[tex]x=\frac{2a+3}{3a-2}[/tex]
[tex]\frac{x-1}{2x+1}[/tex]
The Knowledge required here is substitution, the value of x is given. Substitute [tex]x=\frac{2a+3}{3a-2}[/tex] in any place x is seen in the numerator and the denominator.
The numerator
x - 1
substituting the value of x
[tex]\frac{2a+3}{3a-2}-1[/tex]
[tex]\frac{(2a+3)-(3a-2)}{3a-2}[/tex]
[tex]\frac{2a+3-3a+2}{3a-2}[/tex]
[tex]\frac{5-a}{3a-2}[/tex]
The denominator
2x + 1
substituting the value of x
[tex]2*\frac{2a+3}{3a-2} +1[/tex]
[tex]\frac{4a+6}{3a-2} +1[/tex]
[tex]\frac{(4a+6)+(3a-2)}{3a-2}[/tex]
[tex]\frac{7a+4}{3a-2}[/tex]
combining the fraction
Here the numerator and the denominator is brought together and division of fraction is used to solve
[tex]\frac{\frac{5-a}{3a-2}}{\frac{7a+4}{3a-2}}[/tex]
[tex]\frac{5-a}{3a-2}}*\frac{3a-2}{7a+4}[/tex]
[tex]\frac{5-a}{7a+4}[/tex]
Using substitution as required, then expressing the equation in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]
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As a children's librarian, Jodi Hassam earns $15.35 per hour plus time and a hall for weekend work Last week she worked her regular 40 hours plus 16 hours on the weekend. What was her total pay for the week?
Answer:
Jodi's total pay for the week is $ 982.40
Step-by-step explanation:
Jenna is now x years old and Amy is 3 years younger than Jenna. In terms of x, how old will Amy be in 4 years?
Answer:
x-3+4 = x+1
Step-by-step explanation:
x-3+4 = x+1.
-3( v + 2) - 2v simplify use distributive property
NOTE -3 MUST MULTIPLY EVERYTHING IN THE BRACKETS.
[tex] = - 3(v) - 3(2) - 2v \\ = - 3v - 6 - 2v \\ = - 3v - 2v - 6 \\ = - 5v - 6[/tex]
GOODLUCK.
for every integer m, 7m 4 is not divisible by 7. construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order.
Answer: CAELYNN YOU WWELCOME
Step-by-step explanation:
7 +7+7+7+7+7
d = 4n-2 solve for n
The value of the equation d = 4n - 2 for n is (d + 2) ÷ 4.
Given data, d = 4n - 2
For finding the value of n first add 2 to both the side,
d + 2 = 4n - 2 + 2
d + 2 = 4n
Now, divide 4 into both sides of the equation:
(d + 2) ÷ 4 = 4n ÷ 4
(d + 2) ÷ 4 = n
∴ The value of n after solving the equation d = 4n - 2 is (d + 2) ÷ 4.
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please help me to find x,y and z
arabella graphed the following systems equations. she says that (0.5,2.5) is the solution.
what is one way you can use substitution to see if Arabella is correct
substitute __ for ___
Answer:
4x y
Step-by-step explanation:
Graph the function 6=3y
guage arts
Science
Social studies
Y.10 Solve one-step and two-step equations: word problems HCP
Submit
Recommendations
Skill plans
Brianna is very good at keeping her school binder organized. Every time her teacher returns
an assignment, Brianna puts it in the right section. Brianna has 113 assignments in the
history, science, and art sections combined. The rest of her assignments are in the math
section. Brianna has 182 assignments in total.
Use an equation to find the number of assignments in the math section of Brianna's binder.
assignments
You
The number of mathematics assignments are 69.
How to form an equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.
Given : Brianna has 113 assignments in history, science and art.
Let x be the number of assignments that are in math section. There are 182 assignments in total.
The equation to represent this is
113 + x = 182
x = 182 - 113 = 69.
So the number of math assignments are 69.
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Determine if 0.59136363636363636... is rational or irrational and give a reason for your answer.
Need answer ASAP
Based on the given number which is 0.59136363636363636, we can infer that this is a rational number because it is repeating.
How to know a rational number?A rational number is a number that when the denominator divides the numerator, the result is a decimal that is either terminating, or repeating. This means that the decimal will either stop at some point, or will keep repeating the same numbers.
The number, 0. 59136363636363636, is a rational number because it is a repeating decimal.
The part that is repeating is "63636" so this is a rational number.
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The given recurring decimal 0.59136363636 is a rational number.
Given that,
To determine whether the given recurring decimal value is rational or irrational.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
Here,
The given recurring decimal = 0.591363636
From the above definition,
A rational number is a number that does have a repeating value after a certain value beyond the decimal point, unlike an irrational number that has repetition just after the decimal point.
So, the given number 0.59136363636 = 0.591 + 0.000363636
It is a rational number because it has repetition after 591 of 36 frequently.
Thus, the given recurring decimal 0.59136363636 is a rational number.
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Please HELP ME!!! due at 8pm tonight 10/12/22
Answer:
y=2x+4
Step-by-step explanation:
get x is get two point let’s say (-2,0) and (0,4)
The 4-0/0-(-2)=4/2=2 so 2 is x and (0,4) is where it hit the y axis so 4 is b plug in
Y=2x+2
Properties of equality can be used to justify steps in solving an equation.
Equation is 4x-1 =27. that means the correct answer is 27
The equals sign is used in mathematical formulas to show that two expressions are equal. In contrast to English, where an equation is defined as any well-formed formula that consists of two expressions joined by the equals sign, French defines an equation as containing one or more variables. The first stage in resolving a variable equation is determining the values of the variables that lead to equality.
Here, 4x-1 =27
We know that x=7
4x=27+1
4x= 28
Therefore x = 28÷4 = 7.
Hence, 4x-1 =27
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136/12 times 12 = ?
Anyone here have pinterest.....
Answer:
136 divided by 12 you get 11.3 times 12 you get 136
Answer:
(136÷12) × 12 = 136
Step-by-step explanation:
You start with the numbers in the parentheses ( which look like "( )" ), which is 136÷12 which is 11.3
1.) 136÷12=11.33
Then you multiply it by 12 which will get you 136.
2.) 11.33× 12=136
Your final answer will be 136
Have a nice day!
1 The parent function f(x) = x was shifted
7 units down to create function b. Which
represents function?
A
b(x) = -7f(x)
B b(x) = f(x) - 7
C
b(x) = f(x + 7)
D
b(x) = 7-f(x)
What is the answer ?
The answer is b(x)=f(x)-7, which is option B.
The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The parent linear function is given below.
f(x) = x
The function is shifted downward direction by 7 units. Then the function b(x) will be given as,
b(x) = f(x) - 7
The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.
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