You are driving on a highway and are about 140 miles from a state borer. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. write and absolute value equation to model the situation. solve it to find the minimum and maximum numbers of hours you will have cruise control on.
The absolute value function is
|d - 140| = 30.
Using the absolute value function, we have that:
The minimum time is of 1.83 hours.
The maximum time is of 2.83 hours.
Absolute value function:
Basically, absolute value function providing the distance the number is from zero on a number line.
The absolute function is defined by:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
It measures the distance of a point x to the origin,
For example,
|2| = |-2| = 2.
Given,
You are driving on a highway and are about 140 miles from a state borer. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side.
Here we need to write and absolute value equation to model the situation. And we are also solve it to find the minimum and maximum numbers of hours you will have cruise control on.
In this problem, the minimum and maximum distances are within 30 miles of 140,
Hence, the absolute value function is,
|d - 140| = 30.
So, the minimum distance is of:
=> d - 140 = -30
=> d = -30 + 140
=> d = 110.
Hence the minimum time(distance divided by velocity) is:
=> 110/60 = 1.83 hours.
Then the maximum distance is of:
=> d - 140 = 30
=> d = 30 + 140
=> d = 170
Hence the maximum time(distance divided by velocity) is:
=> 170/60 = 2.83 hours.
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j + (-6); j = -3 “evaluate each expression for the given value”
Answer:
-3+(-6)= -9
Step-by-step explanation:
A school has 1000 students. of these, 3/4 are boys. how many of the students are boys? how many of the students are girls?
Answer:
750 students are boys, 250 are girls.
Step-by-step explanation:
1/4 of 1000 is 250.
250 + 250 + 250 = 750 boys.
if 3/4 are boys, then 1/4 (the rest of the school population) are girls.
150 students are girls.
The function f(x) = x² + 4 is defined on the domain [-8, 8]. Which of the following is the correct associated range?
O [4, 68]
O [0, 4]
O [-60, 4]
O (-∞, 4]
O [-60, 68]
0 (-∞, ∞)
========================================================
Explanation:
The parabola has its lowest point when either x = -8 or x = 8
Plug either value into the function
f(x) = -x^2 + 4
f(-8) = -(-8)^2 + 4
f(-8) = -60
You should find that f(8) = -60 as well
This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval [tex]-8 \le \text{x} \le 8[/tex]
The highest point is at the vertex (0, 4), so the largest output is y = 4
------------
We have the lowest output y = -60 and the highest output y = 4
The possible set of outputs is the interval [tex]-60 \le \text{y} \le 4[/tex] which turns into the interval notation [-60, 4]
Check out the graph below.
PLS HELP IM SO CONFUSED
The student says that the proof shows that AOM BOM because they are vertical angles.
Which statement best corrects the student's interpretation?
A. CON = BOM because they are vertical angles.
B. AOM = BOM because they are supplementary, not because they are vertical angles.
C. AOM = BOM because they are complementary, not because they are vertical angles.
D. AOM = BOM because they are both congruent to the same angle, not because they are vertical angles.
∠AOM ≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.
How to Identify Congruent Angles?
From the image of the angles attached, we are given that;
∠AOM ≅ ∠DON
Now, from the vertical angle theorem, we can say that;
∠AOM ≅ ∠CON
Similarly, by vertical angles theorem, we can also say that;
∠BOM ≅ ∠DON
From transitive property of congruence, we can equally say that since ∠AOM and ∠BOM are equal to the same angle, then;
∠AOM ≅ ∠BOM
From transitive property of congruence, we can equally say that since ∠CON and ∠BOM are equal to the same angle, then;
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Answer: ∠AOM≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.
Step-by-step explanation:
cause I did the mastery test
use the diagram to find bc.
Answer:
BC = 12
Step-by-step explanation:
from the diagram
AB + BC = AC , that is
18 + BC = 30 ( subtract 18 from both sides )
BC = 12
A three-centimeter cube has been painted red on all sides. it is cut into one centimeter cubes. how many cubes will be there with only one side painted red?
There will be only 6 cubes with only one side painted red.
Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.
According to the question
A 3 cm cube is divided into one centimeter cube.
Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.
Since there are 6 faces,
cubes painted one side red = 6x1=6.
Therefore , There will be only 6 cubes with only one side painted red.
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In a population of 200 mice brown fur is dominant to gray fur. of 120 of the 200 mice have brown fur, what is the frequenzy?
The frequency of mice that are heterozygote is 0.3492
It is required to find the frequency.
What is frequency?The number of waves that pass a fixed point in unit time being, measured in hertz(Hz).The number of cycles or vibrations undergone during one unit of time by a body in periodic motion.
Given:
Population =200 mice
Gray fur mice= 120 mice
By the use of Hardy-Weinberg equation we have,
Hardy-Weinberg equation is given by
p² + 2pq + q² = 1 and p + q = 1
where, 2pq is the heterozygote frequency.
p² = 120/200
p = 0.7746
p + q = 1
q = 0.2254
Heterozygote frequency = 2pq = 2(0.2254)(0.7746) = 0.3492
Therefore, the frequency of mice that are heterozygote is 0.3492.
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Andrew made an error in determining the polynomial equation of the smallest degree whose roots are 3, 2+2i and 2-2i. review andrew's work, identify the error and correct all work from that point forward that is affected by this error.
The polynomial equation is (x³ - 7x² + 20x - 24) = 0 and the Error that made by Andrew is incorrect factors of the roots.
Polynomial Equation:
The equations formed with variables, exponents and coefficients are called as polynomial equations.
Roots of the Polynomial:
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.
Given,
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i.
Here we need to find the error he made and the correct form of the equation.
According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x).
According to this definition:
=> (x - 3) , (x - (2 + 2i)) , (x - (2 - 2i))
are factors of the required polynomial.
Simplifying the brackets, we get:
=> (x - 3), (x - 2 - 2i), (x - 2 + 2i)
are factors of the required polynomial.
This is the step where Andrew made the error.
The factors will always be of the form (x - a) , not (x + a).
Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be:
=> (x - 3)(x - 2 - 2i)(x - 2 + 2i) = 0
=> (x - 3) (x² - 2x + 2xi - 2x + 4 - 4i - 2xi - 4i - 4i²) = 0
When we simplify it, then we get,
=> (x - 3)(x² - 4x + 4 + 4) = 0
=> (x - 3)(x² - 4x + 8) = 0
=> (x³ - 4x² + 8x - 3x² + 12x - 24) =0
=> (x³ - 7x² + 20x - 24) = 0.
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If h = 20 inches, l = 27 inches, and w = 16 inches, what is the area of the figure shown above?
Answer:
8640in²
Step-by-step explanation:
A = I * W * H
A= 27*16*20
A=8640in²
How long will it take you to bike 225 miles at
a
speed of 15 miles per hour?
Am I supposed to divide
Answer:
15
Step-by-step explanation:
225/15
Hot tea is around 181 degrees Fahrenheit, and the room temperature is 72 degrees Fahrenheit. The rate of the hot tea cooling on a desk in the room is about 6.5% every minute. You need to determine how hot the tea will be after t minutes? Which function models this situation?
The function that models the given situation is; f(x) = 109(0.935)^(t) + 72
How to interpret function models?
We are given that;
Temperature of hot tea = 181°F
Room temperature = 72°F
Rate of the hot tea cooling on a desk in the room = 6.5% every minute
We know that an exponential function is of the form of;
y = A(r)^(x)
where;
A is the initial value.
r is the rate of increase/decrease in decimals.
Thus, our initial value is;
A = 181 - 72 = 109
The rate of increase/decrease in decimals = 1 - (6.5%) = 0.935
Since the room temperature is 72 degrees Fahrenheit, then the function is;
f(x) = 109(0.935)^(t) + 72
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19.44 is what percent of 54
Answer:
36%
Step-by-step explanation:
19.44 = ( ? percent ) × 54
This is the question in an equation form :
Divide both sides by 54 :
19.44 ÷ 54 = (? percent )
0.36 = ? percent
0.36 as a percentage is
0.36 ×100 = 36%
Hope this helped and have a good day
Which data type is used to store real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42?
The float type of data stores real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42.
What is data- type?A data type, in programming, is a classification that specifies which type of value a variable has and what type of mathematical, relational or logical operations can be applied to it without causing an error.
All number types that allow for the possibility of a fractional component, such as 42.7 or pi, are known as floating point types.
The precision of various floating point data types varies depending on how many bits are utilized to represent the digits, which is directly proportional to the total number of bits in the number. In the IEEE standard, for instance:
Single precision floats have a range of around 10-38 to 1038 with a precision of about 7 decimal digits using a total of 32 bits and 24 bits for the digits.Double precision floats, commonly referred to as doubles, have a precision of about 16 decimal digits and a range of roughly 10^-308 to 10^308. They require 64 total bits and 53 bits for digits.Quadruple precision floats, Quad doubles, sometimes known as double doubles, have a precision of about 34 decimal digits and a range of roughly 10^-4932 to 10^4932 using 128 total bits and 113 bits for the digits.Hence, the type of data is floating point.
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Find the measurement of each marked angle
Answer:
see below
Step-by-step explanation:
The interior angle of the triangle on the right is 180 - ( 9x+12)
this plus the other two sum to 180 degrees
180 - (9x+12) + 4x-3 + 6x + 3 = 180
x = 12
then the angles are 6(12) + 3 = 75 4(12) -3 = 45 and 60°
Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one half times the quantity x plus 4 end quantity squared minus 3 question mark
The graph of g(x) is narrower than f(x) and is shifted to the right 4 units and down 3 units.
The graph of g(x) is narrower than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the right 4 units and down 3 units.
Beginning with the graph of f(x) = x2, The transformations that are needed to form [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is
The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units
This is further explained below.
What is transformations?Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.
The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.
In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.
[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]
The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.
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Answer:
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
Step-by-step explanation:
I got it right.
An explanation needed, thx
The points (-4,2) and (4,2) are two vertices of a square. State all other order pairs that could be the other two vertices of the square.
Helpppppppppppppppppppppppppppp
The marching band is holding a fundraiser. The band is selling t-shirts for $20 and yearbooks for $24. The goal is to sell at least $2,400 in merchandise. Which of the following is a solution to this scenario?
50 t-shirts and 59 yearbooks
51 t-shirts and 57 yearbooks
60 t-shirts and 48 yearbooks
62 t-shirts and 48 yearbooks
The answer to this question is 50 t-shirts and 59 yearbooks
We get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.
Selling price of t shirts = $ 20
Selling price of year books = $ 24.
Let the number of t shirts sold be x and the number of yearbooks sold be y.
Goal to sell at least = $ 2400 in merchandise.
So, we get the equation as:
20 x + 24 y ≥ 2400
5 x + 6 y ≥ 600
Now, we are given some options:
50 t-shirts and 59 yearbooks
Substituting it, we get that:
5 ( 50) + 6 ( 59) ≥ 600
250 + 354 ≥ 600
604 ≥ 600
which is true.
51 t-shirts and 57 yearbooks
Substituting it, we get that:
5 ( 51) + 6 ( 57) ≥ 600
255 + 342 ≥ 600
597 ≥ 600
which is not true
60 t-shirts and 48 yearbooks
Substituting it, we get that:
5 ( 60) + 6 ( 48) ≥ 600
300 + 288 ≥ 600
588 ≥ 600
which is not true
62 t-shirts and 48 yearbooks
Substituting it, we get that:
5 ( 62) + 6 ( 48) ≥ 600
310 + 288 ≥ 600
598 ≥ 600
which is not true.
Therefore, we get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.
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Answer:
50 tshirts and 59 yearbooks is the correct answer.
Step-by-step explanation:
Round 9.19 to the nearest 25 cents
The rounded form of the number 9.19 which represents $9 and 19 cents to the nearest 25 cents is; 9.25
What is the rounded form of 9.19 to the nearest 25 cents?It follows from the task content that the number is required to be rounded off to the nearest 25 cents.
On this note, it follows that only 25 cent intervals are considered.
Hence, the number in discuss can either be rounded up to 9.25 or 9.00.
However, since the fractional 19 cents is closer to 25 more than it is to 0 on the number line, the rounded form of the number is;
= 9.25.
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number 7 show your work , someone help please.
Answer:
Step-by-step explanation: Replace u with (3)
Multiply 5x3+3/2
Answer: 9
Step-by-step explanation:
remember, a variable is only a placeholder for an actual value.
so, when we get an actual value, we put it into every location of the variable in the expression and simply calculate.
6.
25/(r - 4) for r = 9
that means
25/(9 - 4) = 25/5 = 5
7.
(5u + 3)/2 for u = 3
that means
(5×3 + 3)/2 = (15 + 3)/2 = 18/2 = 9
i need help with the plotting and bottom questions pls
All the data points are plotted on the number line and mentioned clearly as an image with the solution.
What is a number line?
A number line is a visual depiction of numbers on such a straight line created either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on those when they are written down on a number line. A number line is thought to begin at zero (0).For easy plotting on the number lines and for comparison of points, we will be converting all the fractions into decimals.
Kloee : [tex]3\frac{1}{4} = \frac{13}{4} =3.25[/tex]
High School :1.0
Middle School : 1.5
Football field : 5.7
KB: [tex]-4\frac{1}{8} = \frac{-33}{8} =-4.125[/tex]
Ben : -2.65
All the data points are plotted on the number line and mentioned clearly as an image with the solution.
(a) Distance between Ben and Kloee - 5.9
Plotted on the number line and mentioned clearly as an image with the solution.
(b) Distance of middle school from football field- 4.2
Plotted on the number line and mentioned clearly as an image with the solution.
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What transformations of the graph of (x)=|x| are applied to graph the function g?
The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.
What transformation must be applied to modify the absolute value function?
In this problem we find a resulting expression, that is, the function g(x) = - |x| + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.
After a quick inspection, we find that two rigid transformations were used in the following order:
Reflection around the x-axis.Translation 2 units up.Now we proceed prove this procedure:
f(x) = |x|
Step 1
f'(x) = - |x|
Step 2
g(x) = - |x| + 2
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Which situation could be represented by the equation-30 + 30=0 ?
Answer:30x0
Step-by-step explanation:
Write the decimal equivalent for each rational number. Use a bar over any repeating digits 3/11
Answer:
see below
Step-by-step explanation:
1/11=0.0909....
3/11=0.090909...*3 or 0.27272727...
g(n)=n+3
f(n)=-n-5
Find g(3)-f(3)
Answer:
14
Step-by-step explanation:
g(3)=(3)+3
g(3)=6
f(3)=-(3)-5
f(3)=-8
6-(-8)=14
please help !! lots of points (35)
Answer: A= 2, B= −2, C= −2
Step-by-step explanation:
A = −1^2 −3 (−1) −2
= 1 + 3 -2 = 2
A = 2
B = 0^2 −3 (0) −2
= 0 − 0 − 2 = −2
B = −2
C = 3^2 −3 (3) −2
= 9 − 9 − 2
C = −2
Answer:
A = 2
B = -2
C = 16
Step-by-step explanation:
Plug in the numbers into the equation.
y = x^2 - 3x - 2
y = -1(-1) - 3 (-1) - 2
y = 1 + 3 - 2
y =2
y = 0^2 - 3(0) - 2
y = 0 - 0 - 2
y = -2
y = 3^2 - 3(3) - 2
y = 9 - 9 - 2
y = -2
Which expression represents the product of n and
25?
A. 25n
C. 25 + n
B. 25-n
D. 25 ÷ n
Answer:
25n
Step-by-step explanation:
product of n and 25
Product means multiply
25n
y is inversely proportional to the square of x find an equation for y in terms of x
hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16
a)
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}[/tex]
b)
when y = 16, what's "x"?
[tex]16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}[/tex]
Stimulus: The student is presented with a polygon (square,
rectangle, parallelogram, or night triangle) on a grid and the scale
factor at which it was created.
Example Stem: This diagram of a rectangular city park was drawn
using a scale factor of 1 centimeter to 20 meters.
In the diagram shown, assume each square on the grid is 1
centimeter in length.
What is the area, in square meters, of the actual park on which this
scale drawing is based?
Scale factor for the drawing from actual park = 1/20
Area of the actual park = 1200 cm²
Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension
Length of the rectangular city park = 5 cm
Width of the rectangular park = 6 cm
Using scale factor 1 cm = 20 meters
Scale factor = Length of the park in drawing/ actual length of park
⇒1/20.
5/actual length of park = 1/ 20
Actual length = 5 × 20 = 100 meters
Actual width = 6 × 20 = 120 meters
Area of the rectangular park = length × width
square meters
Therefore, Scale factor from actual length to the length in drawing = 1 : 20
Area of the rectangular park = 1200 square feet
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