The correct interpretation of the inequality 108 + x < 352 is given as follows:
Amanda's family has already traveled 108 miles, and needs to fill the tank after traveling more 244 miles.
What is the meaning of the inequality?
The inequality for this problem is defined as follows:
108 + x < 352.
The variable x represents the number of miles that the car can still travel until needing to refill the gas tank.
The solution is obtained similarly to an equality, isolating the variable x and obtaining a range of values, as follows:
x < 352 - 108
x < 244.
(the difference is that the solution of the inequality obtains a range of a values, while for the equality it is a single value).
Hence the family can travel at most 244 miles until needing to refill the tank again to continue the trip.
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2
3
P() = 0
O x + 1 is a factor of P(x)
O x + 1 is not a factor of P(x)
X
4
$
5
6
7
3
Use the Factor Theorem to determine whether x + 1 is a factor of P (x) = − xª¹ − x³ + 2x + 4.
Specifically, evaluate P at the proper value, and then determine whether x + 1 is a factor.
8
00
To use the Factor Theorem to determine whether x + 1 is a factor of P(x) = -x^4 - x^3 + 2x + 4, we need to evaluate P at x = -1. If the result is 0, then x + 1 is a factor of P(x). If the result is non-zero, then x + 1 is not a factor of P(x).
Substituting x = -1 into the function P(x) gives us:
P(-1) = (-1)^4 + (-1)^3 + 2(-1) + 4
= 1 + -1 + -2 + 4
= 2
Since P(-1) is non-zero, x + 1 is not a factor of P(x).
2√2
Solving radicals
The expression 2√2 is equivalent to 2.83.
What are radicals?A radical, or root, is the mathematical opposite of an exponent, in the same sense that addition is the opposite of subtraction. Mathematically -
[tex]$\underbrace{\sqrt[n]{x} \times \sqrt[n]{x} \times \dots}_{n \text{ times}} = x[/tex]
Given is the expression as -
2√2
We can write -
2√2 = 2[tex]$(2)^{\frac{1}{2}}[/tex]
2√2 = 2 x 1.414
2√2 = 2.83
Therefore, the expression 2√2 is equivalent to 2.83.
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1. WX=_________ units.
The value of WX is 3 units.
What is range?The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.
For example if the ages of 10 set of students are 12,14,10,18,9,11,10,17,18,20. The range of their ages is the highest age - the lowest age = 20- 9 = 11.
A number line is a horizontal line that has equally spread number increments. In the number line the highest value is 1 and the lowest value is -2.
From range = highest value- lowest value
range = WX
therefore WX = 1-(-2)
= 1+2 = 3
Therefore the range value between W and X is 3 units.
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Determine the value of x 4/5(x+9) - 1/5x=3/5(x+12)
Answer:
infinite number of solutions
Step-by-step explanation:
[tex]\frac{4}{5}[/tex] (x + 9) - [tex]\frac{1}{5}[/tex] x = [tex]\frac{3}{5}[/tex] (x + 12)
multiply through by 5 to clear the fractions
4(x + 9) - x = 3(x + 12) ← distribute parenthesis on both sides
4x + 36 - x = 3x + 36
3x + 36 = 3x + 36
since both sides are the same then any value of x will make the equation true.
Thus there are an infinite number of solutions
2. Which expression is the simplest form of (8x^-0)^1/3 ?
x^6 / 2
2 / x^2
8 / x^2
x^2 / 2
The simplest form of the expression is x^2/2. Option D
What is simplification?
When we want to simplify, we are trying to write the expression in a manner that we can not be able to break it further. Thus the simplest form of the expression implies that there is now way that we can be able to break the expression into something that is quite smaller.
We can see that we have the expression that has been given as;
(8x^-6)^1/3
We have to apply the laws of indices step by step and we have;
2x^-2
2/x^2
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What is 0.5% of 75?????????????? And tell me step by step
Answer:
0.375
Step-by-step explanation:
convert percent to decimal:
[tex]\frac{0.5}{100}=0.005[/tex]
multiply by 75
[tex](0.005)(75)=0.375[/tex]
Hope this helps
What are the quotient and remainder of (3x³ - 2x² - 8) + (x + 5)?
a.
3x² - 17x+85; 433
b. 3x² - 17x+85; -433
C.
d.
O A
OB
O C
OD
3x² - 15x+85; 433
3x² - 15x+85; -433
Please select the best answer from the choices provided
Answer:
Step-by-step explanation:
The quotient : 3x^2 — 17x + 85
The remainder = — 433
Step-by-step explanation:
3x^3-2x^2-8)/(x+5)
The above can be solved by following the illustration in the attached file.
Select True or false to answer these statements
Only functions that are represented in the same form can be compared
Any function can be represented as a graph,table of values and an equation
To compare the rate of change of a function represented in a graph with the rate of change of a function represented as a pair of points, you must find the first graph the line formed by the two points
The y-intercept of a function represented by an equation I'm slope intercept form can be compared to the y intercept of a function represented by a graph
Answer:
False. Functions can be compared even if they are not represented in the same form. For example, you can compare the rate of change of a function represented by a graph with the rate of change of a function represented by a table of values, as long as you have a way to compare the two.
True. Any function can be represented in a variety of different forms, including as a graph, a table of values, or an equation.
False. To compare the rate of change of a function represented in a graph with the rate of change of a function represented as a pair of points, you need to find the slope of the line formed by the two points, not the graph.
True. The y-intercept of a function represented by an equation in slope-intercept form can be compared to the y-intercept of a function represented by a graph. The y-intercept of a function is the point where the function crosses the y-axis, and it can be identified in both a graph and an equation in slope-intercept form.
perpendicular to y = 5/2 x - 6 and has the point (5,-7)
The equation of line that passes through (5,-7) and is perpendicular to y = 5/2 x - 6 is y = (-2/5)x - 5.
What is the equation of line that passes through the given point and is perpendicular to y = 5/2 x - 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line
y = (5/2)x - 6
Using the slope intercept, slope m is 5/2
Now, the equation of a perpendicular line to y = (5/2)x - 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 5/2 )
Slope of perpendicular line = -2/5
Plug the slope m = -2/5 and point (5,-7) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - (-7) ) = -2/5( x - 5 )
( y + 7 ) = -2/5( x - 5 )
y + 7 = (-2/5)x - (-2/5)(5)
y + 7 = (-2/5)x + (2)
y + 7 = (-2/5)x + 2
y = (-2/5)x + 2 - 7
y = (-2/5)x - 5
Therefore, the equation of the perpendicular line is y = (-2/5)x - 5.
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Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vot+at², to find a. In this formula, d is displacement,
Vo is initial velocity, a is acceleration, and it is time.
d+vot = at²
2 (d+vot) = at²
2 (d-vot)= at²
d-vot = at²
a=
a=
2(d+ vot)
2(d-vot)
The steps to find acceleration a are:
Step 1: d = vt + (1/2)at²
Step 2: d - vt = (1/2)at²
Step 3: 2(d - vt) = at²
Step 4: a = 2(d - vt) / t²
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
d = vt + (1/2)at²
We will find a.
d - vt = (1/2)at²
2(d - vt) = at²
a = 2(d - vt) / t²
Thus,
Step 1: d = vt + (1/2)at²
Step 2: d - vt = (1/2)at²
Step 3: 2(d - vt) = at²
Step 4: a = 2(d - vt) / t²
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Which of the following is a like radical to
6 3*/2x
A: 6 3*/x
B: 6 4*/2x
C:-5 3*/2x
D:6 3*/2x 2*
* is for exponents when put on the right and / is for square roots for clarification also all 6 and -5 are not exponents as well and in dead the 2 at the end is the only exponent that is apart of 2x
So for the square roots in answer D it is 2x and then the exponent of 2 just to make sure I made that clear and the exponents for all square roots are 3 for the question and 3 for A 4 for B 3 for C and finally 3 for D
Answer: D. 6 3*/2x 2*
Step-by-step explanation:
All of the answer choices you provided involve radicals, which are numbers or expressions that include a square root (or other root) symbol. In order to determine which answer choice is a like radical to the given radical (6 3*/2x), we must compare the coefficients, the indices, and the radicands of each radical.
The coefficient of a radical is the number that appears before the radical symbol, while the index is the number written as a small superscript to the right of the radical symbol. The radicand is the number or expression that is inside the radical symbol.
For the given radical (6 3*/2x), the coefficient is 6, the index is 3, and the radicand is 2x.
With this information in mind, we can compare the answer choices as follows:
A. 6 3*/x - This radical has the same coefficient and index as the given radical, but the radicand is different (it is x instead of 2x). Therefore, this is not a like radical to the given radical.
B. 6 4*/2x - This radical has the same coefficient and radicand as the given radical, but the index is different (it is 4 instead of 3). Therefore, this is not a like radical to the given radical.
C. -5 3*/2x - This radical has the same index and radicand as the given radical, but the coefficient is different (-5 instead of 6). Therefore, this is not a like radical to the given radical.
D. 6 3*/2x 2* - This radical has the same coefficient and index as the given radical, and the radicand is 2x, which is the same as the given radical. However, there is an additional exponent of 2 after the radical symbol, which is not present in the given radical. Therefore, this is not a like radical to the given radical.
Therefore, the correct answer is:
D. 6 3*/2x 2*
Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?
A. 2 albums and 2 singles
B. 2 albums and 5 singles
C. 5 singles and 2 albums
Brandi can buy 2 albums and 5 singles.
Brandi wants to spend no more than $25 in total, and she wants to purchase at least 5 singles, which cost $1 each. That means the total cost of the singles must be at least 5 * $1 = $<<5*1=5>>5.
The remaining budget is $25 - $5 = $<<25-5=20>>20, which is the maximum amount that Brandi can spend on albums.
Since each album costs $10, Brandi can purchase a maximum of $20 / $10 = <<20/10=2>>2 albums.
So, a possible combination of albums and singles that Brandi could purchase and stay within her guidelines is 2 albums and 5 singles.
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A possible combination of albums and singles that Brandi could purchase and stay within her guidelines is option c is correct- Brandi can buy 2 albums and 5 singles.
the solution is as follows:-
Brandi wants to spend no more than $25 in total, and she wants to purchase at least 5 singles, which cost $1 each. That means the total cost of the singles must be at least 5 * $1 = $<<5*1=5>>5.
The remaining budget is $25 - $5 = $<<25-5=20>>20, which is the maximum amount that Brandi can spend on albums.
Since each album costs $10, Brandi can purchase a maximum of $20 / $10 = <<20/10=2>>2 albums.
So, a possible combination of albums and singles that Brandi could purchase and stay within her guidelines is 2 albums and 5 singles.
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3, 6, 12, 24, ...
Which of the following would not be a term of this sequence?
Α. 48
B. 64
C. 96
D. 192
Answer:
B. 64
If write sequence in order
3 6 12 24 48 96 196
it's very clear each sequence got multiplied by 2 to obtain other element
how many solutions does 3x+15=6x+2-3x have?
Answer:
This equation has no solution.
Step-by-step explanation:
To find out how many solutions an equation has, you can just solve it. If you get an answer, that is one solution. Let's look at the equation.
3x+15=6x+2-3x
Combine like terms.
3x + 15 = 3x + 2
Subtract 3x from both sides.
15 = 2
Ruh-roh! 15 = 2 is a false statement. Since the variable fell out of the equation and what was left is false, there are no solutions.
NO number can be substituted into the equation that will make it true. There are no solutions.
Evaluate when x=5:
(x²-3) / 2
Answer:
11
Step-by-step explanation:
Given x value is 5.
Substitute the value of x in the given equation.
5^2 is 5*5 = 25
Subtract 3 from 25 ---> 25 - 3 = 22
Divide 22 by 2 ---> 22/2 = 11
Hence, the answer is 11.
12) In the diagram of ΔA B C below, BD is drawn to side AC.
If m∠A=35, m∠A B D=25, and m∠C=60, which type of triangle is ΔBCD (1) equilateral
(2) scalene
(3) obtuse
(4) right
The triangle in the figure given is a scalene triangle
What are types of triangleThere are three main types of triangles: right triangles, acute triangles, and obtuse triangles. Right triangles have one angle that is 90 degrees, while acute triangles have all angles less than 90 degrees, and obtuse triangles have one angle that is greater than 90 degrees.
1. Equilateral Triangle: All sides and angles are equal in an equilateral triangle.
2. Isosceles Triangle: Two sides and two angles are equal in an isosceles triangle.
3. Scalene Triangle: No sides or angles are equal in a scalene triangle.
4. Right Triangle: A right triangle has one angle that is 90 degrees.
5. Acute Triangle: All angles in an acute triangle are less than 90 degrees.
6. Obtuse Triangle: One angle in an obtuse triangle is greater than 90 degrees.
The angles given in this triangle have all their values less than 90 degrees. This makes them a scalene triangle.
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y=3x^ 2 linear or nonlinear
Answer:
non linear
Step-by-step explanation:
it is a quadratic equation, with its derivative proportional to x but not a constant.
so it is non linear
which operation (addition, subtraction, multiplication, or division) can be used to rearrange the slope formula into the point-slope form of a line?
Answer:
Multiplication
Step-by-step explanation:
Multiply both sides of the Slope equation by the denominator (bottom number) and you get the Point-Slope Equation.
see image.
0.0095 in science notation
Answer:
9.5 x 10^-3
Step-by-step explanation:
Move the decimal place until the leading digit is between 1 and 10, about three places to the right.
The exponent we use to notate our movement is negative, as we moved it to the right, so since we moved it three places to the right, it is -3.
Write it in the notation form m x 10^n, where m is that number between 1 and 10, and n is the exponent.
Your answer is 9.5 x 10^-3
If You write all numbers from 30 to 65 including 30 and 65 how many times would you write the digit 4?
The number of times you would write the digit of 4 from 30 to 65, would be 14 times.
How to find the number of times ?From the range of 30 to 39, the digits with 4 are:
34
From the range of 40 to 49, the digits with 4 are:
40, 41, 42, 43, 44, 45, 46, 47, 48, 49
From the range of 50 to 59, the 4s are:
54
From 60 to 65 the 4s are:
64
The number of times you write 4 is therefore the sum of the number of times you see 4 above, and this is: 14 times
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d Bula drives to work and
back every day. One way,
the trip is fifty miles.
How many miles does
she drive in five days?
Answer:
500 miles
Step-by-step explanation:
We want to find the distance traveled
50 miles one way
We need to multiply by 2 to find the distance traveled there and back
50 * 2 = 100
She does this for 5 days
5 * 100 = 500
She travels 500 miles to work and back in 5 days
Distance travelled. both way
50×2=100
After 5 days,
[tex] \longmapsto \: 100 \times 5 = 500miles[/tex]
PLS HELPPPPPPPPPPP ILL MARK YOU BRAINLEST
Answer:
a) 14 , b) -13 , c) 9
Step-by-step explanation:
use a calculator
Answer:
a) 14
b) -13
c) 9
Step-by-step explanation:
c) y = 3x +2
29 = 3x + 2
Subtract 2 from both sides
27 = 3x
x = 9
solve 3/8+1/4+1/2-2/3
Select the correct answer.
Which expression is equivalent to
Answer:
A
Step-by-step explanation:
Write an equation of the line passing through the point A(-6,5) that is perpendicular to the line y= 1/2x-7
Answer:
Below
Step-by-step explanation:
Line y = 1/2 x -7 is of the line-equation form y = mx = b where m = slope ....this slope is 1/2 a perpindicular slope is - 1/m ( ya just gotta remember that ) = - 1/ (1/2) = - 2
for the new line , point-slope form through the point (-6,5) would be
y - 5 = -2 ( x - - 6) simplifies to
y = - 2x -7
What is the solution to this equation?
I
Answer:
x=10922
Step-by-step explanation:
Given f(x) = x^2 – 3 and g(x)= x+2/x. Find (g ° f)(4).
a. 11/13
b. 6
c. 15/13
d. -6
Answer:
c. [tex]\frac{15}{13}[/tex]
Step-by-step explanation:
[tex](g \circ f)(4)=g(f(4)) \\ \\ f(4)=4^2-3=13 \\ \\ g(13)=\frac{13+2}{13}=\frac{15}{13}[/tex]
27.
Select from the drop-down lists to correctly complete each sentence.
The height of the parallelogram is equal to the ________ of the circle. The base of the parallelogram is equal to _________ of the circle. Therefore, the area of the circle (πr2) is equal to the ___________ and the circumference of the circle is equal to 2 times pi times the radius
The sentence is completed as follows
The height of the parallelogram is equal to the radius of the circle. The base of the parallelogram is equal to half the circumference of the circle. Therefore, the area of the circle (πr2) is equal to the area pf the parallelogram and the circumference of the circle is equal to 2 times pi times the radius
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).
For a parallelogram formed by joining the 8 triangles which are segments of a circle.
In this case the sides of the triangles are the radius of the circle. The height of the triangle is also a radius since it is also a distance from the center to the circumference.
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please i’m begging someone to solve these for me ..
The dotplot shows the number of days on which the train arrived late in 100 repetitions of the simulation
4. Explain what the dot at 7 represents.
5. Use the results of the simulation to estimate the probability that the train will arrive late on 3 or more of 20 days.
6. Based on the actual result of 3 late arrivals in 20 days and your answer to Question 5, is there convincing evidence that New Jersey Transit's claim is false? Explain your reasoning.
4. Train arrived late once on 7th day according to the simulation.
5. The probability that the train will arrive late on 3 or more of 20 days is 0.30.
6. There is no convincing evidence that New Jersey Transit's claim is false.
What is a simulation?
Simulation is the imitation of chance behavior, based on a model that accurately reflects the situation.
The dot at 7 represents that on the 7th day the train arrived late once.
Assuming the probability that each train is late is 0. 1, the estimate of the probability that that train is late on 3 or more of 20 days is -
30/100 = 0.30.
Since, the actual result is that train is late 17 times on 3 days so the result will be 0.17. But since these are just simulations and real-life incidents there is no proper evidence.
Therefore, the train company's claim is not entirely false.
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FEBRUARY 15 JUNE 10 Calculate the number of days from 15 February 2007 to 10 June
The total number of days from 15 February 2007 to 10 June 2007 will be;
⇒ 115
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The days to count from 15 February 2007 to 10 June 2007.
Now,
Since, 2007 is not a leap year.
Hence, Number of days in Feb. 2007 = 28 - 15
= 13
And, Number of days in march 2007 = 31 days
Number of days in April 2007 = 30 days
Number of days in May 2007 = 31 days
Number of days in 10 June 2007 = 10 days
Thus, Total days from 15 February 2007 to 10 June 2007 is,
⇒ 13 + 31 + 30 + 31 + 10
⇒ 15 days
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