Answer: f(x)= -2x - 3
Step-by-step explanation
What is the answer to 2x + 6<30
Steps to solve:
2x + 6 < 30
~Subtract 6 to both sides
2x + 6 - 6 < 30 - 6
~Simplify
2x < 24
~Divide 2 to both sides
2x/2 < 24/2
~Simplify
x < 12
Best of Luck!
A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches. Which equation can be used to find the volume of the container?
The equation that can be used to find the volume V of the container is: Option A. [tex]V = 12 \pi}[/tex]
To find the volume V of the popcorn container, which is an inverted cone, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]Given:
The diameter of the circular opening is 4 inches, so the radius [tex]\( r \) is \( \frac{4}{2} = 2 \) inches.[/tex]The height h of the cone is 9 inches.Now substitute these values into the formula:
[tex]\[ V = \frac{1}{3} \pi (2)^2 (9) \][/tex]Calculate [tex]\( (2)^2 \):[/tex]
[tex]\[ (2)^2 = 4 \][/tex]Now substitute r = 2 and h = 9 into the formula:
[tex]\[ V = \frac{1}{3} \pi[/tex] × 4 × 9Simplify the multiplication:
[tex]\[ V = \frac{1}{3} \pi[/tex] × 36Now calculate [tex]\( \frac{1}{3}[/tex] x 36
[tex]\[ \frac{1}{3}[/tex] x 36 = 12Full Question
A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches.
A. [tex]V = 12 \pi}[/tex]
B. V=(4)(9) 3
C. V=(4)(9)²
D. V-(2)(9)² wr
HELPPPPPP!!!
Consider the given equation that models a train’s distance from its departing station, where:
• y represents the distance in miles,
• x represents the speed of the train in miles per hour, and
• t represents the time traveled from the departing station in hours.
=t
Enter an equation for which the solution is the speed of the train, in miles per hour, where the train’s
distance from the departing station is 162 miles and it has traveled for 3 hours.
Answer:
[tex]x = 54\ mi/hr[/tex]
Step-by-step explanation:
Given:
The given equation is.
[tex]y=xt[/tex]
Where:
y represents the distance in miles,
x represents the speed of the train in miles per hour, and
t represents the time travelled from the departing station in hours.
y = 162 miles
t = 3 hours
Solution:
The given equation is.
[tex]y=xt[/tex]
Rewrite the given equation for x or speed.
[tex]x=\frac{y}{t}[/tex]
Substitute y and t value in above equation.
[tex]x=\frac{162}{3}[/tex]
[tex]x = 54\ mi/hr[/tex]
Therefore, the speed of the train is [tex]54\ mi/hr[/tex].
solve for x: 3x-4/6+1/3=3x/2
Answer:78
Step-by-step explanation:
Line m passes through the Point (2, 1) and has a slope of -2/7. What is the equation of Line m in standard form?
7x + 2y = 11
7x + 2y = 16
2x + 7y = 11
2x +7y = 16
Answer:
Step-by-step explanation:
Slope m = -2/7
Points are (2,1)
y1 = 1 and x1 = 2
y - y1 = m(x - x1)
y -1 = -2/7(x - 2)
Multiple each term by 7
7y - 7 = -2(x - 2)
7y - 7 = -2x + 4
7y = -2x + 4 + 7
2x + 7y = 11
15 POINTS
Question 6
Write an equation of a line with the given slope and y-intercept.
m = 1, b = 4
a.
y = 4x + 1
b.
y = x + 4
c.
y = x – 4
d.
y = –1x + 4
Answer:
B
Step-by-step explanation:
y = mx + b
m = 1
b = 4
y = 1(x) + 4
y = x + 4
A club's membership increased from 250 to 300 members. Express the new membership as a percent of the old membership. Then, Express the old membership as a percent of the new membership.
Answer:
The new membership as a percent of the old membership = 120 %
The old membership as a percent of the new membership = 83.33 %
Step-by-step explanation:
Formula to find the percent of Comparing Quantities
Percent=Quantity/Whole x 100
i) To Express the new membership as a percent of the old membership
In this case the old membership is the whole and the new membership is a quantity.
Let A is the unknown percent to be find.
A =250/300 x 100
A =120 % answer -1
i) To Express the old membership as a percent of the new membership
In this case the new membership is the whole and the old membership is a quantity.
Let A is the unknown percent to be find.
A =300/250 x 100
A =83.33 % answer 2
Find a average daily rainfall for a 30 days month if the total rainfall during that period was 16.8 inches.
Average = 0.56 inches
Solution:
Given data: Total rainfall = 16.8 inches
Total number of days for a month = 30
To find the average of the rainfall.
Formula for average:
[tex]\text {Average}=\frac{\text {Sum of the observations}}{\text {Total number of observations}}[/tex]
[tex]\text {Average}=\frac{16.8}{30}[/tex]
= 0.56 inches
Average = 0.56 inches
Hence, average of daily rainfall is 0.56 inches.
A ski run has an angle of elevation of 24.4 degrees and a vertical drop of 1100 feet . To the nearest foot how long is the ski run
Answer:1100 feet
Step-by-step explanation: the drop is 11 feet
To find the length of the ski run, we use tangent of the angle of elevation (24.4 degrees) which equals the vertical drop (1100 feet) divided by the length of the run. Calculating this gives a length of approximately 2433 feet for the ski run.
Explanation:To calculate the length of the ski run with an angle of elevation of 24.4 degrees and a vertical drop (rise) of 1100 feet, we use trigonometry, specifically the tangent function.
Tangent of an angle in a right triangle equals the opposite side (rise) divided by the adjacent side (run). In this case, we have:
tan(24.4 degrees) = rise / run
Plugging in the known value for the rise (1100 feet), we get:
tan(24.4 degrees) = 1100 / run
This allows us to solve for the run (length of the ski run):
run = 1100 / tan(24.4 degrees)
Using a calculator, we find that:
run ≈ 1100 / 0.4525
run ≈ 2432.96 feet
This can be rounded to the nearest foot to give a ski run length of approximately 2433 feet.
jenny's weight is 65kg. 1stone=14 pounds. what is jenny's weight in stonesand pounds
Answer:
910
Step-by-step explanation:
65×14=910
Which parent function is f(x) = x2?
Linear quadratic or absolute or exponential
quadratic function
Step-by-step explanation:
Which is the rationalized form of the expression look at picture
Answer:
[tex] \frac{ \sqrt{x} }{ \sqrt{x} + \sqrt{5} } ( \frac{ \sqrt{x} - \sqrt{5} }{ \sqrt{x} - \sqrt{5} } ) = \frac{x - \sqrt{5x} }{x - 5} [/tex]
The correct answer is C.
What document changed the purpose of the Civil War from one of states' rights to that of slavery?
the Thirteenth Amendment
Declaration of Independence
the Fugitive Slave Law
Emancipation Proclamation
Answer:
The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.
Step-by-step explanation:
The Emancipation Proclamation is the document that changed the purpose of the Civil war from one of states' rights to that of slavery.
The main idea behind this document was to clearly state that " all persons held as slaves" in the southern states "are, and henceforward shall be free."
When the north won the civil the above mentioned words in quotes of the Emancipation Proclamation document effectively guaranteed the freedom of all people held as slaves in all of United States of America.
Simplify and determine the coefficient of (-x)(5y)(-2x).
A. -4
B. 1/5
C. 1
D. 4
Answer: 10
Step-by-step explanation:(-x)(5y)(-2x)
=(-5xy)(-2x)
=10x^2y
therefore,the coefficient of the equation is 10.
w+6≤−3 solve the inequality
To solve the inequality, isolate/get w (the variable) by itself in the inequality
w + 6 ≤ -3 Subtract 6 on both sides
w + 6 - 6 ≤ -3 - 6
w ≤ - 9
2 less than the product of 9 and a number is 4 what is the equation
Answer:
Step-by-step explanation:
2 less then the product of 9 and a number is 4
" the product " is the result of multiplication
the product of 9 and a number...9x
2 less......-2
is 4...= 4
9x - 2 = 4 <===
. Ms. Jenson needs to rent a ballroom for an event and she must spend less than $625 for the
rental fee. The cost to rent the ballroom is $350 for 3 hours. The cost for each additional hour is
$125. She wrote the inequality, 625 > 350 + 125h, to find h, the number of extra hours she can
rent the ballroom. Which value for h makes the inequality true?
A. 2 b.3 c . 5 d . 7
Answer:
The value of h that makes the inequality true is 2.
Step-by-step explanation:
Ms. Jenson needs to rent a ballroom for an event and she must spend less than $625 for the rental fee. The cost to rent the ballroom is $350 for 3 hours. The cost for every extra hour is $125.
She wrote the inequality,
625 > 350 + 125h
to find h, the number of extra hours she can rent the ballroom.
Solving this inequality we get
125h < 275
⇒ h < 2.2
So the value of h that makes the inequality true is 2. (Answer)
The required value of h < 2 or the number of extra hours she can rent the ballroom.
Given that,
She must spend less than $625 for the rental fee,
The cost to rent the ballroom is $350 for 3 hours,
The cost for each additional hour is $125,
She wrote the inequality, 625 > 350 + 125h.
We have to find,
The value of h, the number of extra hours she can rent the ballroom. Which value for h makes the inequality true.
According to the question,
She must spend less than $625 for the rental fee. The cost to rent the ballroom is $350 for 3 hours.
The cost for each additional hour is $125. She wrote the inequality,
[tex]650>350+125h,[/tex]
Solving the equation to find h, the number of extra hours she can rent the ballroom.
[tex]650>350+125h\\\\650-350>125h\\\\300>125h\\\\h<\frac{300}{125} \\\\h<2.2\\\\h<2 approx[/tex]
Hence, The required value of h < 2 for the number of extra hours she can rent the ballroom.
For more information about Inequality click the link given below.
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amanda ran 4 laps around the school track. Clifford ran half as many laps as brian ran. Together the 3 friends ran 13 laps. How many laps did bryan run
Answer: 6 laps
Step-by-step explanation:
13 - 4= 9 left 6 and half would be three
To find out how many laps Bryan ran, an equation was formulated combining the laps Amanda and Clifford ran with the total laps, which, when solved, showed Bryan ran 6 laps.
Explanation:To solve the problem, let's denote the number of laps Bryan ran as B, Amanda ran 4 laps, and Clifford ran half as many laps as Bryan, so that's B/2 laps.
According to the problem, together they ran a total of 13 laps.
Now we can write an equation based on the information given:
4 + (B/2) + B = 13
Next, we solve for BD:
Combine like terms:
B + B/2 = 13 - 4
1.5B = 9
Divide by 1.5 to solve for B:
B = 9 / 1.5
B = 6
So, Bryan ran 6 laps.
What is the equation of the perpendicular line 2x-4y=7 passing through the points (2,-5/4)?
Answer:
[tex]y= 2x-5\frac{1}{4}[/tex]
Step-by-step explanation:
We are given;
The equation 2x + 4y = 7
A point (2, -5/4)
We are supposed to determine the equation of a line perpendicular to the given line;
First, we determine the slope of the given line by writing the equation in the form of y= mx + c
2x + 4y = 7
y = -1/2x + 7/4
m₁ = -1/2
But, for perpendicular; m₁×m₂= -1
Therefore;
-1/2 × m₂ = -1
m₂ = 2
Thus, we can get the equation of the line;
Taking another point (x, y)
[tex]\frac{y+\frac{5}{4} }{x-2}=2[/tex]
[tex]y+\frac{5}{4}= 2(x-2)[/tex]
[tex]y+\frac{5}{4}= 2x-4[/tex]
[tex]y= 2x-4-\frac{5}{4}[/tex]
[tex]y= 2x-5\frac{1}{4}[/tex]
Thus, the equation of the line in question is [tex]y= 2x-5\frac{1}{4}[/tex]
The vertices of about isosceles trapezoid are located at (2,5),(6,5),(9,3) and?
To determine the fourth vertex of an isosceles trapezoid given three vertices, we use symmetry and properties of isosceles trapezoids, concluding the missing vertex is likely at (-1,3).
Explanation:To find the fourth vertex of an isosceles trapezoid given three vertices, we need to use the properties of isosceles trapezoids. The properties pertinent to solving this problem include parallel bases and non-parallel sides of equal length. Given vertices at (2,5), (6,5), and (9,3), we know the top base is parallel to the x-axis, as the y-coordinate is the same (5) for the first two points.
For the trapezoid to be isosceles, the fourth vertex must follow the pattern of equal non-parallel sides. Observing the pattern of the given points, and noting that the length of the non-parallel side from (9,3) should equal that of the side starting from (2,5), we conclude the missing point must maintain this equality in distance and form a right angle, mirroring the shape on the opposite side.
Without specific lengths, we apply symmetry principles. The height difference between the known base and the third vertex (3) indicates a 2-unit drop, suggesting the opposite side will mirror this. Thus, the fourth vertex should be 2 units below the other base vertex, at (2,5), making the y-coordinate 3. Given the distances in x are equal (4 units from each end vertex to their respective base vertex), the fourth vertex is at (-1,3).
13x-y=-5 in slope intercept form
Answer:
y = 13x + 5
Step-by-step explanation:
will mark brainliest please hurray The table below shows selected points from a function.
1 (the picture for this question is the chart ) The rate of change for the interval shown in the table is ( constant or not constant) so the function is a ( linear or non-linear)
2 (this goes with the chart that says hawk on it) Pick the correct equation for the line below: A y=x^2+90 B y = 3x +90 C y = 90x-10 D y = -10x + 90
3 ( the picture that goes with this one is the normal graph) Look at the graph shown: Which equation best represents the line? (4 points)
y = 1 over 3 x − 1
y = 3x − 1
y = −x + 1 over 3.
y = 3x + 1
Answer:
The answers are given below.
Step-by-step explanation:
1. The rate of change for the interval shown in the table is constant. So, the function is linear.
2.From the graph, the line passes through (0, 90) and the slope of the line is negative.So, the correct equation for the line is,
y = -10x + 90
3.According to the question and the graph, the equation is a straight line with y - intercept equal to -1.So, the equation which best represents the line is,
y = 3x - 1
What is a debit card most like?
Debit Card Definition: A debit card is a payment card that allows you to make secure and easy purchases online and in person by withdrawing funds directly from your checking account. You don't borrow from a line of credit like you would with a credit card; the money on your debit card is yours.
There are 25 students in the class. 36% of the students ate hot dogs for lunch. How many students ate hot dogs?
Answer:
25 * 36% = 9
Step-by-step explanation:
25 * .36 = 9
What is the measure of the missing angle? round answer to the nearest whole number PLEASE HELP I NEED IT BY TOMORROW, 20 POINTS
Answer:
x ≈ 31°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{20}[/tex], thus
x = [tex]tan^{-1}[/tex]([tex]\frac{12}{20}[/tex]) ≈ 31° ( to the nearest whole number )
The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in table #3.2.9 (Lee, 1994). a.) Find the mean and median.
b.) Find the range.
c.) Find the variance and standard deviation.
Without the specific lengths of the rivers, it's not possible to calculate the precise mean, median, range, variance, and standard deviation. In general, these values provide insights into the distribution and variability of river lengths on the South Island of New Zealand.
Explanation:Unfortunately, the specific lengths of the rivers mentioned in the question were not provided, so it's not possible to calculate the mean, median, range, variance, and standard deviation without that data. In general, to calculate these statistical terms:
Mean is calculated by adding up all the lengths of the rivers and dividing by the number of rivers.Median is the middle value when the river lengths are arranged in ascending order. If there is an even number of rivers, it's the average of the middle two values.Range is found by subtracting the shortest river length from the longest.Variance is the average of the squared differences from the Mean.Standard deviation is the square root of the variance, indicating how much the river lengths vary from the average length.These calculations are essential for understanding the distribution and variability of river lengths on the South Island of New Zealand.
Determine which relation is a function. Question 13 options: a) {(3, 0), (– 2, – 2), (7, – 2), (– 2, 0)} b) c) y = 15x + 2 y = 1 5 x + 2 d)
Answer:
x=3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5
Step-by-step explanation:Solving for x. Want to solve for y or solve for d instead?
1 Simplify 0-20−2 to -2−2.
3,-2,-27,-2-2,02y=1,5x+2d3,−2,−27,−2−2,02y=1,5x+2d
2 Simplify -2-2−2−2 to -4−4.
3,-2,-27,-4,02y=1,5x+2d3,−2,−27,−4,02y=1,5x+2d
3 Subtract 2d2d from both sides.
3-2d,-2-2d,-27-2d,-4-2d,02y-2d=1,5x3−2d,−2−2d,−27−2d,−4−2d,02y−2d=1,5x
4 Divide both sides by 1,51,5.
\frac{3-2d}{1},5,\frac{-2-2d}{1},5,\frac{-27-2d}{1},5,\frac{-4-2d}{1},5,\frac{02y-2d}{1},5=x
1
3−2d
,5,
1
−2−2d
,5,
1
−27−2d
,5,
1
−4−2d
,5,
1
02y−2d
,5=x
5 Factor out the common term 22.
\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-4-2d}{1},5,\frac{02y-2d}{1},5=x
1
3−2d
,5,
1
−2(1+d)
,5,
1
−27−2d
,5,
1
−4−2d
,5,
1
02y−2d
,5=x
6 Factor out the common term 22.
\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{02y-2d}{1},5=x
1
3−2d
,5,
1
−2(1+d)
,5,
1
−27−2d
,5,
1
−2(2+d)
,5,
1
02y−2d
,5=x
7 Factor out the common term 22.
\frac{3-2d}{1},5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x
1
3−2d
,5,
1
−2(1+d)
,5,
1
−27−2d
,5,
1
−2(2+d)
,5,
1
2(y−d)
,5=x
8 Simplify \frac{3-2d}{1}
1
3−2d
to (3-2d)(3−2d).
3-2d,5,\frac{-2(1+d)}{1},5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,
1
−2(1+d)
,5,
1
−27−2d
,5,
1
−2(2+d)
,5,
1
2(y−d)
,5=x
9 Simplify \frac{-2(1+d)}{1}
1
−2(1+d)
to (-2(1+d))(−2(1+d)).
3-2d,5,-2(1+d),5,\frac{-27-2d}{1},5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,
1
−27−2d
,5,
1
−2(2+d)
,5,
1
2(y−d)
,5=x
10 Simplify \frac{-27-2d}{1}
1
−27−2d
to (-27-2d)(−27−2d).
3-2d,5,-2(1+d),5,-27-2d,5,\frac{-2(2+d)}{1},5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,−27−2d,5,
1
−2(2+d)
,5,
1
2(y−d)
,5=x
11 Simplify \frac{-2(2+d)}{1}
1
−2(2+d)
to (-2(2+d))(−2(2+d)).
3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,\frac{2(y-d)}{1},5=x3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,
1
2(y−d)
,5=x
12 Simplify \frac{2(y-d)}{1}
1
2(y−d)
to (2(y-d))(2(y−d)).
3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,2(y-d),5=x3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5=x
13 Switch sides.
x=3-2d,5,-2(1+d),5,-27-2d,5,-2(2+d),5,2(y-d),5x=3−2d,5,−2(1+d),5,−27−2d,5,−2(2+d),5,2(y−d),5
Done
If week 1=5, week 2=3, week 3=7, week 4=5 what will week 5 be?
Answer: 11
Step-by-step explanation:
The sequence goes +4, +1, +5, +1... so obviously the next number will be +6. So, 5+6=11
The answer is week 5=11
Week 5 will be 9.
This is a question that has to do with one's reasoning. Since we are given that week 1=5, week 2=3, week 3=7, week 4=5, we can infer that the sequence used is +4, +1, +4, +1, ....
In this case, the last week was week 4 and was given as week 4=5, in this case +1 was used, therefore the next week will have +4. In this case, week 5 will be:
= 5 + 4
= 9
Therefore, week 5 will be 9
Read related link on:
https://brainly.com/question/11765997
In one U.S city, the taxi cost is $2 plus $0.60 per mile. If you are traveling from the airport, there is an additional charge of $5.50 for tolls. How far can you travel from the airport by taxi for $43.50?
Answer:
60 miles
Step-by-step explanation:
Let
x ----> the number of miles
we know that
The number of miles multiplied by $0.60 per mile plus $2 plus the charge of $5.50 for tolls (because you are travelling from the airport) must be equal to $43.50
so
The linear equation that represent this problem is
[tex]0.60x+2+5.50=43.50[/tex]
Solve for x
Combine like terms left side
[tex]0.60x+7.50=43.50[/tex]
subtract 7.50 both sides
[tex]0.60x=43.50-7.50[/tex]
[tex]0.60x=36[/tex]
divide by 0.60 both sides
[tex]x=60\ miles[/tex]
George is twice as old as Edward, and Edward’s age exceeds Robert’s age by 4 years. If the sum of the three ages is at least 56 years, what is Robert’s minimum age?
To find Robert's minimum age, we need to determine the ages of George and Edward first. Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x. Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4. The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56.
Explanation:To find Robert's minimum age, we need to determine the ages of George and Edward first.
Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x.
Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4.
The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56. Simplifying this, we get 4x - 4 >= 56. Adding 4 to both sides, we have 4x >= 60. Dividing by 4, we find that x >= 15.
Therefore, Edward's minimum age is 15 years, and Robert's minimum age is 15 - 4 = 11 years.