A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
Answers
It is to be noted that at the seven and half year, is when the revenue of both ads became equal. This is a graph problem. See the explanation below.
What is the explanation for the above answer?Step 1:
Note that the amount of money earned by routine company activities is known as revenue, which is calculated by dividing the average sales price by the number of units sold.
Step 2:
Note that the graph is to be used to justify the statement by the lead executive.
Step 3
From the graph, we know that the revenue in the 10th year for printed ads was $ 2,000,000 and $ 3,000,000 for online ads. Represented on as coordinates, that would be (0,3); (10, 2).
Thus, we can create an equation that states:
(y-2) = [(3-2)/(0-10)] * (x - 10)
⇒ y - 2
= [-1/10] * [x - 10]
Hence,
10y - 20 = - x + 10
10 y + x = 30 ........Lets call this equation A
We can also state that:
Online revenue coordinates on the graph are (0,0,) (10, 3)
Thus,
(y-0) =
[(3-0)/(10-0)] (x -0)
⇒ y = [3x/10] [10y - 3x] = 0.........Lets make this equation B
For printed Ad Revenue:
Year 12= x
10y + 12 = 30
Y = 18/10
y = 1.8
For online Ad revenue
Year = 12 = x
10y = 36
Y = 36/10
y = 3.6
From the above, it is clear that in year 10, the online ad revenue got doubled as same as that of revenue from printed ads.
In order to get the year in which the revenue were equal, we solve both equations simultaneously:
+ 10y + x = 30
± 10y ≠ 3x = 3
4x = 30
x thus, = 30/4
= 7.5
Thus, it is correct to state that both revenue's became equal by the mid of the 7th year going to the eight year.
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Full Question:
Missing graph is attached.
Related Questions
Five hats and three shirts cost $176. Three hats and five shirts cost $208. What is the cost of one hat?
The cost of one hat is __ dollars.
Answers
Let hats be x
Let shirts be y
We can set up a system of equations to figure out the cost of one hat.
5x+3y = 176 and 3x+5y = 208
Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.
5(5x+3y = 176) --> 25x+15y = 880
-3(3x+5y = 208) --> -9x-15y = -624
We can now add the 2 equations together and solve for x.
25x+15y = 880
-9x-15y = -624
+>>>>>>>>>>>>>>>
16x = 256
x = 16
So the the cost of one hat is 16 dollars.
Answer:
$16
Step-by-step explanation:
Define the variables:
Let x = cost of one hatLet y = cost of one shirtCreate two equations using the defined variables and the given information.
Equation 1
Five hats and three shirts cost $176.
⇒ 5x + 3y = 176
Equation 2
Three hats and five shirts cost $208.
⇒ 3x + 5y = 208
Rewrite Equation 2 to make y the subject:
[tex]\implies \sf 3x+5y-3x=208-3x[/tex]
[tex]\implies \sf 5y=208-3x[/tex]
[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]
[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]
Substitute the found expression for y into Equation 1 and solve for x:
[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]
[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]
[tex]\implies \sf 5x+124.8-1.8x=176[/tex]
[tex]\implies \sf 3.2x+124.8=176[/tex]
[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]
[tex]\implies \sf 3.2x=51.2[/tex]
[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]
[tex]\implies \sf x=16[/tex]
Therefore, the cost of one hat is 16 dollars.
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Part B The mass of an average grain of rock salt is about 40 times the mass of an average grain of table salt. If you multiply the mass of table salt in standard notation by 40, what value do you get?
Answers
Answer:
0.012
Step-by-step explanation:
We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.
answer - 0.0003 X 40 = 0.012
Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
Answers
The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point (-6,8) is -6x+8y=100.
Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]
and point at which the tangent meets the circle is (-6,8).
A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.
Linear equation looks like y=mx+c.
Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:
xz+ty=[tex]a^{2}[/tex].
We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at (-6,8).
It will be as under:
x(-6)+y(8)=100
-6x+8y=100
Hence the equation of tangent to the circle at the point (-6,8) is -6x+8y=100.
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If f(x + 1) = x + 2 then f(x - 1) is
Answers
Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]
Step-by-step explanation:
Given function
f(x + 1) = x + 2
Isolate [ x + 1 ] on the right-hand side
f(x + 1) = x + 1 + 1
f(x + 1) = (x + 1) + 1
Substitute [ x + 1 ] with x
f(x) = x + 1
Substitute [ x ] with [ x - 1 ]
f(x - 1) = (x - 1) + 1
[tex]\Large\boxed{f(x-1)=x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
Answers
The point that is a solution to the system of inequalities is (5, 0)
How to determine the points on the solution?The system of inequalities is given as:
y ≤ 2x + 2
y ≥ -5x + 4
Next, we test the given options.
From the list of options, we have
(x, y) = (5, 0)
Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4
y ≤ 2x + 2
0 ≤ 2 * 5 + 2
0 ≤ 12 -- this is true
y ≥ -5x + 4
0 ≥ -5 * 5 + 4
0 ≥ -21 -- this is true
Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)
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Complete question
Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2
y ≥ -5x + 4
A. (1,6)
B. (-6,0)
C. (0,5)
D. (5,0)
What is the annual interest paid on an account that has a $1000 balance if the rate is [tex]7\frac{1}{2}[/tex]%?
Answers
The annual interest paid on the account is $75
How to determine the annual interest
The formula for determining annual interest is given as;
Interest = PRT/100
where;
P is the principal amount = $1000R is the rate = 7. 5%T is the time = 1 year, since it's an annual paymentSubstitute the values
Annual Interest = 1000 × 7. 5 × 1/ 100
Annual interest = 7500/ 100
Annual interest = $75
Thus, the annual interest paid on the account is $75
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let h(x)=-1/3x+2. Find -4h(9)
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]
we need to find -4 h(9) :
[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]
[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]
[tex]\qquad❖ \: \sf \:4[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answers
Given :-
2x + 5 < x + 1 / 4Solution :-
>> 2x + 5 < x + 1 / 4
>> 4 (2x + 5) < x + 1
>> 4 × (2x + 5) < x + 1
>> 8x + 20 < x + 1
>> 8x - x < 1 - 20
>> 7x < 1 - 20
>> 7x < -19
>> x = -19 / 7
[tex]\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}[/tex]
Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.
[tex]\boldsymbol{\sf{8x+20 < x+1 }}[/tex]
Resta x en los dos lados.
[tex]\boldsymbol{\sf{8x+20-x < 1 }}[/tex]
Combine 8x and −x to get 7x.
[tex]\boldsymbol{\sf{7x+20 < 1 }}[/tex]
Subtract 20 on both sides.
[tex]\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}[/tex]
[tex]\boldsymbol{\sf{7x < -19 }}[/tex]
Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.
[tex]\boldsymbol{\sf{x < -\dfrac{19}{7} } }[/tex]
As the end result, it is not simplified or divided, then
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}[/tex]
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https://brainly.com/question/23265395On the unit circle, where 0 undefined?
Answers
5. In a recent year, the population of Springfield, Illinois was one hundred
sixteen thousand, four hundred eighty-two. Write this number in standard
form. Show your work in the space below. Remember to check your solution
Answers
Answer: 16482
Step-by-step explanation:
Let's divide the number into three parts:
sixteen thousand | four hundred |eighty-two
A thousand is 1000, so sixteen thousand should be 16000.
A hundred is 100, so four hundred should be 400.
Eighty-two is just 82.
Let's add all of these:
[tex]16000+400+82=16482[/tex]
ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ .
Answers
Answer: try 35
Step-by-step explanation:
You conduct a quasi-experiment to assess the impact of raising the speed limit from 55 to 65 miles per hour. You find that there are more accidents in the 6-month period following the speed limit change than in the 6-month period before the speed limit change. Although it is tempting to say that raising the speed limit caused higher accident rates, you must be careful because
Answers
It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.
Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.
The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.
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Type the correct answer in each box. use numerals instead of words. the surface area of a cylinder is approximately 640.56 square meters. the radius of the cylinder is 5 meters less than the height of the cylinder. to the nearest whole meter, what are the radius and height of the cylinder? the radius is approximately meters, and the height is approximately meters.
Answers
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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Answer:
Step-by-step explanation:
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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The slope of the line shown in the graph is __ and the y-intercept of the line __
Answers
Answer:
slope
(0, 6) and (-9, 0)
0 - 6 / -9 - 0 = -6/-9 = 2/3
y intercept is when the line intercepts the y axis and x = 0
The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6
Answer:
slope is 2/3
y intercept is 6
Step-by-step explanation:
We can find the slope of the line by using two point
(-9,0) and (0,6)
The slope formula is
m = ( y2-y1)/(x2-x1)
= ( 6 - 0) /( 0 - -9)
= (6-0)/(0+9)
= 6/9
= 2/3
The y intercept is where it crosses the y axis ( the value where x is 0)
The y intercept is 6
Each gallon of porch and deck paint covers 200 square feet. how many gallons are needed to cover 1241 square feet?
Answers
7 gallons are needed to cover 1241 square feet.
In this question,
Each gallon of porch and deck paint covers 200 square feet.
To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.
We use the unitary method to find out how many gallons of paint needs.
Using unitary method,
1241 / 200 = 6.205
However, we cannot buy a fraction of a gallon of paint.
So, the amount of gallons of paint needed is approximately equal to 7 gallons.
Therefore, 7 gallons are needed to cover 1241 square feet.
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The line y= mx + c is parrallel to the line y=2x + 8
The distance AB is 9 units
Find the value of m and the value of c.
Answers
Answer: 2 and -10 respectively
Step-by-step explanation:
m in the equation is 2 as it is parallel to a line with a slope of 2
Both point A and B are on the x-axis so both of them have a y value of 0
To find the x value of A, we have to substitute y = 0 into the equation
2x + 8 = 0
x = -4, so the coordinate for A is A(-4,0)
As AB is 9 units, we can figure out that B(5,0)
Substitute x = 5 and y = 0 into the equation y = 2x + c to find c
0 = 2(5) + c
c = -10
So m = 2 and c = -10
neeed help please pleasee
Answers
Answer:
Y = 2+- square root of 6
Step-by-step explanation:
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]
a = 1b = -4c = -2[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 16 - ( - 8)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]
Create an equivalent system of equations using the sum of the system and the first equation. x 4y = 8 4x y = 2 x 4y = 8 5x y = 2 x 4y = 8 5x 5y = 2 x 4y = 8 4x 5y = 10 x 4y = 8 5x 5y = 10
Answers
An equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
What are equations?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.[tex]3x+5=14[/tex], for example, is an equation in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by a '=' sign.Given:
[tex]x+4y=8\\4x+y=2[/tex]
Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]
Therefore, an equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.
x + 4y = 8
4x + y = 2
x + 4y = 8
5x + y = 2
x + 4y = 8
5x + 5y = 2
x + 4y = 8
4x + 5y = 10
x + 4y = 8
5x + 5y = 10
Find the least positive integer N so that the value of 2020 + N
is both
• a perfect cube, and
• a multiple of 56.
Answers
Answer:724
Step-by-step explanation: Let us go through trail and error method.
Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.
2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01
Let us divide, 2744 with 56.
i.e., 2744/56= 49. ___ equation -02
As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.
i.e., 2020+N= 2744
N= 2744-2020
Therefore; N= 724.
Answer:
724,
Step-by-step explanation:
14^3 = 2744 is the next perfect cube > 2020.
2744 / 56 = 49.
So that fits the requirements in the question.
So N = 2744 - 2020
= 724,
[tex]4 {}^{x } + 6 {}^{x} = 9 {}^{x} [/tex]
please find x. and with explanation thanks
Answers
So, the value of x is 1.19
The question is an exponential equation
What is an exponential equation?An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.
How to find x?
Since [tex]4^{x} + 6^{x} = 9^{x}[/tex],
Dividing through by 4ˣ, we have
[tex]\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }[/tex]
Let y = (3/2)ˣ
So,
1 + y = y²
y² - y - 1 = 0
Using the quadratic formula to find y,
[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
where a = 1 b = -1 and c = -1
Substituting the values of the variables into the equation, we have
[tex]y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618[/tex]
Since y = (3/2)ˣ
Takung logarithm of both sides, we have
㏒y = ㏒(3/2)ˣ
㏒y = x㏒(3/2)
x = ㏒y/㏒(3/2)
x = ㏒y/㏒1.5
Since we do not have logarithm of a negative number, we use y = 1.618.
So, x = ㏒y/㏒1.5
x = ㏒1.618/㏒1.5
x = 0.2090/0.1761
x = 1.19
So, the value of x is 1.19
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Here is the histogram of a data distribution. What is the shape of this distribution?
Answers
Considering it's histogram, the shape of the distribution is given by:
D. Bimodal.
What is an histogram?An histogram of a data-set is a graph that shows the number of times each element of x was observed.
In this problem, elements 1 and 10 were each observed 5 times, meaning that there are two modes in the data-set, hence the data-set is bimodal and option D is correct.
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Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 12
Answers
Answer:
16
Step-by-step explanation:
6/3 = 2 postcards per day
2x8 = 16 postcards
6/3 = 2 postcards a day
Factor the greatest common factor: −5k2 20k − 30. −1(5k2 − 20k 30) −5(k2 − 4k 6) −5k(k2 − 4k 6) −5(k2 4k − 6)
Answers
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
What is meant by the greatest common factor?The most common factor in mathematics is the highest number that may divide evenly into two other numbers.The largest factor that splits both numbers is the greatest common factor. List the prime factors of each integer before calculating the greatest common factor. One 2 and one 3 are shared by those aged 18 and 24. We multiply them to obtain the GCF. Therefore the GCF for 18 and 24 is 2 * 3 = 6.The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.To find the greatest common factor:
−5k2 20k − 30.
Factor the expression: [tex]5(-k^{2} +4k-6)[/tex]
Factor the expression: [tex]5(-k^{2} -4k+6)[/tex]
Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]
The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
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The complete question is:
Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]
a) [tex]-1(5k^2- 20k+ 30)[/tex]
b) [tex]-5(k^2 -4k+ 6)[/tex]
c)[tex]-5k(k^2 - 4k +6)[/tex]
d) [tex]-5(k^2 +4k - 6)[/tex]
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.
Given : −5k² + 20k − 30.
Taking common -5 from each term, we get
−5k² + 20k − 30 = -5 ( k² - 4k + 6 ).
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
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Create the smallest cone possible with the tool, and record the values of the radius, height, and volume in terms of . Then scale the original CONE
by the given scale factors, and record the resulting volumes (in terms of 7), to verify that the formula V=V xk³ holds true for a cone.
Answers
The Created cone with the possible record of the the values of the radius, and height is given in the image attached.
How do yo create the volume of the smallest cone?A scale factor is known to be a number that is known to often multiplies (doubles or triples, etc.,“scales”) a given quantity.
Since the volume is not attached, it will be manually created here.
Note that the resulting volumes must be in terms of 7.
Hence:
Volume Formula: V=V x k³
When scale factor is 2, radius = 4, height = 8, then volume will be:
7π x 2³
= 56π
When scale factor is 3, radius = 6, height = 18, then volume will be:
7π x 3³
= 189π
When scale factor is 4, radius = 8, height = 24, then volume will be:
7π x 4³
= 448π
Hence the volume that will be fixed into the scale factor diagram will be:
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The smallest bone on the body, the stirrup-shaped stapes found in the middle ear, has a typical length of less than 0.33 cm. how long in inches is the typical maximum length of the stapes?
Answers
Answer:
0.13 inches.
Step-by-step explanation:
1 inch = 2.54 cm
So 1 cm = 1/ 2.54 in
0.33 cm = 0.33/2.54 in
= 0.13 inches.
Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answers
The solution to the system of equations is x = 3 and y = 11
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y equals x plus 8
y equals 3 x plus 2
Rewrite properly as
y = x + 8
y = 3x + 2
Substitute y = x + 8 in y = 3x + 2
x + 8 = 3x + 2
Evaluate the like terms
2x = 6
Divide by 2
x = 3
Substitute x = 3 in y = x + 8
y = 3 + 8
Evaluate
y = 11
Hence, the solution to the system of equations is x = 3 and y = 11
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The solution to the system of equation is as follows:
x = 3
y = 11
How to solve the system of equation?y = x + 8
y = 3x + 2
Using substitution method,
3x + 2 = x + 8
subtract x from both sides
3x - x + 2 = x - x + 8
2x + 2 = 8
subtract 2 from both sides
2x + 2 - 2 = 8 - 2
2x = 6
divide both sides by 2
2x / 2 = 6 / 2
x = 3
y = 3 + 8 = 11
y = 11
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What is the slope of the line represented by the equation y- 6 = 2(x+3)?
Answers
And m is slope and b is the y-intercept -
In this equation y-6=2(x+3)
m is 2 because if u multiply 2 to (x+3) it will become 2x+6
since m is 2 and b is 6
The slope is 2
And the y-int. is 6
So the slope is 2.
Answer: 2
Step-by-step explanation:
remember y=mx^2+c
where m = gradient = slope
∴ expand and simplify y-5=2(x+3)
y-5=2x+6
y=2x+11
m=2 ∴ slope: 2
Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
Answers
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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Which function in vertex form is equivalent to f(x) = 4 + x² - 2x?
O f(x) = (x - 1)² + 3
O f(x) = (x-1)² + 5
O f(x) = (x + 1)² + 3
O f(x) = (x + 1)² +5
Answers
Answer:
f(x)=(x-1)^2+3
Step-by-step explanation:
Both equations vertexes equal (1, 3) while the rest do not match.
f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.
We can use the technique of completing the square to rewrite the given function f(x) in vertex form.
f(x) = 4 + x² - 2x
f(x) = (x² - 2x) + 4
Adding and subtracting (1) inside the parentheses
f(x) = (x² - 2x + 1) + 4 - 1
f(x) = (x - 1)² + 3
So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.
Therefore, the correct option is f(x) = (x - 1)² + 3.
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Solve for n
-19=-8+n
Answers
Answer:
8-18=n
-10=n
therefore
n=-10
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Answer: [tex]\textsf{n = -11}[/tex]
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Given: [tex]\textsf{-19 = -8 + n}[/tex]
Find: [tex]\textsf{Solve for n}[/tex]
Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.
Add 8 to both sides
[tex]\textsf{-19 + 8 = -8 + 8 + n}[/tex][tex]\textsf{-19 + 8 = n}[/tex][tex]\textsf{-11 = n}[/tex]Therefore, the final answer would be that n is equal to -11.