The measure of the angle between the vectors
[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].
What is the measure of the angle between the vectors?
Given:
[tex]$\mathrm{u}=\langle -3,2\rangle$[/tex] and [tex]$v=\langle 2,1\rangle$[/tex]
Computing the angle between the vectors, we get
[tex]$\quad \cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]
To estimate the lengths of the vectors, we get
Computing the Euclidean Length of a vector,
[tex]$\left|\left(x_{1}, \ldots, x_{n}\right)\right|=\sqrt{\sum_{i=1}^{n}\left|x_{i}\right|^{2}}$[/tex]
Let, [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex] and [tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]
If [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex]
[tex]$|u| &=\sqrt{-3^{2}+(2)^{2}} \\[/tex]
[tex]$&=\sqrt{5}i \\[/tex] and
[tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]
[tex]$|v| &=\sqrt{2^{2}+(1)^{2}} \\[/tex]
[tex]$&=\sqrt{5}[/tex]
Finally, the angle is given by:
Computing the angle between the vectors, we get
[tex]$ $\cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]
[tex]$&\cos (\Phi)=-\sqrt{13 } i/ \sqrt{5 } \\[/tex]
simplifying the above equation, we get
[tex]$&\Phi=\arccos (\cos (\Phi))[/tex]
[tex]$=\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex]
Therefore, the measure of the angle between the vectors
[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].
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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.
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
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]
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.
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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Each gallon of porch and deck paint covers 200 square feet. how many gallons are needed to cover 1241 square feet?
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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Solve for n
-19=-8+n
Answer:
8-18=n
-10=n
therefore
n=-10
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{n = -11}[/tex]
-------------------------------------------------------------------------------------------------------------
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.
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?
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
Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
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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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
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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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.
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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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
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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If f(x + 1) = x + 2 then f(x - 1) is
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
let h(x)=-1/3x+2. Find -4h(9)
[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]
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/23265395Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
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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Find the least positive integer N so that the value of 2020 + N
is both
• a perfect cube, and
• a multiple of 56.
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,
What is the slope of the line represented by the equation y- 6 = 2(x+3)?
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 point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
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)
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.
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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On the unit circle, where 0 undefined?
What is the annual interest paid on an account that has a $1000 balance if the rate is [tex]7\frac{1}{2}[/tex]%?
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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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
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]
The sum of two numbers is 56. The first number is 2 times greater than the second number. What is the second number?
Answer:
y = 56/3
Step-by-step explanation:
We need to write equations to solve
Let the two numbers be x and y
The sum is 56
x+y = 56
The first number is 2 times greater than the second number.
x = 2*y
Substitute this into the first equation
x+y = 56
2y+y=56
3y = 56
y = 56/3
Step-by-step explanation:
Let the numbers be x and y
The sum of the two numbers is 56 :
Step 1:
X + Y = 56.......... (1)
Also, the first number is 2 times greater than the second number:
Step 2:
2X + Y = 0........... (2)
By substitution method, make Y the subject from (2)
Step 3:
Y = -2X .......... (3)
Put (3) into (1)
Step 4
X - 2X = 56
-X = 56
[tex] \frac{ - x}{ - 1} = \frac{56}{ - 1} [/tex]
X = -56
Put X=56 into (3)
Step 5
[tex]y = - 2( - 56)[/tex]
[tex]y = 112[/tex]
The second number is now 112.
Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 12
Answer:
16
Step-by-step explanation:
6/3 = 2 postcards per day
2x8 = 16 postcards
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?
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.
Factor the greatest common factor: −5k2 20k − 30. −1(5k2 − 20k 30) −5(k2 − 4k 6) −5k(k2 − 4k 6) −5(k2 4k − 6)
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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[tex]4 {}^{x } + 6 {}^{x} = 9 {}^{x} [/tex]
please find x. and with explanation thanks
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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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
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
Here is the histogram of a data distribution. What is the shape of this distribution?
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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Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
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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ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ .
Answer: try 35
Step-by-step explanation: