Answer:
(x - 3)(x - 12)
Step-by-step explanation:
Given
x² - 15x + 36
Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)
The factors are - 3 and - 12, since
- 3 × - 12 = + 36 and - 3 - 12 = - 15, hence
x² - 15x + 36 = (x - 3)(x - 12) ← in factored form
The factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12). This can be obtained by using the steps of splitting the middle term method.
Find the factored form using splitting the middle term:Given the polynomial, x² − 15x + 36
Step 1:First we should multiply first term and last term, x²×36=36x²Step 2:This product ,that is 36x², should be slit such that the factors sum is the middle term, -15x.(-3x)×(-12x)=36x² and (-3x)+(-12x)= - 15x
-3x and -12x are the required factors of 36x²
Step 3:Substitute the factors in the place of middle term,x² - 3x - 12x+36
Step 4:Take common terms from the first two terms and last two terms,x² - 3x - 12x+36 = x(x - 3) - 12(x - 3)
=(x - 3)(x - 12)
Hence the factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12).
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Complete the table for the given rule y=x-3
For the first row, where x is equal to 7, to find y plug 7 in for x like so...
y = 7 - 3
y = 4
For the second row, where y is equal to 1, to find x plug 1 in for y like so...
1 = x - 3
To solve for x add 3 to both sides. This will cancel 3 from the right side:
1 + 3 = x - 3 + 3
4 = x + 0
x = 4
For the third row, where y is equal to 7, to find x plug 7 in for y like so...
7 = x - 3
To solve for x add 3 to both sides. This will cancel 3 from the right side:
7 + 3 = x - 3 + 3
10 = x + 0
x = 10
First row: y is 4
Second row: x is 4
Third row: x is 10
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the slope of the line that passes through the points (-1, 1) and (2, 7).
Answer:
2 is your slope
Step-by-step explanation:
Find the slope. Use the slope-formula:
m (slope) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (-1 , 1)
(x₂ , y₂) = (2 , 7)
Plug in the corresponding numbers to the corresponding variables:
m = (7 - 1)/(2 - (-1))
Simplify:
m = (6)/(2 + 1)
m = 6/3
m = 2
2 is your slope (or rise 2, run 1).
~
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (2, 7)
m = [tex]\frac{7-1}{2+1}[/tex] = [tex]\frac{6}{3}[/tex] = 2
Which of the following equations is of a parabola with a vertex at (0,3)?
y= (x - 3)2
y= (x + 3) 2
y=x2-3
y= x2 + 3
Answer:
[tex]y=x^{2}+3[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex
In this problem we have the vertex at point (0,3)
substitute
[tex]y=a(x-0)^{2}+3[/tex]
[tex]y=ax^{2}+3[/tex]
therefore
The option [tex]y=x^{2}+3[/tex] is the answer
In this case the coefficient a is equal to 1
Which of the following would be the most logical first step to solving this
quadratic equation?
2x2-x+ 2 = -11
O
A. Divide both sides by x.
O
B. Take the square root of both sides.
O
C. Set up smaller equations using the zero product rule.
O
D. Add 11 to both sides.
Answer:
D is correct option
Step-by-step explanation:
The correct option is D.
The standard quadratic equation is ax²+bx+c=0
Where a and b are coefficients and c is constant.
It means that constant are on the L.H.S and there is 0 on the right hand side.
Therefore to make it a quadratic equation first of all you have to add 11 at both sides so that the R.H.S becomes 0.
The given equation is:
2x2-x+ 2 = -11
If we add 11 on both sides the equation will be:
2x2-x+ 2 +11= -11+11
2x^2-x+13=0
Thus the correct option is D
You can further solve it by applying quadratic formula....
Final answer:
The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to set up smaller equations using the zero product rule and then applthe quadratic formula. The correct option is c.
Explanation:
The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to:
C. Set up smaller equations using the zero product rule.
Once the equation is rearranged, apply the quadratic formula to determine the values of x.
Using the quadratic formula yields the solutions by substituting the values of a, b, and c correctly.
help with 1-6 , please !!!!!
Answer:
sum of angles of triamgle is 180 degree
the half base× hight ue1/2×b×h
use the formula for all qusetions
Factor each expression. Show your work. 11. r2 + 12r + 27 12. g2 – 9 13. 2p3 + 6p2 + 3p + 9
Answer:
11. r^2 + 12r + 27 = (r+3)(r+9)
12. g^2-9 = (g+3)(g-3)
13. 2p^3 + 6p^2 + 3p + 9 = (2p^2+3)(p+3)
Step-by-step explanation:
[tex]11.\ r^2 + 12r + 27\\Factorizing\\= r^2+9r+3r+27\\=r(r+9)+3(r+9)\\=(r+3)(r+9)\\\\12. g^2-9\\The\ expression\ will\ be\ factorized\ using\ the\ formula\\(a+b)(a-b)=a^2-b^2\\So,\\g^2-9\\=(g)^2-(3)^2\\=(g+3)(g-3)\\\\13. 2p^3 + 6p^2 + 3p + 9\\=2p^2(p+3)+3(p+3)\\=(2p^2+3)(p+3)[/tex] ..
If point P is 4/7 of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?
4:1
4:3
4:7
4:10
Answer:
4:3
Step-by-step explanation:
Given that P divides segment MN into 4/7, let MN to be x units in length then
MP = 4/7 x =4x/7 --------(i)
But MN =MP+PN so;
x=4x/7 +PN
x- 4X/7 =PN
3x/7 =PN ----------(ii)
To get the ratio of MP:PN
MP: PN
4x/7:3x/7
MP/PN = 4x/7 / 3x/7
MP/PN =4/3
MP:PN = 4:3
Answer: 4:3
Step-by-step explanation:
Given : A point P is 4/7 of the distance from M to N.
∴ Let the distance between M to N be d.
[tex]\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}[/tex]
Also, the point P partition the directed line segment from M to N .
Thus , MN = MP+PN
[tex]\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d[/tex]
Now, the ration of MP to PN will be :-
[tex]\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}[/tex]
∴ Point P partitioned the line segment MN into 4:3.
Determine algebraically whether f(x) = x^2(x^2 + 9)(x^3 + 2x) is even or odd.
[tex]f(x) = x^2(x^2 + 9)(x^3 + 2x)\\\\f(-x) = (-x)^2((-x)^2 + 9)((-x)^3 + 2\cdot(-x))\\f(-x)=x^2(x^2+9)(-x^3-2x)\\f(-x)=-x^2(x^2+9)(x^3+2x)\\\Large f(-x)\not =f(x)\implies\text{not even}\\\\-f(x)=-x^2(x^2+9)(x^3+2x)\\ -f(x)=f(-x)\implies \text{odd}[/tex]
(4^((-11/3))/(4^((-2)/3))
simplify the following expression
Answer:
[tex]\large\boxed{\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}=\dfrac{1}{64}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=4^{-\frac{11}{3}-\left(-\frac{2}{3}\right)}=4^{-\frac{11}{3}+\frac{2}{3}}=4^{-\frac{9}{3}}=4^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{4^3}=\dfrac{1}{64}[/tex]
The simplification of the expression is [tex]\dfrac{1}{64}[/tex].
What are some basic properties of exponentiation?Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\[/tex]
Given ;
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})}[/tex]
We know that
[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})} = 4^({-11/3 + 2/3})\\\\\\= 4 ^{-9/3}\\\\= 4^{-3}\\\\[/tex]
Hence, [tex]\dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
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ali and jake went on a cross country trip they took a train part of the way and took a bus the rest of the way they traveled a total of 1450 riding on the train 150 more kilometers than on the bus
let x=kilometers traveled by bus
let y = kilometers traveled by train
question how many kilometers did they travel by train?
Answer:
=800 km
Step-by-step explanation:
Let the distance traveled by train be y and by bus be x.
Bus -x
Train -y
y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)
The sum of the two is equal to 1450
x+y=1450
y=x+150
These two form simultaneous equations.
y+x=1450..............i
y-x=150.................ii
Adding ii to i gives:
2y=1600
Divide both sides by two
y=800
Distance traveled by train =y=800 km
Answer:
800
Step-by-step explanation:
URGENTTTTTTT!!!!!!!!!!
Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.
Answer:
Circle A and circle B are similar
Step-by-step explanation:
* Lets explain similarity of circles
- Figures can be proven similar if one, or more, similarity transformations
reflections, translations, rotations, dilations can be found that map one
figure onto another
- To prove all circles are similar, a translation and a scale factor from a
dilation will be found to map one circle onto another
* Lets solve the problem
∵ Circle A has center (-1 , 1) and radius 1
∵ The standard form of the equation of the circle is:
(x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center
and r is the radius
∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²
∴ Equation circle A is (x + 1)² + (y - 1)² = 1
∵ Circle B has center (-3 , 2) and radius 2
∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²
∴ Equation circle B is (x + 3)² + (y - 2)² = 4
- By comparing between the equations of circle A and circle B
# Remember:
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
∵ -3 - -1 = -2 and 2 - 1 = 1
∴ The center of circle A moves 2 units to the left and 1 unit up to
have the same center of circle B
∴ Circle A translate 2 units to the left and 1 unit up
∵ The radius of circle A = 1 and the radius of circle B = 2
∴ Circle A dilated by scale factor 2/1 to be circle B
∴ Circle B is the image of circle A after translation 2 units to the left
and 1 unit up followed by dilation with scale factor 2
- By using the 2nd fact above
∴ Circle A and circle B are similar
This circle is centered at the point (3, 2), and the length of its radius is 5. What
is the equation of the circle?
Answer:
(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
what is the slope intercept equation of the line below
Answer:
y=2x-3
Step-by-step explanation:
The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.
The y-intercept is where it crosses the y-axis. It cross the y-axis in your picture at -3 so b=-3.
Now the slope=rise/run. So starting at (0,-3) we need to find another point that crosses nicely on the cross-hairs and count the rise to and then the run to it. So I see (1,-1) laying nicely. So the rise is 2 and the run is 1.
If you don't like counting. You could just use the slope formula since we already identified the two points as (-1,1) and (0,-3).
The way I like to use the formula is line up the points and subtract vertically then put 2nd difference over 1st difference.
(0,-3)
-(1,-1)
----------
-1 -2
So the slope is -2/-1 or just 2.
We have that m is 2 and b is -3.
Plug them into y=mx+b and you are done.
y=2x-3.
Slope intercept equation of the line is y = 2x - 3.
What is slope-intercept form?Slope intercept form gives the graph of a straight line and is represented in the form of y=mx + c.
By checking the graph by drawing manually.
From that we get the equation
y = 2x - 3
Comparing above equation with the standard slope-intercept form y = mx +c, we get
Slope : m = 2
Now, given equation can be re-written as :
2x - y = 3
Divide by 3 on both sides
[tex]\frac{2x}{3} -\frac{y}{3} =\frac{3}{3}[/tex]
[tex]\frac{x}{\frac{3}{2} } -\frac{y}{3} =1[/tex]
Comparing above equation with intercept form:
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex], we get
x-intercept : [tex]a=\frac{3}{2}[/tex]
y-intercept : [tex]b=-3[/tex]
Now the given straight line intersects the coordinate axes at [tex](\frac{3}{2} ,0)[/tex] and [tex](0,-3)[/tex]. Specify these plots on XY-plane & join by a straight line to get a plot.
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what are the zeros of the polynomial function f(x)=x^3-x^2-6x
Answer:
x = -2, x = 0, and x = 3
Step-by-step explanation:
it was right lol
The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary. r = 7.8 mm, d = ? , C = ? Question 1 options: d = 15.6 mm, C = 24.50 mm d = 15.6 mm, C = 49.01 mm d = 3.9 mm, C = 49.01 mm d = 3.9 mm, C = 24.50 mm
Answer:
Second option:
[tex]d = 15.6\ mm,\ C = 49.01\ mm[/tex]
Step-by-step explanation:
We can observe that the radius of the circle is given. This is:
[tex]r = 7.8\ mm[/tex]
And the missing measures are the diameter of the circle and the circumference.
Since the diameter of a circle is twice the radius, we get that this is:
[tex]d=2r\\\\d=2(7.8\ mm)\\\\d=15.6\ mm[/tex]
To find the circumference of the circle, we can use this formula:
[tex]C=2\pi r[/tex]
Where "r" is the radius of the circle.
Substituting the radius into the formula, we get:
[tex]C=2\pi r\\\\C=2\pi (7.8\ mm)\\\\C=49.01\ mm[/tex]
The volume of the spheres is 500/3 pie cubic units What is the value of X?
Answer:
125
Step-by-step explanation:
500 ÷ 4 = 125
I think this is the right answer. sorry if I'm wrong.
Answer:
x=5 assuming that x is the radius.
x is the radius?
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.
We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.
We are asked to find the value of x. If x is not the radius, please correct me:
[tex]V=\frac{4}{3}\pi r^3[/tex] with [tex]V=\frac{500}{3} \pi[/tex] and the assumption that x is r.
[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]
If you multiply both sides by 3, then you would have:
[tex]500 \pi=4 \pi x^3[/tex]
If you divide both sides by [tex]\pi[/tex] you will have:
[tex]500=4x^3[/tex]
If you divide both sides by 4, you will have:
[tex]125=x^3[/tex]
The last step would be to take the cube root of both sides:
[tex]\sqrt[3]{125}=x[/tex]
[tex]5=x[/tex]
[tex]x=5[/tex]
Solve 3x − 2 = 37. please help me
To solve the equation 3x - 2 = 37, you add 2 to both sides to get 3x = 39. Then, you divide by 3 to solve for x, obtaining x = 13.
Explanation:To solve the equation
3x − 2 = 37
for x, you start by moving the -2 to the other side of the equation by adding 2 to both sides. This gives you
3x = 39
. Then, you isolate x by dividing every term by 3. After dividing, you find that
x = 13
. So the solution to the equation 3x - 2 = 37 is x = 13.
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To solve the equation, add 2 to both sides and then divide by 3 to isolate the variable x. The solution is x = 13.
Explanation:To solve the equation 3x - 2 = 37, we need to isolate the variable x. Here are the steps:
Add 2 to both sides of the equation to get rid of the constant term. This gives us 3x = 39.Divide both sides of the equation by 3 to solve for x. This gives us x = 13.Therefore, the solution to the equation is x = 13.
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¿Cuál de las siguientes funciones es una función constante? a. Y=x+1 b. Y=x+2 c. X=y+3 d. Y=3
Answer:
Option D y=3
Step-by-step explanation:
The question in English is
Which of the following functions is a constant function?
we know that
A constant function is a function whose output value is the same for every input value
so
Verify each case
case A) y=x+1
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case B) y=x+2
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case C) x=y+3
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case D) y=3
This is a constant function
Is a function whose output value is the same for every input value
If g(x) = xsquared +2, find the g (3)
Answer:
g(3)=11 I think
Step-by-step explanation:
Since x is 3, you substitute it in for the x. So it would be 3 squared +2.
I'm not sure if this is right but I tried helping.
Answer:
g(3) =11
Step-by-step explanation:
g(x) = x^2 +2
Let x =3
g(3) = 3^2 +2
= 9+2
= 11
Solve the equation over the interval [0,2pi) 4cscx + 6= -2
[tex]\bf 4csc(x)+6=-2\implies 4csc(x)=-8\implies csc(x)=\cfrac{-8}{4}\implies csc(x)=-2 \\\\\\ \cfrac{1}{sin(x)}=-2\implies \cfrac{1}{-2}=sin(x)\implies sin^{-1}\left( -\cfrac{1}{2} \right)=x\implies x= \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]
Expand and simplify (X+5)(X+1)
Answer:
Step-by-step explanation:
(X+5)(X+1) = x²+x+5x+5 = x² +6x+5
(X+5)(X+1)
Use the FOIL method to expand.
This means multiply each term in the first set of parenthesis by each term in the second set.
x *x = x^2
x*1 = x
5*x = 5x
5*1 = 5
Now you have x^2 + x + 5x + 5
Now simplify by combining like terms:
x^2 + 6x + 5
PLEASE HELP ASAP If mZYWZ - 17, what is mw
?
34
73
56
17
Answer:
73°
Step-by-step explanation:
Since WX = WZ then ΔWXZ is isosceles and WY is perpendicular to XZ
Hence ∠XYW = 90°
YW bisects XWZ, hence ⇒ ∠ YWX = ∠YWZ = 17°
The sum of the 3 angles in ΔWXY = 180°, hence
∠WXY = 180° - (90 + 17)° = 180° - 107° = 73°
The original price of a skateboard was reduced by $15. The new price is $49.
Answer:
The original price of a skateboard is $64
Step-by-step explanation:
Let
x ----> the original price of a skateboard
y ----> the new price of a skateboard
we know that
The linear equation that represent this problem is equal to
y=x-15 ----> equation A
y=49 ---> equation B
substitute equation B in equation A and solve for x
49=x-15
Adds 15 both sides
49+15=x
64=x
Rewrite
x=$64
Write an equation for a rational function with:
Vertical asymptotes of x = 2 and x = -3
x intercepts of (-6,0) and (3,0)
Horizontal asymptote of y = 6
Use y as your output variable.
Answer:
y=(6(x+6)(x-3))/((x-2)(x+3))
Step-by-step explanation:
The vertical asymptote should be in the denominator. The x-interceps should be in the numerator. Because we have horizontal asymptote y=6, then we have to put 6 in the numerator. the horizontal asymptote is the leading coefficient of the numerator ÷ the leading coefficient of the denominator, when the degree of the numerator and denominator are the same.
Given the horizontal asymptote, vertical asymptotes and x intercepts, the equation of the rational function is y = 6((x+6)(x-3))/((x-2)(x+3)). The vertical asymptotes are found by setting the function's denominator equal to zero, while the x-intercepts come from setting the numerator to zero.
Explanation:In this question, we are asked to write the equation of a rational function based on given conditions. The function's vertical asymptotes are located at x = 2 and x = -3, and has x-intercepts at (-6,0) and (3,0), with a horizontal asymptote at y = 6.
The general form of a rational function is y = (ax+b)/(cx+d). Asymptotes help define the behavior and boundaries of the function. In this situation, we can set the denominator of our function equal to zero to find our vertical asymptotes, giving us (x-2)(x+3). To achieve our stated x-intercepts, we set the numerator equal to zero, providing (x+6)(x-3). Combining these, the function becomes y = ((x+6)(x-3))/((x-2)(x+3)). The output of the function approaches the horizontal asymptote as x approaches infinity. Thus to have y = 6 as our horizontal asymptote, we adjust our function to maintain this behaviour, settling on y = 6((x+6)(x-3))/((x-2)(x+3)).
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After graduating from college, Carlos receives two different job offers. Both pay a starting salary of
$62000 one job promises a $3720 raise per year. What will the salary be in one year
Answer:
$65720
Step-by-step explanation:
The job pays a starting salary of $62000, and raises $3720 per year. In one year, Carlos will be earning $62000 + $3720 = $65720
Final answer:
Carlos's salary in one year will be $65720, which is the sum of his starting salary, $62000, and the promised annual raise of $3720.
Explanation:
After graduating from college, Carlos has received two different job offers, both offering a starting salary of $62000, and one includes a promise of a $3720 raise per year. To calculate his salary in one year, we need to add this annual raise to his starting salary.
Starting salary: $62000
Raise after one year: $3720
Carlos's salary in one year: $62000 + $3720 = $65720
This computation shows that with the promised annual raise, Carlos's salary for the next year would be $65720.
The value of x is?
84
96
132
264
HELPPPP!!!!
Answer:
x =96 degree.
Step-by-step explanation:
Given : Triangle .
To find : The value of x is
Solution : We have given triangle
Exterior Angle sum property of triangle : Sum of all exterior angle of triangle is 360.
130 + 134 + x = 360 .
264 + x = 360.
On subtracting both sides by 264 .
x = 360 - 264 .
x = 96.
Therefore, x =96 degree.
Using Exterior Angle sum property of the triangle, The value of x will be 96 degree.
What is the Exterior Angle sum property?Exterior Angle sum property of the triangle states that the Sum of all exterior angles of the triangle is 360.
Given: Two exterior angles measure of 130 and 134 degrees.
To find: The value of x is
So,
130 + 134 + x = 360 .
264 + x = 360.
x = 360 - 264 .
x = 96.
Using Exterior Angle sum property of the triangle, The value of x will be 96 degrees.
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The length of a rectangle exceeds its width by 3
inches, and the area is 54 square inches. What
are the length and width of the rectangle?
Answer:
The length is 9 and the width is 6.
Step-by-step explanation:
6*9 = 54 and 9 is 3 greater than 6.
A pathway divides a rectangular garden into two parts as shown. Find the measure of angle A
Answer:
m < A = 101 degrees.
Step-by-step explanation:
The transverse line crosses 2 parallel lines (opposite angles of a rectangle are parallel) , so the same side angles add up to 180 degrees.
m < A + 79 = 180
m < A = 101 degrees.
Answer:
A=101°
Step-by-step explanation:
The two lengths of the rectangle are parallel and therefore the sides of the path form two parallel transversals.
The angle marked 79° and the angle marked A are supplementary ( they add up to 180°)
A+79=180°
A=180-79
=101°
which geometric object is defined as the set of ballpoints in a plane at a given distance A.Parabole B. Line segment C. Line D. circle
Answer:
Answer is Circle
Step-by-step explanation:
Check the picture below.
notice, all points are equidistant from the center of it, wherever the center happens to be.
PLEASE HELP AND ANSWER!!!!! Which of the following reveals the minimum value for the equation 2x2 + 12x − 14 = 0?
2(x + 6)2 = 26
2(x + 6)2 = 20
2(x + 3)2 = 32
2(x + 3)2 = 30
Answer:
The correct option is 3.
Step-by-step explanation:
The given equation is
[tex]2x^2+12x-14=0[/tex]
It can be written as
[tex](2x^2+12x)-14=0[/tex]
Taking out the common factor form the parenthesis.
[tex]2(x^2+6x)-14=0[/tex]
If an expression is defined as [tex]x^2+bx[/tex] then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.
In the above equation b=6.
Add and subtract 3^2 in the parenthesis.
[tex]2(x^2+6x+3^2-3^2)-14=0[/tex]
[tex]2(x^2+6x+3^2)-2(3^2)-14=0[/tex]
[tex]2(x+3)^2-18-14=0[/tex]
[tex]2(x+3)^2-32=0[/tex] .... (1)
Add 32 on both sides.
[tex]2(x+3)^2=32[/tex]
The vertex from of a parabola is
[tex]p(x)=a(x-h)^2+k[/tex] .... (2)
If a>0, then k is minimum value at x=h.
From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.
The equation [tex]2(x+3)^2=32[/tex] reveals the minimum value for the given equation.
Therefore the correct option is 3.
The correct answer is option 3. [tex]2(x + 3)^2 = 32[/tex].
To find the minimum value of the quadratic equation [tex]2x^2 + 12x - 14[/tex] = 0, we can rewrite it in vertex form, which reveals the minimum or maximum value of a quadratic function.
The given options are attempts at rewriting the quadratic equation in vertex form. Let’s rewrite the equation:
First, complete the square:
1. Start with the equation: [tex]2x^2 + 12x - 14[/tex]
2. Factor out the coefficient of x² from the first two terms: [tex]2(x^2 + 6x) - 14[/tex]
3. Complete the square inside the parentheses:
- Take [tex](\frac{6}{2})^2 =9[/tex] - Add and subtract 9 inside the parentheses: [tex]2(x^2 + 6x + 9 - 9) - 14[/tex]
- Simplify inside the square: [tex]2((x + 3)^2 - 9) - 14[/tex]
4. Distribute and simplify: [tex]2(x + 3)^2 - 18 - 14 = 2(x + 3)^2 - 32[/tex]
Comparing this with the options, we have [tex]2(x + 3)^2 = 32[/tex].
The correct answer is: [tex]2(x + 3)^2 = 32[/tex].