Answer:
-38. I did something like this before
Solve the equation x^2 - 4x + 6 = 9 by completing the square.
Hello!
x² - 4x + 6 = 9 <=>
<=> x² - 4x + 6 - 9 = 0 <=>
<=> x² - 4x - 3 = 0 <=>
<=> x = -(-4)±√(-4)²-4×1×(-3)/2×1 <=>
<=> x = 4±√16+12/2 <=>
<=> x = 4±√28/2 <=>
<=> x = 4±2√7/2 =>
=> x = 4+2√7/2 and x = 4-2√7/2 =>
=> x = 2+√7 and x = 2-√7
The equation has two solutions.
Good luck! :)
Answer: [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
how i got it?
[tex]x^2 - 4x + 6 = 9[/tex]
*subtract 9 on both sides*
[tex]x^2 - 4x + 6 - 9 = 0[/tex] ( which turns to) [tex]x^2 - 4x - 3=0[/tex]
a=1 or x, b=-4, c=-3
Step 2: Use quadratic formula with a=1, b=-4, c=-3.
[tex]x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)[/tex]
which turns to: x= 4 + or - √28 divided by 2
the final answer should be [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
help with geometry!!!!!
Answer:
NO
Step-by-step explanation:
To find the length of AB
AB = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( 2 - -1)^2+ ( -1 -3)^2)
= sqrt( 3^2 + (-4)^2)
= sqrt(9+16)
= sqrt(25)
= 5
To find the length of AC
AC = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( -4 - -1)^2+ ( -1 -3)^2)
= sqrt( ( -3)^2 + (-4)^2)
= sqrt(9+16)
= sqrt(25)
= 5
To find the length of BC
BC = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( -4-2)^2+ ( -1 --1)^2)
= sqrt( ( -6)^2 + (0)^2)
= sqrt(36)
= 6
This is not an equilateral triangle since BC is not equal to AB = AC
Answer:
AB = AC = 5 units BC = 6 units No it is not a equilateral triangleStep-by-step explanation:
Some coordinates of a triangle is given to us. And we need to find the length of AB , BC and AC . The given coordinates are ,
[tex]\rm\implies Coordinates = A(-1,3) , B(2,-1) \ and \ C(-4,-1) [/tex]
We can use the Distance Formula to find the length of sides of the triangle .
Finding length of AB :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{AB}= \sqrt{ (-1-2)^2+(-1-3)^2} \\\\\rm\implies \overline{AB}= \sqrt{ (-3)^2+(-4)^2} \\\\\rm\implies \overline{AB}= \sqrt{ 9 + 16} \\\\\rm\implies \overline{AB}= \sqrt{25} \\\\\rm\implies\boxed{\red{\rm \overline{AB}= 5 \ units}}[/tex]
Finding length of AC :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{AC}= \sqrt{ (-1+4)^2+(-1-3)^2 }\\\\\rm\implies \overline{AC}= \sqrt{ (-3)^2+(-4)^2} \\\\\rm\implies \overline{AC}= \sqrt{ 9 + 16} \\\\\rm\implies \overline{AC}= \sqrt{25} \\\\\rm\implies\boxed{\red{\rm \overline{AC}= 5 \ units}}[/tex]
Finding length of BC :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{BC}= \sqrt{ (-4-2)^2+(-1-1)^2} \\\\\rm\implies \overline{BC}= \sqrt{ 6^2+0^2} \\\\\rm\implies \overline{BC}= \sqrt{ 36+0} \\\\\rm\implies \overline{BC}= \sqrt{36} \\\\\rm\implies\boxed{\red{\rm \overline{BC}= 6 \ units}}[/tex]
Is it a Equilateral triangle ?
No the given triangle is not a equilateral triangle since the measure of all sides is not same.
Find the value of x.
Find the following sums. Please help.
Answer:
5m-n-4p
4a^2+6x-3
Step-by-step explanation:
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
Combine like terms
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
(3-5+7)m +(-4+9-6)n +(7-6-5)p
5m-n-4p
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
Combine like terms
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
(1+1+2)a^2 +(-3+9+0)x +(1-6+2)
4a^2+6x-3
#1
[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]
[tex]\\ \sf\longmapsto 5m-n-4p[/tex]
#2
[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]
[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]
[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]
Please answer only questions 18 and 20 please help me
Answer:
18 is 64 days
20 is 1 37/128
Step-by-step explanation:
I looked it up if I am being completely honest with you but it should be correct
what is the volume of the cylinder?
write you answer in terms of pi
The volume of a cylinder is V=πr^2*h.
The volume of this cylinder is V=π(7)^2*12, which it V=588π.
Which graph represents an exponential function?
Answer: where's the pic?
Step-by-step explanation:
Ms. Jones wants to paint her kitchen's wall. She knows that 2 gallons of paint cover 80 square feet, and each gallon costs $20.80. If the area of the kitchen is 320 square feet, how much will she pay to buy the gallons of paint needed? Round your answer to the nearest cent (HUNDRED TH), and write ONLY a number (NO $)
− 10x− 6y= 12
4x+ 7y=− 14
Answer:
x = 0, y = -2
Step-by-step explanation:
[tex]\left \{ {{-10x-6y=12} \atop {4x+7y=-14}} \right. = \left \{ {{-10x=12+6y} \atop {4x+7y=-14}} \right. = \left \{ {{x=\frac{12+6y}{-10} }(1) \atop {4x+7y=-14}} \right[/tex]
Replace x from formula (1) to formula (2), we got:
[tex]4*\frac{12+6x}{-10}=-14 <=> \frac{-2}{5}(12+6y)+7y=-14 <=> \frac{-24}{5} + \frac{-12}{5}y+7y=-14 <=> \frac{23}{5}y = \frac{-46}{5} <=> y = -2\\=> x= \frac{12+6*(-2)}{-10} = 0[/tex]
Evaluate the expression for x = 10 . 3x + 4(x - 8) - 14
Answer:
[tex]{ \tt{3x + 4(x - 8) - 14}} \\ = { \tt{3x + 4x - 32 - 14}} \\ = { \tt{7x + 46}}[/tex]
Alyssa invested $180 in an account paying an interest rate of 8 and 3/8 % compounded annually. Lily invested $180 in an account paying an interest rate of 8 and 1/8 % compounded continuously. To the nearest hundredth of a year, how much longer would it take for Alyssa's money to triple than for Lily's money to triple?
Answer:
Step-by-step explanation:
Please check out the attachments for the solution :)
Hanz’s class had a goal to collect 250 cans of food for the school food drive. They collected 290 cans. What percent of their goal did they achieve?
Given:
Goal = 250 cans
Number of collected cans = 290
To find:
The percent of their goal they achieved.
Solution:
The percent of their goal they achieved is:
[tex]\text{Required percent}=\dfrac{\text{Number of collected cans}}{\text{Goal}}\times 100[/tex]
[tex]\text{Required percent}=\dfrac{290}{250}\times 100[/tex]
[tex]\text{Required percent}=\dfrac{29}{25}\times 100[/tex]
[tex]\text{Required percent}=29\times 4[/tex]
[tex]\text{Required percent}=116[/tex]
Therefore, they achieved 116% of their goal.
which one of these numbers is a whole number?
Answer:
0 is the whole number
Step-by-step explanation:
negative numbers are negative so they can't be counted as whole numbers which means -5 isn't an option.
Whole numbers can't be stated in fraction form so 2/3 is not applicable here.
32.8 is also not the answer as decimals are part of a whole number, not actual whole numbers.
so, 0, is the only right answer here
Susan's graduation picnic will cost $78 if it has 26 attendees. At most how many attendees can there be if Susan budgets a total of $81 for her graduation picnic?
Answer:
27 attendees
Step-by-step explanation:
First, we can find the cost per attendee.
78÷26
3
So $3 per attendee.
Then divide 81 by 3 to find the number of possible attendees.
81÷3=27
I hope this helps!
y is directly proportional to the cube of x. If x is tripled, what happens to the value of y?
Answer:
it becomes 27 times larger
Step-by-step explanation:
y = k [tex]x^{3}[/tex]
vs.
y = k[tex](3x)^{3}[/tex]
y = k 27 x^3
What is the greatest common factor of the polynomial below?
12x2-9x
A. 3x2
B. 3x
C. 4x2
D. 4x
Answer:
3x
Step-by-step explanation:
factoring it we get
3x(4x-3)
The legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
show work.
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 +10 ^2 = c^2[/tex]
2. [tex]c^2 = 125[/tex]
3. [tex]c = 5\sqrt{5}[/tex]
Answer:
approximately 11.18 inches or [tex]5\sqrt{5[/tex] inches
Step-by-step explanation:
We have to use Pythagorean Theorem for this problem. a^2 + b^2 = c^2, where c is the hypotenuse and a/b are legs of the right triangle.
5^2 + 10^2 = c^2, 25 + 100 = c^2, 125 = c^2, sqrt125 = c
sqrt125 can be simplified to 5sqrt5 (25 * 5 = 125, sqrt25 = 5)
The hypotenuse is approximately 11.18 inches or [tex]5\sqrt{5[/tex] inches.
Determine the value of K that will cause f(x)=Kx^2+4x-3 to intersect the line g(x)=2x-7 at one point. SHOW ALL YOUR STEPS, DON'T USE DECIMALS INSTEAD USE FRACTIONS PLEASE!!!!!
Given:
The function are:
[tex]f(x)=Kx^2+4x-3[/tex]
[tex]g(x)=2x-7[/tex]
The graph of f(x) intersect the line g(x) at one point.
To find:
The value of K.
Solution:
The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.
We have,
[tex]f(x)=Kx^2+4x-3[/tex]
Differentiate this function with respect to x.
[tex]f'(x)=K(2x)+4(1)-(0)[/tex]
[tex]f'(x)=2Kx+4[/tex]
Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:
[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]
On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get
[tex]m=2[/tex]
So, the slope of the tangent line is 2.
[tex]2Kx_0+4=2[/tex]
[tex]2Kx_0=2-4[/tex]
[tex]x_0=\dfrac{-2}{2K}[/tex]
[tex]x_0=-\dfrac{1}{K}[/tex]
Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get
[tex]y_0=2x_0-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get
[tex]y_0=2(-\dfrac{1}{K})-7[/tex]
[tex]y_0=-\dfrac{2}{K}-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).
[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]
Multiply both sides by K.
[tex]-2-7K=-3-3K[/tex]
[tex]-2+3=7K-3k[/tex]
[tex]1=4k[/tex]
[tex]\dfrac{1}{4}=K[/tex]
Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].
Which of the equations below could be the equation of this parabola?
O A. y = -1/2 x2
O B. y = 1/2 x2
O C. y= 1/2 y2
O D. x= -1/2 y2
After answering the question provided, we can predict that the result will be as The position and direction of the relevant parabola will determine the appropriate response.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
It is hard to tell which equation may be the equation of the parabola without further details on the parabola's orientation and location.
The equations in options A and B are parabolas with upward or downward openings and a vertex at the origin. The equation of a parabola with its vertex at the origin and an opening to the right or left is in Option C. The equation of a parabola with an upwards or downwards opening and its vertex at the point is in Option D. (0,0).
The position and direction of the relevant parabola will determine the appropriate response.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Find the greatest common factor of 15 x²y³ and -18 x³yz.
_x--y--
Answer:
3x^2y
Step-by-step explanation:
Its common factor it this ^ this symbol represent power
What is the measure of
60° because it's an equilateral triangle
Which is the pair of congruent right angles?
Answer:
2nd
2nd option <cba=<dea
Answer:
B
as DE=CB
<C=<D
<B= <E
Therefore it is congruent
Have a nice day!
What is the quotient ? 7-6 72 1 o 1 o 1 72 O 73 0 78
Answer:
A. 1/7^8
Step-by-step explanation:
Given
(7^-6) / 7²
Both numerator and denominator has the same base, so just one of the bases will be picked
Division sign changes to minus in indices
(7^-6) / 7²
= 7 ^(-6-2)
= 7^-8
= 1/7^8
Note: a^-b
= 1/a^b
The same rule is used at the last step of the calculation
Answer is
A. 1/7^8
Find the slope of the line for each pair of points (-17, -5) (15, -13)
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer. PLEASE HELP ITS RLLY IMPORTANT
Kevin jogged 2 1/2 miles in 1/3 of an hour. What was his average rate in speed in miles per hour? Show your work.
Answer:
7.5 miles per hour
Step-by-step explanation:
Average Speed = Total Distance/Total Time
[tex]\frac{2 \frac{1}{2} }{\frac{1}{3} }[/tex]= 7.5 miles/hour
Answer from Gauthmath
The diameter of a cylinder is twice the height (h) of the cylinder. Show that the total surface area of the cylinder is:
[tex]4\pi \ {h}^{2} [/tex]
Answer:
Please check explanations
Step-by-step explanation:
The diameter is twice the height;
if diameter is d and height is h
Then;
d = 2h
But, we know that the radius is half the diameter size. Which means that the diameter is twice the radius
Thus;
2r = 2h
Then r = h
Mathematically the total surface area of a cylinder is;
2pi r (r + h)
substitute h for r
2pi h(h + h)
= 2pi * h * 2h
= 4 pi h^2 (QED)
You have to evaluate the question for a and b
Answer:
11
Step-by-step explanation:
a+b^2
Let a=2 and b=3
2+3^2
2 + 9
11
Answer: 11
2 + (3 x 3 )
2 + 9
The required answer would be 11 :)
Step-by-step explanation:
Find the area of the circle x^2+y^2=16 by the method of intregration
Answer:
Hello,
[tex]16\pi[/tex]
Step-by-step explanation:
[tex]I=\dfrac{Area}{4} =\int\limits^4_0 {\sqrt{16-x^2} } \, dx \\\\Let\ say\ x=4*sin(t),\ dx=4*cos(t) dt\\\\\displaystyle I=\int\limits^\frac{\pi }{2} _0 {4*\sqrt{1-sin^2(t)} }*4*cos(t) \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {cos^2(t)} \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {\frac{1-cos(2t)}{2}} \, dt \\\\=8*[t]^\frac{\pi }{2} _0-[\frac{sin(2t)}{2} ]^\frac{\pi }{2} _0\\\\=4\pi -0\\\\=4\pi\\\\\boxed{Area=4*I=16\pi}\\[/tex]
flor ha colocado ¹1/4 kg de papa sobre una balanza . si un cliente le quiere comprar 2 kg de papa , ¿cuantos kilogramos (kg) de papa debe agregar flor sobre l balanza para cumplir con el pedido?
a)3/4 kg de papa
b)¹ 3/4 kg de papa
c1/4 kg de papa
d)¹ 1/4
RAPIDO POR FAVOR E UN EXAMEN SALVEMME LA VIDA
Answer:
a). 3/4 kg de papa
Step-by-step explanation:
Given that,
Patata colocada en balanza = 1 1/4 Kg
Flor de papa total quiere = 2 kg
Encontrar,
Se agregará más peso en la báscula para que sea de 2 kg =?
Procedimiento:
Peso requerido para ser colocado = Peso total - peso colocado
= 2 - [tex]1\frac{1}{4}[/tex]
= 2 - 5/4
= (8 - 5)/4
= 3/4 kg
