The solution of the given equation is [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Given equation:-
[tex](x+3)^2=6[/tex]
We have to find the value of x by solving the given equation.
We can rewrite the given equation as:-
[tex]x^2+6x+9=6\\x^2+6x+3=0[/tex]
We can solve the the quadratic equation by finding the discriminant.
[tex]x = \frac{-6+-\sqrt{6^2-4*1*3} }{2*1}[/tex]
[tex]x = \frac{-6+-\sqrt{36-12} }{2}[/tex]
[tex]x=\frac{-6+-2\sqrt{6} }{2}=-3+-\sqrt{6}[/tex]
Hence, the values of x are [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Discriminant
In arithmetic, a polynomial's discriminant is a function of the polynomial's coefficients.
Quadratic equation
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
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I need help to know how to solve graphing a system of inequalities2x - 3y > -12x + y ≥ -2
Answer
2x - 3y > -12 (in red ink)
x + y ≥ -2 (in black ink)
The solution region is the region that the two shaded regions have in common.
Explanation
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
Step 1
For this question, we easily see that the first inequality will have a broken line and the second one will have an unbroken line.
To plot each of the lines, we will use intercepts to obtain the coordinates of two points on each line
Recall, we will first plot the lines like they are equations of a straight line.
To plot the graph
2x - 3y = -12
when x = 0,
2(0) - 3y = -12
-3y = -12
Divide both sides by -3
(-3y/-3) = (-12/-3)
y = 4
First point on the line is (0, 4)
when y = 0
2x - 3(0) = -12
2x = -12
Divide both sides by 2
(2x/2) = (-12/2)
x = -6
Second point on the line is (-6, 0)
For the second line,
To plot the graph,
x + y = -2
when x = 0
0 + y = -2
y = -2
First point on the line is (0, -2)
when y = 0
x + 0 = -2
x = -2
Second point on the line is (-2, 0)
So, for the plotting, we connect the two points for each of the lines.
Step 2
The shaded region now depends on whether the inequality sign is facing y or not.
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
2x - 3y > -12
Can be rewritten as
-3y > -2x - 12
Divide through by -3 (this changes the inequality sign)
y < (2x/3) + 4
Here, we see that the inequality sign is not facing y, hence the numbers below the broken line plotted are the shaded region (in red ink)
x + y ≥ -2
We can rewrite this as
y ≥ -x - 2
Here, we see that the the inequality sign is facing y, hence, the numbers above the unbroken line plotted are the shaded region (in black ink)
The graph of this system of inequalities is presented above under 'Answer'
Hope this Helps!!!
Which of the following best describes terms that have the same degree in the same radicand? A. like rational termsB. like fractional termsC. like radical termsD. like polynomial terms
Two radical expressions are called like terms if they have the same degree and the same radicand.
So, like radical terms, best describes terms that have the same degree and the same radicand.
Like radicals are those, that have the same root number and radicand.
So, the correct answer is option C.
Ronda ate 2/5 of the pie. Connor ate .375 of the pie. How much did they eatcombined? (Express your answer either as a fraction or decimal)
To convert 2/5 to a decimal;
[tex]undefined[/tex]Factor the expression. 12y + 14
Answer:
2(6y+7)
Explanation:
To factor the expression:
[tex]12y+14[/tex]First, find the greatest whole number that divides 12 and 14.
The number = 2, therefore:
[tex]\begin{gathered} 12y+14=2\mleft(\frac{12y}{2}+\frac{14}{2}\mright) \\ =2(6y+7) \end{gathered}[/tex]What is the equation, in slope-intercept form, of a line that passes through the points(-8,5) and (6,5)?
Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,5) \\ (x_2,y_2)=(6,5) \\ \Rightarrow m=\frac{5-5}{6-(-8)}=\frac{0}{6+8}=0 \\ m=0 \end{gathered}[/tex]since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:
[tex]y=5[/tex]in slope-intercept form the equation would be:
[tex]y=0x+5[/tex]Determine the height of the lift, in metres, above the gym floor. show all your work algebraically. round to the nearest cm, if necessary.
Height of lift = x + x = 2x
We can find x using triangle ABC by the cosine rule
[tex]\begin{gathered} x^2=5.6^2+5.6^2-2(5.6)(5.6)\cos40^0 \\ x^2=62.72-48.04352 \\ x^2=14.67648 \\ x=\sqrt{14.67648} \\ x=3.831m \end{gathered}[/tex]Height of lift = 2 X 3.831m = 7.662m
This will be converted to cm by multiplying by 100
Height of lift = 7.662 X 100 cm
= 766.2 cm
= 766cm ( nearest cm )
Hence the answer is 766cm
I’ve already done this problem, but I’m being told it’s wrong and I need to simplify but I don’t know how to do it with this question.
Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?
Notice that:
[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]Therefore 3 is a root of the given polynomial.
Now, we can use this root to factor the polynomial:
[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]Using the synthetic division algorithm we get that:
[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]The roots of the above polynomial are:
[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]Therefore:
[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]Answer:
[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]You draw 7 cards from a standard deck of cards. What is the probability of drawing 3 diamonds and 2 clubs?
Solution
For this case we can do the following:
[tex]p=\frac{\text{possible}}{\text{total}}[/tex]and we can find the answer with this:
[tex]p=\frac{(13C3)(13C2)(26C2)}{52C7}=0.0541[/tex]Answer below! Thank you :) and try to explain how you got it!
The value of the equation that we have here is given as 16r² + 24
How to solve the expressionThe equation that we are to simplify here is given as -2r(-13r+5r-12).
In order to open the brackets we would have to multiply -2r with all of the values that are in the bracket.
The mathematical signs that are used in the question have to be well thought of as well before the calculation is done
We would have 26r² - 10r² + 24
26r² - 10r² + 24
because they have the same powers they would be able to subtract
16r² + 24
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Linear Expressions MC)
Simplify -2r(-13r+5r-12).
O-162-24r
162+24
162+24r
O-162 + 24r
Rick buys a $4,500 stove with an installment plan that requires 12% down. How much
is the down payment?
O $540
O $375
O $250
O $125
Answer: 540
Step-by-step explanation: 12% of 4500 is 540
If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?
There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row
The probability of selecting two solid chocolates in a row is 0.0607 .
In the question ,
it is given that
there are total 39 chocolates in the box .
number of chocolates filled with nuts = 16
number of chocolates filled with caramel = 13
number of chocolates filled with solid = 10
Probability of selecting first chocolate as a solid is 10/39.
Now , there are 38 chocolates , with 9 solid chocolates ,
hence the probability of selecting second chocolate as a nut is = 9/38
So, the probability of selecting two solid chocolates in a row = 10/39×9/38
= 90/1482
= 0.0607
Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .
The given question is incomplete , the complete question is
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
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there are 14 square and 18 rectangles. what is the simplest ratio of squares to rectangles?
The simplest ratio of squares to rectangles can be obtained as follows:
There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:
[tex]\frac{14}{18}=\frac{7}{9}[/tex]Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.
The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?
As given by the question
There are given that area of rectangle and width of a rectangle
[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]Now,
From the formula of area of a rectangle:
[tex]\text{Area}=\text{length}\times width[/tex]Then,
Put the value of an area and width into the above formula
So,
[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]Then,
[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]Hence, the value of length is ( b + 6 ).
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2
We have to calculate the zeros of the function with the quadratic formula.
[tex]f(x)=x^2-8x+2[/tex][tex]\begin{gathered} x=\frac{-(-8)}{2\cdot1}\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=\frac{8}{2}\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{\frac{56}{4}}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}[/tex]The roots are x1=7.742 and x2=0.258, both reals., both
Sean johnson 1. The angles of a triangle are described as follows: angle A is the largest angle: its measure is twice the measure of angle B. The measure of angle C is 2 less than half the measure of angle B. Find the measures of the three angles in degrees.
Explanation
Let
angle A is the largest angle
[tex]m\measuredangle A=m\measuredangle A[/tex]its measure is twice the measure of angle B,( in other words you have to multiply angle b by 2, to get angle A)
[tex]2(m\measuredangle B)=m\measuredangle A[/tex]how do we do this one there two parts to i t
Given:
[tex]8\sqrt{y}=x-5y[/tex]Find: differentiation
Explanation: on differentitaion with respect to x
[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex][tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]put the value of
[tex]\frac{dy}{dx}[/tex]we get,
[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]A reflection across which line(s) carries the trapezoid onto itself?
If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.
Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
EXPLANATION
The probability that Event A happening is the following:
[tex]P(A)[/tex]
The probability of Event A not happening is the following:
[tex]100-P(A)[/tex]Therefore, we have:
[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]Plugging in the terms into the expression:
1.8 + P(Not malfunctioning) = 100%
Subtracting -1.8 to both sides:
[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]Subtracting numbers:
[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]In conclusion, the probability of not malfunctioning is 0.982
theres 2 fill in the blank boxes and 3 drop down menus, below i will list the options in the drop down menus.box 1 - apply quotient identities, apply Pythagorean identities, apply double-number identities, apply even-odd identities.box 2 - apply cofunction identities, use the definition of subtraction, apply even-odd identities, Write as one expresssion combine like terms.box 3 - apply cofunction identities, apply double-number identities, apply Pythagorean identities, apply even-odd identities.
Solution
Box 1 : Apply Quotient Identities
[tex]cotx-tanx=\frac{cosx}{sinx}-\frac{sinx}{cosx}[/tex]The answer for the first box is
[tex]\begin{equation*} \frac{cosx}{sinx}-\frac{sinx}{cosx} \end{equation*}[/tex]Box 2: Write as one expression
[tex]\begin{gathered} cotx-tanx=\frac{cosx}{s\imaginaryI nx}-\frac{s\imaginaryI nx}{cosx} \\ cotx-tanx=\frac{cosx(cosx)-sinx(sinx)}{sinxcosx} \\ cotx-tanx=\frac{cos^2x-sin^2x}{sinxcosx} \end{gathered}[/tex]The answer for the second box is
[tex]\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx}[/tex]Before the box 3, please note the identity
Note: Trigonometry I dentities
[tex]\begin{gathered} cos^2x-s\mathrm{i}n^2x=cos2x \\ 2sinxcosx=sin2x \end{gathered}[/tex]Box 3: Apply Double - Number Identities
[tex]\begin{gathered} cotx-tanx=\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx} \\ Applying\text{ the above trigonometry identities} \\ cotx-tanx=\frac{cos2x}{sinxcosx} \\ cotx-tanx=\frac{cos2x}{sinxcosx}\times\frac{2}{2} \\ cotx-tanx=\frac{2cos2x}{2sinxcosx} \\ cotx-tanx=\frac{2cos2x}{sin2x} \end{gathered}[/tex]It goes from -1 to 1 on the x axis.
ANSWER :
EXPLANATION :
Solve for y Simplify your answer as much as possible Find by linear equation.
Given the equation:
[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]We will solve the equation to find y
Multiply the equation by 4 to eliminate the denominators
[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]Combine the like terms
[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]Subtract (17) to both sides
[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]Divide both sides by (-15)
[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]So, the answer will be y = 3
For the equation E=, h is a proportionality con- stant. When 1-14, E =20. So, if n=7, what is the conesponding value of 6? O 40 O 0.1 O 10 0 0.025 O 0.25
Substitute 14 for n and 20 for E in the equation to determine the value of proportionality constant.
[tex]\begin{gathered} 20=\frac{h}{14} \\ h=20\cdot14 \\ =280 \end{gathered}[/tex]Substitute 280 for h and 7 for n in the equation to obtain the value of E.
[tex]\begin{gathered} E=\frac{280}{7} \\ =40 \end{gathered}[/tex]So value of E is 40.
Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.
Let call w the number of weeks she has been saving.
Then, we can write the expression for her saving in function of the number of weeks as:
[tex]S(w)=105+30\cdot w[/tex]We now have to find the number of weeks it will take for her savings to reach $720.
We can find it by calculating w for S(w)=720:
[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]Answer: it will take her 21 weeks to have enough savings.
in the graph below line k,y = -x makes a 45 degree angle with the X and Y axes complete the following
The point with a coordinate of (2,5) will be translated into y=-x line.
The transformation for y=-x would be:
1. x'= -y
2. y'= -x
For x=2 and y=5 would be:
x'= -y
x'= -5
y'= -x
y'= -2
The translated coordinate would be: (-5, -2)
3 A free diver can dive at a rate of -0.75 meters per second. About how long would it take to reach a depth of -145 meters?
Answer:193.33s or 3.2 mins
Step-by-step explanation:
Here the diver dives at -0.75 constant velocity. So we can use the formula s = vt
from there we can find out the time when s = -145 m and v = -0.75m/s
Question
Find the values for x and y .
Step-by-step explanation:
6x+3=75° ( being alternate angle )
6x = 72°
x=12
75+45+y= 180
y= 60°
I’ve been trying to figure out how to solve this and was wondering how to do this correctly!
SOLUTION
To solve this we will use the form for exponential growth to determine the formula to use.
Exponential growth has the form
[tex]\begin{gathered} P=P_0e^{rt} \\ P=\text{population after timer t} \\ P_0=\text{ initial population growth } \\ r=\text{ percent growth rate} \end{gathered}[/tex]Now the frogs tripple in population after 9 days. Initially they were 21. So in 9 days they become
[tex]21\times3=63\text{ frogs }[/tex]Applying the formula, we have
[tex]\begin{gathered} P=P_0e^{rt} \\ 63=21e^{9r} \\ 3=e^{9r} \\ \text{taking ln of both sides } \\ \ln 3=\ln e^{9r} \\ \ln 3=9r \\ r=\frac{\ln3}{9} \end{gathered}[/tex]The time for the frogs to get to 290 becomes
[tex]undefined[/tex]Four more than three times a number, is less than 30. Which of the following is not a solution?61278
Solution
- To solve the question, we simply need to interpret the question line by line.
- Let the number be x.
- "Four more than three times a number" can be written as:
[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]- "Four more than three times a number is less than 30" can be written as:
[tex]4+3x<30[/tex]- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:
[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]- This means that all correct solutions to the inequality lie below 8.666...
- This further implies that any number greater than this is not part of the solutions of the inequality.
- 12 is greater than 8.666
Final Answer
The answer is 12