Answer:
[tex]\large\boxed{x^2+11x+24=0\Rightarrow(x+5.5)^2=6.25}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\x^2+11x+24=0\qquad\text{subtract 24 from both sides}\\\\x^2+(2)(x)(5.5)=-24\qquad\text{add}\ 5.5^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(5.5)+5.5^2}_{(*)}=-24+5.5^2\\\\(x+5.5)^2=-24+30.25\\\\(x+5.5)^2=6.25\Rightarrow x+5.5=\pm\sqrt{6.25}\\\\x+5.5=-2.5\ \vee\ x+5.5=2.5\qquad\text{subtract 5.5 from both sides}\\\\x=-8\ \vee\ x=-3[/tex]
To rewrite x^2 + 11x + 24 = 0 by completing the square, we first organize terms, then add the square of half the coefficient of x to both sides to create a perfect square. Taking the square root of both sides then provides the solution for x, resulting in x = -5.5 ± √6.25.
Explanation:To rewrite the equation x^2 + 11x + 24 = 0 by completing the square, we first need to make the quadratic and linear terms to create a square.
1. Rewrite the equation as: x^2 + 11x + __ = -24 + __
2. Take half of the coefficient of x, (11/2) and square it. (11/2)^2 = 30.25
3. Add this value on both sides of the equation:
x^2 + 11x + 30.25 = -24 + 30.25
4. Now, the left side of the equation is a perfect square and it can be written as:
(x + 5.5)^2 = 6.25
5. Finally, to solve for x, take the square root of both sides to get:
x + 5.5 = ± √6.25
x = -5.5 ± √6.25
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Which equation represents a circle with a center Jat (-3, -5) and a radius of 6 units?
(x - 3)2 + (y – 5)2 = 6
(x - 3)2 + (y – 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
[tex]\large\boxed{(x+3)^2+(y+5)^2=36}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center at (-3, -5) and the radius r = 6. Substitute:
[tex](x-(-3))^2+(y-(-5))^2=6^2\\\\(x+3)^2+(y+5)^2=36[/tex]
Does 6 (x + 5) = 6x + 11 have one solution ?
6(x + 5) = 6x + 11
6x + 30 = 6x + 11
now, let's take a peek at both equations on the sides of the equal sign, since they're both in slope-intercept form, y = mx+b.
the left-hand-side has a slope of "6".
the right-hand-side has a slope of "6".
well, that's a flag that both lines are parallel.
now, they have different y-intercepts, one has 30 the other 11, that means one line is above the other, however they're both parallel, so they will never meet and thus do not have a solution, since recall that a solution is where they both meet or intersect.
What are all of the keys that must be pressed, in correct order, on the calculator
Find the quotient. x + 4/x2 ÷ 2 /x
The simplified form of the expression [tex]\( \frac{x + 4}{x^2} \div \frac{2}{x} \) is \( \frac{x + 4}{2x} \).[/tex]
To simplify the given expression, we'll first deal with the division of fractions by turning it into multiplication with the reciprocal of the divisor.
So, the given expression [tex]\( \frac{x + 4}{x^2} \div \frac{2}{x} \)[/tex] becomes:
[tex]\[ \frac{x + 4}{x^2} \times \frac{x}{2} \][/tex]
Next, let's factor the numerator x+4 and simplify:
[tex]\[ \frac{x + 4}{x^2} \times \frac{x}{2} = \frac{x + 4}{x^2} \times \frac{x}{2} = \frac{(x + 4) \cdot x}{x^2 \cdot 2} \][/tex]
Now, we'll simplify the expression by canceling out common factors:
[tex]\[ = \frac{x(x + 4)}{2x^2} \]\[ = \frac{x(x + 4)}{2x^2} = \frac{x(x + 4)}{2x \cdot x} \][/tex]
[tex]\[ = \frac{x + 4}{2x} \][/tex]
−5 < 4x + 3 ≤ 14 how to solve this
[tex]\bf -5<4x + 3 \leqslant 14\implies \begin{cases} -5<4x+3\\ 4x+3 \leqslant 14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -5<4x+3\implies -8 < 4x\implies \cfrac{-8}{4}<x\implies \boxed{-2<x} \\\\[-0.35em] ~\dotfill\\\\ 4x+3\leqslant 14\implies 4x\leqslant 11\implies \boxed{x\leqslant \cfrac{11}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -2<x\leqslant \cfrac{11}{4}~\hfill[/tex]
you could also do it as a triplet at once
[tex]\bf -5<4x+3\leqslant 14\implies -8<4x\leqslant 11\\\\\\ \cfrac{-8}{4}<x\leqslant \cfrac{11}{4}\implies -2<x\leqslant \cfrac{11}{4}[/tex]
What is the solution to the equation
Answer:
-8
Step-by-step explanation:
Distribute.
-8x - 12 = 2x + 6 - 8x - 2
Combine like terms.
2x = -16
Divide by 2 on both sides
x = -8
Answer:
The solutions of given equations is x = -8
Step-by-step explanation:
It is given that,
-4(2x + 3) = 2x + 6 - (8x + 2)
To find the solution of given equation
-4(2x + 3) = 2x + 6 - (8x + 2)
-8x - 12 = 2x + 6 - 8x - 2
-8x - 12 = 4 - 6x
-8x + 6x = 4 + 12
-2x = 16
x = 16/(-2) = -8
Therefore the solutions of given equations is x = -8
PLEASE HELP :(
Given the system of linear equations. Choose all of the options that could be used to solve the system using addition
(x + y = 7
12x + y = 5
Multiply the first equation by-1 and add the equations together.
Multiply the second equation by -1 and the first equation by -1, then add the equations together.
Multiply the second equation by -1 and add the equations together.
Multiply the first equation by -2 and add the equations together.
Multiply the first equation by 2 and the second equation by -1, then add the equations together.
Answer:
First option: Multiply the first equation by-1 and add the equations together.
Third option: Multiply the second equation by -1 and add the equations together.
Step-by-step explanation:
The method to solve a system of equations using addition is known as Elimination Method.
The idea is to get an equation with one variable, solve for that variable to find its value and the substitute this into any original equation to find the value of the other variable.
In this case, multiplying the first equation by -1, you get:
[tex]\left \{ {{-x -y =-7} \atop {12x + y = 5}} \right.\\.................\\11x=-2\\\\x=-5.5[/tex]
[tex]x + y = 7\\\\-5.5+y=7\\\\y=12.5[/tex]
Multiplying the second equation by -1, you get:
[tex]\left \{ {{x + y = 7} \atop {-12x - y = -5}} \right.\\.................\\-11x=2\\\\x=-5.5[/tex]
[tex]x + y = 7\\\\-5.5+y=7\\\\y=12.5[/tex]
Answer:
The options that could be used to solve the system of linear equations are:
1. Multiply the first equation by -1 and add the equations together.
2. Multiply the second equation by -1 and add the equations together.
Step-by-step explanation:
Given two equations, what we need to solve them is apply some operations on each of them and add them in such a way that one of the variables cancels each other. Then we can simply solve for the other variable.
We have:
x + y = 7
12x + y = 5
We can multiply equation 1 by -1 and add the equations and then solve for x:
(-1)(x+y)=(-1)(7)
-x-y = -7 Now add it in equation 2:
-x-y + 12x+y = 5+7
11x = 12
x = 12/11
Then put x = 12/11 in one of the equations to get y.
Similarly we can multiply equation 2 by -1 and add the equations and follow the same steps afterwards.
whats measure of abd?
<ABD+<DBC=180 because they are supplementary angles.
180-<DCB-<BDC=<DBC because the sum of all the angles in a triangle is 180.
Combine these equations and solve for n:
<ABD+180-<DCB-<BDC=180
4n+6+180-60-2n=180
*Combine like termsI
2n+126=180
*Subtract 126 from both sides*
2n=54
*Divide both sides by 2*
n=27
Plug in 27 for n to calculate <ABD:
4(27)+6
<ABD=114
Hope this helps!!
Answer: It’s C 114 degrees
Step-by-step explanation: Just took the assignment
for any positive number b not equal to 1 and any number or variable n, evaluate the following expression. log_b(b^n)
Answer:
㏒b^bn = n
Step-by-step explanation:
Answer:
㏒b^bn = n
Step-by-step explanation:
Tyler knows that the ratio of male to female horses on the farm is 2 to 3. If there are 12 male horses, how many female horses are there?
20 POINTS
Answer:
18 female horses.
Step-by-step explanation:
By proportion 2 : 3 = 12 : x where x is the number of female horses.
12 / 2 = x / 3
2x = 3*12 = 36
x = 18.
Solve the following proportion for v. V/13=11/13
Round your answer to the nearest tenth.
Answer:
V = 11
Step-by-step explanation:
All you have to do here is to multiply both sides of this equation by 13. This will eliminate the fractions. You'll be left with V = 11.
To solve the proportion V/13 = 11/13, we can equate V to 11 since identical denominators imply equal numerators. No further calculations or rounding needed as V is a whole number.
Explanation:To solve the proportion V/13 = 11/13 for V, we can see that both sides of the equation are divided by the same number, 13. Since the denominators are equal, we can deduce that the numerators must also be equal for the proportion to be true.
Therefore, the value of V must be equal to 11, as V/13 matches 11/13. There is no need for further calculations or rounding since 11 is already a whole number.
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Solve for x in the diagram shown.
A) 2.7
B) 2.9
C) 3.0
D) 3.1
E) 3.2
The correct answer is C) 3.0. The value of [tex]x[/tex] is 3.0.
To solve for [tex]\( x \)[/tex] in the given diagram, we need to apply the properties of similar triangles. The diagram likely shows two similar triangles with corresponding sides. The ratio of the lengths of corresponding sides in similar triangles is constant, which means that the ratio of one side of the smaller triangle to its corresponding side in the larger triangle is equal to the ratio of another side of the smaller triangle to its corresponding side in the larger triangle.
Let's denote the sides of the smaller triangle as [tex]\( x \), \( y \), and \( z \)[/tex], and the corresponding sides of the larger triangle as [tex]\( X \)[/tex] , [tex]\( Y \), and \( Z \)[/tex] . Given that the triangles are similar, we have the following proportion:
[tex]\[ \frac{x}{X} = \frac{y}{Y} = \frac{z}{Z} \][/tex]
From the question, we are given the lengths of some of these sides. Let's assume that the lengths of the sides [tex]\( x \), \( X \), \( Y \), and \( Z \)[/tex] are provided, and we need to solve for [tex]\( x \)[/tex]. We can use the proportion involving [tex]\( x \)[/tex] and [tex]\( X \)[/tex] as well as [tex]\( Y \) and \( Z \)[/tex] to set up an equation:
[tex]\[ \frac{x}{X} = \frac{Y}{Z} \][/tex]
To solve for [tex]\( x \)[/tex], we multiply both sides of the equation by [tex]X[/tex]:
[tex]\[ x = \frac{Y}{Z} \cdot X \][/tex]
Now, we need to plug in the values for [tex]\( Y \), \( Z \),[/tex] and that [tex]\( X \)[/tex]are given in the diagram. Since the actual values are not provided in the conversation, we will assume that the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as a ratio, and [tex]\( X \)[/tex] is a single value. By multiplying this ratio by [tex]\( X \)[/tex] , we can find [tex]\( x \)[/tex].
Let's assume the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as [tex]\( \frac{3}{4} \)[/tex] and [tex]\( X \)[/tex] is given as 4. Then we have:
[tex]\[ x = \frac{3}{4} \cdot 4 \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, [tex]\( x \)[/tex] is 3.0, which corresponds to option C.
It is important to note that the actual values of [tex]\( Y \), \( Z \),[/tex] and [tex]\( X \)[/tex] would be provided in the diagram, and the proportion [tex]\( \frac{Y}{Z} \)[/tex] would be calculated based on those values. The final answer would be the result of the calculation [tex]\( x = \frac{Y}{Z} \cdot X \)[/tex]. In this case, the calculation led to the answer 3.0, which matches option C.
Simplify.
|-17|
|-17|=? (Simplify your answer.)
Answer:
17
Step-by-step explanation:
The absolute value of a number, negative or positive, always makes the number positive.
Answer:
The answer is 17
Step-by-step explanation:
-17 is 17 steps away from 0, so |-17| = 17...
Examine the two-step equation
-7/4 + x/4 = 2
Which property of operations allows you to add the same constant term to both sides
Answer:
The answer is C: Adition property of equality.
Hope this helps pls mark brainliest
Answer:
The answer is C: Addition property of equality.
Step-by-step explanation:I HOPE THIS HELPS!!!
If F(x) = 3x-2and g(x) = 2x+ 1,find (f-g)(x)
Answer:
(f - g)(x) = x - 3Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
We have f(x) = 3x - 2 and g(x) = 2x + 1. Substitute:
(f - g)(x) = (3x - 2) - (2x + 1)
(f - g)(x) = 3x - 2 - 2x - 1 combine like terms
(f - g)(x) = (3x - 2x) + (-2 - 1)
(f - g)(x) = x - 3
A hardware store sells light bulbs in different quantities. the graph shows the cost of various quantities. according to the graph, what is the cost of a single lightbulb?
Looking at the two black dots
5 bulbs cost $9
Divide total cost by number of bulbs bought:
9 / 5 = $1.80 per bulb.
10 bulbs cost $18
Divide total cost by number of bulbs bought:
18 / 10 = $1.80 per bulb
The cost for one bulb is $1.80
A parallelogram whose vertices have coordinates R(1, -1), S(6, 1), T(8, 5), and U(3, 3) has a shorter diagonal of ___ . 5 √(13) √(97)
Answer:
[tex]|SU|=\sqrt{13}[/tex]
Step-by-step explanation:
The given parallelogram has vertices R(1, -1), S(6, 1), T(8, 5), and U(3, 3) .
Recall the distance formula;
We use the distance formula to determine the length of the diagonals.
For diagonal R(1,-1) and T(8,5), We have;
[tex]|RT|=\sqrt{(8-1)^2+(5--1)^2}[/tex]
[tex]|RT|=\sqrt{(7)^2+(6)^2}[/tex]
[tex]|RT|=\sqrt{49+36}[/tex]
[tex]|RT|=\sqrt{85}[/tex]
For the diagonal S(6,1) U(3,3)
[tex]|SU|=\sqrt{(6-3)^2+(5-3)^2}[/tex]
[tex]|SU|=\sqrt{(3)^2+(2)^2}[/tex]
[tex]|SU|=\sqrt{9+4}[/tex]
[tex]|SU|=\sqrt{13}[/tex]
Therefore the shorter diagonal is:
[tex]|SU|=\sqrt{13}[/tex]
Help please! 20 points!
[tex]x+100+3x=180\\4x=80\\x=20[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{Note: This line/triangle have a degree of 180}[/tex]
[tex]\text{Firstly, you have to set up your equation, which is:}[/tex] [tex]\text{x + 100 + 3x =180}[/tex]
[tex]\text{Next, COMBINE your like terms: x + 3x}[/tex]
[tex]\text{x + 3x = 4x (Side note: the x by itself is equal to a(n) invisible 1)}[/tex]
[tex]\text{100 stays the same because it doesn't have a like term}[/tex]
[tex]\text{4x + 100 = 180}[/tex]
[tex]\text{Thirdly, we have to SUBTRACT by 100 on your sides:}[/tex] [tex]\text{4x + 100 - 100}\\\text{180 - 100}[/tex]
[tex]\text{Cancel out: 100 - 100 because it equals to 0}[/tex]
[tex]\text{Keep: 180 - 100 because it helps us solve for our answer}[/tex]
[tex]\text{Our new equation becomes: 4x = 80}[/tex]
[tex]\text{Fourthly, we have to DIVIDE by 4 on each of your sides:}[/tex] [tex]\dfrac{4x}{4}=\dfrac{80}{4}[/tex]
[tex]\text{Cancel out:}\dfrac{4x}{4}\text{ because it gives us the result of 1}[/tex]
[tex]\text{Keep:}\dfrac{80}{4}\text{ because it helps us solve for our answer}[/tex]
[tex]\uparrow\text{If you solved the kept answer correctly you would have your answer for x}[/tex]
[tex]\boxed{\boxed{\bf{Answer: x = 20}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~ [tex]\frak{LoveYourselfFirst:)}[/tex]
PLEASE HELP ASAP?!!!!!!!
Answer:
76.9 in^2
Step-by-step explanation:
Area of circle
= (3.14) x(10.7)^2
= 3.14 x 114.49
= 359.4986 in^3
Let x = area of the smaller sector
x/77 = 359.4986/360
360x = 359.4986 x 77
360x = 27,681.3922
x = 76.9 (to the nearest tenth)
Is the expression 125x^3 + 216 a sum of cubes?
[tex]\bf 125x^3+216~~ \begin{cases} 125=5^3\\ 216=6^3 \end{cases}\implies 5^3x^3+6^3\implies \stackrel{\textit{yes, it is}}{(5x)^3+6^3}[/tex]
PLEASE HELP!! Express 9x−2y=−36 in slope-intercept form.
Answer:
y=(9/2)x+18
Step-by-step explanation:
Solve for y:
9x-2y=-36
Subtract 9x on both sides
-2y=-9x-36
Divide both sides by -2
y=(9/2)x+18
Answer:
y = 9/2 x +18
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
9x−2y=−36
We need to solve for y
Subtract 9x from each side
9x-9x−2y=-9x−36
-2y = -9x -36
Divide by -2
-2y/-2 = -9x/-2 -36/-2
y = 9/2 x +18
Which of the following is the graph of y = g(x-4)-2
The function y = g(x-4)-2 indicates a horizontal shift 4 units to the right and a vertical shift 2 units down from the original graph of g(x).
Explanation:The question at hand involves understanding how the graph of a given function, y = g(x-4)-2, is transformed from its original form. This expression indicates that the function g undergoes two main transformations: a horizontal shift and a vertical shift. First, the (x-4) inside the function indicates a horizontal shift 4 units to the right of the original graph of g(x). Secondly, the -2 outside the function signifies that the graph is then shifted 2 units down.
Graphically, if one were to plot the original g(x) function, these transformations mean that every point on g(x) would move 4 units to the right and 2 units downward. This understanding is crucial for correctly interpreting or drawing the graph of the given function. Such transformations are basic yet fundamental concepts in the study of functions in mathematics, enabling insights into how various operations affect the graphical representation of functions.
Of 300 students in the cafeteria 140 had lunch. Write the ratio of the students in the cafeteria to the students that had lunch
Answer:
140 / 300 or 7:15 or 7/15
Step-by-step explanation:
Final answer:
The ratio of students in the cafeteria to the ones who had lunch is 300 to 140, which simplifies to 15 to 7.
Explanation:
To find the ratio of students in the cafeteria to students that had lunch, we divide the total number of students in the cafeteria by the number that had lunch. There were 300 students in the cafeteria and 140 students had lunch. So, the ratio would be the number of students in the cafeteria to the number of students that had lunch, which is 300 to 140. This can be simplified by dividing both numbers by their greatest common divisor, which is 10. So, the simplified ratio is 30 to 14, which can be further simplified to 15 to 7.
which equation(s) have x=2 as the solution.
Answer:
A and B
Step-by-step explanation:
Have a GREAT day!
Answer:
This one is A and B, next question is A and C
Step-by-step explanation:
edge 2020
6x – 3y = 5
y – 2x= 8
Answer:
PA GEN SOLISYON --> "NO SOLUTION"
Step-by-step explanation:
Whether you multiply the top equation by ⅓ to make "-y" and "2x", or multiply the bottom equation by 3 to make "3y" and "-6x", you will see that 9⅓ ≠ 0, or 24 ≠ 0, therefore the result is "NO SOLUTION".
is the term 18m^2n^2 is a monomial
ANSWER
[tex]18 {m}^{2} {n}^{2} [/tex]
EXPLANATION
A monomial is a simplified polynomial with only one term.
The given expression is
[tex]18 {m}^{2} {n}^{2} [/tex]
This is an algebraic expression in m and n.
The 18 is a constant.
The 18 is the coefficient.
The degree is the sum of the exponents of the variable which is 2+2=4
We cannot simplify this polynomial further and it has only one term.
Therefore
[tex]18 {m}^{2} {n}^{2} [/tex]
is a monomial.
A chemical reaction took 7380 seconds. How many hours did the reaction
take? If necessary, round your answer to the nearest hundredth of an hour.
Answer: 2.05 hours
Step-by-step explanation: There are 60 seconds in a minute, and 60 minutes in an hour. To find the seconds in an hour, multiply 60 by 60.
60 x 60 = 3600
There are 3600 seconds in an hour. Divide 7380 by 3600 to find the number of hours.
7380/3600 = 2.05
The reaction took 2.05 hours.
What is the value of a in the equation 5a-10b=45 , when b=3 ?
Answer:
a = 15
Step-by-step explanation:
Plug in b = 3 into 5a-10b=45
5a-10(3) =45
5a - 30 = 45
5a = 75
a = 15
Answer:
a = 15Step-by-step explanation:
[tex]\text{Put b = 3 to the equation}\ 5a-10b=45\ \text{and solve for}\ a:\\\\5a-10(3)=45\\5a-30=45\qquad\text{add 30 to both sides}\\5a=75\qquad\text{divide both sides by 5}\\a=15[/tex]
Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute?
Answer: 720 feet
Step-by-step explanation: 120 x 6= 720
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
find image of (1,2) after a reflection about y=-1 followed by a reflection about y= 1
Answer:
(1,6)
Step-by-step explanation:
first we reflect over y=-1 and because 2 is 3 above that we go three below -1 to get -4. then we reflect over y = 1 and since we are 5 below that we go 5 up to get 6. the x value how ever remains unchanged.
(pls mark brainliest)
After a reflection about y = -1 followed by a reflection about y = 1, the point (1,2) becomes (1,6).
To find the image of the point (1,2) after a reflection about y = -1 followed by a reflection about y = 1, we can break it down into two steps.Step 1: Reflection about y = -1When we reflect a point across the line y = -1, we can think of it as flipping the point over this line. The new y-coordinate will be the same distance from the line as the original y-coordinate, but on the opposite side. In this case, the original y-coordinate of 2 is 3 units away from y = -1, so the new y-coordinate will be -1 - 3 = -4. The x-coordinate remains the same. So, after the first reflection, the point becomes (1, -4).Step 2: Reflection about y = 1Now, we reflect the point (1, -4) across the line y = 1. Again, we flip the point over this line, keeping the same distance from it. The original y-coordinate of -4 is 5 units away from y = 1, so the new y-coordinate will be 1 + 5 = 6. The x-coordinate remains unchanged. Thus, after the second reflection, the point becomes (1, 6).So, the image of the point (1,2) after a reflection about y = -1 followed by a reflection about y = 1 is (1, 6).For more questions on reflection -
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