-Quadratic Equations- Determine the number and the nature of the solutions to (3a + 24)² = -36 and then solve
Answers
ANSWER
There are two solutions and they are both complex solutions. The solutions are:
[tex]a=2i-8;a=-2i-8[/tex]EXPLANATION
We want to determine the number and nature of solutions to the equation:
[tex](3a+24)^2=-36[/tex]To do this, solve the equation by first, finding the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{(3a+24)^2}=\pm\sqrt[]{-36}=\pm\sqrt[]{-1\cdot36} \\ \Rightarrow3a+24=\pm\mleft\lbrace\sqrt[]{36}\cdot\sqrt[]{-1}\mright\rbrace \\ 3a+24=\pm6i \end{gathered}[/tex]Now, solve the equation for a:
[tex]\begin{gathered} 3a=\pm6i-24 \\ \Rightarrow a=\pm\frac{6i}{3}-\frac{24}{3} \\ \Rightarrow a=2i-8;a=-2i-8 \end{gathered}[/tex]Hence, there are two solutions and they are complex solutions.
Related Questions
13.3x + 8.1 = 74.6 solve for x
Answers
Answer:
x = 5
Step-by-step explanation:
1) Get rid of the 8.1
Whenever you are given a question like this you have to try get rid of any other numbers on the side with the x that don't include the x.
We can see that we can first get rid of the 8.1 to do this we have to subtract 8.1 from both sides.
13.3x + 8.1 -8.1 = 13.3x
74.6 - 8.1 =66.5
2) Isolate the x
To get our final value of x you have to divide both sides from 13.3! This is because we were previously left with 13.3x = 66.5 and we can see that you have to multiply 13.3 by x to get 66.5, in return to find x you should have to do the inverse.
66.5 ÷ 13.3 = 5
HINT:
For every question like this you have to do the inverse of whatever you are given. For example, we had to take away 8.1 because in the question it says add!
Hope this helps, have a great day!
Triangle 1 has a 50 degree angle, a 60 degree angle and one side that is 15 cmlong. Triangle 2 has a 50 degree angle, a 60 degree angle, and one side that is 15cm long. Are the triangles guaranteed to be congruent? No Yes
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Congruent triangles have exactly the same three sides and three angles. The triangles may be rotated to see the congruency between them. In other words congruent triangles has corresponding sides equal and corresponding angles equal.
The 2 triangles have equal corresponding
Which of the following statements are true of this equation select all that apply. 5 1/6 ÷ 2 5/12 = 2 4/29
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The left hand side of the equation is equal to right hand side.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
5 1/6 ÷ 2 5/12 = 2 4/29
We can write -
5 1/6 ÷ 2 5/12 = 2 4/29
31/6 ÷ 29/12 = 62/29
31/6 x 12/29 = 62/29
62/29 = 62/29
Therefore, the left hand side of the equation is equal to right hand side.
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for a school science project, john noted the temperature at the same time every day for 1 week the high temperature for the week was 27 Fahrenheit and the low temperature for the week was -3 Fahrenheit what is the difference between the high and low temperatures down recorded
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To answer the question we shall use a number line that begins with zero and moves in the right direction for positive values and then towards the left direction for negative values.
The high temperature recorded was 27 (positive). The low temperature was -3 (negative). The difference therefore is, 30. That is 27 to the right and from zero to the left, 3, altogether the difference is 30 on the number line.
This can better yet be expressed as follows;
[tex]\begin{gathered} \text{Difference}=27-\lbrack-3\rbrack \\ \text{Difference}=27+3 \\ \text{Difference}=30 \end{gathered}[/tex]mr. emmer gave a test in his chemistry class. the scores were normally distributed with a mean of 82 and a standard deviation of 4. what percent of students would you expect to score between 78 and 36?
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Where:
[tex]\begin{gathered} X1=36 \\ X2=78 \\ \mu=82 \\ \sigma=4 \end{gathered}[/tex]So:
[tex]\begin{gathered} P(36\le X\le78)=P(\frac{78-82}{4}\le Z\le\frac{86-82}{4}) \\ P(36\le X\le78)=P(-1\le Z\le1) \\ P(36\le X\le78)=0.6827\approx0.68 \end{gathered}[/tex]As a percentage: 68%
Don José es un conocido comerciante. Al inicio de la semana tenía una suma de dinero, de la cual invirtió 2,000 pesos en mercancía. Al término de la semana, ingresó por ventas tres veces el capital con que contaba después de comprar la mercancía; de modo que su capital llegó al doble del inicial. Determina cuál es el capital inicial de Don José.
Seleccione una:
O a. 4,000
O b. 10,000
O c. 6,000
Answers
Answer:
The Initial capital is 6000 pesos
Step by step explanation:
x: initial capital of Don José
Start of the week:
I buy merchandise in 2000 pesos
At the end of the week:
Sales income twice the capital you had after buying the merchandise: 2(x-2000)
Income - purchases = Profit
Capital + Profit = Final capital
Capital + Income - purchases = Final Capital
x+ 2(x-2000) - 2000 = 2x
x+2x-4000-2000 = 2x
3x-6000 = 2x
x = 6000
The Initial capital is 6000 pesos
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Step-by-step explanation:
[tex]8 \sqrt[5]{11} - 4 \sqrt[5]{11} [/tex]Simplify the expression
Answers
3 x 1 + 4 x 1/100 + 7 x 1/1000 as a decimal number
Answers
Answer:
3.047
Step-by-step explanation
show how the quadratic formula can be used to rewrite : f(x) = 9x^2 - 149x - 234IN FACTORED FORM
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To factor the function using the quadratic formula we equate it to zero and solve for x:
[tex]\begin{gathered} 9x^2-149x-234=0 \\ x=\frac{-(-149)\pm\sqrt[]{(-149)^2-4(9)(-234)}}{2(9)} \\ x=\frac{149\pm\sqrt[]{30625}}{18} \\ x=\frac{149\pm175}{18} \\ \text{then} \\ x=\frac{149+175}{18}=18 \\ or \\ x=\frac{149-175}{18}=-\frac{26}{18}=-\frac{13}{9} \end{gathered}[/tex]Now we write the function as:
[tex]f(x)=(x-a)(x-b)[/tex]where a and b are the roots we found above, then we have:
[tex]\begin{gathered} f(x)=(x-18)(x-(-\frac{13}{9})) \\ f(x)=(x-18)(9x+13) \end{gathered}[/tex]Therefore:
[tex]f(x)=(x-18)(9x+13)[/tex]Hi I need help solving for each of the sides in this equation.CDABSolve to the nearest hundredth
Answers
Length of CD
From the picture, we know two sides and an angle of the triangle CDE. We define the sides and angle:
• a = EC = 440.68,
,• b = ED = 470.43,
,• c = CD = ?,
,• γ = 60° 06' 09''.
From trigonometry, we know that the Law of Cosines states that:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cdot\cos\gamma, \\ c=\sqrt{a^2+b^2-2ab\cdot\cos\gamma}. \end{gathered}[/tex]Where the angle γ and the sides a, b and c are defined by:
Replacing the values from above in the equation for side c, we get:
[tex]c=\sqrt{(440.68)^2+(470.43)^2-2\cdot440.68\cdot470.43\cdot\cos(60\degree06^{\prime}09^{\prime}^{\prime})}\cong457.10.[/tex]Length of AB
To compute the length of AB, first, we must compute the length of sides AE and EB.
Side EB
From the picture, we see a triangle ECA. Using the data of the picture, we have:
• EC = 440.68,
,• ∠E = 60° 06' 09'',
,• EA = ?,
,• ∠A = ?.
,• ∠C = 97° 17' 42''.
Angles ∠A, ∠E and ∠C are the inner angles of triangle ECA, so they must sum up 180°, so we have:
[tex]\begin{gathered} ∠A+∠E+∠C=180\degree, \\ ∠A=180\degree-∠E-∠C, \\ ∠A=180\degree-60\degree06^{\prime}09^{\prime\prime}-97\degree17^{\prime}42^{\prime\prime}=22°36^{\prime}9^{\prime\prime}. \end{gathered}[/tex]Now, we define the following sides and angles:
• c' = EC = 440.68,
,• γ' = ∠A = 22° 36' 9''
,• a' = EA = ?,
,• α = ∠C = 97° 17' 42''.
Now, from trigonometry, we know that the Law of Sine states that:
Using the equation that relates a' and c', we have:
[tex]\begin{gathered} \frac{a^{\prime}}{\sin\alpha^{\prime}}=\frac{c^{\prime}}{\sin\gamma^{\prime}}, \\ a^{\prime}=c^{\prime}*\frac{\sin\alpha^{\prime}}{\sin\gamma^{\prime}}. \end{gathered}[/tex]Replacing the values from above, we get:
[tex]EA=a^{\prime}=440.68*\frac{\sin(97°17^{\prime}42^{\prime\prime}^)}{\sin(22°36^{\prime}9^{\prime\prime})}[/tex]Side AE
From the picture, we see a triangle EDB. Using the data of the picture, we have:
• b' = ED = 470.43,
,• ∠E = 60° 06' 09'',
,• a' = EB = ?,
,• α' = ∠D = 180° - 87° 20' 24'' = 92° 39' 36'',
,• β' = ∠B = 180° - ∠D - ∠E = 180° - 92° 39' 36'' - 60° 06' 09'' = 27° 14' 15''.
Applying the law of sines, we have that:
[tex]\begin{gathered} \frac{a^{\prime}}{\sin(\alpha^{\prime})}=\frac{b^{\prime}}{\sin(\beta^{\prime})}, \\ EB=a^{\prime}=b^{\prime}*\frac{\sin(\alpha^{\prime})}{\sin(\beta^{\prime})}. \end{gathered}[/tex]Replacing the values from above, we get:
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Answer
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Which functions are inverses of each other?a. Both Pair 1 and Pair 2b. Pair 1 onlyc. Pair 2 onlyd. neither Pair 1 nor Pair 2
Answers
Solution
For pair 1
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ \mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x-6 \\ f(x)=y \\ y=2x-6 \\ x=2y-6 \\ x+6=2y \\ \text{divide both side by 2} \\ \frac{x+6}{2}=\frac{2y}{2}_{} \\ y=\frac{x}{2}+3 \end{gathered}[/tex]They are inverse of each other
For pair 2
[tex]\begin{gathered} f(x)=7x,g(x)=-7x \\ \text{Inverse of f(x) = x/7} \end{gathered}[/tex][tex]\begin{gathered} f(x)=7x \\ y=7x \\ x=7y \\ y=\frac{x}{7} \end{gathered}[/tex]They are not inverse of each other
Therefore only pair 1 are inverse of each other
Hence the correct answer is Option B
In a group of 60 students, the probability that at most 30 of them like to swimis 56%. What is the probability that at least 31 of them like to swim?
Answers
Answer= 44%
P(A)= the probability that at most 30 of them like to swim
P(B)= the probability that at least 31 of them like to swim
Notice that P(A)+P(B) have to add up 100%
P(A)+P(B)=100% then solving for P(B)
P(B)= 100% - 56%= 44%
Find the degree of the polynomial – 3x + x² +3.
Answers
The degree of the polynomial is the largest power of the variable
The degree of the polynomial is 2
whats the absolute value between the points -45 and -11
Answers
For two real numbers u and v, |u-v| is the absolute value between the points:
|-45-(-11)|=|-34|=34
8 А 400 11 1200 С Which triangle can be proven congruent to AABC shown above? (G.6)(1 point) O A. 11 200 400 O B. 22 11 28 C. 1200 200 40° O D. 11 400 28
Answers
Answer:
Triangle A.
Explanation:
We need to look for a triangle which has the same angle measures and same side measurement of corresponding side lengths.
Now in the original triangle we know two angles and one side length; therefore, by AAS another triangle which has two angles and one side length given and they are congruent to that of the corresponding measurements of the first triangle, then the two triangles are congruent.
Now for choice A the problem is that we are given angle measurements different from those given in the original triangle. However, we can use the fact that the angles must sum to 180 degrees to find the third angle and it turns out to be 120.
Hence, at this point triangle A has the same angle and side length measurements as the original triangle; therefore, by AAS the two triangles are congruent.
I need help with homework I got the picture with the questions and will send it to you
Answers
3a.
DVA + AVB = 180 (straight line), so
75 + Angle AVB = 180
Angle AVB = 180 - 75
Angle AVB = 105 degrees
3b.
Angle DVC and Angle BVA are vertical angles.
Vertical angles form when we have a geometrical "X".
Vertical angles are equal so,
DVC = BVA
60 = 60
BVA = 60 degrees
3c.
BVC and CVD are in a straight line, so
BVC + CVD = 180
2x + 35 + 3x + 45 = 180
Let's solve for x:
5x + 80 = 180
5x = 100
x = 100/5
x = 20
Angle BVC = 2x + 35 = 2(20) + 35 = 40 + 35 = 75 degrees
Angle CVD = 3x + 45 = 3(20) + 45 = 60 + 45 = 105 degrees
I don’t know if I’m right I need to know
Answers
ANSWER
[tex]x=3[/tex]EXPLANATION
We want to identify the positive solution to the graph.
The solutions to a quadratic graph are the points where the graph touches the x-axis on the coordinate plane. The positive solution to the graph is the point where the graph touches the positive x-axis.
Hence, the positive solution to the given graph is x = 3.
geometry special parallelogramsSide LK = Side KO =Side OL = Side KM = Side NL =
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KLMN is a square
NM = 8
Side LK = 8
Side KO = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side OL = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side KM = sqrt(KN² + NM²) = sqrt(8² + 8²) = sqrt(64 + 64) = sqrt(128) = sqrt(64*2) = 8 * sqrt(2)
Side NL = 8 * sqrt(2)
45°
90°
45°
90°
Answers in BOLD
Fill out the blank to make the given table a probability distribution.
Answers
Answer:
[tex]0.06[/tex]Explanation:
Here, we want to fill out the blank
For us to have a probability distribution, the sum of the individual probabilities should be one
Mathematically, for us to get the value of the blank, we have to subtract the sum of the probabilities from 1. This is because the value of the area under the probability distribution is 1 square unit
Thus,we have it that:
[tex]\begin{gathered} P(-1)\text{ = 1 - (0.11 + 0.25 + 0.36 + 0.18 + 0.04)} \\ P(-1)\text{ = 0.06} \end{gathered}[/tex]find the value of x in the figure given then find the measure of angle y
Answers
Answer:
x = 33
Angle Y = 105°
Explanation:
The sum of the interior angles of a polygon with 5 sides is equal to 540°. So, we can write the following equation:
4x + 113 + (3x+8) + (2x + 9) + 113 = 540
So, solving for x, we get:
4x + 113 + 3x + 8 + 2x + 9 + 113 = 540
9x + 243 = 540
9x + 243 - 243 = 540 - 243
9x = 297
9x/9 = 297/9
x = 33
Then, using the value of x, we can calculate the value of the angle with measure (2x + 9) as:
(2x + 9) = 2(33) + 9
(2x + 9) = 75
Finally, this angle and the angle Y are supplementary, the sum of them is equal to 180°, so the measure of angle Y can be calculated as:
(2x + 9) + Y = 180°
75° + Y = 180°
Y = 180° - 75°
Y = 105°
So, x is equal to 33 and the measure of angle Y is 105°
May I please get help finding this. I can’t seem to get the correct solution for the length.
Answers
Triangle ABE is similar to traingle ACD; in similar triangles, corresponding sides are always in the same ratio:
[tex]\frac{DC}{EB}=\frac{AC}{AB}[/tex]Use the equation above to find the length of x:
[tex]\begin{gathered} \frac{x}{4}=\frac{6+9}{6} \\ \\ \frac{x}{4}=\frac{15}{6} \\ \\ x=4\cdot\frac{15}{6} \\ \\ x=\frac{60}{6} \\ \\ x=10 \end{gathered}[/tex]Then, the length of x is 10factor as the product of two binomial x^2+3x+2= _____
Answers
We are given the trinomial
[tex]x^2+3x+2[/tex]We can factor it as the product two binomials as
[tex](x+a)(x+b)[/tex]Where
a and b are two numbers that has
• a product of 2
,• a sum of 3
So, which two numbers multiplied gives us "2" and added gives us "3"?
It is "+2" and "+1".
Thus, we can factor the trinomial as:
[tex]\begin{gathered} x^2+3x+2 \\ =(x+2)(x+1) \end{gathered}[/tex]Find an equation of variation in which y varies directly as x and y=28 when x=7. Then find the value of y when x=16.
Answers
the circle graph shown above represents the distribution of the grades of 40 students in a certain geometry class. How many students received Bs or Cs?
Answers
Given:
Total number of students = 40
From the circle graph given, let's determine the number of students that received Bs or Cs.
Given:
Percentage of students that received Bs = 30%
Percentage of students that received Cs = 40%
Percentage of student that received Bs or Cs = 40% + 30% = 70%
Thus, to find the number of students who received Bs or Cs, we have the equation below:
No of students who received Bs or Cs = (% of students who received Bs or Cs) x (Total n0 of students)
[tex]\text{ No of student who received Bs or Cs = 70\% of 40}[/tex]Thus, we have:
[tex]\begin{gathered} \text{ No of students who received Bs or Cs = }\frac{70}{100}\ast40 \\ \\ =0.70\ast40 \\ \\ =28 \end{gathered}[/tex]Therefore, the number of students who received Bs or Cs are 28
ANSWER:
C. 28
Graph x + 4y = 8The y-intercept is ___ (I got this already its 8)
Answers
Answer
The y-intercept = 2
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we just have to write the given equation in this form and the y-intercept will become apparent.
x + 4y = 8
4y = -x + 8
Divide through by 4
(4y/4) = (-x/4) + (8/4)
y = -0.25x + 2
Comparing this with y = mx + b
We can see that
b = y-intercept = 2
Hope this Helps!!!
How would you describe the graphs of the sine and cosine functions? The sine and cosine functions are periodic functions. What does it mean to be a periodic function?
Answers
The sine and cosine functions are wave-like functions that repeat themselves on the plane an infinite number of times. The fundamental difference between the two functions is that the valley of the sine function is intersected by the y-axis. In contrast, the crest of the cosine function intersects the y-axis.
Given a function f(x)
[tex]f(x)=\sin (ax)[/tex]We can find its period using the formula below
[tex]\text{period}=\frac{2\pi}{a}[/tex]where the 2pi term is in radians.
The period of the function is the x-distance needed for the function to complete a cycle.
A periodic function is a function that repeats its values at regular intervals (2pi/a as we found above)
which answer shows the correct ratios for the problem? in the forest, the ratio of elm trees to oak trees is 5/7. of the 120 trees, how many are elms? a. 40...b. 85....c..50...d...60
Answers
Answer:
The number of elms tree in the forest is;
[tex]50[/tex]Explanation:
Given that the ratio of elm trees to oak trees is 5:7.
And there are 120 trees in total in the forest.
For the ratio of the elms tree to the total number of trees is;
[tex]=\frac{5}{5+7}=\frac{5}{12}[/tex]Let's now calculate the number elms tree in the forest;
[tex]\begin{gathered} n=\frac{5}{12}\times120\text{ tr}ees \\ n=50\text{ tre}es \end{gathered}[/tex]Therefore, the number of elms tree in the forest is;
[tex]50[/tex]What integer value of b would make this not factorable
Answers
Answer:
Any integer other than -14 or 14.
[tex](x - 1)(x - 3) = {x}^{2} - 14x + 13[/tex]
[tex](x + 1)(x + 3) = {x}^{2} + 14x + 13[/tex]
Which is not a correct description of the graph below? nh -2TT -TK 2TT The graph of y = cos & shifted to the left by 34 units. Зл 2 The graph of y = sin e shifted to the left by n units. O y = sin(0 + 21) = O y = cos(0+ y = 3 Зл 2
Answers
Verify each statement
N 1 -----> is true
because
y=cosx , shifted to the left by 3pi/2 is y=cos(x+3pi/2)
N 2 ----> is false
N 3 -----> is true
N4 ----> is true
therefore
the answer is option N 2List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)f(x) = 2x3 + 3x2 − 8x + 5
Answers
We will list all the possible rational zeros for the polynomial
[tex]f(x)=2x^3+3x^2-8x+5[/tex]to find it we will apply the Rational root theorem. It states that each rational zero(s) of a polynomial with integers coefficients is of the form
[tex]\frac{p}{q}[/tex]where:
* p is a factor of the coefficient of the zero order term in the polynomial ( in our case this coefficient is 5)
* q is a factor of the leading coefficient , that is the coefficient that multiply the variable to the biggest power (in our case that coefficient is 2)
* p and q are relative primes, that is , they does not have common factors.
Finding the possibilities for rational roots:
Just summarizing the information until now, we have:
[tex]p=5\text{ and q=2}[/tex]
we also have that:
[tex]factors\text{ of 5= \textbraceleft1,5,-1,-5\textbraceright}[/tex]and
[tex]factors\text{ of 2 = \textbraceleft1,-1,2,-2\textbraceright}[/tex]So, on the right of the equations above, we have all the possible values that can take p and q, respectively. It only rests to construct all the possibilities, we do