Answers
we have the next equation
[tex]5x^2-36x+36=0[/tex]we will use the formula to find the values of x of a second-grade equation
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where
a=5
b=-36
c=36
we substitute the values in the formula
[tex]x_{1,2}=\frac{36\pm\sqrt[]{36^2-4(5)(36)}}{2(5)}=\frac{36\pm\sqrt[]{576}}{10}=\frac{36\pm24}{10}[/tex][tex]x_1=\frac{36+24}{10}=\frac{60}{10}=6[/tex][tex]x_2=\frac{36-24}{10}=\frac{6}{5}[/tex]the values of x are
x=6 and x=6/5
Related Questions
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {1, 2, 3, 5, 7}, and C = {1, 3, 6, 7}. Find A ∩ Ø a) { } b) {1, 3, 5, 7} c) {1, 2, 3, 4, 5, 6, 7} d) {2, 4, 6}
Answers
we know that
A=[2,4,6]
we have that
A ∩ Ø=Ø
therefore
The answer is the option aUse the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.sin(35%)cos(115) + cos(35) sin(115)
Answers
To solve this problem, we will use the following identity:
[tex]\sin (a+b)=\sin a\cos b+\cos a\sin b\text{.}[/tex]Using the above identity we can rewrite the given expression as follows:
[tex]\sin (35^{\circ}+115^{\circ}).[/tex]Simplifying the above result, we get:
[tex]\sin (150^{\circ})\text{.}[/tex]Answer:
[tex]\sin (150^{\circ})\text{.}[/tex]Espen
Deandre deposits $500 into an account that pays simple interest at a rate of 4% per year. How much Interest will he be paid in the first 2 years?
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5
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The Interest I paid on a deposited amount (principal) at a certain certain rate r over a period of time t is;
[tex]I=\frac{prt}{100}[/tex][tex]\begin{gathered} p=\text{ \$500} \\ r=4\text{ \%} \\ t=2\text{years} \end{gathered}[/tex][tex]\begin{gathered} I=\frac{500\times4\times2}{100} \\ I=40 \end{gathered}[/tex]Hence, the interest paid after the first two years is $40
on a number line, where is -1 in relation to the -7?
Answers
Given:
The two numbers on a number line are, -1 and -7.
Explanation:
-1 is to the right of -7 on a number line.
Final Answer:
-1 is to the right of -7 on a number line.
Express 21 10(cos(270') + i sin(270°)) in rectangular form.Express your answer in exact terms.21
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The rectangular form of a complex number can be written as:
[tex]z=a+bi[/tex]For real numbers a and b.
Starting from the given z₁, we can distribute the 10:
[tex]\begin{gathered} z_1=10\lbrack\cos (270\degree)+i\sin (270\degree)\rbrack \\ z_1=10\cos (270\degree)+10i\sin (270\degree) \end{gathered}[/tex]Now, from the unit circle, we can see that:
[tex]\begin{gathered} \cos (270\degree)=0 \\ \sin (270\degree)=-1 \end{gathered}[/tex]So, substituting them, we get:
[tex]\begin{gathered} z_1=10\cos (270\degree)+10i\sin (270\degree) \\ z_1=10\cdot0+10i(-1) \\ z_1=-10i \end{gathered}[/tex]A time traveler can take 4 books with him, and he has 90 books to choose from. How many different ways can the books be selected?
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Solution:
The time traveler has 90 books to choose from, but he can only take 4 books
since we need to find the number of ways he can choose 4 books, we know that the order in which he takes the books does NOT matter
Hence, we will use a combination:
We know that the formula for combination is
[tex]\frac{n!}{r!(n-r)!}[/tex]in this case, n = 90, and r = 4. Thus, we get the following equation:
[tex]\frac{90!}{4!(90-4)!}=\frac{90!}{4!(86)!}=2555190[/tex]so that, the correct answer is:
[tex]2555190[/tex]Check off all of the equations that would give one solution
Answers
Solution:
Given the equations:
[tex]\begin{gathered} 5x+10=5x-15 \\ collect\text{ like terms,} \\ 5x-5x=-15-10 \\ 0=-25 \\ thus,\text{ there's no solution.} \end{gathered}[/tex][tex]\begin{gathered} 3x+12=4x-21 \\ collect\text{ like terms,} \\ 3x-4x=-21-12 \\ \Rightarrow-x=-33 \\ divide\text{ both sides by -1,} \\ -\frac{x}{-1}=-\frac{33}{-1} \\ \Rightarrow x=33 \\ thus,\text{ there's a solution} \end{gathered}[/tex][tex]\begin{gathered} 3(x+4)=3x+12 \\ open\text{ parentheses,} \\ 3x+12=3x+12 \\ thus,\text{ there's infinitely many solutions.} \end{gathered}[/tex][tex]\begin{gathered} 5x+10=6x-8 \\ collect\text{ like terms,} \\ 5x-6x=-8-10 \\ \Rightarrow-x=-18 \\ divide\text{ both sides by -1,} \\ -\frac{x}{-1}=-\frac{18}{-1} \\ \Rightarrow x=18 \\ thus,\text{ there's a solution.} \end{gathered}[/tex][tex]\begin{gathered} 2(3x-4)=6x-8 \\ open\text{ parentheses,} \\ 6x-8=6x-8 \\ thus,\text{ there's infinitely many solutions.} \end{gathered}[/tex][tex]\begin{gathered} 6x-8=2(3x-3) \\ open\text{ parentheses,} \\ 6x-8=6x-6 \\ collect\text{ like terms,} \\ 6x-6x=-6+8 \\ 0=2 \\ thus,\text{ there's no solution.} \end{gathered}[/tex]Hence, the equations that would give one solution are:Perform the indicated operation if possible.- 11 - 10- 2 - 1-4-653-7- 82 1Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The resulting matrix is(Simplify your answer.)OB. The resulting matrix does not exist because the operation is not possible.
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SOLUTION
Concept: Matrix Subtraction
When carrying out matrix subtraction or addition, we subtract element occupying corresponding position
The subtraction of the matrix above will produce
[tex]\begin{gathered} -11-(-2)=-11+2=-9 \\ -10-(-1)=-10+1=-9 \\ -4-5=-9 \\ -6-3=-9 \\ -7-2=-9 \\ -8-1=-9 \end{gathered}[/tex]The matrix is writing as
Hence the resulting matrix is a 3 x 2 constant matrix.
Can you help me with this? Also the word at the beginning is what. It is the only thing that got cut off.
Answers
To be able to simplify the given expression, let's recall some of the trigonometric identities.
1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
From those identities above, we can replace the numerator and denominator in the given expression with their equivalent value. Thus, the expression becomes:
[tex]\frac{1}{sec^2\theta}[/tex]Now, sec²θ is also just equivalent to 1/cos²θ. So, we can rewrite the expression as:
[tex]1\div\frac{1}{cos^2\theta}[/tex]Then, applying the rules of dividing fractions, the expression becomes:
[tex]1\times cos^2\theta=cos^2\theta[/tex]Therefore, the equivalent expression is cos²θ. (Option 1)
How many combinations are possible assume the items are distinct 7 items chosen 5 times
Answers
SOLUTION:
Case: Combination
Method:
distinct 7 items chosen 5 times
Selecting 5 from 7 items is:
[tex]\begin{gathered} 7C_5 \\ \frac{7!}{(7-5)!5!} \\ \frac{7!}{2!\times5!} \\ \frac{7\times6\times5!}{2\times1\times5!} \\ \frac{7\times6}{2\times1} \\ \frac{42}{2} \\ =21 \end{gathered}[/tex]Final answer:
There are 21 ways 5 items can be selected from 7 distict items
Justin needs to make a illustrations for an art book. He had made 40%of the illudtrations. Make a bar model to show his progress. How many illustrations does he have
Answers
Justin has made 40% of the illustrations. First, calculate the number of illustrations Justin has made, by calculating the 40% of 80, just as follow:
(40/100)(80) = 32
that is, 40% is claculated by multiplying 40/100 by 80.
Then, justis has made 32 illustrations. To obtain the number of illustrations Justin has not made even, subtract the previous result to 80:
80 - 32 = 48
Then, Justin has not made 48 illustrations.
A bar model representing the previous situation is shown below:
where the red regios corresponds to the 32 illustrations made by Justin
Gwen can read 2 7/9 pages of a book in a minute. If she read 4 5/6 minutes, how much would she have read?
Answers
The rate of reading has been given as
[tex]\begin{gathered} 2\frac{7}{9}\text{ pages =1minute} \\ \text{If 1 minute is 2}\frac{7}{9},\text{ then it means any amount of time greater than 1 minute would simply be } \\ \text{Number of pages per minute times the number of minutes given} \\ \text{That is, 2 minutes would be 2}\frac{7}{9}\times2.\text{ And so on}\ldots \\ \text{Therefore, 4}\frac{5}{6}\min utes\text{ would be;} \\ 4\frac{5}{6}\min =2\frac{7}{9}\times4\frac{5}{6}pages \\ 4\frac{5}{6}\min =\frac{25}{9}\times\frac{29}{6}\text{pages} \\ 4\frac{5}{6}\min =\frac{725}{54}pages \\ 4\frac{5}{6}\min =13\frac{23}{54}pages \\ \end{gathered}[/tex]The results shows that she would read 13 23/54 pages in the time given
I need help please it says find the area of each shaded sector. Round to the nearest hundredth place.
Answers
Step 1
State the formula for the area of a sector of a circle
[tex]A=\frac{\theta}{360}\times\pi\times r^2[/tex]Step 2
Find the value of θ.
[tex]m\angle WZV=\theta=180-108=72^{o^{}}(sum\text{ of angles on a straight line is }180^o)[/tex]r=wz= 5.3km
Step 3
Find the area of the shaded part.
[tex]\begin{gathered} A=\frac{72}{360}\times\pi\times(5.3)^2 \\ A=\frac{1}{5}\times\pi\times28.09 \\ A=\frac{2809}{500}(\pi)km^2 \end{gathered}[/tex]Since there are 2 of such shaded sectors, they both will have the same area. Therefore the total area of the shaded sectors will be;
[tex]\begin{gathered} \frac{2809}{500}(\pi)km^2\times2 \\ =35.29893506 \\ \approx35.30km^2 \end{gathered}[/tex]Answer; The area of the shaded sector approximately to the nearest hundredth is = 35.30km²
8. Solve the system and write the answer as an ordered triple:x + y - z = 42x + 3y - z = 8x - y = -z
Answers
EXPLANATION
First, isolate x for x+y-z=4:
[tex]x=4-y+z[/tex][tex]\mathrm{Substitute\:}x=4-y+z[/tex][tex]\begin{bmatrix}2\left(4-y+z\right)+3y-z=8\\ 4-y+z-y=-z\end{bmatrix}[/tex]Simplifying the equations by applying the distributive property and adding like terms:
[tex]\begin{bmatrix}y+z+8=8\\ -2y+z+4=-z\end{bmatrix}[/tex]Isolate y for y+z+8=8
[tex]y=-z[/tex][tex]\mathrm{Substitute\:}y=-z[/tex][tex]\begin{bmatrix}-2\left(-z\right)+z+4=-z\end{bmatrix}[/tex]Simplify:
[tex]\begin{bmatrix}3z+4=-z\end{bmatrix}[/tex][tex]z=-1[/tex][tex]\mathrm{For\:}y=-z[/tex][tex]\mathrm{Substitute\:}z=-1[/tex][tex]y=-\left(-1\right)[/tex][tex]\mathrm{Simplify}[/tex][tex]y=1[/tex][tex]\mathrm{For\:}x=4-y+z[/tex][tex]\mathrm{Substitute\:}z=-1,\:y=1[/tex][tex]x=4-1-1[/tex][tex]\mathrm{Simplify}[/tex][tex]x=2[/tex][tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex][tex]x=2,\:z=-1,\:y=1[/tex]Expressing as an ordered triple:
[tex](2,1,-1)[/tex]On a map that shows the location of movie stars' houses, two Hollywood actors' houses are 8 centimeters apart. If the map uses a scale of 2 centimeters = 1 kilometer, how far apart are the actors' houses in real life?
Answers
Answer
The actors' houses in real life will be 4 kilometers apart.
Explanation
If the two Hollywood actors' houses are 8 centimeters apart, and the map uses a scale of 2 centimeters = 1 kilometer, then the actors' houses in real life will be
[tex]\frac{8\text{ centimeters }\times1\text{ kilometer}}{2\text{ centimeters}}=4\text{ kilometers}[/tex](1) I spent 1/8th of my life as a child before I started school. Then, Ispent 3/8th of my life as a student and ½ of my life as a workingperson. I have been working for 24 years. How old am I?
Answers
You spent half your life as an adult working so you spent the other half in school and growing up. 24x2 = 48
Therefore, you are 48 years old.
answer this question 6/7×1/2=?
Answers
Sandra, this is the solution:
6/7 * 1/2 = 6/14
And we can simplify, as follows:
6/14 = 3/7
The answer is 3/7
javier said I have to get atleast an 75 on the test to keep my A in the class if T represents javier's score on the test which inequality matches his statement
Answers
T ≥ 75
Explanations:Javier score = T
Since Javier has to score at least 75 to keep his A, it means he has to score 75 and above.
This means that Javier's score (T) must be greater than or equal to 75
This can be represented mathematically as:
T ≥ 75
Find the missing length of the solid figure.3 m3 m8 m
Answers
Let's begin by identifying key information given to us:
We have the total length of the side = 8 m
We have the length of 2 out of the 3 sides:
a cookie cake is cut into 8 equal slices Damon is 1/8 of the cake shaunita eats 1/2 of the cake and Michael least two slices how many slices remain
Answers
1 - (1/8) - (1/2) - 2(1/8)
1 - (5/8) = 3/8
Only 3/8 of the cake remain or 3 slices.
whic fractions haveva least common denominater of 40 1/2 and 3/20 1/4 and 3/ 10 1/8 and 2/5 1/8 and 3 / 15
Answers
1/8 and 2/5 is the answer
their LCD is 40
1/2 and 3/20 LCD is 20
1/4 and 3/10 LCD is 20
1/8 and 3/15 LCD is 120
LCD means least common denominator
110 Sketch = in standard position. 6 х X ? 1 Drag to show the angle.
Answers
We want to draw the angle, theta, in standard position in the unit circle.
We will start off from x = 0 degrees.
First, let's convert the angle (in radians) to degrees. The conversion is shown below:
[tex]\frac{11\pi}{6}\times\frac{180}{\pi}=\frac{11(180)}{6}=330\degree[/tex]We know that 360 degrees is one full circle. So, 330 degree from x = 0 (right side of origin) COUNTERCLOCKWISE to 330 degree will be in the 4th quadrant. Thus,
An online advertisement asks you to participate in a survey. The survey asks how you feel about the current U.S. President. Would this sample have bias no bias-every population would be equally represented yes bias- there is a population that is over or under represented
Answers
The given situation represents a biased data recollection because the survey is based on subjective information like feelings and personal opinions.
Hence, the answer is Yes, there is a population that is over or under-represented.[tex]y = x {}^{2} + 8x + 16[/tex]what is the vertex
Answers
Answer:
Vertex: (-4, 0)
Axis of Symmetry: x = -4
Maximum Value: Does Not Exist
Minimum Value: y = 0
Explanation:
The vertex form of an equation is
[tex]y=a(x-h)^2+k[/tex]where the coordinates of the vertex are
[tex]V=(h,k)[/tex]Tofind the vertex of the parabola, we first convert the equation to the vertex form.
-2x + 4y = 16a. y = 2x + 4b. y = -2x + 4C. y = 1/2x + 4 D. y = 1/2x - 4
Answers
Given the following equation:
[tex]-2x+4y=16[/tex]You can follow the steps shown below in order to solve for "y":
Step 1. You must apply the Addition property of equality by adding 2x to both sides of the equation:
[tex]\begin{gathered} -2x+4y+(2x)=16+(2x) \\ 4y=2x+16 \end{gathered}[/tex]Step 2. Finally, you must apply the Division property of equality by dividing both sides of the equation by "4", as following:
[tex]\begin{gathered} \frac{4y}{4}=\frac{2x+16}{4} \\ \\ y=\frac{2x}{4}+\frac{16}{4} \end{gathered}[/tex]Step 3. Simplifying the right side of the equation, you get:
[tex]y=\frac{1}{2}x+4[/tex]The answer is: Option C.
The angle t is an acute angle and sint is given. Use the Pythagorean identity sin’t+ cos?t= 1 to find costsint =6
Answers
we have
[tex]\sin (t)=\frac{\sqrt[]{5}}{6}[/tex]Remember that
[tex]\sin ^2(t)+\cos ^2(t)=1[/tex]substitute the given value
[tex](\frac{\sqrt[]{5}}{6})^2+\cos ^2(t)=1[/tex][tex]\begin{gathered} \frac{5}{36}+\cos ^2(t)=1 \\ \cos ^2(t)=1-\frac{5}{36} \\ \cos ^2(t)=\frac{31}{36} \\ cos(t)=\pm\frac{\sqrt[]{31}}{6} \end{gathered}[/tex]the angle t is an acute angle and the sine is positive, that means, the angle t lies in the first quadrant
so
the cosine is positive
therefore
[tex]cos(t)=\frac{\sqrt[]{31}}{6}[/tex]Graph the quadrilateral with vertices (0, 4), (5, 8), (10, -7), and (-3, -7).
Answers
Answer:
Explanation:
From the figure above, we see that the vertices are labelled as follows;
A(0, 4), B(5, 8), C(10, -7), and D(-3, -7).
A bag contains 30 marbles , some transparent and some green. The ratio of transparent marblesbto green is 3:3. How many transparent marbles are there,
Answers
From the information given we deduce that half of the marbles are transparent. So , the number
of transparent marbles is 15.
Which graphic organizer correctly groups the following numbers? 3.4 -2 3 -1.2
Answers
3.4 is a rational number
-2 is a integer number
3 is a whole number
-1.2 is a rational number
therefore answer is: the first one
Solve the system by substitution.5x - 2y + 3z = 6-2x - 4y - 3z = 142 + 6y - 8z = 12yPls see the picture
Answers
Given the System of Equations:
[tex]\begin{cases}5x-2y+3z=6 \\ \\ 2x-4y-3z=14 \\ \\ x+6y-8z=12\end{cases}[/tex]You can solve it using the Substitution Method:
1. Solve for "y" from the third equation:
[tex]\begin{gathered} 6y=12-x+8z \\ \\ y=2-\frac{x}{6}+\frac{4z}{3}\text{ (Equation I)} \end{gathered}[/tex]2. Add the first and the second equation:
[tex]\begin{gathered} \begin{cases}5x-2y+3z=6 \\ \\ 2x-4y-3z=14 \\ \end{cases} \\ ---------------- \\ 7x-6y=20\text{ (Equation II)} \end{gathered}[/tex]3. Solve for "y" from Equation I:
[tex]\begin{gathered} -6y=20-7x \\ \\ y=\frac{20}{-6}-\frac{7}{(-6)}x \\ \\ y=-\frac{10}{3}+\frac{7}{6}x\text{ (Equation III)} \end{gathered}[/tex]4. Substitute Equation III into the third equation and simplify:
[tex]\begin{gathered} x+6(-\frac{10}{3}+\frac{7}{6}x)-8z=12 \\ \\ x-\frac{60}{3}+\frac{7}{6}x-8z=12 \\ \\ \frac{13}{6}x-8z=32 \end{gathered}[/tex]5. Substitute Equation I into the second equation and simplify:
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