Answers
The solutions are:
x = -2.11 or 1.11
Explanation:Given the equation:
[tex]3x^2=-3x+7[/tex]This can be written as:
[tex]3x^2+3x-7=0[/tex]Comparing this with the general equation;
[tex]ax^2+bx+c=0[/tex]We see that;
[tex]\begin{gathered} a=3 \\ b=3 \\ c=-7 \end{gathered}[/tex]The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values of a, b, and c
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\times3\times(-7)}_{}}{2\times3} \\ \\ =\frac{-3\pm\sqrt[]{9+84}}{6} \\ \\ =\frac{-3\pm\sqrt[]{93}}{6} \\ \\ =\frac{-3\pm9.64}{6} \\ \\ x=\frac{-3+9.64}{6}=1.11 \\ \\ OR \\ x=\frac{-3-9.64}{6}=-2.11 \end{gathered}[/tex]Related Questions
In which quadrant will the image lie if AB is reflected in the c-axis?
Answers
The quadrants on a xy frame are numbered as below:
The image is originally in the Quadrant I, if we reflect it in the x-axis, then it'll be placed on the fourth quadrant. So the answer is D Quadrant IV.
on a map. 1 inch equals 10.1 miles . if two cities are 3.5 inches apart on the map, how far are they actually apart?
Answers
Since each inch equals 10.1 miles, mutliply 3.5 times 10.1 to find how far are two cities that are 3.5 inches apart on the map:
[tex]3.5\times10.1=35.35[/tex]Therefore, they are 35.35 miles apart.
Sparks garden is in the shape of a trapezoid and the dimensions are shown belowa gardener needs to spread fertilizer over the flower beds each bag of fertilizer he uses covers 125 square meters and he can only buy full bags how many bags of fertilizer will he need to cover the entire garden
Answers
To be able to determine the bags of fertilizer that the gardener will need, let's first determine the area of the garden.
Since the shape of the garden is a trapezoid, we will be using the following formula:
[tex]\text{ Area = }\frac{1}{2}H(B_1+B_2)[/tex]We get,
[tex]\text{ Area = }\frac{1}{2}H(B_1+B_2)[/tex][tex]\text{ = }\frac{1}{2}(50)(70\text{ + 40)}[/tex][tex]\text{ = }\frac{1}{2}(50)(110\text{) = }\frac{50\text{ x 110}}{2}[/tex][tex]\text{ = }\frac{5,500}{2}[/tex][tex]\text{ Area = }2,75m^2[/tex]Let's determine how many bags of fertilizer will be used.
[tex]\text{ No. of Bags of Fertilizer = }\frac{\text{ Area of Garden}}{\text{ Area that a Bag of Fertilizer can cover}}[/tex]We get,
[tex]\text{ = }\frac{2,750(m^2)}{125\frac{(m^2)}{\text{bag}}}[/tex][tex]\text{ No. of Bags of Fertilizer = }22\text{ Bags}[/tex]Therefore, the gardener will be needing 22 Bags of Fertilizer.
describe the appearance of the graph
Answers
the equation is a line because the variable is of the first degree, this is because x is raised to 1.
a first degree equation is a line and the slope is the coefficient of the variable, on this case the slope is -4, then the slope get down because the slope is negative
so the right option is fourth
A probability experiment consist of rolling a 15-sided die. Find the probability of the event below. rolling a number divisible by 6
Answers
SOLUTION
A 15-sided die has 15 faces numbered 1 to 15.
So the total possible outcome is 15.
Of all the numbers from 1 to 15, only 6 and 12 are divisible by 6. Therefore the numbers divisible by 6 is 2.
So the required outcome = 2
Probability =
[tex]\text{Probability = }\frac{required\text{ outcome}}{\text{total possible outcome}}[/tex]So,
[tex]\begin{gathered} \text{Probability = }\frac{required\text{ outcome}}{\text{total possible outcome}} \\ \\ \text{Probability = }\frac{2}{\text{1}5} \end{gathered}[/tex]GRE verbal reasoning scores has an unknowndistribution with a mean of 150.1 and astandard deviation of 9.4. Using the empirical rule,what do we know about thepercentage of GRE verbal reasoning scoresbetween 131.3 and 168.9?
Answers
Empirically we can see the σ ranges of a Gaussian distribution in the following figure
From exercise we know that:
[tex]\begin{gathered} \bar{x}\bar{}=150.1 \\ \sigma=9.4 \end{gathered}[/tex]We will calculate how many sigmas the given range is to know what the percentage of scores :
[tex]\begin{gathered} x=\bar{x}-A\sigma \\ x=131.3 \\ 131.3=150.1-A(9.4) \\ 150.1-131.3=9.4A \\ A=\frac{18.8}{9.4} \\ A=2 \\ \end{gathered}[/tex]The score 131.3 is 2 sigmas from the mean
[tex]\begin{gathered} x=\bar{x}+A\sigma \\ x=168.9 \\ 168.9=150.1-A(9.4) \\ 168.9-150.1=9.4A \\ A=\frac{18.8}{9.4} \\ A=2 \end{gathered}[/tex]The score 168.9 is 2 sigmas from the mean
The range of reasoning scores between 131.3 and 168.9 is ±2σ which corresponds to 95.5% (see initial graph)solve for 2 cos x+sqrt2 =0 for o
pi/4
3pi/4
5pi/4
7pi/4
it's 3pi/ 4 and 5pi/4
Answers
Answer:
[tex]\frac{3\pi }{4} \ and \ \frac{5\pi }{4} .[/tex]
Step-by-step explanation:
[tex]1. \ cosx=-\frac{\sqrt{2} }{2};\\x=^+_-\frac{3 \pi}{4}+2 \pi n, \ where \ n=Z.[/tex]
2. finally, the answer is
[tex]\frac{3\pi }{4} \&\frac{5\pi }{4} .[/tex]
the solution set of an equation of a circle is all if the points that lie on the circle true or false
Answers
A circle is the set of all points in a plane at a given distance called the radius of a given point called the center. In this sense the points that lie on the circle represent the solutions for the equation of a given circle. Therefore, the statement is true
in triangle XYZ, point M is the centroid. If XM=8, find the length of MA
Answers
Centroid theorem: the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.
For the given triangle:
[tex]XM=\frac{2}{3}XA[/tex]XA is the sum of XM and MA:
[tex]XA=XM+MA[/tex]Use the two equations above to find MA:
[tex]\begin{gathered} XM=8 \\ \\ 8=\frac{2}{3}XA \\ \\ XA=\frac{3}{2}(8) \\ \\ XA=12 \\ \\ \\ 12=8+MA \\ MA=12-8 \\ \\ MA=4 \end{gathered}[/tex]Then, MA is equal to 4The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 37 minutes of calls is$13.21 and the monthly cost for 70 minutes is $17.50. What is the monthly cost for 45 minutes of calls?
Answers
Given:
The monthly cost is 37 min is $13.21
70 min cost is $17.50
Find-:
The monthly cost for 45 minutes of calls
Explanation-:
The linear equation is:
[tex]\begin{gathered} y=mx+c \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=Y-\text{ Intercept} \end{gathered}[/tex]The formula of the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point is:
[tex]\begin{gathered} (x_1,y_1)=(37,13.21) \\ \\ (x_2,y_2)=(70,17.50) \end{gathered}[/tex]So, the slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{17.50-13.21}{70-37} \\ \\ m=\frac{4.29}{33} \\ \\ m=0.13 \end{gathered}[/tex]Slope is:
The general equation of a line:
[tex]\begin{gathered} y=mx+c \\ \\ y=0.13x+c \end{gathered}[/tex]The value of "c" is:
[tex]\begin{gathered} y=0.13x+c \\ \\ (x,y)=(37,13.21) \\ \\ 13.21=0.13(37)+c \\ \\ c=13.21-4.81 \\ \\ c=8.4 \end{gathered}[/tex]The equation is:
[tex]\begin{gathered} y=mx+c \\ \\ y=0.13x+8.4 \end{gathered}[/tex]Cost at 45 min. is:
[tex]\begin{gathered} x=45 \\ \\ y=0.13x+8.4 \\ \\ y=0.13(45)+8.4 \\ \\ y=5.85+8.4 \\ \\ y=14.25 \end{gathered}[/tex]The 45 min cost is $14.25
Find the measure of angle R, given that the largest triangle is a right triangle.A)27B)18C)72D)45
Answers
we know that
The central angle is 90 degrees
so
18+R=45 degrees
R=45-18
R=27 degreesThe table shows a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to city B.City A - 26City B - 36City C - 18City D - 18City E - 2
Answers
Given:
The table shows a survey of 100 people selected at random at an airport
We will find the probability that a person selected at random is going to city B
As shown: City B - 36
So, the probability will be as follows:
[tex]probability=\frac{36}{100}=0.36[/tex]So, the answer will be probability = 0.36
the next model of a sports car will cost 14.4% more than the current model the current model cost $41,000 how much would a price increase in dollars what would the price of the next model?
Answers
Given that the current model of the car cost;
[tex]\text{ \$41,000}[/tex]We are informed that the next model of a sports car will cost 14.4% more than the current model.
The price increase in dollars will then be given as;
[tex]\begin{gathered} \frac{14.4}{100}\times41000 \\ =\text{ \$}5904 \end{gathered}[/tex]Answer 1: Price increase in dollars is $5904
The cost of the next model will then be the sum of the current model and the price increase in dollars.
This would give;
[tex]\text{ \$41000+\$5904=\$46904}[/tex]Answer 2: The cost of the next price model is $46904
I just need answers. No need longer to explain.Solve a
Answers
We need to find the period of the sinusoidal function in this case we have the next form
[tex]y=A\sin \frac{2\pi}{T}(x+a)+b[/tex]First, we need to find the amplitude in this case
[tex]A=\frac{5+1}{2}=\frac{6}{2}=3[/tex]The amplitude is 3
Then we need to find the period
[tex]T=\frac{2\pi}{3}[/tex]and the the displacement b is 2
Then for a we have
[tex]a=\frac{5}{12}\pi[/tex]Therefore we have
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]ANSWER
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]Write an equation for a function that has a graph with the given characteristics.The shape of y= 1/x shifted down 4 units.
Answers
Given:
y = 1/x
Required:
equation for a function that shifted down 4 units
Solution:
y' = 1/x - 4
Answer:
y' = 1/x - 4
Can you help me figure out if figure in a polygon. is it a polygon the name of it by the number of the size
Answers
2)
A polygon has an infinite number of sides and they are connected to each other end to end. This means that it is an enclosed figure. Looking at the figure, it has all these characteristics. Thus,
It is a polygon
Next, we would count the number of sides. In this case, it is 10. A 10 sided polygon is called a Decagon. Thus, the given figure is a Decagon
I need help with this please. I have tried multiple times but still could not get the correct answers
Answers
Recall that the diagonals of a rhombus are perpendicular bisectors of each other, therefore all the right triangles formed by the diagonals as shown in the given diagram are congruent, therefore:
[tex]\begin{gathered} \measuredangle1=\measuredangle4=\measuredangle2, \\ \measuredangle3=39^{\circ}, \\ \measuredangle1+39^{\circ}=90^{\circ}. \end{gathered}[/tex]Solving the last equation for angle 1 we get:
[tex]\begin{gathered} \measuredangle1=90^{\circ}-39^{\circ}, \\ \measuredangle1=51^{\circ}. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} m\angle1=51^{\circ}, \\ m\angle2=51^{\circ}, \\ m\angle3=39^{\circ}, \\ m\angle4=51^{\circ}. \end{gathered}[/tex]Which of the following methods of timekeeping is the least precise?A. Using a stopwatchB. Using a wrist watchC. Counting your heartbeatsO D. Using a calendar
Answers
It’s c counting your heartbeats
My reasoning is that a wrist watch, a calendar and a stop watch all function on metered, constant intervals of time. A heart beat doesn't. It changes from person to person, from moment to moment. It isn't regular enough to be a precise unit of measure.
determine the composition of transformation that would map figure ABCD to figure A"B"C"D". 1. the transformation that would map vertex B to B' isa: a transformation down and rightb: a rotation of 90° about Bc: a rotation of 360° about B
Answers
Answer:
b: a rotation of 90° about B
Explanation:
A transformation down and right of the figure look like this:
Where the figure is just translated, so the orientation of the figure is the same.
In the same way, a rotation of 360° doesn't change the figure, because it is equivalent to make a full turn of the figure.
Finally, a rotation of 90° about B looks like this:
Where each segment of the initial figure forms an angle of 90° with its corresponding segment of the reflected figure. For example, BA is perpendicular to B'A'
Therefore, the answer is b: a rotation of 90° about B.
The number of accidents that occureach day at a certain intersection alongwith the corresponding probabilities areshown.Accidents01234Probability.935.03.02.01.005Find the expected number of accidentseach day.
Answers
Answer:
0.12
Explanation:
The expected value of a probability distribution can be obtained using the formula:
[tex]\sum ^n_{i\mathop=1}x_i\cdot P(x_i)[/tex]Therefore, the expected number of accidents will be:
[tex]\begin{gathered} E(X)=(0\times0.935)+(1\times0.03)+(2\times0.02)+(3\times0.01)+(4\times0.005) \\ =0+0.03+0.04+0.03+0.02 \\ =0.12 \end{gathered}[/tex]The expected number of accidents each day is 0.12.
Write - 4 - 2y= - x in standard form.
Answers
Answer:
[tex]-x\text{ + 2y = -4}[/tex]Explanation:
Here, we want to write the given equation in standard form
The equation of a line in standard form is as follows:
[tex]Ax\text{ + By = C}[/tex]What we have to do now is to bring the x and y terms together
We can have this as follows:
[tex]-x\text{ + 2y = -4}[/tex]-4 - 2y = -x
We want to leave -4 alone on the left
That means we have to transfer -2y that is there with it
To transfer -2y over the equality sign , its sign changes
-4 = +2y - x
But +2y can be written as 2y only
Finally by re-arrangement:
-x + 2y = -4
i forgot how i solved this and i need help understanding the second step done by lorne, thank u!
Answers
Given:
[tex](-3x^3+5x^2+4x-7)+(-6x^3+2x-3)[/tex]The second step is writing the terms individually and the addition sign between them, so, we will use the property of the opposite addition
For example, instead of writing: (1 - a), we can write it as 1 + (-a)
So, the expression will be:
[tex](-3x^3)+5x^2+4x+(-7)+(-6x^3)+2x+(-3)[/tex]From a 12 foot roll of rubber hose, a person cuts lengths of 2 3/8 feet, 2 1/2 feet, and 3 1/4 feet. How much hose is left on the roll?
Answers
Sum the lengths that the person cuts:
To sum mixed numbers:
[tex]2\frac{3}{8}ft+2\frac{1}{2}ft+3\frac{1}{4}ft=[/tex]1. Add the whole numbers:
[tex]2ft+2ft+3ft=7ft[/tex]2. Add fractions
[tex]\begin{gathered} \frac{3}{8}ft+\frac{1}{2}ft+\frac{1}{4}ft \\ \\ \text{Write all as fractions with denominator 8:} \\ \\ \frac{3}{8}ft+\frac{4}{8}ft+\frac{2}{8}ft=\frac{3ft+4ft+2ft}{8}=\frac{9}{8}ft \\ \\ \\ \end{gathered}[/tex]Then, the person cuts 7 9/8 ft, substract it from the initial 12 ft roll of rubber hose:
[tex]\begin{gathered} \text{Write the mixed number as a fraction:} \\ 7\frac{9}{8}ft=7ft+\frac{9}{8}ft=\frac{56ft+9ft}{8}=\frac{65}{8}ft \\ \\ \text{Substract the fraction above from 12ft}\colon \\ \\ 12ft-\frac{65}{8}ft=\frac{96ft-65ft}{8}=\frac{31}{8}ft \\ \\ \text{Write the result as a mixed number:} \\ \\ \frac{31}{8}ft=\frac{24}{8}ft+\frac{7}{8}ft=3\frac{7}{8}ft \end{gathered}[/tex]Then, 3 7/8 ft of hose are left on the rollThe safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 4 inches wide, 8 inches high, and 216 inches long can hold a load of 5050 pounds. What load would a beam 2 inches wide, 5 inches high, and 144 inches long, of the same material, support? Round your answer to the nearest integer if necessary.
Answers
We have the following, L, of the beam varies as the product of the width and the square of the height:
[tex]L\propto w\cdot h^2[/tex]And varies inversely as the lenght of the wooden beam:
[tex]L\propto\frac{w\cdot h^2}{l}[/tex]therefore:
[tex]L=k\cdot\frac{w\cdot h^2}{l}[/tex]where k is the proportionality constant
w = 4, h=8, l = 216 and L = 5050
[tex]\begin{gathered} 5050=k\cdot\frac{4\cdot8^2}{216} \\ k=\frac{5050\cdot216}{256} \\ k=4260.93 \end{gathered}[/tex]now, if w = 2, h = 5, l = 144:
[tex]\begin{gathered} L=4260.93\cdot\frac{2\cdot5^2}{144} \\ L=1479.5 \end{gathered}[/tex]Use words to describe each algebraic expression. 3. 6c4. X-15. t/26. 3t - 4
Answers
3. 6c
It multiplication between six and c.
Six times a number c.
4.
x-1
Its a subtraction.
A number minus one.
5.
t/2
A number divided by two.
6.
3t-4
Three times a number minus 4
Please walk me through these questions step by step (Simplifying the following terms)
Answers
The only formulas you have to know are:
[tex]\begin{gathered} \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b} \\ i^2=-1\rightarrow i=\sqrt{-1} \end{gathered}[/tex]When you do not know the root of a number, you have to express its root like a product of its main factors, for example:
[tex]\sqrt{75}=5\sqrt{3}[/tex]To find these factors, we can divide the original number among other numbers and multiply them, for example:
When we know those factors, we can use the laws of roots to simplify:
[tex]\begin{gathered} 75=5^2\cdot3 \\ \sqrt[]{75}=\sqrt{5^2\cdot3}=5^{\frac{2}{2}}\cdot\sqrt{3}=5\sqrt{3} \end{gathered}[/tex]With this in mind, we can now solve the exercise:
First term:
[tex]\begin{gathered} \frac{-20\pm\sqrt{75}}{5} \\ \\ \frac{-20\pm5\sqrt{3}}{5}\text{ \lparen Divide each term of the numerator by the denominator\rparen} \\ \\ -4\pm\sqrt[]{3} \end{gathered}[/tex]Second term:
*Notice that
[tex]\sqrt{-81}=\sqrt{(-1)\cdot(81)}=\sqrt{81}\cdot\sqrt{-1}=\sqrt{81}i=9i[/tex][tex]\begin{gathered} \frac{6\pm\sqrt{-81}}{3} \\ \\ \frac{6\pm9i}{3} \\ \\ 2\pm3i \end{gathered}[/tex]Third term:
*Notice the followings:
[tex]\sqrt{-28}=\sqrt{28\cdot-1}=\sqrt{28}\cdot\sqrt{-1}=\sqrt{4\cdot7}i=2\sqrt{7}i[/tex]Finally,
[tex]\begin{gathered} \frac{-4\pm\sqrt{-28}}{8} \\ \\ \frac{-4\pm2\sqrt{7}i}{8} \\ \\ \frac{-4}{8}\pm\frac{2\sqrt{7}}{8}i \\ \\ \frac{-1}{2}\pm\frac{\sqrt{7}}{4}\imaginaryI \end{gathered}[/tex]
generate ordered pairs for tha function y=x² - 9 using x = -4, -2,0,2 and 4
Answers
Generating ordered pairs is to solve for "y" using the function above with the given "x" values -4, -2, 0, 2, and 4.
If x = -4, then y = 7.
y = (-4)² - 9
y = 16 - 9
y = 7
If x = -2, then y = -5.
y = (-2)² - 9
y = 4 - 9
y = -5
If x = 0, then y = -9
y = 0² - 9
y = 0 - 9
y = -9
If x = 2, then y = -5
y = 2² - 9
y = 4 - 9
y = -5
If x = 4, then y = 7
y = (4)² - 9
y = 16 - 9
y = 7
To summarize, the ordered pairs for the function y = x² - 9 using the given x - values are:
1. (-4, 7)
2. (-2, -5)
3. (0, -9)
4. (2, -5)
5. (4, 7)
Below is the graph of the equation. Due to the nature of the equation, the graph is a parabola.
What are the coordinates (x,y) of the solution to the system of equations?
Answers
The system of equations given are
[tex]\begin{gathered} y=-8x+10 \\ y=x-8 \end{gathered}[/tex]ExplanationSolve the given system of equations using elimination method
[tex]\begin{gathered} y=-8x+10..........1 \\ y=x-8......2 \end{gathered}[/tex]Subtract equation 1 by equation 2.
[tex]\begin{gathered} (y+8x-10)-(y-x+8)=0 \\ 8x-10+x-8=0 \\ 9x=18 \\ x=2 \end{gathered}[/tex]Now find the value of y by substitute the value of x in equation 1.
[tex]\begin{gathered} y=-8\times2+10 \\ y=-16+10 \\ y=-6 \end{gathered}[/tex]AnswerHence the coordinates of x and y to the system of equations is
[tex](2,-6)[/tex]Find the square root. Assume that the variable is unrestricted, and use absolute value symbols when necessary. (Simplify your answer completely)
Answers
We are given the following expression:
[tex]\sqrt[]{81x^2}[/tex]To simplify this expression we will use the following property of radicals:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]Applying the property we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}[/tex]Now, the first radical is equal to 9 since 9 x 9 = 81, therefore, we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}=9\sqrt[]{x^2}[/tex]For the second radical we will use the following property of absolute values:
[tex]\lvert x\rvert=\sqrt[]{x^2}[/tex]Replacing we get:
[tex]\sqrt[]{81x^2}=\sqrt[]{81}\sqrt[]{x^2}=9\sqrt[]{x^2}=9\lvert x\rvert[/tex]Therefore, the expression reduces to the product of 9 and the absolute value of "x".
What are the next 4 terms of the sequence 1, 6, 11...?
Answers
The formula to find the sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]Where a1 is the first term of the sequence, n is the number of terms and d is the common difference. We can find the common difference by the following formula:
[tex]d=a_n-a_{n-1}[/tex]With the given terms of the sequence we can find d:
[tex]\begin{gathered} d=11-6=5 \\ or \\ d=6-1=5 \end{gathered}[/tex]The common difference is d=5.
Now, apply the formual to find the next 4 terms of the sequence:
[tex]\begin{gathered} a_4=1+(4-1)\cdot5=1+3\cdot5=1+15=16 \\ a_5=1+(5-1)\cdot5=1+4\cdot5=1+20=21 \\ a_6=1+(6-1)\cdot5=1+5\cdot5=1+25=26 \\ a_7=1+(7-1)\cdot5=1+6\cdot5=1+30=31 \end{gathered}[/tex]The next 4 terms are: A. 16,21,26,31