Answers
Given the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]The general solution of the quadratic equation is given by the expression:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the problem, we have the quadratic equation:
[tex]3x{}^2+2x-225=0[/tex]Identifying the coefficients:
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-225 \end{gathered}[/tex]Then, using the general solution formula:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt{4+2700}}{6}=\frac{-2\pm52}{6} \\ \\ \Rightarrow x_1=\frac{25}{3} \\ \\ \Rightarrow x_2=-9 \end{gathered}[/tex]And the solutions on the number line are:
Related Questions
How would you classify 8/2?
Answers
8/ 2 is a whole number, this is because 8 divided by 2 is 4. and 4 is a whole number.
4 is an integer. An integer is a whole number that can be positive, negative or zero. A rational numbe is a number that can be mode
3. If the function below (left) has a reflection about the "Y-AXIS", its new functionwould be below (right). *y=√xy = – VĩO TrueO FalseOther:
Answers
The graph for the original function y=√x is:
And the graph for the new function y=-√x
As we can see, the reflection is about the x-axis, not the y-axis.
So, the Answer is FALSE.
Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs. Find the kinetic energy for a mass of 4 grams and a velocity of 6 centimeters per second.
Answers
72 ergs
Explanation
Step 1
Kinetic energy varies jointly as the mass and the square of the velocity,then
[tex]E_k=\lambda\cdot m\cdot v^2[/tex]where
m is the mass, v is the velocity and
[tex]\lambda\text{ is a constant}[/tex]A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs
[tex]\begin{gathered} E_k=\lambda m\cdot v^2 \\ 36\text{ erg=}\lambda\cdot8\cdot3^2 \\ 36=\lambda\cdot8\cdot9 \\ 36=\lambda\cdot72 \\ \text{divide both sides by 72} \\ \frac{36}{72}=\lambda \\ \lambda=\frac{1}{2} \end{gathered}[/tex]so, the equation is
[tex]\begin{gathered} E_k=\lambda\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot m\cdot v^2 \end{gathered}[/tex]Step 2
now , we know the equation to find the kinetic energy of a object if we know its mass and its velocity
Let
mass= 4 grams
velocity = 6 cms per sec
then
[tex]\begin{gathered} E_k=\frac{1}{2}\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot(6\frac{\operatorname{cm}}{\sec})^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot36\frac{\operatorname{cm}}{\sec ^2} \\ E_k=72\text{ erg} \end{gathered}[/tex]I hope this helps you
what is the distance between points A(3,12) and B(6,15)? round to the nearest whole number
Answers
The distance between two points is given by:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then, in our case, we have:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(6-3)^2+(15-12)^2} \\ =\sqrt[]{(3)^2+(3)^2} \\ =\sqrt[]{9+9} \\ =\sqrt[]{18} \\ =4.2426 \end{gathered}[/tex]Therefore the distance between the points (rounded to the nearest whole number) is 4.
--212x21 4 Kuta Software - Infinite Algebra 2 Graphing Absolute Value Equations Graph each equation. 1) y=x-11 De 36 2) -\ x41
Answers
The expression below is an absolute expression
y = | x + 4|
An absolute value can be expressed as either plus or minus
Therefore, the equation can be written as
y = ( x + 4) or -(x + 4)
y = (x + 4)
y = -( x + 4)
We will need to graph this equation one after the other
y = x + 4
To find x, let y = 0
0 = x + 4
x = 0 - 4
x = -4
(-4, 0)
To find y, let x = 0
y = 0 + 4
y = 4
(0, 4)
The second equation is given as
y = -x - 4
To find x, let y = 0
0 = -x - 4
-x = 0 + 4
-x = 4
x = -4
(-4, 0)
To find y, let x = 0
y = -0 - 4
y = -4
(0, -4)
We will be graphing the above points
(-4, 0), (0, 4) and (-4, 0) (0, -4)
Which equation represents a circle? (x – 2)222+(y – 3)232=1 (x – 4)232+(y + k)212=1 x222+y222=1 x212+y232=1
Answers
Given:
Four different equations are given
Required:
To tell Which equation represents a circle?
Explanation:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis this means it touches the x-axis at that point
[tex]\begin{gathered} \frac{x^2}{2^2}+\frac{y^2}{2^2}=1 \\ \\ x^2+y^2=2^2 \\ \\ so\text{ r =2} \end{gathered}[/tex]That is others are in the form of ellipse equation.
How do you find the general form of an ellipse?
The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]else three options resemble with ellipse equation
Required answer:
[tex]\frac{x^{2}}{2^{2}}+\frac{y^{2}}{2^{2}}=1[/tex]A surveying crew has two points A and B marked along a roadside at a distance of 400 yd. A third point C ismarked at the back corner of a property along a perpendicular to the road at B. A straight path joining C to A forms a 28° angle with the road. Find the distance from the road to point C at the back of the property andthe distance from A to C using sine, cosine, and/or tangent. Round your answer to three decimal places.
Answers
In order to calculate the distance from B to C, we can use the tangent relation of the angle 28°.
The tangent is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan(28°)=\frac{BC}{AB}\\ \\ 0.5317094=\frac{BC}{400}\\ \\ BC=0.5317094\cdot400\\ \\ BC=212.684 \end{gathered}[/tex]Now, to calculate the distance from A to C, we can use the cosine relation.
The cosine is equal to the length of the adjacent leg to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \cos(28°)=\frac{AB}{AC}\\ \\ 0.8829476=\frac{400}{AC}\\ \\ AC=\frac{400}{0.8829476}\\ \\ AC=453.028 \end{gathered}[/tex]I will make seafood salad using strawberries and blueberries he uses 5 cups of strawberries for every 3 cups of blueberries which measure represents the amount of strawberries Alan uses for every bowl of fruit salad
Answers
His salad calls for 8 cups of salad to maintain the given ratio. (5 cups of strawberries for every 3 cups of blueberries) So the ratio is 5/8 for the strawberries.
Let x be what he needs for 1 cup of fruit
5/8 = x
That's because there are 5 cups of strawberries for every 8 ( 5 strawberries + 3 blueberries ) items he needs.
solve the equation 3b-13+4b=7b+1
Answers
Answer:
The given equation has no solution.
Explanation:
Given the equation:
[tex]3b-13+4b=7b+1[/tex]To solve, Firstly let's collect the like terms;
[tex]\begin{gathered} 3b-13+4b=7b+1 \\ 3b+4b-13=7b+1 \\ 7b-13=7b+1 \end{gathered}[/tex]From the resulting equation, we can see that the left side of the equation is not equal to the right side.
Adding 13 to both sides;
[tex]\begin{gathered} 7b-13+13=7b+1+13 \\ 7b=7b+14 \end{gathered}[/tex]Therefore, the given equation has no solution.
Arectangular field has an area of 646 square feet. The width of the field is 19 feetWite a number in the box to show the missing measurement What is the length of the field?
Answers
The area of a rectangle is
[tex]A=19\cdot x=76[/tex]x is the number missing in the box
[tex]x=\frac{76}{19}=4[/tex]the length of the field is 30+4 =34 feet
Ryhanna has a container with a volume of 1.5 liters. She estimates the volume to be 2.1 liters. What is the percent error?
Answers
We know that Ryhanna has a container with a volume of 1.5 liters and that she estimates the value to be 2.1 liters. We want to find the percent error.
For doing so, we remember that the percent error is given by the expression:
[tex]=\frac{\mleft|v_{true}-v_{estimated}\mright|}{v_{true}}\cdot100[/tex]In this exercise, we have that:
[tex]\begin{gathered} v_{\text{true}}=1.5 \\ v_{\text{estimated}}=2.1 \end{gathered}[/tex]So, replacing we obtain:
[tex]\text{error}=\frac{\mleft|1.5-2.1\mright|}{1.5}\cdot100=\frac{0.6}{1.5}\cdot100=0.4\cdot100=40[/tex]This means that Ryhanna estimated the value of the volume with an error of 40%.
5 1 point A high rise apartment is on fire. 1 There are two people in a window that is 14.5 feet above the What angie must the ladder make with the ground in order to 2 Type your answer... 3 4
Answers
Detrmine the angle of ladder by uisng the trigonometric ratio.
[tex]\begin{gathered} \sin \alpha=\frac{14.5}{22} \\ \alpha=\sin ^{-1}(0.66) \\ =41.29 \\ \approx41^{\circ} \end{gathered}[/tex]So answer is 41 degree.
Quadrilateral GHJK is a rectangle. Find each measure if m<1=37
Answers
Answer:
[tex]\begin{gathered} m\angle2\text{ = 53} \\ m\angle3\text{ = 37} \\ m\angle4\text{ = 37} \\ m\angle5\text{ =53} \\ m\angle6\text{ =106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]Explanation:
Here, we want to find the measure of the given angles
From what we have, the angle marked 1 is of a value 37 degrees
For a rectangle, each angle at the edges equal 90 degrees
That makes a total of 360 degrees
Also, we have four isosceles triangle. These are triangles with equal base angle in each
With these in mind, we can proceed to get the value of the missing indicated angles
a)
[tex]\begin{gathered} m\angle1\text{ + m}\angle2\text{ = 90} \\ m\angle2\text{ = 90-37} \\ m\angle2\text{ = 53} \end{gathered}[/tex]b)
[tex]\begin{gathered} m\angle5\text{ + m}\angle1\text{ = 90} \\ By\text{ transition:} \\ m\angle5\text{ = m}\angle2\text{ = 53} \end{gathered}[/tex]c)
[tex]\begin{gathered} m\angle4\text{ + m}\angle5\text{ = 90} \\ m\angle1\text{ = m}\angle4\text{ = 37} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ m}\angle3\text{ = m}\angle4\text{ = 37} \\ \text{Base angles of isosceles triangle are equal} \end{gathered}[/tex]d)
[tex]\begin{gathered} m\angle6\text{ + m}\angle3\text{ + m}\angle4\text{ = 180} \\ \text{sum of interior angles of a triangle} \\ m\angle6\text{ = 180-37-37} \\ m\angle6\text{ = 106} \end{gathered}[/tex]e)
[tex]\begin{gathered} m\angle6\text{ + m}\angle7\text{ = 180} \\ \text{Sum of angles on a straight line} \\ m\angle7\text{ = 180-106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]f)
Which line represents the best fit for the scatter plot data?
Answers
A line of best fit can be roughly determined by drawing a straight line on a scatter plot so that the number of points above and below the line is about equal and the line passes through as many points as possible.
When we look at the fits in B and C, we notice that the line is not following the behavior of the data accurately, so we can rule out these options.
When we look at option D, we can see that the line is above all the points, we can also notice that this line doesn't go through any point of the data, that's why option A, is the best fit for this set of data, since it passes through some points and there are points above and below the line.
The correct graph is A
1. Determine the difference inclock 12 arithmetic bystarting at the first numberand countingcounterclockwise on theclock the number. Of unitsgiven by the second number 1-11=?
Answers
Given:
The identity element is P.
Required:
Determine the inverse if exist of
(a) P (b) Q (c) R
Explanation:
We know that the inverse is the element when combined on the right or the left through the operation, always gives the identity element as the result.
We can see in the first row the identity element P is getting by the operation of P and P. Thus the Inverse of P is itself.
In the second and third rows, the identity element is P is getting by the operation of Q and R.
Thus the inverse of Q is R and the inverse of R is Q.
Both are inverse of each other.
Final Answer:
The Inverse of the following are as:
(a) P = P
(b) Q = R
(c) R =Q
Which equations of the three lines are parallel, perpendicular, or neither?
Answers
The given lines are
[tex]6x-4y=8;y=\frac{3}{2}x+6;2y=3x+5[/tex]Convert each equation in the form
[tex]y=mx+c_{}[/tex]Therefore it follows:
[tex]\begin{gathered} 6x-4y=8\Rightarrow y=\frac{3}{2}x+2 \\ y=\frac{3}{2}x+6\Rightarrow y=\frac{3}{2}x+6 \\ 2y=3x+5\Rightarrow y=\frac{3}{2}x+\frac{5}{2} \end{gathered}[/tex]Therefore the slopes of all three lines are:
[tex]\begin{gathered} m_1=\frac{3}{2} \\ m_2=\frac{3}{2} \\ m_3=\frac{3}{2} \end{gathered}[/tex]The slopes of all three lines are equal therefore all three lines are parallel with each other.
Therefore it follows that:
[tex]l_1\parallel l_2\parallel l_3[/tex]Simplify the following expression by multiplying by theconjugate:6+3/5√5-2
Answers
Answer:
Simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]Explanation:
Given the expression;
[tex]\frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}[/tex]Multiplying both the denominator and numerator by the conjugate of the denominator;
[tex]\begin{gathered} \frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}\times\frac{\sqrt[]{5}+2}{\sqrt[]{5}+2}=\frac{(6+3\sqrt[]{5})(\sqrt[]{5}+2)}{(\sqrt[]{5}-2)(\sqrt[]{5}+2)} \\ =\frac{6\sqrt[]{5}+6\sqrt[]{5}+12+3(5)}{5-4} \\ =\frac{12\sqrt[]{5}+12+15}{1} \\ =27+12\sqrt[]{5} \end{gathered}[/tex]Therefore, simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)O A. y - (x - 1)(x+5)OB. y - (x + 1)(x+5)O C. y - (x + 1)(x - 5)O D. y = (x - 1)(x-5)
Answers
The graph of the function intersect the x-axis at x = 1 and x = 5. So zeos of the function is,
[tex]x=1\text{ and x = 5}[/tex]So factorization quation of polynomial equation is,
[tex]y=(x-1)(x-5)[/tex]Answer: y = (x - 1)(x - 5)
You are comparing two savings accounts based on the interest you would earn and the fees they charge. Assuming you have a savings account with an average balance of $500, which combination of interest rates and fees are a better deal? (Hint: Using a one year period, determine the balance that you would have at Bank A and Bank B). O Bank A offers you a savings account with a 10% annual interest rate and $5/month in fees O Bank B offers you a savings account with 2% annual interest rate and no fees O The two banks deals are equivalent O Trick question -- it's a bad idea to open a savings account with just $500
Answers
Bank B gives the better deal to open the savings account rather than Bank A.
Given that:-
Average balance of savings account = $ 500
Annual interest rate of Bank A = 10 %
Fees of Bank A = $ 5/month
Annual interest rate of Bank = 2 %
We have to find which bank gives the better deal.
In Bank A, after one year the amount of money in my bank account will be:-
500 + 10 % of 500 - 5*12 = 500 + 50 - 60 = 500 - 10 = $ 490.
In Bank B, after one year the amount of money in my bank account will be:-
500 + 2 % of 500 = 500 + 10 = $ 510.
Hence,
Bank B gives the better deal to open the savings account rather than Bank A.
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I will be attaching a picture of the question as you can see the question has already been answered my teacher wants me to type out how she got the answer I need it fast bc this is due in an hour.
Answers
we calculate the radius, i.e. the distance between two points
[tex]\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ r=\sqrt[]{(-1-2)^2+(-8-(-3))^2} \\ r=\sqrt[]{(-3)^2+(-8+3)^2} \\ r=\sqrt[]{(-3)^2+(-5)^2} \\ r=\sqrt[]{9+25} \\ r=\sqrt[]{34} \end{gathered}[/tex]then, we have that the equation of the circle is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where} \\ h=2 \\ k=-3 \\ r^2=(\sqrt[]{34})^2=34 \end{gathered}[/tex]therefore the equation is
[tex]\begin{gathered} (x-2)^2+(y-(-3))^2=34 \\ (x-2)^2+(y+3)^2=34 \end{gathered}[/tex]Which equation shows that the Pythagorean identity is true for 0 = 0?
Answers
The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of theactual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.
Answers
Question
The scale factor of a model of a warehouse to the actual warehouse is 1 to 2. The volume of the actual warehouse is 8,455 ft^3. Find the volume of the model. Round to a whole number.
Solution
The scale factor (or ratio) of the model to the actual is
[tex]1\colon2[/tex]The scalar factor (or ratio) for the volume will be
[tex]\begin{gathered} 1^3\colon2^3 \\ 1\colon8 \end{gathered}[/tex]To find the volume of the model
Let the volume of the model by denoted with x
We use the ratio
[tex]\begin{gathered} \frac{1}{8}=\frac{x}{8455} \\ \text{cross multiply} \\ 8\times x=1\times8455 \\ 8x=8455 \\ x=\frac{8455}{8} \\ x=1056.875 \\ x=1057ft^3\text{ (to the nearest whole number)} \end{gathered}[/tex]Thus, the volume of the model is 1057ft^3
What is the value of x in the solution to this system of equations? 3x-5 y=22 y=-5x+ 32
Answers
The value of x in the system of equations is 6.5
The system of equation:
3x - 5y = 22
y = -5x + 22
Now arrange the above equation in proper order :
As,
3x - 5y = 22
5x + y = 22
Now solve the above equation as:
(3x - 5y = 22) x 1
(5x + y = 22) x 5
We have:
3x - 5y = 22
25x + 5y = 110
On solving above equation by elimination :
28x = 132
x = 6.5
Hence, the value of x in the system of equations is 6.5
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The perfect squares between 54 and 102.
Answers
The perfect squares are between 54 and 102.
54 and 102 are taken,
7 × 7 = 49
8 × 8 = 64
9 × 9 = 81
10 × 10 = 100
11 × 11 = 121
Here, the perfect squares between 54 and 102 are 8, 9, 10.
So, answer is 8 × 8, 9 × 9, 10 × 10
Find the midpoint of AC.B (0, a)C (a, a)D (a,0)a(4)2A (0,0)Enter the value thatbelongs in the green box.Midpoint Formula: M = (*¹*²₁¹²)RE
Answers
The formula to calculate the midpoint between two points is given by
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]we have the coordinates
A(0,0) and C(a,a)
substitute the given coordinates
[tex]\begin{gathered} M=(\frac{0+a}{2},\frac{0+a}{2}) \\ \\ M=(\frac{a}{2},\frac{a}{2}) \end{gathered}[/tex]Which measurement is the best estimate for the volume of the figure? Roundeach measurement to the nearest whole number to get your estimate.A. 9 cubic metersB. 12 cubic metersC. 6 cubic metersD. 8 cubic meters
Answers
we have that
The volume of the rectangular prism is given by
[tex]V=L*W*H[/tex]where
L=3.5 m --------> 4 m
W=0.7 m -------> 1 m
H=2.2 m -------> 2 m
substitute
[tex]\begin{gathered} V=(4)(1)(2) \\ V=8\text{ m}^3 \end{gathered}[/tex]The answer is option DA pianist plans to play 6 pieces at a recital from her repertoire of 26 pieces.
Answers
Answer:
[tex]230230\text{ Recital programs are possible}[/tex]Explanation:
Here, we want to get the number of possible recital programs
We are not concerned about arrangements here
Thus, we have to use combination
We have this as:
[tex]^nC_r\text{ = }\frac{n!}{(n-r)!r!}[/tex]where in this case, n is 26 and r is 6
Substituting the values in the combination formula, we have it that:
[tex]^{26}C_6=\text{ }\frac{26!}{(26-6)!6!}\text{ = 230230}[/tex]
I need your help know
Answers
Answer : 87.9 square inches
Given the following data
Radius of the cylindrical cup = 2 inches
Height of the cylindrical cup = 5 inches
Surface area is given as
[tex]\begin{gathered} A\text{ = 2}\pi rh\text{ + 2 }\cdot\pi\cdot r^2 \\ \text{Where }\pi\text{ = 3.14} \\ A\text{ = 2}\pi r(h\text{ + r)} \\ A\text{ = 2 x 3.14 x 2(5 + 2)} \\ A\text{ = 12.56(7)} \\ A\text{ = 12.56 x 7} \\ A=87.9inches^2 \end{gathered}[/tex]find the coordinates of the ordered pair where the maximum value occurs for equation P equals 5 x + 5y + 42 given these constrains
Answers
Given the equation:
[tex]P=5x+5y+42[/tex]Given the constraints:
[tex]\begin{gathered} -2x+4y\ge-4 \\ x\ge-8 \\ y\le9 \end{gathered}[/tex]Let's find the ordered pair where the maximum value occurs for P.
From the inequality of let's solve for x and y.
At x = -8:
[tex]\begin{gathered} -2x+4y=-4 \\ -2(-8)+4y=-4 \\ \\ 16+4y=-4 \\ \\ \text{Subtract 16 from both sides:} \\ 16-16+4y=-4-16 \\ 4y=-20 \\ \\ \text{Divide both sides by 4:} \\ \frac{4y}{4}=\frac{-20}{4} \\ \\ y=-5 \\ \\ \text{Thus, we have the points:} \\ (x,y)\Longrightarrow(8,-5) \end{gathered}[/tex]At y = 9:
[tex]\begin{gathered} -2x+4y=-4 \\ -2x+4(9)=-4 \\ -2x+36=-4 \\ \\ \text{Subtract 36 from both sides:} \\ -2x+36-36=-4-36 \\ -2x=-40 \\ \\ \text{Divide both sides by -2:} \\ \frac{-2x}{-2}=\frac{-40}{-2} \\ \\ x=20 \\ \\ \text{thus, we have the point:} \\ (x,y)\Longrightarrow(20,9) \end{gathered}[/tex]Input the values of x and y into the equation and solve for evaluate for P.
• (x, y) ==> (-8, -5):
P = 5x + 5y + 42
P = 5(-8) + 5(-5) + 42
P = -40 - 25 + 42
P = -23
• (x, y) ==> (20, 9):
P = 5x + 5y + 42
P = 5(20) + 5(9) + 42
P = 100 + 45 + 42
P = 187
We can see the maximum value of P is 187 at (20, 9)
The maximum value occurs at (20, 9)
• ANSWER:
(20, 9)
Evaluate (10²-8²)÷(5+7)-6
Answers
BODMAS RULE is used in simplification problems. The opertation are done in the following order in simplification.
B-->Bracket
D-->Division
M-->Multiplication
A-->Addition
S-->Subtraction
[tex]\begin{gathered} (10^2-8^2)\div(5+7)-6 \\ =(100-64)\div(12)-6\text{ (Did operations inside brackets)} \\ =36\div12-6\text{ } \\ =3-6\text{ (Did division 36 }\div\text{ 12)} \\ =-3 \end{gathered}[/tex]Therefore, the answer is -3.