The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the circle intersects the parabola at the parabola’s vertex, which statement must be true?
The maximum number of solutions is one.
The maximum number of solutions is three.
The circle has a radius equal to 3.
The circle has a radius less than 9.
Answers
Answer:
"The maximum number of solutions is one."
Step-by-step explanation:
Hopefully the drawing helps visualize the problem.
The circle has a radius of 9 because the vertex is 9 units above the center of the circle.
The circle the parabola intersect only once and cannot intercept more than once.
The solution is "The maximum number of solutions is one."
Let's see if we can find an algebraic way:
The equation for the circle given as we know from the problem without further analysis is so far [tex]x^2+y^2=r^2[/tex].
The equation for the parabola without further analysis is [tex]y=ax^2+9[/tex].
We are going to plug [tex]ax^2+9[/tex] into [tex]x^2+y^2=r^2[/tex] for [tex]y[/tex].
[tex]x^2+y^2=r^2[/tex]
[tex]x^2+(ax^2+9)^2=r^2[/tex]
To expand [tex](ax^2+9)^2[/tex], I'm going to use the following formula:
[tex](u+v)^2=u^2+2uv+v^2[/tex].
[tex](ax^2+9)^2=a^2x^4+18ax^2+81[/tex].
[tex]x^2+y^2=r^2[/tex]
[tex]x^2+(ax^2+9)^2=r^2[/tex]
[tex]x^2+a^2x^4+18ax^2+81=r^2[/tex]
So this is a quadratic in terms of [tex]x^2[/tex]
Let's put everything to one side.
Subtract [tex]r^2[/tex] on both sides.
[tex]x^2+a^2x^4+18ax^2+81-r^2=0[/tex]
Reorder in standard form in terms of x:
[tex]a^2x^4+(18a+1)x^2+(81-r^2)=0[/tex]
The discriminant of the left hand side will tell us how many solutions we will have to the equation in terms of [tex]x^2[/tex].
The discriminant is [tex]B^2-4AC[/tex].
If you compare our equation to [tex]Au^2+Bu+C[/tex], you should determine [tex]A=a^2[/tex]
[tex]B=(18a+1)[/tex]
[tex]C=(81-r^2)[/tex]
The discriminant is
[tex]B^2-4AC[/tex]
[tex](18a+1)^2-4(a^2)(81-r^2)[/tex]
Multiply the (18a+1)^2 out using the formula I mentioned earlier which was:
[tex](u+v)^2=u^2+2uv+v^2[/tex]
[tex](324a^2+36a+1)-4a^2(81-r^2)[/tex]
Distribute the 4a^2 to the terms in the ( ) next to it:
[tex]324a^2+36a+1-324a^2+4a^2r^2[/tex]
[tex]36a+1+4a^2r^2[/tex]
We know that [tex]a>0[/tex] because the parabola is open up.
We know that [tex]r>0[/tex] because in order it to be a circle a radius has to exist.
So our discriminat is positive which means we have two solutions for [tex]x^2[/tex].
But how many do we have for just [tex]x[/tex].
We have to go further to see.
So the quadratic formula is:
[tex]\frac{-B \pm \sqrt{B^2-4AC}}{2A}[/tex]
We already have [tex]B^2-4AC}[/tex]
[tex]\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}[/tex]
This is t he solution for [tex]x^2[/tex].
To find [tex]x[/tex] we must square root both sides.
[tex]x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]
So there is only that one real solution (it actually includes 2 because of the plus or minus outside) here for x since the other one is square root of a negative number.
That is,
[tex]x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]
means you have:
[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]
or
[tex]x=\pm \sqrt{\frac{-(18a+1)-\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex].
The second one is definitely includes a negative result in the square root.
18a+1 is positive since a is positive so -(18a+1) is negative
2a^2 is positive (a is not 0).
So you have (negative number-positive number)/positive which is a negative since the top is negative and you are dividing by a positive.
We have confirmed are max of one solution algebraically. (It is definitely not 3 solutions.)
If r=9, then there is one solution.
If r>9, then there is two solutions as this shows:
[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}[/tex]
r=9 since our circle intersects the parabola at (0,9).
Also if (0,9) is intersection, then
[tex]0^2+9^2=r^2[/tex] which implies r=9.
Plugging in 9 for r we get:
[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2(9)^2}}{2a^2}}[/tex]
[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+324a^2}}{2a^2}}[/tex]
[tex]x=\pm \sqrt{\frac{-(18a+1)+\sqrt{(18a+1)^2}}{2a^2}}[/tex]
[tex]x=\pm \sqrt{\frac{-(18a+1)+18a+1}{2a^2}}[/tex]
[tex]x=\pm \sqrt{\frac{0}{2a^2}}[/tex]
[tex]x=\pm 0[/tex]
[tex]x=0[/tex]
The equations intersect at x=0. Plugging into [tex]y=ax^2+9[/tex] we do get [tex]y=a(0)^2+9=9[/tex].
After this confirmation it would be interesting to see what happens with assume algebraically the solution should be (0,9).
This means we should have got x=0.
[tex]0=\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}[/tex]
A fraction is only 0 when it's top is 0.
[tex]0=-(18a+1)+\sqrt{36a+1+4a^2r^2}[/tex]
Add 18a+1 on both sides:
[tex]18a+1=\sqrt{36a+1+4a^2r^2[/tex]
Square both sides:
[tex]324a^2+36a+1=36a+1+4a^2r^2[/tex]
Subtract 36a and 1 on both sides:
[tex]324a^2=4a^2r^2[/tex]
Divide both sides by [tex]4a^2[/tex]:
[tex]81=r^2[/tex]
Square root both sides:
[tex]9=r[/tex]
The radius is 9 as we stated earlier.
Let's go through the radius choices.
If the radius of the circle with center (0,0) is less than 9 then the circle wouldn't intersect the parabola. So It definitely couldn't be the last two choices.
Answer:
Option A.
Step-by-step explanation:
A circle was drawn with the center at origin (0, 0) and a point (0, 9) on the circle.
So the radius will be r = [tex]\sqrt{(0-0)+(0-9)^{2}}=9[/tex]
Equation of this circle will be in the form of x² + y² = r²
Here r represents radius.
So the equation of the circle will be x² + y² = 9²
Or x² + y² = 81
Now we will form the equation of the parabola having vertex at (0, 9)
y² = (x - h)² + k
where (h, k) is the vertex.
Equation of the parabola will be y² = (x - 0)² + 9
y² = x² + 9
Now we will replace the value of y² from this equation in the equation of circle to get the solution of this system of the equations.
x² + x² + 9 = 81
2x² = 81 - 9
2x² = 72
x²= 36
x = ±√36
x = ±6
Since circle and parabola both touch on a single point (0, 9) therefore, there will be only one solution that is x = 6.
For x = 6,
6² + y² = 9²
36 + y² = 81
y² = 81 - 36 = 45
y = √45 = 3√5
Option A. will be the answer.
Related Questions
Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient.
Answers
Answer:
Part 1) 3 --------> [tex]3\frac{3}{7}[/tex] ÷ [tex]1\frac{1}{7}[/tex]
Part 2) -3 -------> [tex]-2\frac{2}{5}[/tex] ÷ [tex]\frac{4}{5}[/tex]
Part 3) 2 --------> [tex]-12.2[/tex] ÷ [tex]-6.1[/tex]
Part 4) -2 -------> [tex]-16[/tex] ÷ [tex]8[/tex]
Step-by-step explanation:
Part 1) we have
[tex]3\frac{3}{7}[/tex] ÷ [tex]1\frac{1}{7}[/tex]
Convert mixed number to an improper fraction
[tex]3\frac{3}{7}=\frac{3*7+3}{7}=\frac{24}{7}[/tex]
[tex]1\frac{1}{7}=\frac{1*7+1}{7}=\frac{8}{7}[/tex]
Substitute
The quotient is equal to
[tex](\frac{24}{7})/(\frac{8}{7})=\frac{24}{8}=3[/tex]
Part 2)
we have
[tex]-2\frac{2}{5}[/tex] ÷ [tex]\frac{4}{5}[/tex]
Convert mixed number to an improper fraction
[tex]-2\frac{2}{5}=-\frac{2*5+2}{5}=-\frac{12}{5}[/tex]
Substitute
The quotient is equal to
[tex](-\frac{12}{5})/(\frac{4}{5})=-\frac{12}{4}=-3[/tex]
Part 3) we have
[tex]-12.2[/tex] ÷ [tex]-6.1[/tex]
Convert decimal number to an improper fraction
[tex]-12.2=(-12.2)*\frac{10}{10}=-\frac{122}{10}[/tex]
[tex]-6.1=(-6.1)*\frac{10}{10}=-\frac{61}{10}[/tex]
Substitute
The quotient is equal to
[tex](-\frac{122}{10})/(-\frac{61}{10})=\frac{122}{61}=2[/tex]
Part 4) we have
[tex]-16[/tex] ÷ [tex]8[/tex]
Remember that
[tex]-16=-8*2[/tex]
Substitute
The quotient is equal to
[tex](-8*2)/(8)=-2[/tex]
Answer:
the guy above me got it and i needed the points sorry lol
Step-by-step explanation:
Which set represents the range of the function shown{(-1,5),(2,8),(5,3),(13,-4)}
Answers
Answer:
{-4,3,5,8}
Step-by-step explanation:
The function is in (a,b) form. Always remember that range comes after domain. So here a represents the domain and b represents the range.
In the given function:
{(-1,5),(2,8),(5,3),(13,-4)}
The range will be {5,8,3,-4}
We will write it in ascending order
{-4,3,5,8} ....
A triangular portion of a baseball field is marked as shown below. To the
nearest tenth, what is the length of the side labeled c?
Answers
Answer:
im say your answer is between 1 choice and last choice but I'm say last choice 2.2
Answer:
B. 1.6 yards
Step-by-step explanation:
For the given triangle ABC,
We have ∠BAC = 36° and ∠BCA = 28° and side BC = 2 yards
We have to find length of side labeled as c, so using the sine rule we can say
[tex]\frac{c}{sin28} = \frac{2}{sin36} \\\frac{c}{0.4694} = \frac{2}{0.5877}\\c = 3.4030*0.4694\\c = 1.59\\[/tex]
c is equal to 1.59 which is nearly equal to 1.6 yards so the correct option would be D.
What is a true statement about a 45-45-90 triangle?
Answers
Answer:
C. The hypotenuse is √2 times long as either leg.Step-by-step explanation:
Look at the picture.
C. The hypotenuse is √2 ties as long as either leg
What is the point-slope form of a line that has a slope of 5 and passes through the point (3, –4)?
Answers
Answer:
y + 4 = 5(x - 3)
Step-by-step explanation:
In the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are.
Answer:
D. The Equation is y - ( - 4 ) = 5 ( x - 3 )
Step-by-step explanation:
Got It right on Edg.
I NEED HELP WITH THIS PROBLEM!!!!
Answers
Answer:
0
Step-by-step explanation:
The first equation is for when t = 8.
The second equation is for when t = 10.
The third equation is for all other values of t.
For t = 2, we use the third equation.
f(t) = t² − 3t + 2
f(2) = 2² − 3(2) + 2
f(2) = 4 − 6 + 2
f(2) = 0
Find the product. (3p^4)^3 · (p^2)^7
Answers
Answer: [tex]27p^{26}[/tex]
Step-by-step explanation:
In this case, you need to use the Power of a power property, which states that:
[tex](a^m)^n=a^{mn}[/tex]
And the Product of powers property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then, applying this, we get the following product:
[tex](3p^4)^3*(p^2)^7=27p^{(4)(3)}*p^{(2)(7)}=27p^{12}*p^{14}=27p^{(12+14)}=27p^{26}[/tex]
Which statement correctly compares AB and FD?
AB and FD are the same length.
AB is longer than FD.
O
AB is shorter than FD
AB is shorter than or the same length as FD.
Answers
Answer:
AB is longer than FD.
Step-by-step explanation:
This is an SAS triangle problem.
According to the law of cosines,
c^2 = a^2 + b^2 - 2abcosC
In triangle ABC, a = BC, b = AC, and c = AB
In triangle FDE, a = DE, b = FE, and c = FD.
The only difference is that C is 72° in one triangle and 65° in the other.
We know that cos0° = 1 and cos 90° = 0, so cos72° < cos65°.
In triangle ABC, cosC is smaller, so you are subtracting a smaller number from a^2 + b^2.
c^2 is larger, so c is larger.
AB is longer than FD.
That makes sense because, as you widen the angle between your outstretched arms, the distance between your hands increases.
The statement which correctly compares AB and FD is AB is longer than FD.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given two triangles, ABC and DEF.
We have to find the relationship between the sides AB and FD.
Given that,
Sides AC and FE are congruent.
Sides BC and DE are congruent.
Included angles, ∠C = 72° and ∠E = 65°
The side opposite to larger angle will be larger.
So AB is longer than FD.
Hence AB is longer than FD.
Learn more about Angles here :
https://brainly.com/question/30381855
#SPJ7
Translate into algebraic expression:
If Kevin makes c toys in m minutes, how many toys can he make per hour?
Answers
Answer:
The numbers of toys per hour is 60c/m toys
Step-by-step explanation:
* Lets explain how to solve the problem
- an algebraic expression is an expression formed from integer
constants, variables, and the algebraic operations like addition,
subtraction, multiplication, division
- Ex: 5x² − 7xy + a is an algebraic expression
* Lets solve the problem
- Kevin makes c toys in m minutes
∴ His rate is c/m toy per minute
- To find the number of toys in one hour multiply his rate by the time
in minutes
∵ In one hour there are 60 minutes
∵ His rate = c/m (toy/minute)
∵ The time is 60 minutes
∴ The number of toys = c/m × 60 = 60c/m toys
∴ The numbers of toys per hour is 60c/m toys
What is the sum of the lengths of the two trails?
Answers
The correct option is B.
The sum of the lengths of the diagonals in the given parallelogram is 12 miles. This value was derived by first identifying the values of the segments in relation to 'y', calculating for 'y', then using the property of the parallelogram where the diagonals bisect each other.
Explanation:To solve for this geometry problem involving a parallelogram, we need to equate the given values and solve for 'y'. The values given stipulate that DE = EB; therefore, we get:
y+2 = 3y-4
y-3y = -4-2
-2y = -6
y = 3
Solving for y, we obtain y = 3.
Next is to solve AE, which is given as CE = AE and substituting the calculated value of y, we get:
AE = 2y - 3 = 2(3) - 3 = 3 miles.
In this parallelogram, it is a property that the diagonals bisect each other. Hence, DE = EB, and AE = EC. Therefore, AC equals 2 * AE = 2 * 3 miles = 6 miles.
Similarly, DB equals 2 * DE = 2 * 3 miles = 6 miles.
Thus, the sum of the lengths of the two trails, AC and BD, is 6 miles + 6 miles = 12 miles.
Learn more about Parallelogram Diagonal Lengths here:https://brainly.com/question/32934618
#SPJ3
The complete question is given below:
The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles.
What is the sum of the lengths of the two trails?
A. 6 miles
B. 12 miles
C. 16 miles
D. 36 miles
For Carolina's birthday, her mom took her and 4 friends to a water park. Carolina's mom paid $40 for 5 student tickets. What was the price for one student ticket?
Answers
Answer:
The price for one student ticket is $8
Which of the following statements are true ? Check all that apply
Answers
Answer:
Options A) and E)
Step-by-step explanation:
If you use Ruffini's method for polynomials, you can find the roots.
The given picture shows us the first root of the polynomial [tex]5x^{2}-16x+12=0[/tex] wich is 2.
Thus, the original polynomial can be written as
[tex](x-2)*(5x-6)=0[/tex]
Here, you can notice that (x-2) is a factor
The length of a rectangle is (3x - 5) inches, and its width is 2x inches. Find the area of the rectangle.
Answers
Answer:
6x^2 - 10x inches ^2
Step-by-step explanation:
The area of a rectangle is
A = l*w
= (3x-5) * (2x)
= 6x^2 - 10x
Answer:
The area of the rectangle is 6x^2(squared)-10x
Step-by-step explanation:
To find the area of rectangles, you must multiply the length by the width. The formst for this is A=LxW. When you substitute each part of the equation in, it becomes 2x(3x-5). When you have parentheses, distribute the number on the outside to each number(or variable) on the inside. First, multiply 2x by 3x. This leaves you with 6x^2(squared). Then, multiply the 2x by the -5. This leaves you with -10x. Combine each part to get 6x^2(squared)-10x. :)
Tonya wrote the equation below which solves for x.
x=150-6y
Which equation is equivalent to Tonya’s equation?
Answers
Answer:
x+6y=150
Step-by-step explanation:
If you add 6y to both sides of the equation, it becomes this, making it equal.
Answer:
x+6y = 150 (B)
Step-by-step explanation:
Given the equation x = 150-6y
The equation is also equivalent to
x+6y = 150.
This is gotten simply by taking -6y to the other side of the equation but note that if a function or constant is crossing an 'equal to' sign in an equation, it changes the sign. Considering this equation, -6y changed to +6y upon crossing the equal to sign to give is x+6y = 150 which is the required answer.
Louisa has a goal of collecting 100 pounds of dog food for a local shelter. She records how many pounds of food she collects
each week
Answers
Answer:
Louisa needs 28 more pounds of dog food to reach 100 pounds
Step-by-step explanation:
=100 - 20.5 + 18.75 + 32.75
=28
Answer:
Louisa needs 28 pounds more of dog food.
Step-by-step explanation:
We need to find how much dog food she had collected in three weeks. In order to do this we need to add the number of pound collected in each week.
Notice that the pounds collected are given in different notations, so we need to write them ‘‘uniformly’’, in particular we must write the mixed number of the second week in decimal notation:
[tex]18\frac{3}{4} = \frac{18\times 4+3}{4}=\frac{75}{4} = 18.75[/tex]
Now, we add the three numbers:
[tex]20.5+18.75+32.75 = 72[/tex]
Finally, as she wants to collect 100 pounds and already has 72, Louisa only has to collect 28 pound more to complete her goal.
56
There are 134 third-graders and 167 fourth-graders at the annual school and
family picnic. The number of students is 7 times the number of adults.
Each picnic table can seat 9 people. How many picnic tables will need to be
set up for the picnic?
Show your work.
total
301. Student
PRACTICE TEST 1
+63
64
i
n
63
third graders and
Answers
Answer:
39
Step-by-step explanation:
134 + 167 = 301
301/7=43
301+430= 344
344/9 = 38.2 so you would need 39 tables
Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below:
gure
-10-9355321245573 9 10
Figure 2 +
Which two transformations can map figure i onto figure 2?
Answers
Answer:
See below.
Step-by-step explanation:
The first is a reflection in the y-axis.
Then a downward translation of 10 units.
You are a real estate agent. For every house you sell you earn 3.8% commission. This month you sold 2 houses that had a combined total of $560,950. How much commission will you earn?
Answers
Answer:
$ 134,628
Step-by-step explanation:
1. make 3.8 into a percent round decimal to the right 2 times
2.multiply the total with the percent
3.solve
4.take answer and subtracted from the total
5.solve
6. subtract the number you got from the first solution problem from the last problen solution
7.solve
Answer: $21,316.1
Step-by-step explanation:
Given : For every house you sell you earn 3.8% commission.
Which can be written as 0.038.
This month you sold 2 houses that had a combined total of $560,950
Then, the amount of commission you will earn is given by :-
[tex]\$560,950\times0.038=\$21,316.1[/tex]
Therefore, the you will earn $21,316.1 as commission.
it's the same question
1)Louise wants to buy a house priced at $57000 she will need to make a down payment of 25% and pay closing cost of 2.8% of the purchase how much will she need for a down payment
2) how much will she need for the closing costs
Answers
The down payment is 25 percent of 57000. Taking 1/4 of 57000 gives 14250 dollars in down payment. Closing cost is just 2.8 percent. This costs 1596 dollars, so your answers are 14250 and 1596.
Hope this helps!
Help me on number 12 13 14 and 15
Answers
12. 1.625 [terminating]; 13. 0.83 [bar notation over 3 (repeating)]; 14. 900 cm = 9 m; 15. 0.23 cm = 2.3 mm
Repeating decimals are parts of decimals that have repetitive digits; terminating decimals are decimals whose digits end.
Whether you are using Metric or Imperial, you have to determine whether you are going from a small unit to a big unit or vice versa. Then perform your operation. So, in exercise 14, the smaller unit is centimeters, so you would be going from big to small. Exercise 15 has you going from small to big.
There are centimeters in one meter, so multiply 9 by to get 900 centimeters.
There are 10 millimeters in one centimeter, so divide 2.3 by 10 simply by moving the decimal point ONCE to the left [Power of 10].
small to BIG → Division
BIG to small → Multiplication
I am joyous to assist you anytime.
HELP 20 points!!!What is the initial value of the function represented by this table?
0,4
1,9
2,14
A 0
B 4
C 5
D 9
Answers
Answer:
0
Step-by-step explanation:
0 would be the individual function because 0 is only one number so if you were to multiply 0x(x) then it would be 0x.
Answer:
4
Step-by-step explanation:
if we see the table as being a numerical representation of a graph in the x-y plane, the first column will represent the x-values (i.e the domain) and the second column will represent the y-values (i.e the range).
That is to say, the x-values are the inputs into the function that will spit out the y-values as outputs.
By observation, we can see that when x = 0 (i.e the initial value of the input), that the resulting function output is y =4 (i.e the initial value of the output).
Hence the initial value of the function (i.e the output) is 4
identify one characterisitc of exponentional decay
Answers
Answer: it goes down (decreases) steadily
Step-by-step explanation:
Answer:
It goes down/decreases in a steady way.
HELP ASAP
Select all that apply.
Which quadrilaterals have two pairs of parallel sides?
rhombus
trapezoid
rectangle
isosceles trapezoid
Answers
Answer:
rhombus, rectangle
Step-by-step explanation:
All parallelograms have two pairs of parallel sides.
A rhombus is a parallelogram. A rectangle is a parallelogram.
A trapezoid is not a parallelogram.
Answer: rhombus, rectangle
find the zeros of the quadratic polynomial 4√5x^2-24x-9√5 and verify its relationship between its zeroes and coefficients.........answer required urgently for my assignment
Answers
Answer:
The zeros of the quadratic polynomial are
[tex]x=\frac{15\sqrt{5}}{10}[/tex] and [tex]x=-\frac{3\sqrt{5}}{10}[/tex]
The relationship between its zeroes and coefficients in the procedure
Step-by-step explanation:
step 1
Find the zeros
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]4\sqrt{5}x^{2}-24x-9\sqrt{5}=0[/tex]
so
[tex]a=4\sqrt{5}\\b=-24\\c=-9\sqrt{5}[/tex]
substitute in the formula
[tex]x=\frac{-(-24)(+/-)\sqrt{-24^{2}-4(4\sqrt{5})(-9\sqrt{5})}} {2(4\sqrt{5})}[/tex]
[tex]x=\frac{24(+/-)\sqrt{-24^{2}-4(4\sqrt{5})(-9\sqrt{5})}} {8\sqrt{5}}[/tex]
[tex]x=\frac{24(+/-)\sqrt{1,296}} {8\sqrt{5}}[/tex]
[tex]x=\frac{24(+/-)36} {8\sqrt{5}}[/tex]
[tex]x=\frac{24(+)36} {8\sqrt{5}}=\frac{15\sqrt{5}}{10}[/tex]
[tex]x=\frac{24(-)36} {8\sqrt{5}}=-\frac{3\sqrt{5}}{10}[/tex]
step 2
Find the sum of the zeros and the product of the zeros
Sum of the zeros
[tex](\frac{15\sqrt{5}}{10})+(-\frac{3\sqrt{5}}{10})=\frac{12\sqrt{5}}{10}=\frac{6\sqrt{5}}{5}[/tex]
Product of the zeros
[tex](\frac{15\sqrt{5}}{10})*(-\frac{3\sqrt{5}}{10})=-\frac{9}{4}[/tex]
step 3
Verify that
Sum of the zeros= -Coefficient x/Coefficient x²
Coefficient x=-24
Coefficient x²=4√5
substitute
[tex]\frac{6\sqrt{5}}{5}=-(-24)/4\sqrt{5}\\ \\\frac{6\sqrt{5}}{5}=\frac{6\sqrt{5}}{5}[/tex]
therefore
the relationship is verified
step 4
Verify that
Product of the zeros= Constant term/Coefficient x²
Constant term=-9√5
Coefficient x²=4√5
substitute
[tex]-\frac{9}{4}=(-9\sqrt{5})/4\sqrt{5}\\ \\-\frac{9}{4}=-\frac{9}{4}[/tex]
therefore
the relationship is verified
Sathish is going on a 2100-kilometer road trip with 2 friends, whom he will pick up 150 kilometers after he begins the trip and drop off when there are 150 kilometer remaining. The car consumes 6 liters of gas for every 100 kilometers, and gas costs $1.20 per liter.
Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together.
How much will Sathish pay for gas?
Answers
Answer:
Satish will pay $64.8
Step-by-step explanation:
Kilometres when Satish is alone
150 kilometres in the beginning
150 kilometres in the end
Total: 300 kilometres
Kilometres when Satish is with friends
Total km: 2100
Satish Travelled alone: 300
Kilometres when Satish is with friends: 2100-300 = 1800 km
Litres of gas when Satish is alone
6 litres of gas per 100 kilometres
6 x 3 for 300 kilometres = 18 litres
Litres of gas when Satish is with friends
6 litres of gas per 100 kilometres
6 x 18 for 1800 kilometres = 108 litres
Cost of gas when Satish is alone
$1.2 per litre
18 x 1.2 = $21.6
Cost of gas when Satish is with friends
$1.2 per litre
108 x 1.2 = $129.6
Cost for each friend = $129.6/3 = $43.2
Satish will pay: Cost when travelled with friends + Cost when travelled alone
=$43.2+ $21.6
=$64.8
So, Satish will pay $64.8
Answer:
He will pay $ 64.8
Step-by-step explanation:
Given,
The total distance of the trip = 2100 km,
∵ Sathish pick up his 2 friends 150 kilometers after he begins the trip and drop off when there are 150 kilometer remaining.
So, the number of kilometres for which he and his friends pay the costs = 2100 - (150+150)
= 2100 - 300
= 1800 km,
Now, the quantity of gas for 100 km = 6 liters,
So, the quantity of gas for 1800 km = 18 × 6 = 108 liters,
If the cost of gas is $ 1.20 per liters,
Then the total cost paid by them ( when satish is not alone )
[tex]=\text{gas consumed in liters}\times \text{cost per liters}[/tex]
[tex]=108\times 1.2[/tex]
[tex]=\$ 129.6[/tex]
∵ they split this cost evenly,
So, the share of satish ( when he is with his friend ) = [tex]\frac{129.6}{3}[/tex] = $ 43.2
For the remaining 300 km, he paid the cost of gas,
Again, the quantity of gas for 100 km = 6 liters
⇒ The quantity of gas for 300 km = 18 liters,
Thus, the cost he paid when he was alone = 18 × cost of gas for 1 liter
= 18 × 1.2
= $ 21.6
Hence, the total amount paid by satish = $ 43.2 + $ 21.6 = $ 64.8
please help me with this math question
Answers
The ":" is actually a division, a fraction.
So part a is therefore,
[tex]\dfrac{w}{100}=\dfrac{12}{25}[/tex]
Here we use cross multiplication,
[tex]\dfrac{a}{b}=\dfrac{c}{d}\Longleftrightarrow ad=bc[/tex]
And we have,
[tex]
25w=12\cdot100 \\
w=\dfrac{12\cdot100}{25}=\dfrac{1200}{25}=\boxed{48}
[/tex]
Now part b.
First convert 2m to cm. 1m = 100cm therefore 2m is 200cm.
Now we have simplified to,
[tex]\dfrac{180}{200}=\dfrac{1.8}{2}=\dfrac{\dfrac{18}{10}}{2}=\dfrac{\dfrac{9}{5}}{2}=\boxed{\dfrac{9}{10}=9:10}
[/tex]
Hope this helps.
r3t40
The table below shows values for x and y. If y varies directly as x, what is the constant of variation?
Answers
If the table below shows values for x and y. If y varies directly as x, The constant of variation will be 4.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that, The value of y and x are,
y 12 24 36 48
x 3 6 9 12
Suppose k is the constant of proportionality,
Lineae equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y=kx
k=12/3
k=4
Thus, if the table below shows values for x and y. If y varies directly as x, The constant of variation will be 4.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ3
Hassan used the iterative process to locate
0.15 on the number line,
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Which best describes Hassan's estimation?
Hassan is correct because 0.15 0.4.
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because 0.15 is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2.
Answers
Answer: 3.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Step-by-step explanation:
Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.
A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.
Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2.
Find a formula for the exponential function passing through the points (-3,5/64) and (2,80)
Answers
Answer:
[tex]5(4)^{x}[/tex]
That's the exponential function.
Step-by-step explanation:
Simply just use a graphing calculator (there's plenty of apps and websites that are graphing calculators) and follow these steps.
1) Clear out calculator RAM
2) Press STAT button
3) Press ENTER on EDIT
4) Type the X's in L1 and type the Y's L2.
5) Press STAT again
6) Press the RIGHT ARROW once
7) Press 0
8) Press ENTER
9) There's your exponential function!
To find the formula for the exponential function passing through given points (-3,5/64) and (2,80), we assume the function to be y=ab^x, substitute both points into the equation and solve it for a and b. This will provide the desired formula.
Explanation:To find the formula for the exponential function through given points (-3,5/64) and (2,80), we firstly assume the function to be of the form y=ab^x. After that, we substitute the given points into this assumed equation, resulting in a system of two non-linear equations and solve it for the unknowns a and b.
Using our initial guess for the formula, substitute the first point (-3,5/64), we get: 5/64=a*b^-3
Substitute the second point (2,80) into the equation we get: 80=a*b^2
Solving these equations using substitution or elimination methods we will derive the appropriate values for a and b, which we can then substitute back into the y=ab^x to get the desired formula.
Learn more about Exponential Function here:https://brainly.com/question/37289664
#SPJ11
Will pay someone 300$ to complete my online course
Answers
Answer:
Um
Step-by-step explanation: