Answer:
we have two equations:
2*x + y = 20
y = a + 18/x - 3
We want to find the values of a such that the graphs of the equations do not intersect.
The first step is to isolate y in the first equation.
now we get:
y = 20 - 2*x
Then we have the system of equations:
y = 20 - 2*x
y = a + 18/x - 3
If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:
20 - 2*x = y = a + 18/x- 3
We want to find a value of such that this does not happen.
Let's solve that equation and see what we can find.
20 - 2*x = a + 18/x - 3
20 + 3 = a + 18/x + 2*x
23 = a + 18/x + 2*x
(23 - a) = 18/x + 2*x
if we multiply all values by x, we get:
(23 - a)*x = 18 + 2*x^2
Then we have a quadratic equation, we can write this as:
2*x^2 - (23 - a)*x + 18 = 0
Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0 is:
b^2 - 4*a*c
In this case, the determinant is:
(-(23 - a))^2 - 4*2*18
(23 - a)^2 - 144
And this must be smaller than zero, then:
(23 - a)^2 - 144 < 0
23^2 - 2*23*a + a^2 - 144 < 0
529 - 46*a + a^2 - 144 < 0
a^2 - 46*a + 385 < 0
Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.
Then we need to solve:
a^2 - 46*a + 385 = 0
We can use the Bhaskara's equation to find the roots, the roots are given by:
[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]
Then the two roots are:
a₁ = (46 + 24)/2 = 35
a₂ = (46 - 24)/2 = 11
Then for all the values of a suc that:
11 < a < 35
The line does not intersect the curve.
A baseball player earns $3 million in 2015. During the next 15 years, the earnings increase 4% each year.
a. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal.
An exponential growth model is y=
b. In which year will the player's earnings first exceed $5,000,000?
Answer:
[tex]y=3*1.04^{t}[/tex]
in 2029
Step-by-step explanation:
[tex]y=3*1.04^{t}[/tex]
[tex]when y=5\\t=\frac{ln(5/3)}{ln(1.04)} =13.02 ..[/tex]
have to round it up to 14 to exceed
A right triangle has an angle that measures 47°. What is the measurement of the third angle in the triangle?
Answer:
43 degrees
Step-by-step explanation:
every triangle all three angles equal 180 for a right triangle you know that one angle is 90 degrees for this triangle we know that another angle is 47 so
90+47 = 137 now we can take 180 - 137 = 43
so your third angle is 43
hope I helped!!
FOR 15 POINTS ANSWER THESE 3 QUESTIONS AND WILL MARK BRAINLIEST. 1. The courthouse is on the exterior corner of the intersection of any 2 streets. 2. The school and the courthouse are on congruent corresponding angles. 3.The police station forms a linear pair with the courthouse and same-side interior angles with the school.
Answer:
http://collinskarr.weebly.com/uploads/5/7/7/6/57764943/geometrytaskprojectparallellinescityprojectandwritingassignment.pdf
Step-by-step explanation:
i think thes is a life hack thing
i am not a inappropriate robot
Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $300, and she sells her cumin at a fixed price per kilogram. If she sells 120 kilograms of cumin, her weekly net profit is $600.
Answer:
Step-by-step explanation:
The net profit of the marketplace is the difference between the revenue and the expenses. The revenue is the product of number of kilograms sold and the price per kilogram.
Profit = Revenue - Expenses
600 = 120x - 300
The value of x from the equation is 7.5. The answer therefore for the first question is $7.5. Then, the number of kilogram of cumin she needs to sell to cover the expenses is $300/$7.5 and that is equal to 40.
solve for x. -3(x+5)=-9
Answer:
x = -2
Step-by-step explanation:
Help.Find the length of y
What expression is equivalent to 1/3 x -1/5
Help me please answer thanks
Answer:
all of them are right, there's no wrong answer.
Step-by-step explanation:
all answers are x = 20,
A sphere has a radius of 4. what is the volume of the sphere? show your answer in terms of pi. I've been stuck on this for 4 days and I can't get it.
Answer:
ok let me help
Step-by-step explanation:
v=268.08 sooo
r(radius) which is 4
v=4/3 n r³ =4/3×n×4³ = 268.08
Answer:
(256/3)π or 85.33π
Step-by-step explanation:
The equation for volume of a sphere is 4/3πr^3 where r = the radius
So the volume of the sphere in terms of pi would be
4/3(π)(4)^3
(4/3)(64)π
4 x 64 = 256
256/3 = 85.33
In terms of pi the answer is (256/3)π or 85.33π
Determine a quadratic equation in standard form that has each pair of roots.
X=5±√2/3
Step-by-step explanation:
you have to add 5 and 2 which is 7 and decide by 3 or estimate
Find the GCF of ( x ^2 + 2 ) and ( 3x ^2 + 6 ).
Hint: First factor each binomial, then find the common factor.
Answer:
The GCF is 4
Explain:
f(x)= 10x find the inverse of the function
Inverse of f(n)=-2n^3-3
5(x+2) = 20
15 points
Answer:
Step-by-step explanation:
remove the parenthesis
5x+10=20
5x+10-10=20-10
5x=10
x=2
Sin (61) = 24/ x
find x plz show work
Answer:
x=27.44
Step-by-step explanation:
sin(61)=24/x
x*sin(61)=24
x=24/sin(61)
x=27.44
Are these two triangles congruent? *
Answer:
not congruent because none of the angles match
Answer:
Not Congruent
Step-by-step explanation:
No.
Two corresponding sides measure 8 and 4.
The other two corresponding sides measure 7 and 3.5.
In order to be congruent, each pair of corresponding sides has to be congruent.
Mr.Rodriguez has 1/2 cake left from his buthday party. He wants to share it among 4 people What fraction represents how much of the cake each of the 4 people will get
Answer:
Step-by-step explanation:
There is 1/2 cake left, or .5, or 50%.
.5 divided by 4 equals .125, or 1/8, of 12.5%
In fraction form, each person will receive 1/8 slice of cake.
Hope this helps!
Mark Brainliest plz!
Tom had 114 dollars to spend on 9 books. After buying them he had 15 dollars. How much did each book cost?
Answer:
11
Step-by-step explanation:
114-15=99
99÷9=11
if a function f(x)=x^3 has the domain {-3,0,2,4} what is it's range
Step-by-step explanation:
Range is y-values
= {-27,0,8,64}
Chose whether the fraction and percent are equivalent
Yes. No.
A.
40/1,000 and 40%
B.
6/5 and 120%
C.
50/33 and 117%
D.
1/8 and 12.5%
Step-by-step explanation:
A No because it's 4%
B Yes
C No
D Yes
I REALLY NEED THIS ANSWER ASAP !!!
Find the measure of ZP
A) 39
B) 80°
C) 85
D)90°
Answer:
hope this helps..........
There are sixteen girls and twelve boys in block 7 math. At that rate, how many
girls would you expect in a group with two hundred ten boys?
Answer:280
Step-by-step explanation:
If the main group is a ratio of girls to boys 16:12 and the 12 is increased to 210 then do 210/12=17.5 and multiply the 17.5 by 16 to get 280
What is the slope of the line that passes through the points (-2,-1) and (2,-3) answer in simplest form
Answer:
Step-by-step explanation:
(-3 + 1)/(2 + 2)= -2/4= -1/2 is the slope
Please help me -5x-3y=16 y=x
Answer:
the answer is x=2 and y=2
Step-by-step explanation:
-3y=16+5x
-y=(16+5x)3
If using the method of completing the square to solve the quadratic equation
x²-10x – 15 = 0, which number would have to be added to "complete the
square"?
Answer:
For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.
Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:
(x + y)2 = x2 + 2xy + y2 (Square of a sum)
(x − y)2 = x2 − 2xy + y2 (Square of a difference)
To find the roots of a quadratic equation in the form:
\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side.
(v) Equate and solve.
Example 1
Find the roots of x2 + 10x − 4 = 0 using completing the square method.
Answer
Example 2
Solve 4x2 + x = 3 by completing the square.
Answer
Exercises
Solve the following quadratic equations by completing the square
Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s
2
+5s=3Answer
Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x
2
=3−4xAnswer
Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v
2
−6v−2=0Answer
Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0Answer
1. Solving Quadratic Equations by Factoring
3. The Quadratic Formula
Caraline wants to compare the expression's -15-9 and 9-(-15) to determine which result is greater.How cab she do this without finding the value of rach difference? Explain your reasoning.
Answer:
9-(-15)
Step-by-step explanation:
because it would be changed to 9+15
45x^4 + 72x^3 is factored form
Answer: 9 x 3 ( 5 x + 8 )
Step-by-step explanation:
Factor 9 x 3 out of 45 x 4 + 72x 3 .
please help me this is my test for the review of all the math i learned
Answer:
16.752
Step-by-step explanation:
On a coordinate plane, a point is at (1, 2) and (5, 2). Find the distance between (1, 2) and (5, 2). The points lie in the same quadrant . The distance is .
Answer:
The points lie in
✔ the same quadrant
The distance is
✔ 4 units
Step-by-step explanation:
the same quadrant
4 units
The distance between the two points (1, 2) and (5, 2) is 4 units. And both the points (1, 2) and (5, 2) lie in the same quadrant.
What is Distance between the two points?Distance between two points is the length of the line segment that connects two given points.
Formula for the distance between two points[tex]d = \sqrt{(x_{2}-x_{1} ^{2}) +(y_{2}-y_{1} ) ^{2} }[/tex]
According to the given question
We have
Two points
(1, 2) and (5, 2)
Let,
[tex](x_{1},y_{1}) = (1, 2)[/tex]
And, [tex](x_{2},y_{2} ) = (5,2)[/tex]
Therefore,
The distance between the points (1,2) and (5, 2)
= [tex]\sqrt{(5-1)^{2} +(2-2)^{2} }[/tex]
[tex]=\sqrt{(4)^{2}+0 }[/tex]
[tex]=4[/tex] unit.
Hence, the distance between the two points (1, 2) and (5, 2) is 4 units.
Since, the x coordinate and y coordinate of both the points (1,2) and (5, 2) are positive. Therefore, they both lie in the first quadrant. Hence, the points lie in the same quadrant.
Learn more about distance between the two points here:
https://brainly.com/question/18296211
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1. The following triangle has an area of 15.75 cm". What is the value of 2? 7 cm 4.5 cm 3.75 cm 1.125 cm 2.25 cm
