Answer:
The minimum value of this function is -40.
Step-by-step explanation:
Recall that the minimum of a quadratic whose graph is a parabola that opens up, as this one does, is the vertex of the graph. The x-coordinate of the vertex is given by x = -b / (2a), where a is the coefficient of the x^2 term and b is that of the x term.
Here, x = -12 / (2*2), or x = -12/4, or x = -3.
Find the y-value at this x-value: f(-3) = 2(-3)^2 + 12(-3) - 22, or
f(-3) = 2(9) - 36 - 22, or -40.
The vertex is at (-3, -40). The minimum value of this function is -40.
The provided quadratic function y=2x²+12x-22 has no local minimum or maximum, as indicated by the application of the second derivative test, which results in a point of inflection rather than an extrema.
The minimum or maximum of the quadratic function y=2x²+12x-22. To locate the extrema of a quadratic function, we often use the first derivative test. However, the information provided indicates the derivative vanishes at x = 2 (y' = 0), but the second derivative test (y" = 6x - 12) reveals that this point is a point of inflection rather than a minimum or maximum. The second derivative being zero at x = 2 implies that there is no concavity change and hence, no local extrema. Therefore, for this particular quadratic function, there is no local minimum or maximum. The function can be rewritten as y = (x - 2)³ + 8, which shifts the function y = x³ two units to the right and eight units upwards, further emphasizing that it indeed has no local extrema.
for v= 4i - 5j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j.
Answer:
a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
Step-by-step explanation:
The given vector is v= 4i - 5j
The magnitude of this vector is;
[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]
[tex]|v|=\sqrt{16+25}[/tex]
[tex]|v|=\sqrt{41}[/tex]
The unit vector u in the direction of v is;
[tex]u=\frac{v}{|v|}[/tex]
[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]
[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]
We rationalize to get
[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
a segment has endpoints at (1, -2) The midpoint is at (-4, -2). What are the cooordinates of the other endpoint?
Answer:
coordinate of the other endpoint is (-9,-2)
Step-by-step explanation:
Given that a segment has endpoints at (1, -2). The midpoint is at (-4, -2).
Now we need to find about what are the coordinates of the other endpoint.
let the coordinates of other end points are (x,y)
Then mid point of (1,-2) and (x,y) is given by mid point formula:
[tex]\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]
[tex]\left(\frac{x+1}{2},\frac{y-2}{2}\right)=(-4,-2)[/tex]
[tex]\Rightarrow \frac{x+1}{2}=-4, \frac{y-2}{2}=-2[/tex]
[tex]\Rightarrow x+1=-8, y-2=-4[/tex]
[tex]\Rightarrow x=-9, y=-2[/tex]
hence coordinate of the other endpoint is (-9,-2)
Answer:
what the otherperson said
Step-by-step explanation:
just read what the other person said
Find the height of a triangle with an area (a) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, a= 1/2bh
The height of rectangle is 10 inch
Answer:
10 inches
Step-by-step explanation:
Which quantity is proportional to 18⁄3? Check all that are true. 90⁄16 36⁄6 72⁄12 6⁄1 36⁄12
A quantity is proportional to 18/3 if it simplifies to the same value, which is 6. The proportional quantities are 90/15, 36/6, 72/12, and 6/1, as they all simplify to 6. The quantity 36/12 is not proportional since it simplifies to 3.
To determine which quantities are proportional to 18/3, we need to find what 18 divided by 3 equals and then compare this to the given fractions to check for equivalence. Calculating 18/3 gives us 6. Now, let's examine each option:
90/15: This fraction reduces to 6, which is proportional to 18/3.
36/6: This fraction also equals 6 after simplification, so it is proportional to 18/3.
72/12: Simplifying 72/12 gives us 6, making it proportional to 18/3
6/1: 6 divided by 1 is just 6, so this too is proportional to 18/3.
36/12: Simplifying 36/12 results in 3, which is not equal to 6, so it is not proportional to 18/3.
Write a function for the situation described and find the value after 7 yrs. A $16,800 car depreciates 11% each year
Answer:The starting value is 20,300, and the value is decreasing by 9.5% each year.
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.
A decrease by 9.5% corresponds to multiplying by 91.5% each year.
We write . We plug in 11 years for t.
$7,671.18
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Step-by-step explanation:
Answer:
The starting value is 20,300, and the value is decreasing by 9.5% each year.
Step-by-step explanation:
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.A decrease by 9.5% corresponds to multiplying by 91.5% each year.We write . We plug in 11 years for t.
hugo must divide 5 apples among his 3 nephews. Each nephew receives the same amount, and there are no apples left over. How many apples did each nephew receive?
Answer:
D
Step-by-step explanation:
5 divided by 3 is 1.6666 which is the same as 1 and 2/3
The correct answer is D
which of the following could be the system of nonlinear inequalities graphed below?
Answer:
Option A.
Step-by-step explanation:
step 1
we know that
The equation of the solid line is
[tex]y=5[/tex]
The solution is the shaded area above the solid line
so
The equation of the first inequality is
[tex]y\geq 5[/tex]
step 2
The equation of the dashed line is
[tex]y=x^{2} -5x+6[/tex]
The solution is the shaded area above the dashed line
so
The equation of the second inequality is
[tex]y>x^{2} -5x+6[/tex]
therefore
The system of inequalities could be
[tex]y\geq 5[/tex]
[tex]y>x^{2} -5x+6[/tex]
HELP !!!!!!!!!!!!!!!!!!!
Hello There!
Your answer would be “B”
Forget about the -5 and just do 5 multiplied by 3 and you get a product of 15.
Then, make it negative and it would be 4^-15
The measures of the three angles of a triangle are (X)°,(2x)°and (3x)° what is the value of x
Help it’s due TOMORROW!!!!!!
Answer:
x=30
Step-by-step explanation:
Add up all of the values of the angles and set it equal to 180 degrees since a triangle is always made up of angles that have a sum of 180 degrees.
x+2x+3x=180
6x=180
x=30
Find the solutions of the quadratic equation 14x^2+9x+10=014x
2
+9x+10=014, x, start superscript, 2, end superscript, plus, 9, x, plus, 10, equals, 0.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i
28
9
±
28
479
istart fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i
(Choice B)
B
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}i−
28
9
±
28
479
iminus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction, i
(Choice C)
C
-\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}−
28
9
±
28
479
minus, start fraction, 9, divided by, 28, end fraction, plus minus, start fraction, square root of, 479, end square root, divided by, 28, end fraction
(Choice D)
D
\dfrac{9}{28}\pm\dfrac{\sqrt{479}}{28}
28
9
±
28
479
Answer:
Option B. [tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]
Step-by-step explanation:
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]14x^{2}+9x+10=0[/tex]
so
[tex]a=14\\b=9\\c=10[/tex]
substitute in the formula
[tex]x=\frac{-9(+/-)\sqrt{9^{2}-4(14)(10)}} {2(14)}[/tex]
[tex]x=\frac{-9(+/-)\sqrt{-479}} {28}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
substitute
[tex]x=\frac{-9(+/-)\sqrt{479}i} {28}[/tex]
[tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]
The following equation represents the number of fish in a pond, F(x), after x number of weeks. F(x) = 500 (1.2)x. How many fish are in the pond after 4 weeks?
a. 600 fish
b. 1036 fish
c. 2000 fish
d. 2400 fish
How many fish are in the pond after 7 weeks?
a. 600 fish
b. 1036 fish
c. 1791 fish
d. 4200 fish
Answer:
1) d. 2400
2) d.4200
Step-by-step explanation:
As per given data:
F(x) represents number of fish
x represents number of weeks
Relation between F(x) and x is given as
F(x)= 500 (1.2)x
Now part 1:
How many fish are in the pond after 4 weeks=?
x=4
Putting in given equation F(x)= 500 (1.2)x
F(x)= 500(1.2)(4)
= 2400
Now part 2:
How many fish are in the pond after 7 weeks?
x=7
Putting in given equation F(x)= 500 (1.2)x
F(x)= 500(1.2)(7)
= 4200 !
Answer:
Correct choice is b. 1036 fish.
and c. 1791 fish.
Step-by-step explanation:
Given equation is [tex]f(x)=500(1.2)^x[/tex].
There x represents number of weeks. We need to find about wow many fish are in the pond after 4 weeks.
To find that we will plug x=4 into above formula and simplify
[tex]f(x)=500(1.2)^x[/tex]
[tex]f(x)=500(1.2)^{4}[/tex]
[tex]f(x)=500(2.0736)[/tex]
[tex]f(x)=1036.8[/tex]
Which is approx 1036
Hence correct choice is b. 1036 fish.
------
We can repeat same process with x=7 for 2nd problem
[tex]f(x)=500(1.2)^{7}=1791.5904[/tex]
Hence correct choice is c. 1791 fish.
Isabel received 4/7 of the 210 votes for cast for class treasurer. How many votes did she receive? Write your answer in simplest form
Answer:
120 votes
Step-by-step explanation:
So one way to solve this is by creating an equation to solve for x.
So we are given 4/7, that will be one side of the equation.
And we are trying to figure out how many votes out of the 210 she received, so on the other side of the equation we will have x/210, since we are solving for x.
So 4/7 = x/210
We want to get x alone, so we can multiply 4/7 by 210, which equals 120.
So x equals 120!
Isabel received 4/7 of the 210 votes for class treasurer, which equals 120 votes when the total is multiplied by the fraction.
The student is asking for help with a mathematics problem related to finding a fraction of a whole number. Isabel received 4/7 of the total votes cast for class treasurer, and the total number of votes cast was 210. To find how many votes Isabel received, we simply multiply 210 by 4/7:
Isabel's votes = (210) * (4/7)
Isabel's votes = 840 / 7
Isabel's votes = 120
Therefore, Isabel received 120 votes.
How might logarithmic functions relate to earthquakes?
Answer:
Step-by-step explanation:
The way that this function looks when graphed could be similar to the seismic waves recorded when an earthquake hits.
A logarithmic measure known as the Richter scale is used to quantify the overall energy generated during an earthquake. Each number higher on the Richter scale denotes a ten-times-stronger intensity. For instance, a magnitude 5 earthquake is ten times more powerful than a magnitude 4 earthquake.
What is logarithmic function?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
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I need help on number 19 ! Please for brainless answer !!
Answer:
Yes
Step-by-step explanation:
We need to determine the sides of the squares
Area = 9
A = s^2
9 = s^2
Taking the square root of each side
sqrt(9)= sqrt(s^2)
3 =s
Perimeter of a square = 16
P =4s
16 =4s
Divide each side by 4
16/4 =4s/4
4 =s
Side = 5 in
Right triangles obey the Pythagorean theorem
a^2 + b^2 = c^2
Putting the smaller sides in for a and b
3^2 +4^3 = 5^2
9+16=25
25=25
Since this is true, we can arrange the squares to make a right triangle
Answer:
Yes, due to the Pythagorean theorem.
Leg A would be 3
Leg B would be 4
Hypotenuse C would be 5
Explanation:
When making the right triangle, only one side length value is needed.
If the area of square one is 9, 9 divided by 2 is 3.
If the perimeter of square two is 16, 16 divided by 4 is 4.
The single side length for square three is given, which is 5.
The Pythagorean theorem consists of a^2 + b^2 = c^2.
Plug in the values.
3^2 + 4^2 = 5^2
9 + 16 = 25
Hope this helps! :)
Maggie’s bank has assigned her a temporary 3-digit PIN to use with her ATM card. Each digit is a number from 1 to 5, inclusive, and no digit can be used more than once in the PIN. Which multiplication problem can be used to determine the probability that the PIN she was assigned was 123?
A 1/5 1/5 1/5
B 1/5 1/4 1/3
C 4/5 3/4 2/3
D 4/5 4/5 4/5
Answer:
B 1/5 1/4 1/3
Step-by-step explanation:
The first digit Maggie's bank picked from the 5 digit available, so 1/5.
The second digit will be picked from the 4 remaining digits available, so 1/4.
For the final digit, the bank will have only 3 options to choose from, so 1/3.
So the possibility for the 3-digit assigned PIN to be 123 is
[tex]\frac{1}{5} * \frac{1}{4} *\frac{1}{3} =\frac{1}{60}[/tex]
1/60, so the formula is the one presented in the B option: 1/5 1/4 1/3
Confused??? on how to prove the equation, the first part of the problem
Answer:
Asin(wt + φ) = c2sinwt +c1coswt
Step-by-step explanation:
Proof:
wt here is periodic where as φ is constant
taking left hand side
Asin(wt + φ)
Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ
Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]
= Asinwtcosφ +Asinφcoswt
Now as we know φ is constant
so will Asinφ and Acosφ will also be constant
let Asinφ= c1
and Acosφ=c2
Putting in above expression, we get
Asin(wt +φ) = c2sinwt +c1coswt !
Anybody know the answers to these 3?
Answer:
Part 1) The area of the shaded region is [tex]2.1\pi\ m^{2}[/tex]
Part 2) The length of the arc AB is [tex]2.5\pi\ in[/tex]
Part 3) The area of the shaded region is [tex]56.53\pi\ in^{2}[/tex]
Step-by-step explanation:
Part 1) Find the area of the shaded region
step 1
Find the area of the circle
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=3\ m[/tex]
substitute
[tex]A=\pi (3)^{2}[/tex]
[tex]A=9\pi\ m^{2}[/tex]
step 2
we know that
The area of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the area of the shaded region with a central angle of 84 degrees
[tex]\frac{9\pi }{360} =\frac{x }{84}\\ \\x=(9\pi)*84/360\\ \\x=2.1\pi\ m^{2}[/tex]
Part 2) What is the length of arc AB?
step 1
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]C=2\pi (5)[/tex]
[tex]C=10\pi\ in[/tex]
step 2
we know that
The length of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the length of the arc AB with a central angle of 90 degrees
[tex]\frac{10\pi }{360} =\frac{x }{90}\\ \\x=(10\pi)*90/360\\ \\x=2.5\pi\ in[/tex]
Part 3) Find the area of the shaded region given that XY measures 8 in
step 1
Find the area of the circle
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]XY=r=8\ in[/tex]
substitute
[tex]A=\pi (8)^{2}[/tex]
[tex]A=64\pi\ in^{2}[/tex]
step 2
we know that
The area of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the area of the shaded region with a central angle of (360-42)=318 degrees
[tex]\frac{64\pi }{360} =\frac{x }{318}\\ \\x=(64\pi)*318/360\\ \\x=56.53\pi\ in^{2}[/tex]
What is the equation of a circle with center (-3,-1) that contains the point (1,2)?
Answer:
(x + 3)^2 + (y + 1)^2 = 25
Step-by-step explanation:
Equation of a circle with center (h, k) and radius, r.
(x - h)^2 + (y - k)^2 = r^2
The center is (-3, -1), so h = 1, and k = 2.
(x - (-3))^2 + (y - (-1))^2 = r^2
(x + 3)^2 + (y + 1)^2 = r^2
Now we substitute x and y with the values of x and y from the given point, and we solve for r^2.
(1 + 3)^2 + (2 + 1)^2 = r^2
4^2 + 3^2 = r^2
16 + 9 = r^2
r^2 = 25
Now that we know r^2, we substitute it into the equation above.
(x + 3)^2 + (y + 1)^2 = 25
Answer:
The correct answer is,
(x + 3)² + (y +1)² = 25
Step-by-step explanation:
It is given that, What is the equation of a circle with center (-3,-1) that contains the point (1,2)
Formula;-
Equation of the circle passing through the point ( x₁,y₁) with radius r is given by,
(x - x₁)² + (y - y₁)² = r²
To find the radius of circle
r =√[ (1 --3)² + (2 --1)²]
=√(4² + 3²)
= √(16 + 9)
=√25 = 5
To find the equation of the circle
(x₁, x₁) = (-3, -1) and r = 5
(x - x₁)² + (y - y₁)² = r²
(x - -3)² + (y - -1)² = 5²
(x + 3)² + (y +1)² = 25
a fish is 12 meters below the surface of the ocean what is its elevation
The surface of the ocean is 0 meters.
Because the fish is below the surface it would be a negative number. ( it is less than 0)
The elevation of the fish would be -12 meters.
Answer:
-12 meters
Step-by-step explanation:
Elevation is the height above a given level, most often the sea. Therefore, elevation is like a vertical numerical line. If the sea level is 0, and to the right of the 0 is positive numbers, then the left has to be negative.
Therefore, the fish is -12 meters below sea level.
Please help! Thank you
Answer:
336 ft squared
Step-by-step explanation:
Looking for face area, not volume
So...
10*12=120
6*12=72
8*12=96
6*8/2=24
6*8/2=24
24+24+120+72+96=336ft squared
the product of x and the sum of 6 and 8 times the square of x
Answer:
x = 14; x = 0
Step-by-step explanation:
(x)(6 + 8) = x²
(x)(14) = x²
14x = x²
14x - x² = 0
(x)(14 - x) = 0
x = 14; x = 0
Eric wants to find out the most popular after-school activity among high school seniors at his school. What is the population in Eric’s survey?
Answer: The population in Eric's survey is the high school seniors.
Answer:
all high school seniors at Eric’s school
Step-by-step explanation:
Which of the following is an even function
Answer:
number2
Step-by-step explanation:
Answer:
f(x) = |x|
Step-by-step explanation:
function is even if and only if f(-x) = f(x)
f(x) = |x| ; regard to its sign f(x) = x
f(-x) = |-x| ; regard to its sign f(-x) = x
So answer is f(x) = |x| is the even function
What is the range of a cosine function?
Final answer:
The range of a cosine function is the set of output values the function can take, which is always between -1 and +1. This applies to the standard cosine function and is unaffected by horizontal or phase shifts. This range is consistent with the definition of the cosine function as the ratio of the adjacent side to the hypotenuse in a right triangle.
Explanation:
The range of a cosine function refers to the set of possible values that the function can output. In mathematical terms, the cosine function oscillates between +1 and -1 irrespective of any horizontal shifts or phase shifts. A horizontal shift, demonstrated in Figure 15.8 (b), where the function is shifted by an angle φ (phase shift), does not alter the range of values of the function, which remain – from its minimum value of -1 to its maximum of +1.
Similarly, in Figure 16.10, a sine function, which is related to the cosine function, also oscillates between +1 and -1 every 2π radians (a complete cycle). This oscillation represents the wave function amplitude, which in cases other than a cosine can fluctuate between +A and -A.
As illustrated in Figure 2.18, the cosine function can be visualized as the ratio of the adjacent side to the hypotenuse (Ax/A = cos A) in a right triangle, further highlighting that this ratio (and thus the range of the cosine function) is between -1 and 1.
For example, when √(1+1)* approaches 1, it is indicative that cos 0 = 1, representing one end of the cosine function's range.
3x = 2* + 25
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Is the answer 25? Thats what I got.
How did they get 0.97? Please show work, thank you!!
Answer:
see explanation
Step-by-step explanation:
0.97 is the value of cos14° to 2 dec. places
Use your calculator ( ensuring it is in degree mode )
press cos14 then = to obtain value 0.97
Are the triangles congruent? If so, how do you know?
O yes, because all the angles of the triangles are
acute
yes, because the triangles have three congruent,
corresponding angles
yes, because of ASA or AAS
not enough information given
C.yes, because of ASA or AAS
Evaluate the function below for x = 2.
f (x) = 4x^3 - x^2 - 5x+7
Answer: [tex]f(2)=25[/tex]
Step-by-step explanation:
You know that the given function is:
[tex]f(x)=4x^3-x^2-5x+7[/tex]
You know that you must evaluate this function for [tex]x=2[/tex].
Then, to evaluate the function for [tex]x=2[/tex], you need to substitute this value into the given function and simplify it.
Therefore, you get:
[tex]f(x)=4x^3-x^2-5x+7\\f(2)=4(2)^3-(2)^2-5(2)+7\\f(2)=4(8)-(4)-10+7\\f(2)=32-4-10+7\\f(2)=25[/tex]
So, the answer is: [tex]f(2)=25[/tex]
Is the answer is b, please help
The correct answer is b
Which of the following is true?
A.Perpendicular lines never intersect each other.
B.Parallel lines always intersect each other
.C.Parallel lines are always in the same plane.
D.Perpendicular lines are not in the same plane.
Answer:
C.
Step-by-step explanation:
A - Perpendicular lines always touch each other at least once.
B - Parallel lines never touch.
D- Not always true.
C is true. If they are not in the same plane they are skewed lines.
The true statement is C: Parallel lines are always in the same plane. Perpendicular lines do intersect, while parallel lines do not, and perpendicular lines can certainly be in the same plane. Hence, correct option C.
The question seeks to determine the accuracy of given statements about geometric relationships between. Perpendicular lines and parallel lines. Based on the provided theorems, the true statement is: C. Parallel lines are always in the same plane.
This is because if two lines are parallel, they will be equidistant from each other at all points, which can only occur if they are in the same plane. Statements A, B, and D are false.
Perpendicular lines do intersect at a 90-degree angle.
Parallel lines, by definition, never intersect as they are always equidistant.
Perpendicular lines can be in the same plane or in different planes, although a line that is perpendicular to a plane must lie in another plane.