Taking into account the definition of axis of simmetry and vertexn the axis of symmetry is x = 5.
So, first of all, you must know what a quadratic function is. Every quadratic function can be expressed as follows:
f(x) = a*x² + b*x + c
where a, b and c are real numbers.
Axis of symetryThe graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry.
That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are equal of each other.
In other words, the axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves and always passes through the vertex of the parabola.
VertexThe point of intersection of the axis of symmetry with the parabola is called the vertex.
The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
SummaryBeing the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.
Learn more with this examples:
https://brainly.com/question/2799442?referrer=searchResultshttps://brainly.com/question/20862832?referrer=searchResultshttps://brainly.com/question/15266651?referrer=searchResultsThere are 43 students in the orchestra and twice that number in the band. There are 31 boys and 10 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
Answer:
170 students total
Step-by-step explanation:
43x2=86
86+43+31+10=170
Line segment AB is congruent to line segment CD.
Which of the following is an equivalent statement?
AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar
9514 1404 393
Answer:
(b) AB overbar congruent to CD overbar
Step-by-step explanation:
AB with an overbar is the way that line segment AB is designated, where appropriate typesetting is possible. Thus the statement the line segments are congruent is fully equivalent to ...
AB overbar congruent to CD overbar
Which statement can be proved true using the given theorem?
Answer:
BF = 16
Step-by-step explanation:
18/12 = 1.5 * 6 = 9
Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF
DB = EF = 9
24/1.5 = 16
DE = 16
BF = 16
The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.
Congruence theoremBy the congruence theorem;
We can conclude that triangles ABC and EFC are congruent triangles and as such have the ratio of corresponding sides to be equal.Hence, AE/EC = BF/FC.
Therefore; 12/18 = BF/24
Hence, BF = 24× 12/18
BF = 16Read more on congruent triangles;
https://brainly.com/question/1675117
Use the Empirical Rule to answer the questions below:
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 0.7 pounds.
1. What percent of newborn babies weigh more than 8.3 pounds? %
2. The middle 95% of newborn babies weigh between and pounds.
3. What percent of newborn babies weigh less than 6.2 pounds? %
4. Approximately 50% of newborn babies weigh more than pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds? %
Answer:
1. 16%
2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. 2.5%
4. Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. 83.85%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 7.6 pounds, standard deviation of 0.7 pounds
1. What percent of newborn babies weigh more than 8.3 pounds?
7.6 + 0.7 = 8.3.
So more than 1 standard deviation above the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So
[tex]0.32*0.5 = 0.16[/tex]
16% of newborn babies weigh more than 8.3 pounds.
2. The middle 95% of newborn babies weigh between and pounds.
Within 2 standard deviations of the mean, so:
7.6 - 2*0.7 = 6.2 pounds
7.6 + 2*0.7 = 9 pounds.
The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. What percent of newborn babies weigh less than 6.2 pounds?
More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:
[tex]p = 0.05*0.5 = 0.025[/tex]
2.5% of newborn babies weigh less than 6.2 pounds.
4. Approximately 50% of newborn babies weigh more than pounds.
Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.
Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?
6.9 = 7.6 - 0.7
9.7 = 7.6 + 3*0.7
Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So
[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]
83.85% of newborn babies weigh between 6.9 and 9.7 pounds.
50 POINTS
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
work and answers below
Answer:
[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]
Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].
Step-by-step explanation:
Part A:
The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:
[tex]0=-16x^2+22x+3[/tex]
The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
In [tex]-16x^2+22x+3[/tex], assign:
[tex]a\implies -16[/tex] [tex]b\implies 22[/tex] [tex]c\implies 3[/tex]Therefore, the solutions to this quadratic are:
[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]
The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].
Part B:
The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:
[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]
Substitute this into the equation of the parabola to get the y-value:
[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]
Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]
Write an equivalent expression to 1/2 (2n+6).
Answer:
n+3
Step-by-step explanation:
1/2 × 2(n+3)=n +3
I hope this helps
What is the value of 3?
9514 1404 393
Answer:
3 ⇒ 12
Step-by-step explanation:
Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...
f(x) = x(x+1)
Then f(3) = 3(3+1) = 3·4 = 12
_____
Additional comment
IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.
PLEASE HELP FAST!! I MIGHT GIVE BRAINLIEST TO FASTEST AND ACCURATE
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time t, in seconds, and the number of bacteria, B(t) in the petri dish is modeled by the following function:
B(t) = 9300 x (1/64)^t
Complete the following sentence about the rate of change of the bacterial culture
The bacterial culture loses 1/2 of its size every_______ seconds
Answer:
1/6
Step-by-step explanation:
We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation
4650 = 9300 * (1/64)^t
divide both sides by 9300
1/2 = (1/64)^t
First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because
(1/2)^6 = 64
take the 6th root of both sides
(1/2) = (64)^(1/6)
. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds
* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator
Answer:
0.17 seconds
Step-by-step explanation:
i got this correct on Khan :)
i hope it helps
I need help solving 10gallons = miles
Answer:
50?
Step-by-step explanation:
Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is
My flvs teacher said that she was asked to hold off on grading my assignment. She will give me a call back when when gets more information. Anyone have the same problem?
Answer:
yeah, teachers kinda suck
Which equation does the graph represent?
A. x^2 + y^2 = 4
B. x^2/3^2 + y^2/4^2 = 1
C. (X - 1)^2 / 3^2 + y^2/4^2 = 1
D.X^2 / 4^2 + (y + 1)^2 / 3^2 = 1
9514 1404 393
Answer:
B. x^2/3^2 + y^2/4^2 = 1
Step-by-step explanation:
The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...
(x/3)^2 +(y/4)^2 = 1
x^2/3^2 +y^2/4^2 = 1
What is the value if x
Answer:
Step-by-step explanation:
Determine if the function f is an exponential function. If so, identify the base. If not, why not?
f(x)=(1/e)^x
A. This is not an exponential function because the variable is in the exponent position.
B. The base is x.
C. This is a polynomial.
D. The base is e^−1.
Answer: D) The base is e^(-1)
We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e
The 1/e is the base of the exponential (1/e)^x
In general, the exponential b^x has base b.
What is the area if measurements are 6m x 5.2m
Answer:
33.00 355.2
5.0m x 6.7m 33.50 360.6
5.0m x 6.8m 34.00 366.0
5.0m x 6.9m 34.50 371.4
5.1m x 6.0m 30.60 329.4
5.1m x 6.1m 31.11 334.9
5.1m x 6.2m 31.62 340.4
5.1m x 6.3m 32.13 345.8
5.1m x 6.4m 32.64 351.3
5.1m x 6.5m 33.15 356.8
5.1m x 6.6m 33.66 362.3
5.1m x 6.7m 34.17 367.8
5.1m x 6.8m 34.68 373.3
5.1m x 6.9m 35.19 378.8
Add O used 6 cups of whole wheat flour and eggs we flower and ax cups of white flour in the recipe what is the equation that can be used to find the value of Y the total amount of flour that adult used in the recipe and what are the constraints and the values of X and Y
Answer:
6x+y
Step-by-step explanation:
I need help I will give brainlest
I showed a screenshot of the question
X = (18/5)/(3/2)
= 18/5 x 2/3
=(18 x 2) / (5x3)
= 90/15
If you don’t want it as a fraction it’s 6!
Hope this helps!
If an orange seller bought 5 dozen oranges at the rate of tk.60 per four and sold them at the rate of tk50 per four,how much did he lose
Answer:
tk 30
Step-by-step explanation:
5 dozen = 5 * 12 = 60 oranges
12/4 = 3
total cost = 60 * 3 = tk.180
total sell = 50 * 3 = tk 150
total lose = 180 - 150 = tk 30
PLEASE HELP ME ON 6-11 AND SHOW WORK PLEASE!!
Answer:
6) 6[tex]\sqrt{2}[/tex]
9) 40
10) [tex]\frac{5\sqrt{2} }{2}[/tex]
11) 13
Step-by-step explanation:
6)A right triangle rule: if 2 legs are equal, the hypotenuse is the length of that leg*[tex]\sqrt{2}[/tex]
9) Pythagorean Theorem
[tex]a^{2} +b^{2} =c^{2}[/tex]
We know the hypotenuse (41) so we substitute that for c and 9 for b now we need to find a
[tex]\sqrt{41^{2}-9^{2} }[/tex] which gives us 40
10) same with #6 but we do the opposite. SInce we have the hypotenuse, we can divide that by [tex]\sqrt{2}[/tex] because we know that if 2 legs are equal, the hypotenuse is multiplied by [tex]\sqrt{2}[/tex]. Multiply the numerator and denominator by [tex]\sqrt{2}[/tex] because we can't have a square root in the denominator.
11) like #9 we have the a and b but we need to find c
a=5 b=12 c=r
so [tex]\sqrt{5^{2}+12^{2} }[/tex] which gives us 13
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {c}^{2} = {6}^{2} + {6}^{2} \\ {c}^{2} = 36 + 36 \\ c = \sqrt{2( {6}^{2} )} \\ c = \sqrt{2}{\sqrt{ {6}^{{2}} } } \\ c = 6 \sqrt{2} \: \: \: ans[/tex]
9TH PART:- GIVENRIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMBASE = 9HYPOTENUSE= 41SOLUTION->
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {41}^{2} = {x}^{2} + {9}^{2} \\ 1681 = {x}^{2} + 81 \\ 1681 - 81 = {x}^{2} \\ 1600 = {x}^{2} \\ x = \sqrt{40 \times 40} \\ x = 40 \: \: \: ans[/tex]
10 TH PART:-GIVEN
RIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMTWO SIDES ( BASE AND PERPENDICULAR) R EQUAL TO SHYPOTENUSE= 5SOLUTION->[tex]{h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {5}^{2} = {s}^{2} + {s}^{2} \\ 25 = 2 {s}^{2} \\ 12.5 = {s}^{2} \\ \sqrt{12.5} = s \\ 3.5 = s \: \: \: ans[/tex]
11TH PART:- GIVEN RIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMBASE = 5 PERPENDICULAR= 12 SOLUTION ->[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {r}^{2} = {12}^{2} + {5}^{2} \\ {r}^{2} \\ 144 + 25 \\ {r}^{2} = 169 \\ r = \sqrt{13 \times 13} \\ r = 13 \: \: \: \: ans[/tex]
HOPE IT HELPED
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: DEVIL005 \: \star[/tex]
Pls help me? I’m struggling
Answer: Number 1 is 150
Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.
Find the equations of the tangents to the curve x=9t2+3, y=6t3+3 that pass through the point (12,9).
Answer:
The equation will be "[tex]y=x-3[/tex]".
Step-by-step explanation:
Given:
Points (12, 9) = (x, y)
⇒ [tex]x=9t^2+3[/tex]
then,
[tex]\frac{dy}{dt}=18t[/tex]
or,
⇒ [tex]y=6t^3+3[/tex]
then,
[tex]\frac{dy}{dt}=18t^2[/tex]
⇒ [tex]\frac{dy}{dx}=\frac{18t^2}{18t}[/tex]
[tex]=t[/tex]
By using the point slope form.
The equation of tangent will be:
⇒ [tex]y-9=1(x-12)[/tex]
[tex]y-9=x-12[/tex]
[tex]y=x-12+9[/tex]
[tex]y=x-3[/tex]
ESSE
Combine these radicals.
27-3
O √24
O 23
O-23
0 -3/2
here's the answer to your question
I need help with the question below
Answer:
a: 1/12
b: 1/6
c: 1/2
d: 1/2
e: 1/12
f: 1/3
Step-by-step explanation:
write your answer in simplest radical form
Answer:
3 =f
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = f/ sqrt(3)
sqrt(3) tan 60 = f
sqrt(3) * sqrt(3) = f
3 =f
what is the answer to this question
Answer:
18
Step-by-step explanation:
Shape = Isosceles Trapezoid
Area = 1/2 (a+b) h
= 1/2 (9+3) x 3
= 18
Answered by Gauthmath
help pls!!!!!
What is the inequality for this verbal description?
The value of y is greater than or equal to the sum of five times the value of x
and negative three.
Answer:
y ≥ 5x+ (-3)
Step-by-step explanation:
greater than or equal to ≥
The sum means add
y ≥ 5x+ (-3)
Answer:
Option D, y ≥ 5x + (-3)
Step-by-step explanation:
Step 1: Make an expression
The value of y is greater than or equal to the sum of five times the value of x and negative three.
The value of y is greater than or equal to ← y ≥
The sum of five times the value of x and negative three ← 5x + (-3)
y ≥ 5x + (-3)
Answer: Option D, y ≥ 5x + (-3)
Plz help me find side x on the triangle
Answer:
x=71
Step-by-step explanation:
Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.
When the sides are equal, the base angles are equal
x=71
Fine the area and circumference of each circle and round to the nearest tenth.
Answer: A=πr²
A=3.14(1.6inch)² r=d/2⇒3.2/2⇒1.6
A=3.14×2.56in²
A=8.0384in²
A≈8.04
now circumference,
C=2πr
C=2×3.14×1.6in
C=10.048in
C≈10.05
Suppose f(x) = loga(x) and f(7) = 2. Find f(343)
Answer:
6
Step-by-step explanation:
The given function to us is ,
[tex]\rm\implies f(x)= log_a(x) [/tex]
And its value at 7 is 2 , that is ,
[tex]\rm\implies f(x)= log_a(7) =2[/tex]
Taking this ,
[tex]\rm\implies 2= log_a(7) [/tex]
In general we know that ,
[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]
Using this , we have ,
[tex]\rm\implies a^2 = 7 [/tex]
Squarerooting both sides ,
[tex]\rm\implies a =\sqrt{ 7 }[/tex]
Therefore , when x is 343 ,
[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]
We can write , 343 as 7³ ,
[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]
[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]
This can be written as ,
[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]
[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]
Hence the required answer is 6.
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t−t−1, y=1+t2, t=1
Answer:
Step-by-step explanation:
First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.
A map that was created
using a scale of 1 inch : 3 miles
shows a lake with an area of
18 square inches. What is the
actual area of the lake?
9514 1404 393
Answer:
162 mi²
Step-by-step explanation:
The area on the map is ...
18(1 in)²
Then the area on the ground will be ...
18(3 mi)² = 18·9 mi² = 162 mi²
