Step-by-step explanation:
combination
is answer of this question
What are vertices of the conic 16x² - 25y² = 400 ?
Answer:
(-5, 0) and (5, 0)
Step-by-step explanation:
This equation fits the form for a hyperbola with x-intercepts. The standard form for such an equation is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
To get the equation in the question into this standard form, divide each term by 400.
[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]
To find the x-intercepts, make y = 0.
[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]
The vertices are located at the points (-5, 0) and (5, 0).
Note: There are no y-intercepts; making x = 0 produces no real solutions for y.
An airplane started at 0 feet. It rose 21,000 feet at takeoff. It then descended 4,329 feet because of clouds. An oncoming plane was approaching, so it rose 6,333 feet. After the oncoming plane passed, it descended 8,453 feet, at what altitude was the plane flying?
Question of
How many solutions doen 3 -2x=5-x+3+4x have?
A Infinitely many solutions
B. Two solutions
C. No solutions
D. One solution
Answer:
one solution
Step-by-step explanation:
3 -2x=5-x+3+4x
Combine like terms
3-2x = 8+3x
Add 2x to each side
3-2x+2x = 8+3x+2x
3 = 8+5x
Subtract 8 from each side
3-8 =8+5x-8
-5 =5x
Divide by 5
-5/5 = 5x/5
-1 =x
There is one solution
The population of a town is decreasing exponentially according to the formula
P = 7,285(0.97)t, where t is measured in years from the present date. Find the population in 2 years, 9 months. (Round your answer to the nearest whole number.)
Answer: 6669
Step-by-step explanation:
I hope I did this right... anyways,
t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.
Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.
The formula used is:
[tex]7285(0.97)^2^.^9[/tex]
2 6 + 3 * 4 2 + 7 * - 2 /
Answer:
26 + 3 x 42 + 7 x -2 = 138
Step-by-step explanation:
Ok bud, first step we must convert our symbols (Makes it easier to solve)
26 + 3 x 42 + 7 x -2
* subsitutes for multiplication.
I recommend using PEMDAS at times:
1 - Parentheses
2 - Exponents and Roots
3 - Multiplication
4 - Division
5 - Addition
6 - Subtraction
Yet again your numbers were spaced out could they be exponents? if so:
3x^{42}+7x+24
Our answer would round to 24 but he equation was not put in a valid or straight forward way.
which polygon will NOT tessellate a plane?
Answer:
pentagons
Step-by-step explanation:
In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.
Answer:
The Regular Pentagon.
Explanation
I got a 100 % on the quiz
Please,look at this one.
9514 1404 393
Answer:
x = √2
Step-by-step explanation:
A graph indicates the only solution is near x=√2.
__
Square both sides, separate the radical and do it again.
[tex]\displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}[/tex]
Now, we can put this polynomial equation into standard form and factor it.
[tex]x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}[/tex]
The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].
The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.
The only solution is x = √2.
_____
Additional comment
For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)
A company that manufactures and bottles apple juice uses a machine that automatically fills 32-ounce bottles. There is some variation, however, in the amount of liquid dispensed into the bottles. The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce. Determine the proportion of bottles that will have more than 30 ounces dispensed into them. (Round your answer to four decimal places.)
Answer:
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce.
This means that [tex]\mu = 32, \sigma = 1[/tex]
Determine the proportion of bottles that will have more than 30 ounces dispensed into them.
This is 1 subtracted by the p-value of Z when X = 30, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 32}{1}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
1 - 0.0228 = 0.9772
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
I really need the help please and thank you
BBBBB BBBBBBBBBBBBBBBBBBBBBBBBBBBB
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
Learn more about integration here:
brainly.com/question/18125359
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -1x + 2
Step-by-step explanation:
Using the following information to answer the questions.
- A survey asked 75 people if they wanted a later school day start time.
- 45 people were students, and the rest were teachers.
- 50 people voted yes for the later start
- 30 students voted yes for the later start
Use this information to complete the frequency table.
Use the completed table from Part a. What percentage of the people surveyed were teachers?
Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time?
What does the number in the bolded cell represent?
Answer:
Hi! I'll provide the answers in the explanation.
Step-by-step explanation:
a) The table is in the attachment.
b) The percentage is 40%. Looking at the table, we can see that the total of teachers who voted is 30. You'll be able to find the percentage if you divide 30/75, since 75 is the total people who took the survey.
c) The percentage is 40%. For this situation, we have to divide the total of the people who voted for NO by the teachers who voted NO. So it'll be 20/50, which is 0.4. We can simplify that and the solution is 40%.
d) It represents the students who took the survey voted NO for a later start.
Hope this helps! :D
Answer:
5. Use the following information to answer the questions.
A survey asked 75 people if they wanted a later school day start time.
45 people were students, and the rest were teachers.
50 people voted yes for the later start.
30 students voted yes for the later start.
a) Use this information to complete the frequency table. (5 points: 1 point for each cell that was not given above)
Vote YES for later start
Vote NO for later start
Total
Students
30
15
45
Teachers
20
10
30
Total
50
25
75
b) Use the completed table from Part a. What percentage of the people surveyed were teachers? (2 points)
40%
c) Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time? (2 points)
40%
d) What does the number in the bolded cell represent? (1 point)
The number of students that said no to a later start.
Step-by-step explanation:
A p E x
In a scatter plot, each ____. Group of answer choices individual is represented by a single point group mean is represented by a single point individual is represented by two data points group mean is represented by two data points
Answer:
Individual is represented by a single point
Step-by-step explanation:
If an angle of a right angle triangle is 81 find the remaining angle in grades
Answer:
9
Step-by-step explanation:
90+81+mising angle=180, missing angle is 9
Find the missing side of the right triangle.
Answer:
√65
Step-by-step explanation:
you have to use the pythagoras theorem to find x which is the hypotenuse
x²=7²+4²
x²=49+16
√x²=√65
x=√65
I hope this helps
At a hockey game, a vender sold a combined total of 192 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.
Answer:
they sold 64hotdogs and 128 sodas
Step-by-step explanation:
2x+x=192 3x=192 x=64
Find the x-intercepts of the l equation y=3x-6
Answer:
(2,0)
Step-by-step explanation:
the x intercept is when 'y' is equal to 0 :
0 = 3x - 6
6 = 3x
x = 2
Answer:
(2,0)
Step-by-step explanation:
y = 3x-6
The x intercept is found by setting y = 0 and solving for x
0 = 3x-6
Add 6 to each side
6 = 3x-6+6
6 =3x
Divide each side by 3
6/3 = 3x/3
2 =x
The x intercept is
(2,0)
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard deviation 7.1%. Using the normalcdf function on your graphing calculator, what percentage of students would score 70 or better on this entrance exam?
A. 28.4%
B. 18.9%
C. 24.1%
D. 22.3%
Answer:
The correct answer is - C. 24.1%
Step-by-step explanation:
Given:
mean μ = 65%
standard deviation δ = 7.1 %
solution:
Prob( X>70) = 1 - Prob(x<70)
= P (x-μ/δ ≥ 70 -65/7.1)
= 1 - Prob( (70-65)/7.1)
= 1 - Prob ( z < 0.7042553)
= 0.24065
the percentage of students scoring 70 or more in the exam
= 24.065*100
= 24.1%
I need to know the answer ASAP please
By observing the points you can learn a lot about a function. Concretely [tex]f(x)[/tex] passes through [tex](1,1)[/tex] but [tex]g(x)[/tex] passes through [tex](1,-\frac{1}{2})[/tex] that should give you a hint that [tex]g(x)=-\frac{1}{2}x^2[/tex].
Hope this helps :)
I need you guy’s help answer thanks so much
Answer:
(c) (f-g ) (x) = 6x*3 -2x*2 +4x -8
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
in the figure above, three congruent circles are tangent to eachother and have centers that lie on the diameter of a larger circle. if the area of each of these small circles is 9pi, what is the area of the larger circle?
a) 36pi
b) 49pi
c) 64pi
d) 81pi
The area of the larger circle is 81π square units.
Congruent circles are circles that are similar in pattern.
The formula for calculating the area of a circle is expressed as:
[tex]A = \dfrac{\pi d^2}{4}[/tex]
Given that the area of each of the small circles is 9π, then:
[tex]9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units[/tex]
This shows that the diameter of one of the small circles is 6units.
Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;
Diameter of the larger circle = 3(6) = 18units
Get the area of the larger circle:
[tex]A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi[/tex]
Hence the area of the larger circle is 81π square units.
Learn more on the area of circles here: https://brainly.com/question/12298717
Find the missing side round your answer to the nearest tenth
Answer:
x = 38.4
Step-by-step explanation:
tan(38) = 30/x
x = 30/tan(38)
x = 38.4
Answered by GAUTHMATH
Solve the inequality (help pls)
Answer:
B
Step-by-step explanation:
(-2/3x)-10<1/3
(-2/3x)<1/3+10
(-2/3x)<31/3
x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)
1
Select the correct answer.
The graph shows the quadratic function f and the table shows the quadratic function &
f(x)
4
2
X
2
14
M
Х
-5
-4
-3
-2
-1
0
1
g(x)
10
7
6
7
10
15
22
Which statement is true?
Answer:
g(x)
because it is a quadratic equation it is mirrored the other one isn’t even a function
The true statement is The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
The function g has the axis of symmetry as x = 2, since the values of the function below and above x = 2 changes in the same way.
The function f is a parabola.
The axis of symmetry is also x = 2, since the graph is the same before and after the line x = 2.
So the both the functions have same axis of symmetry.
Maximum value of the function f = 4 at x = 2. Since no other values of f is greater than 4.
At x = 2, the value of g = 3
Maximum value of g = 3
So, maximum value of f is greater than the maximum value of g.
Hence the correct option is B.
Learn more about Functions here :
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Your question is incomplete. The complete question is as given below.
The graph shows the quadratic function f and the table shows the quadratic function g.
x : -2 -1 0 1 2 3 4
g(x) -1 0.75 2 2.75 3 2.75 2
Which statement is true?
The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.
The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
The functions f and g have different axes of symmetry and different maximum values.
The functions f and g have the same axis of symmetry and the same maximum values.
A particle moves along line segments from the origin to the points (3, 0, 0), (3, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field F(x, y, z) = z^2i + 4xyj + 5y^2k. Use Stokes' Theorem to find the work done.
Answer:
the first option because I took the test
Which of the following theorems verifies that abc wxy
Answer:
C. AA
Step-by-step explanation:
Since m<Y = 27°, then m<W = 27°.
We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).
Answer: C. AA
please solve the question
Answer:
[tex]g(-1) = -1[/tex]
[tex]g(0.75) = 0[/tex]
[tex]g(1)= 1[/tex]
Step-by-step explanation:
Given
See attachment
Solving (a): g(-1)
We make use of:
[tex]g(x) = -1[/tex]
Because: [tex]-1 \le x < 0[/tex] is true for x =-1
Hence:
[tex]g(-1) = -1[/tex]
Solving (b): g(0.75)
We make use of:
[tex]g(x) = 0[/tex]
Because: [tex]0 \le x < 1[/tex] is true for x =0.75
Hence:
[tex]g(0.75) = 0[/tex]
Solving (b): g(1)
We make use of:
[tex]g(x) = 1[/tex]
Because: [tex]1 \le x < 2[/tex] is true for x =1
Hence:
[tex]g(1)= 1[/tex]
A simple random sample of 27 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses?
Answer:
The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]
The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]
Step-by-step explanation:
Test if the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg.
At the null hypothesis, we test if the standard deviation is of 0.3, that is:
[tex]H_0: \sigma = 0.3[/tex]
At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:
[tex]H_1: \sigma \neq 0.3[/tex]
The sum of the two numbers is 66. The larger number is 10 more than the smaller number. What are the numbers?
Answer:
28 and 38
Step-by-step explanation:
a+b = 66
a + 10 = b
using substitution, a + (a+10) = 66
2a = 56
a = 28
28 + 10 = 38
b = 38
