Which of the following numbers is not a prime number?
9
3
7
13
Using the following equation, find the center and radius of the circle by completing the square.
x2 + y2 + 6x − 6y + 2 = 0
center: (−3, 3), r = 4
center: (3, −3) r = 4
center: (3, −3), r = 16
center: (−3, 3), r = 16
7 eighty percent of all california drivers wear seat belts. if three drivers are pulled over, what is the probability that all would be wearing their seat belts? worksheet
Simplify the rational expression. state any restrictions on the variable. n^4-11n^2+30/n^4-7n^2+10
To simplify the given rational expression, we factor both the numerator and the denominator, cancel out the common factor, and express the result as (n^2 - 6) / (n^2 - 2), with restrictions on n that it can't equate to the square roots of 5 or 2.
Explanation:The question involves simplifying the rational expression n^4 - 11n^2 + 30 divided by n^4 - 7n^2 + 10, and stating any restrictions on the variable. To simplify this, we first factor both the numerator and the denominator.
Numerator: (n^2 - 5)(n^2 - 6)
Denominator: (n^2 - 5)(n^2 - 2)
After factoring, we can cancel out the common factor (n^2 - 5) from both the numerator and the denominator. This leaves us with (n^2 - 6) / (n^2 - 2).
However, we must state the restrictions on the variable n. The original denominator cannot be equal to zero, thus n^2 cannot be equal to 5 or 2, leading to restrictions of n != sqrt(5) and n != sqrt(2).
Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each tree costs $20.75 and a six-pack of pansies costs $2.50. Explain how to write an expression to find Katherine’s final cost.
Answer:
Look below
Step-by-step explanation:
The total cost of the trees must be added to the total cost of the pansies. The tree cost is the cost of one tree times eight. The pansy cost is the cost for 15 pansies multiplied by 8 trees, then divided by the number of pansies in a pack: 20.75(8) + 2.50(15)(8) ÷ 6.
How long will it take the ball to reach the ground
someone help me please!
Answer:
hudadagra what does a say im sorry for putting this in answer but it wont let me comment.
Step-by-step explanation:
i cant see the pic
Which table identifies points on the line defined by the equations y-5x=-9
The equation y - 5x = -9 defines a line that none of the given points (1,5), (2,10), (3,7), and (4,14) lie on, as substituting their x-values in the equation doesn't yield the corresponding y-values.
Explanation:The question involves identifying points on a line described by the equation y - 5x = -9. To verify which points belong to this line, we can substitute the x-values of the given points into the equation and see if the resulting y-values match those in the points. We solve for y in the equation to get y as a function of x (dependence of y on x): y = 5x - 9.
Now, let's examine the points (1,5), (2,10), (3,7), and (4,14) to see if they satisfy this equation:
For (1,5): y = 5(1) - 9 = -4 which does not equal 5, so (1,5) is not on the line. For (2,10): y = 5(2) - 9 = 1 which does not equal 10, so (2,10) is not on the line. For (3,7): y = 5(3) - 9 = 6 which does not equal 7, so (3,7) is not on the line. For (4,14): y = 5(4) - 9 = 11 which does not equal 14, so (4,14) is not on the line.
None of these points lie on the line defined by y = 5x - 9. For a point to be on the line, plugging its x-coordinate into the equation must result in its corresponding y-coordinate.
HELP PLEASE! FAST!!
1.Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
2. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
3. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
IF YOU DO NOT KNOW, DO NOT ANSWER JUST FOR POINTS. YOU WILL BE REPORTED.
(1) The measure of angle B is [tex]140^o.[/tex]
(2) The measure of angle A is [tex]65^o.[/tex]
(3) The measure of angle C is [tex]80.5^o.[/tex]
(1) The quadrilateral [tex]\(ABCD\)[/tex] is inscribed in a circle. For any quadrilateral inscribed in a circle, the opposite angles are supplementary (i.e., their sum is [tex]\(180^\circ\)).[/tex]
In the first image:
[tex]- \( \angle DAB = x^\circ \)\\ - \( \angle DCB = (4x - 20)^\circ \)[/tex]
Since these two angles are opposite angles of the inscribed quadrilateral, we have:
[tex]\[ x + (4x - 20) = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ 5x - 20 = 180 \][/tex]
[tex]\[ 5x = 200 \][/tex]
[tex]\[ x = 40 \][/tex]
Therefore, [tex]\( \angle B = (4x - 20) = 4(40) - 20 = 160 - 20 = 140^\circ \).[/tex]
(2) In the second image:
[tex]- \( \angle ADC = x^\circ \)\\ - \( \angle ABC = 148^\circ \)[/tex]
These are opposite angles of the inscribed quadrilateral. Thus:
[tex]\[ x + 148 = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ x = 180 - 148 = 32 \][/tex]
Therefore, [tex]\( \angle A = (2x + 1) = 2(32) + 1 = 64 + 1 = 65^\circ \).[/tex]
(3) In the third image:
[tex]- \( \angle DAB = (x + 15)^\circ \)\\ - \( \angle DCB = (x + 10)^\circ \)\\ - \( \angle BCD = (x + 24)^\circ \)[/tex]
Using the property that opposite angles are supplementary:
Opposite angles are [tex]\( (x + 15) \)[/tex] and [tex]\( (x + 24) \),[/tex] thus:
[tex]\[ (x + 15) + (x + 24) = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ 2x + 39 = 180 \][/tex]
[tex]\[ 2x = 141 \][/tex]
[tex]\[ x = 70.5 \][/tex]
Therefore, the measure of angle C is [tex]\( (x + 10) = 70.5 + 10 = 80.5^\circ \).[/tex]
If x2 - 4 = 45, then x could be equal to
Simplify completely. square root of 18y^10
A basket contains 4 green marbles and 8 blue marbles. a marble is drawn without replacement. then another marble is drawn. what is the probability that both marbles will be green?
Final answer:
The probability of drawing two green marbles consecutively without replacement from a basket of 4 green marbles and 8 blue marbles is 0.1, or 10%.
Explanation:
The question involves calculating the probability of drawing two green marbles in succession without replacement from a basket containing 4 green marbles and 8 blue marbles. For the first draw, the probability of drawing a green marble is 4 out of 12, which reduces to 1/3 or about 0.3333. Once that marble is drawn, there are 3 green marbles left and 7 blue marbles, making a total of 10.
Therefore, the probability of drawing another green marble is 3 out of 10, or 0.3. To find the probability of both events happening consecutively, we multiply the two individual probabilities: (1/3) * (3/10) = 1/10 or 0.1. Hence, the probability that both marbles will be green is 0.1, or 10%.
Find all solutions in the interval [0, 2π).
2 sin2x = sin x
x = pi divided by three. , two pi divided by three.
x = pi divided by two. , three pi divided by two. , pi divided by three. , two pi divided by three.
x = 0, π, pi divided by six , five pi divided by six
x = pi divided by six , five pi divided by six
Final answer:
The solutions to the equation 2sin^2x = sinx in the interval [0, 2π) are x = 0, π, π/6, 5π/6 and x = π/6, 5π/6.
Explanation:
The given equation is: 2sin^2x = sinx.
To solve this equation, we can first factor out sinx:
sinx(2sinx - 1) = 0.
Setting each factor equal to zero, we get two equations:
sinx = 02sinx - 1 = 0Solving for x, we find:
x = 0, π, π/6, 5π/6x = π/6, 5π/6Which transformation could not map trapezoid 1 to trapezoid 8?
reflection
translation
rotation
Answer:
A rotation
Explanation:
A reflection across the y-axis would map trapezoid 1 to trapezoid 8.
A horizontal translation would also map trapezoid 1 to trapezoid 8.
However, a rotation would map trapezoid 1 to trapezoid 7; it would not map it to trapezoid 8.
Answer: The answer is (c) rotation.
Step-by-step explanation: We are given a figure where 8 trapezoid are drawn on the coordinate plane. We are to select from the given option the transformation that will not map trapezoid 1 to trapezoid 8.
We can easily check that by reflecting and translating that both these transformations will definitely map trapezoid 1 to trapezoid 8.
Only the rotation will not work here. If we rotate trapezoid 1 by 180° taking origin as the centre of rotation, the the image will be opposite of trapezoid 8. Therefore, rotation will not map trapezoid 1 to trapezoid 8.
Thus, (c) is the correct option.
A drama club is planning a bus trip to New York City to see a Broadway play. The table represents the cost per person for the bus rental compared to the number of people going on the trip. What function models the data, and how much per person will it cost if 12 students go on the trip?
Number of Students(n) - Cost per Student(c)
3 - 24$
6 - 12$
9 - 8$
16 - $4.5
A. n/c = 72, $12
B. nc = 9, $10
C. nc = 72, $6
D. n/c = 9, $12,
Cost function: [tex]\( nc = 72 \)[/tex]. Cost per person for 12 students: $6. Answer: C.
To determine the function that models the data and to find the cost per person if 12 students go on the trip, we need to analyze the relationship between the number of students (n) and the cost per student (c).
Given the data:
- When [tex]\( n = 3 \), \( c = 24 \)[/tex]
- When [tex]\( n = 6 \), \( c = 12 \)[/tex]
- When [tex]\( n = 9 \), \( c = 8 \)[/tex]
- When [tex]\( n = 16 \), \( c = 4.5 \)[/tex]
We can observe that as the number of students increases, the cost per student decreases. This suggests an inverse relationship between the number of students and the cost per student. The form of an inverse relationship can be expressed as:
[tex]\[ c = \frac{k}{n} \][/tex]
where [tex]\( k \)[/tex] is a constant.
To find the constant [tex]\( k \)[/tex], we can use one of the data points. Let's use the first data point ([tex]\( n = 3 \), \( c = 24 \)[/tex]):
[tex]\[ 24 = \frac{k}{3} \][/tex]
Solving for [tex]\( k \)[/tex]:
[tex]\[ k = 24 \times 3 = 72 \][/tex]
So the function that models the data is:
[tex]\[ c = \frac{72}{n} \][/tex]
Now, we need to find the cost per person if 12 students go on the trip. We substitute [tex]\( n = 12 \)[/tex] into the function:
[tex]\[ c = \frac{72}{12} = 6 \][/tex]
Therefore, the cost per person if 12 students go on the trip is $6.
The correct answer is:
C. [tex]\( nc = 72 \)[/tex], $6
To confirm this, we can check that this function fits all the provided data points:
1. For [tex]\( n = 3 \)[/tex]:
[tex]\[ c = \frac{72}{3} = 24 \][/tex] (matches the given cost)
2. For [tex]\( n = 6 \)[/tex]:
[tex]\[ c = \frac{72}{6} = 12 \][/tex] (matches the given cost)
3. For [tex]\( n = 9 \)[/tex]:
[tex]\[ c = \frac{72}{9} = 8 \][/tex] (matches the given cost)
4. For [tex]\( n = 16 \)[/tex]:
[tex]\[ c = \frac{72}{16} = 4.5 \][/tex] (matches the given cost)
Hence, the function [tex]\( c = \frac{72}{n} \)[/tex] is validated by all the data points.
if 10% of x is 20, what is 23% of x?
The pressure P (in pounds per square foot), in a pipe varies over time. Ten times an hour, the pressure oscillates from a low of 40 to a high of 280 and then back to a low of 40. The pressure at time t = 0 is 40. Let the function P = f(t) denote the pressure in pipe at time t minutes. Find the formula for the function P=f(t),
To model the pressure function in the pipe that oscillates between 40 and 280 ten times an hour, we can use a sine function. The formula is P = f(t) = 120 sin(π/3 t) + 160.
Explanation:The pressure in the pipe oscillates between 40 and 280 ten times an hour, this is a trigonometric function scenario. Assuming the oscillation is sinusoidal, we can use a sine function to model the pressure in the pipe. The oscillation's period is 6 minutes because the pressure changes happen 10 times per hour. Thus, the function modelling this pressure will be of the form
P = a sin(b(t - c)) + d.
Given that the middle value of the pressure (between the max of 280 and the minimum of 40) is 160, this makes
'd' = 160.
The amplitude 'a' is half the total swing of the pressure which is 120.
To find 'b', we use the fact that the period of a sinusoid in this form is (2π/b).
As our period is 6 minutes, that makes 'b' = π/3.
The pressure is at a minima at t=0 so the phase shift 'c' = 0
Hence the formula P = f(t) = 120 sin(π/3 t) + 160.
Learn more about Oscillating Pressure here:https://brainly.com/question/4116396
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What is the median for the data set? 252, 210, 264, 278, 208, 295, 248, 257, 284, 271
Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2
The hypotenuse of the isosceles right triangle is [tex]\( 12 \)[/tex] units.
In an isosceles right triangle, the legs are congruent, and the hypotenuse can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse [tex]\( c \)[/tex] is equal to the sum of the squares of the lengths of the other two sides [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Given that each leg of the isosceles right triangle has a measure of [tex]\( 6\sqrt{2} \)[/tex], we can substitute this value into the formula:
[tex]\[ c^2 = (6\sqrt{2})^2 + (6\sqrt{2})^2 \]\[ c^2 = 36 \times 2 + 36 \times 2 \]\[ c^2 = 72 + 72 \]\[ c^2 = 144 \][/tex]
Now, we take the square root of both sides to find the length of the hypotenuse [tex]\( c \):[/tex]
[tex]\[ c = \sqrt{144} \][/tex]
[tex]\[ c = 12 \][/tex]
So, the hypotenuse of the isosceles right triangle is [tex]\( 12 \)[/tex] units.
what is the midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i
Answer:
Midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Step-by-step explanation:
The midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
[tex]\dfrac{6-2i-4+6i}{2} \\\\=\dfrac{2+4i}{2}\\ \\=1+2i[/tex]
Hence, midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Answer: 2 + 4 i
Step-by-step explanation:
Hi, to solve this we have to apply the next expression:
(a1 +a2)/ 2 + (b1 +b2 )/2 i=
Where a is the real part, and b is the imaginary part (with i)
For example, for our case:
6 -2i , 6 is the real part (2) and -2 is the imaginary part (b)
Replacing with the values given
(6 -4) /2+ (-2 +6) /2 i = 2 + 4 i
Feel free to ask for more if needed or if you did not understand something.
WILL GIVE BRAINLIEST FOR CORRECT ANSWER
7. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Answer:
x = 8.4 cm
Step-by-step explanation:
Here we have to use the tan ratio to find the value of x.
tan = opposite/adjacent
tan 35 = x/12
Multiplying both sides by 12, we get
x = 12 tan 35 [tan 35 = 0.7]
x = 12*0.7
x = 8.4
Therefore, the value of x = 8.4 cm
Hope this will helpful.
Thank you.
The monthly list of expenditures on your credit card statement can be very helpful at tax time to find items for which you are entitled to tax deductions. true or false
Answer:
true
Step-by-step explanation:
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely. A solar eclipse occurs on your birthday.
Milena's take-home pay is $1200 a month. She spends 12% of her take-home pay on her cable bill. How much is Milena's monthly cable bill?
Answer:
$144
Step-by-step explanation:
Just did test
1.What is the volume of a right circular cylinder with a diameter of 19.6 yd and a height of 23.52 yd?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
2.What is the volume of a right circular cylinder with a base diameter of 18 yd and a height of 3 yd?
Enter your answer in the box. Express your answer using π .
The answer should be 7092.822912 or 7092.82 when rounded to the nearest hundredth because the formula for volume is V= π times r^2 times height to get the answer. So: 3.14 x 9.8^2 x 23.52, and that's the answer.
QUESTION 1
We want to find the volume of a circular cylinder with a diameter of [tex]19.6yd[/tex] and a height of [tex]23.52yd[/tex].
The volume of a cylinder is given by the formula
[tex]V=\pi r^2h[/tex]
where [tex]h=23.52yd[/tex] and [tex]r=9.8yd[/tex] is half the diameter of the cylinder and [tex]\pi=3.14[/tex].
We substitute all these values into the formula to obtain,
[tex]V=3.14\times 9.8^2\times 23.52[/tex]
[tex]V=7092.82[/tex] square yards to the nearest hundredth.
QUESTION 2
We want to find the volume of a right circular cylinder with a base diameter of [tex]18yd[/tex] and a height of [tex]3yd[/tex].
The volume of a cylinder is given by the formula
[tex]V=\pi r^2h[/tex]
where [tex]h=3yd[/tex] and [tex]r=9yd[/tex] is half the diameter of the cylinder.
We substitute all these values into the formula to obtain,
[tex]V=\pi \times 9^2\times 3[/tex]
[tex]V=243\pi[/tex] square yards.
Which of the following fractions is not in simplest form?
3/4
7/10
9/12
4/15
9m2-6/5m+c is a perfect square what is the value of c
The expression given to us is:
[tex] 9m^2-\frac{6}{5}m+c [/tex]
If the above expression is a perfect square then the middle term will have to be 2 times the square root of the first term times the square root of the last term. Thus:
[tex] -\frac{6}{5}m=2\times 3m\times \sqrt{c} [/tex]
[tex] \therefore \sqrt{c}=-\frac{1}{5} [/tex]
Thus, [tex] c=\frac{1}{25} [/tex]
Thus, for 9m^2-(6/5)m+c to be a perfect square, the value of c must be equal to [tex] \frac{1}{25} [/tex] or 1/25
1. What is the sum or difference?
4x^10 - 9x^10 (1 point)
(A). -5x^10
(B). -5x^20
(C). -36x^20
(D). -36x^20
2. What is the sum or difference?
6y^5 - 9y^5 (1 point)
(A). -3y^10
(B). 15y^5
(C). -54y^5
(D). -3y^5
3. Write the Polynomial in standard form. Then name the Polynomial based on its degree and number of terms.
2 - 11x^2 - 8x + 6x^2 (1 point)
(A). -5x^2 - 8x + 2; quadratic trinomial
(B). -5x^2 - 8x; quadratic binomial
(C). -6x^2 - 8x - 2; cubic polynomial
(D). 6x^2 - 8x + 2; cubic trinomial
4. A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.
White-sided jackrabbits: 5.5x^2 - 9.2x + 6.9
Black-tailed jackrabbits: 5.5x^2 + 9.9x + 1.3 (1 point)
(A). 11x^2 + 0.7x + 8.2
(B). 11x^2 - 0.7x + 8.2
(C). 11x^2 - 0.7x - 8.2
(D). -11x^2 + 0.7x - 8.2
Someone please help! Unit 3 Lesson 9, Polynomials and Factoring!
Solving question 1 : What is the sum or difference?
[tex] 4x^{10} - 9x^{10} \\\\
(4-9)x^{10} \\\\
-5x^{10} [/tex]
Hence, option A is correct i.e. [tex] -5x^{10} [/tex].
Solving question 2 : What is the sum or difference?
[tex] 6x^{5} - 9x^{5} \\\\
(6-9)x^{5} \\\\
-3x^{5} [/tex]
Hence, option D is correct i.e. [tex] -3x^{5} [/tex].
Solving question 3 : Write the Polynomial in standard form.
2 - 11x² - 8x + 6x²
We can combine like terms, and rewriting it in decreasing power of x's.
⇒ - 11x² + 6x² - 8x + 2
⇒ (-11 + 6)x² - 8x + 2
⇒ -5x² - 8x + 2
Hence, option A is correct i.e. -5x² - 8x + 2; quadratic trinomial.
Solving question 4 :
White-sided jackrabbits: 5.5x² - 9.2x + 6.9
Black-tailed jackrabbits: 5.5x² + 9.9x + 1.3
Total population = White-sided jackrabbits + Black-tailed jackrabbits
Total population = (5.5x² - 9.2x + 6.9 ) + (5.5x² + 9.9x + 1.3)
Total population = (5.5 + 5.5)x² + (9.9 - 9.2)x + (6.9 + 1.3 )
Total population = 11x² + 0.7x + 8.2
Hence, option A is correct i.e. 11x² + 0.7x + 8.2
Sal bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Sal paid with a $100.00 bill, how much change should he have received?
The correct answer is:
$38.75
Explanation:
35 feet of trim at $1.75 per foot would give us a cost of
35(1.75) = 61.25.
Paying with a $100 bill, he would receive
100-61.25 = $38.75 in change.
I need the answer to question number 12