.help me with this please
Which number line represents all of the values of x for the equation x2 = 36?
yes thats the corrects answer -6 and 6 on the number line.
How do you simplify squats roots
A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amount of material used.
James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution
The distance of saturn from the sun is 1507 million kilometers express this distance in standard form
A point where two or more rays or "arms" of an angle meet
Final answer:
The point where two or more rays meet in optics is known as the focal point, which is crucial in geometric optics. For a converging lens or mirror, it's where light rays converge, while for a diverging lens or mirror, it's where light rays appear to originate.
Explanation:
The point where two or more rays or 'arms' of an angle meet in the context of geometrical optics is known as the focal point. In terms of a converging lens or mirror, the focal point is where converging light rays intersect after passing through the lens or reflecting off the mirror surface. This is a fundamental concept in the study of geometrical optics, which deals with the ray aspect of light. A ray is a straight line that originates at a point and is used in geometric optics to represent the path along which light travels.
For a converging lens, which is also known as a convex lens, parallel light rays entering the lens will refract and converge at a single point on the opposite side of the lens. This single point is the focal point. Similarly, in concave mirrors, ray diagrams show the focal point as the point where reflected rays converge or appear to converge. The distance from the focal point to the mirror along the central axis is referred to as the focal length. Conversely, for a diverging lens or mirror, the focal point is the point from which diverging light rays appear to originate.
Check all that apply: If cos theta = 15/17 then:
A. Sec theta = 17/15
B. Tan theta = 8/15
C. Sin theta = 15/8
D. Csc theta = 17/15
The options (A) and (B) are correct.
What is trigonometric Ratios?"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".
For the given situation,
Cos θ = 15/17
By using Pythagoras theorem,
We know Cos θ = [tex]\frac{base}{hypotenuse}[/tex]
Sine θ = [tex]\frac{perpendicular}{hypotenuse}[/tex]
tan θ = [tex]\frac{perpendicular}{base}[/tex]
By Pythagoras theorem, [tex]Hypotenuse^{2}= base^{2}+perpendicular^{2}[/tex]
⇒[tex]17^{2}=15^{2}+perpendicular^{2}[/tex]
⇒[tex]perpendicular^{2}= 289-225[/tex]
⇒[tex]perpendicular=\sqrt{64}[/tex]
⇒[tex]perpendicular=8[/tex]
Thus, Sec θ = 17/15
Tan θ = 8/15
Sine θ = 8/17
Cosec θ = 17/8.
Hence we can conclude that the options (A) and (B) are correct.
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Answer:
tan and sec
Step-by-step explanation:
A amd B
Solve 2x2 + 20x = −38.
a. −5 ± square root 14
b.−5 ± square root 51
c. −5 ±square root 6
d.−5 ± square root 13
Answer:
c
Step-by-step explanation:
−5 ±square root 6
What is the value of x in the equation 2(x – 3) + 9 = 3(x + 1) + x?
x =
A cylindrical metal can is to have no lid. it is to have a volume of 8Ï in3. what height minimizes the amount of metal used?
To solve this problem let us say that,
h = height of the can
r = radius of the can
We try to minimize the amount of metal used which is the surface area (SA), and the equation for a cylinder is:
SA = 2πrh + πr^2
To get the minima, we take the derivative of this function and set it equal to 0. But first, the function is in two variables so we must eliminate one of them. We use the extra information given in the problem which is volume:
V = 8π = πr^2 h
Therefore,
h = 8/r^2
Plug this into the SA function to have it in terms of one variable only:
SA = 2πrh + πr^2
SA = 2πr(8/r^2) + πr^2
SA = 16π/r + πr^2
Taking the 1st derivative of the function:
0 = −16π r^−2 + 2πr
0 = −16π/r^2 + 2πr
16π/r^2 = 2πr
r^3 = 8
r = 2 in
By obtaining r, we calculate for h:
h = 8/r^2
h = 8/(2)^2
h = 8 / 4
h = 2 in (ANSWER)
In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2
Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.
The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.
Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).
A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes is charged at $.10 per minute. All long distance calls are charged at $.25 per minute. Write and simplify an expression that gives the total monthly bill if x is the number of local minutes and y is the number of long distance minutes. Evaluate the expression if local usage totals 375 minutes and long distance usage totals 54 minutes.
total = 19.99 + 0.10(x-300) + 0.25y
x = 375
y=54
total = 19.99 +0.10(375-300) +0.25(54)
total = 19.99 + 0.10(75) + 0.25(54)
total = 19.99 + 7.50 + 13.50
total = $40.99
The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.
The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:
Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)
Where:
Basic Rate = $19.99Local Extra Charge = $0.10 per minuteExtra Local Minutes = x - 300 (only if x > 300)Long Distance Rate = $0.25 per minuteLong Distance Minutes = yFor x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:
Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)
Total Monthly Bill = $19.99 + $7.50 + $13.50
Total Monthly Bill = $40.99
Let $s$ be the set of points with polar coordinates $(r,\theta)$ such that $ 2 \le r \le 6$ and $\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6} $. find the area of $s$.
Vanessa typically works 8 hours per day in a normal 5 day work week. last week, however, vanessa had to take 90 minutes off on tuesday, 45 minutes off on thursday, and she left two and a half hours early on friday. how many hours did vanessa work last week?
The total number of hours Vanessa work in a week is:
total work hours = (8 hours / day) * 5 day / week
total work hours = 40 hours per week
The total number of hours she did not work:
total hours did not work = (90 minutes)(1 hour / 60 minutes) + (45 minutes)(1 hour / 60 minutes) + 2.5 hours
total hours did not work = 4.75 hours
The amount of hours Vanessa work last week can be calculated using the formula:
work hours = total work hours - total hours did not work
work hours = 40 hours – 4.75 hours
work hours = 35.25 hours
The book Kathy is reading is 540 pages long. So far, she has read 405 pages. What percent of the book does she have left to read?
Answer: b
Step-by-step explanation: i got it right
The equation sec^2x-1=tan^2x is an identity true or false
(6.04)The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
What is the y-intercept of the line of best fit and what does it represent?
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
Please Help!! Find the measure of angle 2. Image Attached
which one of the following sets of numbers represents the lengths of the sides of a right triangle ?
a. 13 35 37
b. 6 9 10
c. 5 12 13
d. 9 40 42
5, 12, 13 are the sides representing lengths of sides of a right triangle.
What is Pythagoras theorem?The theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Given that, lengths of sides of triangles.
If a triangle is a right triangle, then it should follow Pythagoras theorem,
Using Pythagoras theorem,
13² = 169
12² + 5² = 144 + 25 = 169
Therefore, 13² = 12² + 5² is following Pythagoras theorem.
Hence, 5, 12, 13 are the sides representing lengths of sides of a right triangle
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Conjectures can always be proven true.
True or False
The value of y varies jointly with the values of x and z. When x=4 and z=9, the value of y is 360. What is the value of y when x=5 and z=12?
Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time Anderson mows the lawn. His savings account balance can be shown with the following expression:
50 + 5w + 20m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Anderson saves for 10 weeks and mows the lawn 2 times, how much will he have in his account? Show your work to receive full credit. (4 points)
Part C: If Anderson had $85 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
We are given the equation of the savings (s) as:
s = 50 + 5 w + 20 m
Part A.
Coefficient = 5 and 20
Variable = w and m
Constant = 50
Part B.
w = 10
m = 2
Therefore the total savings is:
s = 50 + 5 (10) + 20 (2)
s = $140
Part C.
The coefficient and the constant values are considered as fixed value because they do not change. Therefore only the variable value would change, however the expression 50 + 5 w + 20 m would still be the same. That is only the values of the variable change.
Which is a factor of 54xy + 45x + 18y + 15?
every evening jenna empties her pockets and puts the changein a jar. at the end of the week she had 50 coins, all of them dimes and quarters. when she added them up, she had a totals of $10.25
d=number of dimes q=number of quarters
how many dimes did jenna have?
How many roots does y+x^2-6x+9 have?
A. One
B. Two
C. Zero
D. Three
Brian is waiting at a park across the street from the hockey arena for his dad to pick him up. It rained most of the morning, and the streets still have puddles. At which point should Brian stand to be as far as possible from each street to avoid getting splashed? Explain your answer.
To avoid getting splashed from puddles on the street, Brian should stand in the middle of the park. This would distance him completely from the immediate spray zone of passing vehicles, like being further away from the shore reduces the impact of sprays from waves.
Explanation:To avoid getting splashed by cars driving through the puddles, Brian should stand in the middle of the park. By doing so, he establishes the maximum possible distance between himself and any part of the street. Staying as far away from the streets reduces the risk of any water reaching him when cars pass by.
Think of it like Jill delivering her flyers and retracing her steps: the farthest spot from her house during her journey was at the midpoint of her travel route.
Also consider Peter's driving scenario: The farther he is from other cars, the less likely he is to get affected by their maneuvers. In a similar way, Brian, being in the middle of the park would keep him away from the splash zone of passing cars.
Lastly, akin to Julian and his father on their surfboards, being away from the impact point of the waves (which is near the shore) they get least affected by the spray. This analogy can be compared to Brian's situation with the puddles.
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What is the value of x?
x =
Answer: The value of x is 2 units.
Explanation:
Since we have given that
AB and CD are two chords that are intersected externally at point E.
As we know the relation regarding the above i.e.
[tex]EA\times EB=EC\times ED[/tex]
Here,
EB=x+1
EA=x+1+11 = (x+12)
EC=x+4
ED=x+4+1 = (x+5)
Now, we put the values in the relation given above :
[tex](x+1)(x+12)=(x+4)(x+5)\\\\x^2+13x+12=x^2+9x+20\\\\12+13x=20+9x\\\\13x-9x=20-12\\\\4x=8\\\\x=\frac{8}{4}=2\\\\x=2\ units[/tex]
Hence, the value of x is 2 units.
Answer:
x = 2 is the answer.
Step-by-step explanation:
When two chords AE and ED are drawn from an external point E to a circle then by theorem we know the relation
AE×BE = DE×CE
AE = x + 1 + 11 = x + 12
BE = x + 1
CE = x + 4
DE = x + 4 + 1 = x + 5
Now putting these values in the formula
(x + 12)(x + 1) = (x + 4)(x + 5)
x² + 12x + x + 12 = x² + 5x + 4x + 20
13x + 12 = 9x + 20
13x - 9x = 20 - 12
4x = 8
x = 2
x = 2 is the answer.
(30 points) Enter numbers to write 0.000328 in scientific notation.
Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = eight divided by square root of quantity two x plus four.