The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $72. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
(Algebra 2)
Given the conditional statement: p → ~q Choose the logically equivalent statement.
A. p → q
B. ~p → q
C. q → p
D. q → ~p
Answer: The correct option is
(D) q → ~p.
Step-by-step explanation: We are given to select the statement that is logically equivalent to the conditional statement p → ~q.
We know that
two conditional statements are said to be logically equivalent if the truth tables of both the statements are same.
That is, they have same truth values under similar conditions.
The truth table is given by
p q ~p ~q p → ~q p → q ~p → q q → p q → ~p
T T F F F T T T F
T F F T T F T T T
F T T F T T T F T
F F T T T T F T T
So, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.
Thus, option (D) is CORRECT.
Answer:
D). q → ~p
Step-by-step explanation:
I just did the assignment on Edge... It's 100% correct... Hope this helps!!
Also heart and rate if you found this answer helpful... Have a nice day!! :)
A point on the terminal side of an angle theta is given. Find the value of the indicated trigonometric function of theta.
Given (-4,-1), find sec(theta)
Answer:
-√17/4
Step-by-step explanation:
Because both the x- and the y-coordinates of (-4, -1) are negative, the angle, theta, is in Quadrant III.
tan theta = opp/adj = vertical side / horizontal side = 4/1, or just 4.
The two coordinates are the legs (both shorter than the hypotenuse) of the triangle formed by this terminal side / point.
The length of the hypotenuse is found using the Pythagorean Theorem and is:
√[ (1)² + (4)² = √17.
Again remembering that our terminal side is in Quadrant III,
sin Ф = opp/hyp = -1/√17
cos Ф = adj/hyp = -4/√17
tan Ф = opp/adj = 4 (see discussion above)
The instructions are to "find sec(theta)." The sec function is the inverse of the cos function. Here cos Ф = -4/√17, and so the secant of this angle is
the inverse (reciprocal) of the cosine, and is thus -√17/4
The value of sec(theta) is found by first determining the radius using the Pythagorean theorem and then calculating the reciprocal of the cosine function, which in this case is -√17/4.
Explanation:To find the secant of angle theta (sec(θ)) when given a point (-4,-1) on its terminal side, we first need to understand that sec(θ) = 1/cos(θ). Since cos(θ) is the x-coordinate of the point on the unit circle divided by the radius, we need to find the radius of the circle that would pass through the point (-4, -1). This radius can be found using the Pythagorean theorem.
Let's calculate the radius (r):
r = √((-4)^2 + (-1)^2)
r = √(16 + 1)
r = √17
Now, since the x-coordinate is -4, cos(θ) = -4/r. Plugging in the value of r, we get:
cos(θ) = -4/√17.
Therefore, sec(θ) is the reciprocal of cos(θ):
sec(θ) = -√17/4.
Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle? Explain why or why not
Final answer:
Two tangents meeting at opposite ends of a circle's diameter are parallel and cannot intersect outside the circle, since tangents are perpendicular to the radius at the point of tangency and parallel lines do not meet.
Explanation:
Two tangents that intersect a circle at opposite endpoints of the same diameter cannot intersect outside the circle. This is because a tangent to a circle is perpendicular to the radius at the point of tangency. In the case of tangents at the ends of a diameter, these tangents are parallel to each other since they are perpendicular to the same line (the diameter), which cannot intersect outside the circle by definition of parallel lines.
No, it is not possible for the two tangents to intersect each other outside the circle.
Let's consider the properties of tangents and diameters to a circle to explain why the two tangents cannot intersect each other outside the circle.
1. A tangent to a circle is a line that touches the circle at exactly one point. This point of tangency is perpendicular to the radius drawn to the point of tangency.
2. A diameter of a circle is a chord that passes through the center of the circle and has both endpoints on the circle. The center of the circle bisects the diameter, meaning it divides the diameter into two equal parts.
3. If a tangent intersects a circle at an endpoint of a diameter, then by the definition of a tangent, the tangent is perpendicular to the radius at that point. Since the radius is part of the diameter, the tangent is also perpendicular to the diameter at the point of tangency.
4. Now, consider two tangents, each intersecting the circle at opposite endpoints of the same diameter. Since each tangent is perpendicular to the diameter at its respective point of tangency, the two tangents are parallel to each other because they are both perpendicular to the same line (the diameter).
5. Parallel lines do not intersect. Therefore, the two tangents, being parallel, cannot intersect each other at any point, let alone outside the circle.
In conclusion, because the two tangents are parallel, they cannot intersect each other outside the circle, confirming that the scenario described in the question is not possible.
α and β are angles in standard position whose terminal sides lie in Quadrant II.If cosα = -24/25 and sinβ = 3/5, find cos(α - β).
-4/25
3/5
4/5
117/125
Answer:
The answer is 117/125
Step-by-step explanation:
The identity for the difference of 2 angles as far as cos goes is
cos(α-β) = cosα cosβ + sinα sinβ
We have both alpha and beta in QII. In order to find the sinα, we need the missing leg, the one opposite the reference angle. Applying Pythagorean's Theorem to that right triangle we get that the missing leg is +7 (y values are positive here so the 7 is positive since it is above the y = 0 line). We also have to find the missing leg in beta so we can find the cosβ. Applying Pythagorean's Theorem to that right triangle we get that the missing leg is -4 (negative because x is negative to the left of the origin). Now that we have everything we need to fill in the identity, it looks like this:
[tex](-\frac{24}{25})(-\frac{4}{5})+(\frac{7}{25})(\frac{3}{5})[/tex]
Multiplying that out and then adding gives you
[tex]\frac{96}{125}+\frac{21}{125}=\frac{117}{125}[/tex]
Really trying to pass this exam and graduate can someone smart please help me with these problems im running out of time ..
Answer:
1172.08 square inches
Step-by-step explanation:
Total surface area is area of all the surfaces.
Cylinder:
Top surface = πr^2 = π(4)^2 = 16(3.14) = 50.24
Lateral Surface = 2πrh = 2π(4)(9) = 72π = 72(3.14) = 226.08
Rectangular Prism:
2 sides = 2*(11*11) = 242
front and back = 2*(16*11) = 352
bottom = 16 * 11 = 176
Top part (it is top rectangle - bottom of cylinder) = (16*11) - (π(4)^2) = 125.76
Adding all up, we get:
50.24 + 226.08 + 242 + 352 + 176 + 125.76 = 1172.08 square inches
Refer to the figure and match the theorem that supports the statement
Answer:
from top to bottom: 1, 3, 2
Step-by-step explanation:
For chords and arcs, the "theorem that supports the statement" is essentially a restatement of the statement.
For the relationship to chords and diameters, the second statement on the right applies. A chord and the radii to its ends form an isosceles triangle. The altitude is the perpendicular bisector of the chord (triangle base). Of course, it is also a line segment that intersects the center of the circle (the apex of the isosceles triangle).
Answer:
1 matches with first statement, 2 matches with third statement and 3 matches with second statement i.e, 1,3,2.
Step-by-step explanation:
In circle, when two chords are equal , than their corresponding minor arcs are also equal. Converse is also true, if minor arcs are equal, than their corresponding chords are equal.So, when chords BC and DE are equal, than their minor arcs BC and DE are also equal. In converse, when arcs BC and DE are equal, than their chords BC and DE are also equal. for the third one, Perpendicular from the center bisect the chord, hence AX is ⊥ to BC than BX= XC.
We can say that diameters perpendicular to chord bisect the chord.
1 matches with first statement, 2 matches with third statement and 3 matches with second statement i.e, 1,3,2.
A random sample of 64 freshmen spent an average of 14 hours per week watching television. the sample standard deviation was 32 hours per week. what is the critical value for a 95% confidence interval for the population mean?
Answer:
+/- 1.9983
Step-by-step explanation:
The critical values for a confidence interval for the population mean, with population standard deviation not known, are obtained from the student's t distribution.
The sample size is given as 64. The degrees of freedom will thus be;
sample size - 1 = 64 - 1 = 63
The confidence level is given as 95%. The level of significance will thus be;
100 - 95 = 5%.
The area in the right-tail will thus be 2.5%. Therefore, we looking for a t-value such that the area to its right is 2.5% and the degrees of freedom being 63. From the t-tables we have;
+/- 1.9983
The growth of a new strain of bacteria is represented by y=79.31(1.48)x where x represents the number of days and y represents the number of bacteria. Which is the best prediction for the number of bacteria on day 7?
Answer:
1234
Step-by-step explanation:
Put the number in the expression and do the arithmetic.
y = 79.31(1.48^7) ≈ 79.31 × 15.554 ≈ 1233.56 ≈ 1234
Answer: There are 1233.55 bacteria on day 7.
Step-by-step explanation:
Since we have given that
[tex]y=79.31(1.48)^x[/tex]
Here, x represents the number of days.
y represents the number of bacteria.
We need to find the number of bacteria on day 7.
So, we put x = 7 as there are 7 days given.
So, our equation becomes,
[tex]y=79.31(1.48)^7\\\\y=1233.55[/tex]
Hence, there are 1233.55 bacteria on day 7.
Please help, I'm trying to finish these
2 x length + 2 x width = perimeter.
2(2s-5) + 2(4s-13) = 108
Simplify:
4s-10 + 8s-26 = 108
Combine like terms:
12s - 36 = 108
Add 36 to both sides:
12s = 144
Divide both sides by 12:
s = 144/12
s = 12
Now replace s with 12 in each equation:
2(12) - 5 = 24-5 = 19
4(12) - 13 = 48-13 = 35
The answer is d. 35,35, 19,19
A game has a rectangular board with an area of 44 in2. There is a square hole near the top of the game board in which you must not toss in a bean bag. The square has side lengths of 3 in. What is the probability of not tossing the bag through the hole?
A)9/44
B)3/9
C)3/44
D)35/44
The probability of not tossing the bag through the hole is D) 35 / 44
How to find the probability ?
To find the probability of not tossing the bean bag through the hole, you need to calculate the area of the board where you can toss the bag and then divide it by the total area of the board.
Find the area where you can toss the bag (not through the hole), subtract the area of the hole from the total area:
Area to toss the bag = Total area - Area of the hole
Area to toss the bag = 44 in² - 9 in²
= 35 in²
Ccalculate the probability of not tossing the bag through the hole:
Probability = (Area to toss the bag) / (Total area)
Probability = 35 in² / 44 in²
Probability = (5 x 7) / (4 x 11)
Probability = 5/4 x 7/11
Probability = (5 x 7) / (4 x 11)
Probability = 35/44
PLEASE HELP
In the proof of the Law of Cosines, the equation c^2=h^2+(b-x)^2was created using the Pythagorean theorem. Which equation is a result of expanding (b-x)^2?
A.c^2=h^2+b^2-x^2
B.c^2=h^2+b^2-2bx+x^2
C. c^2=h^2+b^2+x^2
not D
Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.
9.0 yd
16.1 yd
22.1 yd
23.7 yd
Answer:
Q1 B
Q2 23.7yd
Step-by-step explanation:
Solution of Q2 is in the picture
Answer:
a) [tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) TP = 23.7 yards
Step-by-step explanation:
a) We can rewrite [tex](b-x)^{2}[/tex] as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:
[tex](b-x)(b-x)=b^{2}-bx-bx+x^{2}=b^{2}-2bx+x^{2}[/tex]
so the the Law of Cosines equation will be write as:
[tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) Here we can use the Law of sines.
TP is the distance between Tyrone and the pianoDP is the distance between Diego and the pianoTD is the distance between Diego and Tyrone.∠A angle between TD and TP = 65°
∠B angle between TD and DP = 77°
∠C angle between TP and DP = 180° - 77° - 65° = 38°
The equation is:
[tex]\frac{TP}{sin(B)}=\frac{TD}{sin(C)}[/tex]
[tex]\frac{TP}{sin(77)}=\frac{15}{sin(38)}[/tex]
Solving it for TP, we have:
[tex]TP=sin(77)\frac{15}{sin(38)}=23.7 yards[/tex]
I hope it helps you!
What is 3/4 times 710?
Answer:
532.5 or 532[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3/4 x 710
= 3 x 710 ÷ 4
= 532.5 or 532[tex]\frac{1}{2}[/tex]
Final answer:
To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.
Explanation:
The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.
Here's a step-by-step breakdown:
Multiply the whole number 710 by the numerator of the fraction, 3.Therefore, 3/4 times 710 is 532.5.
Determine the height of the triangle.
Round to the nearest foot.
a. 12 ft c. 10 ft
b. 14 ft d. 18 ft
Please select the best answer from the choices provided
Answer:
Option B is correct.
Step-by-step explanation:
We need to find the height of triangle.
The triangle is right angled triangle
We are given Hypotenuse = 25
Perpendicular = h
and angle Ф = 34°
We know that sinФ = Perpendicular / Hypotenuse
sin 34° = h / 25
0.56 = h/25
=> h = 0.56 * 25
=> h = 14 ft
So, the height of triangle is h= 14 ft
So, Option B is correct.
Answer:
It's B!
Step-by-step explanation:
I just took it! Have a good day.
Match the red graph above to the corresponding equation
Answer:
y = -1/3·x³
Step-by-step explanation:
The function is odd (symmetrical about the origin), so corresponds to a function of odd degree. It is shorter and wider than the parent x³ function, so has a vertical scale factor less than 1. The appropriate choice is ...
y = -1/3x³
The corresponding equation that matches the red graph include the following: A. [tex]y=-\frac{1}{3} x^3[/tex].
What is a cubic root function?In Mathematics and Euclidean Geometry, a radical function, cubic function or a cube root function can be represented by using the following mathematical equation:
[tex]f(x)=a\sqrt[3]{x-h} +k[/tex]
where:
h represent the horizontal shift.k represent the vertical shift.By critically observing the graph shown above, we can logically deduce that the red graph represents a cubic function with an odd degree because it is symmetrical about the origin. Also, the parent cubic function [tex]f(x)=x^3[/tex] was vertically compressed by a factor that is less than 1, which is 1/3;
[tex]y=-\frac{1}{3} x^3[/tex]
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I don't understand this. Can someone please help me?
Answer:
a) 16 in²
b) 20 cm²
Step-by-step explanation:
In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)
a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².
__
b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².
The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1.5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.
A. 1
B. 5
C. 10
D. 15
Answer: D. 15
Step-by-step explanation:
Given : The revenue each season from tickets at the theme part is represented by [tex]t(x) = 5x[/tex] .
The cost to pay the employees each season is represented by [tex]r(x) = (1.5)x[/tex].
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
The correct option is d. 15, is the estimated profit after four seasons, rounded to the nearest integer.
Given : The revenue each season from tickets at the theme part is represented by t(x) = 5x .
The cost to pay the employees each season is represented by r(x) = (1.5)x.
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
Evaluate the line integral c (2x3 − y3) dx + (4x3 + y3) dy where c is the unit circle, and verify green's theorem for this case
Parameterize [tex]C[/tex]
[tex]x=\cos t[/tex]
[tex]y=\sin t[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\langle2x^3-y^3,4x^3+y^3\rangle[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_0^{2\pi}\langle2\cos^3t-\sin^3t,4\cos^3t+\sin^3t\rangle\cdot\langle-\sin t,\cos t\rangle\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}(4\cos^4t-2\cos^3t\sin t+\cos t\sin t^3+\sin^4t)\,\mathrm dt=\boxed{\frac{15\pi}4}[/tex]
By Green's theorem, the line integral is equivalent to
[tex]\displaystyle\iint_{x^2+y^2\le1}\left(\frac{\partial(4x^3+y^3)}{\partial x}-\frac{\partial(2x^3-y^3)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le1}(12x^2+3y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(12r^2\cos^2\theta+3r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(9r^3\cos^2\theta+3r^3)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{15\pi}4}[/tex]
To evaluate the line integral along the unit circle, we can parametrize the circle using x = cos(t) and y = sin(t). The resulting integral is 6 times the integral of cos squared(t) times cos(t).
Explanation:To evaluate the line integral, we need to parametrize the unit circle. Let's use x = cos(t) and y = sin(t) as the parameterization. The differential arc length is given by ds = √(dx² + dy²) = dt. Substituting these into the line integral, we get:
∫(2cos³(t) - sin³(t)) dt + ∫(4cos³(t) + sin³(t)) dt = ∫(6cos³(t)) dt
Since the unit circle can be parameterized from 0 to 2π, the integral becomes:
∫[6cos³(t)] dt = 6 ∫[(cos(t))³] dt = 6 ∫[cos³(t)] dt = 6[∫(cos²(t)cos(t)) dt]
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Suppose you have a bucket of sand containing 5.5 billion grains of sand ( 5.5×109 grains). Most of the grains of sand are white, but there are some brown grains mixed evenly throughout. If the concentration of brown sand is 2.0% , how many grains of brown sand are in the bucket?
Answer:
1.1×10^8
Step-by-step explanation:
2% of 5.5 billion is ...
2×10^-2 × 5.5×10^9 = 11×10^7 = 1.1×10^8
About 1.1×10^8 grains of brown sand are in the bucket.
Answer:
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Step-by-step explanation:
Total number sand grains in the bucket =[tex] 5.5\times 10^9 grain[/tex]
Concentration of brown sand grains = 2.0%
Number of brown brain in the bucket be x
[tex]\%=\frac{\text{Brown sand grains}}{\text{Total sand grains}}\times 100[/tex]
[tex]2.0\%=\frac{x}{5.5\times 10^9 grain}\times 100[/tex]
[tex]x=1.1\times 10^8 grains[/tex]
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Please answer this question for 30 points and brainliest!!
Answer:
2.5 cm
Step-by-step explanation:
The ratio of side lengths of similar figures is the same as the ratio of any linear measure on those figures, including perimeter. The second figure's perimeter is 10/16 of that of the first figure, so the shortest side of the second figure will also be 10/16 of the length of the shortest side of the first figure.
(10/16)×(4 cm) = 2.5 cm
The shortest side of the second polygon has a length of 2.5 cm.
Solve 3x^2 + 6x + 6 = 0
Answer:
No real solutions.
Step-by-step explanation:
We need to solve the following equation: 3x^2 + 6x + 6 = 0
First, we should divide the whole equation by 3:
3x^2 + 6x + 6 = 0 ⇒ x^2 + 2x + 2 = 0
Now, the equation has no real results. It happens because the polynomial never crosses the x-axis. (See graph attached).
The imaginary solution is:
x = -1 + i
x= -1 - i
Tony spent $100 on books to give away as prizes to his students. At the store, he bought 4 more books than planned, spending $5 per book. Which equation can be used to find the number of books he originally wanted to buy. X
Answer:
[tex]5x=100[/tex]
[tex]x=20\ books[/tex]
Step-by-step explanation:
I'm going to assume that all books cost the same.
Let
x ------> the number of books he originally wanted to buy
we know that
[tex](x+4)(5)=100+4(5)[/tex]
[tex]5x+20=100+20[/tex]
[tex]5x=100[/tex] -----> equation that can be used to find the number of books he originally wanted to buy
solve for x
[tex]x=100/5[/tex]
[tex]x=20\ books[/tex]
Nick has 21 pencils and Lance has 63 pencils.
Tony spent a total of $100 on books. Since he bought 4 more books than he originally planned, and each book cost $5, let's denote the original number of books he planned to buy as x. Therefore, the total number of books he ended up buying would be x + 4. Given that the cost of each book is $5, we can establish the equation 5(x + 4) = 100 to represent the total expenditure on books.
To find the number of books he originally wanted to buy, we will solve for x in the equation above:
Multiply 5 by the quantity x + 4 to obtain the left side of the equation.
Set that result equal to 100, as this is the total amount spent.
Solve the equation for x by first distributing the 5, which gives us 5x + 20 = 100, and then subtracting 20 from both sides of the equation to get 5x = 80.
Finally, divide both sides by 5 to find the value of x, which results in x = 16.
Therefore, Tony originally planned to buy 16 books.
.Tom is throwing darts at a target. In his last 30 throws, Tom has hit the target 20 times. You want to know the estimated probability that exactly one out of the next three throws does not hit the target.
Step-by-step explanation:
In his last 30 throws, Tom hit the target 20 times and missed 10 times.
p = probability he misses the target = ⅓
q = probability he hits the target = ⅔
Using binomial probability:
P = nCr (p)^r (q)^(n-r)
Given n = 3, r = 1, p = ⅓, and q = ⅔:
P = ₃C₁ (⅓)¹ (⅔)³⁻¹
P = (3) (⅓) (⅔)²
P = 4/9
There is a 4/9 probability that he misses exactly 1 of his next 3 throws.
By applying binomial probability, the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target is 4/9.
How to determine the estimated probability?In order to determine the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target, we would apply binomial probability equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Based on the information given, we can deduce the following points:
Probability that Tom misses the target (p) = 10/30 = ⅓Probability that Tom hits the target (q) = 20/30 = ⅔Number of next throws (n) = 3.Number of throws taken at a time (r) = 1.Substituting the given parameters into the equation, we have;
P = ³C₁ × (⅓)¹ × (⅔)³⁻¹
P = 3 × (⅓)¹ × (⅔)²
P = 3 × ⅓ × (⅔)²
P = 1 × 4/9
P = 4/9.
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For the function f(x)=[tex]\frac{\sqrt{x} }{5} +2[/tex]
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2
B. ƒ –1(x) = 25x2 – 2, x ≥ 0
C. ƒ –1(x) = 5(x – 2)2, x ≥ 0
D. ƒ –1(x) = 25(x – 2)2, x ≥ 0
Answer:
[tex]f^{-1}(x)=25(x-2)^2[/tex]
Step-by-step explanation:
The inverse function can be found by solving ...
f(y) = x
(√y)/5 +2 = x
(√y)/5 = x -2 . . . . . subtract 2
√y = 5(x -2) . . . . . . multiply by 5
y = 25(x -2)² . . . . . square both sides
The inverse function is ...
[tex]f^{-1}(x)=25(x-2)^2[/tex]
_____
About the graph
The inverse of a function is its mirror image across the line y = x.
If [tex]\alpha[/tex] = 65° and j = 11 mm, what is the value of h to the nearest tenth of a millimeter?
A. 4.7 mm
B. 12.1 mm
C. 5.1 mm
D. 8.6 mm
Answer:
C. 5.1 mm
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan alpha = opposite/ adjacent
tan alpha = j/h
tan 65 = 11/h
Multiply both sides by h
h tan 65 = 11/h *h
h tan 65 = 11
Divide each side by tan 65
h tan 65 / tan 65 = 11 / tan 65
h = 11 / tan 65
h =5.12938424
To the nearest tenth
h = 5.1
Answer:
12.1
Step-by-step explanation:
The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg?
A. 18 inches
B. [tex]18\sqrt{3}[/tex] inches
C. [tex]9\sqrt{3}[/tex] inches
D. 9 inches
Answer:
D. 9
Step-by-step explanation:
The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x). The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse). If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:
9√3 = x√3 and solve for x. Divide both sides by the √3 to get that x = 9
Answer:
The correct answer is option D. 9
Step-by-step explanation:
Points to remember
It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2
To find the length of shorter leg
Here it is given that, longer length = 9√3
We have,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 = Shorter leg : 9√3: hypotenuse
Therefore shorter leg = 9√3/√3 = 9
A rectangular garden measures 3 feet by 15 feet the gardener decides to extend the garden 1 foot in each of the four directions what is the perimeter of the new garden in feet
The perimeter of the new garden after extension is 44 feet.
Explanation:To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.
To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:
P = 2(5 + 17) = 2(22) = 44 feet
Therefore, the perimeter of the new garden is 44 feet.
20 points One diagonal of a rhombus has endpoints (-10, 1) and (2, 9).
What are the endpoints of the other diagonal?
(-7, 7) and (-1, 3)
(-4, 7) and (2, 7)
(-2, 2) and (-6, 8)
(-6, 2) and (-2, 8)
Final answer:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other. The endpoints of the other diagonal are (-7, 7) and (-1, 3). Therefore, Option A is the correct answer.
Explanation:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other, meaning they intersect at their midpoints. We can find the midpoint by taking the average of the x-coordinates and the average of the y-coordinates of the given endpoints of the first diagonal.
For the given endpoints (-10, 1) and (2, 9), the midpoint would be ((-10 + 2)/2, (1 + 9)/2), which simplifies to (-4, 5).
Since the diagonals bisect each other, the other diagonal would have the same midpoint. Therefore, the endpoints of the other diagonal would be (-4, 5) and the reflection of (-4, 5) across the midpoint of the given diagonal, which is the midpoint of (-10, 1) and (2, 9). Thus, the correct answer is (-4, 5) and its reflection across (-4, 5), which is (-7, 7) and (-1, 3).
An hour of CFL use consumes 10-2 kWh (kilowatt – hour), if each kilowatthour of electricity use is equivalent to 3.6 X 106 joules of energy, then find out the energy in joules used by the CFL in one hour
Answer:
[tex]3.6*10^{4}\ joules[/tex] or [tex]36,000\ joules[/tex]
Step-by-step explanation:
Let
x -----> the energy in joules used by the CFL in one hour
we know that
using proportion
[tex]\frac{1}{3.6*10^{6}}\frac{kWh}{joules} =\frac{10^{-2}}{x}\frac{kWh}{joules}\\ \\x=(3.6*10^{6})(10^{-2})\\ \\x=3.6*10^{4}\ joules[/tex]
or
[tex]36,000\ joules[/tex]
The swimming team has competed in 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75% success rate?
Pls help soon, will Mark brainliest
Answer:
15 races
Step-by-step explanation:
The team has competed in 45 and has won 30. So the success rate is:
Success rate is:
[tex]Sccess\ rate=r= \frac{30}{45}*100\\ =66.7\ percent[/tex]
We have to find the number of races the team needs to win for 75% success rate
Which means that
[tex]r = \frac{30+x}{45+x} = 0.75\\[/tex]
We have to solve the equation for x
[tex]\frac{30+x}{45+x}=0.75\\ 30+x = 0.75(45+x)\\30+x=33.75+0.75x\\x-0.75x=33.75-30\\0.25x=3.75\\x=\frac{3.75}{0.25}\\ x=15[/tex]
The team needs to win 15 races to get 75% success rate ..