Triangle QRS has vertices Q(8, –6), R(10, 5), and S(–3, 3). What are the coordinates of the vertices of the image of the triangle after a translation of T–7.6, 4.3(x, y)?

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.

The perimeter of the new garden after extension is 44 feet.

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.

Answer:

Step-by-step explanation:

Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...

  Sunitha: 7·5 = 35

  Raseeda: 8·5 = 40

_____

If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:

These can be translated to standard form, which may make some methods of solution easier:

These have solution (r, s) = (40, 35).

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.

∠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!  

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

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.

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!!  :)

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.

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:

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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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.

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]

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).

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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[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]

The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].

Hope this helped!

~Just a girl in love with Shawn Mendes

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:

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

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.

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.

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].

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:

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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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]

Answer:

  A. f(0.6)=0

  C. f(5.1)=5

  D. This is the graph of the greatest integer function.

Step-by-step explanation:

The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.

The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.

Answer:

C, D, E

Step-by-step explanation:

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].

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

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.

Question 10

cos 45 = x/10

cos 45(10) = x

(1/sqrt{2})*10 = x

10/sqrt{2} = x

Rationalize the denominator.

[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x

10•sqrt{2} ÷ 2 = x

5• sqrt{2} = x

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).

Answer with explanation:

Temperature in the living room =68°F

The equation which satisfies ,the  room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies

 t=2 Cos (0.21 m) +68----------(1)

⇒To determine the period of the function

Z= A cos (sx+q)+r

As period of cos x is 2 π.

So,the given function has period

        [tex]=\frac{2\pi}{s}[/tex]            

So, the period of function 1, is given by

        [tex]=\frac{2\pi}{0.21}[/tex]  

⇒The meaning of period of the function is that after every period of   [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.

⇒Cosine function has maximum value of 1 , and Minimum value of -1.

-1 ≤ Cos x ≤ 1

So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature

And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature

Final answer:

The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.

Explanation:

Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.

The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.

The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.

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

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:

Therefore, 3/4 times 710 is 532.5.

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.

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.

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