There are four different sets of objects shown in the answer choices. Select all of the sets of objects that could be modeled by perpendicular lines. Two roads that meet at an intersection. The top of a desk and the floor. A tree and its shadow on the ground. Two stars seen in the sky.

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Answer:

Step-by-step explanation:

The function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x

Transformation techniques

Transformation is the process of changing the position of an object on the xy-plane.

Given the parent function

f(x) = 4x

If the function is not reflected over x-axis, the resulting function will be f(x) = -4x

If the resulting function is compressed by a factors of 1/8, hence the final function rule will be;

g(x) = 1/8(-4x)

g(x) = -1/2x

Hence the function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x

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The solution of the trigonometric equation  are, \(x=\frac{\pi}{2},\frac{3\pi}{2}\)

Given equation are,

           \(cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx\)

We know that,  \(cos(A-B)=cosA cosB+sinAsinB\)

         \(cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx\\\\cos\frac{\pi}{4} *cosx+sin\frac{\pi}{4} *sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx+\frac{\sqrt{2} }{2}sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx=0\\\\cosx=0\\\\x=\frac{\pi}{2},\frac{3\pi}{2}\)

Hence, The solution of the trigonometric equation  are, \(x=\frac{\pi}{2},\frac{3\pi}{2}\)

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The two inequalities have all the solutions larger than 4 in common.

To check this, we just need to solve both inequalities:

The first one is:

-2(c - 4) ≤ -4

-2c + 4 ≤ -4

4 + 4 ≤ 2c

8/2 ≤ c

4 ≤ c

The second one gives:

(1/2)d - 6 > -4

Solving it for d:

(1/2)d > -4 + 6

d > 2*2

d > 4

Then the solutions are:

c ≥ 4

d > 4

The inequalities have almost all the solutions in common, except for c = 4 which is a solution for the first one but not for the second one.

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Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

The value of angle x is 142°

Angles are the measure of the shift of one line to another

Since we are given the figure and we desire to find the angle x, we proceed as follows.

We note that all the angles meet at a point. We know that the sum of angles at a point is 360°.

So, writing the equation, we have that

128° + 52° + 38° + x = 360°

Adding the similar terms, we have that

218° + x = 360°

Subtracting 218° from both sides, we have that

218° - 218°  + x = 360° - 218°

x = 360° - 218°

x = 142°

So, the value of x is 142°

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Answer:

I think the best is: Year Population 1990 10,350 1995 10,750 2000 11,150 2005 11,500 2010 11,650.

Step-by-step explanation:

It shows the population of each year.

Hope this helps...

Please mark me brainliest ♥️

Answer:

line graph

Step-by-step explanation:

edge 2022

Answer:

2a/b1 +b2=h

And

2a/h -b2=b1

Step-by-step explanation:

Answer: A & D.

Step-by-step explanation:

Answer:

The first step is to subtract 32 from both sides

32-12x=24

-32-12x=24-32

-12x= -8

x= \(\frac{-8}{-12}\)

a negative divided by a negative is positive. Now what we do is simplify using the common multiple between 8 and 12. 4 is the answer. So 8/4 is 2 and 12/4 is 3

so x is \(\frac{2}{3}\)

Step-by-step explanation:

since you are solving for the X variable, you want to have the variable by itself on one side. move all numbers to the other side. 32 was a positive, When you move it over the equal sign it becomes negative. If it was a negative in the beginning then it would turn positive after moving it to the other side

Answer:

10

Step-by-step explanation:

\(-2-(-12)\\=-2+12\\=12-2 \\=10\)

The decibel measurement for the quiet room is 54 dB.

To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.

Next, we can use the formula for decibel measurement:

dB = 10 log (I/I0)

where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.

Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:

dB = 10 log (500/1)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.

To correct this mistake, we need to use the formula for decibel measurement with the correct values:

dB = 10 log (500 * I0/I0)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.

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Answer:

  the initial balance

Step-by-step explanation:

5.00 is the value of f(0). It is the balance before any time has elapsed, the initial balance.

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

The probability of a spinner landing on a consonant letter given it is unshaded is 3/8.

The probability of a spinner landing on a consonant letter given it is unshaded is determined as follows:

Favorable outcomes: B, C, F, K, N, P (6 letters)

Total possible outcomes: A to P (16 letters)

Therefore, the probability of the spinner landing on a consonant letter given it is unshaded is:

Probability = 6 / 16

Probability = 3 / 8

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slope = (y2 - y1)/(x2 - x1) = (13 - 5)/(-2-0) = 8/-2 = -4

Answer:

-4

Step-by-step explanation:

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.

3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.

2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.

1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.

Adding these amounts together, we get:

3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

To the nearest cup, this is equal to 7 cups.

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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The critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.

The critical value to be used in constructing the 90% confidence interval is 1.645. This is the z-score associated with a 90% confidence level. In other words, this is the value that is 1.645 standard deviations away from the mean. This value is found using the z-table, which contains the probability values for a standard normal distribution.

Therefore, the critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.

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The correct answer is d. 260 tacos and 156 burritos and Dina gained 260 tacos and 156 burritos.

If each person specializes in the production of the good in which they have a comparative advantage and trade 260 tacos for 156 burritos, this means that both individuals benefit from trade as they can consume more of both goods than they would have without trade. Arturo specializes in producing tacos, which he trades for burritos produced by Dina. Similarly, Dina specializes in producing burritos, which she trades for tacos produced by Arturo. As a result, both individuals gain from trade, and the combined total of tacos and burritos remains the same after trade as before. In this case, both Arturo and Dina would end up with 260 tacos and 156 burritos each, which is the outcome of trade.

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Answer:

Firstly we need to find the gradient of give two points as follows;

M= y

Answer:

Answer: y = -x - 1

Step-by-step explanation:

- Consider a straight line passing through (x, y) from the origin (0, 0). That line with a positive gradient of m and meets at a point (0, c) [y-intercept]

- It has a general equation as below;

\({ \rm{y = mx + c}} \\ \)

- So, consider the line given in our question; Let's find its slope m first;

\({ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \)

- From the points given in the question, (-7, 6) and (3, -4)

\({ \rm{m = \frac{ - 4 - 6}{3 - ( - 7)} }} \\ \\ { \rm{m = \frac{ - 10}{10} }} \\ \\ { \underline{ \rm{ \: m = - 1 \: }}}\)

- Therefore, our equation so far is y = -x + c. Our line has a negative slope that means it slants from top to bottom, its origin is its y-intercept

- Consider point (3, -4);

\({ \rm{y = - x + c}} \\ { \rm{ - 4 = - 3 + c}} \\ { \rm{c = - 1}}\)

- y-intercept is -1

hence equation is y = -x - 1

\({ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}\)

Answer:

a- Vernon practiced soccer 5  3/4hours this week. He practiced 4  1/3hours on weekdays and the rest over the weekend.

Step-by-step explanation:

Hope this helps

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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Answer:

38.71°C

Step-by-step explanation:

Given :

Initial temp, T0 = 20°C

Final temperature, T = 20 + 10 = 30°C

Time, t = 9 seconds

Surrounding temperature, Ts = 100°C

Newton's Law of cooling :

T = Ts + (T0 - Ts) * e^-kt

Obtain the value of k

30 = 100 + (20 - 100) * e^-9k

30 - 100 = - 80e^-9k

-70 = - 80e^-9k

-70 / - 80 = e^-9k

0.875 = e^-9k

Take the In of both sides

In(0.875) = - 9k

−0.133531 = - 9k

k = 0.133531 / 9

k = 0.0148

Hence,

t = 18

T = Ts + (T0 - Ts) * e^-kt

T = 100 + (20 - 100) * e^-0.0148(18)

T = 100 - 80 * e^-0.0148(18)

T = 100 - 80 * 0.7661326

T = 38.709392

T = 38.71°C

Answer:

95%

Step-by-step explanation:

We have the following information:

n = 25, p-value = 0.0667

Besides that H0 is not rejected.

With this information we can affirm that the highest possible significance level you can have is 95%

Because alpha = 0.05

We reached this conclusion thanks to the fact that:

p-value> 0.05 hence we do reject the null hypothesis

Answer:

The slope of the green line is 3

Step-by-step explanation:

The lines are perpendicular, so the slopes are negative inverses

-1/(-1/3)

3

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(-9x + y = 3\implies y = \stackrel{\stackrel{m}{\downarrow }}{9} x +3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so then

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {9\implies \stackrel{slope}{\cfrac{9}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{9}}}\)

so we're really looking for the equation of a line whose slope is -1/9 and passes through (-9 , -1)

\((\stackrel{x_1}{-9}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{1}{9}}(x-\stackrel{x_1}{(-9)}) \\\\\\ y+1=-\cfrac{1}{9}(x+9)\implies y+1=-\cfrac{1}{9}x-1\implies y=-\cfrac{1}{9}x-2\)

Answer:

Answer to the following question is a follows;

Step-by-step explanation:

The following are a few examples of how South Africa's competitiveness policy has been successful:

⇒ Consumers or buyers were given a variety of product options as well as competitive prices.

⇒ In 1984, practises like horizontal cooperation and resale price maintenance and control were ruled illegal.

Answer:

9 inches

Step-by-step explanation:

For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.

The width of the rectangle can be found as 9 inch.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The area and length of rectangle are given as 54 inch² and 6 inches.

Suppose the width of the rectangle be x.

Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,

6x = 54

⇒ x = 54/6

⇒ x = 9

Hence, the width is given as 9 inch.

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