Evaluate the determinant for the following 1 4 4]
5 2 2
1 5 5

Answer:

θ= 30° or θ= 60°

Step-by-step explanation:

Please see attached picture for full solution.

Since √ 3/2 is positive, look at first 2 quadrant. (CAST diagram)

Answer:

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.

Step-by-step explanation:

Let's say b is the speed of the boat in still water, and c is the speed of the current.

Distance = rate × time

Going downstream:

504 = (b + c) × 14

36 = b + c

Going upstream:

504 = (b − c) × 21

24 = b − c

Two equations, two variables.  Solve with substitution or elimination.  To use elimination, add the equations together.

60 = 2b

b = 30

Plug into any equation to find c.

36 = b + c

36 = 30 + c

c = 6

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.

The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let the speed of the boat in still water be x and the speed of water be y.

A boat traveled 504 miles downstream and back. The trip downstream took 14 hours. Then the equation will be

x + y = 504 / 14

x + y = 36      ...1

The trip back took 21 hours. Then the equation will be

x - y = 504 / 21

x - y = 24       ...2

Add equations 1 and 2, then the value of x will be

2x = 36 + 24

2x = 60

x = 30 miles per hour

Then the value of y will be

30 - y = 24

y = 6 miles per hour

The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.

More about the solution of the equation link is given below.

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Answer:

7 hours, 30 minutes

Step-by-step explanation:

90 seconds times 300 = 27,000 seconds. Divided by 60 equals 450 minutes. Divided by 60 equals 7 hours, 30 minutes

Answer:

it will take 7 hours and 30 minutes to complete her invitations

Step-by-step explanation:

time taken for one envelope= 90 secs

time taken for 300 envelopes= 90*300= 27000 secs

Converting it into minutes = 27000/60= 450 minutes

Converting 450 minutes to hours = 450/60= 7.5 hours

Answer:230

Step-by-step explanation:

To get to 100% you need to do 20% 5 times so if 46 people is 20% 46x5 will give you 100% of people surveyed

Answer:

The answer is C, r = -0.83

Step-by-step explanation:

The graph has a negative slope, and the correlation between the points isn't super spread out. Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.

The correlation coefficient best matches the graph. The answer is C,

r = -0.83.

We have given that,

A) r = 0.91

B) r = 0.34

C) r = -0.83

D) r = -0.25

We have to determine the best matches graph.

The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.

The graph has a negative slope, and the correlation between the points isn't super spread out.

Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.

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Answer:

Part 1) The radius is [tex]r=17\ units[/tex]

Part 2) The points (-15,14) and (-15,-16) lies on the circle

Step-by-step explanation:

The correct question is

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

The radius of the circle is  ____units.

The point (-15,

?) ) lies on this circle

step 1

Find the radius of the circle

we know that

The distance from the center to any point on the circumference is equal to the radius.

we have

[tex](-7,-1),(8,7)[/tex]

Find the distance

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute

[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}\\r=\sqrt{(8)^{2}+(15)^{2}}\\r=\sqrt{289}\\r=17\ units[/tex]

step 2

The point (-15,y) lies on the circle

we know that

If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle

The equation of the circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

The center is (-7,-1) an the radius is 17 units

substitute

[tex](x+7)^{2}+(y+1)^{2}=17^{2}\\(x+7)^{2}+(y+1)^{2}=289[/tex]

substitute the x-coordinate of the point and solve for the y-coordinate

For x=-15

[tex](-15+7)^{2}+(y+1)^{2}=289\\(-8)^{2}+(y+1)^{2}=289\\64+(y+1)^{2}=289\\(y+1)^{2}=289-64\\(y+1)^{2}=225[/tex]

square root both sides

[tex](y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16[/tex]

therefore

The points (-15,14) and (-15,-16) lies on the circle

see the attached figure to better understand the problem

The question relates to the properties of a circle in a coordinate system, where the circumference and area can be calculated using the radius. The circumference of a circle is found using C = 2πr, and the area is A = πr². Without a given radius, these formulas are a guide for any calculations that may be done once the radius is known.

The question asks about the properties of a circle given its center and radius, which fall under the topic of Geometry in Mathematics. No specific value for the radius is provided, so the answer should include an explanation of how one might calculate various properties of a circle, such as the circumference or area, given a radius.

Understanding the Circle

A circle with its center located at (-7, -1) means it is positioned on a coordinate system at that point. If a radius was provided, the circumference of the circle would be calculated using the formula C = 2πr and the area using A = πr², where 'r' represents the radius of the circle and 'π' (pi) is approximately 3.14159. For example, if r = 1.2 m, the area calculated to two significant figures would be A = 4.5 m².

For a circle to fit perfectly inside a square, its diameter should be equal to the side of the square; this implies that a = 2r. The area of the square is a² = 4r², and a circle inside this square would have an area of approximately three-quarters of the square, or near πr². The perimeter (circumference) of the circle is somewhat close to 6r as the perimeter should be 2πr.

We need to find the false statement.

The first one is true (m<RPS=m<WPR because RU⊥SW).

The second statement is true because the two angles make a linear pair and are supplementary.

The third one is false because we only know that the angle pair is complimentary. Their measures are not equal.

answer: m∠SPT=m∠UPT

Answer:

a=[tex]17\sqrt{2}[/tex]

Step-by-step explanation:

As we have 2 of the angles, we can find the third. The measure of the third angle is 45 degrees.

As this is the same measure as the other, that means that the side length will be the same.

Now was have two side lengths of 17 in a right triangle, so we can use the Pythagorean theorem to find a.

Recall that the pythagorean theorem states: [tex]a^2+b^2=c^2[/tex]

In this case, a is 17, b is 17, and c is a

Knowing this, we can input our value into this formula and solve for a.

[tex]17^2+17^2=a^2\\\\289+289=a^2\\\\a=\sqrt{578} \\\\a=17\sqrt{2}[/tex]

Answer:

17sqrt2

Step-by-step explanation:

45 45 90 triangles side: hypotenuse  a:a*sqrt2

17*sqrt2=17sqrt2

Answer:

6.09864679092 minutes

Step-by-step explanation:

Mach 27= 33076.19km/h

3,362, at 33076.19km/h

3,362/33076.19

0.101644113182 hours

6.09864679092 minutes

Answer:

Around 6 minutes

Or in other words, fast

Answer:

π(6²)

Step-by-step explanation:

The base of the cone is a circle with area (A) calculated as

A = πr² ← r is the radius

Here diameter = 12 , hence r = 12 ÷ 2 = 6, thus

A = π(6²)

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

[see pdf]

Step-by-step explanation:

The graph makes a straight line, not a curve, so it is linear.

However, the graph has only points, not a full line, so it's also discrete.

(also yes I meant of instead of on in the pdf)

Answer:

A. discrete, C. linear

Step-by-step explanation:

By analysing the graph, it is evident that model is discrete since there is only information of certain points and shows a linear behavior, as there is a constant rate between dependent and independent variable. So, the right choices are A and C.

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slope = difference in y/difference in x

Substitute values in:

slope = (1 - 9)/(-2- (-9)

slope = -7/7

slope = -1

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The first five terms of sequence is 4.5, -27, 162, -972, 5832

Solution:

Given that we have to find first five terms of recursive sequence

Given sequence is:

[tex]a_n = -6a_{n - 1}[/tex]

To find first five terms, substitute n = 2, 3, 4, 5

First term is given = [tex]a_1[/tex] = 4.5

Find second term:

Substitute n = 2 in given sequence

[tex]a_2 = -6a_{2 - 1}\\\\a_2 = -6a_1\\\\a_2 = -6(4.5) = -27[/tex]

Thus second term of given sequence is -27

Find third term:

Substitute n = 3 in given sequence

[tex]a_3 = -6a_{3-1}\\\\a_3 = -6a_2\\\\a_3 = -6(-27) = 162[/tex]

Thus third term of given sequence is 162

Find fourth term:

Substitute n = 4 in given sequence

[tex]a_4 = -6a_{4-1}\\\\a_4 = -6a_3\\\\a_4 = -6(162) = -972[/tex]

Thus fourth term of given sequence is -972

Find fifth term:

Substitute n = 5 in given sequence

[tex]a_5 = -6a_{5-1}\\\\a_5 = -6a_4\\\\a_5 = -6(-972) = 5832[/tex]

Thus the first five terms of sequence is 4.5, -27, 162, -972, 5832

Answer:

gradient = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

Rearrange 2y - 6x = - 8 into this form

Add 6x to both sides

2y = 6x - 8 ( divide all terms by 2 )

y = 3x - 4 ← in slope- intercept form

with gradient m = 3

Answer:

-i

Step-by-step explanation:

Answer:

  y = tan(x +π/2)

Step-by-step explanation:

It can be helpful to start with a simple sketch of the function you have and of the tangent function. Then, you can see the relationship.

The tangent function is always rising, has vertical asymptotes at -π/2 and π/2, and has a zero crossing at x=0.

The function we want is always rising, has vertical asymptotes at x=0 and x=±π, and a zero crossing at x=-π/2.

We can create the function we want by shifting the tangent function to the left by π/2. The formula that does that is ...

  y = tan(x +π/2)

Answer:

−6y+13

Step-by-step explanation:

jsjsdjidedhue

Answer:

See below table

Step-by-step explanation:

[tex]\begin{array}{cccccccc}p&q&r&\sim q&\sim q\rightarrow p&r\vee(\sim q\rightarrow p)&\sim p&[r\vee (\sim q\rightarrow p)]\rightarrow \sim p\\ \\ \\ \\T&T&T&F&T&T&F&F\\ \\T$&T&F&F&T&T&F&F\\ \\T&F&T&T&T&T&F&F\\ \\T&F&F&T&T&T&F&F\\ \\ \\ \\F&T&T&F&T&T&T&T\\ \\F&T&F&F&T&T&T&T\\ \\F&F&T&T&F&T&T&T\\ \\F&F&F&T&F&F&T&T\end{array}[/tex]

Answer:

?

Step-by-step explanation:

Answer: 4,900,000

Step-by-step explanation:

5 million - 100 thousand = 4.9 million

Answer:

Step-by-step explanation:

slope of line perpendicular to x=4 is 0

reqd. eq. of line is y=-5

Answer:

Part 1) [tex]f(g(x))=3(x^2)+2[/tex]

Part 2) [tex]g(f(5))=289[/tex]

Step-by-step explanation:

we know that

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function

we have

[tex]f(x)=3x+2[/tex]

[tex]g(x)=x^{2}[/tex]

Part 1) Determine f(g(x))

To find f(g(x)) substitute the function g(x) as the variable in function f(x)

so

[tex]f(g(x))=3(x^2)+2[/tex]

Part 2) Determine g(f(x))

To find g(f(x)) substitute the function f(x) as the variable in function g(x)

so

[tex]g(f(x))=(3x+2)^2[/tex]

For x=5

[tex]g(f(5))=(3(5)+2)^2[/tex]

[tex]g(f(5))=289[/tex]

Answer:

The length of the ladder is 9.2m

Step-by-step explanation:

Answer:number 3

Step-by-step explanation:

For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1, that is:

[tex]m_ {1} * m_ {2} = - 1[/tex]

So, if we have the slope [tex]m_ {1} = - \frac {1} {3}[/tex]

A perpendicular line will have a slope m_ {2}:

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- \frac {1} {3}}\\m_ {2} = 3[/tex]

Thus, the perpendicular line will have slope [tex]m_ {2} = 3[/tex]

Answer:

The perpendicular line will have slope [tex]m_ {2} = 3[/tex]

Answer: C. Line EF.

Step-by-step explanation: Correct on edge.

Answer:

Infinitely many

Step-by-step explanation:

Answer:

NM and FG

Step-by-step explanation:

To make sure the triangles are congruent by SAS, Ebony needs to compare the lengths of two sides and the measure of the included angle of the triangles.

In order to make sure the triangles are congruent by SAS (Side-Angle-Side), Ebony would need to compare the lengths of two sides and the measure of the included angle of the triangles.

Specifically, Ebony would need to compare:

If the length of segment EF is equal to segment ON and the measure of ∠MON is equal to ∠GEF, then the triangles will be congruent by the SAS postulate.

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Answer:

The initial height from which the ball was dropped = 7.90 meters

Step-by-step explanation:

The correct question is:

In the video, I drop a ball off a three-story balcony. We know that objects in free fall follow the equation for height h, in meters, [tex]h = -4.9t^2 + c[/tex], where [tex]t[/tex] is time in seconds, and [tex]c[/tex] is the initial height. A student timed the drop at 1.27 seconds.

Use this to determine the height from which the ball was dropped, to at least 2 decimal places.

Solution:

The height [tex]h[/tex] of the free falling ball is represented by the equation as:

[tex]h=-4.9t^2+c[/tex] where [tex]t[/tex] is time in seconds, and c is the initial height.

To determine the initial height from which the ball was dropped.

The drop was timed at 1.27 seconds, we will plugin [tex]t=1.27[/tex] in the given height function to find [tex]h(1.27)[/tex]

[tex]h(1.27)=-4.9(1.27)^2+c[/tex]

[tex]h(1.27)=-7.90+c[/tex]

Since, the drop is timed at 1.27 seconds, so in the given time the ball will reach the ground, making [tex]h(1.27)=0[/tex]

So, we have.

[tex]0=-7.90+c[/tex]

Adding both sides by 7.90 to solve for [tex]c[/tex].

[tex]0+7.90=-7.90+7.90+c[/tex]

[tex]7.90=c[/tex]

∴ [tex]c=7.90\ m[/tex]

Thus, the initial height from which the ball was dropped = 7.90 meters

Answer:

92 are the value of x I think