Find the slope of the line that passes through (9,9) and(2,1)

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:

4+4x=20

4x=20-4

4x=16

x=16/4

x=16

AnswerAnswerAnswerAnswerAnswerAnswerAnswer

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 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.

To learn more about the correlation coefficient visit:

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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:

Area = [tex]4x^6+12x^5+8x^4[/tex]

Step-by-step explanation:

The Complete Question:

A rectangle has height  [tex]4x^3[/tex]  and width  [tex]x^3+3x^2+2x[/tex]. What is the area of the rectangle in terms of x?

Solution:

The formula for the area of a rectangle is:

Area = Height * Width

Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:

[tex]A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4[/tex]

This is the area of the rectangle.

Answer:

50

Step-by-step explanation:

Answer:

50

Explanation:

Answer:

12.75 + 0.75v = t

Step-by-step explanation:

12.75 is the fee she has to pay to join so you would add that to the cost of videos she rented. Since 0.75 is the cost of one and you don't know how many she rented you would put a variable which in this case would be "v". So if she payed the fee and rented 2 videos it would be 12.75 + 0.75(2) = 14.25

The correct equation to represent the total amount Sierra pays to rent videos is:

[tex]\[ t = 0.75v + 12.75 \][/tex]

Where [tex]\( t \)[/tex] represents the total cost, [tex]\( v \)[/tex] represents the number of videos Sierra rents, [tex]\( 0.75 \)[/tex] is the cost per video, and [tex]\( 12.75 \)[/tex] is the initial fee Sierra paid to join the video rental club. The term [tex]\( 0.75v \)[/tex] calculates the total cost of renting [tex]\( v \)[/tex] videos, and adding [tex]\( 12.75 \)[/tex] accounts for the initial fee. This equation allows us to determine the total cost [tex]\( t \)[/tex] for any number of videos [tex]\( v \)[/tex] that Sierra rents.

Answer: 14.9 years, approximately 15years.

Step-by-step explanation:

Formular for finding the amount of a compound interest

A = P ( 1 + r/100 )n

From the question given,

A = $14,000; P = $4,000; n = ? (year)

Rate = 8.75%.

Substitute for these values in the above equation, we therefore have

14,000 = 4,000(1+ 8.75/100)n (is raised to the power of n)

Divide both side by 4,000

14,000/4,000 = 4,000(1+8.75/100)n/4,000.solving the one in bracket fractionally

3.5 = {(100 + 8.75)/100}n

3.5 = (108.75/100)n

3.5 = 1.0875n( raised to the power of n).In order to solve for 'n' to know the number of years, we take the logarithm of both side.

Log.3.5 = Log(1.0875)n

Going by the law of logarithm,

Log 3.5 = nLog1.0875

Checking your log table, log 3.5 =0.5441 and log1.0875 = 0.0364

Equating both and solve for n

0.5441 = 0.0364n

Divide through by the coefficient of n,

n = 0.5541/0.0364

n = 14.9 years

Approximately 15 years

Hence it will take $4,000 at 8.75% rate to amount to $14,000 a period of 14.9 years approximately 15years.

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:

[tex]([7]x+[2])^2[/tex]

Step-by-step explanation:

Given:

[tex]49x^2+28x+4[/tex]

We need to factorize the given trinomial.

To solve the above expression we will Split the product of first term and third term to get the second term by either adding or subtracting.

So we get;

[tex]49x^2+14x+14x+4\\\\7x(7x+2)+2(7x+2)\\\\(7x+2)(7x+2)\\\\(7x+2)^2[/tex]

Hence Final Answer is:

[tex]([7]x+[2])^2[/tex]

Answer:

The length of the ladder is 9.2m

Step-by-step explanation:

Answer:

[tex]\cos\theta=\pm0.5[/tex]

Step-by-step explanation:

Given:

[tex]\sin^2\theta=0.75[/tex]

To find [tex]\cos\theta[/tex]

Using trigonometric relations for sums and differences of squares of the ratios.

We know:

[tex]\sin^2\theta+\cos^2\theta =1[/tex]

Plugging in  [tex]\sin^2\theta=0.75[/tex] in the above relation.

[tex]0.75+\cos^2\theta =1[/tex]

Subtracting both sides by 0.75.

[tex]0.75+\cos^2\theta-0.75 =1-0.75[/tex]

[tex]\cos^2\theta =0.25[/tex]

Taking square root both sides.

[tex]\sqrt{\cos^2\theta} =\sqrt{0.25}[/tex]

∴ [tex]\cos\theta=\pm0.5[/tex]  (Answer)

Answer:

11.43 kilometers

Step-by-step explanation:

Answer:

11.43 kilometers.

Step-by-step explanation:

All you have to do is add the two distances (AKA numbers, to make it even simpler). It doesn't matter what distance was traveled by train or bus! The point is that the distances traveled were both in kilometers! With that being said, all we have to do is add 7.22 + 4.21, and voila! We get 11.43!

Hope this answer helps! Please rate it and give me Brainliest! :D

Have a great day!

Answer:

y = 110°

x = 55°

Step-by-step explanation:

The line is a transversal.

∠Y = 110°, according to the rule of transversals.

Also, 2X = Y, since in a transversal the vertical angles are equal.

Vertical angles are the ones that are at the intersection of the parallel line and the transversal.

So, 2X = Y = 110°

⇒ X = 55°

Hence, X = 55° and Y = 110°.

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.

The height of the statue is 19.5 feet.

Why?

We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.

We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)

Using the trignometric formula, we have:

First triangle:

[tex]tg(\alpha )=\frac{h_{1}}{base} \\\\tg(8\°)=\frac{h_{1}}{50ft}\\\\0.14*50ft=h_1\\\\h_1=7ft[/tex]

Second triangle:

[tex]tg(\alpha )=\frac{h_{2}}{base} \\\\tg(14\°)=\frac{h_{1}}{50ft}\\\\0.25*50ft=h_1\\\\h_1=12.5ft[/tex]

Now, the total height of the statue will be:

[tex]TotalHeight=h_1+h_2=7ft+12.5ft\\\\TotalHeight=19.5ft[/tex]

Have a nice day!

In this question, we utilize trigonometry to calculate the height of the statue. By using the tangent of the given angles and the known distance from the observer to the statue, we can find the lines of sight when looking up and down. Subtracting these two measurements gives us the height of the statue, which we find to be 5.2ft.

This question is about applying trigonometry to find the height of an object, in this case, a statue. First, we need to find the height of the line of sight when the person looks up and when they look down. The height for the line of sight when looking up can be found using the formula for the tangent of an angle: tan(θ) = opposite side/adjacent side. Applying this formula, we find that the height of this line of sight is tan(8°) * 50ft = 7.1 ft. Similarly, when looking down, the height is tan(14°) * 50ft = 12.3 ft.

The height of the statue is the difference between these two heights. Therefore, we find: 12.3ft - 7.1ft = 5.2ft

This is a simple application of the concept of the tangent of an angle in a right triangle, a basic part of trigonometry.

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Answer:

$50.95

Step-by-step explanation:

2(11.99)+3(8.99)=50.95

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Here we do not have the options, but ill try to give an answer.

A system of equations is something of the shape:

A1*x + B1*y = C1

A2*x + B2*y = C2

Where this is a linear relationship, you could have a more complex system, but this will work for the example.

If you want to have a unique solution for a system of equations, you need to have the same number of linearly independent equations (this means that the equations are not repeated, like for example in x + y = 2, and 2x + 2y = 4, where the second equation is equal to two times the first one) than the number of variables, so if we have two variables X and Y, we need to have two linearly independent equations.

If we have less, suppose that you have two variables and only one equation, you will have:

A1*x + B1*y = C1

y = (C1 - A1*x)/B1

Here, for each value of x you have a different value of y, so you have infinite solutions.

So for an answer this you need to find the system where the number of linearly independent equations is smaller than the number of variables.

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: 4,900,000

Step-by-step explanation:

5 million - 100 thousand = 4.9 million

Answer:

-i

Step-by-step explanation:

Answer:

92 are the value of x I think

Answer:

were is the diagram

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:

[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.

Answer:

Step-by-step explanation:

slope of line perpendicular to x=4 is 0

reqd. eq. of line is y=-5