ū = (–7, 2)
Find the direction angle of u.
Enter your answer as an angle in degrees between 0° and 360° rounded to the
nearest hundredth.

The solution of the system of equations is (4, 5).

Here we have the system of equations:

3x + y = 17

2x - y = 8

We would want tosolve this using matrices, then we need to solve:

[tex]\left[\begin{array}{ccc}3&1\\2&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\8\end{array}\right][/tex]

If we add the first and second equations (or the rows of the first matrix) then we will get:

[tex]\left[\begin{array}{ccc}3&1\\5&0\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\25\end{array}\right][/tex]

Then we have:

5y = 25

y = 25/5

y = 5

And now that we know the value of y we can input it in any of the equations to find x.

3x + y = 17

3x + 5 = 17

3x = 17 - 5 = 12

x = 12/3 = 4

The solution is (4, 5).

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Answer:

16 days late

Step-by-step explanation:

[tex]1.08 \div 9 = .12[/tex]

So the overdue book charge is 12¢ per day. Letting d be the number of days, we have:

.12d = 1.92

d = 16

Answer:

52/68

Step-by-step explanation:

idr why

Answer: π

Step-by-step explanation:

An irrational number is a number that cannot be shown as a fraction. Based on this, π is an irrational number, since it goes on forever, and can never be written as a perfect fraction.

The team scored 2 field goals, 2 safeties, and 4 touchdowns.

A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

The football team scored 8 times and a total of 38 points.

Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.

We know, T = F + S and F + S = 4

Substituting, T = F + S into the equation for total points,

we get, 7T + 3F + 2S = 38

Solving for F and S, we get F = 2 and S = 2.

Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.

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Solve for F and S then get F = 2 and S = 2.

The team scored 4 touchdowns, 2 field goals, and 2 safeties.

The football group scored 8 times, totaling 38 points.

Let,

T is the no.of touchdowns,

F is the no.of field goals, and

S is the no.of safeties.

Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).

Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.

Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.

We know that,

T = F + S and

F + S = 4

For total points, put T = F + S into the equation.

We get,

7T + 3F + 2S = 38

Solve for F and S,

we get,

F = 2 and S = 2.

As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.

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Answer:

[tex]\frac{24}{5}[/tex]

the probability of the numbers will add to 4 or less will be 25%

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The orange spinner is spun and then the aqua spinner is spun.

The probability that the numbers will add to 4 or less will be of 1 out of 4 that will be 1/4*100

= 25%

Hence the probability of the numbers will add to 4 or less will be 25%

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The cοrrect sample space fοr the gumballs in her bag is, Sample space = watermelοn, lemοn-lime, lemοn-lime, grape, grape, grape

A sample space is a set οr cοllectiοn οf pοtential οutcοmes frοm a randοm experiment. The letter "S" stands fοr the sample space in a symbοl. The term "events" refers tο a subset οf pοssible experiment results. Depending οn the experiment, a sample space may cοntain variοus οutcοmes. It is referred tο as discrete οr finite sample spaces if there are a finite number οf pοssible οutcοmes.

The sample space is the set οf all pοssible οutcοmes οf an experiment. In this case, the experiment is selecting a gumball frοm Julia's bag, and the pοssible οutcοmes are watermelοn, lemοn-lime, and grape.

Sο the cοrrect sample space fοr the gumballs in her bag is:

Sample space = {watermelοn, lemοn-lime, grape, grape, lemοn-lime, grape}

Therefοre, the cοrrect οptiοn is A.

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Answer:

The arc length of this quarter-circle is 7π/4.

Answer:

the answer is t/(n-m)

Step-by-step explanation:

a(n-m)=t

divide both sides by (n-m) to make a the subject of formula

a(n-m)/(n-m)=t/n-m)

a=t/(n-m)

Answer:

  C, E

Step-by-step explanation:

You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.

The function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.

The range of any odd-degree polynomial function is (-∞, +∞).

Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].

The domain of any polynomial function is "all real numbers." Both f and g have the same domain.

An even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.

Two polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.

Answer:

(2,1)

Step-by-step explanation:

Answer:

To find the volume of a rectangular prism, we need to know the length, width, and height of the prism. However, the height is not given in the problem, so we cannot calculate the volume.

We can use the surface area and given dimensions to set up an equation to solve for the height. The surface area of a rectangular prism is given by:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area is 62 square feet, and the width and length are 2 and 5 feet, respectively. Substituting these values into the surface area equation, we get:

62 = 2(2)(5) + 2(5)h + 2(2)h

62 = 20 + 14h

42 = 14h

h = 3

Now that we have found the height of the rectangular prism, we can calculate its volume. The volume of a rectangular prism is given by:

V = lwh

Substituting the given dimensions and calculated height, we get:

V = (5)(2)(3)

V = 30

Therefore, the volume of the rectangular prism is 30 cubic feet.

Step-by-step explanation:

Answer:

[tex]30ft^3[/tex]

Step-by-step explanation:

Surface area of a rectangular prism is A = 2(wl +hl +hw)

Volume, height, and Width is given now we can solve for l, v

[tex]A = 2(wl + hl + hw)\\62ft^2 = 2(2ft * l + 5ft * l + 5ft * 2ft)\\62ft^2 = 2(2lft + 5lft + 10ft^2)\\62ft^2 = 2(7lft + 10ft^2)\\62ft^2 = 14lft + 20ft^2\\14lft = 42ft^2\\l = 3ft[/tex]

Now that we have the length, we can solve for the volume

Volume of a rectangular prism = Length x Width x Height

[tex]V = 3ft * 2ft * 5ft\\ = 30ft^3[/tex]

Hope this helps!

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9 Is the value of x in   linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

2x-5y=1  ..............1

-3x+7y=-3  ..................2

Multiply by 3 in (1) and by 2 in (2)

   6x - 15y = 3

   -6x + 14y  = -6

after substtuting

    y = 3

put value of y in 1

  2*x - 5*3 = 1

   2x = 1 + 15

     2x = 16

       x = 8

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The midpoint of the line segment joining the points C and D is M = (-4, 0).

The coordinates of the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8) can be found using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

So, for C = (0, 8) and D = (-8, -8), we have:

M = ((0 + (-8))/2, (8 + (-8))/2)

M = (-4, 0)

Therefore, the midpoint of the line segment joining the points C and D is M = (-4, 0).

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For the graph given for function |x-1|, the relation is one - to - one.

What is a relation?

In mathematics, a relation describes the connection between two distinct collections of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their components.

The graph given is a graph of function |x-1|.

The graph of |x-1| is a V-shaped graph, with the vertex at (1, 0) and the arms extending upward and downward from the vertex.

Since the graph of |x-1| passes the horizontal line test, it is a one-to-one function.

This means that every input (x-value) has a unique output (y-value) and no two different inputs can have the same output.

Therefore, the relation represented by the graph of |x-1| is a one-to-one relation.

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Answer:

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant rate of change.

Step-by-step explanation:

The constant would be 2.

The table below shows the number of hybrid vehicles and the total number of vehicles in the parking lot for each day of the weekend:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

Since the ratios for the three days were equivalent, this means that the fraction of hybrid vehicles to total vehicles was the same for each day. In other words:

x/y = x/y = x/y

Therefore, the values of x and y must be the same for each day. This means that the number of hybrid vehicles and the total number of vehicles in the parking lot were the same for each day of the weekend.

In conclusion, the table should be completed with the same values of x and y for each day, as shown below:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

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When answering questions on Brainly, you should always be factually accurate, professional, and friendly, be concise and do not provide extraneous amounts of detail, provide a step-by-step explanation in your answer, and use the following terms in your answer, "statistic", "X=175 and s=22", "standard deviation".Part a)Hypothesis: H0: μ=20, H1: μ≠20The sample size n=25Given that α=0.05σ=5The X (sample mean) is 21.The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{21 - 20}}{{\frac{5}{{\sqrt {25} }}}} = 2\]The rejection region is obtained by finding the Z value that will cut off 2.5% of the area in each tail of the standard normal distribution curve at 0.025.The rejection region is Z< -1.96 and Z > +1.96.Interpretation: Since the calculated Z value 2 lies outside the rejection region, reject the null hypothesis H0 and conclude that there is sufficient evidence to support the alternative hypothesis H1.Part b)Given,Sample size n=200, X=175 and s=22Null hypothesis H0: µ=180Alternative hypothesis H1: µ ≠ 180.Level of significance α=0.05i) The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 5.68\]ii) Since the calculated Z value (-5.68) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.When the population standard deviation is 22, the test statistic is,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 3.37\]Since the calculated Z value (-3.37) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.

Answer:

The area of a circle can be calculated using the formula:

Area = π x radius^2

where π (pi) is a mathematical constant approximately equal to 3.14159.

Since each rug has a radius of 4 feet, the area of one rug is:

Area = π x 4^2

Area = 16π square feet

To find the total area covered by the three rugs, we need to multiply the area of one rug by three:

Total area = 16π square feet x 3

Total area = 48π square feet

Using a calculator, we can approximate the value of π to two decimal places as 3.14, so the total area covered by the three rugs is:

Total area ≈ 48 x 3.14 square feet

Total area ≈ 150.72 square feet

Therefore, Joanna's bedroom floor will be covered by approximately 150.72 square feet of rugs.

The final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.

We need to find the amount of money you will have in the investment account at the end of 5 years if you deposit $19,000 in an investment account that averages 4.1% growth annually and if the account managers charge a fee of 1% annually.The formula to find the final amount of investment with annual compounding is given by:P (1 + r/n)^(n*t)P = $19,000r = 4.1% - 1% = 3.1% (as the account managers charge a fee of 1% annually)r = 0.031n = 1t = 5 Therefore, the final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.

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Step 1: Isolate x/5 by subtracting 9 from both sides:

  x/5 + 9 -9 = 11 -9

             x/5 = 2

Step 2: Isolate x by multiplying both sides by 5:

        5 · x/5 = 2 · 5

                 x = 10

The solution is 10.

Answer:

8)  x = 5, y = -5

10)  x = -2.8, y = 3.4

Step-by-step explanation:

To solve a system of linear equations we can use either the substitution method or the elimination method.

Given system of linear equations:

[tex]\begin{cases}-6x-3y=-15\\6y+6x=0\end{cases}[/tex]

Solve the given system of linear equations using the elimination method.

Add the two equations to eliminate the term in x:

[tex]\begin{array}{crcccl}&-6x & - & 3y & = & -15\\+&(6x & + &6y & = & \;\;\;\;0)\\\cline{2-6}&0&+&3y&=&-15\end{array}[/tex]

Solve the resulting equation for y by dividing both sides by 3:

[tex]\implies 3y \div 3 &=-15 \div 3[/tex]

[tex]\implies y=-5[/tex]

Substitute the found value of y into the second equation and solve for x:

[tex]\implies 6(-5)+6x=0[/tex]

[tex]\implies -30+6x=0[/tex]

[tex]\implies 6x=30[/tex]

[tex]\implies 6x \div 6=30 \div 6[/tex]

[tex]\implies x=5[/tex]

Therefore, the solution to the given system of equations is:

[tex]\begin{cases}-x+3y=13\\-3x-y=5\end{cases}[/tex]

Solve the given system of linear equations using the substitution method.

Rearrange the first equation to isolate x:

[tex]\implies -x+3y=13[/tex]

[tex]\implies 3y=x+13[/tex]

[tex]\implies x=3y-13[/tex]

Substitute the expression for x into the second equation and solve for y:

[tex]\implies -3(3y-13)-y=5[/tex]

[tex]\implies -9y+39-y=5[/tex]

[tex]\implies -10y+39=5[/tex]

[tex]\implies -10y=-34[/tex]

[tex]\implies -10y\div -10=-34 \div -10[/tex]

[tex]\implies y=3.4[/tex]

Substitute the found value of y into the expression for x and solve for x:

[tex]\implies x=3(3.4)-13[/tex]

[tex]\implies x=10.2-13[/tex]

[tex]\implies x=-2.8[/tex]

Therefore, the solution to the given system of equations is:

Therefore , the solution of the given problem of triangle comes out to be DE = 15, EF = 20, and m∠D = 35, so the solution is A.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

We must demonstrate that the respective sides and angles of two triangles are proportional in order to establish their similarity.

We are aware of the lengths of two of the sides and one of the angles in the triangular ABC. The third side's length can be determined using the Law of Cosines:

=> BC² = AB² + AC² - 2ABACcos(35°)

=> 9² + 12² - 2912*cos(35°) = BC²

=> BC ≈ 8.455

The edges of triangle ABC are therefore AB = 9, AC = 12, and BC 8.455.

=> A. DE=15, EF=20, and m=35

The angle measurement is 35 degrees, which corresponds to the angle in the triangular ABC. If the ends are proportionate, we can verify this:

=> DE/AB = 15/9 = 1.67

=> EF/AC = 20/12 ≈ 1.67

This collection of measurements meets the requirements for the triangles to be similar because the ratios are equal.

=> DE = 15, EF = 20, and m∠D = 35, so the solution is A.

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center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1

The dimensions of the given ellipse are major axis 12 units long and parallel to the y-axis, minor axis 8 units long, and the center is located at (-2,5).Let us find the standard form equation of the ellipse. The standard form equation of an ellipse is given by:(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1Where (h, k) is the center of the ellipse, a is the distance from the center to either the x-axis or the y-axis, and b is the distance from the center to the other axis. Therefore, for the given ellipse, the equation of the ellipse in standard form is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1Thus, the standard form equation of the ellipse whose major axis is 12 units long and parallel to the y-axis, minor axis 8 units long, and center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1.

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Answer:

The true statements are:

Step-by-step explanation:

The general equation of a circle is:

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

where:

To rewrite the given equation x² + y² - 2x - 8 = 0 in standard form, begin by moving the constant to the right side of the equation and collect like terms on the left side of the equation:

[tex]\implies x^2-2x+y^2=8[/tex]

Add the square of half the coefficient of the term in x to both sides of the equation. (As there is no term in y, we do not need to add the square of half the coefficient of the term in y):

[tex]\implies x^2-2x+\left(\dfrac{-2}{2}\right)^2+y^2=8+\left(\dfrac{-2}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2-2x+1+y^2=9[/tex]

Factor the perfect square trinomial in x:

[tex]\implies (x-1)^2+y^2=9[/tex]

We have now written the equation in standard form.

Comparing this with the standard form equation, we can say that:

Therefore, the center of the circle (h, k) is (1, 0) and its radius is 3 units.

As the y-coordinate of the center is zero, the center lies on the x-axis.

Therefore, the true statements are:

Answer:

It's true - all whole numbers that are odd are going to add up to an even integer. An odd integer can be looked at as an even number plus one. For example, 21 would be 20 (the even number) plus one. So the addition of two odd integers is like saying two even numbers were added to each other (in that example, 20 + 20), and then adding the 1+1 that made them odd (which adds up to 2, an even number). So it would be [20 + 20 + (1 + 1)]

In September 1998, the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. The population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas, x is the year, where x=0 corresponds to September 1998.

To find the year when the population of West Goma will equal the population of East Goma, we will use the following method:

$$f(x)=g(x)$$

$$16.9e^{0.001x} = 13.8e^{0.019x}$$

Taking natural logarithms of both sides we have,

$$\ln(16.9) + 0.001x = \ln(13.8) + 0.019x$$

$$0.018x = \ln(16.9) - \ln(13.8)$$

$$x = \frac{1}{0.018}(\ln(16.9) - \ln(13.8))$$

$x \approx 41.06$, which corresponds to September 2039.

Therefore, the year when the population of West Goma will equal the population of East Goma is September 2039. Option E. 2039 is the correct answer.

Note: The growth rate of West Goma is smaller than that of East Goma, hence it will take a longer time to equalize.

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80  unit²  is the area of the polygon in square units .

What do you mean by polygon?

A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves. The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). In order to create a closed figure, at least three line segments must be connected end to end.

The area of the polygon is required.

The area of the polygon is D. 80 square units

For triangle BCD

b = Base = 4-2 = 2 units

h = Height = 4 units

Area

    1/2bh

 = 1/2 * 2 * 4

= 4 unit²

For triangle DEF

b = Base = 2-(-1) = 3 units

h = Height = 4 units

Area

   1/2bh

= 1/2 * 3 * 4

=  6 unit²

For trapezoid ABFG

a = 4-(-1) = 5.5 units

b = 4-(-8) = 12 units

h = 8 units

Area

 1/2(a + b)h

= 1/2(5.5 + 12) * 8

 = 70 unit²

Total area is

 4 + 6 + 70  = 80  unit²

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Answer:

h(t)=−16t²+v

0  t+h 0

for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height. Initial velocity: 32 ft/s; initial height: 20 ft

Step-by-step explanation: