Solve the system of linear equations

The complete statements are:

The complete question is added as an attachment

The roots are given as:

x = 0 second

and

x = 9.8 seconds

x = 0 implies that the height of the arrow was 0 meters above his bow after 0 seconds

x = 9.8 implies that  it takes approximately 9.8 seconds for the arrow to return to the height of the bow.

The x-value of the vertex is

x = (0 + 9.8)/2

Evaluate

x = 4.9

Approximate

x = 5

This means that the vertex is approximately 5 seconds

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The  accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.

Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.

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Find 3π/4 in degrees

Referance angle

Option A

Answer:

The measure of the reference angle is 45°.

[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

Reference Angle:  The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).

To convert radians to degrees, multiply by 180/π:

[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]

Positive angles are drawn in a counterclockwise direction from the x-axis.

(See attached for diagram of the angle θ and its reference angle).

Angles on a straight line sum to 180°.

Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:

[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]

The angle 135° lies between 90° and 180° and so is in Quadrant II.

Therefore, the exact trigonometric ratios for 135° are:

[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]

[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]

[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]

Therefore, the true statements are:

  The measure of the reference angle is 45°.

  [tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]

Answer:

50

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem to find the hypotenuse. a^2+b^2 = c^2

40^2+30^2 = c^2

1600+900 = c^2

2500 = c^2

50 = c

Answer:

y = -2x + 2

Step-by-step explanation:

slope is found with (change in y/change in x), or in this case, (-4--2,3-2), which is -2

with the equation y = -2x + b, solve for b by plugging in the x and y values of one of the points

using (2, -2):

-2 = -2(2) +b

b = 2

so the equation is y = -2x + 2

The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Given a taxi charges $2.50 for the first mile and $0.40 for each mile

We are required to make an expression showing total cost and total cost of a 20 mile ride.

let the miles ride by tax be x.

Total cost of the product or service=Number of units*price of one units.

We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.

So,the expression showing looks like 2.50+0.40x.

Now to find the cost when taxi travels 20 miles, we have to put x=20,

Cost=2.50+0.40*20

=2.50+(40*20)/100

=2.50+800/100

=2.50+8

=$10.50

Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

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Answer:

Let j = number of shirts Jeff bought and s = the number of shirts Stephen bought.

a.) s + j = 15

b.) 2j - 3 = s

c.) Plug 2j -3 into the equation from question a.

2j -3 + j = 15

3j -3 = 15

3j = 18

j = 6

2j - 3 = s when j = 6

2(6) - 3 = s

s = 9

Jeff bought 6 shirts; Stephen bought 9 shirts.

d.) Jeff cost = 8.99(6) = $53.94

Stephen cost = 8.99(9) = $80.91

Using proportions, the cost of the 17-ounce sundae is of $5.95.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Considering the 12-ounce sundae bought for $4.2, the cost per ounce is given by the following proportion:

$4.2/12 = $0.35.

Hence the cost of a 17-ounce sundae is:

$0.35 x 17 = $5.95.

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Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]

First, get rid of the denominator by multiplying both sides by 2:

[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]

Add both sides by 6 then subtract both sides by x:

[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]

Then divide both sides by 3:

[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]

Therefore, the answer is x ≤ 2

Answer: [tex]x \leq 2[/tex]

Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get [tex]4x - 6 \leq x[/tex].

Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].

Subtracting x from both sides, we get [tex]3x \leq 6[/tex]

Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]

Hope this helped!

Answer:

Here's my answer

it's not number but

hope this help

Answer:

department

Step-by-step explanation:

A "task force" group is another name for a command group.

We have,

A task force is a temporary grouping of individuals or units with a specific objective or mission.

It is typically formed to address a particular task or problem and is led by a designated commander or leader.

Task forces can be assembled from different departments or organizations to collaborate and work together towards a common goal.

Thus,

A "task force" group is another name for a command group.

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I don't know what the options are in the drop-down menu but the function f is symmetric around the point (4,–1) which is called the axis of symmetry. (4,–1) is the minimum of the graph.

11. m ∠ BCE = 25 °

m ∠BAD = 39°

12. n = 11. 5°

13. The quadrilaterals are rectangle and parallelogram. Option A and C

14. HK = 8cm

11. From the figure shown, we have that;

m ∠ EBC = 27°

m ∠ ADE = 52°

To find

m ∠ BCE

Note that m ∠ ADE is alternate and equal to m∠ DEC = 52 and is also on a straight line with ∠BEC

52 +  ∠BEC = 180°

∠BEC = 180 - 52° = 128°

Remember that  ∠BEC,  ∠ BCE  and ∠ EBC are angles in a triangle which sum up to 180°

128° +  ∠ BCE + 27° = 180°

∠ BCE = 180 ° - 155°

∠ BCE = 25 °

To determine m ∠BAD

65° +  76 + m ∠BAD = 180° , sum of angles in a a triangle

m ∠BAD = 180 - 141

m ∠BAD = 39°

12. Value of n is gotten by equating the two lengths

( 10n + 19) = (12n - 4)

collect like terms

10n - 12n = -4 - 19

- 2n = -23

n = -23/-2

n = 11. 5°

13. The only quadrilaterals with congruent diagonals are;

14.  To find line HK

Substract the shortest line, IJ from the longest line GL

HK = GL - IJ

HK = 15 - 7

HK = 8cm

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Considering that we have an isosceles triangle, the length of the missing side is of 11 inches.

An isosceles triangle is a triangle that has two congruent sides.

Researching this problem on the internet, the triangle has two sides of 4 in and 11 in, and one missing side. The missing side is opposite to the side of 4 in, with the same scale, hence the length of the missing side is of 11 inches.

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Answer:

XPY = 15π m

Step-by-step explanation:

XPY is 3/4 of the circumference of the circle.  The perimeter of a circle is given by 2πr, with r = 10m.

C = 2πr

C = 2π(10)

C = 20π

3/4 of C is (3/4)(20π)

XPY = 15π m

The expected outcome of spins based on the probability information is 60.

From the information, Joey decides to spin the wheel 60 times. Therefore, the expected outcome of spins is 60.

The thing that the booth owner can do to make the wheel more profitable for himself is to make winning probability less than that of losing.

Here, the booth owner do makes the wheel more profitable for himself as the winning is smaller.

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Answer:

90 approximately because if AB is 80 then DC should be 90 because AB come before DC in letters

Answer:

112.6 degrees and 105 feet.

Step-by-step explanation:

took the assignment

The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].

Volume exists as a scalar quantity representing the amount of three-dimensional space encircled by a closed surface.

The minimum volume of a shape with measured dimensions exists provided by the lowest values of the dimensions when accounting for measurement error. Maximum Volume: The maximum volume of a shape with measured dimensions exists provided by the highest values of the measurements when accounting for measurement error.

The volume of the cube [tex]= 8*6*4[/tex]

[tex]= 192 cm^3[/tex]

To create the X as the sides of the cube we should add material.

The nearest cube number to 192 exists at 216

The amount of material to be added exists

= 216 -192

[tex]= 24 cm^3[/tex]

The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].

Therefore, the correct answer is an option (4) 24.

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Answer:

Option C

Kindly award branliest

Step-by-step explanation:

Tn = n(n + 1)

T1 = 1(1 +1) = 1(2) = 2

T2 = 2(2+1) = 2(3) =6

T3 = 3(3 + 1) = 3(4) = 12

T4 = 4(4 + 1) = 4(5) = 20

... It obeys

The diameter of a new ball is 4.0ft

According to the statement

we have given that the the company wants to spend a maximum of $1 each.

And we have to find a diameter of a new ball.

Remember that for a sphere of diameter D, the surface area is

A = 4*pi*(D/2)^2

In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:

$0.02*A = $1

A = $1/$0.02 = 50

So the surface of the ball must be 50 square feet.

Then we solve:

50ft^2 = 4*3.14*(D/2)^2

D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft

here the diameter of a ball is 4.0ft.

So, The diameter of a new ball is 4.0ft

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Answer:

9 weeks.

Step-by-step explanation:

m = 11w + 67

m = 17w + 13

So:

11w + 67 = 17w + 13

67 - 13 = 17w - 11w

54 = 6w

w = 9.

The probability that more than 5 students will pass their exam is 0.0188416.

The probability that a student passes their examination = 40% = 0.4

The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam

The probability that 6 students pass their exam =

[tex]7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032[/tex]

The probability that 7 students pass their exam =

[tex]7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384[/tex]

The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384

= 0.0188416

Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.

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Answer:

y=-2x+5

Step-by-step explanation:

The slope is

[tex] \frac{ - 15 - ( - 7)}{5 - 1} = \frac{ - 8}{4} = - 2[/tex]

Substituting into point-slope form,

y + 7 = -2(x-1)

y + 7 = -2x + 2

y = -2x + 5

The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.

Based on the definition of the circumcenter, and Y is the circumcenter, therefore:

YE = FY

Plug in the values

5x - 3 = 3x + 7

5x - 3x = 3 + 7

2x = 10

x = 5

FY = 3x + 7 = 3(5) + 7

FY = 22 units.

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Answer:

D

Step-by-step explanation:

Of students in the sample, 90/200 fraction of the students were male.

To find the fraction of male students:

Number of male students = 90

Number of female students = 110

So, total students = 90 + 110 = 200

Fraction of students who were male =  male students / total students

Fraction of students who were male = 90/200

So, 90/200 fraction of the students were male.

Therefore, 90/200 fraction of the students were male.

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The question you are looking for is given here:

A university surveyed its students on their opinions of campus housing. The following two-way table displays data for the sample of

200 students responded to the survey.

The fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.

According to the question,

There are 22 problems in her assignment and Sabrina finished 8/11 of her math assignment.

In order to find the fraction represents the number of problems completed over the total number of problems in the assignment.

(8/11) * (2/2) = 16/22

Hence, the fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.

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Answer:

2

Step-by-step explanation:

(-1,-4) (2,2)

To find the slope, use the equation y2-y1/x2-x1

2-(-4)/2-(-1) = 6/3

6/3=2

2 is the slope.

The linear function in slope-intercept form for the cost of a visit of x hours is given as follows:

C(x) = 9x + 31.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the rate means that the slope is of m = 9. When x = 3, C(x) = 58, hence the y-intercept is found as follows:

C(x) = 9x + b

58 = 9(3) + b

b = 31.

Hence the equation is:
C(x) = 9x + 31.

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The correct answer is 7/12.

What is probability?

Let A = Getting multiple of  on the first one

     B = A total of  for both roll

P (A U B) = P(A) + P(B) - P(A ∩ B)

               [tex]\frac{18}{36} + \frac{5}{36} - \frac{2}{36} \\\\ = \frac{21}{36} \\[/tex]

                [tex]\frac{7}{12}[/tex]

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