Identify ER rounded to the nearest tenth. The Figure shows right triangle M E R with right angle E. The length of hypotenuse M R is equal to 37 units. Angle R measures 61 degrees.
Answers;
a) ER ≈ 66.7
b) ER ≈ 32.4
c) ER ≈ 17.9
d) ER ≈ 22.3
Please give an explanation! :)

The solution to the system of equations is x = 3 and y = 11

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y equals x plus 8

y equals 3 x plus 2

Rewrite properly as

y = x + 8

y = 3x + 2

Substitute y = x + 8 in y = 3x + 2

x + 8 = 3x + 2

Evaluate the like terms

2x = 6

Divide by 2

x = 3

Substitute x = 3 in y = x + 8

y = 3 + 8

Evaluate

y = 11

Hence, the solution to the system of equations is x = 3 and y = 11

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The solution to the system of equation is as follows:

x = 3

y = 11

y = x + 8

y = 3x + 2

Using substitution method,

3x + 2 = x + 8

subtract x from both sides

3x - x + 2 = x - x + 8

2x + 2 = 8

subtract 2 from both sides

2x + 2 - 2 = 8 - 2

2x = 6

divide both sides by 2

2x / 2  = 6 / 2

x = 3

y = 3 + 8 = 11

y = 11

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The form of deductive reasoning used in the given argument is; Law of Syllogism

The argument we are given is;

If a number ends in 0, then it is divisible by 10.

If a number is divisible by 10, then it is divisible by 5.

If a number ends in 0, then it is divisible by 5.

The law used for the deductive reasoning in the given argument is called Law of Syllogism. This is because this law of mathematical logic states that;

If the following two statements are true:

(1) If p , then q .

(2) If q , then r .

Then we can derive a third true statement:

(3) If p , then r .

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Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:

The range of the sample means is 0.4 pounds.

The true statements on the mean weights to be used by the scientists are:

First, find the sample means of each sample.

Sample 1:

= (3 + 2 + 6 + 4 + 2) / 5

= 3.4 pounds

Sample 2:

= (2 + 2 + 3 + 7 + 3) / 5

= 3.4 pounds

Sample 3:

= (6 + 4 + 2 + 2 + 4) / 5

= 3.6 pounds

Sample 4:

= (5 + 3 + 2 + 5 + 4) / 5

= 3.8 pounds

The range is;

= 3.8 - 3.4

= 0.4

The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.

Using all the sample means as an average captures the data better than if a single sample mean is used.

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Answer:

10/13

Step-by-step explanation:

There are 52 cards in a standard deck. There are 4 queens (queen of spades, clubs, hearts, diamonds) and 36 (2 - 10 of four suites) number cards. Therefore the probability of drawing a queen or a number card is (4 + 36)/52 = 40/52 = 10/13.

Answer:

x^2-3/3x

Step-by-step explanation:

=x*x-1*3/3*x

=x^2-3/3x

a. The rocket splashes down after 63.94 seconds.

b. The rocket peaks at 7386.68 m

Since the height of the rocket is h(t) = -4.9t² + 370t + 402, the rocket splashes down when h(t) = 0.

So, h(t) = 0

-4.9t² + 370t + 402 = 0

Using the quadratic formula, we find t.

[tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = -4.9, b = 370 and c = 402

So, [tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}\\= \frac{-307 +/- \sqrt{(307)^{2} - 4(-4.9)(402)} }{2(-4.9)}\\= \frac{-307 +/- \sqrt{94249 + 7879.2} }{-9.8)}\\= \frac{-307 +/- \sqrt{102128.2} }{-9.8)}\\= \frac{-307 +/- 319.58}{-9.8)}\\= \frac{-307 + 319.58}{-9.8)} or \frac{-307 - 319.58}{-9.8)}\\= \frac{12.58}{-9.8)} or \frac{-626.58}{-9.8}\\= -1.28 or 63.94[/tex]

Since t cannot be negative t = 63.94 s

So, the rocket splashes down after 63.94 seconds.

Since h(t) = -4.9t² + 370t + 402, to find the time the rocket reaches it peak, we differentiate h(t) with respect to t and equate to zero.

Soi, dh(t)/dt = d(-4.9t² + 370t + 402)/dt

= -9.8t + 370

dh(t)/dt = 0

-9.8t + 370 = 0

-9.8t = -370

t = -370/-9.8

t = 37.76 s

Substitung t = 37.76 into h(t), we have

h(t) = -4.9t² + 370t + 402

h(37.76) = -4.9(37.76)² + 370(37.76) + 402

h(37.76) = -4.9(1425.82) + 370(37.76) + 402

h(37.76) = -6986.518 + 13971.2 + 402

h(37.76) = 7386.682 m

h(37.76) ≅ 7386.68 m

So, the rocket peaks at 7386.68 m

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Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Use it to rewrite the equation in terms of cos only.

[tex]12 (1 - \cos^2(x)) + \cos(x) - 6 = 0[/tex]

[tex]-12 \cos^2(x) + \cos(x) + 6 = 0[/tex]

Factorize the left side.

[tex]-(3\cos(x) + 2) (4\cos(x) - 3) = 0[/tex]

Solve the two cases for [tex]\cos(x)[/tex].

[tex]3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0[/tex]

[tex]\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34[/tex]

From the first equation, we get one family of solutions:

[tex]\cos(x) = -\dfrac23[/tex]

[tex]x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi[/tex]

From the second equation, we get another family:

[tex]\cos(x) = \dfrac34[/tex]

[tex]x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi[/tex]

where [tex]n[/tex] is an integer.

We get solutions in the given domain for

[tex]n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}[/tex]

[tex]n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}[/tex]

Answer:

y=[-4]x+[10]

Step-by-step explanation:

For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.

The slope [tex]\frac{1}{4}[/tex] turns into [tex]\frac{4}{1}[/tex] and is then multiplied by -1 to become [tex]\frac{-4}{1}[/tex] which can be simplified down to: [tex]-4[/tex]

Now that we know the slope we need the line to pass through a point, so we will use point slope form:

[tex]y-y1=m(x-x1)[/tex]
Substitute in our slope and point values:

[tex]y-2=-4(x-2)[/tex]

Now solve for y:

[tex]y-2=-4(x-2)\\y-2=-4x+8\\y=-4x+10[/tex]

Then you will find that line [tex]y=-4x+10[/tex] runs perpendicular to [tex]y=\frac{1}{4}x-8[/tex] and intersects point (2,2).

Answer: 17

Step-by-step explanation:

substitute -3 for a and -5 for b. the equation will be[tex]\frac{(-3)^{2}+(-5)^{2} }{-3-(-5)}[/tex]. then when you simplify, you will get [tex]\frac{9+25}{-3+5}[/tex]. finally, add and you will get [tex]\frac{34}{2}[/tex] which is 17.

The lowest grade he could earn is 120% of the grade at the end of the semester.

The following statement is given:

I have 90% after about 75% of the semester.

We are asked to find the lowest grade by the end of this semester.

A percentage is a number expressed as a fraction of 100.

- 50% = 50/100 = 1/2

- 25% = 25/100 = 1/4

- 20% = 20/100 = 1/5.

We can write this statement "I have a 90% grade after about 75% of the semester" as:

90% grade  =  75% semester.............(1)

By the end of the semester means at 100% semester.

Multiplying equation (1) by 100/ 75 on both sides of the equation.

We get,

(100/75) x 90% grade = (100/75) x 75% semester

(100 x 90)/75 % grade = 100% semester

120% grade = 100%

Thus the lowest grade he could earn is 120% of the grade at the end of the semester.

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The measure of angle < APD = 98°. That is option D

Angle APB = 62°

Angle DPC = 102°

But length AD = BC

Therefore, angle APD = BPC

Also, the angle at a point = 360°

The sum of the angles given = 102 + 62 = 164°

The remaining angle = 360 - 164 = 196°

Therefore angle APD = 196/2 = 98°

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Answer:

A plastic board

The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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By algebraic handling, the value of k of the system of equations is equal to 2.

Herein we find a system formed by two equations, a linear function and a quadratic equation with the following characteristics:

y = x² + b · x + 5        (1)

y = 2 · x + b               (2)

If we eliminate y in (1) and (2), then we have this expression:

x² + b · 3 + 5  = 2 · x + b

3² + b · x + 5 = 2 · 3 + b

3 · b + 14 = 6 + b

14 = 6 - 2 · b

8 = - 2 · b

b = - 4

By (2), y = k, x = 3 and b = - 4, we find the value of k:

k = 2 · 3 - 4

k = 6 - 4

k = 2

By algebraic handling, the value of k of the system of equations is equal to 2.

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In the  expression written below. the value of equation x  is known to be x=10/c.

From the question, we were given: 3(cx-7)=9

Therefore, we have to simply it to  make x the subject of the formula (to look for x)

Hence: 3(cx-7)=9

=(cx-7)=3

=cx=10  

x=10/c

Therefore, In the  expression written below. the value of equation x  is known to be x=10/c.

See full question below

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Solve the following equation for x, and express its value in terms of c. 3(cx-7)=9

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Answer:

12a^3b^2+18a^2b

Step-by-step explanation:

12 3b2+182b

Answer:

1) c = 25m + 90

2) c = 17m; $85

3) c = 10m + 15; $135

Step-by-step explanation:

Let m = number of months

1)

c = 25m + 90

2)

c = 17m

For 5 months, m = 5.

c = 17m = 17 × 5 = 85

$85

3)

c = 10m + 15

1 year = 12 months, so m = 12

c = 10m + 15 = 10 × 12 + 15 = 120 + 15 = 135

$135

Answer:100

Step-by-step explanation: The question asks us to round the given numbers to the nearest hundred. 295 rounded to the nearest hundred is 300 and 198 rounded to the nearest hundred is 200. 300-200 is 100, so they need to sell 100 more tickets for the show to be houseful.

Answer:

(2, - 1 )

Step-by-step explanation:

3x - y = 7 → (1)

2x + 3y -= 1 → (2)

multiplying ( 1) by 3 and adding to (2) will eliminate y

9x - 3y = 21 → (30

add (2) and (3) to eliminate y

11x = 22 (divide both sides by 2 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2(2) + 3y = 1

4 + 3y = 1 (subtract 4 from both sides )

3y = - 3 ( divide both sides by 3 )

y = - 1

solution = (2, - 1 )

Measures of central tendency are called such because they all find approximately the same "center" of a data set (option B).

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.

Mode refers to a value that appears most frequently in a data set.

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Answer:

-0.5, either ⅙ or ⅓

Step-by-step explanation:

slope = rise / run

3) slope = (6 - 7) / (3 - 1)

slope = -1 / 2

slope = -0.5

ur mouse is blocking 4 (I'll do 2 scenarios):

4) slope = (-4 - -5) / (2 - -4)

slope = 1 / 6

I will leave it in fractional form

4) slope = (-4 - -6) / (2 - -4)

slope = 2 / 6

slope = 1/3

slope = 0.33

Answer:

Please make the question clearer, but I would say B

Step-by-step explanation:

I am not sure what you mean, to me the question is unclear

The solution to this problem is (s2+1)Y(s)−2s−1=2s2+4 .

We let  L[y(t)]=Y(s) . With that, tabular Laplace-transform laws entail

L[y′]=sY(s)−y(0)=sY(s)−2

L[y′′]=s2Y(s)−sy(0)−y′(0)=s2Y(s)−2s−1

∴L[y′′+y]=(s2+1)Y(s)−2s−1 .

Since the Laplace transform of  sin(kt)  is  ks2+k2 , we have

(s2+1)Y(s)−2s−1=2s2+4 .

This equation readily solves to  Y(s)=2s3+s2+8s+6(s2+1)(s2+4) . We compute its partial fraction decomposition as  Y(s)=2s+53s2+1+−23s2+4 .

Our final step is to use tabular Laplace-transform laws ( sin(kt)↦ks2+k2 , and  cos(kt)↦ss2+k2 ) to get  y(t)=2cost+53sint−13sin(2t) . One can check that this indeed satisfies the initial value problem.

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Adam says that the number 4 has four factors. The above statement is incorrect as 4 only three factors 1,2, and 4.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{b} + 10 = \cfrac{9}{b} + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{9}{b} - \cfrac{1}{b} = 10 - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{8}{b} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \cfrac{8}{3} [/tex]

Answer:

[tex]b=\dfrac{8}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{b}+10=\dfrac{9}{b}+7[/tex]

Subtract 10 from both sides:

[tex]\implies \dfrac{1}{b}+10-10=\dfrac{9}{b}+7-10[/tex]

[tex]\implies \dfrac{1}{b}=\dfrac{9}{b}-3[/tex]

Multiply both sides by b:

[tex]\implies \dfrac{1 \cdot b}{b}=\dfrac{9 \cdot b}{b}-3b[/tex]

[tex]\implies 1=9-3b[/tex]

Add 3b to both sides:

[tex]\implies 1+3b=9-3b+3b[/tex]

[tex]\implies 3b+1=9[/tex]

Subtract 1 from both sides:

[tex]\implies 3b+1-1=9-1[/tex]

[tex]\implies 3b=8[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3b}{3}=\dfrac{8}{3}[/tex]

[tex]\implies b=\dfrac{8}{3}[/tex]

Apply the exponent rule (x^a)^b= x^ab.

(b^9)^3= b^9*3= b^27

Answer:

  (a)  h^-1(x) = (x+6)/6

Step-by-step explanation:

The inverse relation can be found by solving for y: x = h(y).

  x = h(y) . . . . . the inverse relation

  x = 6y -6 . . . . . use the function definition

  x +6 = 6y . . . . add 6

  (x +6)/6 = y . . . . divide by 6

The inverse function is ...

  [tex]\boxed{h^{-1}(x)=\dfrac{x+6}{6}}[/tex]

Answer:

[tex]3^{3}[/tex]

Step-by-step explanation:

Note: When you divide exponents with the same constant, the exponent will be subtracted, and vice-versa, when you multiply exponents with the same constant, the exponents will be added.

[tex]\frac{3^{-9} }{3^{-12} } \\= 3^{-9-(-12)} \\=3^{-9+12} \\=3^{3}[/tex]