Consider Line 1 with the equation: x = − 17 Give the equation of the line parallel to Line 1 which passes through ( 3 , 8 ) :

Answer:

[tex] a = 3\sqrt{6} [/tex]

Step-by-step explanation:

θ = 30°

Opposite side length to θ = 3√2 in.

Adjacent side length = a

Apply the trigonometric ratio, TOA:

[tex] tan(\theta) = \frac{Opp}{Adj} [/tex]

Plug in the known values

[tex] tan(30) = \frac{3\sqrt{2}}{a} [/tex]

Multiply both sides by a

[tex] a*tan(30) = 3\sqrt{2} [/tex]

[tex] a*\frac{1}{\sqrt{3}} = 3\sqrt{2} [/tex] (tan 30 = 1/√3)

Multiply both sides by the inverse of 1/√3 which is √3

[tex] a = 3\sqrt{2}*\sqrt{3} [/tex]

[tex] a = 3\sqrt{2*3} [/tex]

[tex] a = 3\sqrt{6} [/tex]

In this question, the relations between velocity, distance and time are explored to first express the dependence of s on v, given the data in the exercise, and then to find the value of v for which s = 363.

-------------------------

Relation between velocity, distance, and time:

We have that velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

-------------------------

A car traveled s kilometers in 6 hours with a speed of v kilometers per hour.

This means that [tex]d = s, t = 6[/tex]

-------------------------

Express the dependence of s on v.

Taking the above values of d and t, and the formula, we have that:

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{s}{6}[/tex]

[tex]s = 6v[/tex]

Thus, the dependence of s on v can be expressed as: [tex]s = 6v[/tex]

-------------------------

Using the formula, find: v for s=363

We have that:

[tex]s = 6v[/tex]

And thus

[tex]v = \frac{s}{6}[/tex]

Considering [tex]s = 363[/tex]:

[tex]v = \frac{363}{6} = 60.5[/tex]

Thus, for s = 363, v = 60.5.

For an example of a problem using this formula, you can check here: https://brainly.com/question/14307500

Answer:

v=s/6 is the formula

and if s=363, v=60.5

hope this helped!

9514 1404 393

Answer:

  a.  $19817.10

  b.  $21998.87

Step-by-step explanation:

The formula for the future value of an annuity with payments "A" and interest at rate r compounded quarterly for t years is ...

  FV = A((1 +r/4)^(4t) -1)/(r/4)

The attachment shows this evaluated for ...

a. A = 900, r = 0.04, t = 5. FV = $19817.10

b. A = 450, r - 0.04, t = 10. FV = 21,998.87

Answer:

b) LeBron is relatively taller because he has a larger z-score.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

LeBron James:

Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{81 - 69.5}{2.7}[/tex]

[tex]Z = 4.26[/tex]

Candace Parker:

Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{76 - 64.2}{3.2}[/tex]

[tex]Z = 3.69[/tex]

Who is relatively taller?

Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.

Answer:

4 + 42s

Step-by-step explanation:

When y = 6 and x = 4,

Answer:

C

Step-by-step explanation:

The profit (in thousands of dollars) of a company is given by the function:

[tex]\displaystyle P(x) = -8x^2+32x+14[/tex]

And we want to find the maximum profit of the company.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

Find the x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 14. Hence:

[tex]\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2[/tex]

To find the maximum profit, substitute this value back into the function. Hence:

[tex]\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46[/tex]

Therefore, the maximum profit of the company is 46 thousand dollars.

Our answer is C.

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Answer:

115

Step-by-step explanation:

The opposite angles (115degree angle and angle 4) are equal.

Angle 3=65

Angle 4=115

Angle 5=115

Angle 6=65

Angle 7=65

Angle 8=115

Brainliest please~

6 19/24

Step-by-step explanation:

I can't really explain things properly, but I hope it helps

Answer:

11/2

Step-by-step explanation:

Given 12x+16y=11

Halving both sides gives 6x+8y=11/2.

Answer:

99, 113

Step-by-step explanation:

X-the first bus

X+14-the second bus

5x+5(x+14)=1060

10x+70=1060

10x=990

X=99-the first bus

99+14=113-the second bus

Answer:

The slope is 2

Step-by-step explanation:

The Slope formula is y2-y1/x2-y1.

1. Plug the numbers into the slope equation which is 1-(-5)/4-1=2

Answer:

A. 9

Step-by-step explanation:

First find the slope (m) using two given pairs of values form the table, say (1, 6) and (2, 3):

Slope (m) = change in y/change in x

Slope (m) = (3 - 6)/(2 - 1) = -3/1

Slope (m) = -3

Next, substitute (1, 6) = (x, y) and m = -3 into y = mx + b and solve for y-intercept (b).

Thus:

6 = -3(1) + b

6 = -3 + b

Add 3 to both sides

6 + 3 = -3 + b + 3

9 = b

b = 9

y-intercept = 9

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

__

Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

Answer:

[tex](x + 3)(x - 2)(x - 1)[/tex]

Step-by-step explanation:

[tex] {x}^{3} - 7x + 6[/tex]

Factor using Rational Root Theorem.

This means our possible roots are

positve or negative (1,2,3,6). If we try positve 1, it is indeed a root.

This means that

[tex](x - 1)[/tex]

is a root.

We can divide the top equation by the root (x-1). Our new equation is

[tex]( {x}^{2} + x - 6)[/tex]

Now we can factor this completely

[tex](x + 3)(x - 2)[/tex]

So this equation in factored form is

[tex](x + 3)(x - 2)(x - 1)[/tex]

Answer:

A=0

Step-by-step explanation:

DAC=BAD

A=0

Answer is 24

Step by step:

2,3,16

Let the fourth proportion be x

2/3 = 16/x

or, 2x = 3×16

or, x = 3×16/2

or, x = 3×8

or, X = 24

Answer:

y ≥  x^2 - 1

Step-by-step explanation:

First, we can see that the shaded region is above what seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)

Then:

y ≥ a*x^2 + b*x + c

where a*x^2 + b*x + c is the general quadratic equation.

Now let's find the equation for the parabola:

f(x) = a*x^2 + b*x + c

We also can see that the vertex of the parabola is at the point (0, -1)

This means that:

f(0) = -1 = a*0^2 + b*0 + c

     = -1 = c

then we have that c = -1

Then:

f(x) = a*x^2 + b*x - 1

Now we can look at the graph again, to see that the zeros of the parabola are at +1 and -1

Which means that:

f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1

f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1

Then we got two equations:

a + b - 1 = 0

a - b - 1 = 0

from this we can conclude that b must be zero.

Then:

b = 0

and these equations become:

a - 1 = 0

a - 1 = 0

solving for a, we get:

a = 1

Then the quadratic equation is:

f(x) = 1*x^2 + 0*x - 1

f(x) = x^2 - 1

And the inequality is:

y ≥  x^2 - 1

a perfect square trinomial, (x + y)² = x² + 2xy + y²

so, if we have the x of the bx, what is left is the b

the expression would have to be (x + 7)², since we have the 49 and the x²

so, what's left: x² + 14x + 49,

b = 14

hope it helps :)

Answer:

The solutions of this system of equation is (-5,3) and (-1,-5).

Answer: (-3,-1) and (-5,3)

Step-by-step explanation:

The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ 3x² + 17x - 6 = 0

Now, We can solve the equation as;

⇒ 3x² + 17x - 6 = 0

⇒ 3x² + (18 - 1)x - 6 = 0

⇒ 3x² + 18x - x - 6 = 0

⇒ 3x (x + 6) - 1 (x + 6) = 0

⇒ (3x - 1) (x + 6) = 0

This gives two solutions,

⇒ 3x - 1 = 0

⇒ x = 1/3

And, x + 6 = 0

⇒ x = - 6

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ2

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

It is given that,

→ 10(2x-3) = 10

Then find required value of x,

→ 10(2x-3) = 10

→ 20x-30 = 10

→ 20x = 10+30

→ 20x = 40

→ x = 40/20

→ [x = 2]

Hence, the value of x is 2.

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

Answer:

you can make 3 outfits

Step-by-step explanation:

because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.

for the socks, one people wear 2 socks so there you have 3 outfits

Answer:

[tex]810[/tex]

Step-by-step explanation:

For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.

Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.

Answer:

$ 2,600 was invested at 4% and $ 3,600 was invested at 9%.

Step-by-step explanation:

Given that in investing $ 6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest, and the rest was invested in a riskier mini-mall development plan paying 9% annual simple interest, and the combined interest earned for the first year was $ 428, to determine how much money was invested at each rate, the following calculation must be performed:

3000 x 0.04 + 3200 x 0.09 = 408

2500 x 0.04 + 3700 x 0.09 = 433

2600 x 0.04 + 3600 x 0.09 = 428

Therefore, $ 2,600 was invested at 4% and $ 3,600 was invested at 9%.

Answer:

6 samples

Step-by-step explanation:

Given :

Sample size, = n

Standard deviation, = 6000

Margin of Error = 2000

Confidence interval, α = 95%

Zcritical at 95% = 1.96

n = (Zcritical * σ) / margin of error

n = (1.96 * 6000) /2000

n = 11760 / 2000

n = 5.88

n = 6 samples

Answer:

110100

Step-by-step explanation:

==========================================================

Explanation:

I'm assuming you meant to say

y = (3/2)*tan( (1/3)x )

If so, then that equation is in the form

y = A*tan(Bx)

The B coefficient is B = 1/3 and it directly ties together to the period T.

T = pi/B

T = pi/(1/3)

T = pi*(3/1)

T = 3pi .... answer is choice C

Side note: This formula only works for tangent and cotangent functions.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{15 - 7x = 14}[/tex]

[tex]\large\text{-7x + 15 = 14}[/tex]

[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]

[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]

[tex]\large\text{14 - 15 = \bf -1}[/tex]

[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]

[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]

[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]

[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]

[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]

[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]

[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

11, 18, 25, 32, .....

Option D

Step-by-step explanation:

The formula for the nth term of an AP is a+(n-1)d

a+(n-1)d=a+(n-1-1)d+7

a+nd-d=a+nd-2d+7

d=7

As the common difference is 7.

The only option given which is in an AP is the 4th option