if R is the midpoint of QS, RS = 2x-4, ST = tx-1, and RT = 8x-43

Answer:

andrew

Step-by-step explanation:

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

Step-by-step explanation:

nCr = n! / r!(n-r)!

n=46

r=6

=46!/6!(46-6)!

=46!/[6!(40)!]

=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)

Cancel out 40!

=46*45*44*43*42*41/(6*5*4*3*2*1)

=6744109680/720

=9366819

Possible different selection 9366819

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

Formula

V=a^2h/3

a is the base area

h is the height

V= 16^2×15/3

V=1280cm^3

Answer:

$594

Step-by-step explanation:

8.25% of $7,200 =

= 0.0825 × $7,200

= $594

(a) The probability that a point chosen randomly inside the rectangle is in the square is 0.6.

(b) The probability that a point chosen randomly inside the rectangle is outside the square is 0.4.

The probability that a point chosen randomly inside the rectangle is in each given shape is calculated as follows;

The area of the triangle is calculated as follows;

area = ¹/₂ x base x height

area = ¹/₂ x 4 x 5

area = 10 sq.units

The area of the rectangle is calculated as follows;

area = 4 x 4

area = 16 sq.units

The probability that a point chosen randomly inside the rectangle is in the square is calculated as;

P = outcome / total possible outcome

P = ( 10 ) / 16

P = 0.625 ≈ 0.6

The probability that a point chosen randomly inside the rectangle is outside the square;

P = 1 - p(inside)

P = 1 - 0.6

P = 0.4

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Answer:

You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear.

Step-by-step explanation:

Hope this helped~

Answer:

You can tell if a table is linear by looking at how X and Y change.If,as X increases by 1, Y increases by a constant rate,then a table is linear.

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

34.50$

Step-by-step explanation:

30 * 0.15 = 4.50Then we add this surcharge (4.50$) to the base price of the ticket (30$) to get the total value of (34.50$).

Answer:

$34.50

Step-by-step explanation:

Handling surcharge = 15% of  30

                                  \(=\dfrac{15}{100}*30\)

                                  = $ 4.50

Total price  = base price + handling surcharge

                  = 30 + 4.50

                    = $ 34.50

Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

The equation that represents the relationship between x and y in the table is (L.) y = -5x + 3.

In mathematics, an equation is a relationship between two expressions that are expressed as equality on each side of the equal to sign.

Given in the table is the relationship between x and y respectively.

Substitute the values of x in the respective equations to find the value of y, the resulting value which matches the value of y in the table determines the correct equation.

J. y = -5x -27

⇒ For x = -3, y = -5(-3) - 27 = 15 -27 = -12 ≠ 18

K. y = -5x + 18

⇒ For x = -3, y = -5(-3) + 18 = 15 + 18 = 33 ≠ 18

L. y = -5x + 3

⇒ For x = -3, y = -5(-3) + 3 = 15 + 3 = 18 ≈ 18

For x = -1, y = -5(-1) + 3 = 5 + 3 = 8

For x = 2, y = -5(2) + 3 = -10 + 3 = -7

For x = 6, y = -5(6) + 3 = -30 + 3 = -27

All the values of x and y in the table satisfy the equation y = -5x + 3. Hence this is the required equation that represents the relationship.

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From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

Answer:

b. 576

Step-by-step explanation:

(-4)(6)(-4)(6)

(-24)(-24)

= 576

Answer:

FOR QUESTION 2

1. Segment addition postulate

2. Substitution

3. Substitution

4. Addition property of equality

5. Division property of equality

6 symmetric property

FOR QUESTION 3

1. given

2. Definition of complementary angles (complementary angles add upto 90)

3. Substitution

4. Subtraction property of equality

FOR QUESTION 4

1. Given

2. Definition of supplementary angles (supplementary angles add upto 180)

3. Definition of supplementary angles

4. Substitution

5. Subtraction property if equality

6. Definition of congruent angles (congruent angles are equal)

Step-by-step explanation:

Answer:

I not understand your questions

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

Answer:

No probllem linked

Step-by-step explanation:

9514 1404 393

Answer:

   (a)  34 ft²

Step-by-step explanation:

The "top" and "back" together have a height of 2 ft + 1 1/2 ft = 3 1/2 ft. The bottom and front will have the same height, so the central vertical rectangle in the net will have a height of 2×(3 1/2 ft) = 7 ft. It is shown as having a width of 4 ft, so its area is ...

  A = WH = (4 ft)(7 ft) = 28 ft²

__

The two areas labeled "left" and "right" are shown as having a height of 1 1/2 ft. Their width is the same as the width of the bottom (or top), so is 2 ft. The total area of the left and right sides is then ...

  left + right = 2WH = 2(2 ft)(1 1/2 ft) = 6 ft²

That makes the area of the entire net be ...

  total surface area = 28 ft² +6 ft² = 34 ft²

The surface area of the box is 34 square feet.

The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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Answer:

None of the above

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think its 3

The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

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Answer:

I’m sorry but I don’t understand the question

Step-by-step explanation:

The maximum height of the golf ball on Mars is about 48.8 meters.

To find how much longer it would take for the golf ball hit on Mars to reach the ground, we can use the given equation h = -1.9t² + 26t, where h is the height of the object and t is the time in seconds. First, we need to find the time it takes for the golf ball to reach the ground on Mars. Setting h = 0, we get:

0 = -1.9t² + 26t

Solving for t using the quadratic formula, we get t = 13.684 or t = 0.856. Since the golf ball is launched upward, we need the positive value of t, so it takes about 13.7 seconds for the golf ball to reach the ground on Mars. Therefore, it takes 13.7 − 5.4 = 8.3 seconds longer for the golf ball hit on Mars to reach the ground than the golf ball hit on Earth.

To find the maximum height of the golf ball on Mars, we can use the formula h = -1.9t² + 26t, where t is the time when the height is maximum. Since the formula is a quadratic equation, the maximum height occurs at the vertex of the parabola, which is at t = -b/2a.

In this case, a = -1.9 and b = 26, so the time at maximum height is t = -26 / 2(-1.9) = 6.842. Plugging this value into the equation for h, we get:

= -1.9(6.842)² + 26(6.842) ≈ 48.8 meters

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Yes, the expressions S+S+S+S AND 4S as required in the task content are equivalent expressions.

It follows from the task content that the expressions given S+S+S+S AND 4S are to be compared and determine if they are equivalent or not.

Since the given expressions are; S + S + S + S and 4S.

S + S + S + S can be written by factorisation as;

S ( 1 + 1 + 1 + 1 ) = S (4)

= 4S.

On this note, it can be inferred that the two expressions given are equivalent expressions.

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Answer:

I believe 457 operations

Answer:

Step-by-step explanation:

In 2017, California led the nation with 858 pedestrian fatalities. Arizona had only 216. The 2017 population of California was 39,536,653 and of Arizona was 7,016,270. Compute and compare the rate of pedestrian fatalities per 100,000 residents.

Solution

The pedestrian fatality rate for California per 100,000 residents

= pedestrian fatality in California / total population in California × 100,000

= (858 / 39,536,653) × 100,000

= 2.17 people per 100,000

The pedestrian fatality rate for Arizona per 100,000 residents

= pedestrian fatality in Arizona / total population in Arizona × 100,000

= (216 / 7,016,270) * 100,000

= 3.08 people per 100,000

This means that, though California may have a higher number of pedestrian fatalities compared to Arizona, the rate of pedestrian fatalities per 100,000 residents in California is lower compared to Arizona.

9514 1404 393

Answer:

  3/(x +1) -4/(x +1)^2

Step-by-step explanation:

The partial fraction expansion will be of the form ...

  A/(x+1)^2 +B/(x+1)

We can find the values of A and B by writing the sum of these terms:

  = (A +B(x +1))/(x +1)^2

Then we require ...

  B = 3

  A +B = -1   ⇒   A = -4

So, the desired expansion is ...

  3/(x +1) -4/(x +1)^2

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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