Which expression is irrational?
A 18
B 18
C 64
D 364

Everything is correct except for option (a). That is PR = 3x is wrong while others are right.

An isosceles triangle is a type of triangle that has two sides of equal length. This means that two of the three sides of the triangle are congruent. The angles opposite the congruent sides are also congruent.

Given an isosceles triangle with the following properties:

PQ = x + 0.1

PR = 3x - 0.4

RQ = x + 1.4

But

PR = RQ (equal sides of isosceles triangle)

with this fact, we can calculate the value of x

Recall that:

PR = RQ

3x - 0.4 = x + 1.4

3x - x = 1.4 + 0.4

2x = 1.8

x = 0.9

Knowing the value of x now, we can substitute to the above equations:

Recall:

PQ = x + 0.1

     = 0.9 + 0.1

PQ = 1.0

RQ =  x + 1.4

     = 0.9 + 1.4

     = 2.3

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Answer:

Volume of Burj Khalifa Prism = 4000 \(cm^2\)

Volume of CN Tower Prism = 2671 \(cm^2\)

Step-by-step explanation:

Given

Height of Burj Khalifa = 828 m

Height of CN Tower in Toronto = 553 m

Base of rectangular prism is a square with sides 10 cm \(\times\) 10 cm.

Height of Burj Khalifa prism = 40 cm

828 m is represented as 40 cm

\(\Rightarrow 553 m\) is represented as \(\frac{40}{828 } \times 553 = 26.71\ cm\)

So, height of rectangular prism of CN Tower = 26.71 cm

Volume of a Prism is given by the Formula:

\(V=Area\ of\ Base \times Height\)

Base is a square, so Area of base = \(Side^2\)

Volume of Burj Khalifa Prism:

\(V_B=10^2 \times 40 = 4000\ cm^2\)

Volume of CN Tower Prism:

\(V_C=10^2 \times 26.71 = 2671\ cm^2\)

So, the answer is:

Volume of Burj Khalifa Prism = 4000 \(cm^2\)

Volume of CN Tower Prism = 2671 \(cm^2\)

Answer:

x = 1

y = 1

Step-by-step explanation:

3x + 2y = 5

3x - 2y = 1 (subtract these equations)

––––––––––––

4y = 4

divide by two

y = 1

input y = 1 the other equations

3x + 2 = 5

simplify

3x = 3

x = 1

Answer:

3x+2y=5.......(1)

3x-2y=1.........(2)

subtracting equation 1 by 2

3x+2y=5

3x-2y=1.

- +. =-

_________

3x-3y+2y-(-2y)=5-1

2y+2y=4

4y=4

y=4/4=1answer

adding equation 1 &2 we get

3x+2y=5

3x-2y=1

+

________

3x+3x+2y-2y=5+1

6x=6

x=6/6=1

:.x=1&y=1

The quadratic function graphed in this problem is defined as follows:

y = (x + 4)² - 1.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-4, -1).

Hence:

y = a(x + 4)² - 1.

When x = 0, y = 15, hence the leading coefficient a is obtained as follows:

15 = a(0 + 4)² - 1

16a = 16

a = 1.

Hence the equation is:

y = (x + 4)² - 1.

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The correct answer in this scenario is a) The courts are likely to consider ChromaLite Builders's performance as a substantial performance, and Jessica will have to pay something but not the full amount; i.e. she is entitled to monetary damages.

This is because ChromaLite Builders did not fully comply with the contract by installing grade A carpeting instead of grade A+ carpeting, but the difference may not be significant to most people. As a result, the courts are likely to consider this a minor breach of contract and award Jessica some monetary damages but not the full cost of the contract.

It is important to note that if the difference between the two grades of carpeting was significant and clearly stated in the contract, Jessica may have had a stronger case for refusing to pay. However, in this scenario, it seems that the breach of contract was not significant enough to justify a complete refusal to pay.

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The volume of a sphere can be calculated using the formula: Volume = (4/3) * pi * (radius)^3

Given that the diameter of the ball bearing is 2.5 cm, we can calculate the radius by dividing the diameter by 2:

Radius = 2.5 cm / 2 = 1.25 cm

Now we can substitute the radius into the volume formula:

Volume = (4/3) * 3.14 * (1.25 cm)^3

Volume = (4/3) * 3.14 * 1.953125 cm^3

Volume ≈ 8.183 cm^3

Rounding to the nearest hundredth, the volume contained inside the ball bearing is approximately 8.18 cm^3. Therefore, the correct option is 8.18 cm^3.

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Answer:

The slope is 3/2, and the y-intercept (b) is -1

Step-by-step explanation:

The slope-intercept form is y=mx+b. m is the slope and b is the y-intercept.

Answer:

The value of x is 5.8

Step-by-step explanation:

Here. we want to find the value of x

To do this, we need the appropriate trigonometric identity

As we can see 10 is the opposite as it faces the side given

x is the adjacent

The trigonometric identity relating opposite and adjacent is tan . Tan is the ratio of the opposite to the adjacent

Thus, mathematically;

Tan 60 = 10/x

x = 10/tan 60

x = 5.8

Answer:

31

Step-by-step explanation:

3-51 = -48

-2+81= 79

79+(-48)= 31

Answer:

31

Step-by-step explanation:

(3-51) + (-2+81)

-48 + 79

31

Answer: The card is 28 cm by 23 cm

Check out the diagram below

Explanation:

I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.

Answer:

90 5/6

Step-by-step explanation:

23 + 67 + 1/2 + 1/3

= 90 + 3/6 + 2/6

= 90 + 5/6

= 90 5/6

Answer:

u do it to me i do it back

Step-by-step explanation:

Answer:

x= 68

Step-by-step explanation:

do u need the work 4 it?

Answer:

32

Step-by-step explanation:

Relying solely on statistics on real GDP during World War II may give a misleading indication of prosperity. It is crucial to consider a broader range of indicators and factors, such as living standards, employment conditions, social well-being, and the overall human experience, to assess the true impact of the war on the economy and society.

Statistics on real GDP during World War II may give a misleading indication of whether it was a period of prosperity because GDP measures the total value of goods and services produced within a country's borders, but it does not capture the full picture of economic well-being and quality of life.

During World War II, the increased production of military goods and services significantly boosted GDP. The war effort led to a surge in government spending, mobilization of resources, and expansion of industries related to defense production. This contributed to a substantial increase in GDP figures, creating the appearance of economic growth and prosperity.

However, it is essential to consider the context and the underlying factors that influenced these GDP numbers. World War II was a time of conflict and immense human suffering. The war resulted in widespread destruction, loss of life, displacement, and significant social and economic disruptions. Resources were redirected towards war production, which often came at the expense of civilian consumption and investment.

Furthermore, GDP does not account for the distribution of wealth and income. While some sectors of the economy thrived during the war, others faced hardships and scarcity. Rationing and resource allocation measures were implemented, which limited the availability of consumer goods for the general population. Additionally, the impact of inflation and wartime price controls can distort the true economic conditions experienced by individuals and households.

Moreover, the human cost of war cannot be captured by GDP alone. The loss of lives, physical and emotional trauma, and long-term social and economic consequences cannot be adequately reflected in GDP figures.

Therefore, relying solely on statistics on real GDP during World War II may give a misleading indication of prosperity. It is crucial to consider a broader range of indicators and factors, such as living standards, employment conditions, social well-being, and the overall human experience, to assess the true impact of the war on the economy and society.

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Answer:

To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:

(x-xc)^2+(y-yc)^2=r^2

where (xc,yc) is the centre of the circle, and r=radius of the circle.

If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle.  If the left-hand side is equal to r^2, the point is ON the circle.

Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.

For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7

(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2

A. (-1,1),

(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49  [inside circle]

B. (10,0)

(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49  [on circle]

C. (4,-8)

(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49  [outside circle]

Step-by-step explanation:

The answer is (b) I = 13/12.

We can use the degree 2 Taylor polynomial of f(x) centered at 0, which is given by:

f(x) ≈ f(0) + f'(0)x + (1/2)f''(0)x^2

where f(0) = e^0 = 1, f'(x) = (-1/2)xe^(-x^2/4), and f''(x) = (1/4)(x^2-2)e^(-x^2/4).

Integrating the approximation from 0 to 1, we get:

∫₀¹ f(x) dx ≈ ∫₀¹ [f(0) + f'(0)x + (1/2)f''(0)x²] dx

= [x + (-1/2)e^(-x²/4)]₀¹ + (1/2)∫₀¹ (x²-2)e^(-x²/4) dx

Evaluating the limits of the first term, we get:

[x + (-1/2)e^(-x²/4)]₀¹ = 1 + (-1/2)e^(-1/4) - 0 - (-1/2)e^0

= 1 + (1/2)(1 - e^(-1/4))

Evaluating the integral in the second term is a bit tricky, but we can make a substitution u = x²/2 to simplify it:

∫₀¹ (x²-2)e^(-x²/4) dx = 2∫₀^(1/√2) (2u-2) e^(-u) du

= -4[e^(-u)(u+1)]₀^(1/√2)

= 4(1/√e - (1/√2 + 1))

Substituting these results into the approximation formula, we get:

∫₀¹ f(x) dx ≈ 1 + (1/2)(1 - e^(-1/4)) + 2(1/√e - 1/√2 - 1)

≈ 1.0838

Therefore, the closest answer choice is (b) I = 13/12.

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Answer:

Human coastal development has also helped jellyfish thrive. The structures and construction that we have placed in the water, such as piers, marinas, oil platforms, artificial reefs, refuse, rubble, aquaculture pens and structures, etc. provide an abundance of habitats for polyps to settle on.

Answer:

Step-by-step explanation:

Using formula

Substitute values

Option A is correct

Answer:CB,CH,AE,AB

Step-by-step explanation:

The bends on a track for car racing are semicircular, and the track is banked at an angle of 28.0° to the horizontal. Suppose the radius of the curvature of the bends is 120 m.

a) The formula to calculate the minimum velocity is given as follows:Vmin = √(rgtanθ)Where;Vmin is the minimum velocity needed to stay on the track;g is the acceleration due to gravity;r is the radius of the turn;θ is the angle of banking.r = 120 m, θ = 28.0°, and g = 9.8 m/s²Substitute the values into the formula, we get;Vmin = √(rgtanθ)=√(9.8 m/s² * 120 m * tan(28.0°))=40.6 m/sTherefore the minimum velocity the car should maintain is 40.6 m/sb) If the car speed is twice that in (a).

(i) The free-body diagram of the car is as shown below;

(ii) The value of the frictional force f is as follows;There are two forces acting on the car, namely; the normal force and the gravitational force. When the car moves at a constant speed around the bend, the centrifugal force Fc is also acting towards the center of the circular path. The centrifugal force Fc is given by the formula;Fc = mv²/rWhere;F c is the centrifugal force;m is the mass of the carv is the velocity of the car in m/sr is the radius of the curve.

Therefore;f = F s, max= μsNWhere;Fs, max is the maximum static frictional force that can be applied;N is the normal force acting on the car;μs is the coefficient of static friction.Because the car is not sliding, the maximum frictional force that can act is equal to the centripetal force, Fc.Thus;Fs, max = F c= 21,333.3 NThe frictional force f can now be determined as;f = Fs, max= μsN= 21,333.3 N= μsmgCosθwhere m is the mass of the car, and g is the acceleration due to gravity.

Substitute the values into the formula;μ s = f/mgCosθ= 21,333.3 N / 800 kg * 9.8 m/s² * Cos(28.0°) = 0.58Therefore the coefficient of static friction is 0.58.

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The interest tax shield of 1.26% lowers Summit's WACC by 0.76%

Let’s calculate the interest tax shield on Summit Builders' debt. Interest tax shield = Interest expense x tax rate

Summit Builders’ debt is 1.50 times the value of its equity.

So, the total value of its capital is equal to 1 + 1.50 = 2.50

The weight of debt is equal to debt/(equity+debt) = 1.50/2.50 = 0.6

The weight of equity is equal to equity/(equity+debt) = 1/2.50 = 0.4

The interest expense = 6% of debt

The tax rate is given as 21%.

Therefore,Interest tax shield = Interest expense x tax rate= 6% x 21%= 1.26%

The interest tax shield from its debt lowers Summit's WACC by the following amount:

WACC = wdebt*Kd*(1-t) + wEquity*Ke= 0.6 * 6% * (1 - 21%) + 0.4 * Ke= 2.4% + 0.4 * Ke

The interest tax shield of 1.26% lowers Summit's WACC by:1.26% x 0.6 = 0.756%≈0.76%

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The result of each operation is given as follows:

a) a U b = {0, 1, 2, 3, 4, 5, 6, 7, 8}.

b) a ∩ b = {}.

c) a - b = {0, 2, 4, 6, 8}.

The union and intersection sets of multiple sets are defined as follows:

Item a:

The union set is composed by the elements that belong to at least one of the sets, hence:

a U b = {0, 1, 2, 3, 4, 5, 6, 7, 8}.

Item B:

The two sets are disjoint, that is, there are no elements that belong to both sets, hence the intersection is given by the empty set.

Item c:

The subtraction is all the elements that are on set a but not set b, hence:

a - b = {0, 2, 4, 6, 8}.

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(1) The significant figure will be 710.

Hence the correct option is (b).

(2) (a) The modulus of A and B are,

| A | = √62

| B | = √30

(b) The value of A + B = 7 i - 2 j + 9 k

(c) The value of A - B = -3 i - 4 j + 5 k

(3) (a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Given lines are parallel because the cross product of the vectors along that lines is zero vector.

(1) Given the multiplication is,

20.6 × 5.5 × 6.27

That gives the result,

20.6 × 5.5 × 6.27 = 710.391

Here significant figure will be 710.

So the correct option is (b).

(2) Given the vectors are,

A = 2 i - 3 j + 7 k

B = 5 i + j + 2 k

(a) The modulus of A and B are,

| A | = √[2² + (-3)² + 7²] = √62

| B | = √[5² + 1² + 2²] = √30

(b) The value of A + B vector is,

A + B = [2 i - 3 j + 7 k] + [5 i + j + 2 k] = 7 i - 2 j + 9 k

(c) The value of A - B vector is,

A - B = [2 i - 3 j + 7 k] - [5 i + j + 2 k] = -3 i - 4 j + 5 k

(3) We know that the cross product gives vector result and dot product gives scalar result.

The statements are,

(a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Here for first line vector is,

A = [(-2) - (-4)] i + [0 - (-6)] j + [(-3) - 1] k = 2 i + 6 j - 4 k

for second line vector is,

B = [5 - 10] i + [3 - 18] j + [14 - 4] k = -5 i - 15 j + 10 k

So now the cross product is,

A × B = \(\left[\begin{array}{ccc}i&j&k\\2&6&-4\\-5&-15&10\end{array}\right]\) = 0 i + 0 j + 0 k

So the cross vector is a zero vector so the initial vectors are parallel to each other.

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Answer:

the graph of f represents a direct variation

Step-by-step explanation:

All direct variations are going to be linear functions, thus the graph of f represents a direct variation. However, I will give you a longer way to solve this problem, a more visual one, that will help understand this concept in an easier manner.

the basic formula for a direct variation is "y = k·x" and the basic formula for an inverse variation is "y = \(\frac{k}{x}\)" (with k representing any costant)

we can solve this question by using the basic formulas to write inverse and direct variations, graph them, and see which one is the most similar to the one given in the question.

Since line f has a slope of 2, I decided to use 2 as the constant for both functions. Now we just substitute k for 2 in each function and graph it.

direct variation: y = 2x

inverse variation: y = \(\frac{2}{x}\)

After re-writting the functions, I graphed them on desmos to see what they would look like. After comparing the original graph to the ones I created on Desmos, it can be seen that the red line graph (direct variation) is identical to the original one. Thus, the graph of f represents a direct variation.

p.s.: be familiar with teh formulas for direct and indirect variation, as they will be used a lot in the years to come (regaring math classes), even in AP Calculus

hope this helps! :)

Answer:

-6

Step-by-step explanation:

-4+8=4

4-10= -6

Answer:

The side lengths that are the legs are 6 and 12 because the hypotenuse is the largest side length of a triangle (since there are three side lengths shown).  

Answer:

6 & 12

Step-by-step explanation:

In a right triangle, the greatest side length belongs to hypotenuse, other 2 numbers represent the legs

so as per the given, 14 is hypotenuse ans 6 & 12 are legs

Answer:

r = 4

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

Given:

V = 100.48

h = 6

π = 3.14

Work:

V = πr²(h/3)

100.48 = r²(3.14)(6/3)

100.48 = r²(3.14)(2)

100.48 = r²6.28

r² = 100.48/6.28

r² = 16

\(\sqrt{r^2} =\sqrt{16}\)

r = 4

Using exponential function, The value after 10 will be P(10) = 2125.0.05¹⁰.

A mathematical function with the following form is an exponential function: f ( x ) = an x. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

This is an exponential behavior expressed as:

P(t) = Abⁿ

P(t) = Ae^(n ln b)

Where P(t) is the  worth after 10 years,

A is the original investment,

and b is the percentage (87% in this case).

From the problem, we identify:

A = 2125

b = 0.05

The final model is:

P(t) = 2125.0.05¹⁰

After 10 years (t = 10),

the investment will be (to the nearest whole number):

P(10) = 2125 ×0.05¹⁰

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Answer:

Step-by-step explanation:

Answer:

The answer would be

f(x)= x^2-8x+17

Step-by-step explanation: