Choose 1 answer:
A: Replace one equation with the sum/difference of both equations.
B: Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations.
C: Replace one equation with a multiple of itself.
D: Replace one equation with a multiple of the other equation.

Answer:

1278in^3

Step-by-step explanation:

21×8=168

168×6=1008in^3

5×9=45

45×6=270in^3

1008+270=1278in^3

Answer:

Step-by-step explanation:

The least common denominator for 1/6 + 3/8 is 24

first find the multiples of 6 and 8

6= 6, 12, 18, 24, 30

8 = 8, 16, 24, 32

Next circle the number that appear in both

That number will be 24 which is the least common denominator.

1) A  perpendicular bisector in kite ABCD is; BD

2) An isosceles triangle in kite ABCD is; ΔABC

3) A right triangle in kite ABCD is; ΔABM

In geometry, a kite is defined as a quadrilateral with reflection symmetry across a diagonal.

here, we have,

1) A perpendicular bisector is defined as a line segment which bisects another line segment at 90 degrees.

Looking at the diagram, Line BD bisects Line AC and as such BD is the perpendicular bisector.

2) An Isosceles triangle is defined as a a triangle in which two sides have the same length.

In this case, in Triangle ABC, AB and BC have the same length and as such Triangle ABC is the Isosceles Triangle.

3) A right triangle is defined as a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

In this case if Mis the intersection of BD and AC, then the right angle triangle is ABM

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Answer:

Let's assume that the amount of saving is x.

According to the problem, the ratio of expenditure to saving is 4:1, so the amount of expenditure can be expressed as 4x.

The total income of the family is Rs. 500000, and it can be expressed as the sum of expenditure and saving:

Expenditure + Saving = 500000

Substituting the values of expenditure and saving, we get:

4x + x = 500000

Simplifying this equation, we get:

5x = 500000

Dividing both sides by 5, we get:

x = 100000

Therefore, the amount of saving is Rs. 100000, and the amount of expenditure is 4 times this value, which is Rs. 400000.

It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.

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A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is  0.064. The correct answer is A.

The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.

In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).

Using the formula, we can calculate the probability of the player making zero free throws as follows:

P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064

Therefore, the correct answer is (A) 0.064.

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The general solution of a fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di can be determined by using the fact that the general solution of a linear ODE is the sum of the solutions corresponding to each of the roots.

For the real root r, the solution is given by:
y1 = C1 * e^(r*x)

For the complex roots a ± bi, the solution is given by:
y2 = C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x)

For the complex roots c ± di, the solution is given by:
y3 = C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)

The general solution of the fifth order linear ODE is the sum of these solutions:
y = y1 + y2 + y3
= C1 * e^(r*x) + C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x) + C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)

This is the general solution of the fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di.

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The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)

What is the logarithms?

Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.

We can use the property of logarithms that states:

logb (a∙c) = logb a + logb c

to expand the expression as a sum of logarithms:

ln(√z) = ln(z^(1/2))

Using the power rule of logarithms, we can simplify this as:

ln(z^(1/2)) = (1/2)ln(z)

Hence, we can write:

ln(√z) = (1/2)ln(z)

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To solve the given equations, we need to follow these steps:

1. Isolate the radical on one side of the equation.
2. Square both sides of the equation to eliminate the radical.
3. Solve the resulting equation for the variable.
4. Check for extraneous solutions by plugging the solution back into the original equation.
5. If there are rational exponents, use the same steps but raise both sides of the equation to the reciprocal of the exponent.

Let's apply these steps to the sample problems:
1. V4x + 1 - Vx+ 10 = 2
First, isolate the radical on one side:
V4x + 1 = Vx+ 10 + 2
V4x + 1 = Vx+ 12
Next, square both sides to eliminate the radical:
(4x + 1) = (x+ 12)^2
4x + 1 = x^2 + 24x + 144
Solve for x:
0 = x^2 + 20x + 143
Using the quadratic formula:
x = (-20 ± √(20^2 - 4(1)(143)))/(2(1))
x = (-20 ± √(400 - 572))/2
x = (-20 ± √(-172))/2
x = (-20 ± √172i)/2
There are no real solutions for this equation.

2. V2x+30 = (x+3)
Isolate the radical:
V2x+30 = x+3
Square both sides:
2x + 30 = (x+3)^2
2x + 30 = x^2 + 6x + 9
Solve for x:
0 = x^2 + 4x - 21

Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-21)))/(2(1))
x = (-4 ± √(16 + 84))/2
x = (-4 ± √100)/2
x = (-4 ± 10)/2
x = 3 or x = -7
Check for extraneous solutions by plugging the solutions back into the original equation:
V2(3)+30 = (3+3)
V36 = 6
6 = 6 (True)
V2(-7)+30 = (-7+3)
V16 = -4
4 = -4 (False)

Therefore, the only solution is x = 3.

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]

Answer: C, 2 2/8

Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:

4 3/8 = 35/8

2 1/8 = 17/8

Now, since the denominators are equivalent, all we need to do is subtract the numerators.

35/8 - 17/8 = 18/8

The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.

18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.

So the correct choice would be (C).

The distance between any point on the parabola and the directrix is equal to the distance between that point and the focus. This property is what defines a parabola.

To draw a parabola given the directrix and focus, follow these steps:

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Answer:

17,000

Step-by-step explanation:

17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.

The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:

Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.

Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.

Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

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The Zeros of the equation would be x = -5/2.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given the equation as;

[tex]f(x)=-8x^3-20x^2[/tex]

We can factor;

4x^2 ( 2x+5)  

Using the zero product property

2x = 0

2x + 5 = 0

x = -5/2

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Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:

d(t) = f(t) + g(t) = 10 + 65t

So, after 2 hours of driving, the distance that the car has traveled from the city is:

d(2) = 10 + 65(2) = 10 + 130 = 140 miles

Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.

Step-by-step explanation:

AMSAA growth model

The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.

A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).

| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28            | 1 | 3.33|
| 146           | 2 | 4.98|
| 258           | 3 | 5.55|
| 426           | 4 | 6.05|
| 521           | 5 | 6.26|
| 1027          | 6 | 6.93|
| 1273          | 7 | 7.15|

Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:

C = βlnT - η

Using linear regression, we get β = 1.11 and η = 3.82.

To estimate the MTTF at the conclusion of the test cycle, we can use the formula:

MTTF = (T/C)^(1/β)

Plugging in the values for T (1273), C (7), and β (1.11), we get:

MTTF = (1273/7)^(1/1.11) = 232.59 hours

B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)

Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:

T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours

Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.

C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:

C = βlnT - η

Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:

10 = 1.11ln(5000) - 3.82

ln(5000) = (10 + 3.82)/1.11 = 12.47

5000 = e^(12.47) = 260753.13

Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.

D) If the testing in (c) continues for only 600 more hours, we can use the formula:

C = βlnT - η

Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:

C = 1.11ln(600) - 3.82 = 1.75

Therefore, the expected number of failures in 600 more hours of testing is 1.75.

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An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)

The correct answer is an option (A)

Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.

We know that the formula for the area of a square  is A = s²

where 's' is the side of a square.

Sides of three square rooms measure 13 feet each.

So, the area of the three rooms would be:

A₁ = 3 × a²

A₁ = 3 × 13²

And sides of two square rooms measure 15 feet each.,

So, the area of the two rooms would be:

A₂ = 2 × b²

A₂ = 2 × 15²

Total area of the five rooms A =  A₁ + A₂  

So, we get an expression:

A = 3 × 13²  + 2 × 15²

A = 3 × 169 + 2 × 225

A = 957 ft²

Therefore the total area of the five rooms be 957 ft².

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The complete question is:

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?

a.(3 × 13^2) + (2 × 15^2)

b.(2 × 13^3) + (2 × 15^2)

c.(3 × 15^2) + (2 × 13^2)

d.(3 × 13^2) × (2 × 15^2)

Javier has 90 more uncommon cards than rare cards.

To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:

Uncommon cards - Rare cards = Difference

First, we'll multiply the number of packs by the number of each type of card:

45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards

Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:

135 uncommon cards - 45 rare cards = 90

So, the number of uncommon cards is 90 more than the rare cards.

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Answer:

I think its 560

Step-by-step explanation:

Keegan's error is that he did not provide enough information to fully determine the result of the given composition of transformations, namely (R90•D2)(Triangle ABC).

To be able to graph the image of Triangle ABC under the composition of R90 (a 90-degree counterclockwise rotation) and D2 (a dilation with center the origin and scale factor 2), we need to know the center of rotation for the rotation R90.

The reason for this is that the composition of a rotation and a dilation is not commutative, meaning that the order of the transformations matters. Specifically, the result of the composition depends on whether the dilation is applied before or after the rotation. If the dilation is applied before the rotation, then the center of dilation becomes the center of rotation for the rotation. If the rotation is applied before the dilation, then the center of dilation is not affected by the rotation.

Therefore, without knowing the center of rotation for the rotation R90, we cannot determine the exact result of the composition (R90•D2)(Triangle ABC), and thus we cannot graph it accurately.

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The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035

The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33

Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.

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In the quadrilateral ABCD if AB ||CD and  AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.

Parallelogram's characteristics

In the quadrilateral ABCD:

Thus, the quadrilateral ABCD is both parallelogram and trapezium.

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The area of the trapezoid in simplest radical form is 78 feet².

Given a trapezoid.

Length of the bases are 10 feet and 16 feet.

We have to find the height.

Consider the smaller right triangle formed by the height of the trapezoid.

Triangle base length or one leg = 16 - 10 = 6 feet

Since one of the angle is 45°, the other angle in the right triangle is also 45°.

Since it is isosceles, opposite sides for 45° angles are same.

Other leg = 6 feet, which is the height.

Area of the trapezoid = 1/2 (a + b)h, where a and b are bases and h is the height.

A = 1/2 (10 + 16) 6

   = 78 feet²

Hence the correct option is b.

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Answer:

see explanation

Step-by-step explanation:

(a)

• the opposite sides of a rectangle are congruent

then

4x + 1 = 2x + 12

(b)

solving

4x + 1 = 2x + 12 ( subtract 2x from both sides )

2x + 1 = 12 ( subtract 1 from both sides )

2x = 11 ( divide both sides by 2 )

x = 5.5

(c)

the perimeter (P) is the sum of the 4 sides of the rectangle , that is

P = 4x + 1 + x + 2x + 12 + x ( collect like terms )

  = 8x + 13 ( substitute x = 5.5 )

  = 8(5.5) + 13

  = 44 + 13

  = 57

Answer:

a) Because two opposite sides of the rectangle have the same sizes

B)

[tex]x = \frac{11}{2} [/tex]

c)

[tex]57[/tex]

Step-by-step explanation:

b)

[tex]4x + 1 = 2x + 12 \\ 4x - 2x = 12 - 1 \\ 2x = 11 \\ \frac{2x}{2} = \frac{11}{2} \\ x = \frac{11}{2} [/tex]

c) Perimeter

[tex]p = 2(x + y) \\ 2( \frac{11}{2} + 23) \\ 2( \frac{57}{2} ) \\ 57[/tex]

23 comes from

[tex]2x + 12 \\ x = \frac{11}{2} \\ 2( \frac{11}{2} ) + 12 \\ 11 + 12 \\ \\ 23[/tex]

1. The positive x-intercept of the function f(x)= -1201(x-88)^2 + 151058 is 88 feet.

2. The y-intercept of the function f(x) = -1201(x-88)^2 + 151058 is 151058 feet.

3. The maximum height that the football reaches is 151058 feet, and the horizontal distance from Patrick Mahomes when this happens is 88 feet.

4. Yes, Travis Kelce will be able to catch the football, since it reaches a height of 10 feet or lower at the horizontal distance of 160 feet from Patrick Mahomes.

5. The horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet is 176 feet.

1. The positive x-intercept represents the horizontal distance from Patrick Mahomes at which the football is initially released.

2. The y-intercept of the function represents the height of the football when it is released from Patrick Mahomes.

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Check the picture below.

\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{18}{12} = \frac{3}{2} \)Explanation: We are given that \( \operatorname{det} A=12 \) and \( \operatorname{det} B=3 \). We need to find the determinant of \( 2 A^{-1} B^{2} \). We can use the properties of determinants to simplify the expression. Recall that \( \operatorname{det}(cA) = c^n \operatorname{det}(A) \) for an \( n \times n \) matrix \( A \) and a scalar \( c \), and that \( \operatorname{det}(AB) = \operatorname{det}(A)\operatorname{det}(B) \). Using these properties, we can write:\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \operatorname{det}(2) \operatorname{det}(A^{-1}) \operatorname{det}(B^{2}) \)\( = 2^3 \operatorname{det}(A^{-1}) \operatorname{det}(B)^2 \)\( = 8 \cdot \frac{1}{\operatorname{det}(A)} \cdot (\operatorname{det}(B))^2 \)\( = 8 \cdot \frac{1}{12} \cdot (3)^2 \)\( = \frac{18}{12} = \frac{3}{2} \)Therefore, \( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{3}{2} \).

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Answer:

Step-by-step explanation:

For this triangle, we can find the angle adjacent to side length 4 using trig:

tan(theta) = 7/4

theta = tan^-1(7/4)

theta = 60.26

Now we use sine to find x:

sin(60.26) = 7/x

x = 7/sin(60.26)

x = 8.06

I don't know how far you need to round, so it can either be this or 8.1

Hope this helps!