A student transformed the system of
equations shown below by multiplying
the second equation by a constant and
then adding the resulting equation to the
first equation.
x + 4y = 12
3x - y = 10

Answer:

4x² - 11xy - 3y²

Step-by-step explanation:

(4x + y)(x - 3y) =

Multiply each term of the first binomial by each term of the second binomial.

= 4x² - 12xy + xy - 3y²

Now combine like terms.

= 4x² - 11xy - 3y²

Answer:

Step-by-step explanation:

m/1 = m  (Any number, except zero, divided by itself is 1)

m : 8 = 133 : 1

m = 8 * 133 : 1

m = 1064

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

check

1064 : 8 = 133 : 1

133 = 133

the answer is good

These fractions are equivalent fractions by algebraic property:

Case 1: YES

Case 2: NO

Case 3: YES

Case 4: NO

Case 5: YES

Case 6: YES

Case 7: NO

Case 8: YES

Case 9: YES

Case 10: YES

Case 11: NO

Case 12: YES

Case 13: NO

Case 14: YES

Case 15: YES

Case 16: YES

Case 17: NO

Case 18: YES

In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:

a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.

Now we proceed to determine if each pair is equivalent:

Case 1

2 / 3 = (2 · 2) / (3 · 2)

2 / 3 = 4 / 6 (YES)

Case 2

2 / 6 = (2 · 3) / (6 · 3)

2 / 6 = 6 / 18 (NO)

Case 3

9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)

Case 4

3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)

Case 5

7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)

Case 6

4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)

Case 7

5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)

Case 8

2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)

Case 9

6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)

Case 10

4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)

Case 11

9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)

Case 12

1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)

Case 13

12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)

Case 14

8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)

Case 15

5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)

Case 16

6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)

Case 17

3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)

Case 18

10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)

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Answer:

first option

Step-by-step explanation:

differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

then

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{dt}[/tex] × [tex]\frac{dt}{dx}[/tex] = [tex]\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

y = t² + 4t

[tex]\frac{dy}{dt}[/tex] = 2t + 4

x = t - 3

[tex]\frac{dx}{dt}[/tex] = 1

then

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{2t+4}{1}[/tex] = 2t + 4

Answer:

2t + 4

Step-by-step explanation:

A parametric equation is one where x and y are defined separately in terms of a third variable (often the parameter t).

To find dy/dx from parametric equations, differentiate each equation with respect to the parameter t, then use the chain rule:

[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}}[/tex]

Differentiate the two parametric equations with respect to t:

[tex]x=t-3 \implies \dfrac{\text{d}x}{\text{d}t}=1[/tex]

[tex]y=t^2+4t \implies \dfrac{\text{d}y}{\text{d}t}=2t+4[/tex]

Use the chain rule to combine them:

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}\\\\&=(2t+4) \times \dfrac{1}{1}\\\\&=2t+4\end{aligned}[/tex]

Therefore:

[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=2t+4}[/tex]

Answer:

20

Step-by-step explanation:

just a substitute 3 in x so 3x3=9

11+9=20

Answer:

[tex]\sqrt[]{72}[/tex]

6.3141414141414...

[tex]\sqrt[4]{64}[/tex]

8.121 121 112 111...

Step-by-step explanation:

irrational numbers are real numbers that cannot be expressed as a ratio of integers.

example of irrational number [tex]\sqrt[]{2}[/tex]

example of rational number 2, 3, -4, etc.

Answer:

The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.

Step-by-step explanation:

The aspects of the scenario that bring the validity of the conclusion made by the representatives of the government would be:

The sample size used by the representatives in the survey was only 50 individuals, which might not be sufficient to represent the views of the entire town's population accurately. A more extensive sample size would provide a more precise approximation of the public opinion.

Moreover, the conductance of the survey on the existing boardwalk presents the possibility of sampling bias since those who visit the boardwalk could hold different opinions towards the new construction than those that do not visit.

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The value of f(1) is 3.

An estimate of the value of f(-1) is -0.2.

The values of x for which f(x) = 1 are: x = (0, 3).

The value of x such that f(x) = 0 is x = -0.5.

The domain of f is {-2, 4}.

The range of f is {-1, 3}.

The interval over which f is increasing is {-2, 1}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of the function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-2, 4}.

Range = {-1, 3}.

In conclusion, we can logically deduce that this function is increasing over the [-2, 1] and decreasing over the interval [1, 4].

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Answer:

-13

Step-by-step explanation:

To add fractions, find the lowest common denominator and then combine

The volume of a sphere of radius 9.5 cm is approximately 3589.5 cm³

From the question, we are to calculate the volume of a sphere

The volume of a sphere is given by the formula

V = 4/3 πr³

Where V is the volume of the sphere

and r is the radius of the sphere

From the given information,

r = 9.5 cm

Thus,

Volume of the sphere = 4/3 × π × 9.5³

Put π = 3.14

Volume of the sphere = 4/3 × 3.14 × 9.5³

Volume of the sphere = 3589.54333 cm³

Volume of the sphere ≈ 3589.5 cm³

Hence,

The volume of the sphere is 3589.5 cm³

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If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

Option A is the correct answer.

We have,

A horizontal translation moves every point of a figure the same distance in the same direction.

In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.

A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.

A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.

A 90° clockwise rotation would rotate the figure 90 degrees to the right.

Thus,

If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

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a) The polar coordinates of point A are (√(18), π/4).

b) The curve is a circle centered at the origin with radius 6.

c) The directed distance is the value of r, which is 6 √(3).

To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:

r = √(x² + y²)

θ = arctan(y/x)

Using the values of point A, we have:

r = √((-3)² + (-3)²) = √(18)

θ = arctan((-3)/(-3)) = arctan(1) = π/4

To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:

x = r cos(θ)

y = r sin(θ)

Using these formulae, we can rewrite the equation as:

r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0

Simplifying this equation, we get:

r = -6 sin(θ) / (1 - cos²(θ))

To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:

r = -6 sin(4 π/3) / (1 - cos²(4 π/3))

r = -6(-√(3)/2) / (1 - (-1/2)²)

r = 6 √(3)

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Answer:

The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.

X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.

We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.

To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.

We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.

Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.

Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.

Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.

See the attached image.

As shown in the attached figure:

L = AO Tan 8°

L = 1035 * Tan 8°

L = 1035 * 0.14054083470239144683811769343281

L = 1035 * 0.14054083470239144683811769343281

L = 145.46 Feet


BO = L/Tan 5°
BO =  145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet

Since AB = BO-AO
AB = 1662.6-1035

AB = 627.6 Ft.

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Answer:

y = x + 2

Step-by-step explanation:

y = mx + b

Point (0, 2) shows that the y-intercept is 2, so b = 2.

y = mx + 2

Now we find the slope using the 2 points, (0, 2) and (2, 4).

m = (4 - 2)/(2 - 0) = 1

y = x + 2

The bearing of C to A is 239⁰.

The bearing of C to A is calculated by finding the value of angle C using cosine rule since we know the value of all the sides of the triangle.

AB² = AC² + CB² - 2(AC)(CB) cosC

12.5² = 16.25² + 8.5² - 2(16.25 x 8.5) x cos C

156.25 = 336.3125 - 276.25cosC

276.25cosC = 180.06

cosC = 180.06/276.25

cos (C) = 0.6518

C = cos⁻(0.6518)

C = 49.3⁰

The value of angle A is calculated as follows;

Sin A/CB = Sin C/AB

sin A/8.5 = sin 49.3/12.5

sin A = 8.5 [sin 49.3/12.5]

sin A = 0.5157

A = sin⁻¹ (0.5157)

A = 31⁰

The bearing of C to A is calculated as;

= 270⁰ - 31⁰

= 239⁰

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The value of this country's net capital outflow is $200 billion.

We have,

The formula for net capital outflow (NCO) is:

NCO = Domestic Investment - Foreign Investment

Since the problem only gives us information about domestic investment, we need to use another formula to calculate foreign investment.

The formula for national saving (S) is:

S = GDP - Consumption Expenditures - Government Spending

We can rearrange this formula to solve for foreign investment:

Foreign Investment = GDP - Consumption Expenditures - Government Spending - Domestic Investment

Substituting the given values, we get:

Foreign Investment = $1000 billion - $650 billion - $250 billion - $150 billion

Foreign Investment = $1000 billion - $1050 billion

Foreign Investment = -$50 billion

The negative sign indicates that there is a net capital inflow (i.e., foreign investment is greater than domestic investment).

Therefore, the value of this country's net capital outflow is:

NCO = Domestic Investment - Foreign Investment

NCO = $150 billion - (-$50 billion)

NCO = $150 billion + $50 billion

NCO = $200 billion

Thus,

The value of this country's net capital outflow is $200 billion.

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No, It is not possible for 75% of the people surveyed at the park to purchase any two combination of the treats unless 14 people from the 'No preference group" decide to pick a treat. The two best frozen treat to pick will be Ice-cream sandwich and frozen fruit bar. With these two, 174 people are guaranteed to purchase the product.

To find the 75% chance of people surveyed buying any two combination we say

58 + 95 + 79 + 17 = 250

75% of 250 = 187.5 which is 188

We need to see if 188 of people will pick up a treat based on the survey

58 + 95 = 153 < 188

95 + 79 = 174 < 188  however, if  14 people from no preference group purchase, then, this is the best combination.

58 + 79 =  137 < 188

The answer provided is based on the question below as seen in the picture;

Is it possible to select a combination of two frozen treats so that 75% of the people surveyed would be able to purchase their favorite? If so, which two types of frozen treats should you select? Use words and numbers to justify your answer

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Answer:

A = 11.4 ft²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the height between the bases

here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²

The value of 3u - (2v-w) is  -6i + 25j.

We have,

u = -2i+9j, v = 2i- j, and w= -4i.

Now, 3u - (2v - w)

= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]

= -6i + 27j - [4i - 2j + 4i]

= -6i + 27j - 4i - 2j + 4i

= -6i + 25j

Thus, the value of 3u - (2v-w) is  -6i + 25j.

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The missing lengths and angles in the geometric systems are listed below:

Case 8: x = 60

Case 9: x = 48

Case 10: x = 5.535

Case 11: x = 5.665

Case 12: x = 9.103

Case 13: θ = 60°

Case 14: θ = 23.025°

In this problem we find two cases of geometric systems formed by triangles:

First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:

Case 8

100 / x = x / 36

x² = 3600

x = 60

Case 9

x / 36 = 64 / x

x² = 36 · 64

x = 48

Case 10

x = 17 · sin 19°

x = 5.535

Case 11

x = 11 · cos 59°

x = 5.665

Case 12

x = 13 · tan 35°

x = 9.103

Case 13

cos θ = 7 / 14

cos θ = 1 / 2

θ = 60°

Case 14

tan θ = 17 / 40

θ = 23.025°

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4 is the value of the variable x.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

We can simplify the left side of the equation by using the properties of exponents:

[tex](7q^{3x})^3 = 7^3 * (q^{3x})^3 = 343q^{9x}\\\\343q^{9x} = 343q^{36}\\\\q^{9x} = q^{36[/tex]

Now we can use the property that if [tex]a^b = a^c[/tex], then b = c. Therefore:

9x = 36

Dividing both sides by 9, we get:

x = 4

Therefore, the value of x that satisfies the equation is 4.

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The number of the different outfits do David have to choose is 768.

Here we will use the concept of Combinations,

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

Different outfits do Damian have to choose, will be;

⇒ 8C₁×4C₁×8C₁×3C₁

⇒ 8×4×8×3

⇒ 768

Hence, the number of the different outfits do David have to select is 768.

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Answer:

7 should go in the green blank.

10/x = x/7

There 1365 ways to choose four people from the group of fifteen.

b. There are 70 ways to choose  four Republicans from the group of eight Republicans.

C. The probability is about  0.0513, or  5.13%.

a.  To know the ways that four people can be selected from this group of fifteen is by:

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

Where:

n  = total number of items

r = is the number of items to be selected,

!  = the factorial of a number.

Putting in the values into the the formula:

15C4 = 15! / (4! x (15-4)!)

(15-4)! = 11!

15C4 = 1365

B.  Since:

n = 8

r = 4

Putting in the values into the the formula:

8C4 = 8! / (4!  x (8-4)!)

(8-4)! = 4!

8C4 = 70

c. The  Probability = Number of ways to choose four Republicans / Number of ways to choose four people

Hence  Probability = 70 / 1365

                             =  0.0513

Therefore, the probability that the selected group will consist of all Republicans is about  0.0513, or  5.13%.

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It will take approximately 8 days for the virus to grow from 180 to 260.

We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.

The proportion can be set up as follows;

(Change in value) / (Time taken) = (Change in value) / (Time taken)

Using the given information, we have;

(260 - 180) / x = (230 - 180) / 5

Simplifying the fractions on both sides of the equation, we get:

80 / x = 50 / 5

Cross-multiplying, we have;

80 × 5 = 50 × x

400 = 50x

Dividing both sides of the equation by 50, we get;

x = 400 / 50

x = 8

Therefore, it will take 8 days.

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Answer: 7.35 km = 7350000 mm

Step-by-step explanation:

Multiply km by 1000000

7.35 * 1000000 = 7350000 mm