Solve the system of linear equations by substitution.

y=4x
x+y=-10

The expression that represents the change that the cashier handed Michelle is $20 - $P.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

A collection of numbers, symbols, and operators (like + and ) that represent a value.

Examples: The phrase 2 + 3 is one.

We must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

So, Michelle purchased a notepad for P dollars with $20 cash.

Now, considering that Michelle paid P dollars for a notepad using a $20 bill.

As a result, the cashier gave Michelle $20 - $P.

Therefore, the expression that represents the change that the cashier handed Michelle is $20 - $P.

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Correct question:
Michelle used a $20 bill to pay for a notebook that only costs P dollars

How much change did Michelle receive from the cashier?

Write your answer as an expression.

1. The first statement is a universally quantified predicate that states for all x, either Px or Dx is true.

2. The second statement is the negation of Da, which means Da is false. From this, we can infer that Pa is true.

1. The first statement, (∀x)(Px v Dx), expresses that for all x, either Px or Dx is true. This means that every element x satisfies the condition of being either Px or Dx. It does not specify which elements satisfy Px or Dx, but it applies to all x universally.

2. The second statement, ~Da, indicates that Da is false. From the negation of Da, we can infer the truth of its negation, which is Pa. Therefore, we can conclude that Pa is true based on the given information.

By combining the conclusions from the two statements, we can deduce the following:

- (∀x)(Px v Dx) is true for all x.

- ~Da is true, which implies Pa is true.

However, there is no direct relation or implication between Pa and the statement GC / Hc. Without further information or logical connections, we cannot derive the conclusion Hc based solely on the given premises.

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We are approximately 17.88 meters from the base of the plateau.

An angle of elevation is the angle formed between a horizontal line and a line of sight that is directed upward to an object or point above the horizontal level. It is commonly used in trigonometry and geometry to determine the height or distance of an object, such as a building, tower, or mountain.

We can use trigonometry to solve this problem. Let's call the distance we are from the base of the plateau "x".

From the problem, we know that the height of the plateau (the opposite side) is 40m and the angle of elevation (the angle between the horizontal and the line of sight to the top of the plateau) is 20 degrees.

Using the tan function, we get,

tan(20) = 40/x

To solve for x, we can cross-multiply:

x * tan(20) = 40

Then, we can divide both sides by tan(20):

x = 40 / tan(20)

Using a calculator, we get:

x ≈ 17.8798 meters

Therefore, we are approximately 17.88 meters from the base of the plateau.

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Answer:

Approximately 50% of the Apple computers can be used for editing movies.

Step-by-step explanation:

With the information provided, you can use a rule of three to find the percent that represent the 7 computers that have the specialized movie editing software given that there are 14 Apple computers which represents 100%:

14 → 100%

7   →   x

x=(7*100)/14=50%

According to this, the answer is that approximately 50% of the Apple computers can be used for editing movies.

Based on the fact that the line passes through (-2, 7) and the slope, the value of a can be found to be  -1

To find the value of a, you first need to find the y-intercept to complete the linear equation which takes the form:

y = slope (x) + y-intercept

7 = -5(-2) + y-intercept

7 = 10 + y-intercept

y-intercept = 7 - 10

y-intercept = -3

The line equation is:

y = -5x - 3

The line y = -5x - 3 is passing through the point (a,2) is:

2 = -5(a) - 3

3 + 2 = -5a

a = 5 / -5

a = -1

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Answer:

the answer is  -1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

a+18=20-> a+18-18=20-18->a=2

Answer:

a = 2

Step-by-step explanation:

-18  -18 (Subtract 18 from both sides.)

a = 2 (Simplify)  

Using concepts of proportional relationships, it is found that the solution of the system is (0,0).

\(y = kx\)

In this problem, the system consists of two different proportional relationships, that is:

\(y = k_1x\)

\(y = k_2x\)

\(k_1 \neq k_2\)

Hence, equaling both equations for y, we have that:

\(k_1x = k_2x\)

Simplifying by x:

\(k_1 = k_2\)

Which is never true, hence, the only solution is (0,0).

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1. The balloon's initial temperature was ____ °C.

2. The temperature of the oil is ____ °C.

1. To find the balloon's initial temperature, we can use the combined gas law, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature. Given that the volume changes to 76.4% of its initial volume and the final temperature is -80.0 °C, we can solve for the initial temperature. First, we convert the volume change to a decimal by dividing 76.4% by 100, giving us 0.764. Plugging in the values into the combined gas law equation, we can rearrange it to solve for the initial temperature.

2. To determine the temperature of the oil, we can use the ideal gas law, which states that the pressure times the volume divided by the temperature is equal to the gas constant times the number of moles. Since the volume remains constant and we are given the initial and final pressures, we can solve for the temperature. By plugging in the values into the ideal gas law equation and solving for the temperature, we can find the temperature of the oil in °C.

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Slope=

Equation in point slope form

Answer:

\(y=-4x+1\)

Step-by-step explanation:

We have been given two points on the line, so:

\(\textsf{let}\:(x_1,y_1)=(-1,5)\)

\(\textsf{let}\:(x_2,y_2)=(1,-3)\)

Calculate the slope using the slope formula:

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-3-5}{1-(-1)}=-4\)

From inspection of the graph, it appears that the y-intercept (where the line crosses the y-axis) is at (0, 1).  However, just to be sure, use the point-slope form of linear equation.

Point-slope form of linear equation:  \(y-y_1=m(x-x_1)\)

(where m is the slope and (x₁, y₁) is a point on the line)

\(\implies y-5=-4(x-(-1))\)

\(\implies y-5=-4x-4\)

\(\implies y=-4x+1\)

Therefore, the equation of the line in slope-intercept form is:

\(y=-4+1\)

The volume of the rectangular pyramid with a length of 8m, width of 5m and height of 12m is 160 m³.

A rectangular pyramid is simply a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

From the diagram:

Length l = 8 meters

Width w = 5 meters

Height h = 12 meters

Volume V = ?

Plug the given values into the above formula and solve for the volume:

V = (1/3) × l × w × h

V = (1/3) × 8 × 5 × 12

V = 160 m³

Therefore, the volume of the pyramid is 160 m³.

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Answer: 14000

Step-by-step explanation:

From the question, the first thing is to first calculate the simple interest (S.I). This will be:

S.I = (principal × rate × time)/100

where principal = 10,000

rate = 4%

time = 10 years

Simple interest = (10,000 × 4 × 10)/100

= 400000/100

= 4000

The total value after 10 years will be th addition of the amount invested and the interest. This will be:

= 10,000 + 4000

= 14000

Answer:

Step-by-step explanation:

I just tried numbers

2     1

2     6           first grid, so 2nd column is 7

or

1  2

3 5        also 7

The speed of the 10 g bullet was approximately 1.732 m/s. This can be answered by the concept of conservation of momentum.

To find the speed of the 10 g bullet, we can use the conservation of momentum and the potential energy stored in the spring. The initial momentum of the bullet-block system is equal to the final momentum after the bullet embeds itself in the block, and the potential energy in the spring equals the initial kinetic energy of the bullet-block system.

1. Convert the bullet mass to kg: 10 g = 0.01 kg
2. Convert the compression of the spring to meters: 45 cm = 0.45 m

First, find the potential energy stored in the spring when it is compressed by 0.45 m:
PE_spring = 0.5 × k × x²
PE_spring = 0.5 × 55 N/m × (0.45 m)²
PE_spring = 6.06875 J

Now, equate the potential energy to the initial kinetic energy of the bullet-block system:
KE_initial = PE_spring

Since KE = 0.5 × m × v², we can write:
0.5 × (0.01 kg + 2.0 kg) × v² = 6.06875 J

Solve for v (bullet's speed):
v^2 = (6.06875 J) / (0.5 × (0.01 kg + 2.0 kg))
v^2 = 2.9971
v = 1.732 m/s

So, the speed of the 10 g bullet was approximately 1.732 m/s.

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Answer:

b

Step-by-step explanation:

The standard deviation is 4 The variance is equal to 16.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Answer:

if im correct, x = 64

Step-by-step explanation:

since a triangle's angles must sum to 180°, i subtracted 52 from 180 which gave me 128. then, i divided 128 in two so that it could equal to both of the sides of the triangle.  128/2 = 64

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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Aymptotes exist when a function gets very close to a value but never reaches it, for vertical asymptotes we draw vertical lines, in this case, at x equals 2, for horizontal asymptotes draw a horizontal line, in this case at y equals 1.

Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

\(\sqrt{(10-4)^2+(9-3)^2}\)

√(36 + 36)

= 8.485

Part c:

Base = \(\sqrt{(6-2)^2+(1-5)^2}\)

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

Two vectors in ℝ⁴ are orthogonal if their dot product is zero.

Two vectors in ℝ⁴ are said to be orthogonal if their dot product is zero. The dot product of two vectors measures the similarity or alignment between them. When the dot product is zero, it signifies that the vectors are perpendicular to each other and do not share any common direction.

Geometrically, orthogonality between two vectors in ℝ⁴ means that they are linearly independent and span different directions in four-dimensional space. It implies that there is no projection of one vector onto the other, and they are completely perpendicular to each other.

The concept of orthogonality is fundamental in many areas of mathematics, physics, and engineering. In linear algebra, orthogonal vectors play a crucial role in defining orthogonal bases and orthogonal projections. They also have applications in vector calculus, where they are used to define gradients and normal vectors. In physics, orthogonal vectors are relevant in studying forces, velocities, and geometric transformations. Overall, understanding orthogonality is essential for analyzing vector relationships and geometric properties in multi-dimensional spaces.

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Answer:

10cm

Step-by-step explanation:

5x2x1=10

Answer:

x=-29

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−0.64x+0.44x=5.8

(−0.64x+0.44x)=5.8(Combine Like Terms)

−0.2x=5.8

−0.2x=5.8

Step 2: Divide both sides by -0.2.

-0.2x/-0.2=5.8/-0.2

x=-29

Answer:

i believe the answer is 0.85

Step-by-step explanation:

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. hope this helps

Answer:

45% chance that a homeowner is on the community watch.

Step-by-step explanation:

Answer:

approximately 0.4084

Step-by-step explanation:

The average time allowed the 15 selected students to be 3.06hours

What is Average?

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

With a sample size of 15 and a p value of 0.04

From binomial probability, (nCx)px(1p) is where the application of binomial probability originates from (n-x)

1 - p = 0.96

a) P(x=1) is the probability that precisely 1 received a special accommodation.

= 15C1 x (0.04)^1 x (0.96) ^14 = 0.3388

b) P(x >=1) = 1 - P(x = 0) is the likelihood that at least 1 person received a special accommodation.

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 = 0.4579

c) the likelihood that two people at least obtained special accommodations

= [P(x = 0) + P(x = 1)] - [P(x>=2) = P(x>=2)

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 + 15C1 x (0.04)^1 x (0.96)^14]

= 1 - [0.5420 + 0.3388] .3388]

= 0.1192

d) likelihood that the proportion of the 15 who received a special accommodation is within two standard deviations of the proportion you would anticipate receiving one;

= P( x<=1) = P( x= 0) = 0.5429

e) expected average time = 0.04 x 4.5 + 0.96 x 3 = 3.06hours

Hence, The average time allowed the 15 selected students to be 3.06hours

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Answer:

see below

Step-by-step explanation:

Vertical lines have the same x coordinates

The slope is given by

m = (y2-y1)/(x2-x1)

The x values are the same

m = (y2-y1)/(x-x)

m = (y2-y1)/ 0

Any number, except 0, divided by 0 is undefined

After solving, the equivalent resistance of the given circuit is 1.6Ω.

The voltage across the element in a parallel circuit is the same, but the current is divided equally among the parallel branches.

The total current is distributed in three branches that are I1, I2 and I3 and voltages for these branches are same.

The expression for the equivalent resistance of the circuit is given by,

1/Req = 1/R1+1/R2+1/R3

Substitute 3.0Ω for R1 , 6.0Ω for R2 and 9.0Ω for R3 in the above equation,

1/Req = 1/3.0 Ω +1/6.0 Ω +1/9.0 Ω

1/Req = {(6.0 Ω)(9.0 Ω)+ (3.0 Ω) (9.0 Ω)+ (3.0 Ω)(6.0 Ω)}/{(3.0 Ω)(6.0 Ω)(9.0 Ω)}

1/Req = 54.0Ω^2+27.0Ω^2+18.0Ω^2/162Ω^3

1/Req = 99/162 Ω

Rearrange the above for equivalent resistance,

Req = 162.0/99Ω

Req = 1.6

The equivalent resistance of the given circuit is 1.6Ω.

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The right question is:

A circuit is built based on this circuit diagram. What is the equivalent resistance of the circuit?

a. 0.61 Ω

b. 1.6 Ω

c. 7.5 Ω

d. 18 Ω