X - y = 4
X + y =8

The x-coordinate of the solution to the system shown is

1. 12
2. 4
3. 6
4. 2

Answer: 148cm²

Step-by-step explanation:

The volume of the cuboid is the length, height, and width multiplied together. Since the problem gives us the volume, we can set an equation.

\(l*w*h=120 cm^3\)

Since the area of the base of 30cm², we can get another equation.

\(l*w=30cm^2\)

We can plug in our equations.

\(30cm^2*h=120cm^3\)          [divide both sides by 30cm²]

\(h=4cm\)

Now, we know the height of the cuboid.

Since we aren't given a specific length and width, it can be any of the combinations that give 30 cm² when multiplied.

We can have 1,30 or 2,15 or 3,10 or 5,6.

I will work out 5,6 with l=5 and w=6.

The surface area of a cuboid is \(2(lw+wh+lh)\).

\(2(30+24+20)=2(74)=148cm^2\)

This is one possible answer. There are multiple ones with the pair choices above.

False. The metric system is a decimalized system of measurement, but it is not used exclusively in the United States.

In fact, the United States primarily uses the U.S. customary system, while the metric system is widely used in most other countries around the world.

Most nations throughout the world use the metric system, a decimal-based measurement system that is universally recognised. It offers a standardised method for gauging temperature, length, mass, and other physical attributes. The metre (for length), kilogramme (for mass), second (for time), ampere (for electric current), kelvin (for temperature), mole (for amount of material), and candela (for luminous intensity) are the basic units of the metric system. Because the metric system is based on powers of 10, converting between units is simple. Global communication and trade are made easier by its promotion of usability, consistency, and compatibility across scientific, industrial, and everyday uses.

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Answer:

1/14

Step-by-step explanation:

There is only 1 common multiple of 4 and 6 between 1 and 14.

So the probability is:

\(P = \frac{1}{14}\)

Answer:

5/14

Step-by-step explanation:

the multiples of 6 are 6 and 12. the multiples of 4 are 4,8,12(but its the same as 4 so we don't add that one), and 14. Add 2 and 3 and you get 5.

The total is 14 so it ends up being a 5/14 chance.

Answer:

good luck with this, i have got a good mark in this lesson back then and i would gladly like to help you miss gilr

Step-by-step explanation:

Option D is representing the inequality 2(x - 3) - 5x < x-2​ on the number line.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

Given that the inequality is 2(x - 3) - 5x < x-2​. The inequality will be solved as,

2(x - 3) - 5x < x-2​

2x - 6 - 5x < x - 2

-3x - 6 < x - 2

-3x - x < 6 - 2

-4x < 4

x > -1

The number line of the inequality is attached with the answer below.

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The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Answer:

\((x+3)^{2} +(y+5)^{2} =16\)

Step-by-step explanation:

the general equation of a circle is

\((x-h)^{2} + (y-k)^{2} =r^{2}\)

with (h,k) being the centre of the circle and r the radius

The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:

y = (1/4p)(x - h)^2 + k

where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.

Comparing the given equation to the standard form, we have:

5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2

From this, we can determine that the vertex is at the origin (0, 0).

To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.

Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.

In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

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The speed of the river is ...

.. (40 m/min)*(60 min/h)*((1 km)/(1000 m)) = 2.4 km/h

Here, we have,

speed = distance/time

Let d represent the distance between the ports. Let s represent the speed of the ship.

Downstream, we have

.. s +2.4 = d/4.5

.. s = d/4.5 -2.4

Upstream, we have

.. s -2.4 = d/6/3

.. s = d/6.3 +2.4

Now, we have the speed of the ship represented two ways. We assume the speed of the ship doesn't vary. so these are equal.

.. (d/6.3) +2.4 = (d/4.5) -2.4

.. 4.8 = d(1/4.5 -1/6.3) = d(4/63) . . . . . rearrange and simplify

.. 75.6 = d . . . . . . . . . . . . . . . . . . . . . . .multiply by 63/4

The distance between the two ports is 75.6 km.

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The number of hours each 12 inches candle will last, found using the linear equation  obtained from Mason's measurement  is 24 hours

A linear function is a relationship between  two variables, that when plotted produces a straight line graph.

The initial length of the candle = 12 inches

Number of hours the candle has been lit, 1 1/2 hour = 1.5 hour

4 1/2 hour = 4.5 hour

11 1/4 inches = 11.25 inches

9 3/4 inches = 9.75 inches

The ordered pair of the height of the candle and height are;

(1.5, 11.25), (4.5, 9.75)

The slope of the line that represent the height as a function of time is therefore;

(9.75 -  11.25)/(4.5 - 1.5) = -0.5

The equation of the line in point-slope form is therefore;

y - 11.25 = (-0.5) × (x - 1.5) = -0.5·x + 0.75

y - 11.25 = -0.5·x + 0.75

y   = -0.5·x + 0.75  + 11.25

y = -0.5·x + 12

The above equation  produces the height y after a time x

When the candle finishes, the  height is zero, therefore;

y = 0 = -0.5·x + 12

0.5·x = 12

x = 12 ÷ 0.5 = 24

The number of hours the candle will last, x = 24 hours

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The margin of error of the 98.4% confidence interval for snapdragons  is 3.71.

The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.

The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:

`Margin of error z*(standard deviation/√n`).

The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:

`standard deviation = (range/4) * √n / 1.96`

Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`

Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`

Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`

Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`

Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`

Now that we know the sample size, we can calculate the standard error of the mean:

`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.

The margin of error is `1.96 * 1.89 = 3.71`.

The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.

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Answer:

0.3636363636

Step-by-step explanation:

Answer:

I think it's 2/9 goodluck:)!!

Answer:

a° = 41°

b° = 139°

Step-by-step explanation:

a° = ∠DB

a° = 41°  

b° + 41° = 180°

b° = 180° - 41°

b° = 139

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer:3.6%

Step-by-step explanation:

The value of p when a = 16, b = 9 and c = 13 is 38

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

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Given that:

p = a + b + c

Substituting the values of a, b and c:

p = 16 + 9 + 13

p = 38

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Answer:

6 9 2 3

Step-by-step explanation:

thats the domain

Answer:

{6, 9, 2 , 3, 6}

Step-by-step explanation:

domains are usually listed in the left column

The length of line segment AB in the triangle using the midsegment theorem is 64.

The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."

From the diagram:

Midsegment = 3x + 5

Third side = 7x + 1

First, we solve for x, using the midsegment theorem:

( 3x + 5 ) = 1/2 × ( 7x + 1 )

Multiply both sides by 2:

2( 3x + 5 ) = ( 7x + 1 )

6x + 10 = 7x + 1

Collect and add like terms:

7x - 6x = 10 - 1

x = 10 - 1

x = 9

Now, we solve for line AB:

Line AB = 7x + 1

Plug in x = 9

Line AB = 7(9) + 1

Line AB = 63 + 1

Line AB = 64

Therefore, the line segment AB is 64.

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Answer:

no it's equal to 3/2 because 2 negatives equal a positive number

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

No, it's not equivalent

Step-by-step explanation:

\(-(\frac{3}{2} ) = 1\frac{1}{2\\}\)

\(-\frac{3}{2} = -1\frac{1}{2}\)

1) ABCD is a parallelogram (given)

2) \(\overline{BC} \parallel \overline{AD}, \overline{AB} \parallel \overline{CD}\) (opposite sides of a parallelogram are parallel)

3) \(\angle BCA \cong \angle CAD, \angle BAC \cong \angle ACD\) (alternate interior angles theorem)

4) \(\angle A \cong \angle C, \angle B \cong \angle D\) (congruent angles added to congruent angles form congruent angles)

Given the equation:

-39 = 4w + 7(w-3)

Let's solve the equation for w.

To solve take the following steps.

• Step 1.

Apply distributive property

• Step 2.

Combine like terms

• Step 3.

Add 21 to both sides

Step 4.

Divide both sides by 11

ANSWER:

w = -1.63

Answer:

-1

3

Step-by-step explanation:

Answer:

1. -1, 3

2. 4 could be a multiplicity of the root at x = 1.

The number of stores located in California at the end of 2016 was 16, so the answer is (d) 16.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to represent part of a whole or a proportion of a quantity.

At the end of 2010, the business had 140 stores in the United States.

By the end of 2016, the number of stores in the United States had increased by 60%. To find out how many stores there were at the end of 2016, we need to add 60% of the original number of stores to 140:

Number of stores at end of 2016 = 140 + 0.6*140 = 140 + 84 = 224

So there were 224 stores in the United States at the end of 2016.

If 1/14 of these stores were located in California, we can calculate the number of stores located in California as follows:

Number of stores in California = (1/14) * 224 = 16

Therefore, the number of stores located in California at the end of 2016 was 16, so the answer is (d) 16.

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Answer:

Mean: 17.6 Median: 18 Mode: N/A Range: 27

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

From 3 to 10th term is 7 d's       ( d = common difference)

3 - 7d = third term

3 - 7(3)  =  -18

According to the question we have  the 99% UCB on the mean time of the race is 223.

The formula for finding the upper confidence bound (UCB) is UCB = Mean + (Zα/2)(σ/√n), where Mean is the sample mean, Zα/2 is the z-score for the desired level of confidence, σ is the population standard deviation (which is not given, so we'll use the sample standard deviation instead), and n is the sample size.

We are given the sample of times as follows:137, 143, 153, 162, 168, 176, 190, 192, 196, 203, 218, 223, 236, 243, 252, 269, 271, 276, 283, 287.

We'll need to calculate the sample mean and standard deviation before we can find the UCB. Using a calculator, we get: mean ≈ 207.65s ≈ 48.41 Next, we'll use a table or calculator to find the z-score for a 99% confidence interval, which is Zα/2 = 2.576.

Now we can plug in the values we know to get the UCB:UCB = mean + (Zα/2)(σ/√n)UCB ≈ 207.65 + (2.576)(48.41/√20)UCB ≈ 223.02 .Therefore, the 99% UCB on the mean time of the race is 223.

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Answer:

28.8 yd^2

Step-by-step explanation:

Area of triangle = (1/2) · b · h

Base = 9 yd

Height = 6.4 yd

We take

(1/2) · 9 · 6.4 = 28.8 yd^2

So, the area of the triangle is 28.8 yd^2

The solution to the equation is x = -2, -1.46, -1, x = 5.46

From the question, we have the following parameters that can be used in our computation:

0 = x^{5}+x^{4}-20x^{3}-68x^{2}-80x-32

Express properly

So, we have

x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0

Next, we plot the graph of x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0 to determine the solution graphically

See attachment for graph

From the graph, we have

x = -2, -1.46, -1, x = 5.46

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