What value of x makes this equation true?

-2x + 3 = -15

Answer:

212.

Step-by-step explanation:

Given: 3m^2 + 2p^2 - 15

When m = 3 and p = 10

Substituting the values

= 3(3)^2 + 2(10)^2 - 15

By further calculation

= 3(9) + 2(100) - 15

So we get

= 27 + 200 - 15

= 212

Therefore, the value of the expression is 212.

Answer:

No, there is no change in the relationship. The slopes of AC and DE continue to be equal, and the length of DE remains half of the length of AC.

Step-by-step explanation:

The answer is from Plato. I hope this helps :)

Answer:

No, the connection has not changed. The slopes of AC and DE are still equal, and the length of DE is still half that of AC.

Step-by-step explanation:

From Plato but in my own words! :)

The graph that represents the solution for the open sentence 3|p|−5<7 is:

a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables

: the collection of all points whose coordinates satisfy a given relation (such as a function)

: a collection of vertices and edges that join pairs of vertices

Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.

Image with alt text: Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.

In this graph, the open points at -4 and 4 indicate that the values of p that make the inequality true do not include -4.

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Answer:

y = 2x + 2

Step-by-step explanation:

Answer:

5(5r - 6)

Step-by-step explanation:

25r - 30

we can factor out a 5 since 25 and 30 are both multiples of 5

so we get 5(5r - 6)

hope this helps!

ps i love ur pfp

Answer:

It's the solution for the first one, but not the second one

Step-by-step explanation:

(3,8) (x,y)

The first one works, because it does equal 20

4*3= 12+8= 20

The second one does not work, because it equals 7 and not 8

3*3= 9-2= 7

Answer:

123

Step-by-step explanation:

65.573 --> 66
56.65 --> 57

66 + 57 = 123

To solve the given differential equation, we need to first find the general solution of the equation and then use the initial conditions to determine the particular solution.

Let's begin by assuming a solution of the form v = f(t) + g(t), where f(t) satisfies the homogeneous part of the differential equation and g(t) satisfies the non-homogeneous part.

The homogeneous part of the differential equation is given by d²v/dt² + 2dv/dt + v = 0, which has characteristic equation r² + 2r + 1 = 0. Solving this equation, we get r = -1 (repeated root). Therefore, the homogeneous solution is given by f(t) = (C₁ + C₂t)e^{-t}, where C₁ and C₂ are constants determined by the initial conditions.

Next, we need to find the particular solution for the non-homogeneous part of the equation. Since the right-hand side is a constant, we assume a constant solution of the form g(t) = a. Substituting this into the differential equation, we get 2a + a = 3, which gives us a = 1.

Therefore, the general solution is v(t) = (C₁ + C₂t)e^{-t} + 1.

Using the initial condition y(0) = 6, we get C₁ + C₂ = 6. Using the initial condition y'(0) = 3, we get -C₁ + C₂ - 1 = 3. Solving these equations simultaneously, we get C₁ = 5 and C₂ = 1.

Therefore, the particular solution that satisfies the initial conditions is v(t) = (5 + t)e^{-t} + 1.

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We write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

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Answer:

C

Step-by-step explanation:

parallel means no matter how far you stretch it the 2 lines will never touch and these 2 lines won’t EF and CD

Hopes this helps please mark brainliest

Answer:

The value of m2 is 1/7(m1 + 54)

Step-by-step explanation:

Answer:

  63.4

Step-by-step explanation:

x° is an acute angle in a right triangle with the opposite and adjacent sides given. That means the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(x°) = 18/9 = 2

The value of the angle is found using the inverse tangent function:

  x° = arctan(2) ≈ 63.4°

  x = 63.4 . . . . . . . rounded to tenths

The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Answer:

Step-by-step explanation:

1) nth therm = dn + (a - d)

-10n + (11+10)

-10n + 21

t11 = -110 + 21 = -89

2) nth therm = 3n + (-66 - 3)

3n - 69

t16 = 48 - 69 = -21

The slope and y-intercept of the line that passes through the points (-2,6) and (4,-3) are - 3 / 2 and 3 respectively.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the slope of the line is the change in the independent variable with respect to the change in the dependent variable.

Therefore,

using (-2, 6)(4, -3)

m = slope = -3 - 6 / 4 + 2

slope = - 9 / 6

slope = - 3 / 2

Therefore, the y-intercept of the line can be found using (4, -3)

-3 = - 3 / 2(4) + b

-3 = -6 + b

b = -3 + 6

b = 3

Therefore, the y-intercept is 3

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Given that the household is located in the northeast, there is a 0.230 probability that the randomly chosen US household makes more than $75,000.

Given info;

19.1% of US households, according to the US Census Bureau, are in the Northeast. Additionally, 4.4% of households in the US earn $75,000 or more annually and are situated in the northeast.

let, A represents the U.S. households in the Northeast.

     B represents the U.S. households earning $75,000 or more.

To determine the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast.

P(A) = 19.1% = 0.191

P(A ∩ B) = 4.4% = 0.044

P(B I A) = P(A ∩ B) / P(A)

            = 0.044 / 0.191

            = 0.230

Hence, the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast is 0.230.

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(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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The work needed to lift both chain and anvil to the platform is 31348 J (approx).

The given data in the question are: A chain with a density of 1.6 kg/m is 20m long

An anvil weighing 70 kg and 0.25m in height is attached to the end of the chain

The platform is 25 meters above the ground

.From the above data, the following information can be inferred :

The total height that the chain and anvil have to be lifted is 20m + 25m = 45m

Now, the potential energy of the chain and anvil when it is at the ground level is given by :

Potential Energy at ground level = Mass × gravity × height

= (1.6 kg/m) × (20 m) × (9.8 m/s²) × (0.5)(70 kg) × (9.8 m/s²) × (20.125 m)

= 31348 J (approx)

Therefore, the work needed to lift both chain and anvil to the platform is 31348 J (approx).

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Answer:

5

Step-by-step explanation:

Because, you have to divide the $20 by the $100

The complete solution for every value of t is:

\(a \times b(t) =\) 0, for t < 1

2(e^(-t/2) - e^(-1/2)), for 1 ≤ t < 2

2(e^(-1/2) - 1), for t ≥ 2

To compute the convolution between the given functions, a(t) = e^(-t/2)u(t-1) and b(t) = rect(t-1), we can use the formula for convolution:

\(a \times b(t)\) = ∫[0 to t] a(τ)b(t-τ) dτ

First, let's break down the problem step by step:

Determine the limits of integration: Since both functions have a support starting from t = 1, the limits of integration will be from 1 to t.

Rewrite the functions within the limits of integration:

a(τ) = e^(-τ/2)u(τ-1)

b(t-τ) = rect(t-τ-1)

Apply the convolution formula:

\(a \times b(t) = \int[1 to t]\) e^(-τ/2)u(τ-1)rect(t-τ-1) dτ

Now, let's evaluate the integral for different intervals of t:

For t < 1:

The convolution will be 0 since both functions have a support starting from t = 1.

For 1 ≤ t < 2:

The integral can be simplified as:

\(a \times b(t)\) = ∫[1 to t] e^(-τ/2)rect(t-τ-1) dτ

= ∫[1 to t] e^(-τ/2) dτ

= 2(e^(-t/2) - e^(-1/2))

For t ≥ 2:

The integral can be simplified as:

\(a \times b(t)\) = ∫[1 to 2] e^(-τ/2)rect(t-τ-1) dτ + ∫[2 to t] e^(-τ/2)rect(t-τ-1) dτ

= ∫[1 to 2] e^(-τ/2) dτ + 0

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

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Answer:

The equation in slope-intercept form is \(y=\frac{1}{14}x\).

Step-by-step explanation:

Given points are;

(-14, -1 ) and (0,0)

Slope of a line is given by;

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{0-(-1)}{0-(-14)}\)

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

General equation in slope intercept form is,

y = mx + b

Putting (-14, -1) and m = 1/14 in Equation to find b

-1 = \(\frac{1}{14}(-14) +b \\\)

-1 = -1 + b

b = -1 + 1

b = 0

As y-intercept is 0, the equation in slope-intercept form would be

\(y = \frac{1}{14}x\)

Hence,

The equation in slope-intercept form is \(y=\frac{1}{14}x\).

Using the conversion from microgram to milligram, we get, 10mcg is equal to 0.01mg.

1 mcg (microgram) is equal to 0.001 mg (milligrams). Therefore, to convert 10mcg to mg, we simply need to multiply 10 by 0.001:

10 mcg * 0.001 mg/mcg = 0.01 mg

So, 10mcg is equal to 0.01mg.

To explain further, the prefix "micro" means one millionth (1/1,000,000), while the prefix "milli" means one thousandth (1/1,000). Therefore, to convert a value from micrograms to milligrams, we need to divide the value by 1000 (or multiply by 0.001), because there are 1000 micrograms in a milligram. It is important to use the correct units when working with medication dosages, as small differences in dose can have significant effects on the patient's health.

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The total amount of income Xander earns from selling y books algebraically is C = 25000 + xy + 0.08y.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.

In this situation, Xander writes math textbooks that sell x dollars each, he received a bonus of $25,000 for signing a contract, and he receives 8% commission on each book sale.

c = total amount

y = number of books.

The total amount of income will be:

= 25000 + (x × y) + (8% × y)

= 25000 + xy + (0.08 × y)

C = 25000 + xy + 0.08y

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The given system of linear equations consists of four equations with four variables: x, y, z, and w. To solve the system, we can use various methods, such as Gaussian elimination or matrix operations.

By performing row operations, we can reduce the system to its row-echelon form or solve it directly to find the values of x, y, z, and w. We will solve the system of linear equations using the method of Gaussian elimination. The augmented matrix representation of the system is:

[1 1 2 -1 | -2]

[0 3 1 2 | 2]

[1 1 0 3 | 2]

[-3 0 1 2 | 5]

First, we'll perform row operations to transform the matrix into the row-echelon form:

R2 = R2 - 3R1

R3 = R3 - R1

R4 = R4 + 3R1

The resulting matrix after these operations is:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | 5]

Next, we'll perform additional row operations to further simplify the matrix:

R4 = R4 - 3R2

The matrix now becomes:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | -19]

Finally, we'll perform the last row operation:

R3 = R3 + 2R2

The matrix is now in row-echelon form:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 0 14 | 20]

[0 3 1 2 | -19]

From this row-echelon form, we can solve for the variables. Starting from the bottom row, we obtain:

3w + z + 2w = -19, which simplifies to 5w + z = -19.

Next, we have 0x + 0y - 5z + 5w = 8, which simplifies to -5z + 5w = 8.

Lastly, x + y + 2z - w = -2.

At this point, we have three equations with three variables: x, y, and z. By solving this simplified system, we can find the values of x, y, and z.

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Answer: 1 quarter or 0.25 cents.

Step-by-step explanation: According to the illustration shown, we can infer that the coin we are looking for is for 1 value. So, if we subtract the amount shown (total) from the other coins (pennies in this case), 0.27 - 0.02 = 0.25 which is equivalent to the coin of the quarter (worth $0.25 USD) So, the blanks would look like this:

1 quarters

0 dimes

0 nickles

2 pennies

I hope this helped!

Answer:

18.2 m = height of the building

Step-by-step explanation:

Let x = the distance from the top of the girl's head to the top of the building

tan 45 = x/16

x = 16 tan 45

x = 16 m

16 + 2.2 = 18.2 m = height of the building

Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.

The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

A line segment that divides an angle into two equal parts is referred to as an angle bisector.

From the proof given, we know that;

m∠DEK = 2(m∠DEF)

m∠DEK = 2(44) = 88°

With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.

Then, KF = 1/2(DK) = 1/2(16) = 8.

The complete proof is show in the image attached below.

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The solution is, 76,000 mg chlorine is in the pool.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The pool has 2.5 milligrams of chlorine per liter of water.

There are 8000 gallons of water in the swimming pool.

we know,

1 gallon = 3.785 liters

Water in pool = 8000 x 3.785

Water in pool = 30,280 liters

so, we get,

Chlorine dosage = 2.5 mg / liter

Chlorine = 2.5 x 30,280

Chlorine = 75,700 mg

To the nearest thousand milligram:

Chlorine = 76,000 mg

Hence, The solution is, 76,000 mg chlorine is in the pool.

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Answer:

14x-55

Step-by-step explanation:

(6x+8x)+(-5-50)

Answer: 14x - 55

Step-by-step explanation:

Combine like terms

6x+8x=14x

-5+-50=-55

So the answer would be 14x-55