Your friends have locked themselves out of the house, and they need yourhelp to get back in.

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer: 30 units^2

Step-by-step explanation:

base of ABC = AC = 15 units

Height of ABC = 4 units

Area of ABC = 1/2 (base) (height) = 1/2 (15 units) (4 units) = 30 units^2

The area of the triangle is 30 units^2. the height of the triangle is 4 units.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle can be calulated by the herons formula

base of ABC = AC = 15 units

Height of ABC = 4 units

Semi perimeter s = 5 + 12.65 + 15/ 2 = 32.65 / 2 = 16.32

Herons formula

\(Area = \sqrt{s(s-a) (s-b)(s-c)}\\\\Area = \sqrt{16.32(16.32-5) (16.32-12.65)(16.32-15)}\\\\Area = \sqrt{16.32(11.32) (3.675)(1.32)}\\\\Area = 29.93\)

Area of ABC is 30 units^2 approximately.

Height of the triangle = 2( area) / base

                                    = 2( 30) / 15

                                    = 4.

WE can see that

Area of ABC = 1/2 (base) (height)

                     = 1/2 (15 units) (4 units)

                      = 30 units^2

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Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Since the value of y varies directly with x, the value of x when y equals 9 is 9/13

Given the following data:

x = 195

y = 15

To find the value of x when y = 9:

This is a direction proportion exercise and you're required to solve for the value of x when the value of y is equal to 9.

First of all, we would determine the constant of proportionality (k) for the mathematical expression.

y = kx

15 = 195k

k = 13

Now, we can find x:

y = kx

9 = 13 x

x = 9/13

Therefore, the value of x when y equals 9 is 9/13

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complete question:

The value of y varies directly with x. If x = 195 when y = 15, what is the value of x when y = 9?

Answer:

140000000

Step-by-step explanation:

Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality.

The nine basic characteristics of equality are addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root. Real number-based algebraic problems can be resolved with the aid of the addition, subtraction, multiplication, and division properties of equality.

When you add the same amount to both sides of an equation that has two equal expressions, the equation will stay equal. Finding the value of the variable that makes an equation true is the process of solving an equation.

The Subtraction Property of Equality asserts that when an equal value is subtracted from or removed from two equal objects, a new equal quantity is created. A mathematical statement with two equivalent sides is denoted by an equal sign. The formula for the subtraction property is if a = b, then a - c = b - c.

According to the equality's multiplication property, an equation's two sides stay equal when multiplied by the same amount.

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Answer:

120 I think is the answer not sure tho sorry if u get it wrong

Step-by-step explanation:

the transformation ABC is not similar to A”B”C”. hence the statement is false.

We say the statement is false because the ratios of the grid squares are not similar.

We notice that the first triangle is up to over 3 and the other triangle is up 4 over 4 so in order for them to be similar the first triangle would have to be up 3 over 3.

A transformation is described as  a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

#complete question:

Please help this is due today and I’m so stressed!I will mark Branliest!!!

Tanya performs two transformations on ABC to form A"B"C" as shown on the coordinate grid below.

True or False:ABC is similar to A”B”C”?

Answer:5

Step-by-step explanation:

Answer:

m<C = 66°

Step-by-step explanation:

Perpendicular bisector, AB divides angle CAD into two equal parts. Therefore:

(5x + 9)° = (7x + 3)°

Solve for x

5x + 9 = 7x + 3

Collect like terms

5x - 7x = -9 + 3

-2x = -6

Divide both sides by -2

x = 3

✔️m<C + m<CBA + m<BAC = 180° (sum of triangle)

m<C + 90° + (7x + 3)° = 180 (substitution)

Plug in the value of x and solve

m<C + 90 + 7(3) + 3 = 180

m<C + 90 + 21 + 3 = 180

m<C + 114 = 180

m<C = 180 - 114 (Subtraction property of equality)

m<C = 66°

Answer:

Step-by-step explanation:

The equation

Given:-

To find:-

The given vectors are parallel, orthogonal or neither.

So now we check, the given vectors is orthogonal or not.

The given vectors are not orthogonal because if the vectors are orthogonal the dot product should be zero.

So now we check, the given vectors is parallel or not,

Also,

So now,

So we get the value of theta as 90 degree. So the given vectors are Parallel.

It looks like we're given

z₁ = 1 - (2 - √3) i

z₂ = -2 - 2i

and we want to find

(i z₁ z₂)²

z₁ lies in the fourth quadrant of the complex plane, so

|z₁| = √(1² + (-2 + √3)²) = 2√(2 - √3)

arg(z₁) = arctan(-2 + √3)

while z₂ lies in the third quadrant, so

|z₂| = √((-2)² + (-2)²) = 2√2

arg(z₂) = arctan(-2 / -2) - π = arctan(1) - π = -3π/4

so their polar forms are

z₁ = 2√(2 - √3) exp(i arctan(-2 + √3))

z₂ = 2√2 exp(-i 3π/4)

Before we continue, we can actually simplify the argument to z₁. Let θ = arg(z₁). From its polar form, it's evident that

2√(2 - √3) cos(θ) = 1

which reduces to

cos(θ) = 1 / (2√(2 - √3))

Recall the half-angle identity,

cos²(x) = (1 + cos(2x))/2

By taking squares on both sides, we have

cos²(θ) = 1 / (8 - 4√3)

(1 + cos(2θ))/2 = 1 / (8 - 4√3)

1 + cos(2θ) = 1 / (4 - 2√3)

cos(2θ) = (-3 + 2√3) / (4 - 2√3)

cos(2θ) = √3/2

2θ = arccos(√3/2) + 2nπ   or   2θ = -arccos(√3/2) + 2nπ

(where n is any integer)

2θ = π/6 + 2nπ   or   2θ = -π/6 + 2nπ

θ = π/12 + nπ   or   θ = -π/12 + nπ

We know that z₁ lies in the fourth quadrant, so θ = -π/12.

All this to say

z₁ = 2√(2 - √3) exp(-i π/12)

z₂ = 2√2 exp(-i 3π/4)

Since i = exp(i π/2), we then have

i z₁ z₂ = 4 √(4 - 2√3) exp(i (π/2 - π/12 - 3π/4))

… = 4 √(4 - 2√3) exp(-i π/3)

and squaring both sides gives

(i z₁ z₂)² = 16 (4 - 2√3) exp(-i 2π/3)

ROUNDING

=================================================================

There are two rules for rounding :

1. If the number you are rounding is followed by 0-4, you simply drop it.

2. If the number you are rounding is followed by 5-9, you add 1.

Let's see these rules in action!

3.892 -> followed by 2, which is in the set 0-4, we drop it

3.89 -> followed by 9, we add 1 to 8

3.9

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Answer:5:55pm

Step-by-step explanation:

7:30-0:20=7:10-1:00=6:10-0:15=5:55pm

Step-by-step explanation:

Weighted Average = (A * 1 + B * 1 + C * 2) / (1 + 1 + 2)

Since the weights are 1, 1, and 2 respectively, we can simplify the equation further:

Weighted Average = (A + B + 2C) / 4

Therefore, the average of the points A, B, and C with weights 1, 1, and 2 respectively is (A + B + 2C) / 4.

The average of the points A, B, and C with respective weights of 1, 1, and 2 can be calculated using the weighted average formula: (1*a + 1*b + 2*c) / (1+1+2). The values of points A, B, and C are represented as a, b, and c.

The question asks for the average of points A, B, and C, which are weighted 1, 1, and 2 respectively. To calculate a weighted average, we multiply each value by its respective weight and then sum these products. We then divide this sum by the sum of the weights. So, let's assume the values of points A, B, and C be a, b, and c respectively. Using the formula for weighted average we get Average = (1*a + 1*b + 2*c) / (1+1+2)This formula will give us the average of the points A, B, and C with the specified weights.

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Answer:

12 girls

28 boys

Step-by-step explanation:

Multiply 40 by 30/100 to get 12 girls.

Subtract 12 from 40 to get 28 boys.

The linear equation that describes this situation is:

y = 2500 + 300*x

A general linear equation is written as:

y = ax + b

where a is the slope and b is the initial value.

Here we know that she starts with 2,500 points in the game, and then she wins 300 points for every minute.

Then the initial value is 2,500, and the slope is 300, then we can write the linear equation:

y = 2500 + 300*x

That is the correct option.

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Answer:

B

Step-by-step explanation:

Because the 5 in the hundreds place multiplied by 10 will result in the product of 5,000.

Answer:

i think b is answer. i think this is useful to you

The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Answer:

f(3) = g(3)

Step-by-step explanation:

on the graph the only point, where both lines cross (both functions create the same functional value) is at x=3.

since both lines have the same y-value there, we express this in math by the "=" sign. and both functions have the same input value (x=3) there.

The solution for variables x, y, and z are -

The given linear equation are-

x - 6y - 2z = -8   .......equation 1.

-x + 5y + 3z = 2 ......equation 2.

3x - 3y - 4z = 15 .......equation 3.

Add equation 1 and 2; gives

-y + z = -6   .....equation 4

multiply equation 2 and subtract it with equation 3;

12y + 5z = 21 ......equation 5

multiply equation 4 with 5 and subtract it from equation 5.

17 y = 51

y = 3.

Put y = 3 in equation 4 and find z.

z = -6 + 3

z = -3

Put the value of y and z in equation 1 and find x.

x = -8 + 18 + 6

x = 100

Therefore, the solution for variables x, y, and z are -

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Answer:

95%

Step-by-step explanation:

Answer:

Step-by-step explanation:

87

99

128

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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