Algebra 1 > EE.10 Dilations of functions 6EC
What kind of transformation converts the graph of f(x) = -9x² - 7 into the graph of g(x) =
-x² - 7?
vertical stretch
horizontal shrink
horizontal stretch
vertical shrink
O
M

Answer:

9.14

Step-by-step explanation:

To add these numbers, we first need to rewrite them in standard form, which means expressing them as a number between 1 and 10, multiplied by a power of 10.

The first number, (8.8 × 10^-2), is already in standard form.

The second number, (3.4 × 10^-4), is not in standard form. To rewrite it in standard form, we divide 3.4 by 10 twice:

(3.4 × 10^-4) = (0.34 × 10^-2) = (3.4 × 10^-3)

Now that both numbers are in standard form, we can add them:

(8.8 × 10^-2) + (3.4 × 10^-3) = 8.8 + 0.34 = 9.14

The final answer is 9.14.

Answer:

9.14

(8.8 × 10 − 2) + (3.4 × 10 − 4) = 9.14

You will have 3 1/2 left of apples

Answer:6.5 apples

Step-by-step explanation:

7 *.5=3.5 whole apples

10 apples- 3.5 apples=6.5 apples

Common data sources like social media comments are categorized as unstructured data. (Option 2)

Unstructured data refers to information that does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured data is a dataset that is not stored in a specific structured format and is generally text-heavy, but may contain data such as dates, numbers, and facts. Unstructured data does have an internal structure, but it is not predefined through data models. It might be human generated, or machine generated in a textual or a non-textual format. Examples of unstructured data are social media comments, blog posts, videos, and documents.

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y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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Answer:

Look at the sides and angles.

Step-by-step explanation:

See which sides are equal pr seem so. Use logic.

Answer:

3 x y (y + x)

Step-by-step explanation:

Factor the following:

(y + x)^3 - (y^3 + x^3)

Factor the sum of two cubes. y^3 + x^3 = (y + x) (y^2 - x y + x^2):

(y + x)^3 - ((y + x) (y^2 - x y + x^2))

Factor y + x out of (y + x)^3 - (y + x) (y^2 - x y + x^2), resulting in (y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2)):

(y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2))

3 - 1 = 2:

(y + x) ((y + x)^2 - (y^2 - x y + x^2))

(y + x) (y + x) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = y^2 + 2 x y + x^2:

(y + x) ((y^2 + 2 x y + x^2) - (y^2 - x y + x^2))

-(y^2 - x y + x^2) = -y^2 + x y - x^2:

(y + x) (x^2 + 2 x y + y^2 + (-y^2 + x y - x^2))

Grouping like terms, y^2 - y^2 + 2 x y + x y + x^2 - x^2 = (2 x y + x y) + (y^2 - y^2) + (x^2 - x^2):

((2 x y + x y) + (y^2 - y^2) + (x^2 - x^2)) (y + x)

x y 2 + x y = x y×3:

(3 x y + (y^2 - y^2) + (x^2 - x^2)) (y + x)

y^2 - y^2 = 0:

(3 x y + (x^2 - x^2)) (y + x)

x^2 - x^2 = 0:

Answer: 3 x y (y + x)

Answer:

Step-by-step explanation:

6-(-2^3)+-2

Answer:

B

Step-by-step explanation:

Solve (x + y(x)) (-(dy(x))/(dx) + 1) = (dy(x))/(dx) + 1:

Let v(x) = x + y(x), which gives (dv(x))/(dx) = (dy(x))/(dx) + 1:

(-(dv(x))/(dx) + 2) v(x) = (dv(x))/(dx)

Simplify:

-((dv(x))/(dx) - 2) v(x) = (dv(x))/(dx)

Solve for (dv(x))/(dx):

(dv(x))/(dx) = (2 v(x))/(v(x) + 1)

Divide both sides by v(x)/(v(x) + 1):

((dv(x))/(dx) (v(x) + 1))/v(x) = 2

Integrate both sides with respect to x:

integral((dv(x))/(dx) (v(x) + 1))/v(x) dx = integral2dx

Evaluate the integrals:

log(v(x)) + v(x) = 2 x + c_1, where c_1 is an arbitrary constant.

Solve for v(x):

v(x) = W(e^(2 x + c_1))

Simplify the arbitrary constants:

v(x) = W(c_1 e^(2 x))

Substitute back for y(x) = -x + v(x):

Answer:  y(x) = -x + W(c_1 e^(2 x))

Dimensions of the rectangular garden are 45 yards each and area with  the calculated dimensions are 2025 square yards.

As given in the question,

Perimeter of the rectangular garden is equal to 180 yards

Let 'x' be the length and 'y' be the width of the rectangular garden

2 ( x + y ) = 180

⇒ x + y = 90

⇒ y = 90 -x

Area of the rectangular garden 'A' = xy

⇒ A = x ( 90 - x)

⇒ A = 90x - x²

To maximize the area dA/dx = 0

dA/dx = 90 - 2x

⇒ 90 - 2x = 0

⇒ 2x = 90

⇒ x = 45 yards

⇒ y = 45 yards

Area of the rectangular garden = 45 × 45

                                                 = 2025 square yards

Therefore, the dimensions of the garden are 45 yards each and area of the rectangular garden is equal to 2025 square yards.

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Answer:

(3,1)

Step-by-step explanation:

hii ! for this question, x = 3, which is your first point. for the second part, you're going to need to plug x into the 5x.

5(3)-4y=11

15-4y=11

subtract 15 from each side

-4y=-4

y=1

(3,1) is gonna be your answer !

The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

The number of ways in which we can select a software engineer, an administrative assistant, and a sales representative is 48.

Since we are only choosing one option from each category, the number of alternatives for each category is equal to the number of combinations for each category .

Using the equation for each pair and then adding them up,

C (n,r) = n! / (r! (n - r)! )

we get the required number of combinations as 48.

Factorial

There are n! techniques of arranging n unique things into an ordered sequence, permutations where n = r.

Combination

The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

Permutation

The number of ways to choose a sample of r elements from a set of n distinct objects when order does matter and replacements are not allowed. When n = r this reduces to n! , a simple factorial of n.

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 By solving 13 = 8- 5d we get the value of ‘d ’ is equal to -1.

This equation can be solved by arranging the non – algebraic equations on one side and letting the algebraic number on the other side.

13 = 8 – 5d

5d = 8-13

5d = -5

d = -5/5

d = -1.

While arranging the non - algebraic numbers on one side their signs should be changed after taking the number into another side. Similarly, while arranging the algebraic equations on one side, signs of the numbers should be changed. In an algebraic equation, the terms addition, subtraction, multiplication, division, raising to a power, and extraction of a root are applied to a set of variables to construct a statement of the equality of two expressions.

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Therefore, number of strings can be made by using 4 lower case english letters is 66,351 strings.

Combination refers to an arrangement of objects where the order is not crucial. Contrary to permutation, where the order is important. Consider how the letters A, B, and C would be arranged. ABC and ACB are not the same arrangement in a permutation.

Here,

Repetition is permitted as long as we're only looking at lowercase letters.

Number of strings of length 4=[tex]26^{4}[/tex]

Other than x, how many strings of length 4 exist=[tex]25^{4}[/tex]

 [tex]26^{4}[/tex]- [tex]25^{4}[/tex]=66,351 strings.

Therefore number of strings can be made by using 4 lower case english letters is 66,351 strings.

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Median and IQR are better statistics than mean and standard deviation for describing skewed probability distributions because it's based on values that come from the middle half of the distribution, it's unlikely to be influenced by outliers.

Because it is unaffected by outliers, the IQR is frequently regarded as a more accurate measure of spread than the range. The variance and standard deviation are indicators of how widely the data are dispersed from the mean. Each observed data value's proximity to the mean is summarized.

The best indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on values that come from the middle half of the distribution.

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The minimum amount of fence that he can use is 1600 ft.

Given ;

Area of rectangular = 80,000 sq. ft

i.e.  xy = 80,000

Total fencing needed ,

      x + y + x + y + 2y = 2x + 4y

To minimize 2x + 4y, constrained to  xy = 80,000

i.e.   xy = 80,000

   ⇒  y = 80,000/x

⇒ so, s = 2x + 4 (80,000/x) to be minimized

⇒ To minimum value at ds/dx = 0

i.e.  s = 2x + 4 (80,000/x)

        = 2x + (3,20,00/x)

⇒ Now, ds/dx = 0 = 2 + (3,20,000) - [tex]\frac{1}{x^{2} }[/tex]

                              ⇒ [tex]\frac{320000}{x^{2} } = 2[/tex]

                              ⇒ [tex]x^{2} = 160000[/tex]

                              ⇒ x = 400

∴ x = 400 ft  

y = 80,000/400 = 200

∴ y = 200 ft

Total frencing is

               ⇒ 2x + 4y = 2 × 400 + 4 × 200

                                = 800  +  800

                                = 1600 ft

∴ The minimum amount of fence that he can use is 1600 ft.

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Answer:

The property tax that must be paid on the lot is $864.

Step-by-step explanation:

The assessment value of the lot is $36,000, and the tax rate is 2.4 cents per $1, or 0.024. So the total amount of tax due is calculated as follows:

$36,000 * 0.024 = $<<36000*0.024=864>>864

The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.

The second derivative may be used to determine the local extrema of a function under certain conditions.

A function is said to have a local (relative) extremum at a critical point if the derivative of the function changes sign near that location. At the critical point, the function has a local (relative) maximum if the derivative switches from being positive (growing function) to negative (decreasing function). The function, however, has a local (relative) minimum at the critical point if the derivative switches from negative (decreasing function) to positive (growing function). The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.

Under certain circumstances, one can utilize the second derivative to identify the local extrema of a function. A function has a local minimum at this point if it has a critical point when f′(x) = 0 and the second derivative is positive. However, if the function contains a critical point at which the second derivative is negative and f′(x) = 0, then f has a local maximum at this location. The Second Derivative Test for Local Extrema is the name of this method.

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The result is not statistically significant.

To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.

The null hypothesis is

H₀ : μ ≥ 1520

The alternative hypothesis is

Hₐ : μ ≤ 1520

then the test statistic is,

t = (x - μ)/(s/√n)

 = (1501 - 1520)/(53/√20)

t = - 1.603

The t-test statistic is - 1.603.

Degree of freedom n - 1 = 20 - 1 = 19

Hence the t-critical value is -1.792.

The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.

The result is not statistically significant.

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The dimensions of the rectangular corral:

length = 75 ft and width = 5 ft

Let m be the length of the rectangular corral and n be the width of the rectangular corral.

The perimeter of the rectangular corral,

P = 2m + 2n

The rectangular corral split into 2 pens of the same size.

So, P = 2m + 3n

The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.

300 = 2m + 3n

n = (300 - 2m)/3

Area of the rectangular corral,

A = m * n

A(n) = m * (300 - 2m)/3

A(m) = (300/3)*m - (2/3)*m

Taking derivatives on both sides of the equation:

A'(m) = 100 - (4/3)*m

for A'(m) = 0,

100 - (4/3)*m = 0

m = 100 * (3/4)

m = 75

So, n = (300 - 2(75))/3

n = 50

Therefore, the length of the rectangular corral = 75 ft and width = 5 ft

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Answer:

Gary would weigh 176 ounces.

Step-by-step explanation:

One pound is sixteen ounces so just multiply sixteen and 11. ( 16 * 11 = 176 )

I hope this helped you! Have an amazing day :)

Answer: 176 ounces

Step-by-step explanation:

To convert pounds to ounces, multiply the initial value by 16. Since we have  the weight of Gary's cat as 11 pounds, their weight in ounces should be 11 * 16 = 176 ounces.

Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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Answer:

Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:

x + 2y = 29

Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:

x = 2y + 1

Substituting this expression for x in the first equation, we get:

2y + 1 + 2y = 29

Combining like terms on both sides, we get:

4y + 1 = 29

Subtracting 1 from both sides, we get:

4y = 28

Dividing both sides by 4, we get:

y = 7

Substituting this value for y in the expression for x, we get:

x = 2(7) + 1 = 14 + 1 = 15

Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.

the answer is 1

Step-by-step explanation:

The value of f(2) is 4.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), alternative shorthand symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or uncertain.

Given function is

f(x) = x²

Putting x = 2 in the given function:

f(2) = 2²

Putting 2² = 4 in the above function:

f(2) = 4

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Answer: B.180

Step-by-step explanation:

number of acres = 60

area required for one goat = 1/3 of an acre

number of goats one acre can hold =  3

number of goats her land can support = 60*3 = 180

Answer:

Step-by-step explanation:

x+80=145

x=65

The actual percentage of female people with ppd is more than 12%.

Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.

And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale

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Solving the given equation we get value of x as -3/2 i.e option (a) is correct option.

What are exponents and its properties?

A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2×2×2×2 can be expressed as [tex]2^{4}[/tex]. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."

Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times.

Raise a power to a power

[tex](x^{a}) ^{b}=x^{ab}[/tex]

This is called the power of a power property

Negative exponents are the reciprocals of the positive exponents.

[tex]x^{-a}=\frac{1}{x^a}[/tex]

The same properties of exponents apply for both positive and negative exponents.

[tex](1/25)^x = 125\\ 25^{-x} = 125\\(5^2)^{-x} = 5^3\\5^{-2x} = 5^3\\\implies -2x = 3\\\implies x = -3/2[/tex]

i.e.

Option (a) is correct.

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