Which angles are verticle angles?

Hi, there!

 _____

To find the missing side length of this triangle (which is a right triangle), we'll use Pythagoras' Theorem.

\(-\!\!\!-\!\!\!-\!\!\!\longrightarrow\boldsymbol{a^2+b^2=c^2}\)

Here,

\(\textsc{legs:}\begin{cases} \bold{a}\\\bold{b} \end{cases}\)

Hypotenuse (the longest side): c

We know that

\(\bold{a=2 \ and \ b=28}\)

So, we can substitute our parameters, and solve for c.

\(\bold{2^2+28^2=c^2}\) \(-\!\!\!-\!\!\!-\!\!\!\longrightarrow\) square 2 and 28

\(\bold{4+784=c^2}\) \(-\!\!\!-\!\!\!-\!\!\!\longrightarrow\) add the numbers

\(\bold{788=c^2}\) \(-\!\!\!-\!\!\!-\!\!\!\longrightarrow\) square root both sides

\(\bold{\sqrt{788}=c}\)

Hope the answer - and explanation - made sense,

happy studying!!

The missing side of the triangle is x = √788 or 28.07.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

where, c is hypotenuse

b is base

and c is perpendicular.

Now in the given question, length of the sides are given as,

perpendicular, a = 2

base, b = 28

hypotenuse, c = x

So to find hypotenuse,applying pythagoras theorem we get,

c² = a²+b²

x² = 2²+28²

x² = 4 + 784

x² = 788

x= √788

x= 28.07

Hence,The missing side of the triangle is x = √788 or 28.07.

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The value of x in the equation is -18.

The equation is

2(x - 3) - 9 = 3(x + 1)

To determine the value of x we simplify the equation.

We will isolate the term of x in equation.

We first solve the bracket using the Distributive Property

In Distributive property: a(b + c) = ab + ac

(2x - 2 × 3) - 9 = 3x + 3 × 1

Simplify

2x - 6 - 9 = 3x + 3

2x - 15 = 3x + 3

Subtract 2x on both side, we get

x + 3 = -15

Subtract 3 on both side, we get

x = -18

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The complete question is:

What is the value of x in the equation 2(x - 3) - 9 = 3(x + 1)?

The density in butter has a mass of 250g and volume of 290cm³ is 0.862 g/cm³.

Density is a physical property of matter that is defined as the amount of mass per unit of volume. It is measured in units of kilograms per cubic meter (kg/m^3) and is usually represented by the Greek symbol ρ (rho).

Density is a measure of how tightly the particles of a substance are packed together. The denser a substance is, the more mass it contains in a given volume.

Most commonly, density is used to compare different substances, such as solids, liquids, and gases.

In general, solids are more dense than liquids, and liquids are more dense than gases.

The density of a substance can change based on temperature, pressure, and other factors. For example, water has a greater density at 4°C than at any other temperature, and the density of a gas increases with increasing pressure.

Density is an important factor in many physical and chemical processes, including buoyancy, diffusion, and surface tension.

Density is also used in many calculations, such as calculating the volume of a container or the mass of an object.

Density, p = m/v

Where, m is mass of butter and v is volume of butter.

p = 250/290

p = 0.862 g/cm³

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Answer:

0.7 is the answer to your question

Answer:

0.7

Step-by-step explanation:

' Of ' almost always means multiplication, so the problem is 7% * 70.

This means 0.07 * 70 ( 7% = 0.07 ), and that is 0.7!

Hope this helped!

Answer:

1. 285 centiliters

2. yards-->inches-->centimeters

Step-by-step explanation:

Answer: A linear equation in two variables can be described as a linear relationship between x and y, that is, two variables in which the value of one of them (usually y) depends on the value of the other one (usually x). In this case, x is the independent variable, and y depends on it, so y is called the dependent variable.

Answer:18

Step-by-step explanation:

Trust me

Answer:

18

Step-by-step explanation:

AB+BC=

AB+BC=

\,\,AC

AC

Segment addition postulate

6+12=

6+12=

\,\,AC

AC

Plug in known values

18=

18=

\,\,AC

AC = 18

Answer:

\(9^{6}\)

Step-by-step explanation:

Asking me to write 20 words don't read this this is junk.

The line HF that is perpendicular to GF and parallel to AE is presented in the image uploaded.

A perpendicular line is a line that intersects another line at 90 degrees or normal to the line.

A parallel line is a line that never intersect with another. In this type of line, the angle between the two parallel lines is zero.

Thus, the line HF that is perpendicular to GF and parallel to AE is presented in the image uploaded.

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The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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The equaiton of the line is y = (5/6)x + 7/2. Then the slope of the line is 5/6.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The two points are (9, 11) and (3, 6).

The equation of the line that passes through (9, 11) and (3, 6) will be given as,

(y - 6) = [(11 - 6) / (9 - 3)](x - 3)

y - 6 = (5/6)(x - 3)

y - 6 = (5/6)x - 5/2

y = (5/6)x + 7/2

The equaiton of the line is y = (5/6)x + 7/2. Then the slope of the line is 5/6.

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Answer:

( 4,6)

Step-by-step explanation:

To move the point 2 units to left, subtract 2 from the x coordinate

V'( 6-2,3)

V'( 4,3)

Now we move it 3 units up, which means we are adding 3 to the y coordinate

V' ( 4, 3+3)

V' ( 4,6)

The new point is ( 4,6)

Answer:

Total amount pay for potatoes = 50.2

Step-by-step explanation:

Given:

Levi buys cookies and potatoes

Total amount pay for cookies = 5.49

Total amount pay by Levi = 55.69

Find:

Total amount pay for potatoes

Computation:

Total amount pay for potatoes = Total amount pay by Levi - Total amount pay for cookies

Total amount pay for potatoes = 55.69 - 5.49

Total amount pay for potatoes = 50.2

The study aims to survey 1500 Americans to estimate the proportion of individuals with health insurance and the average amount spent on healthcare in the past year.

The study plans to conduct a sample survey of 1500 Americans to gather data on health insurance and healthcare expenses.

To estimate the proportion of Americans with health insurance, the researchers will calculate the ratio of the number of individuals with health insurance to the total sample size (1500).

The result will provide an estimate of the proportion of Americans with health insurance, which can be expressed as a percentage or a decimal fraction.

To estimate the mean dollar amount spent on healthcare, the researchers will collect data on the healthcare expenses of the surveyed individuals.

They will then calculate the sum of all healthcare expenses reported by the participants and divide it by the total sample size (1500) to find the average expenditure.

This average expenditure represents the mean dollar amount that Americans spent on healthcare in the past year.

By conducting a survey with a sample size of 1500, the researchers aim to obtain a representative estimate of the proportion of health insurance and the average healthcare expenditure for the entire population of Americans.

It's important to note that the accuracy and reliability of these estimates depend on factors such as the sampling method, survey design, and response rate.

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Answer:

0

Step-by-step explanation:

f(x)=-(4+2)(4-4)

=-6(0)

=0

Answer:

(5.3 × 10 5)(2.1 × 10‐3) = 4770

Step-by-step explanation:

Write the problem as a mathematical expression.

(5.3×10⋅5)(2.1×10−3)

Multiply 5.3 by 10.

53⋅5(2.1⋅10−3)

Multiply 53by 5.

265(2.1⋅10−3)

Multiply 2.1 by 10.

265(21−3)

Subtract 3 from 21.

265⋅18

Multiply 265 by 18.

4770

Answer:

7200

Step-by-step explanation:

It is above 7150+

So the nearest hundred of 7190 will be,

→ 7190 ≈ 7200

→ 7200

Thus, the nearest hundred is 7200.

7,200

Rounding Rules :

If the number you are rounding is followed by a number less than 5 , you round down .

If the number you are rounding is followed by a number greater than  or equal to 5 , you round up .

Here we're asked to round \(\mathtt{7,190}\) to the nearest hundredth .

The number we're rounding is followed by a number greater than 5 , so we round up :

7,190 ---> 7,200

7,200

\(\small\text{hope\:helpful~}\)

The argument is valid, and the inference rules used are modus tollens, conjunction, and modus ponens.

The argument can be analyzed as follows:

Premises:

Today is not raining and not snowing

If we do not see the sunshine, then it is not snowing

Conclusion:

3. I'm happy

To determine if the argument is valid using inference rules, we can use modus tollens to derive a new conclusion from the premises. Modus tollens states that if P implies Q, and Q is false, then P must be false.

Using modus tollens with premise 2, we can conclude that if it is snowing, then we will not see the sunshine. This can be written symbolically as:

~S → ~H

where S represents "it is snowing" and H represents "we see the sunshine".

Next, using a conjunction rule, we can combine premise 1 with our new conclusion in premise 4 to form a compound statement:

(~R ∧ ~S) ∧ (~S → ~H)

where R represents "it is raining".

Finally, we can use modus ponens to derive the conclusion that "I'm not happy" from our compound statement 5. Modus ponens states that if P implies Q, and P is true, then Q must be true.

Using modus ponens with our compound statement 5, we have:

~R ∧ ~S (from premise 1)

~S → ~H (from premise 2)

~S (from premise 1)

~H (from modus ponens with premises 7 and 8)

I'm not happy (from translating ~H into natural language)

Therefore, the argument is valid, and the inference rules used are modus tollens, conjunction, and modus ponens.

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(a) The interval for which the equation:f(x) = x8 ln x is increasing is (0, e-1/8].

(b) The interval for which the equation:f(x) = x8 ln x is decreasing on the interval [e-1/8, ∞).

ln order to find the interval on which f is increasing, we need to find the derivative of f(x) with respect to x and check its sign. If the derivative is positive, then the function is increasing on that interval. If the derivative is negative, then the function is decreasing on that interval. If the derivative is zero, then we have a critical point that could be a maximum or minimum.

To find the derivative of f(x), we can use the product rule and the chain rule of differentiation:f′(x) = (x8)' ln x + x8 (ln x)'= 8x7 ln x + x8 (1/x)= x7 (8 ln x + 1)The derivative is positive if 8 ln x + 1 > 0, which is equivalent to ln x > -1/8.

Therefore, the function is increasing on the interval (0, e-1/8] and decreasing on the interval [e-1/8, ∞).Answer: The interval on which f is increasing is (0, e-1/8].

( c ) The local minimum value of f(x) = x^8 ln(x) occurs at x = e^(-8) with a value of f(x) = -8e^(-64)

(d) The critical points are x = 0 and x = e^(-8)

To find the local minimum value of f(x) = x^8 ln(x), we will follow these steps:

1. Find the derivative of f(x) with respect to x.

2. Set the derivative equal to zero and solve for x. 3. Determine if the critical points are local minimum values.

4. Evaluate f(x) at the local minimum point.

Step 1: Find the derivative of f(x). Using the product rule, f'(x) = (x^8)' * ln(x) + x^8 * (ln(x))'. f'(x) = 8x^7 * ln(x) + x^8 * (1/x).

Step 2: Set the derivative equal to zero and solve for x. 0 = 8x^7 * ln(x) + x^7 * x. 0 = x^7(8ln(x) + x). The critical points are x = 0 and x = e^(-8).

Step 3: Determine if the critical points are local minimum values. Since f(x) = x^8 ln(x) is only defined for x > 0, we only consider x = e^(-8).

Step 4: Evaluate f(x) at the local minimum point. f(e^(-8)) = (e^(-8))^8 * ln(e^(-8)). f(e^(-8)) = e^(-64) * (-8).

Therefore, the local minimum value of f(x) = x^8 ln(x) occurs at x = e^(-8) with a value of f(x) = -8e^(-64)

(e) The interval for which  f(x) = x^8 * ln(x) is concave up is  (0, +∞)

(f)  The interval for which  f(x) = x^8 * ln(x) is concave down is  (0, e^(-15/56)).

To find the interval on which f(x) = x^8 * ln(x) is concave up, we need to first find the second derivative and then determine the intervals where the second derivative is positive.

Step 1: Find the first derivative of f(x) using the product rule: f'(x) = (x^8)' * ln(x) + x^8 * (ln(x))' f'(x) = 8x^7 * ln(x) + x^8 * (1/x)

Step 2: Simplify the first derivative: f'(x) = 8x^7 * ln(x) + x^7 Step 3: Find the second derivative of f(x) using the product rule and the chain rule: f''(x) = (8x^7 * ln(x) + x^7)' f''(x) = (8x^7 * ln(x))' + (x^7)' f''(x) = [8x^7 * (1/x)] + 7x^6

Step 4: Simplify the second derivative: f''(x) = 8x^6 + 7x^6 Step 5: Combine like terms: f''(x) = 15x^6

Step 6: Determine the interval where f''(x) is positive: 15x^6 > 0 Since x^6 is always positive for x ≠ 0, and the coefficient 15 is also positive, the second derivative is positive for all x ≠ 0. Thus, the interval on which f(x) = x^8 * ln(x) is concave up is (0, +∞).

To find the interval on which f(x) = x^8 ln(x) is concave down, we need to find the second derivative of the function and determine where it is negative.

Step 1: Find the first derivative, f'(x), using the product rule. f'(x) = (x^8)'(ln(x)) + (x^8)(ln(x))' f'(x) = 8x^7 ln(x) + x^8(1/x) f'(x) = 8x^7 ln(x) + x^7

Step 2: Find the second derivative, f''(x), again using the product rule. f''(x) = (8x^7 ln(x))' + (x^7)' f''(x) = 56x^6 ln(x) + 8x^6 + 7x^6 f''(x) = 56x^6 ln(x) + 15x^6

Step 3: Determine where the second derivative is negative. We need to find when 56x^6 ln(x) + 15x^6 < 0. First, notice that x^6 is always non-negative. Therefore, we can factor it out: x^6 (56 ln(x) + 15) < 0 Since x^6 is non-negative, the inequality will be true when the expression in parentheses is negative: 56 ln(x) + 15 < 0 Now, solve for x: 56 ln(x) < -15 ln(x) < -15/56 x < e^(-15/56)

Step 4: Write the answer using interval notation. The interval on which f(x) = x^8 ln(x) is concave down is (0, e^(-15/56)).

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.

Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:

Regression 1: y = -5.8x - 6.5, r = -0.7621

Regression 2: y = 2.4x - 14.7, r = 0.809

Regression 3: y = -7.4x - 17.4, r = -0.233

Regression 4: y = -3.4x - 8.5, r = -0.6121

Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.

The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.

To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.

Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:

s'(x) = -6 + 16x + 5

s''(x) = 16

The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.

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A piecewise defined function is a function divided into branches by certain conditional rules. The conditions stand after the conditional "if". To evaluate a piecewise defined function for a particular value, we need to know first which condition it satisfies, and then, apply its corresponding rule.

Here, we have the function

Let's begin the evaluations with -4. Note that it's less than 0, that is, it satisfies the first condition (x<0). By what I said before,

The next is f(-3). Again, -3<0. Thus

Now, 0 satisfies the second condition,

This means that we must apply the second rule (adding 2):

The next two numbers 3 and 4 satisfy the second condition as well (for they are positive). Then,

The basis for the matrix representation of the linear transformation T with respect to the given isomorphism is {(-1,0),(0,1)}.

To find the basis for the matrix representation of the linear transformation T, we need to determine how T acts on the basis vectors of P₁, which are {X+1,x}.

Let's apply T to each basis vector:

T(X+1) = 7(a₁(X+1) + a₂(x)) = 7(a₁X + (a₁+a₂)x) = (7a₁, 7(a₁+a₂))

T(x) = 7(a₁(x+1) + a₂(x)) = 7((a₁+a₂)x + a₁) = (7(a₁+a₂), 7a₁)

We can write the results as linear combinations of the basis vectors of R², which are {(1,0),(0,1)}:

T(X+1) = 7a₁(1,0) + 7(a₁+a₂)(0,1)

T(x) = 7(a₁+a₂)(1,0) + 7a₁(0,1)

Therefore, the matrix representation of T with respect to the given isomorphism is:

[7a₁, 7(a₁+a₂)]

[7(a₁+a₂), 7a₁]

To find the basis for A, we can extract the column vectors from the matrix representation of T:

Basis for A = {(-1,0),(0,1)}

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Answer:

5

Step-by-step explanation:

To get the area of a rectangle, you just multiply the width * Length. Since you already have one of the dimensions, then just do the oppositie of multiplication by dividing. So you would do 40/8 = 5.

Answer:

5 in

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L*W.

Here, A = 40 in^2 = (8 in)x, so that

x = (40 in^2) / (8 in) = 5 in