Identify a pair of corresponding angles.

Answer:

Step-by-step explanation:

=-9+7i+5+i

=-4+8i

Answer:

It's indeterminate; because a negative number can't have an rational root when goes under an even radical.

The part of exponent, x, will have the value 7/4 according to the expression of exponent.

As we see the base on both sides is same, concerning this we can equate the exponents for equal values on Left Hand Side and Right Hand Side of the equation.

5x + 9 = 9x + 2

Rearranging the equation for like terms on each side

9x - 5x = 9 - 2

Subtracting the values in each side of the equation to find the value of x

4x = 7

Rearrange the formula

x = 7/4

Hence, the value of x will be 7/4.

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Answer:

The number of boxes sold for each item were:

Chocolates: 214

Caramels: 321

Step-by-step explanation:

6h + 5a = 2889         Eq. 1

h + a = 535                Eq. 2

h = Number of boxes of chocolate sold

a = Nuber of boxes of caramel sold

From Eq. 2

h = 535 - a       Eq. 3

Replacing Eq. 3 in Eq. 1

6(535-a) + 5a = 2889

(6*535 + 6*-a) + 5a = 2889

(3210 - 6a) + 5a = 2889

-6a + 5a + 3210 = 2889

-a = 2889 - 3210

-a = -321

a = 321

From Eq. 3

h = 535 - a

h = 535 - 321

h = 214

Check:

From Eq. 1

6h + 5a = 2889

6*214 + 5*321 = 2889

1284 + 1605 = 2889

Answer:

X<-4 and -4>x

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 +55

When it comes to saving effectively, it is advisable to make regular payments rather than relying solely on a lump sum. By making consistent contributions over time, you can benefit from compounding interest and develop a disciplined saving habit. Additionally, seeking professional advice from financial advisors can help you understand the best strategies to maximize your savings.

To save effectively, it is generally recommended to make regular payments instead of relying on a single lump sum contribution. By consistently saving money over time, you can take advantage of the concept of compounding interest, where your initial savings generate earnings that are reinvested and generate further returns. This compounding effect can significantly increase your savings over the long term. Additionally, by making regular payments, you develop a disciplined saving habit, which can be beneficial in achieving your financial goals.

In order to optimize your savings strategy, it is advisable to consult with financial advisors or professionals who specialize in personal finance. They can provide guidance tailored to your specific financial situation, helping you understand the various investment options available and determining the most suitable approach for your savings goals. Financial advisors can also assist in assessing your risk tolerance, diversifying your portfolio, and creating a comprehensive savings plan that aligns with your objectives and time horizon. Seeking professional advice can provide valuable insights and increase the likelihood of successful long-term savings.

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The average birthweight of a nonsmoker was between 1,000 and 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

Given,

What is the newborn's weight?

A newborn's body weight is referred to as birth weight. At birth, babies of European descent typically weigh between 2.5 and 4.5 kilograms, or about 3.5 kilograms on average. South Asian and Chinese babies typically weigh 3.26 kg.

Here,

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

However, there are some obvious disparities between the two groups' typical ranges of birth weights. Since there are fewer newborns in the lower weight groups, over half of neonates among nonsmokers (56 out of 115, 48.7%) had birth weights between 3,000 and 4,000 grams. Less infants are born in the heavier weight categories; 40 of the 74 newborns delivered to smokers, or 54% of them, had birth weights between 2,000 and 3,000 grams.

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The length of HI is given as follows:

HI = 15.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

3/HI = 5/25

Applying cross multiplication, the length of HI is given as follows:

3/HI = 1/5

HI = 3 x 5

HI = 15.

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The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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Answer:true

Step-by-step explanation: trust me

The probability that the offices will be assigned to 2 of the men and 1 of the women will be 3/5

Lets find all the combinations of 2 men and 1 woman that can be chosen

(men, men, women) m m w

3/5 x 2/4 x2/3

(men, women, men) m w m

3/5 x 2/4 x 2/3

(women, men, men) w m m

2/5 x 3/4 x2/3

then just add those probabilities together:

= 3/5x2/4x2/3+3/5x2/4x2/3+2/5x3/4x2/3

= 12+12+12/60

this simplifies to 3/5

Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics explains the examination of events that can occur subject to probability.

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Answer:

122

Step-by-step explanation:

Use the formula P=2(l+W)

the length would be 65ft and the perimeter would be 374

ASK ONE QUESTION!!

But to help you with one, the problem is.... h(x) + x with power of 2 - 5x

ANSWER= x(h+x−5)

SOLUTION= x(x+h−5) you had this equation and then you factor out x

(a) Descartes' Rule of Signs can be used to determine the number of possible positive and negative real zeros of a polynomial function.

(b) The Rational Zeros Theorem can be applied to find the possible rational zeros of a polynomial function.

(a) To apply Descartes' Rule of Signs, we count the number of sign changes in the coefficients of the terms in the polynomial. In this case, there are two sign changes, indicating that there are either two positive real zeros or no positive real zeros. Additionally, if we evaluate the polynomial at -x, we have f(-x) = x^3 - 10x^2 - 28x - 6x + 45, which has one sign change. This means that there is one negative real zero or no negative real zeros.

(b) The Rational Zeros Theorem states that if a polynomial has a rational zero p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, then p/q is a potential rational zero. In this case, the constant term is 45, which has factors ±1, ±3, ±5, ±9, ±15, ±45. The leading coefficient is -1, which has factors ±1. By considering all possible combinations of these factors, we can generate a list of potential rational zeros.

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Answer:

530, 556 C.

Step-by-step explanation:

Just did it

Answer:

c

Step-by-step explanation:

When group members contribute less to the group than the average member, particularly as the group grows in size, those group members are engaged in social loafing.

Social loafing refers to the phenomenon where individuals exert less effort when working in a group compared to when working alone. As the group size increases, individual accountability diminishes, leading to a diffusion of responsibility and a decrease in individual effort.

This can result in some group members contributing less than the average member, taking advantage of the collective efforts of others.

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Answer:

\(\boxed{ \frac{9\pm \sqrt{33}}{ 4}}\longrightarrow \boxed{2x^2-9x+6=0}\)

\(\boxed{\frac{4 \pm \sqrt{6}}{2} }\longrightarrow\boxed{ 2x^2-8x+5=0}\)

\(\boxed{ \frac{9 \pm \sqrt{89}}{ 4} }\longrightarrow \boxed{2x^2-9x-1=0 }\)

\(\boxed{ \frac{4 \pm \sqrt{22}}{ 2}}\longrightarrow \boxed{2x^2-8x-3=0}\)

Step-by-step explanation:

In order to solve for the solution set of a quadratic equation, we can use the quadratic formula:

\(\boxed{\bold{x = \frac{-b \pm\sqrt{b^2 - 4ac}}{2a}}}\)

where a, b, and c are the coefficients of the quadratic equation.

For 2x^2-8x+5=0

Comparing the above equation with ax^2+bx+c
In this case, the coefficients are:

a = 2

b = -8

c = 5

Plugging these values into the quadratic formula, we get:

\(x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(2)(5)}}{ 2*2}\)

\(x = \frac{8 \pm 2\sqrt{6}}{ 4}\)

\(x = 2*\frac{4 \pm \sqrt{6}}{ 4}\)

\(x = \frac{4 \pm \sqrt{6}}{2}\)

\(\hrulefill\)

For 2x^2-10x-3=0

Comparing the above equation with ax^2+bx+c
n this case, the coefficients are:

a = 2

b = -10

c = -3

Plugging these values into the quadratic formula, we get:

\(x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(2)(-3)}}{ 2*2}\)

\(x = \frac{10 \pm \sqrt{89}}{ 4}\)

\(\hrulefill\)

For 2x^2-8x-3=0  
Comparing the above equation with ax^2+bx+c
n this case, the coefficients are:

a = 2

b = -8

c = -3

Plugging these values into the quadratic formula, we get:

\(x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(2)(-3)}}{ 2*2}\)

\(x = \frac{8 \pm 2\sqrt{22}}{ 4}\)

\(x = 2*\frac{4 \pm \sqrt{22}}{ 4}\)

\(x = \frac{4 \pm \sqrt{22}}{ 2}\)

\(\hrulefill\)For 2x^2-9x-1=0

Comparing the above equation with ax^2+bx+c
n this case, the coefficients are:

a = 2

b=-9

c = -1

Plugging these values into the quadratic formula, we get:

\(x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(2)(-1)}}{ 2*2}\)

\(x = \frac{9 \pm \sqrt{89}}{ 4}\)

\(\hrulefill\)

For 2x^2-9x+6=0
n this case, the coefficients are:

a = 2

b = -9

c = -6

Plugging these values into the quadratic formula, we get:

\(x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(2)(6)}}{ 2*2}\)

\(x = \frac{9\pm \sqrt{33}}{ 4}\)

In other words, y-2 goes in the first box and 5 goes in the second box.

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

Work Shown:

y^2 - 4y - x + 9 = 0

y^2 - 4y + 9  = x

x = y^2 - 4y + 9

x = y^2 - 4y + 4 + 5 .... rewrite 9 as 4+5

x = (y^2-4y+4) + 5

x = (y-2)^2 + 5  .... apply the perfect square factoring rule

So we'll have y-2 go in the first box and 5 goes in the second box

note: One version of the perfect square factoring rule says (a-b)^2 = a^2-2ab+b^2.

Answer:

A

Step-by-step explanation:

The rhombus cuts the shorter side of the rectangle in half so it's equal to 5

we use pythagoras

\(13^{2} = 5^2+x^2\\x^2= 169-25\\x^2= 144\\x=12\)

so the larger side is 2x=24

so the area is 24*10=140cm^2

Answer:

B

C/15=3

Step-by-step explanation:

They devided the coconuts among 15 children

3x15 =45

45÷3 =15

So the number of coconut the kids gathered is 45

C/15=3 multiply by 15 on both side

15/1 ×c/15=3×15

C=3×15

C=45

The probability that a student is in choir, given that the student is in the school musical is (c) 56%

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

School musical and choir = 18%

School musical = 32%

The requird probabilty is calculated as

P = School musical and choir/School musical

Substitute the known values in the above equation, so, we have the following representation

P = 18%/32%

Evaluate

P = 56%

Hence, the probability is (c) 56%

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Answer:

not a function

Step-by-step explanation:

{(7,4),(5, -1),(3,-8),(1,-5),(3,6)}

This is not a function

The input of x=3 goes to two different outputs y=-8 and y=6

Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

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The derivative of the function f(x) = -2x^9 + 7x^5 + 9x - 2 is f'(x) = -18x^8 + 35x^4 + 9.

To find the derivative of the function f(x) = -2x^9 + 7x^5 + 9x - 2, we can differentiate each term separately using the power rule of differentiation.

The power rule states that for a term of the form ax^n, the derivative is given by nax^(n-1).

Let's differentiate each term of the given function:

f(x) = -2x^9 + 7x^5 + 9x - 2

The derivative of -2x^9 is:

-2 * 9x^(9-1) = -18x^8

The derivative of 7x^5 is:

7 * 5x^(5-1) = 35x^4

The derivative of 9x is:

9 * 1x^(1-1) = 9

The derivative of -2 is:

0 (the derivative of a constant term is zero)

Putting it all together, we have:

f'(x) = -18x^8 + 35x^4 + 9

Therefore, the derivative of the function f(x) = -2x^9 + 7x^5 + 9x - 2 is f'(x) = -18x^8 + 35x^4 + 9.

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In general, a differential equation can be both linear and separable, but it must be of the form \(y' + p(x) y = q(x) y^n\)

A differential equation is called linear if it is of the form

a(x) y' + b(x) y = c(x)

where y' denotes the derivative of y with respect to x, and a(x), b(x), and c(x) are functions of x.

On the other hand, a differential equation is called separable if it can be written in the form

g(y) dy/dx = f(x)

where g(y) and f(x) are functions of y and x, respectively.

The differential equation dy/dt = (y + c)g(t) is separable, but it is not linear, since it is not of the form a(t)y' + b(t)y = c(t) for any functions a(t), b(t), and c(t).

In general, a differential equation can be both linear and separable, but it must be of the form

\(y' + p(x) y = q(x) y^n\)

where p(x) and q(x) are functions of x, and n is a constant. This is known as a Bernoulli differential equation, and it can be transformed into a linear differential equation by a suitable change of variables.

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Answer:

-5.4

Step-by-step explanation:

because -3 x 1.8= -5.4

Answer: -5.4

Step-by-step explanation: 1.8b means to multiply 1.8 by b and b=-3 therefore, 1.8(-3)= -5.4

Hope this helps ^_^

Step 1) Divide the figure into separate shapes

Triangle: 4 x 4

Large rectangle: 19 x 8

Small rectangle: 7 x 5

Long rectangle: 4 x 7

Step 2) Find the area of each shape

Triangle: A = 1/2 x 4 x 4 = 8

Large rectangle: A = 19 x 8 = 152

Small rectangle: A = 7 x 5 = 35

Long rectangle: A = 4 x 7 = 28

Step 3) Add all of the areas of the shapes together

A = 8 + 152 + 35 + 28 = 223 square feet

Hope this helps! :)

The table of solutions for the given equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.

In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;

At x = -2, the value of point y is as follows:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At x = -1, the value of point y is as follows:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At x = 0, the value of point y is as follows:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At x = 1, the value of point y is as follows:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At x = 2, the value of point y is as follows:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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Answer:

Bryan and Yuan will meet after 5 hours, having traveled 20 miles each.

Step-by-step explanation:

Given that Bryan and Yuan left their homes at different periods of time and at different speeds, to determine how long they will meet and how much distance they will have traveled, the following calculation must be performed:

B = 5 + (3X)

Y = 4X

B = 5 + 3x2 = 11

Y = 4x2 = 8

B = 5 + 3x3 = 14

Y = 4x3 = 12

B = 5 + 3x4 = 17

Y = 4x4 = 16

B = 5 + 3x5 = 20

Y = 4x5 = 20

Therefore, Bryan and Yuan will meet after 5 hours, having traveled 20 miles each.