3,286-(1,221+217)…….

Answer:

x=7

y=8

(x+y)= 15

(x-y)= -1

Step-by-step explanation:

let x and y be the numbers

x + y = 15 ------ 1

2x - y = 6 ------ 2

add both equation 1 and 2

3x = 21

x = 21\3

x=7

subtitute 7 for x in equation 1

7 + y = 15

y = 15-7

y=8

The first number x = 7

The second number y = 8

thus x + y = 7 + 8 = 15

x - y = 7 - 8 = -1

The point (5, 10) has not been translated in the given figure.Hence this statement is false.

The graph shows five points.

A point has been translated right and up.

Now, the statements that are true based on the graph are as follows:

The point (9, D) has been translated right and up.Answer: False

There is no information given about point (9, D).

So, we cannot say anything about the translation of point (9, D).

The point (1, 8) has been translated right and up.Answer: True

As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.

The point (2, 9) has been translated right and up.Answer: False

The point (2, 9) has not been translated in the given figure.

So, this statement is false.

Statement 4: The point (8, B) has been translated right and up.Answer: True

The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.

The point (5, 10) has been translated right and up.Answer: False

The point (5, 10) has not been translated in the given figure.

So, this statement is false.

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By mathematical induction, P(m) is true for all integers m > 1. for every integer m > 1, am = cm (mod n).

P(1) is true: a = c(mod n) implies a1 = c1 (mod n), which is true by definition of congruence.

Assume P(k): ak = ck (mod n) for some integer k > 1.

We need to show that P(k+1) is true: ak+1 = ck+1 (mod n).

Since ak = ck (mod n) and a = c(mod n), we have ak = a + kn and ck = c + ln for some integers k, l.

Then ak+1 = aak = a(a+kn) = a2 + akn and ck+1 = cck = c(c+ln) = c2 + cln.

Since ak = ck (mod n), we have a2 + akn = c2 + cln (mod n).

Subtracting akn from both sides, we get a2 = c2 + (l-k)n (mod n).

Since n > 1, we have l - k ≠ 0 (mod n), so (l - k)n ≠ 0 (mod n).

Thus, we can divide both sides of the congruence by (l - k)n to get a2/(l-k) = c2/(l-k) (mod n).

Since l - k ≠ 0 (mod n), we can cancel (l - k) to get a2 = c2 (mod n).

Substituting back, we get ak+1 = ck+1 (mod n).

Therefore, P(k+1) is true.

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Answer: (a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

Step-by-step explanation: First, you need to simplify the fraction in the first term:

(a^2 - 4)/(x^2 - 9)

Next, you simplify the fraction in the second term:

(a^2 - 2a + (2-y))/(xy + 3y)

Then you subtract (x-3) from the fractions obtained in step 1 and 2:

(a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

This is the final result of the operation.

It is important to note that the answer is a simplified fraction and only valid if x does not equal 3. If x=3, the denominator x-3 would be equal to zero, which is not allowed in mathematics.

Answer:

check pic

step-by-step explanation

check pic

Answer:

see below

Step-by-step explanation:

tan ^2 x -sin ^2 x = tan ^2x sin ^2x

tan = sin / cos

sin ^2 x / cos ^2 x -sin ^2 x = sin ^2 x / cos ^2 x * sin^2 x

Multiply each side by cos ^2

cos ^ x (sin ^2 x / cos ^2 x -sin ^2 x) = cos ^2 x(sin ^2 x / cos ^2 x * sin ^2x)

sin ^2 x  - cos ^2 x sin ^2 x = sin ^2 x  * sin ^2x

Factor out sin ^2 x

sin ^2 x(1  - cos ^2 x) = sin ^2 x  * sin^2 x

We know that 1 - cos ^2 x = sin ^2 x

sin ^2 x(sin ^2 x) = sin ^2 x  * sin^2 x

Answer:

It usually has 1 solution, but sometimes it can have zero

Step-by-step explanation:

Answer:

1. C

2. C

3. E

Step-by-step explanation:

I added photos of my solutions

The solution to the system of equations is x = 1/2 and y = 3/2.

The solution is x = 1 and y = 4.

The solution to the system of equations is (x, y) = (2, 1/2).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Part 1:

To solve the system of equations:

3x + y = 3

x + y = 2

We can solve for one of the variables in one of the equations and substitute it into the other equation.

For example, we can solve for y in the second equation:

y = 2 - x

Then we can substitute this expression for y into the first equation:

3x + (2 - x) = 3

Simplifying this equation gives:

2x + 2 = 3

Subtracting 2 from both sides gives:

2x = 1

Dividing both sides by 2 gives:

x = 1/2

Now we can use this value of x to find the value of y:

y = 2 - x

y = 2 - 1/2

y = 3/2

Therefore, the solution to the system of equations is:

x = 1/2 and y = 3/2.

Part 2:

Substitute the first equation into the second equation:

x + 3y = 13

(y - 3) + 3y = 13 (substituting x = y - 3)

4y - 3 = 13

4y = 16

y = 4

Now substitute y = 4 into the first equation to solve for x:

x = y - 3

x = 4 - 3

x = 1

Therefore, the solution is x = 1 and y = 4.

Part 3;

To solve the system of equations:

x + 2y = 3 ...(1)

3x - 2y = 5 ...(2)

We can add the equations vertically to eliminate the y-variable:

(1) + (2): x + 2y + 3x - 2y = 3 + 5

Simplifying: 4x = 8

Dividing both sides by 4: x = 2

Now, we can substitute x = 2 into either equation to solve for y.

Let's use equation (1):

x + 2y = 3

2 + 2y = 3

Subtracting 2 from both sides: 2y = 1

Dividing both sides by 2: y = 1/2

Therefore, the solution to the system of equations is (x, y) = (2, 1/2).

Thus,

The solution to the system of equations is x = 1/2 and y = 3/2.

The solution is x = 1 and y = 4.

The solution to the system of equations is (x, y) = (2, 1/2).

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Answer:

Step-by-step explanation:

1 Km / min

In one minute the distance traveled = 1 km

In 60 minute the distance traveled = 1 * 60 = 60 km

1 Km /min = 60 km/h    

Answer:

Step-by-step explanation:

Answer:

The angle measures approximately 18.19°.

Step-by-step explanation:

Since we want to find the angle and we are given the side adjacent to the angle and the hypotenuse, we can use the cosine ratio. Recall that:

\(\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\)

The adjacent side is 19 and the hypotenuse is 20. Substitute:

\(\displaystyle \cos \theta = \frac{19}{20}\)

We can take the inverse cosine of both sides:

\(\displaystyle \theta = \cos^{-1}\frac{19}{20}\)

Use a calculator (make sure you're in Degrees Mode!). Hence:

\(\theta \approx 18.19^\circ\)

The angle measures approximately 18.19°.

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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The picture given is completely black,

I will edit my answer if needed and will help once fixed.

It's a black picture, and I'm really confused.

Answer attached as picture with explanation. Please check.

Answered by Benjemin

A deficiency in the release of vasopressin (ADH) by the posterior pituitary gland causes diabetes insipidus. Option C

Diabetes insipidus is a condition characterized by the inability of the body to regulate water balance due to a deficiency in the release of vasopressin, also known as antidiuretic hormone (ADH), by the posterior pituitary gland. Vasopressin plays a crucial role in regulating water reabsorption in the kidneys, thereby controlling urine concentration and volume.

When there is a deficiency of vasopressin, the kidneys are unable to properly reabsorb water, leading to excessive urination and increased thirst. This condition is called diabetes insipidus, which is different from diabetes mellitus, a condition related to blood sugar regulation.

Hypoglycemia refers to low blood sugar levels and is not directly associated with a deficiency in vasopressin. Dwarfism, on the other hand, is a condition characterized by stunted growth and is caused by various factors such as genetic mutations or hormonal imbalances, but not specifically by a deficiency in vasopressin.

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Answer:

2 12/27

Step-by-step explanation:

4^x/3=2 and 8^x/27=12/27

Median should be used to determine which location typically has the cooler temperature, considering the data provided.

When comparing the data, the measure of center that should be used to determine which location typically has the cooler temperature is the median, because Desert Landing is skewed.

Skewness refers to the asymmetry of a distribution. In the case of Desert Landing, the graph is titled "Temps in Desert Landing," and it is described that the shaded bar stops at 2 above the interval 60 to 69, which means the frequency of temperatures in that range is lower compared to the other intervals. Similarly, the shaded bar stops at 4 above the interval 70 to 79, indicating a higher frequency of temperatures in that range. This suggests a skewed distribution where the data is not evenly distributed around the center.

In a skewed distribution, the mean can be influenced by extreme values, while the median is a more robust measure of center. The median represents the middle value when the data is ordered from lowest to highest. Since Desert Landing has a skewed distribution, the median would be more appropriate to determine which location typically has the cooler temperature.

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By dividing the sum of squares of all observations or SS(Total) by (n-1), we can retrieve the sample variance.

When conducting a statistical analysis, it is often necessary to compare different groups or treatments to determine if there is a significant difference between them. One way to do this is through the use of hypothesis testing, where a null hypothesis is proposed and tested against an alternative hypothesis.

In the context of the given question, if the null hypothesis is found to be true, then the sum of squares of all observations or SS(Total) can be used to calculate the variance of the population. Specifically, dividing SS(Total) by (n-1), where n is the sample size, gives an unbiased estimate of the population variance.

This estimate is commonly referred to as the sample variance and is often denoted by s^2. It represents the average squared deviation of individual observations from the sample mean and is an important parameter for many statistical analyses, including hypothesis testing and confidence interval estimation.

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Answer:

= 20 + 7x

Step-by-step explanation:

2(5+3x) + (x + 10)

10 + 6x + (x + 10)

= 20 + 7x

The simplified expression is 20+7x.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given:

2(5+3x) + (x + 10)

Now, simplifying

10 + 6x + x +10

=10 + 10 + 6x + x

=20 + 7x

Hence, the simplified expression is 20+7x

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Given:

A polynomial has a root of −2.

To find:

The factor that will divide evenly into the polynomial.

Solution:

We know that, if c is a root of a polynomial P(x), then (x-c) is a factor of polynomial P(x).

we have,

-2 is a root of polynomial.

⇒ (x-(-2)) is a factor of polynomial.

⇒ (x+2) is a factor of polynomial.

⇒ (x+2) will divide the polynomial completely.

Therefore, the factor (x+2) will divide evenly into the polynomial.

The factors of a polynomial divide the polynomial evenly, without remainder

The factor of the polynomial is x + 2

The root of the polynomial is given as:

\(\mathbf{Root = -2}\)

Assume the polynomial is a function of x.

i.e. the variable of the polynomial is x

Then the root can be represented as:

\(\mathbf{x= -2}\)

Add 2 to both sides

\(\mathbf{x + 2= -2 +2}\)

So, we have:

\(\mathbf{x + 2= 0}\)

Hence, the factor of the polynomial is x + 2

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Using sine ratio in trigonometric ratio, the length of the ladder is 29.6 feet

Trigonometric ratios are ratios of the sides of a right triangle that are used to describe the angles of the triangle. They are used in many different branches of mathematics, including geometry, calculus, and trigonometry. The most common trigonometric ratios are sine, cosine, and tangent.

To solve this problem, we have to determine which of the ratio we need.

Data;

Since we have the opposite side and angle, we can find the hypothenuse using sine ratio

sinθ = opposite / hypothenuse

sin 71 = 28 / x

x = 28 / sin 71

x = 29.6 feet

The length of the ladder is 29.6 feet

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Answer:

29.61

Step-by-step explanation:

Answer:

I don't see the answer  but it is 3/2x - 3 = y

Step-by-step explanation:

did it on edge 2020

The equation of the line representing the graphed function is y = ( 3/ 2 ) x - 3. Option E is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The equation is formed by finding the slope using the coordinates ( 0,-3 ),( 2, 0 ) and ( 4, 3 ).

The slope is calculated as,

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

x₁ = 0, y₁ = -3 and x₂ = 2, y₂ = 0.

The equation is given as,

y = mx + c

y = (-3/2)x - 3

Therefore, the equation of the line representing the graphed function is y = ( 3/ 2 ) x - 3.

The complete question is given below;-

A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).

Which equation represents the graphed function?

–3x + 2 = y

–x + 2 = y

x – 3 = y

2x – 3 = y

y = ( 3/ 2 ) x - 3.

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Answer: Sample D is most representative.

Step-by-step explanation:

Sample D is most representative as the percentage per shape stays the same within the sample and the population.

Answer:

sample D is most representative

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

(-2, -2)

Step-by-step explanation:

You can isolate one variable, x or y, from any of the given equations and substitute to find the solution.

Let's isolate y from 4x + 3y = -14.

To do this, we can substract 4x to get 3y = -4x - 14.

Then, we divide both sides of the equation by 3 to result in y = -4/3x - 14/3.

Next, substitute -4/3x - 14/3 for y in 8x + 10y = -36.

The equation then becomes 8x + 10(-4/3x - 14/3) = -36.

Multiply the quantity in the parentheses by the given number 10, and the equation is now 8x + (-40/3x) + (-140/3) = -36.

Solve the equation by adding like terms.

8x + -40/3x = -16/3x

-16/3x + -140/3 = -36

You can multiply both sides of the equation by -3 to remove the fraction and negative.

16x + 140 = 108

16x = -32

x = -2

Finally, substitute x in any of the equations to find y.

4(-2) + 3y = -14

-8 + 3y = -14

3y = -6

y = -2

So, the solution is (-2, -2).

To find the solution of the given system of equations, use the method of elimination.

To find the solution of the given system of equations, we can use the method of elimination. Multiply the first equation by 2 to make the coefficients of y in both equations equal:

8x + 6y = -28

8x + 10y = -36

Now subtract the first equation from the second equation:

(8x + 10y) - (8x + 6y) = -36 - (-28)

4y = -8

Divide both sides of the equation by 4:

y = -2

Substitute the value of y into either of the original equations:

4x + 3(-2) = -14

4x - 6 = -14

4x = -8

x = -2

So the solution to the system of equations is (-2, -2).

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Answer:

y = 6

Step-by-step explanation:

I'm going to assume you want to solve for y.

Step 1: Move all constants to 1 side, isolating y and its coefficient:

14 = 3y - 4

14 + 4 = 3y - 4 + 4

18 = 3y

Step 2: Divide both sides by 3 to solve for y:

3y = 18

3y / 3 = 18 / 3

y = 6

Final answer: y = 6

After 44 minutes is the temperature of each piece of metal the same.

The mathematical description of two things that are equal—one on each side of a "equals" sign—is called an equation. Equations help us address problems in our daily lives. Most of the time, we seek pre algebra assistance to answer challenges in real life. The fundamentals of math are found in pre-algebra ideas.

Given,

A piece of metal at 20°C is warmed at a steady rate of 2 degrees per

the same time, another piece of metal at 240°C is cooled at a steady rate of 3 degrees per minute.

Let time be t

Equation,

20 +2t = 240 - 3t

2t + 3t = 240 - 20

5t  = 220

t = 44

After 44 minutes is the temperature of each piece of metal the same.

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Answer:

5

Step-by-step explanation

Step-by-step explanation:

for x=8,y=4

4=8x-4

8x=4+4

8x=8

x=1

y=8 (8)-4

y=64-4

y=60

for x=0.5, y= -4

-4=8x-4

8x= -4+4

8x=0

x=0

y=8 (0.5)-4

y=4-4

y=0

for x=2,y=-4

-4=8x-4

8x=4-4

8x=0

x=0

y=8 (2)-4

y=16-4

y=12

for x= -4,y=8

8=8x-4

8x=8+4

8x=12

x=1.5

y=8 (-4)-4

y= -32-4

y= -36

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

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

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25