Expand and simplify y(2y+5) +4(2y+3)

The brace must be approximately 38.1 cm long.

To find the length of the brace for the closet rod holder,

we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the vertical side is 15 cm and the horizontal side is 35 cm.

Let's call the length of the brace (the hypotenuse) "c".

According to the Pythagorean theorem:
[tex]c^2 = (15 cm)^2 + (35 cm)^2[/tex]
[tex]c^2 = 225 cm^2 + 1225 cm^2[/tex]
[tex]c^2 = 1450 cm^2[/tex]
Now, to find the length of the brace, we need to take the square root of both sides:
[tex]c = \sqrt{(1450 cm^2)}[/tex]
c ≈ 38.1 cm.

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Answer:

B

Step-by-step explanation:

a² + 14a - 51 = 0 ( add 51 to both sides )

a² + 14a = 51

to complete the square

add ( half the coefficient of  the x- term )² to both sides

a² + 2(7)a + 49 = 51 + 49

(a + 7)² = 100 ( take square root of both sides )

a + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )

a = - 7 ± 10

then

a = - 7 + 10 = 3

a = - 7 - 10 = - 17

The area of the path running around the square field is 475 square meters.

To find the area of the path running around a square field with a side of 45 meters and a path width of 2.5 meters,

Calculate the area of the entire square (including the path):

Side of the larger square = 45 M (side of the field) + 2.5 M (width of the path on one side) + 2.5 M (width of the path on the opposite side) = 50 M

Area of the larger square = (Side of the larger square)²

                                          = (50 M)²

                                          = 2500 M²

Calculate the area of the square field (without the path):

Side of the field = 45 M

Area of the square field = (Side of the field)²

                                       = (45 M)²

                                       = 2025 M²

Subtract the area of the square field from the area of the entire square to find the area of the path:

Area of the path = Area of the larger square - Area of the square field

                           = 2500 M² - 2025 M²

                           = 475 M²

So, the area of the path running around the square field is 475 square meters.

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The solution to the equation is 3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1 and it has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be described by the four fundamental operations, sometimes known as "arithmetic operations." Operations like quotient, product, sum, and difference come before operations like division, multiplication, addition, and subtraction in mathematics.

We are given an equation as:

[tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]

Now, we will simplify the equation first.

⇒ [tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]

⇒ [tex]\frac{3(z+1) - z(z-1)}{3 (z-1)}[/tex] = [tex]\frac{2}{z-1}[/tex]

Now, on cross multiplying we get,

⇒[3 (z + 1) - z (z - 1)] * (z - 1)  = 2 (3z - 1)

⇒[3z + 3 - [tex]z^{2}[/tex] - z] * (z - 1)  = 6z - 2

⇒3[tex]z^{2}[/tex] + 3z - [tex]z^{3}[/tex] - [tex]z^{2}[/tex] - 3z - 3 + [tex]z^{2}[/tex] + z = 6z - 2

⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] - 3 + z = 6z - 2

⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1

Hence, the required solution has been obtained.

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Answer:

[tex] \frac{25}{121} [/tex]

Step-by-step explanation:

Given:

r (dartboard) = 11 m

r (shaded area) = 5 m

π = 3,14

First, let's find the area of the dartboard:

A (dartboard) = πr^2 = 3,14 × 121 = 379,94 m^2

A (shaded area) = 3,14 × 25 = 78,5 m^2

Let's call this event A:

A - "A dart must hit the shaded area":

All outcomes:

n = 379,94

Favorable outcomes:

m(A) = 78,5

[tex]p(a) = \frac{78.5}{379.94} = \frac{25}{121} [/tex]

I assume, this is the right answer

Account I.

$822.12

$17.88

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So:

(0.4x10^-6)(0.7x10^-2) = (0.4)(0.7)x10^(-6-2) = 0.28x10^-8

Therefore, the answer is 0.28 x 10^−8 in scientific notation.

Answer:

A. The rate of change of the table is equal to the rate of change of the graph.

No, Johnny does not have enough fruit to make smoothies for his 5 friends because he is short 383.51 ounces of juice.

Therefore, the probability that a student who did not complete the homework passed the test is 2/5 or 0.4 (or 40%).

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (getting heads) out of two possible outcomes (getting heads or tails).

Let's define the following events:

A: passing the test

B: completing the assignment

We know that:

[tex]P(A) = 18/28 = 9/14[/tex] (since 18 students out of 28 passed the test)

[tex]P(B) = 19/28[/tex] (since 19 students out of 28 completed the assignment)

P (A ∩ B) = P(B) = 19/28 (since every student who completed the assignment also took the test)

We want to find P (A | not B), which represents the probability of passing the test given that the student did not complete the assignment.

Using Bayes' theorem, we have:

P (A | not B) = P (not B | A) * P (A) / P (not B)

We know that:

P (not B | A) = P (A' ∩ B') / P(A') = 7/28 / 10/28 = 7/10 (since 7 students failed the test and did not complete the assignment)

P (not B) = 1 - P(B) = 9/28 (since not completing the assignment is the complement of completing the assignment)

Plugging in these values, we get:

[tex]P(A | not B) = (7/10) * (9/14) / (9/28)[/tex]

[tex]P(A | not B) = 2/5[/tex]

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Answer:

y in (7,y) = 14

Step-by-step explanation:

A General Linear function is as the following:

y = mx + c, Where: m: slope of the line, c: y-intercept

Given that:

Point 1 (P1) = (1,5)

Point 2 (P2) = (3, 11)

Point 3 (P3) = (7,y)

By substituting in the linear function with P1:

5 = m + c  ---> (1)

By substituting in the linear function with P2:

11 = 3m + c   ---> (2)

By multiplying equation (1) times 3 and subtracting eq. (2) from it:

(15 = 3m + 3c) - (11 = 3m + c) =

4 = 2c

Then, c = 2

By substituting with "c" in eq. (1):

5 = m + 2

Then, m = 3

Hence,

the function of this line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23


Another Solution:

by getting the slope of the line:

[tex]Slope = \frac{\triangle y}{\triangle x}[/tex] Where: Δy: change in y points, Δx: change in x points

by utilizing P1 & P2 in slope formula:

[tex]slope = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3[/tex]

By substituting with P1 in the linear function:

5 = 3 + c

Then, c = 2

the function of the line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23



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According to the given question, the center of the circle is (-9, 46) and its radius is approximately 11.09.

The equation of a circle is a formula that describes the relationship between the x and y coordinates of any point on the circle.

The standard equation of circle is:

(x - h)²+(y - k)²=r²

This equation states that the sum of the squares of the differences between the x-coordinate and the center, and the y-coordinate and the center, is equal to the square of the radius.

The equation of the circle is given by (x+9)² + (y-46)² = 123.

Comparing this to the standard equation of a circle, (x-h)² + (y-k)² = r², we can see that the center of the circle is (-9, 46) and the radius is √(123) = 11.09.

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Answer: the value of x is 29

Step-by-step explanation:

Answer:

it's in the attachment

Step-by-step explanation:

the one that are the same value as the given value on the transversals are either opposite interior angles or opposite exterior angles

the ones that have different values as the given value on the transversal are subtracted from 180⁰

Answer:

I think the answer is

1760

Proof that one million boards aren't enough. .Therefore, one million boards are not enough to reach (2023, 2023).

A total of 2023 boards are needed to reach (2023, 2023).

This problem is a mathematical puzzle that involves traversing a hazardous area to reach a specific point using a limited number of resources.

The problem is set in the Cartesian plane, where the first quadrant (i.e., the region where both x and y coordinates are positive) is covered with lava, making it impossible to traverse.

Let's assume that we can reach (2023, 2023) with one million boards. We know that each board can cover a distance of at most 1. Therefore, the total distance we can cover with one million boards is at most one million. However, the distance between the origin (0, 0) and (2023, 2023) is ✓2023² + ✓2023² = 2855.9

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classify the different measurement systems into one of the four types

of scales. (Exercise)

1. Your checking account number as a name for your account.

2. Your checking account balance as a measure of the amount of money you

have in that account

3. The order in which you were eliminated in a spelling bee as a measure of your

spelling ability.

4. Your score on the first statistics test as a measure of your knowledge of

statistics.

5. Your score on an individual intelligence test as a measure of your

intelligence.

6. The distance around your forehead measured with a tape measure as a

measure of your intelligence.

7. A response to the statement "Abortion is a woman's right" where "Strongly

Disagree" = 1, "Disagree" = 2, "No Opinion" = 3, "Agree" = 4, and "Strongly

Agree" = 5, as a measure of attitude toward abortion.

8. Times for swimmers to complete a 50-meter race

9. Months of the year Meskerm, Tikimit…

10.Socioeconomic status of a family when classified as low, middle and upper

classes.

11. Blood type of individuals, A, B, AB and O.

12.Pollen counts provided as numbers between 1 and 10 where 1 implies there is

almost no pollen and 10 that it is rampant, but for which the values do not

represent an actual counts of grains of pollen.

13.Regions numbers of Ethiopia (1, 2, 3 etc.)

14.The number of students in a college;

15.the net wages of a group of workers;

16.the height of the men in the same town;

The solutions for y are:

We can simplify the expression sqrt(160) by factoring 160 into its prime factors:

160 = 2^5 * 5

Taking the square root of each factor, we get:

sqrt(160) = sqrt(2^5 * 5) = sqrt(2^4 * 2 * 5) = 2^2 * sqrt(2 * 5) = 4 * sqrt(10)

Therefore, we can simplify the expression for y as follows:

y = (7 +- sqrt(160))/10 = (7 +- 4sqrt(10))/10

So the solutions for y are:

y = (7 + 4sqrt(10))/10

y = (7 - 4sqrt(10))/10

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The relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

Lοοking at the given pοints, we can see that the input x = -5 has an οutput y = 1, and the input x = 5 alsο has an οutput y = 1.

This means that there are twο different inputs (x-values) that cοrrespοnd tο the same οutput (y-value), viοlating the definitiοn οf a functiοn.

Tο determine if the relatiοn is a functiοn, we need tο check if fοr each input (x-value), there is exactly οne οutput (y-value).

Therefοre, the relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

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Answer:

381.7 cubic inches.

a=b, The curve approaches the line y=a as x approaches infinity or negative infinity.

since the y-intercept is the point where the curve intersects the y-axis, i.e., x=0.

Since we have (0, a) as our y-intercept, then a=b, where a and b are constants.

The y-intercept, as indicated in the question, is (0, a) meaning that for the function f(x), when x=0, then f(x) = a.

The horizontal asymptote of a function is a horizontal line that the graph approaches as x approaches infinity or

negative infinity.

If the horizontal asymptote is y=b, it means that the value of y approaches b as x approaches infinity or negative infinity.

Therefore, since a=b, the curve approaches the line y=a as x approaches infinity or negative infinity.

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The equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

The definitiοn οf an equatiοn οf the line is a linear equatiοn with degree 1. X and Y are twο variables in the equatiοn fοr the line. The slοpe οf the line, which reflects the elevatiοn οf the line, is the third parameter.

The general fοrm οf the equatiοn οf the line:-

y = mx + c

m = slοpe

c = y-intercept

Given that Line, v has an equatiοn οf y=–109x–3. Perpendicular tο line v is line w, which passes thrοugh the pοint (2,3).

The slοpe οf the required line will be inverse and the οppοsite οf the given line,

m = 1/109

The intercept will be calculated as,

y = mx + b

3 = (1/109)2 + b

3 = 2/109 + b

327/109 = 2/109 + b

325/109 = b

The equatiοn οf the line is written as,

y = (1/109)x + (325/109)

Therefοre, the equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

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f(x) = 12x and  [tex]g(x)= \sqrt{x-12}[/tex] both include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

The set containing all input values is known as a function's domain while a function's range is the collection of all possible output values.

Function f(x) is defined by: f(x) = 12x.

Function g(x) is defined by: [tex]g(x)= \sqrt{x-12}[/tex]

Therefore, the correct option is (d) Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

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The graph which shows a system of linear-equations with one unique solution at (0,5) is option-B which shows lines, intersecting at (0,5).

What is system of linear equations?

The collection of two or more linear equations is called as system of linear equations. The linear equations have the degree of variable as one. Though a single linear equation can have infinite number of solutions, but a pair of linear equation can be classified as consistent or inconsistent. The equations which are consistent have either one solution or infinte solutions. The intersecting pair of consistent equations have unique solution whereas the coinciding pair of consistent equations have infinite number of solutions. The equations which are inconsistent are the parallel lines which do not have any solution.

Here the system must have one unique solution as (0,5)

a)graph as parallel lines: which means they are inconsistent & do not have any solution.

b)The graph shows lines intersecting at (0,5): which means the system is consistent with unique solution (0,5)

c)The graph shows lines intersecting at (1,6): which means the system is consistent with unique solution (1,6)

d)graph shows two lines which appear as one: means the lines are coinciding with infinite solutions.

So the answer is option-B

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Answer:

  cos(L) = (√46)/11

Step-by-step explanation:

You want cos(L) in simplest terms, given right triangle side lengths LK=√46 and JK=√75.

The cosine is the ratio ...

  Cos = Adjacent/Hypotenuse

The side adjacent to vertex L is LK. The hypotenuse of the triangle is LJ. This means the desired ratio is ...

  cos(L) = LK/LJ

The length of hypotenuse LJ can be found using the Pythagorean theorem.

  LJ² = LK² +JK²

  LJ² = (√46)² +(√75)² = 46 +75 = 121

  LJ = √121 = 11

Then the desired ratio is ...

  cos(L) = (√46)/11

In terms of using specific terms in your answer, you should incorporate any keywords or phrases from the student's question that are relevant to your response.

For example, in response to the question "a restaurant wants to know if its customers like its new menu. in surveys 100 randomly selected customers over one week. what is the population in this study?" you might write:"

In this study, the population refers to the entire group of customers who might potentially like or dislike the restaurant's new menu.

While the study only surveyed 100 randomly selected customers over one week, the population could include all customers who visited the restaurant during that time period or even a larger group of potential customers who have not yet visited the restaurant."

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Answer:

true

Step-by-step explanation:

The possible lengths x for the side of square A. The possible lengths x for the side of the square is the interval [-7,7].

Since the area of a square is given by the formula A = x^2, where x is the length of the side, we can solve for x to find the possible lengths of a square with area 49 square feet or less.

A ≤ 49

x^2 ≤ 49

|x| ≤ 7

So the possible lengths for the side of the square are any values of x between -7 and 7, inclusive.

Therefore, the answer is: A. The possible lengths x for the side of the square is the interval [-7,7].

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