In the following two questions, find the area of each figure.

The possible value of x that is here, a are 8 and 12, when the sum of two number and product is given.

A group of two or more equations that must be solved all at once is known as a system of equations. The values of the variables in a system of equations that make all of the equations in the system true are known as the solutions. Several approaches, including substitution, elimination, and graphing, can be used to solve systems of equations. Several branches of mathematics, science, and engineering employ systems of equations to represent and solve issues that arise in the real world.

Let us suppose the two numbers = a and b.

Thus, from the given statement we have:

a + 2b = 20 (Equation 1)

and

ab ≤ 48 (Equation 2)

Using equation 1:

a = 20 - 2b

Substituting this expression for "a" into Equation 2, we get:

(20 - 2b)(b) ≤ 48

-2b² + 20b - 48 ≤ 0

b² - 10b + 24 ≥ 0

This inequality can be factored as:

(b - 4)(b - 6) ≥ 0

Since we want the product of the two numbers to be less than or equal to 48, both "a" and "b" must be positive.

We only need to consider the values of "b" that make this inequality true:

b ≤ 4 or b ≥ 6

Plug each of these values of "b" back into Equation 1:

When b = 4, we get:

a + 2(4) = 20

a = 12

When b = 6, we get:

a + 2(6) = 20

a = 8

Therefore, the possible values of "a" are 8 and 12.

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Answer:

Below

Step-by-step explanation:

Domain    'x' can be any value except 10 <====which would make the denominator = 0 which is not allowed

   (-∞, 10 )  U (10 , +∞)

Range :   horizontal asymptote    the degree of the numerator and the denominator is the same : 1     so the horizontal asymptote will be

          3 / -1 = -3    ( The coefficients of 'x' in the num and den)

   the vertical asymptote occurs at x = 10 ...then the value of y goes to + inf

        so range is   ( -3, +∞)

Inverse Does exist , switch x's and y's in the original equation

   x = (3y+1) / (10-y)     now solve for   y

     and you will get  f^-1 (x) = (10x-4) / (x+3)

Here is graph of f(x) , f^-1(x)   and  x=y :

Answer:

The probability that both grab oranges would be = 1/30

Step-by-step explanation:

bc 1/8 * 2/9 = 1/30

hope this helps

Answer: The probability that both grab oranges would be =1/36

Step-by-step explanation:

Given,

A bowl contains,

Apples = a = 5

Oranges = o = 2

bananas = b = 2

Total fruits in bowl = x = a + o + b = 5 + 2 + 2 = 9

Now, Christian and Aaron come home from school and randomly grab one fruit each.

The probability of first selecting orange would be = o/b =2/9

Now, the oranges left would be 2 - 1 = 1

and total fruits would be = 9 - 1 = 8

Hence, the probability of selecting second orange would be = 1/8

Therefore, the probability that both grab oranges would be = 1/8 2/9 =1/36

The derivative of y = tan(x) is sec²(x).

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

y=tanx

dy/dx = dy/dx = cos x.cos x - sin x(-sin x) / cos² x

⇒ dy/dx = (cos² x + sin² x) / cos² x

⇒ dy/dx = 1 / cos²x

⇒ dy/dx = sec²(x)

Thus, the derivative of y = tan(x) is sec²(x).

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The value of f(15) is approximately 346.42.

An exponential function is a mathematical function of the form f(x) = abˣ, where a and b are constant and b is greater than zero and not equal to 1. An example is f(x) = 2ˣ

We can use the properties of exponential functions to find the value of f(15). Since f(x) is an exponential function, we can write it in the form:

f(x) = a × bˣ

f(4.5) = 16 = a × b⁴.5

f(9.5) = 60 = a × b⁹.5

Dividing second equation by first equation gives:

f(9.5)/f(4.5) = (a × b⁹.5)/(a × b⁴.5) = b⁵

Substituting the given values, we get:

60/16 = b⁵

b = (60/16)¹/⁵

b ≈ 1.46

Substituting b into the first equation gives:

16 = a × 1.46⁴.5

a ≈ 0.30

Therefore, the exponential function is:

f(x) = 0.30 × 1.46ˣ

To find f(15), we can substitute x = 15 into the function:

f(15) = 0.30 × 1.46¹⁵

f(15) ≈ 346.42

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Answer:

7 times 5 = 35

Step-by-step explanation:

The equations that can be used to find the number of students in the homeroom are:

4 = 20 - 1/2m

1/2m + 4 = 20

An equation is a statement that expresses the equality of two expressions in mathematics. It is two expressions that are connected by an equals to sign.

4 + 1/2m = 20

Where m is the number of students in Bryan's home room

In order to determine the value of m, take the following steps:

Combine similar terms:

1/2m = 20 - 4

Add similar terms

1/2m = 16

Multiply both sides of the equation by 2

m = 16 x 2

m = 32

Substitute for m in the above equation:

4 + 1/2(32) = 20

4 + 16 =20

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Answer:

See below.

Step-by-step explanation:

We are asked to identify the Proof for Statement 7.

To start, we already have 2 sides and 1 angle proven, meaning that we can prove ΔABX ≅ ΔABY by the Side-Angle-Side Triangle Congruency Theorem. (SAS).

Because both Triangles are congruent, every side, and angle of the triangles are congruent. ASA, and SAS are incorrect choices, they're only used to prove that 2 triangles are congruent. HL is incorrect as well, the HL (Hypotenuse - Leg Theorem) is only used to prove that 2 triangles are congruent also. Our only option is CPCTC (Corresponding parts of congruent triangles are congruent); Meaning that every angle and every side of the 2 triangles are congruent.

For Statement 7, AX ≅ AY proved by CPCTC.

Answer:

murray= 58÷2= 29

kris=78÷3=26

Logan=84÷3=28

Taylor=92÷4=23

answer=logan

Answer:

C

Step-by-step explanation:

84÷3 = 28

which means that logan was able to solve 28 problems per minute

The p-value is 0.1138 for the given hypothesis.

What exactly is a p-value?

A p-value, or probability value, is a statistical measure that helps to determine the strength of evidence against a null hypothesis in a hypothesis test. In hypothesis testing, a null hypothesis is a statement or assumption about a population parameter that we want to test using sample data. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed test statistic, assuming the null hypothesis is true.

Now,

To test the hypothesis,

 we need to perform a hypothesis test using a significance level (α) to determine whether the sample proportion of satisfied customers is significantly different from 0.9.

The null hypothesis (H0) is that the true proportion of satisfied customers is equal to 0.9. The alternative hypothesis (H1) is that the true proportion is not equal to 0.9.

We can use the normal approximation to the binomial distribution to test this hypothesis, since the sample size is large (n = 1000) and both np and n(1-p) are greater than or equal to 10, where p is the true proportion of satisfied customers.

The test statistic is given by:

z = (P - p0) / √(p0(1 - p0) / n)

where p0 is the proportion (0.9), P is the sample proportion (850/1000 = 0.85), and n is the sample size.

Plugging in the values, we get:

z = (0.85 - 0.9) / √(0.9 * 0.1 / 1000) = -1.5811

The P-value is the probability of getting a test statistic as extreme as -1.5811 or more extreme, assuming the null hypothesis is true. Since this is a two-tailed test (H1: p ≠ 0.9), we need to find the area in both tails of the standard normal distribution.

Using a standard normal distribution table, we find that the area to the left of -1.5811 is 0.0569, and the area to the right of 1.5811 is also 0.0569. Therefore, the total area in both tails is:

p-value = 0.0569 + 0.0569 = 0.1138

So,

     the p-value is 0.1138.

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Answer:

First, we need to find the slope and y-intercept of the linear regression line:

Using a calculator or statistical software, we get:

Slope (b) = 0.621

Y-intercept (a) = 50.4

Therefore, the linear regression equation is:

y = 0.6x + 50.4

To find the projected test grade for a student with a homework grade of 45, we substitute x = 45 into the equation:

y = 0.6(45) + 50.4

y = 27 + 50.4

y = 77.4

Rounding to the nearest integer, the projected test grade for a student with a homework grade of 45 is 77.

Answer: Let's call the number of large boxes purchased "L" and the number of small boxes purchased "S".

From the problem, we know that:

Each small box has 100 nails, so the total number of nails from the small boxes is 100S.

Each large box has 450 nails, so the total number of nails from the large boxes is 450L.

The contractor bought 3 more small boxes than large boxes, so S = L + 3.

The total number of nails purchased is 2500, so 100S + 450L = 2500.

We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for L:

100S + 450L = 2500

Substituting S = L + 3:

100(L + 3) + 450L = 2500

Expanding the parentheses:

100L + 300 + 450L = 2500

Combining like terms:

550L + 300 = 2500

Subtracting 300 from both sides:

550L = 2200

Dividing both sides by 550:

L = 4

So the contractor purchased 4 large boxes of nails.

We can use the equation S = L + 3 to find the number of small boxes purchased:

S = L + 3 = 4 + 3 = 7

So the contractor purchased 7 small boxes of nails.

Therefore, the contractor purchased 4 large boxes and 7 small boxes of nails.

Step-by-step explanation:

Answer:

x > -6/5

Step-by-step explanation:

2 < 8 + 5x

-6 < 5x

x > -6/5

This is the correct answer, but I don't see it in the options list.

Answer:A

Step-by-step explanation:

The surface area of the cylinder is 3,428 square centimeter, the curved surface area of the cylinder is 2,198 square centimeter and the volume of the cylinder is 15,386 cubic centimeter.

What is area and volume?

A flat, two-dimensional object's area is the space it takes up in a plane. A three-dimensional object's volume is the area it takes up in space.

We know that

Curved surface area = 2πrh

So, using this we get

⇒Curved surface area = 2 × 3.14 × 14 ×25

⇒Curved surface area = 2,198 square centimeter

Similarly,

Total surface area = 2πr (r + h)

So, using this we get

⇒Total surface area = 2 × 3.14 × 14 (14 + 25)

⇒Total surface area = 2 × 3.14 × 14 (39)

⇒Total surface area = 3,428 square centimeter

Similarly,

Volume = π[tex]r^{2} h[/tex]

So, using this we get

⇒Volume = 3.14 × [tex]14^{2}[/tex] × 25

⇒Volume = 15,386 cubic centimeter

Hence, the area and volume of the cylinder have been obtained.

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In the back of the maze, you will see two numbers at the start and end points of the maze. Let's call these numbers a and b.

To solve the maze, we need to find the geometric mean of a and b, which is the value that, when multiplied by itself, gives us the product of a and b.

The formula for the geometric mean is:

Geometric Mean = √(a × b)

So, to solve the maze, we need to find the geometric mean of the starting and ending numbers, and then follow the path in the maze that matches that value. This path will lead us to the end of the maze.

Once we find the geometric mean of the starting and ending numbers, we can use a calculator or mental math to simplify the expression and find the value.

I need help with the back of the geometric mean maze

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Using the Law of Cosines the length of l, to the nearest 10th of a centimeter is 4.6 cm.

To find the length of side l in triangle LMN, we can use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C.

In this case, we have:

a = 5.9 cm

b = 8.7 cm

C = 163°

First, we need to convert the angle from degrees to radians by multiplying it by π/180:

C = 163° × π/180 = 2.847 radians

Now we can plug in the values into the Law of Cosines:

l² = 5.9² + 8.7² - 2(5.9)(8.7)cos(2.847)

Simplifying the right-hand side:

l² = 68.81 - 60.83 × cos(2.847)

Taking the square root of both sides:

l ≈ 4.6 cm

Therefore, the length of l to the nearest 10th of a centimeter is 4.6 cm.

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The number of weeks until Riley and Amari would have earned the same, would be 10 weeks.

Variables:

Let x be the number of weeks they work.

Let y be their total earnings in dollars.

System of equations:

For Riley: y = 5x

For Amari: y = 20 + 3x

Setting the two expressions for y equal to each other, we get:

5x = 20 + 3x

5x - 3 x = 20

x = 20 / 2

x = 10 weeks

Therefore, their earnings will be the same after 10 weeks of work.

We can also solve the system of equations graphically by plotting the two equations and finding the point of intersection. The point of intersection is (10,50). Therefore, their earnings will be the same after 10 weeks of work and their total earnings will be $50.

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The question, when translated to English is:
Riley and Amari earn weekly chore allowances for the summer, Riley is paid $5 a week and Amari is paid $20 at the beginning of the summer and then earns $3 a week.

When will their earnings be the same?

We can say that after answering the offered question The ladder is Pythagorean theorem therefore 15 feet long, rounded up to the next foot. Thus, 15 feet is the solution.

The Pythagorean Theorem is the foundational Euclidean geometry connection that exists between the three sides of the right triangle. According to this rule, the area of either a cube with the length x side is equal to the total of the regions of triangles shared by its other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the perfect angle is the combined squares that spanned its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

The ladder serves as the hypotenuse in this basic example of a right triangle, which also includes the distance from the house as one of its legs and the ladder's height as its second leg. The Pythagorean theorem can be used to find the ladder's length.

[tex]c^2 = a^2 + b^2[/tex]

In this instance, we know that the distance from the house (a) is 9 feet, and the height of the ladder (b) is 12 feet. Hence, we can enter these values into the formula as follows:

[tex]c^2 = 9^2 + 12^2 c^2 = 81 + 144\sc^2 = 225\sc = √225\sc = 15[/tex]

The ladder is therefore 15 feet long, rounded up to the next foot. Thus, 15 feet is the solution.

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Answer:2>x[tex]\geq[/tex]-3

Step-by-step explanation:

when we divide each side with a negative number "<" turns into ">",">" turns into "<" and so on.

we can divide each side with -1, the we get,

2>x[tex]\geq[/tex]-3

[tex]-2 < -x \leq 3 \iff 2 > x \geq -3[/tex]

[tex]-3 \leq x < 2 \implies x \in [-3;2)[/tex]

Answer:

Step-by-step explanation:

the answer would be 5/4 i belive

When simplified, the above expression translates to = 4(x + 9) / (x + 6) where the restrictions are stated as: x ≠ -8, 4, -6.

In mathematics, restrictions refer to conditions or limitations placed on the values that a variable can take, either to ensure the validity of a mathematical expression or to satisfy a particular requirement.

With regard to the above,

We can simplify the given expression as follows:

(x^2 + 5x - 36) / (x^2 + 4x - 32) * (4x + 32) / (x + 6)

= [(x + 9)(x - 4) / (x + 8)(x - 4)] * [4(x + 8) / (x + 6)]

= (x + 9) * 4 / (x + 6)

= 4(x + 9) / (x + 6)

The restrictions on the variable are:

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x + 4y = -52.

The point-slope form of the equation of a line passing through the point (x1, y1) with slope m is:y - y1 = m(x - x1)Here, the point (x1, y1) = (18, -17) and the slope m = -1/4Therefore, the equation of the line in point-slope form is:y + 17 = (-1/4)(x - 18)Expanding the equation:4(y + 17) = -x + 18 => 4y + 70 = -x + 18 => x + 4y = -52The required equation of the line is x + 4y = -52.

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The reject the null hypothesis with α=0.05.

Based on the above calculations, we should reject the null hypothesis with α=0.05.

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Answer: Your answer is C

Step-by-step explanation:

Have a nice day

Answer:

6 / b - 7

Step-by-step explanation:

After answering the presented question, we can conclude that If the star equation player is in the starting lineup, there are 210 distinct starting lineups imaginable.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

If the starting lineup includes the star player, there are only four spaces left to fill with the remaining ten players. The number of possible starting lineups is the number of ways to select four players from the remaining ten, which may be calculated using the combination formula:

C(10,4) = 10! / (4! * 6!) = 210

If the star player is in the starting lineup, there are 210 distinct starting lineups imaginable.

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Answer: Emmy Watson made a down payment of 20%, which means she paid 20% of the total cost of the oven upfront.

20% of 915.0 = 0.20 x 915.0 = 183.0

So, Emmy Watson paid $183.0 as a down payment.

To find out how much she financed, we need to subtract the down payment from the total cost of the oven:

Financed amount = Total cost - Down payment

Financed amount = $915.0 - $183.0

Financed amount = $732.0

Therefore, Emmy Watson financed $732.0.

Step-by-step explanation: