Solve the simultaneous equations
x^2+y^2=9
x+y=2
Give your answers correct to 2 decimal places

The length of the side b of the right triangle is 76 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. Therefore, the side b of the right triangle can be found as follows:

tan 30° = opposite / adjacent side

where

opposite side = a = 44 units

adjacent side = b

Therefore,

tan 30° = 44 / b

cross multiply

b = 44 / tan 30

b = 44 / 0.57735026919

b = 76.2102710661

Therefore,

b = 76 units

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The surface area of the cylinder is approximately 3015.93square inches when rounded to the nearest hundredth.

To find the surface area of a cylinder, we need to add the areas of the top and bottom circles, and the area of the lateral surface, which is the curved part of the cylinder.

The formula for the surface area of a cylinder is:

S.A. = 2πr² + 2πrh

where r is the radius of the cylinder, h is the height, and π is approximately equal to 3.14.

Given that the diameter is 32 inches, we can find the radius by dividing by 2:

r = d/2 = 32/2 = 16 inches

Now we can substitute the values into the formula and simplify:

S.A. = 2πr² + 2πrh

S.A. = 2π(16)² + 2π(16)(14)

S.A. = 2π(256) + 2π(224)

S.A. = 512π + 448π

S.A. = 960π

To approximate the answer to the nearest hundredth, we can use the value of π rounded to two decimal places (3.14):

S.A. ≈ 960(3.14)

S.A. ≈ 3015.93 square inches

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The surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.

From the figure we have that:

r = 16 in

h = 14 in

surface area = 2 × 3.14 × 16 in × 16 in + 2 × 3.14 × 16 in × 14 in

surface area = 1607.68 in² + 1406.72 in²

surface area = 3014.40 in²

Therefore, the surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

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Answer:

Step-byeat -step explanation:

Step-by-step explanation:

706 -25 = 681 ====>    which is three pieces of 681/3 = 227 m

              but one is 25 m longer so 227,  227 , and 227 + 25 =252 m

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.

given

Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:

[tex]a = a1 + (n - 1) * d[/tex]

In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:

[tex]a = 7 + (n - 1) * 15[/tex]

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

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Step-by-step explanation:

always and you come across a question that needs you to find the time or the distance or the speed the first thing that you need to think of is a triangle based formula so this is what you do you're right DStv in a triangle but you won't include the V therefore it will be DST and you just look at mainly at the formulas and try to identify the one that you're looking for and the way forward for example distance I have already drawn my small triangle and it's revealing that distance is equal to speed times time and speed is equal to a distance divided by time and time is equal to distance divided by speed in this case we're looking for the distance therefore I supposed to say speed time so was supposed to say 70 * 49,000 to get your answer

Answer:

the on side to side is the x axes and the y one is up and down

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

7 1/2 divided by 5/6 would equal 9.

first step: convert the mixed number into an improper fraction.

7 1/2 = 15/2

2nd step: change the operation. (KCF)

keep the first term - change the operation - flip the second term

so, 15/2 x 6/5 =.

15x6=90

2x5=10

90/10 = 9

hope it helps!

Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.

The given graph is oriented toward x direction

Domain of function =x≥2

For every value of x the y is always positive

So, range =y≥0

Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}

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The correct term in each box, if necessary, use / for the fraction bar are a = 1/7-4i, b = 1/13.

In mathematics, a fraction bar is a visual representation of fractions that facilitates fraction comparison and fraction operation. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.

We need to be aware of an aspect of imaginary numbers in order to determine the values of variables a and b. The following rule applies to the hypothetical unit:

Therefore, the correct terms are 1/7-4i, b = 1/13.

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A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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Answer: should be 24?

Step-by-step explanation:

im not sure

The value of the line AC is  100. 07 inches

Trigonometric identities are equations that involve trigonometric functions such as sine, cosine, and tangent, which hold true for all values of the variables in the equation.

Note that there are six trigonometric identities. They are;

From the information given, we have;

Using the sine identity, we have;

sin 58 = Line AC/118

cross multiply the values

Line AC = 100. 07 inches

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Answer:

Step-by-step explanation:

x + 5 = 3x - 7

-2x = -12

x = 6

x + 5 = 6 + 5 = 11

3(6) - 7 = 18 - 7 = 11

The value of angle B and C are 63° and 61° respectively.

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore;

32/sin56 = 34/sinC

32sinC = 34sin56

32sinC = 28.187

divide both sides by 32

sinC = 28.187/32

sinC = 0.88

C = sin^-1(0.88)

C = 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore, B = 180-(61+56)

B = 180-(117)

B = 63°

therefore the value of angle B and C are 63° and 61°.

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In the formula, A is the amount after interest, P is the principal, r is interest rate in decimals, n is the amount of times the interest is compounded per year, and t is the amount of years.

The value of the variables 'x' and 'y' will be 8√2 cm and 9√2 cm, respectively.

Given that:

Area of a small triangle, A = 72 square cm

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The equation is given as,

x² / (32)² = y² / (36)² = 72 / (1/2 x 32 x 36)

The value of 'x' is calculated as,

x² / (32)² = 72 / (1/2 x 32 x 36)

x = 8√2 cm

The value of 'y' is calculated as,

y² / (36)² = 72 / (1/2 x 32 x 36)

y = 9√2 cm

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The value of P for A and B to be independent is 3/8.

Probability is a mathematical concept used to determine the likelihood or chance of an event occurring. It's a measure of how likely it is that a specific outcome will happen in a given situation. Probability values are expressed as numbers between 0 and 1, where 0 means the event is impossible, and 1 means it is certain to occur.

The probability of an event is calculated by dividing the number of outcomes that favor the event by the total number of possible outcomes. The total number of outcomes is the number of ways the event could happen, while the number of favorable outcomes is the number of outcomes that satisfy the event's conditions.

Probability theory has many applications in various fields, including finance, economics, science, engineering, and statistics. It is an essential tool for analyzing data, predicting outcomes, and making decisions.

Two events A and B are independent if and only if P(A and B) = P(A) * P(B).

Using the formula for the probability of the union of two events, we have:

P(A or B) = P(A) + P(B) - P(A and B)

Substituting the given values, we get:

1/2 = 1/5 + P - P(A and B)

Simplifying, we get:

3/10 = P - P(A and B)

We also know that P(A) = 1/5. Using the formula for the probability of the intersection of two events, we have:

P(A and B) = P(A) * P(B | A)

Substituting the given values, we get:

P(A and B) = (1/5) * P

Since we want to find the values of P for which A and B are independent, we can substitute this expression for P(A and B) in the earlier equation:

3/10 = P - (1/5) * P

Simplifying and solving for P, we get:

P = 3/8

Therefore, A and B are independent if and only if P = 3/8.

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The amounts needed to make 6 servings are given as follows:

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Hence the amounts for six servings are given as follows:

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The property of equality that the statement m(n-p) = mn - mp illustrates is (d) the distributive property

Given that

m(n-p) = mn - mp

The above property is the distributive property

The distributive property states that

a(b - c) = ab - ac

This case

a = m

b = n

p = c

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

m(n-p) = mn - mp

Hence, the property of equality that the statement illustrates is the distributive property

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On day zero, the number of students who know the rumor are 2 people who are Susanna and Liz.

On day 2, the number of students would be 12 students.

The number of days till 32 students know the rumor is 6 days.

2 students (Susanna and Liz) know the rumor on day 0.

On day 2, the number of students who know the rumor will be the initial number of students (2) plus 5 students for each day that has passed (5 * 2 = 10). So, on day 2, 2 + 10 = 12 students know the rumor.

To find the number of days it will take for 32 students to know the rumor, we can set up an equation using the given information:

2 (Susanna and Liz) + 5 x number of days = 32

Now, we can solve for the number of days:

5 x number of days = 32 - 2

5 x number of days = 30

number of days = 30 / 5

number of days = 6

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Step-by-step explanation:

AREA = pi r^2

144 = pi r^2     shows      r = 6.77  m       ( or sqrt ( 144/pi)  ) 

        then          diameter = 2 * r = 13.54 m    (or   2 sqrt (144/pi)  )

Answer:

7.64

Step-by-step explanation

This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D

The reasonable constraint so the function is at least 600 would be A. 0 ≤ x ≤ 20.

Given the function y = -2x² + 40x + 600, we want to find the constraint for x so that the function's value is at least 600.

Since the parabola opens downward (as a is negative), the function will be at least 600 for all values of x within the interval where the parabola is above y = 600. The vertex of the parabola is at its maximum value, so we should look for the interval around the vertex (10, 800).

Looking at the given constraints, the option "0 ≤ x ≤ 20" is a reasonable constraint that ensures the function is at least 600. The parabola starts at a value of 600 at x = 0, reaches its maximum value at the vertex, and then returns to a value of 600 at x = 20.

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A box contains 5 orange pencils, 8 yellow pencils, and 8 green pencils. Two pencils are selected, one at a time, with replacement.

There are a total of 21 pencils in the box.

The probability of selecting a green pencil on the first draw is 8/21, since there are 8 green pencils out of 21 total.

After replacing the first pencil, there are still 21 pencils in the box, including 8 yellow pencils.

The probability of selecting a yellow pencil on the second draw, given that a green pencil was selected first, is 8/21.

By the Multiplication Rule of Probability, we can multiply these probabilities together to find the probability of both events occurring

P(green and yellow) = P(green) × P(yellow|green)

P(green and yellow) = (8/21) × (8/21)

P(green and yellow) = 64/441

Therefore, the probability of selecting a green pencil first and a yellow pencil second is 64/441 or approximately 0.145.

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Step-by-step explanation:

yes .. when you put x=2 y will be 3 .. you get it?

The incorrect statement regarding the dilation is given as follows:

2. The transformation can be represented by (7x/3, 7y/3).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, we have that:

Hence the scale factor is given as follows:

k = 3/7.

And the rule is then given as follows:

(3x/7, 3y/7).

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Answer: A

Step-by-step explanation: The distance for the ball to travel straight from Jose to Harlan is less than what it would be if she were to pass it to Alma first. You can use the distance formula to find this (find the distance between Jose and Harlan, and compare it to the sum of the distances between Jose and Alma and Alma and Harlan)

Answer:

dependent

Step-by-step explanation:

its dependent because the names getting pulled depends on the names pulled first

(c)  [tex]q \le \pi[/tex]

(d)  [tex]2 \ge d \ge 1[/tex]

Explanation:

The "less than or equal to" sign is ≤ which has a "less than sign" placed on top of a single horizontal bar. It can be thought of something like this [tex]\stackrel{ < }{=}[/tex] except there isn't a second horizontal bar.

The "d is between 2 and 1" seems to have a strange order to it. I have a feeling your teacher is wanting 2 ≥ d ≥ 1 because of that order. Normally we would list things from smallest to largest. We involve "or equal to" if we want to include the endpoints.

Part a: q is less than or equal to π: q ≤ π.

Part b: d is between 2 and 1: 1 < d < 2.

Less than (<), more than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the inequality symbols.

Numbers are compared using inequalities to identify the range (or ranges) of values which satisfy the requirements of a certain variable.

Part a: q is less than or  equal to π.

In this case:

q < π and q = π

Combining both:

q ≤ π

Part b: d is between 2 and 1

Here values 1 and 2 will not be taken for d.

d < 2 and d > 1

Thus,

1 < d < 2

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