Identify the equation that shows direct variation

The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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a)

Values of the given angles  ∠A = 123°  , ∠B = 123° ,∠C = 57.

Given ,

One angle of the figure as 123°.

Now,

∠C and 123° form linear pair.

So,

∠C + 123° = 180°

∠C = 57°

Now,

∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.

∠C + ∠B = 180°

Substitute the value of ∠C

53° + ∠B = 180°

∠B = 127°

Now,

∠B and ∠A are vertically opposite angles.

Thus,

∠B = ∠A

So,

∠A = 127° .

Hence,

∠A= 127°

∠B = 127°

∠C = 57°

b)

Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .

Given one angle as 82°

Now,

∠F and 82° form linear pair.

So,

∠F + 82° = 180°

∠F = 98°

Now,

∠D and ∠F are corresponding angles. Thus,

∠D = ∠F

∠D = 98° .

Now,

∠D and ∠E are vertically opposite angles.

Thus,

∠D = ∠E

∠E = 98°.

Hence,

∠D = 98°

∠E = 98°

∠F = 98°

c)

Values of ∠G = 75° and ∠H = 75°

Given one angle as 75° .

∠H and 75° are corresponding angles. Thus,

∠H = 75°

Now,

∠H and ∠G are vertically opposite angles.

So,

∠G = 75° .

Hence,

∠G = 75°

∠H = 75°

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Answer:

Hello,

I just think that it is A

Why you may ask?

Because it has a Zero and that is an undefined number than

Step-by-step explanation:

Please I want brainest

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Step-by-step explanation:

Number of green and white jelly beans

= Number of green + Number of white

= 4 + 2 = 6.

Probability = Number of green and white jelly beans / Total number of jelly beans * 100%

= 6 / (4 + 2 + 5) * 100% = 54.55%.

The probability that you pick a green jelly bean or a white jelly bean should be 54.55%.

Since there are 4 green jelly beans, 2 white jelly beans and 5 purple jelly beans in a jar

So here the probability is

\(= 6\div (4 + 2 + 5)\)

= 54.55%

Therefore, The probability that you pick a green jelly bean or a white jelly bean should be 54.55%.

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Answer:

a = 70t + 600

b = 35t+ 950

high school a will have 140 more students than high school b in 14 years.

Step-by-step explanation:

high school a already has 600 students, so we keep that the same. because the school will grow by 70 students each year, and we want to know how many there will be in 14 years, so we have to multiply 70 by 14 to get 980. add 980 to the preexisting population of 600 students, and we end up with a total of 1,580.

high school b already has 950 students, so we keep that the same. the school is projected to grow by 35 students per year, and we need to know how many there will be in 14 years, so we multiply 35 by 14 to get 490. add the 490 new students to the current population of 950 students to get a total of 1,440.

high school a has a higher projected population, so we subtract high school b's population of 1,440 from high school a's population of 1,580. we find that in 14 years, high school a will have 140 more students than high school b.

Answer:

8

Step-by-step explanation:

4c ÷ 2 x 2       c=8

4 x 8 ÷ 2 x 2

4 x 8 ÷ 4

You can cancel the 4’s or multiply 4 x 8 then divide by 4, which is 8 :)

Given:-

\( \: \)

\( \: \)

Solution:-

\( \: \)

now , put the given value of c = 8 in equation

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━

hope it helps ⸙

Answer:

The circumference of the back wheel is 2.62 inches

Step-by-step explanation:

Given

\(d_1 = 5in\) --- diameter of front wheel

\(d_1 : d_2 = 3:1\) --- ratio of the diameters

Required

The circumference of the back wheel

First, we calculate the diameter of the back wheel.

We have:

\(d_1 : d_2 = 3:1\)

Substitute: \(d_1 = 5in\)

\(5in: d_2 = 3 : 1\)

Express as fraction

\(\frac{d_2}{5in} = \frac{1}{3}\)

Make \(d_2\) the subject

\(d_2 =5in * \frac{1}{3}\)

\(d_2 = \frac{5}{3}\ in\)

So, the circumference (C) of the back wheel is:

\(C =\pi d\)

\(C = 3.14 * \frac{5}{6}\ in\)

\(C = \frac{3.14 * 5}{6}\ in\)

\(C = \frac{15.7}{6}\ in\)

\(C = 2.62\ in\)

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Answer:

If a function has an axis of symmetry x = a,

Step-by-step explanation:

then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Answer:

B. Faelyn should realize that her work shows that the polynomial is prime

Step-by-step explanation:

The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:

Step 1: (6x⁴ – 8x²) + (3x² + 4)

Step 2: 2x²(3x² – 4) + 1(3x² + 4)

Since they do not have a common factor, Faelyn should realize that her work shows that the polynomial is prime. A prime polynomial cannot be factored further because it is at its lowest common term and cannot be factored into any other polynomial of a lower degree. Prime polynomials have integer coefficients. A prime polynomial is also referred to as an irreducible polynomial.

Answer:

b

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

2(3x + 7) + (2x - 3) =

= 6x + 14 + 2x - 3 =

= 6x + 2x + 14 - 3 = 8x + 11 ← the end

Answer:

yasghfeiruhiurgwhruihrgrgrgh

Step-by-step explanation:

rhewrgbwjyefjyewhuyfgeurghguhgggggg

Answer:

Let the price of the garden table be x.

The bench would cost x-77 dollars.

x+x-77=777

2x-77=777

2x=854

x=427

The bench costs 350 dollars.

Let me know if this helps!

The product of the five complex numbers is 52 + 18i.  (i - 1) / 4 is the first term in the original product, (1/ (1 + i)) * (1 - i / (1 - i)). Therefore, we can see that the simplified result and the first term in the pair are reciprocals of each other, and they are both related algebraically to the original product through the use of reciprocal and conjugate pairs

.

a.

To perform the multiplication (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we can use the associative and distributive properties of multiplication, as well as the fact that i^2 = -1.

First, we can simplify (2 + i)(3 - i) by using the distributive property:

(2 + i)(3 - i) = 6 - 2i + 3i - i^2 = 7 + i

Next, we can simplify (1 + 2i)(1 - i) by using the difference of squares formula:

(1 + 2i)(1 - i) = 1 - i + 2i - 2i^2 = 3 + i

Finally, we can multiply (7 + i)(3 + i)(3 + i) using the distributive property:

(7 + i)(3 + i)(3 + i) = (733 + 73i + i33 + i3i) + (73i + 7ii + i3i + iii)

= (63 + 28i + 4i^2) + (21i + 7i^2 + 3i^2 + i^3)

= (63 + 28i - 4) + (21i - 7 - 3i - i)

= 52 + 18i

Therefore, the product of the five complex numbers is 52 + 18i.

b.

To simplify the expression [(1/ (1 + i)) * (1 - i / (1 - i))], we can start by finding a common denominator for the two fractions:

[(1/ (1 + i)) * (1 - i / (1 - i))] = [(1 - i) / (1 + i)(1 - i)] * [(1 - i) / (1 - i)]

= (1 - 2i + i^2) / (1 - i^2)

= (1 - 2i - 1) / (1 + 1)

= -i/2

The simplified result -i/2 is related to the first term in the product (1/ (1 + i)) in that they are reciprocals of each other. That is, the first term in the product is the reciprocal of (1 + i), and -i/2 is the reciprocal of the product (1 + i). Algebraically, this can be shown as follows:

(1/ (1 + i)) * (-i/2) = (-i/2) / (1 + i) = (-i/2) * (1 - i) / (1 - i^2)

= (-i/2) * (1 - i) / 2 = (i - 1) / 4

Note that (i - 1) / 4 is the first term in the original product, (1/ (1 + i)) * (1 - i / (1 - i)). Therefore, we can see that the simplified result and the first term in the pair are reciprocals of each other, and they are both related algebraically to the original product through the use of reciprocal and conjugate pairs.

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Answer:

x=5

Step-by-step explanation:

     May I have brainiest I'm trying to level up!

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Answer:

x=5

Step-by-step explanation:

6x-3 = 3x +12

+3            +3

6x = 3x +15

-3x   -3x

3x = 15

divided both sides by 3 to get your answer

To find the arc length for the curve y = 3x² − (1/24) ln x with the starting point p0(1, 3), we need to integrate the expression √(1 + (dy/dx)²) with respect to x over the desired interval. The resulting value will give us the arc length of the curve.

To find the arc length, we need to integrate the expression √(1 + (dy/dx)²) with respect to x over the given interval. In this case, the given function is y = 3x²− (1/24) ln x. To compute the derivative dy/dx, we differentiate each term separately. The derivative of 3x² is 6x, and the derivative of (1/24) ln x is (1/24x). Squaring the derivative, we get (6x)² + (1/24x)².

Next, we substitute this expression into the arc length formula:

∫√(1 + (dy/dx)²) dx. Plugging in the squared derivative expression, we have ∫√(1 + (6x)² + (1/24x)²) dx. To evaluate this integral, we need to employ appropriate integration techniques, such as trigonometric substitutions or partial fractions.

By integrating the expression, we obtain the arc length of the curve between the starting point p0(1, 3) and the desired interval. The resulting value represents the distance along the curve between these two points, giving us the arc length for the given curve.

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

19x + .66y = total acid

Step-by-step explanation:

The answer is , an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m = 1 and m = -0.3183

To find an approximate value of m such that the equation cos(x) = mx has exactly two solutions, we can use the fact that the graph of y = cos(x) intersects the line y = mx at exactly two points.

The graph of y = cos(x) is a periodic function with a maximum value of 1 and a minimum value of -1.

Since we want the line y = mx to intersect the graph of y = cos(x) at exactly two points, the slope m must satisfy the condition -1 ≤ m ≤ 1.

Furthermore, for the line y = mx to intersect the graph of y = cos(x) at exactly two points, the line must pass through the maximum and minimum points of the graph of y = cos(x).

These occur at x = 0 and x = π.

At x = 0, we have cos(0) = 1 and the equation cos(x) = mx becomes 1 = m(0), which simplifies to m = 1.

At x = π, we have cos(π) = -1 and the equation cos(x) = mx becomes -1 = m(π), which simplifies to m = -1/π.

Therefore, an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m ≈ 1 and m ≈ -0.3183 (rounded to four decimal places).

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Answer:

6=-009885654

Step-by-step explanation:

The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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Answer:

Sorry, I need more context. What are the y-values?

Step-by-step explanation:

Answer:

Each of the three letter combinations can be combined with any of the three number combinations so the total is 17,576 x 1000 = 17,576,000 different combinations possible.

Step-by-step explanation:

I hope this help you

Answer:

-8 is the final answer

Step-by-step explanation:

-(2⁵)^3/5

-2³

-8

If angle Z is greater than angle X plus angle Y in triangle XYZ, then it must be true that triangle XYZ is an obtuse triangle. An obtuse triangle is a triangle in which one of the angles is greater than 90 degrees. In this case, angle Z must be greater than 90 degrees, which means that triangle XYZ cannot be an acute triangle (where all angles are less than 90 degrees) or a right triangle (where one angle is exactly 90 degrees). Therefore, the only possible option is that triangle XYZ is an obtuse triangle.

Answer: ITS c

Step-by-step explanation: