help follow the polyas method​

Given that the third side of the triangle is shorter than the sum of the other two sides' lengths and longer than the difference between the other two sides' lengths, the necessary expression will be "4x cm h 10x cm."

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. A mixture of numbers, variables, and functions is called an expression (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A mathematical statement using just numbers and one or more operation symbols is known as a numerical expression. Here,

The third side of the triangle is shorter than the sum of the other two sides' lengths and longer than the difference between the other two sides' lengths,

(h>7x - 3x) and (h<7x + 3x)

(7x - 3x) cm < h < (7x+ 3x) cm

4x cm < h < 10x cm

The required expression will be "4x cm< h< 10x cm" as the third side of the triangle is shorter than the sum of the other two sides' lengths and longer than the difference between the other two sides' lengths.

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Answer:

37 / 40 or 0. 925

Step-by-step explanation:

5/ 8 + 3 / 10

= 37 / 40

= 0. 925

Mark brainliest pls

This might acually affect Lebron's Legacy

Answer:

Step-by-step explanation:

(10+2)S(x)=2x

Answer:

The 2nd option is correct.

i.e.

y = 10+1, because the rate of change of the graphed function is 3.

Step-by-step explanation:

From the graph,

Taking two points

Finding the rate of change or slope between (0, 0) and (3, 9)

Using the formula

Rate of change = Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [9 - 0] / [3 - 0]

               = 9 / 1  

               = 3

Thus, the rate of change or slope of the line = m = 3

The slope-intercept form of the line equation

\(y = mx+b\)

where

Considering the function in 2nd option

y = 10x+1

Comparing with the slope-intercept form of the line equation y = mx+b

The rate of change or slope = m = 10

Conclusion:

The rate of change or slope of the graphed line: m = 3

The rate of change or slope of y = 10x+1 is: m = 10

Thus, the rate of change of y = 10x+1 i.e. m = 10 is greater than the rate of change of the graphed line i.e. m = 3.

Hence, the 2nd option is correct.

i.e.

y = 10+1, because the rate of change of the graphed function is 3.

Answer:

rational

Step-by-step explanation:

sqrt( 6+30)

sqrt(36)

6

6 is rational

Answer:

62 trees = 100%

62 / 2 = 31 trees

100% / 2 = 50%

31 trees = 50%

Step-by-step explanation:

What the given experiment demonstrates is; The magnitude of acceleration according tp newton's second law of motion

Newton's second law of motion states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

This law basically establishes a relationship between the net force and the acceleration, which is expressed as;

∑ F = m a

where;

∑F is the sum of the external forces

m the mass of the body

a is the acceleration of the body

The initial situation in the question shows the block and a baking mass. This means that an acceleration is created towards the hanging mass expressed as;

W₁ = M₁ g

F = ma

Thus;

M₁g = m a

a = (M₁g/m)

where;

W₁ is the weight of the body  

M₁ is the mass of the body hanging under the acceleration of gravity.

For the second case, there are two masses, with one on each side, and so we have;

∑ F = W₁ - W₂

∑F = (M₁ - M₂) g

Using Newton's second law of motion gives us;

(M₁ - M₂ )g = ma

a = (M₁ - M₂ )mg

Thus, the acceleration depends on the difference of the hanging masses which proves Newton's second law of motion.

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

1,440

Step-by-step explanation:

London 962

Rio       +118.5%

One percent of 962 is 9.62 you get that by moving the decimal place over one place, multiply by 118.5 to get 1,139.97 there is no partial medals so round to the nearest whole number and you get 1,140.

hope this helped! :) feel free to ask any questions and please mark my answer if it helped you thanks!

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

The value of v in terms of i and j is v = 3i + 3j

We are given that;

P₁ = (-5,3), P₂ = (-2,6)

Now,

To find the component form of a vector, we need to subtract the coordinates of the initial point from the coordinates of the terminal point3.

We have P₁ = (-5,3) and P₂ = (-2,6).

v = P₂ - P₁ = (-2 - (-5), 6 - 3) = (3, 3). We can write v in terms of i and j as v = 3i + 3j.

Therefore, by vectors the answer will be v = 3i + 3j.

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According to trigonometric properties, the value of (16-x2) for x as 4sinx is 4cosx.

Trigonometry is a branch of mathematics concerned with angle relationships and length ratios. The field arose in the Hellenistic world during the third century BC from geometric applications to astronomical studies. Trigonometry is a branch of mathematics concerned with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are commonly used. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and abbreviations (csc).

Here,

=√(16-x²)

x=4sinx

=√(16-(4sinx)²)

=√(16-16sin²x)

=4√(1-sin²x)

=4cosx

The value of √(16-x²) for x as 4sinx is 4cosx by trigonometric properties.

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In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

BD = 88

BC = 27

CD = 61.

Given that BD is equal to 7x, BC is equal to 4x, and CD is equal to 5x,

It is evident from the above figure that Points B, C, and D are parallel. On line segment BD, point C is located.

BD = BC + CD

In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

7x - 10 = (4x - 29) + (5x - 9)

When we combine similar phrases, we obtain

7x - 10 = (4x + 5x) + (-29 - 9 )

7x - 10 = 9x - 38

38 plus 38 on either side.

7x - 10 + 38 = 9x

7x + 28 = 9x

Take 7x away from both sides.

28 = 9x - 7x

28 = 2x

By 2, divide both sides.

14 = x

Consequently, x has a value of 14.

BD  = x - 10 = 7(14) - 10 = 88

88 units are BD's worth.

BC = 4x - 29 = 4(14) - 29 = 27

BC has a value of 27 units.

CD = 5x - 9 = 5(14) - 9 = 61.

The CD is worth 61 units.

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Answer:

-8

Step-by-step explanation:

x - 16 = 3x

Solve for x

-2x = 16

x = -8

5/4 x 3/5=3/4 lb

hope this helps

Answer:

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

in this case there is a rotation same angles and same sides

your answer is: TRUE

The best answer choice among the given options is O 15 m², as none of the provided options match the correct Ccalculation.

To find the area of a rhombus, we need the lengths of the diagonals. In this case, the lengths of the diagonals are not provided. However, we can use the given information to determine the area based on the side lengths.

A rhombus is a quadrilateral with all sides of equal length, so the given side lengths of 5.5 m and 2 m can help us find the area.

We know that the diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. Each side of the rhombus is the hypotenuse of one of these triangles.

Given that the side length is 5.5 m, we can consider one of these right triangles. One leg of the right triangle is half of the side length, which is (5.5 m)/2 = 2.75 m. The other leg of the triangle is the length of the diagonal, which is unknown.

Using the Pythagorean theorem, we can find the length of the diagonal:

(diagonal)^2 = (leg)^2 + (leg)^2

(diagonal)^2 = (2.75 m)^2 + (2 m)^2

(diagonal)^2 = 7.5625 m² + 4 m²

(diagonal)^2 = 11.5625 m²

diagonal ≈ √11.5625 m ≈ 3.4 m (rounded to the nearest tenth)

Since the diagonals of a rhombus are perpendicular bisectors of each other, the length of the other diagonal would also be approximately 3.4 m.

Now, we can calculate the area of the rhombus using the formula: area = (diagonal1 * diagonal2) / 2

area = (3.4 m * 3.4 m) / 2

area = 5.8 m²

The area of the rhombus is approximately 5.8 m².

The best answer choice among the given options is O 15 m², as none of the provided options match the correct area calculation.

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Answer:

\(\frac{p}{p-2}=\frac{-p(p+2)}{4-p^2}\)

Step-by-step explanation:

\(\frac{p}{p-2} = \frac{p}{p-2}\times\frac{p+2}{p+2}=\frac{p(p+2)}{(p-2)(p+2)}=\frac{p(p+2)}{p^2-4}=\frac{p(p+2)}{p^2-4}\times\frac{-1}{-1}=\frac{-p(p+2)}{4-p^2}\)

Answer:

\(\frac{-p^{2}-2p }{4-p^{2} }\)

Step-by-step explanation:

Answer:

The answer is 2 hope this helped!

Step-by-step explanation:

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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Answer:

Hi, there--

THE PROBLEM:

We invested $10,000 in 2 bank accounts. One account earns 14% per year the other earns 8%

per year. How much did we invest into each account if after the first year, the combined

interest from the 2 accounts is $1238?

A SOLUTION:

Define Variables:

Let x be the amount you originally invested in the first account.

Let y be the amount you originally invested in the second account.

Write Expressions and Equations:

Since you invested a total of $10,00 in two accounts. An equation that represents this is

x + y = 10000

One account (say the first one) earns 14% per year. Recall that the decimal form of 14% is

0.14. An expression for the amount of interest you earn after the first year in this account is

0.14x.

The other account earns 8% per year. The decimal representation of 8% is 0.08. The amount

of interest you earn after one year in this account is 0.08y.

The combine interest from both account after one year is $1238. An equation representing

the total interest earned is

0.14x + 0.08y = 1238

Now we have a system of two equations with two variables. We can solve for x and y. Rewrite

the first equation in "y=" form.

x + y = 10000

y = 10000 - x

Substitute 10000-x for y in the second equation.

0.14x + 0.08y = 1238

0.14x + 0.08(10000 - x) = 1238

Solve this equation for x. Use the Distributive Property to clear parentheses.

0.14x + 800 - 0.08x = 1238

Combine like terms (0.14x-0.08x is 0.06x).

0.06x + 800 = 1238

Subtract 800 to both sides to isolate x on the left.

0.06x = 1238 - 800

0.06x = 438

Divide both sides of the equation by 0.06.

x = 438/0.06

x = 7300

In the context of this problem, x=7300 means that you invested $7300 in the first account.

Since you invested a total of $10000, you invested 10000-7300=$2700 in the second account.

Check your work by verifying that these amounts will yield the correct amount of interest.

Substitute 7300 for x and 2700 for y in the interest equation.

0.14x + 0.08y = 1238

0.14(7300) + 0.08(2700) = 1238

1022 + 216 = 1238

1238 = 1238

Check!

Hope this helps! Feel free to email if you have any questions about the

Answer:

6u²−3uv²−4u⁴+5uv

Step-by-step explanation:

i had a test with this and got it right

The number of students in the class​ is 36 students

Let the total number of people that read physics be n(P)

Let the total number of people that read Mathematics be n(M)

Let the number of people that read both subjects be n(PnM)

The total number of students in the class will be represented as n(PUM)

Based on the set formula

n(PUM) = n(P) + n(M) - n(PnM)

n(PUM) = 24 + 21 - 9

n(PUM) = 45 - 9

n(PUM) = 36

Hence the number of students in the class​ is 36 students

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Answer:

x^2 +3x -3

Step-by-step explanation:

f(x) = 3х – 5

g(x) = х^2+ 2,

(f+g)(x) = 3х – 5 +х^2+ 2

Combine like terms

         = x^2 +3x -3

Answer:

yes

yes

no

yes

Step-by-step explanation:

The dimension of the yard is  175ft x 125 ft.

Given that,

L = length = 2W-75 feet

P = perimeter = 600 feet

Since yard is have a rectangular size,

And rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

W = width;

Since, perimeter is 2 times of sum of length and width of rectangle.

P=2(L+W)

⇒600ft=2(L+W)

Divide each side by 2.

300 feet = L+W

L can be substituted.

300ft = 2W-75ft + W Take 75 feet off each side.

375 ft = 3W

Divide each side by three to get

W = 125 ft

It is 125 feet wide.

L=2W-75ft

L=2(125ft)-75ft

L=250ft-75ft

L=175ft

Thus dimension is 175ft x 125 ft.

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Answer:

b

Step-by-step explanation:

b

The y-intercept of the line of fit is approximately 43.94 fluid ounces.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.

No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.

The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.

Therefore,  The y-intercept of the line of fit is approximately 43.94 fluid ounces.

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Elementary row operations to find system of equation solutions in row echelon or reduced row echelon form.

We first write the augmented matrix [A|B] by combining the coefficients of the variables and the constants on the right side of the equations:

x + y + 6z | 8

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0.

Here are the steps to perform Gauss-Jordan row reduction on the augmented matrix [A|B]:

Step 1: Divide the first row by x + y + 6z to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0

Step 2: Subtract the first row multiplied by 1/3 from the second row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

1/2 x | -z | 0

Step 3: Subtract the first row multiplied by 1/2 from the third row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 4: Divide the second row by -2/3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 5: Subtract the second row multiplied by 5/2 from the third row to eliminate y:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 3z | -15/2

Step 6: Divide the third row by 3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 1 | -5

Thus, the reduced row echelon.

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