Chloe needs a 1.25-meter piece of wood for a desk that she is building. How many centimeters need to be cut off a 2-meter piece of wood in order to use it for her desk.

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

8 raspberries

Step-by-step explanation:

\( \large \mathfrak{Answer : }\)

The degree of a polynomial is the highest power among its terms .

i.e 8 for the above expression :

9x² + 3x⁸ + 6x + 586 - 7x⁵

Answer:

yes it is 604892÷4=151,223

Answer:

Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.

Step-by-step explanation:

Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.

The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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The area of the kite is A = 48 units²

Given data ,

Let the area of the kite be represented as A

Now , the value of A is

Let the first diagonal of the kite be d₁ = 12 units

Let the second diagonal of the kite be d₂ = 8 units

Now , Area of kite = ( 1/2 ) d₁ x d₂

On simplifying , we get

A = ( 1/2 ) ( 12 ) ( 8 )

A = 48 units²

Therefore , the value of A is A = 48 units²

Hence , the area of the kite is A = 48 units²

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Answer:

Step-by-step explanation:

Let's begin by assigning variables to represent the three mixed numbers. Let a be the greatest mixed number, b be the middle mixed number, and c be the least mixed number. Then we can write:

a + b + c = 18 (the sum of the three mixed numbers is 18)

a - c = 5 1/5 (the difference between the greatest and least mixed numbers is 5 1/5)

To solve for a, b, and c, we can use substitution. From the second equation, we can solve for a in terms of c:

a = c + 5 1/5

Substituting this expression for a into the first equation, we get:

(c + 5 1/5) + b + c = 18

Simplifying, we get:

2c + b = 12 4/5

Now we need to find three mixed numbers that satisfy this equation. We can start by choosing a value for c. Let's choose c = 2 1/2, which is the smallest possible value for c that will allow the mixed numbers to be non-negative. Then we can solve for b:

2c + b = 12 4/5

2(2 1/2) + b = 12 4/5

5 + b = 12 4/5

b = 7 4/5

Finally, we can solve for a using the equation a = c + 5 1/5:

a = c + 5 1/5

a = 2 1/2 + 5 1/5

a = 7 3/5

Therefore, three mixed numbers that satisfy the conditions of the problem are:

The greatest mixed number: 7 3/5

The middle mixed number: 7 4/5

The least mixed number: 2 1/2

And indeed, their sum is 18 and the difference between the greatest and least mixed numbers is 5 1/5.

Answer:

-20% discount

Step-by-step explanation:

subtract the two numbers:

1020-1360= -340 (is a percentage reduction, so I have to subtract the larger number from the smaller one)

divide the result by the original value:

-340÷1360= -0,25

to turn it into a percentage, multiply it by 100:

-0,25×100= -25%

Hope it helps!

Answer:

there's a decrease of 25%

or

-25%

Step-by-step explanation:

100% = 1360

___% = 1020

\( \frac{1020 \times 100}{1360} = 75\)

100- 75= 25%

Answer:

I think it is the rectangle

Step-by-step explanation:

I wish it is really helpful for u

Answer: D. Trapezoid

Step-by-step explanation:

From the question, it tells us that each angle was congruent to its opposite angle, since in a rectangle all angles are 90 degrees, rectangles won’t be correct. Parallelograms is self explanatory. Rhombuses have 2 pairs of same angles, which only leads to a trapezoid with 2 different bases, leading to different angles in it’s opposite corner.

Step-by-step explanation:

Volume of a cylinder = pi r^2 h      diameter =1.5 ft so r = .75 ft

                                  pi * .75^2 * 25 = 44.18 ft^3

Find price (based on $ 12.09 /ft^3)

44.18 ft^3  *  $  12.09 /ft^3  = $ 534.12

Answer:

Falls to the left and rises to the right

Step-by-step explanation:

because

degree =5

leading coefficient =4 and positive it will rise to the right

those are tips to use to determine it :

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

Total area = 104+24 = 128 sq.in ,  Option C is the right answer.

The missing figure is attached with the answer.

The space occupied by a two dimensional figure is called Area.

The figure given in the question can be divided into two figure

A rectangle of 8 * 13 inch

and a triangle of 8 * 6 inch

The area of a rectangle is given by

Length * Breadth

8 * 13

= 104 sq.inch

The area of the triangle is given by

(1/2) * base * height

= (1/2) * 8 * 6

= 24 sq.inch

Total area = 104+24 = 128 sq.in

Therefore Option C is the right answer.

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Answer:

\(3\frac{5}{9} or \frac{32}{9}\)

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Answer:

India's population will reach 2 billion during the year of 2050.

Step-by-step explanation:

India's population in t years after 2008 is modeled by the following equation:

\(P(t) = P(0)(1+r)^{t}\)

In which P(0) is the population in 2008 and r is the growth rate, as a decimal.

Population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year.

This means that \(P(0) = 1.14, r = 0.0134\). So

\(P(t) = P(0)(1+r)^{t}\)

\(P(t) = 1.14(1+0.0134)^{t}\)

\(P(t) = 1.14(1.0134)^{t}\)

If the population continues following this trend, during what year will the population reach 2 billion?

t years after 2008.

t is found when P(t) = 2. So

\(P(t) = 1.14(1.0134)^{t}\)

\(2 = 1.14(1.0134)^{t}\)

\((1.0134)^{t} = \frac{2}{1.14}\)

\(\log{(1.0134)^{t}} = \log{\frac{2}{1.14}}\)

\(t\log{1.0134} = \log{\frac{2}{1.14}}\)

\(t = \frac{\log{\frac{2}{1.14}}}{\log{1.0134}}\)

\(t = 42.23\)

2008 + 42 = 2050

India's population will reach 2 billion during the year of 2050.

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

The predicted population in 2021 is 8.15 billion.

To predict the population in 2021 using a doubling time of 40 years need to calculate the number of doubling periods between 2013 and 2021.

Number of doubling periods = (2021 - 2013) / 40

= 0.2

To calculate the population in 2021 by multiplying the initial population of 7.1 billion by 2 raised to the power of the number of doubling periods:

Population in 2021 = \(7.1 billion \times 2^{0.2\)

= 7.1 billion x 1.1487

= 8.15 billion (rounded to two decimal places)

The predicted population in 2021 is 8.15 billion.

Calculating the number of doubling cycles between 2013 and 2021 is necessary in order to anticipate the population in 2021 using a doubling time of 40 years.

The number of doubling periods is equal to (2021–2013)/40

=0.2.

The original population of 7.1 billion by 2 raised to the power of the number of doubling periods, we can get the population in 2021:

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Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer:

2 independent sample t test

Step-by-step explanation:

This test is also called the two sample t-test. This test is an inferential yet which is used to know if a significant difference exists statistically in 2 unrelated groups.

In this question, we have 2 different soda brands. These 2 brands are to be rates in a random order. The hypothesis test that is best for this is the 2 independent sample t-test.

When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

Given are two right triangles we need to find the missing sides,

We will use Trigonometric ratios to find the same.

We know that,

Sin a = perpendicular / hypotenuse

Cos a = base / hypotenuse

Tan a = perpendicular / base

1) Sin 60° = x / 4√3

x = √3/2 × 4√3

x = 6

Cos 60° = y / 4√3

1/2 × 4√3 = y

y = 2√3

2) Cos 60° = x / 98

x = 1/2 × 98

x = 49

Sin 60° = y / 98

√3/2 = y / 98

y = 49√3

Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

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Answer:

The base of the triangle is decreasing at a rate of 1.4167 inch/hour.

Step-by-step explanation:

Area of a triangle:

The area of a triangle of base b and height h is given by:

\(A = bh\)

In this question:

We have to derivate the equation of the area implicitly in function of time. So

\(\frac{dA}{dt} = b\frac{dh}{dt} + h\frac{db}{dt}\)

The altitude of a triangle is increasing at a rate 2 inch/hour while the area of the triangle is decreasing at a rate of 0.5 square inch per hour.

This means that:

\(\frac{dh}{dt} = 2, \frac{dA}{dt} = -0.5\)

At what rate is the base of the triangle is changing when the altitude is 6 inch and the area is 24 square inch?

This is \(\frac{db}{dt}\) when \(h = 6\)

Area is 24, so the base is:

\(A = bh\)

\(24 = 6b\)

\(b = \frac{24}{6} = 4\)

Then

\(\frac{dA}{dt} = b\frac{dh}{dt} + h\frac{db}{dt}\)

\(-0.5 = 4(2) + 6\frac{db}{dt}\)

\(6\frac{db}{dt} = -8.5\)

\(\frac{db}{dt} = -\frac{8.5}{6}\)

\(\frac{db}{dt} = -1.4167\)

The base of the triangle is decreasing at a rate of 1.4167 inch/hour.