Solve the inequality: four times a number increased by five is at least 33

The lowest value of the equation is at x = -2 when (x + 2) = 0.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given the function,

x² + 4x + 2

to find the lowest value,

factorize the function,

x² + 4x + 2

add and subtract 4 from the function,

x² + 4x + 2 + 4 - 4

x² + 4x + 4 - 2

(x + 2)² - 2

here (x + 2)² is always positive,

and lower value will be x = -2 when (x  + 2)  = 0

Hence lowest value will be at x = -2.

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The correct question is,

Lowest value of  x² + 4x + 2.

Answer:

y=-3/2+3

Step-by-step explanation:

so you have to solve for y

The student can take 8 months of lessons if he has $649 to spend on lessons and the book.

The arithmetic action of division is the opposite of multiplication. It is employed to determine how frequently one quantity is included within another. Divide the dividend by the divisor to execute a division, which can be represented with the division symbol () or a fraction bar (/). The outcome of division is the quotient, which shows how many times the dividend can be divided by the divisor. For instance, if you divide 8 apples into 4 equal portions, each portion would include 2 apples.

First, let's find the total cost of the lessons by multiplying the cost per month by the number of months:

$78/month × n months = $78n, where n is the number of months of lessons.

Next, we add the cost of the book to find the total cost:

$78n + $25 = $649.

Now, we can solve for n by subtracting the cost of the book from both sides of the equation:

$78n = $649 - $25 = $624.

Finally, we divide both sides of the equation by 78 to find the number of months of lessons:

n = $624 ÷ $78/month = 8 months.

So, the student can take 8 months of lessons if he has $649 to spend on lessons and the book.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 400\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ I = (400)(0.05)(2) \implies I = 40[/tex]

Answer:

  (d)  6.3

Step-by-step explanation:

You want the measure of side CD in ∆CDE ~ ∆CFG with CG=6, GE=2.4, and FD=1.8.

The corresponding sides of the two triangles are proportional:

  CD/CE = FD/GE

  CD = CE×FD/GE = (6+2.4)×1.8/2.4

  CD = 6.3

__

Additional comment

Lengths on segment CD are 3/4 of those on segment CE, so CF = 4.5. CD is the sum of CF and FD: 4.5 +1.8 = 6.3.

Answer:

All the answers are bolded in the step-by-step explanation.

Hope it helps :)

Step-by-step explanation:

The radius of the top of a cylinder is always the same length as the radius of the base of a cylinder.

Radius of the base of can A: 10 cm

Radius of the base of can B: 18 cm

To find the area of the bases, use the area formula that you put as your first answer.

Area of the base of can A:

[tex]A=\pi (10^{2} )[/tex]

[tex]A=100\pi[/tex]

[tex]A=314[/tex] cm (Assuming we're only using 3.14 and not any other decimals)

Area of the base of can B:

[tex]A=\pi (18^{2} )[/tex]

[tex]A=324\pi[/tex]

[tex]A=1017.36[/tex] cm (Again, assuming we're only using 3.14 and not any other decimals)

The base of can B has a greater Area

To find the height, look at the diagram

Height of can A: 28cm

Height of can B: 9cm

Can A has a greater height

To find the volume, use the equation that you put as your answer for question 2 or just multiply the area of the base times the height.

Volume of can A:

[tex]314*28=V[/tex]

[tex]V=8792[/tex]

Volume of can B:

[tex]1017.36*9=V[/tex]

[tex]V=9156.24[/tex]

Can B holds more paint

Answer: 8.9 and 6.7

Step-by-step explanation:

These are right triangles, so you can use the Pythagorean theorem, a² + b² = c², where a and b are the legs, or shorter sides, of the triangle and c is the hypotenuse, or the longest side.

1. 4² + 8² = c²

16 + 64 = c²

80 = c²

c = √80

c = 8.9

2. 6² + 3² = c²

36 + 9 = c²

45 = c²

c = √45

c = 6.7

The system of linear equations that has an unique solution has this feature:

Different slopes.

Then we must replace into the equations the variables x = 2 and y = -1, and verify if the equations are satisfied.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

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The probability of winning the quiz is 0.19 or 19% when the contestant answers randomly to each question.

The number of possible outcomes for answering 3 multiple-choice questions with 3 choices each is [tex]3^3[/tex] = 27. Out of these 27 possible outcomes, 9 of them result in the contestant getting 2 or more questions correct.

So, the probability of winning the quiz can be calculated as follows:

P(Winning) = 9/27 = 1/3 = 0.3333...

Rounding to two decimal places, the probability of winning the quiz is approximately 0.33 or 33%.

However, since the contestant is answering randomly to each question, the probability of winning can also be expressed as the sum of the probabilities of getting exactly 2, or 3 questions right. This is calculated using the binomial distribution. The probability of getting exactly 2 questions right is:

The probability of getting exactly 3 questions right is:

The sum of these probabilities gives the total probability of winning:

Rounding to two decimal places, the probability of winning the quiz is approximately 0.19 or 19%.

Since the contestant is answering randomly to each question, the probability of winning is approximately 0.19 or 19%.

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The evaluation of expression is 5/4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The expression; ( 6^2 - 4^2 ) x ( 1/4 )^2

=( 6^2 - 4^2 ) x ( 1/4 )^2

=(36-16)*(1/16)

=20*1/16

=5/4

Therefore, the algebraic expression answer will be 5/4.

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The probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.

Simply put, the probability is the likelihood that something will occur.

We can discuss the likelihood of several outcomes or the potential of one outcome when we are unsure of how something will turn out.

Statistics is the study of events that fall into a probability distribution.

Therefore, there is a chance that each one is unique:

6/6 * 5/6 * 4/6 = 120/216

Therefore, the likelihood that at least two of them will display the same face is:

1 - 120/216 = 96 / 216 =44.44%

Therefore, the probability that we get the same faces when we roll 3 fair six-faced dice is 44.44%.

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the ordered pair will be (3,-1) lies in the inverse function.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

function g(x)=∛(x−4)

So the inverse of the function

g ¬(x) = x³+4

So the ordered pair will be (3,-1)

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Answer:

A. 12 TT

B. 6 TT

C. 9 TT

D. 18 TT

The correct answer is D. 18 TT. The formula for circumference is C = 2TT x radius, so with TT equal to 3.14, the circumference of the circle is 18.28 TT which is approximately equal to 18 TT.

The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.

Max to min value is the range. Range can substantially change if there are any outliers.

Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.

Outliers cause variance to be misinterpreted since they vastly increase variance.

Interquartile range:

You may determine the spread of the midpoint of your distribution using the interquartile range.

The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).

The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.

The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.

The IQR provides a reliable indicator of variability for both skewed and normal distributions.

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Answer:

50% or 1/2

Step-by-step explanation:

Because there are 4 animals in the barn, if two animals leave (out of 4), then there are 50% of the animals in the barn and 50% of the animals leaving the barn.

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No. A triangle cannot be formed with side lengths of 2, 4, and 5. option (d)

The sum of the lengths of the two shorter sides (2 + 4 = 6) must be greater than the length of the longest side (5). This is known as the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side. In this case, the two shorter sides do not meet this requirement, so it is not possible to form a triangle with these side lengths.

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Complete Question:

Is it possible to form a triangle with side lengths 2, 4, and 5? If so, will it be scalene, isosceles, or equilateral?

A.Yes; scalene

B. Yes; isosceles

C. Yes; equilateral

d. no

Answer:

4 Lessons

Step-by-step explanation:

55 * 4 = 220   +     140    =    360

75 * 4 = 300   +      60    =     360

Price per lesson, times number of lessons, plus deposit cost, equals total amount when the lessons will be the same price.

Hope this helps!

Answer:

Step-by-step explanation:

6 km = 6000 m

5 min = 300 s

6000m / 300s  = 20 m/s

Answer:

20 m/s

Step-by-step explanation:

The average speed of the fish can be calculated by dividing the distance traveled by the time taken.

First, we need to convert the distance from km to meters:

6 km = 6,000 meters

Next, we need to convert the time from minutes to seconds:

5 minutes = 5 × 60 = 300 seconds

Finally, we divide the distance traveled by the time taken:

Average speed = 6000 meters / 300 seconds = 20 m/s

So, the average speed of the fish is 20 m/s.

Answer:

d = 3

Step-by-step explanation:

4d+9=21

4d = 12

d = 3

Let's check

4(3) + 9 = 21

12 + 9 = 21

21 = 21

So, d = 3 is the correct answer.

Answer: 3 = d

Step-by-step explanation:

4d + 9 = 21

     - 9   - 9

4d = 12

—     —

4       4

d = 3

The distance between the star from the Sun in astronomical units

is 28.6 AU.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

From the reference angle of 2 degrees, d can be thought of as the adjacent side and the distance from the Sun and the Earth can be thought of as the opposite side.

Now, We know tan = opposite/adjacent.

tan2° = 1/d.

d = 1/0.035.

d = 28.6 AU.

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Answer: 7

Step-by-step explanation: 13 + 7 = 20

Answer: 7

Step-by-step explanation:

q+13=20

subtract 13 on both sides and you get

q=7

The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.

The test does not prove the alternative hypothesis correct, because when performing a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. However, rejecting the null does not necessarily mean that the alternative hypothesis is true. It is possible for the null hypothesis to be rejected even when it is true, due to the occurrence of random fluctuations. Therefore, the test does not prove that the alternative hypothesis is correct, as there is always a possibility that the null hypothesis is true despite being rejected. To prove that the alternative hypothesis is correct, a series of hypothesis tests must be conducted to show that the population parameter is consistent with the alternative hypothesis.

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The simplified expression of 1+sin^2-cos^x / 2sin^2x  issin^2(x) / 2(1 + cos(x)) + 1 / 2(1 - cos(x))

To simplify this expression, we can first simplify the numerator by combining the terms inside the parentheses:

1 + sin^2(x) - cos(x) = sin^2(x) + 1 - cos(x)

Next, we can factor the denominator trigonometric identity sin^2(x) + cos^2(x) = 1:

2 sin^2(x) = 2(1 - cos^2(x)) = 2 - 2cos^2(x)

Now we can substitute these simplified expressions into the original expression:

(1 + sin^2(x) - cos(x)) / (2 sin^2(x))

= (sin^2(x) + 1 - cos(x)) / (2 - 2cos^2(x))

= [(1 - cos(x)) + sin^2(x)] / [2(1 - cos(x))(1 + cos(x))]

1+sin^2-cos^x / 2sin^2x = [sin^2(x) / 2(1 + cos(x))] + [1 / 2(1 - cos(x))]

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The juice is 27 and the tornadoes are 21.

An equation is a mathematical statement that shows that two expressions are equal by using an equal sign (=). Equations are used to find the value of an unknown variable or to show the relationship between variables.

We know that the number of the juice and the tornadoes can be x and y

We then have that;

5x + 3y = 24 ----- (1)

4x + 2y = 30 ----- (2)

Multiply equation 1 by 4 and equation 2 by 5 we have that;

20x + 12y = 96 ---- (3)

20x + 10y = 150 ----- (4)

Subtract (3) from (4)

-2y =54

y = -27

Then;

5x + 3(-27) = 24

x = 21

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Answer:

3.41

Step-by-step explanation:

41/12

The cost price of cloth that John bought per meter is Php 46.00 (Option C). To find the cost price per meter, divide the total cost by the number of meters of cloth.

In this case, the total cost is Php 425.50 and the number of meters is 9.25. By dividing the total cost by the number of meters, we get Php 46.00 per meter. This means that John paid Php 46.00 for every meter of cloth he bought. This is the cost price per meter and it is option C, Php 46.00.

The specific value that corresponds to the unit price that was purchased is reflected in retail systems by the cost price. In some stock market theories, this value is used to determine the value of stock holdings, and it is used as a key factor in determining profitability.

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The expanded form of the expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex] is [tex]\frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex].

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex].

We know, (a ± b)² = a² ± 2ab + b².

Therefore, [tex]\frac{a^2 - (b + c)^2}{c^2 - (a - b)^2}[/tex]

[tex]= \frac {a^2 - (b^2 + 2bc + c^2)}{c^2 - (a^2 - 2ab + b^2)}[/tex]

[tex]= \frac{a^2 - b^2 - 2bc - c^2}{c^2 - a^2 + 2ab - b^2}[/tex]

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