5c-2=3c then 24=c
how do i work this problem?

The degree of a polynomial function with the leading term 7\(x^{5}\)  is 5.

A variable in an equation, such as a quadratic equation or cubic equation, is said to be polynomial if it only contains the positive integer exponents or non-negative integer powers. For instance, the polynomial 3x+5 has an exponent of 1.

What is degree?

The highest degree among the polynomial's monomials with non-zero coefficients is referred to as the polynomial's degree in mathematics.

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the term of this polynomial is 5.

degree of the polynomial is the highest degree of any of the terms; in this case, it is 5.

Hence, polynomial function with leading term 7\(x^{5}\) has a degree of 5.

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Answer:

BODMAS RULE

(c-3)²=100

c²-6c+9=100

c²-6c=100-9

c²-6c=91

c²-6c-91=0

then factories

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

1) The respective answers for the maximum height, time in the air and vertical velocity are; 215.25 ft; 6.54 s; -117.28 ft/s

2) The respective answers for the equation that models the height of the ball and the value of maximum height of the ball are;

s(t) = -16t² + 48t + 3.5

Maximum height = 39.5 ft

1) (a) We are given that;

The equation that represents the height at time t is;

S(t) = -16t² + 92t + 83

The maximum height will occur at the time of the x-value of the line of symmetry of the parabola.

Thus; t = -b/(2a) = -92/(2 * -16)

t = 2.875 s

Thus, maximum height is;

S(2.875) = -16(2.875)² + 92(2.875) + 83

S(2.875) = 215.25 ft

1b) The time that the ball is in the air is at S(t) = 0 ft.

Thus;

-16t² + 92t + 83 = 0

From online quadratic equation calculator;

t = 6.54 s

1c) The vertical velocity when it hits the ground is gotten by differentiating the height equation and putting 6.54 s for t. Thus;

v(t) = s'(t) = -32t + 92

v(6.54) = -32(6.54) + 92

v(6.54) = -117.28 ft/s

2a) We are given;

Thus, equation that models  the height of the ball t seconds after it is thrown is;

s(t) = -16t² + 48t + 3.5

2b) The maximum height will occur at the time of the x-value of the line of symmetry of the parabola.

Thus; t = -b/(2a) = -48/(2 * -16)

t = 1.5 s

Thus, maximum height is;

S(2.875) = -16(1.55)² + 92(1.5) + 3.5

S(2.875) = 39.5 ft

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The linear equation represented by the table is:

y = 3x + 2

Here we have a table that represents what seems to be a linear function.

Remember that a general linaer function can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁,y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the first two points in the table (3, 11) and (5, 17) we will get the slope:

a = (17 - 11)/(5 - 3)

a = 6/2 = 3

So we can write:

y = 3x + b

We know that when x = 3, y = 11, then:

11 = 3*3 + b

11 = 9 + b

11 - 9 = b

2 = b

the line is:

y = 3x + 2

That is the correct option.

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Answer:

Average

Step-by-step explanation:

Mean is the average of a set of numbers that you are given.

To get the mean you need to add up all the numbers and divide that total number by the amount of numbers you had.

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

C) 8

Step-by-step explanation:

Consecutive angles are equal to 180. So 22x+4+180. Solve that to get x=8. Hope I helped and post more questions :)

Answer : 0.99

Explanation :  15 * 6.6/100 For The Tax.

Total : 15.99

a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

Question 7

Domain: (-2,3]

Range: (1,4]

Question 8

a) No

b) x=4 and x=-2

c) (0,3)

d) (3,0) and (-1,0)

Step-by-step explanation:

Question 7

Domain refers to the span of x-values that a function encompasses. We can see from the graph that the lowest x value is -2 and the highest one is 3, and we also note the open circle at x=-2 (meaning x=-2 itself isn't included, which we note using curved brackets) and the closed circle at x=3 (meaning x=3 itself is included, which we note using square brackets). This leaves us with a domain of (-2,3]

Range meanwhile refers to the span of y-values that a function encompasses. We can see from the graph that the lowest y value is 1 and the highest one is 4, and we also note the open circle at y=1 (meaning y=1 itself isn't included, which we note using curved brackets) and the closed circle at y=4 (meaning y=4 itself is included, which we note using square brackets). This leaves us with a range of (1,4]

Question 8

a)

If the point (1,-3) is on the graph, then subbing 1 in for x and -3 in for f(x) should equate:

f(x)=x²-2x-3

-3=1²-2(1)-3?

-3=1-2-3?

-3=-4?

Since this doesn't equate, we can say the point is not on the line.

b)

The condition is that (x,5) is on the graph, so let's sub 5 in for f(x):

f(x)=x²-2x-3

5=x²-2x-3

x²-2x-8=0

(x-4)(x+2)=0

x=4 and x=-2

c)

The y-intercept is the point(s) at which the graph crosses the y-axis, ie where x=0, so to find it we sub 0 in for x:

f(x)=x²-2x-3

f(0)=0²-2(0)-3=-3

Therefore the y-intercept is (0,3)

d)

The c-intercept is the point(s) at which the graph crosses the x-axis, ie where y=0, so to find it we sub 0 in for f(x):

f(x)=x²-2x-3

0=x²-2x-3

(x-3)(x+1)=0

x=3 and x=-1

Therefore the x-intercepts are (3,0) and (-1,0)

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer: a. The mode of the data set is the most frequently occurring value. From the results, the most frequent sum is 7, which occurs 6 times. Therefore, the mode of the data set is 7.

b. To find the median, we need to arrange the data set in numerical order. The median is the middle value of the data set. Since the data set has 36 values, and 36 is an even number, the median will be the average of the 18th and 19th values in the ordered data set.

c. The mean of a data set is found by adding all the values and dividing by the number of values. To find the mean of this data set, we add up all the sums (2+3+4+...+12) and divide by 36.

d. The range is the difference between the largest and smallest values in a data set. In this case, the largest sum is 12 and the smallest sum is 2, so the range is 12-2 = 10

Please note that this is a simulation, if you want real results you should collect the data by throwing the dice 36 times and record the scores.

Step-by-step explanation:

The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

It is given that:

24 children were asked which is their favourite colour from a choice of red, blue

green or yellow

From the data given in the question.

Red : 6

Blue: 4

Green: 8

Yellow : 1 (half of 2)

Pink: 1 (half of 2)

Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

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hopefully this is correct..

it's either e = 1/3 or 3

Answer:

1/3 or 3^-1

Step-by-step explanation:

please mark me as brainlest

Answer:

4

3 72/120

÷24 ÷24

3 3 / 5 = 3 + 3/5 = 3 + 6/10 = 3 + 0.6 = 3.6 ≈ 4 rounded to the nearest half since 3.6 is closer to 4 than 3

Step-by-step explanation:

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The simple radical form is 72√2.

What is simple radical form?

If we know the prime factorization of 32, we can write the simplest radical form of the square root of 32. Thus, the prime factorization of 32 is 2 × 2 × 2 × 2 × 2. If it is written in the radical form, then the simplest radical form of the square root of 32 is 4√2. Square Root of 32 in Radical Form: 4√2.

Given,

3√2•2√8•√3•√6

= 3×√2×2×√8×√3×√6

as we know √ab = √a√b

we can write, √8 = √2√4 and √6 =√2√3

we get,

=3×√2×√2×√4×√3×√3×√2

=3×2×2×3×√2

=72√2

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The parabola \(y = √(x - 4)\) opens upward.

The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.

The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.

This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.

The parabola \(y = √(x - 4)\) opens upward.

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F(x) is an antiderivative of f(x) because F'(x) = f(x)

An anti-derivative is the integral of a function

To verify that F is an antiderivative of f where

F(x) = √(3x² - 4) and f(x) = 3x/√(3x² - 4)

This means that F(x) = ∫f(x)

This implies that F'(x) = f(x)

So, we verify as follows

F(x) = √(3x² - 4)

Taking the derivative with respect to x, we have that

dF(x)/dx = d√(3x² - 4)/dx

Let u = 3x² - 4

So, dF(x)/dx = d√u/dx

= d√u/du × du/dx

= 1/(2√u) × du/dx

Now,du/dx = d(3x² - 4)/dx

= 6x

So,

dF(x)/dx  = 1/(2√u) × du/dx

= 1/(2√(3x² - 4)) × 6x

= 1/(√(3x² - 4)) × 3x

= 3x/(√(3x² - 4))

= f(x)

So, F(x) is an antiderivative of f(x) because F'(x) = f(x)

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Answer:

Refraction is what happens when light passes through some medium and changes it's direction because of it. For instance, when light travels through a lens light is bent as it goes from air to glass and back to air again. :)

Answer:

Because you can't divide by zero.

Step-by-step explanation:

If x = -2, it makes the denominator 0. This will result in the equation being undefined because you can't have zero in the denominator.

The solution to the inequality will be greater than or equal to negative 5 but at x = -2, the function is not defined.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3 / (x + 2) + 4 ≥ 3

Simplify the inequality, then we have

3 / (x + 2) + 4 ≥ 3

[3 + 4(x + 2)] ≥ 3(x + 2)

3 + 4x + 8 ≥ 3x + 6

4x - 3x ≥ 6 - 8 - 3

x ≥ -5

The solution to the inequality will be greater than or equal to negative 5 but at x = -2, the function is not defined.

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Answer:

Cevap B

Step-by-step explanation:

fcxssazhgfxghfhdhddd

Answer:

x = –5

Step-by-step explanation:

Answer:

X equals 1, and Y equals 2

\(2x = 2 * 1\)

\(3y = 3 * 2\)

\(2 * 1 = 2\)

\(3 * 2 = 6\)

\(6 + 2 = 8\)

________________________________________________________

Now, we go over what we learned.

________________________________________________________

We learned how to make inequalities true by assigning values to substitutions.

Questions related to this topic? Ask me in the comments box.