For what value of x is line a parallel to line b?

Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.

An algebraic expression is a mathematical expression that uses coefficients, unknown variables, algebraic operations, and constants. However, it is not acceptable to use an equality symbol in an expression.

Mathematical expressions and sentences come in a wide variety. the relationships between equations, numerical expressions, and algebraic expressions.

The difference between 10 am and 6 am

is 4 hours, So the the time he arrives will be a multiple of 50 grater than 4 hours

50x > 4 × 60

50x > 240

x > 240/50

x > 4.8

x = 5 (as 5 is nearest single digit no. to 4.8)

50x = 50 × 5

= 250 minutes

250 mins = 4 hours and 10 mins

6 am  + 4 hours and 10 mins

= 10 hour and 10 min or 10:10 am

Thus, Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.

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Answer:

Choice B: x = 3

Step-by-step explanation:

The standard equation of a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]

where

(h, k) is the vertex and |p| is the focal length

The given equation is
[tex](y - 3)^2 = 8(x - 5)[/tex]

Convert this to standard form and compare with general equation

Answer: Choice B: x = 3

If riley needs to make punch for a party. One batch of punch has the ingredients shown. The cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups is 6 cups.

Total cup of juice for one batch:

Total cup of juice for one batch = 4+ 1 +2 +2

Total cup of juice for one batch = 9

Since 2 cup of the 9 cups are orange juice so 2/9 of each batch will be orange and since the bowl can hold 27 cups now let find the cups of orange juice.

Cups of orange juice = 2/9 ×27

Cups of orange juice =6 cups

Therefore we can conclude that the cups of orange juice is 6 cups.

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Answer:

[tex]\boxed{y = 4x + 7}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values

Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]

Difference in y values [tex]= -1 -3 = -4[/tex]

Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]

Slope

 [tex]m = \dfrac{-4}{-1} = 4[/tex]

So the equation of the line is of the form
[tex]y = 4x + b[/tex]

To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b

Let's take point (-1, 3)

Plug in values:

[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]

Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]

Therefore , the solution of the given problem of vectors comes out to

be -25.

An object with both magnitude and direction is referred to as a vector. A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

Here,

Given:

lul=3,|v|=4 and |w|=5

Also, u+v+w=0

On squaring both sides, we get

=> u2+v2+w2+2(u.v+v.w+w.u) = 0

=> 32+42+52 +2(u.v+v.w+w.u) = 0

=> 9+16+25+2(u.v+v.w+w.u) = 0

=> u.vv.w+w.u

=> -50 = -25

Therefore , the solution of the given problem of vector comes out to

be -25.

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Answer: x³ - 3x² + 4x - 12

Step-by-step explanation:

Using FOIL:

x³ - 3x² + 4x - 12

Answer:

x=1

Step-by-step explanation:

(x^2+4)(x-3)

"x^2=x*x=x"

(x+4)(x-3)

x+1

x/x/

x=1

Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.

Step-by-step explanation:

-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.

[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]

that's about 74 years and 325 days more or less.

based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.

Step-by-step explanation:

let the number of weeks be w

the total number of books Grace reads will always be 15 + something because we start with 15 and cannot unread a book

for each week, she reads 2 books. this can be represented as 2 * w

books Grace already read + books Grace reads each week = total books

15 + 2 * w = total books

Using cosine law and sine law, the value of angle E and D are 14° and 35° and the length of side d is 19 units

The law of cosines is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).

In this given problem, triangle DEF can be;

f² = e² + d² - 2(e)(d) cos(F)

But we don't know the length of side d

Using sine law

f / sin F = e / sin E

25 / sin 131 = 8 / sin E

sin E = 8 * sin 131 / 25

E = 13.97°

E = 14°

Using sum of angles in a triangle

D + E + F = 180°

D = 180 - (14 + 131)

D = 180 - 145

D = 35°

Using cosine law;

d² = e² + f² - 2(e)(f)cos(D)

Substituting the values into the formula;

d² = 8² + 25² - 2(8)(25)cos(35)

d = 19

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Answer:

-5 and -3

Step-by-step explanation:

-2x + 1 > 6

[tex]-2(-\frac{5}{2}) + 1 > 6\\6 > 6[/tex]

Not an answer

-2(-5) + 1 > 6

11 > 6

An answer

-2(-2) + 1 > 6

5 > 6

Not an answer

[tex]-2(-\frac{3}{2}) + 1 > 6\\4 > 6[/tex]

Not an answer

-2(0) + 1 > 6

1 > 6

Not an answer

-2(-3) + 1 > 6

7 > 6

An answer

Answer:

5 combination 3

5 fictorial divided by (5-3)! 3!

by using the above method 10 will be your answer

The number of fabric used for headband and wristband for each player is 25.8in and 9.3 in

Word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations.

Represent the number of fabric used on headband by x and the number of fabric used on wristband by y

Therefore;

31x +3x = 876.52

34x = 876.52

divide both sides by 34

x = 876.52/34

x = 25.8 inches

31y = 288.61

dive both sides by 31

y = 288.61/31

y = 9.3 inches

therefore 25.8 inches of fabrics and 9.3 inches of fabrics are used on headband and wristband of each player

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When the thickness of a textbook is b mm the expressions for:

thickness of 5 stacked textbooks = 5b mm

thickness of each page, if the pages are numbered to 225 = b / 225

The thickness for each of the condition is written as follows

For the thickness of 5 stacked textbooks

= b + b + b + b + b

= 5b

For thickness of each page, if the pages are numbered to 225

In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book

= b / 225

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The ones which are equation are

[tex]\frac{3}{4}l = -9\\ 4m + 2m = 72[/tex]

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

here

-3 = d/-8

or, d = 24 (different from answer)

14 = 25 - k

or, k = 11 (different from answer)

j + 1 = j/3

or, 3j + 3 = j

or, j = -3/2 (different from answer)

3/4 l = -9

or, l = -12 ( same as answer)

-15 = n + 8

or, n = -23 (different from answer)

4m + 2m = 72

or, m = 12 (same as answer)

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Answer:

y = 2x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 6 ) and (x₂, y₂ ) = (9, 20 )

m = [tex]\frac{20-6}{9-2}[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute either of the 2 points into the partial equation

using (2, 6 ), then

6 = 2(2) + c = 4 + c ( subtract 4 from both sides )

2 = c

y = 2x + 2 ← equation of line

Answer:

a) 6a+5 b)4

Step-by-step explanation:

a) 3a+3a+5 = 6a+5

b)6a + 5 = 29

6a = 29-5

6a = 24

6 6

a = 4

Answer:

a = 18

Step-by-step explanation:

The slopes of parallel lines are equal as

[tex]m_{2}=m_{1}[/tex]

We know that the slope formula is

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2, x2, y1, and y2 are any two points.

Thus, since the slopes are equal, we can use the slope formula to find the slopes of both lines and set them equal to each other to find a:

[tex]\frac{9-2}{4-a}=\frac{3-11}{(a+1)-3} \\\\\frac{7}{4-a}=\frac{-8}{a-2} \\\\7(a-2)=-8(4-a)\\7a-14=-32+8a\\7a=-18+8a\\-a=-18\\a=18[/tex]

If we plug in a for any of the two lines, we see that the slope is -1/2

Line 1 w/ (a, 2) & (4, 9):

[tex]\frac{9-2}{4-18}\\ \frac{7}{-14}\\ \frac{-1}{2}[/tex]

Line 2 w/ (3, 11) & (a+1, 3):

[tex]\frac{3-11}{18+1-3}\\ \frac{-8}{19-3}\\ \frac{-8}{16}\\ \frac{-1}{2}[/tex]

Answer:

Step-by-step explanation:

1.75?

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]

Answer:

[tex]\boxed{\bf Slope(m):-1}[/tex]

Step-by-step explanation:

We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).

The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.

[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]

[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]

[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]

[tex]\bf m=-\cfrac{5}{5}[/tex]

[tex]\bf m=-1[/tex]

Therefore, the slope is -1.

__________________

Hope this helps!

Have a great day!

Answer:

Step-by-step explanation:

The general formula for finding the antiderivative of a polynomial function is to add one to the exponent of each term and divide by that new exponent.

To find the antiderivative of y = 5x -6x² +9x³, we need to integrate each term individually, using the general formula:

∫ (5x) dx = (5/1)x^(1+1) = 5x^2 + C

∫ (-6x²) dx = (-6/2)x^(2+1) = -3x^3 + C

∫ (9x³) dx = (9/4)x^(3+1) = (9/4)x^4 + C

So the antiderivative of y = 5x -6x² +9x³ is:

∫ y dx = 5x^2 - 3x^3 + (9/4)x^4 + C

Where C is the constant of integration, which can take any real value.

Answer: x = 2

Step-by-step explanation:

Multiply each term between the parentheses by 2 1/3.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the expression of the multiplication.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the multiplication and division of rational numbers.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]

We convert the mixed fraction to improper.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]

We move the constant to the right side and change the direction of the sign.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]

Answer:

A.

Arithmetic mean: The sum of the data divided by the number of data points. (For the first set of data: (30+25+23+41+39)/5 = 31.4)

Median: The middle value when the data is arranged in order. (For the first set of data: 30, 23, 25, 39, 41 => 25)

Mode: The value that appears most frequently in the data. (For the first set of data: No value appears more than once, so there is no mode.)

Range: The difference between the highest and lowest values in the data. (For the first set of data: 41-23 = 18)

B.

To find the upper and lower quartile, you need to first arrange the data in order and then divide it into four equal parts.

Lower quartile (Q1) is the median of the lower half of the data.

Upper quartile (Q3) is the median of the upper half of the data.

For the first set of data: Q1 = (23+25)/2 = 24, Q3 = (39+41)/2 = 40

7th and 50th Percentile:

To find 7th percentile, pick 7th item from ordered data set and if not possible then take the average of 6th and 8th items.

To find 50th percentile, pick the median of the data set.

For the first set of data: 7th percentile = 25, 50th percentile = 25

C.

Variance: A measure of the spread of the data. It is calculated by taking the average of the squared differences from the mean.

Coefficient of variation (CV) : A normalized measure of the spread of the data. It is the ratio of the standard deviation to the mean.

D.

Pearson coefficient of skewness: A measure of the asymmetry of the data about the mean. A positive skewness indicates that the tail on the right side of the probability density function is longer or fatter than the left side. Conversely, a negative skewness indicates that the tail on the left side is longer or fatter than the right side.

Kurtosis: A measure of the "peakedness" of the data. A high kurtosis means that the data has heavy tails (outliers) or a distinct peak near the mean, whereas a low kurtosis means that the data has light tails (no outliers) or a flat peak near the mean.

Answer:

y = - 3

Step-by-step explanation:

A line parallel to the x- axis is a horizontal line with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (2, - 3 ) with y- coordinate - 3 , then

y = - 3 ← equation of line

The value of 3x₁ + x₂ is 7/2

A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.

5/x - 2/x² = 2

The LCM of x and x² is x². So we have:

(5x - 2)/x² = 2

Cross multiply:

5x - 2 = 2x²

2x² - 5x + 2 = 0

Factorize:

(2x - 1)(x - 2) = 0

2x - 1 = 0 or x - 2 = 0

2x  = 1 or x = 2

x  = 1/2 or x = 2

Thus, x₁ = 1/2 and x₂ = 2

Therefore, the value of 3x₁ + x₂ will be:

3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2

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Answer:

P(EF) > 0.72 and in general, P(EF) > P(E) + P(F) - 1

Step-by-step explanation:

We know that P(EF) = P(E and F) = P(E|F) * P(F) = P(F|E) * P(E) (by the definition of conditional probability).

For the specific case given, P(E)= 0.9 and P(F) = 0.8,

P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > P(E) * P(F) = 0.72

In general,

P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > min(P(E|F) * P(F), P(F|E) * P(E) ) = P(E) * P(F)

P(EF) > P(E) * P(F) = P(E) + P(F) - 1

This is because P(E|F) and P(F|E) are always less or equal to 1.

Answer:

21.6%

Step-by-step explanation:

Each day is independent, so the probability of snow all three days is:

(0.60)³ = 0.216

There is a 21.6% chance that it snows all three days.

The representation of the fraction 10/8 as a mixed number is given as follows:

[tex]\frac{10}{8} = 1\frac{1}{5}[/tex]

The fraction in this problem is given as follows:

10/8.

A mixed number is composed by two parts, as follows:

The integer part and the fractional part are defined as follows:

For the division of 10 by 8, we have that:

Then the mixed number is given as follows:

[tex]1\frac{2}{10}[/tex]

The fraction 2/10 can be simplified as 1/5, hence the simplified representation is given as follows:

[tex]1\frac{1}{5}[/tex]

The problem asks to represent the fraction 10/8 as a mixed number

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The mean number of goals for two seasons is 2.44 goals per match.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

Given, Last season Rio's football team scored 50 goals in 20 matches.

This season they scored 60 goals in 25 matches.

Therefore, The mean number of goals per match for each season is,

= (50 + 60)/(20 + 25).

= 110/45.

= 2.44 goals per match.

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The multiplicative inverse of 6 + 2i is 3/20 - 1/20i.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2-1 since it fulfills the formula: 2 x 2-1 = 2 x 12 = 1. It is also known as a number's reciprocal.

Use the following method to determine a complex number's multiplicative inverse:

The original complex number is reciprocated to find the inverse. The complex number (6+2i) has a reciprocal of 1/6+2i. Simplify by multiplying the reciprocal's numerator and denominator by the conjugate of the denominator:

1/6+2i × 6 - 2i/6 - 2i

3/20 - 1/20i.

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