Find X and RDB:




X =
RDB =

Answer:

A =-6, B = 1, and C =25

Step-by-step explanation:

The equation y -7 = 6(x + 3) can be rearranged to the standard form y = Ax + B by isolating y on one side and collecting all the constant terms on the other side. To do this, we'll first expand the expression 6(x + 3) and then subtract 7 from both sides:

y - 7 = 6(x + 3)

y - 7 = 6x + 18

y = 6x + 25

So, the equation in standard form is:

y = 6x + 25

Now, if we are given that the standard form has A = -6, we can substitute this value into the equation:

y = -6x + B

since B is coefficient of y so

B=1

again

C is constant so C=25

Answer:

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}\)

The standard form of a linear equation  Ax + By = C  has the x and y terms on the left side and the constant on the right side. The coefficients of the variables must be integers.  

Given equation:

\(y -7 =6(x+3)\)

Expand the brackets:

\(y-7=6x+18\)

Switch sides:

\(6x+18=y-7\)

Subtract y from both sides:

\(6x-y+18=-7\)

Subtract 18 from both sides:

\(6x-y=-25\)

Therefore, the given equation in standard form is:

However, as your question states that A = -6, multiply both sides of the equation by negative 1 to make the coefficient of x negative:

Therefore,

Please note that this is not strictly in standard form, as A should be a positive integer.

The answer is C: (-3,-1)

To test if points satisfy an equation, all you need to do is test the numbers in both of the equations it provides you

Here is proof the answer is C :

y > x - 2

(lets plug in point C)

-1 > -3 - 2

solve

-1 > -5 ?

Yes this statement is true- onto the next inequalitity!

y > 2x + 2

-1 > 2(-3) + 2

solve

-1 > -6 + 2

-1 > -4 ?

Yes, this inequality is true too!

Know we know answer c (-3,-1) is the right answer!

The point (x,y) satisfies the given system of inequalities is C. (-3,-1).

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Given that The graph below represents the following system of inequalities.

y> - 2

y > 21 + 2

So, y > x - 2

Lets plug in point C;

-1 > -3 - 2

solve;

-1 > -5 ?

Yes this statement is true- onto the next inequalitity.

y > 2x + 2

-1 > 2(-3) + 2

solve;

-1 > -6 + 2

-1 > -4 ?

Yes, this inequality is true too!

Therefore, the point (x,y) satisfies the given system of inequalities is C. (-3,-1).

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The side length of the cube is x = ∛(x² - x + 7) units

First, we need to know the formula.

The formula for calculating the volume of a cube is expressed as;

Note that all the sides of a cube are equal

Then, we have that the equation is;

V = a³

Such that the parameters are;

From the information given, we have that;

Volume = x² - x + 7

Now, substitute the value, we have;

x² - x + 7 = x³

Find the cube root of both sides, we have;

x = ∛(x² - x + 7) units

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\( \Large{\boxed{\sf y = x - 7}} \)

\( \\ \)

We are given a linear equation, and we would like to express it in slope-intercept form.

\( \\ \)

\( \Large{\left[ \begin{array}{c c c} \underline{\tt Slope-Intercept \: Form \text{:}} \\ ~ \\ \tt y = mx + b \end{array} \right] } \)

Where:

\( \\ \)

Given linear equation:

\( \sf 4y - 4x = -28 \)

\( \\ \)

To find the slope-intercept form of the equation, we have to solve for y.

First, add 4x to both sides of the equation:

\( \sf \longrightarrow 4y - 4x + 4x = -28 + 4x \\ \\ \\ \longrightarrow \sf 4y = 4x - 28 \)

\( \\ \)

Then, divide both sides of the equation by 4:

\( \sf \longrightarrow \dfrac{4y}{4} = \dfrac{4x - 28}{4} \\ \\ \\ \longrightarrow \sf y = \dfrac{4x}{4} - \dfrac{28}{4} \\ \\ \\ \longrightarrow \boxed{\boxed{\sf y = x - 7}} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

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First , Add 4x to both sides :

➱ \(\sf{4y-4x=-28}\)

➱ \(\sf{4y=-28+4x}\)

Next , Divide all terms by 4 to get y all alone

➱ \(\sf{y=-7+x}\)

Rearrange so that our result matches the format for slope - intercept :

➱\(\sf{y = x +7}\)

Henceforth, Equation : y = x + 7 .

The probability that a male student chooses chocolate ice cream is 13/23.

Probability exists as the branch of mathematics that examines the possible results of given events together with the outcomes' relative likelihoods and distributions.

Probability defines the odds that a random event would occur. The odds that the event would occur lie between 0 and 1.

The probability that a male student chooses chocolate ice cream

= number of males that chose ice cream / total number of males

= 13 / 23

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Answer:

the answer is 3/22

Step-by-step explanation:

Answer:

111base2multply(1111base2+1010base2) = 0

It is impossible to sketch a graph or determine the orientation of the graph.

Without a specific function or data set provided, it is impossible to sketch a graph or determine the orientation of the graph. The orientation of a graph refers to the direction of the graph and can be described as either increasing or decreasing.

In order to sketch a graph, we must first have a set of data points or a function to plot. Once we have the necessary information, we can plot the points or graph the function and then determine the orientation of the graph.

To determine the orientation of a graph, we look at the direction of the graph as we move from left to right. If the graph is moving upward as we move from left to right, then the orientation is increasing.

If the graph is moving downward as we move from left to right, then the orientation is decreasing. If the graph is neither increasing nor decreasing, then the orientation is said to be undefined.

In summary, the orientation of a graph is determined by the direction of the graph as we move from left to right. Without a specific function or data set provided,

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The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

Convert the percent to a decimal: according to the local weather report, the probability of rain in Boston on February 9 is 78% is 0.78%.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability theory is used to study random phenomena, such as the outcome of a coin toss or the results of an election. It is also used to make predictions about the future, such as whether it will rain tomorrow.

The probability of choosing a student selected for the AP math class is 13/40 (6 girls and 7 boys selected for the AP math class). Therefore, the probability of choosing a boy or a student selected for the AP math class is 32/40 (19 boys plus 13 students selected for the AP math class out of 40 students).

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The complete question is: According to the local weather report, the probability of rain in Boston on February 9 is 78%. What is 78% converted to a decimal?

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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Step-by-step explanation:

the solution is in the picture

Answer:

the first one makes the most sense

Step-by-step explanation:

the others would equal to much but the first one would not

Step-by-step explanation:

so, we calculate the perpendicular slope, and then we start with the point-slope form (since we were given a specific point of the line), and transform into the regular slope-intercept form.

the slope in

y = 2x + 2

is the factor of x : 2 or 2/1

the perpendicular slope is turning this upside down and flips the sign : -1/2

the point- slope form is

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being the point.

y - 9 = -1/2(x - -2)

y - 9 = (-1/2)x - 1

y = (-1/2)x + 8

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

Decreases

Step-by-step explanation:

The direction on the x axis will go down with a increasing

I hope this helps!

Answer:

A it increases

Step-by-step explanation:

This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

In-state corresponds to students who are residents of the same state as the university, out-of-state corresponds to students from different states, and foreign corresponds to students from countries other than the university's country.

To match the vocabulary word with its corresponding example in the context of the state university survey, we need to understand the terms and their meanings.

Here are the vocabulary words and their corresponding examples:

Vocabulary Word: In-state

Example: A student who is a resident of the same state where the university is located.

They pay lower tuition fees compared to out-of-state or foreign students.

Vocabulary Word: Out-of-state

Example: A student who is not a resident of the state where the university is located.

They typically pay higher tuition fees compared to in-state students.

Vocabulary Word: Foreign

Example: A student who is from a country other than the country where the university is located.

They are international students who may have different visa requirements and tuition fees.

To match these vocabulary words with their corresponding examples:

In-state: A student from the same state as the university, paying lower tuition fees.

Out-of-state: A student from a different state than the university, paying higher tuition fees.

Foreign: A student from a country other than the country where the university is located, with potential differences in visa requirements and tuition fees.

By associating each vocabulary word with its respective example, we can accurately describe the three categories of students based on their residency and origin in the context of the state university's survey.

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The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).

Given the polynomials in the question:

x² - 9

x² + 8x + 15

To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.

First, factorize x² - 9:

Using the difference of sqaure formula

a² - b² = ( a + b )( a - b )

x² - 9

x² - 3² = (x - 3)(x + 3)

Next, factorize x² + 8x + 15:

Using AC method

( x + 3 )( x + 5 )

From the factorizations, we can see that both expressions have a common factor of (x + 3).

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Answer:

a. The given equation is (y - 3)^2 -10 = 71. To determine the number and type of solutions, we need to use the discriminant, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0). In this case, the equation can be rewritten as (y - 3)^2 = 81, which is in the form of (y - k)^2 = r^2, where k = 3 and r = 9. Therefore, the equation can be written as (y - k)^2 - r^2 = 0, which is a quadratic equation with a = 1, b = -6, and c = -72. The discriminant is then b^2 - 4ac = (-6)^2 - 4(1)(-72) = 300. Since the discriminant is positive, there are two real solutions.

b. To solve the equation (y - 3)^2 -10 = 71, we first add 10 to both sides to get (y - 3)^2 = 81. Then, we take the square root of both sides to get y - 3 = ±9. Adding 3 to both sides, we get y = 3 ± 9, which gives us two solutions: y = 12 and y = -6.

Therefore, the equation (y - 3)^2 -10 = 71 has two real solutions, which are y = 12 and y = -6.

Step-by-step explanation:

Answer:  type: real   number of solutions:2   y=12,-6

Step-by-step explanation:

see images for explanations

As Tan A=Perpendicular/Base, x has the value of 21.56. Tan 54 = x/32, or x = 21.56, in this case.

When two lines cross at a 90-degree angle, they are said to be perpendicular. The definition of a parallel line is a line with constant spacing. being perfectly vertical or upright: making a straight angle with one another or another given line or plane. Adverbial phrase meaning "perpendicularly"

As a result of two lines meeting at a right angle, the word "perpendicular" denotes "at right angles." Including up and down, across, and side to side, perpendicular lines can face in any direction. Additionally, they don't need to be standing straight up from the bottom or side of the page.

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The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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Answer:

y=-4x+0

Step-by-step explanation:

Slope form is y=mx+b

m is the slope, and b is the y intercept. If the line must pass through (0,0) then the y intercept would be zero.

This give you y=mx+0

Now to find the slope you need a perpendicular line to the previous line. This would mean you have to swap 1/4 which is the previous lines slope.

1/4 is a positive so make it a negative, -1/4

Now flip -1/4 to make is -4/1 which also equals -4

Now with the slope -4 and y-intercept 0, you know you equation

y=-4x+0

Answer:

b) 0.324 < p < 0.416

Step-by-step explanation:

b) 0.324 < p < 0.416

The book has a lower cost per minute than the movie.

To find the cost per minute of the book, we divide the cost by the number of minutes:

cost per minute of book = $15 / 200 minutes = $0.075 per minute

To find the cost per minute of the movie, we need to convert the time to minutes.

2 hours and 39 minutes is equal to:

2 hours x 60 minutes/hour = 120 minutes

39 minutes = 39 minutes

Total minutes = 120 + 39 = 159 minutes

cost per minute of movie = $14 / 159 minutes = $0.088 per minute

Therefore, the book has a lower cost per minute than the movie.

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Answer:

hi Road trip was awesome to have 6am in a sequential of my friends

Step-by-step explanation:

who were not able for the first two bones of a

Answer:

40

Step-by-step explanation:

First calculate how many 9-inch pieces of ribbon can be cut from one 6 ft roll.

1 foot = 12 inches

⇒ 6 feet = 6 × 12 = 72 inches

Divide the total number of inches per roll by the length of the piece of ribbon:

⇒ 72 inches ÷ 9 inches = 8

Therefore, eight 9-inch pieces of ribbon can be cut from one roll.

To find how many 9-inch pieces can be cut from 5 rolls, simply multiply the number of 9-inch pieces for ribbon that can be cut from one roll by 5:

⇒ 8 × 4 = 40

Therefore, the dressmaker can cut forty 9-inch pieces of ribbon from 5 rolls.

Note: The total number of inches of ribbon the dressmaker has is: