The distance from the point A(-9,-3) to the line y = x - 6 is calculated using the formula for the distance from a point to a line in the coordinate plane. After substituting the values in the formula, the distance is approximately 8.5 units.
Explanation:To find the distance from point A (-9,-3) to the line y = x - 6, we use the formula for the distance from a point to a line in two-dimensional space. This formula is |Ax1+ By1 + C| / sqrt(A^2 + B^2), where (x1,y1) is the point and Ax+By+C=0 is the equation of the line.
Firstly, we need to rewrite our given equation in the standard form. The equation y = x - 6 becomes x - y - 6 = 0. Therefore, A=1, B=-1, and C=-6.
Substitute A, B, C and the coordinates of point A into the formula, we get the distance as |[1*(-9) - 1*(-3) - 6]| / sqrt((1)^2 + (-1)^2) = |-12| / sqrt(2) = 8.48, rounding this to the nearest tenth, we get 8.5.
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The distance from the point A (-9,-3) to the line y = x - 6 is approximately 4.2 units when rounded to the nearest tenth.
Explanation:You asked to find the distance between point A (-9,-3) to the line y = x - 6. The formula to find the shortest distance, d, from a point to a line is given by the absolute value of |Ax1 + By1 + C| divided by the square root of A squared plus B squared, where (x1, y1) are the coordinates of the point and the line equation can be written in the standard form as Ax + By + C = 0. In this case, A = 1, B = -1, C = 6 (because y - x = 6 can be re-written as y - x - 6 = 0). Plugging in the coordinates of point A and the values of A, B, and C into the formula, we get |1*(-9) + -1*(-3) + 6| divided by the square root of [tex](1)^2 + (-1)^2[/tex], which simplifies to |-6| divided by the square root of 2, or 6 divided by sqrt(2). Converted to a decimal and rounded down, this equals approximately 4.2 units. Therefore, the distance from the point to the line is 4.2 units, rounded to the nearest tenth.
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Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy? PLEASE SHOW YOUR WORK. thank you
Mrs. Bailey had a 75% decrease in the number of candies she had after giving away 9 out of the original 12 pieces.
Explanation:To calculate the percent decrease of candy Mrs. Bailey had, we begin by identifying the initial amount and the final amount of candy. Mrs. Bailey started with 12 pieces and ended with 3 pieces, which means she gave away 12 - 3 = 9 pieces of candy. To find the percent decrease, we use the formula: “part over total, times one hundred, equals percent.” Here, the “part” is the amount of candy she gave away (9), and the “total” is the original amount she had (12).
The formula for the percent decrease is:
9 / 12 × 100 = 75%
So, the percent decrease in the number of candies Mrs. Bailey had is 75%.
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What was the total cost of the bond (to the nearest whole cent)?
$943.82
$1,064.44
$534.77
$2,054.22
None of these choices are correct.
Answer:
None of these choices are correct.
Step-by-step explanation:
The quoted value of 99.875, means that this bond is sold at 99.875% of the face value and not at a price of $99.875.
Therefore, calculate price;
Price = 0.99875 * 1000
Price = $998.75
Since brokerage fees is 5.5% of the selling price, Leona will pay additional cost to the quoted price making the total cost to be more than $998.75;
Brokerage fees = (0.055*998.75) = $54.93
Total cost = $998.75 +$54.93
= $1053.68
Therefore, none of the choices is correct.
What is X = to in -3x+4x=2•4-x
Answer:
x=4
Step-by-step explanation:
-3x+4x=2*4-x
x=8-x
8=x+x
8=2x
x=8/2
x=4
Elijah has 5 United states coins ranging in value from $0.01 to $0.25. What is the least amount of money Elijah can have if he has no more than 2 coins alike
Answer:
2 pennies 2 nickels and a dime 22 cents
What are the zeros of A(x) = (x - 2)(x+ 7)? Select all that apply.
しか
MAX=21
ロロロロ
ロ D.x=7
Answer:
The zeros of the function are x=-7 and x=2
Step-by-step explanation:
we have
[tex]A(x)=(x-2)(x+7)[/tex]
we know that
The zeros or roots of the function are the values of x when the value of the function is equal to zero (also is called the x-intercepts)
so
For A(x)=0
[tex](x-2)(x+7)=0[/tex]
Remember that
The Zero Product Property states that
if ab = 0, then either a = 0 or b = 0, or both a and b are 0
so
Let
[tex](x-2)=0[/tex] ----> [tex]x=2[/tex]
[tex](x+7)=0[/tex] ----> [tex]x=-7[/tex]
therefore
The zeros of the function are x=-7 and x=2
Factor completely.
X^4-10x^2+24
Answer:
(x^2-6)(x+2)(x-2)
Step-by-step explanation:
x^4-10x^2+24
(x^2-6)(x+2)(x-2)
helpppppp me plssss
Answer: B
Step-by-step explanation:
Slope = rise/run (aka change in y/change in x)
Slope = (-9-(-9.75))/(-4-(-1)) = 0.75/-3 = -1/4
The sum of x and 3/5 is 5/7 what is the value of x
Answer:
4/35
Step-by-step explanation:
5/7-3/5=
find common denominator =35
5/7*5/5=25/35
3/5*7/7=21/35
25/35-21/35=4/35
Answer:
[tex]x + \frac{3}{5} = \frac{5}{7}[/tex]
[tex] \times = \frac{5}{7} - \frac{3}{5} [/tex]
[tex]x = \frac{25}{35} - \frac{21}{35} [/tex]
[tex]x = \frac{4}{35} [/tex]
Answer fast!!!!
Match the careers with the career clusters
Answer:education and training- speech Language pathologist And curriculum developer
Government and public administration- tax auditor and federal aid coordinator
Law, public safety corrections and security- attorney and paralegal
Step-by-step explanation:
The career clusters and some example careers within each cluster are Agriculture, Food, and Natural Resources (e.g. agricultural engineer, food scientist, forester), Business, Management, and Administration (e.g. accountant, human resources specialist, operations manager), and Health Science (e.g. medical doctor, nurse, medical laboratory technologist).
Explanation:The career clusters and some example careers that fall under each cluster are as follows:
1. Agriculture, Food, and Natural ResourcesAgricultural engineerFood scientistForester2. Business, Management, and AdministrationAccountantHuman resources specialistOperations manager3. Health ScienceMedical doctorNurseMedical laboratory technologistThese are just a few examples, and there are many other careers within each career cluster.
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If Miranda flips a coin twice, what is the probability that both coins will land heads up? The probability that the first coin will land heads up is 1/8, 1/4, 1/2, 3/4? . The probability that the second coin will land heads up is 1/8, 1/4, 1/2, 3/4. The probability that both coins will land heads up is 1/8, 1/4, 1/2, 3/4?
Answer:
I just did it and got it right so hoped it helped you ;)
1/2
1/2
1/4
Step-by-step explanation:
The probability that both coins will land heads up when Miranda flips them twice, assuming each coin is fair and has an equal chance of landing heads or tails, is 1/4. Each flip has a probability of 1/2 for heads, and these probabilities multiply for sequential independent events.
Explanation:If Miranda flips a coin twice, the probability that both coins will land heads up needs to be calculated by multiplying the probability of the first coin landing heads up by the probability of the second coin doing the same. Since the chance of a coin landing on heads (assuming it is a fair coin) is usually 50%, that is 1/2 for each flip. Therefore, to find the probability of both coins landing heads up, we multiply these probabilities together: 1/2 × 1/2 = 1/4.
In a broader context, the more times you flip a coin, the closer you are likely to get to 50% heads due to the law of large numbers. Notably, in experiments such as one conducted by Karl Pearson, after 24,000 coin flips, the relative frequency of heads was 12,012/24,000 ≈ 0.5005, closely aligning with the theoretical probability of 1/2. An essential assumption in determining these probabilities is that the coin is fair and each flip is independent of the others.
PLZZ HELP I’m bad at math.
Answer:
y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.
Step-by-step explanation:
The graph shows representation of inequality,
Here, Line passes through points say, A(3,0) and B(0,1)
The slope of line is given by m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{1-0}{0-3}[/tex]
m=[tex]\frac{-1}{3}[/tex]
and Y-intercept is c=1
The equation of line is given by y=mx+c
y=[tex]\frac{-1}{3}[/tex]x+1 is equation of line in graph.
To decide which side you are going to shaded area on the graph
Take test of origin.
If (0,0) is statisfy the equation then, shaded the graph towards the origin.
Let suppose,
Take, y<[tex]\frac{-1}{3}[/tex]x+1
0<[tex]\frac{-1}{3}[/tex](0)+1
0<1
TRUE,
Therefore, y<[tex]\frac{-1}{3}[/tex]x+1 is inequality shown on graph.
117 divided by 13 in equal groups
Answer:
Step-by-step explanation:
1x117 = 117
3x39 = 117
9x13 = 117
The result of the division , 117 divided by 13 is 9.
Given the parameters which can be used in our calculation:
Numerator = 117Denominator = 13We can write the expression thus :
117/13Now we have :
117/13 = 9The result of the division operation is 9
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The lengths of the sides of a quadrilateral are in extended ratio 1:1:2:3. the perimeter is 56 feet what are the lengths of the sides
Length of sides of quadrilateral are 8 feet, 8 feet, 16 feet, 24 feet
Solution:Given that length of the sides of a quadrilateral are in extended ratio 1:1:2:3
Perimeter of the quadrilateral = 56 feet
Need to determine length of the sides
As length of the sides of a quadrilateral are in extended ration 1: 1: 2: 3
lets assume that four sides of rectangle = 1x, 1x, 2x and 3x
Perimeter of quadrilateral = sum of length of four sides
=> Perimeter of quadrilateral = 1x + 1x + 2x + 3x = 7x
As given that perimeter = 56 feet
=> 56 = 7x
x = 8
Then the length of sides are:
1x = 1(8) = 8 feet
1x = 1(8) = 8 feet
2x = 2(8) = 16 feet
3x = 3(8) = 24 feet
If D=25 use information in the figure below to determine angle F
Answer:
130°
Step-by-step explanation:
DEF is an isosceles triangle with base DE and DF = EF.
By definition, base angles of an isosceles triangle are equal.
Hence ∠FDE = ∠DEF = 25°
Angle F = 180° - ∠FDE - ∠DEF
= 180° - 25° - 25°
= 130°
40 point question ....... pls urgent
the minute hand in a clock is 17cm long. find the area swept by it in 12 mins. the clock is a circle. no spamssssssssss pls
The area swept by the minute hand in 12 minutes is 181.58 cm²
Step-by-step explanation:
In the circle clock
The circumference of the circle is divided into 12 equal arcsThe central angle of each arc is 30°, because the measure of the circle is 360° and divided by 12 The central angle between each two consecutive hours is 30°There are 5 minutes between each two consecutive hours, then the central angle between each two consecutive minutes is 6° because 30° ÷ 5 = 6°When the minute hand is moved than the radius of the circle is the length of the minute handWhen the hour hand is moved than the radius of the circle is the length of the hour hand∵ The minute hand is swept by 12 minutes
∵ The central angle between each two consecutive minutes = 6°
∴ The central angle when the minute hand swept 12 minutes =
6 × 12 = 72°
∵ The area of a sector of a circle = [tex]\frac{x}{360}*\pi r^{2}[/tex] ,
where r is the radius of the circle and x is the central angle of
the sector
∵ The radius of the circle is the length of the minute hand
∵ The minute hand in a clock is 17 cm long
∴ r = 17 cm
∵ The measure of the central angle is 72°
∴ x = 72°
- Substitute these values in the rule of the area of a sector
∵ Area = [tex]\frac{72}{360}*\pi (17)^{2}[/tex]
∴ Area = 181.58 cm²
The area swept by the minute hand in 12 minutes is 181.58 cm²
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The table shows the gallons of water in a pool over time.
A two column table with six rows. The first column, Time in minutes, has the entries, 0, 1, 2, 3, 4, 5. The second column, Water in Pool in gallons, has the entries, 50, 44, 38, 32, 26, 20.
Choose the term that describes the slope of the line of a graph representing the data in the table.
The slope of a line graphed to represent the volume of water in a pool over time would be described as .
Answer:
negative
Step-by-step explanation:
The slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table
y = - 6x + 50
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have a table as given in the question as follows -
Time (in minutes) Water (in gallons)
0 50
1 44
2 38
3 32
4 26
5 20
We can write the slope of the line as follows -
The slope of the line will be -
m = (y₂ - y₁)/(x₂ - x₁)
m = (44 - 50)/(1 - 0)
m = -6
At [x] = 0, the [y] coordinate is 50. Therefore, the equation of the line representing the table -
y = - 6x + 50
Refer to the graph attached.
Therefore, the slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table y = - 6x + 50
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A triangle has a perimeter of 450.
Natalie creates a scale drawing of the triangle with the scale factor 1/15.
What is the perimeter of the scale drawing?
First one to answer will get Brainleist !!!
Answer: The perimeter of the scale drawing is [tex]30[/tex].
Step-by-step explanation:
You need to analize the information provided in the exercise.
You know that the perimeter of rectangle is [tex]450[/tex] and the scale factor Natalie used to create the scale drawing, was:
[tex]scale\ factor=\frac{1}{15}[/tex]
From this you can identify that, in order to find the perimeter of the scale drawing of the triangle (Which can be represented with [tex]P_2[/tex]), you must multiply the original perimeter ((Which can be represented with [tex]P_1[/tex]), by the scale factor Natalie used.
Therefore, you get that the perimeter is:
[tex]P_{2}=\frac{1}{15}P_1\\\\P_2(\frac{1}{15})(450)\\\\P_2=30[/tex]
Hot chocolate sales and outside temperatures. Which is the independent variable and the dependent variable
Dependent variable: Hot chocolate sales
Independent variable: Outside temperatures
If it is 75°F I don't think people will be buying hot chocolate
But if it's 35°F more people will be buying hot chocolate. The sales of the hot chocolate depends on what the outside temperature is. While the temperature depends on nothing
You have a budget of 3600 a week for payroll. You have 6 employees. Each one gets paid the same per hour. How much can you afford to pay each person per hour?
Answer:
$12 per hour
Step-by-step explanation:
3600/6=600
600/50=12
Clare knows that Priya has a bunch of nickels and dimes in her pocket and that
$1.25. (From Unit 2, Lesson 5.)
ch of nickels and dimes in her pocket and that the total amount is
a. Find one possibility for the number of nickels and number of dimes that could
pocket
b.
Write an equation that describes the relationship between the number of dimes and me
number of nickels in Priya's pocket.
c.
Explain what the point (13,6) means in this situation.
d.
Is the point (13,6) a solution to the equation you wrote? Explain your reasoning.
Answer:
a) 21 nickels and 2 dimes
b) [tex]5x+10y=125[/tex]
c) There are 13 nickels and 6 dimes
d) The point (13,6) a solution to the equation you wrote
Step-by-step explanation:
Let x be the number of nickels and y be the number of dimes in Priya's pocket.
1 nickel = 5 cents
x nickels = 5x cents
1 dime = 10 cents
y dimes = 10y cents
b. Total amount in nickels and dimes is [tex]5x+10y[/tex] cents that is $1.25. Convert $1.25 into cents:
[tex]\$1.25=125\ cents,[/tex]
so the equation that describes the relationship between the number of dimes and number of nickels is
[tex]5x+10y=125[/tex]
a. To find one possible solution, substitute an arbitrary value of y and find x. Let y = 2, then
[tex]5x+10\cdot 2=125\\ \\5x+20=125\\ \\5x=125-20\\ \\5x=105\\ \\x=21[/tex]
21 nickels and 2 dimes
c. The point (13,6) means that there are 13 nickels and 6 dimes.
d. Substitute x = 13 and y = 6 intoe the equation and check whether it is true:
[tex]5\cdot 13+6\cdot 10=65+60=125[/tex]
True, so the point (13,6) a solution to the equation you wrote
Michael's father brought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal size lengths for his shelves.
The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board?
Answer:
The remaining wood will be 1.25 inches shorter.
Step-by-step explanation:
Only 10 cuts are required to cut the board into 11 equally sized lengths. Thus, the length of the board after these cuts have been made will be
10(0.125 inches), or 1.25 inches, shorter.
By making 10 cuts, the total length of the board will be reduced by 1.25 inches due to the saw blade reduction. After converting this to feet, Michael will have approximately 15.896 feet of board left.
Explanation:Michael has a 16-foot board that he plans on cutting into 11 equal lengths. This means he will need to make 10 cuts (as the 11th 'cut' is actually the end of the board not actually needing a cut). The saw blade will decrease the length of the board by -0.125 inches for each cut. To solve this, we multiply the number of cuts by the length that will be reduced by the saw blade. That gives us 10 x -0.125 = -1.25 inches. That means that the total usable length of the board will be reduced by 1.25 inches. We need to convert this to feet since the original length of the board is in feet. There are 12 inches in foot, so -1.25 inches is about -0.104 feet. Thus, the total length of the board after all the cuts will be 16 - 0.104, or approximately 15.896 feet.
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The expression below shows a number in
expanded form. What is the standard form of
the number?
(2 x 10) + (3 x 1/10+ (9 X 1/100) + (7 X 1/1,000)
Answer:
20.397
Step-by-step explanation:
The expression below shows a number in expanded form:
[tex](2\times 10) + \left(3\times \dfrac{1}{10}\right)+ \left(9 \times \dfrac{1}{100}\right) +\left (7 \times \dfrac{1}{1,000}\right)[/tex]
This expanded form tells you that the number has
[tex]2[/tex] at tens place;[tex]3[/tex] at tenths place;[tex]9[/tex] at hundredths place;[tex]7[/tex] at thousandths place.Hence, this number is [tex]20.397[/tex]
DOES ANYONE KNOW HOW TO DO THIS??????????? NEED HELP QUICK!!!!!!!!
Answer:
1. Figure 4
2. Figure 2
3. Figure 4
Answer:
1. Figure 2
2. Figure 3
3. Figure 1
Step-by-step explanation:
Brainlest?
A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?
Answer:
17% ?
Step-by-step explanation:
that seems like the most logical answer
Answer:
16.4
Step-by-step explanation:
this is right
A cell phone company orders 400 new phones from a manufacturer. If the probability of a phone being defective is 2.1%, predict how many of the phones are likely to be defective.
Answer:
9
Step-by-step explanation:
gave picture to explain
9 out of 400 phones are likely to be defective.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
If the probability of a phone being defective is 2.1%, we can use this probability to predict how many of the 400 new phones are likely to be defective.
The expected number of defective phones can be found by multiplying the probability of a phone being defective by the total number of phones ordered:
Expected number of defective phones = probability of a phone being defective × total number of phones ordered
In this case, the probability of a phone being defective is 2.1%, or 0.021 as a decimal.
The total number of phones ordered is 400.
So, we can write:
Expected number of defective phones = 0.021 × 400 = 8.4
We can't have a fractional number of defective phones, so we need to round to the nearest whole number.
Since 0.4 is greater than or equal to 0.5, we round up to 9. Therefore, we can predict that 9 of the 400 new phones are likely to be defective.
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HOMEWORK
Solve.
3. Henry's desk is 1 meter long. His nametag is
8 centimeters long. Henry says his nametag is
7 centimeters longer than his desk. What error
did Henry make? Explain how to correct it.
Answer:
1 meter is 100 centimeters
Henry misread the meters part and assumed his desk was 1 centimeter, which is why he thought his nametag was 7 cm longer.
In reality, his desk is 92 cm longer (100 cm - 8 cm = 92 cm)
How many seconds are in 35 minutes
Answer:
there are 2100 seconds in 35 minutes
There are 60 seconds in a minute, if you times 60 by how many minutes there are, you get how many seconds there are. Here is how I got the answer:
60 x 35 = 2100
I hope this helps you and you can use it for future reference! :)
a line passes through point (-2,5) and has a slope of 2/3 points a (x,3) and b ( -2, y) lie on the line what is the value of y and x
Answer:
The value of y is 5 , and The value of x is - 5
Step-by-step explanation:
Given as :
The line passes through point ( - 2, 5)
The slope of line is m = [tex]\frac{2}{3}[/tex]
Equation of line is written as
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
Since line passes through line ( - 2 , 5 ) and have slope [tex]\frac{2}{3}[/tex]
So, y - 5 = [tex]\frac{2}{3}[/tex] × (x + 2)
Or, 3 × ( y - 5 ) = 2 × ( x + 2 )
Or, 3 y - 15 = 2 x + 4
Or, 3 y - 2 x - 19 = 0 is the equation of line
Now points ( x , 3 ) lies on the line 3 y - 2 x - 19 = 0
So, 3 × 3 - 2 x - 19 = 0
or, 9 - 2 x - 19 = 0
or, 2 x = - 10
∴ x = - [tex]\frac{10}{2}[/tex]
I.e x = - 5
Again points ( - 2 , y ) lies on the line 3 y - 2 x - 19 = 0
So, 3 × y + 2 × 2 - 19 = 0
Or, 3 × y + 4 -19 = 0
or, 3 y = 15
∴ y = [tex]\frac{15}{3}[/tex]
I.e y = 5
Hence The value of y is 5 , and The value of x is - 5 . Answer
Liam Had 250. Then, he and his classmate buy present for their teacher, evenly splitting the P cost among the 24 of them. How much does Liam have left. Write your answer as an expression
Ingrid has $28 to buy oil paints for her painting class. Each tube of paint
costs $8. How many tubes can she buy? Do not include units in your answer.
Answer:
28/8=3.5...so probably just 3
Step-by-step explanation: