The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
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Express 675 dam in cm
Expressing 675dam is 675000cm
What is a centimeter?A centimeter (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a meter, the current SI base unit of length. A centimeter is part of a metric system.
What is a decameter?A decameter (American spelling: dekameter, symbol: dam) is a measurement of distance equal to ten meters. This measure is included mostly for completeness
0.001. dam in 1 cm
Formula:
dam x 1,000 = cm
675 dam x 1,000 = 675,000 cm
Therefore, 675 dam is equal to 675000cm
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Please help, I’ll mark your answer as brainliest.
The human brain has approx 100 billion neurons on average and many more neuroglia that nourish and protect the neurons.
What are synapses?The places of contact within neurons are known as synapses which is where data is transferred from one cell to the next.
As we know, from the definition of synapses, synapses which is where data is transferred from one cell to the next.
Also, the human brain has approximately 100 billion neurons on average and many more neuroglia that nourish and protect the neurons.
Thus, the human brain has approx 100 billion neurons on average and many more neuroglia that nourish and protect the neurons.
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Analyze the worked example for the multiplication of three binomials. a. Use a graphing calculator to verify graphically that the expression in factored form is equivalent to the product written in standard form. b. Will multiplying three linear factors always result in a cubic expression? Explain your reasoning.
where is the example? What are the binomials?- or do we use any three?
Which group contains numbers that all round most closely to 1? 1 (1 /5, 2/9, 4/8,)
2 (10/11, 5/6, 7/9,) 3(3/5, 2/4, 4/7,) 4(1/2, 2/7, 9/10,)
The group that contains numbers that all round most closely to 1 is group 2 (10/11, 5/6, 7/9,)
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, it should be noted the group 2 that has 10/11, 5/6, and 7/9 are close to 1.
Therefore, the correct option is B.
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Suppose a college student pays $1100 for tuition fees. However, she also has to pay $225 for her textbooks (ouch!). What percent of her total education costs does she pay for her books?
Answer: Her books represent percent (as a decimal) of her total costs.
Write your answer to the nearest tenth of a percent, but in decimal form. For example, for 34.67%, you would round to 34.7% and enter .347 as your answer.
The percentage she spends on books from her total edducational expenses is 0.17
What is Percentage?
A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Solution:
Assuming there are only these two expenses on education,
the total expenses are 1100 + 225 = $1325
amount the student pays on books = $225
Percentage = (225/1325) * 100
Percentage = 16.98% = 17% (approx)
So, the final answer is 0.17
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QUESTION 3
Solve the following using the correct order of operations
70+(3-11)/6+8x42
Answer:
≈ 404.6666667
Step-by-step explanation:
70 - 8 ÷ 6 + 8 x 42
70 - 1.33333333 + 8 x 42
70 - 1.33333333 + 336
68.6666667 + 336
404.6666667
I need quick help! I just want know if this is correct! Will give brainliest to the first correct answer.
The sum of three consecutive even numbers is 120. What is the smallest of the three numbers?
Answer:
Step-by-step explanation:
the consecutive are 39,40,41 and the smallest here is 39
Hope this helped
Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place.
P=a+b+c; P=36, a=11, b=10 (Perimeter of a triangle)
c=
Answer:
c = 15
Step-by-step explanation:
P = 36; a = 11; b = 10
P = a + b + c
36 = 11 + 10 + c
36 = 21 + c
Subtract 21 from both sides.
15 = c
c = 15
Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.
Donna also drove at a constant rate. This table shows the number of miles she had driven in different numbers of hours.
How do the unit rates compare?
Select from the drop-down menus to correctly complete the statement.
Miguel has a
Choose...
unit rate of change than Donna because
Choose...
is greater than
53 mph
.
Number of hours Total miles driven
3 144
6 288
9 432
Miguel has a higher unit rate of change than Donna because 53mph is greater than 48mph.
What is unit rate?The unit rate is used to show the relationship between the variables illustrated. Since Miguel drove for 8 hours at a constant rate and drove a total of 424 miles. The rate will be:
= 424 / 8
= 53 miles per hour.
The unit rate for Donna will be:
Miles / Time
= 144 / 3
= 48 miles per hour.
Therefore, Miguel has a higher rate.
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value iteration is guaranteed to converge if the discount factor 0 < γ < 1.
a. true
b. false
It is TRUE to state that w/ a discount factor less than 1, value iteration is guaranteed to converge.
What is a discount factor?The discount factor ranges from 0 to 1. To represent the importance of a reward R that happens N steps in the future from the current state, multiply it by γⁿ. Consider γ= 0.9 and a reward R = 10 that is three steps ahead of our current condition.
Hence, it is correct to indicate that value iteration is assured to converge if the discount factor 0 < γ < 1.
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Full Question:
For an infinite horizon MDP w/ a finite # of states and actions and w/ a discount factor γ that satisfies 0 < γ < 1, value iteration is guaranteed to converge.
a. true
b. false
WORTH 100 POINTS NEED BETTER GRADE C 78%
Applying Side-side-side (SSS), the two-column proof that explains why ∠T ≅ ∠S is shown below.
What is the Side-side-side (SSS) Congruence Postulate?The side-side-side (SSS) postulate states that two triangles that have all their three corresponding sides equal are definitely congruent triangles.
The two-column proof that shows that ∠T ≅ ∠S is explained below:
Statement Reason
1. U is the midpoint of ST 1. Given
2. RT ≅ RS 2. Given
3. TU ≅ SU 3. Definition of a midpoint
4. UR ≅ UR 4. Reflexive property
5. ΔTUR ≅ ΔSUR 5. Side-side-side (SSS)
6. ∠T ≅ ∠S 6. CPCTC
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Answer:
[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$U$ is the midpoint of $ST$}&1.\;\sf Given\\\cline{1-2}2.\;RT \cong RS&2.\; \sf Given\\\cline{1-2}3.\;TU \cong SU & 3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;UR=UR&4.\;\sf Reflexive\;property\\\cline{1-2}5.\; \triangle TUR \cong \triangle SUR&5.\;\sf Side-Side-Side\;(SSS)\\\cline{1-2}6.\;\angle T \cong \angle S&6.\;\sf CPCTC\\\cline{1-2}\end{array}[/tex]
Step-by-step explanation:
Midpoint
The point that is halfway between the endpoints of the line segment.
Reflexive Property
For every number a:
a = aSide-Side-Side (SSS) Congruence Theorem
If all three sides of one triangle are equal to all three corresponding sides of another triangle, then the two triangles are congruent.
Corresponding parts of congruent triangles are congruent (CPCTC)
If two or more triangles are congruent, their corresponding angles and sides are congruent.
[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$U$ is the midpoint of $ST$}&1.\;\sf Given\\\cline{1-2}2.\;RT \cong RS&2.\; \sf Given\\\cline{1-2}3.\;TU \cong SU & 3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;UR=UR&4.\;\sf Reflexive\;property\\\cline{1-2}5.\; \triangle TUR \cong \triangle SUR&5.\;\sf Side-Side-Side\;(SSS)\\\cline{1-2}6.\;\angle T \cong \angle S&6.\;\sf CPCTC\\\cline{1-2}\end{array}[/tex]
need help with both of these please. give 20 points
The following gives the variations:
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
The value of y when x=2 is -14
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
General equation for an indirect variation:
y = k/x
substitute y=7 and x= -4
7=k/-4
k=7*-4 = -28
To find y when x=2:
Substitute x=2 and k=-28 into the equation
y=-28/2 = -14
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the dimensions of a square are altered so that one dimension is increased by 5ft while the other is decreased by 3ft. the area of the resulting rectangle is 84ft squared. what is the perimeter of the original square
The perimeter of the original square is 36 ft.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Let the side of square is x,
When one side is increased by 5 ft, the side = 5+x,
And other side is decreased by 3 ft, the side = x-3.
Also given that, the area of rectangle = 84 square ft
The area of rectangle = length×width
84 = (5+x)×(x-3)
By solving the equation, the value of x is 9,
Therefore, the side of the square is 9 ft
Perimeter of the square = 4x = 4×9 = 36 ft
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PLease help me i willlllllllllll faillllllllllllllif someone dont
For the first 3 images.
a) The linear equation is the one in option A:
y = x
b) The linear equation is the one in option B:
y = (1/2)*x + 3
c) The correct option is C, the slope of scenario 1 is 60
How to identify the linear equations?A general linear equation is:
y = a*x + b
So we have a polynomial of degree 1, this means that there can be at most two terms, one that depends of x, and other that is a constant.
From the first list the only linear equation is y = x.
none of the others depend linearly with x.
From the second list the only option that is a linear equation is B.
y = (1/2)*x + 3
Where you can see two terms, the first one depends linearly of x and the second one is a constant.
For the third image.
If you evaluate the equation for scenario 2 in x = 1, you get:
y = 50*1 = 50
So in one hour, you travel 50 miles.
While on scenario 1, on one hour you travel 60 miles.
Then the speed is greater on scenario 1, where the slope is 60, so the correct option is C.
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Question 7 of 10
The amount of time it takes to complete a reading assignment might be a
function of which of the following?
OA. The number of pages in the assignment
OB. The cost of the book
OC. The year the book was published
Answer:
A. The number of pages in the assignment
Step-by-step explanation:
You want to know which of several possibilities the amount of time it takes to complete a reading assignment might be a function of: pages, cost, age of the book.
CorrelationWe expect that an assignment to read more pages will result in a longer completion time. While there might be different completion times for the same number of pages in different assignments (relation not a function), the relation might be a function for assignments in the same book.
There are many factors affecting the cost of a book, including the materials it is made of, the number of printed copies, the difficulty of providing the necessary typesetting and illustrations. These factors may also affect the time it takes to read an assignment. In general, we don't expect that a given number of pages in a book costing $20 will take longer to read than in a book costing $10 or $50. That is, we don't expect completion time to be a function of the cost of the book.
As with book cost, the year of publication may also have a relationship with readability. Older books may use different language, unfamiliar terminology, more (or less) complex illustrations, different typography. These may have a bearing on the time it takes to complete a reading assignment. However, if the same material is presented in the same way in a book published in 1900 versus 2000, we don't expect the assignment completion time to change.
The time it takes to complete a reading assignment is most likely to be a function of the number of pages in the assignment (other factors being equal).
a) Complete the table.
Number
36,892 81,055 7,908 126,388
Rounded to the nearest 10,000
Rounded to the nearest 1,000
Rounded to the nearest 100
helpppp
The rounding up of all the numbers 36,892 81,055 7,908 126,388 to the nearest 10000, 1000 and 100 are as shown below.
How to round up numbers?To round up a number to the nearest 10000, what we do is to check the thousands digit to decide whether to round up or round down.
To round up a number to the nearest 1000, what we do is to check the hundreds digit to decide whether to round up or round down.
To round up a number to the nearest 100, what we do is to check the tens digit to decide whether to round up or round down.
1) 36,892 to the nearest 10000 is; 40000
81,055 to the nearest 10000 is; 80000
7,908 to the nearest 10000 is; 10000
126,388 to the nearest 10000 is; 130000
2) 36,892 to the nearest 1000 is; 37000
81,055 to the nearest 1000 is; 81000
7,908 to the nearest 1000 is; 10000
126,388 to the nearest 1000 is; 126000
3) 36,892 to the nearest 100 is; 36900
81,055 to the nearest 100 is; 81100
7,908 to the nearest 100 is; 7900
126,388 to the nearest 100 is; 126400
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A $1100 certificate of deposit held for 51 days was worth $1110.44. What simple interest rate was earned? Assume a
360-day year.
The certificate of deposit earned an interest rate of %
The interest rate is 6%.
What is an interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Here,
It is given the initial amount was $1100 and after 51 days, it was worth $1110.44.
The interest can be calculated as follows:
Interest = $1110.44 - $1100
= $ 10.44
Now, we find the simple interest
I = PRT
I = 10.44
P = $1100
T = 51 days
R =?
We put the given value in the formula and get
10.44 = (1100 ×51 ×R)/360
R = 0.066 × 100%
R = 6%
Hence, the interest rate is 6%.
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The Gateway Arch in St. Louis is often mistaken to be a parabolic in its shape. In fact, it is a catenary, which has a more complicated formula than a parabola. Note that the Arch is 625 feet high and 598 feet wide at its base. Find the equation of the parabola with the same dimensions.
Answer:
Below
Step-by-step explanation:
A parbola with zeroes at 0 and 598 would look like this:
f(x) = a ( x-0)(x-598) at the midpoint 299 the value is 625
625 = a (299) (299-598) shows a = - 625/89401
-625/89401 (x)(x-598) <======expand as necessary
Mark on the number line with a cross the fraction of the
shape from
(a) that is shaded.
b) Mark on the number line with a cross the fraction of the shape from (a) that is shaded.
a)
5/8
Step-by-step explanation:
ok hope it will help you thanks for watching hope it will happen
Which of the following are partial products for 43 × 17?
A.3
B.21
C.28
D.40
E.400
The options that are partial products for 43 × 17 include:
B. 21
E. 400
How to find the partial products?We want to find the partial products of 43 x 17
Since 43 = 40 + 3
and 17 = 10 + 7
Then
43 x 17 = (40 + 3) x (10 + 7)
We find all the partial products by multiplying one term of the first addition with one term of the second:
43 x 17 = (40 + 3) x (10 + 7)
= (40 x 10) + (40 x 7) + (3 x 10) + (3 x 7)
= 400 + 280 + 30 + 21
The options are B and E.
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A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a hours/week. In the context of the problem, which of the following interpretation is correct?
A. There is a 99% chance that the average amount of time spent studying for all graduate students at this student's school is between 173 and 22.5 hours per week OH
b. Graduate Mudents at this student's school study between 173 and 22 5 hours per week 99% of all weeks during the year
C. At this student's school 99% of all graduate students study between 17 3 and 22.5 hours per week, on average
D. Approximately 99% of all random samples of graduate students from this school will give a mean number of hours studied per week between 172 and 225
E. We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22 5 hours per week
The average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week. which is the correct interpretation would be option (A).
What is the arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations.
A graduate student wanted to determine the average time spent studying between many graduate students at her school. She took a random sample of graduate students from her school and obtained an hour per week.
In the context of the problem,
We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week.
Therefore, the correct interpretation would be option (A).
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How many people were surveyed for the bar graph below?
A. 17
B. 34
C. 21
D. 6
The number of people surveyed in the bar graph is 34
What is bar graph?The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph.
How to find the number of people surveyedThe number of people surveyed is calculated by adding up the frequencies of each bar
The frequency shows the number of people using cell phones starting from zero cell phone user which is 1 to 6 cell phone users which is 5
The calculation
1 + 5 + 6 + 8 + 9 + 5 = 34
Hence the number people surveyed is gotten to be 34
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Alika scored -3, 8, 9, -7, and 13. What integer represents her average score for the 5 rounds?
Answer:
4
Step-by-step explanation:
-3 + 8 + 9 + (-7) + 13 = 20
20/5 = 4
A t-shirt increased in price by 1/4
After the increase it was priced at £65.
What was the original price of the t-shirt?
Answer:
£52 was the original price
Step-by-step explanation:
Suppose it takes John 10 minutes to run1 mile. How long would it take if he to run 4 kilometers
solve the system for the subsitution
x-4y=-8
5y-1=x
Answer:
X=-36
Y=-7
Step-by-step explanation:
If 5y-1=x
then you can substitute x into the first equation
x-4y=-8
as we know x=5y-1 then
(5y-1)-4y=-8 is true
5y-4y is just y
so we are left with y-1=-8
add 1 to both sides
y=-7
substitute this into other equation
5(-7)-1=X
-35-1=X
X=-36
Hormones like to bind to what on the surface of cells? A. signals B. receptors C. towers
Answer: Protein receptors - B)
Step-by-step explanation:
Once hormones find a target cell, they bind with specific protein receptors inside or on the surface of the cell and specifically change the cell's activities.
Which statement correctly represents the distance between points E and F?
The statement that correctly represents the distance between points E and F is
d = √(0-0)² + (0 − 6)² + (5 − 5)²How to find distance between two points in x-y-z coordinate systemThe distance between points measured as d between two points in the x y z coordinate system is given by
d = √{(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²}
From the graph point E = (0, 0, 5) and F = (0, 6, 5)
comparing the points to (x, y, x), the points are substituted and it written as
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Answer:
the answer is the second
Step-by-step explanation:
I took the quiz
PLease help me i willlllllllllll faillllllllllllllif someone dont
The scenario with the greater speed is scenario 1, then the correct option is C
"Scenario 1 because the slope is 60"
Which scenario shows a greater speed?
Remember that speed is defined by:
distance = speed*time
On scenario 2 we have the linear equation:
y = 50*x
Where y is distance and x is the time in hours, so the speed is 50 miles per hour.
If we look at the graph, we can see a proportional relationship also of the form y = k*x
Where the slope k is the speed.
The first graphed point is (1, 60), then:
60 = k*1
60/1 = k
So here the speed is 60 miles per hour.
Then the correct option is C, the speed in scenario 1 is greater.
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