The distance from the line y = -3 to the point (5,2) is 5 units.
Distance from the line ax+by+c=0 from the point (m,n) is calculated by
[tex]distance=\frac{|am+bn+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]y=-3[/tex] ⇒ [tex]y+3=0[/tex]
equation of line becomes 0.x+1.y+3=0
given the point (5,2)
Substituting the values in the distance formula we get
[tex]d=\frac{0*5+1*2+3}{\sqrt{0^{2} +1^{2} } }[/tex]
[tex]=\frac{2+3}{1} \\ \\ =\frac{5}{1} \\ \\ =5[/tex]
Therefore , the distance from the line y = -3 to the point (5,2) is 5 units.
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Solve each equation. Check each solution.4/x-2 = x-1/x-2
The solution of equation 4/x-2 = x-1/x-2 is x = 5
In this question, we have been given an equation.
4/x-2 = x-1/x-2
We need to find the solution of given equation.
4/x-2 = x-1/x-2
Here, denominator is same on both the sides.
So, we can cancel it from both the sides.
So, given equation would be,
4 = x - 1
4 + 1 = x
x = 5
We need to check above solution.
Substitute x = 5 in LHS of given equation.
LHS
= 4/x - 2
= 4/(5 - 2)
= 4/3
Also, substitute x = 5 in RHS of given equation.
RHS
= x - 1 / x - 2
= (5 - 1)/(5 - 2)
= 4/3
So, LHS = RHS
Therefore, the solution of equation 4/x-2 = x-1/x-2 is x = 5
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Which equivalent to log 20?
A. log 10 x log 2
B. log 15 + log 5
C. log 30 - log 10
D. log 60/log 3
E. log 80 - log 4
==========================================
Reason:
log(80) - log(4)
log(80/4)
log(20)
The rule used is log(A) - log(B) = log(A/B)
Using a calculator,
log(80) - log(4) = 1.30103 approximatelylog(20) = 1.30103 approximatelywhich helps confirm the answer. The logs I used were base 10, but it could be any base really.
The weight of a gold bar varies directly with its volume. If a 40 cm³ bar weighs 772 grams, how much will a 100 cm³ bar weigh?
Density is a material's intrinsic (intrinsic) property that depends on how much it occupies a particular space and possibly on temperature.
Density is expressed in units of mass divided by volume. The International Standard Unit (SI) is the kilogram per cubic meter ("cube") or kg/m3. Some commonly used density units are grams per cubic centimeter, or we can also express it as g/cm3; it is more widely used in laboratories.
Mass and volume are related by a term called density.
The formula gives the relation between the mass and the density of an object:
Density = Mass/ Volume
We can extract the desired quantity from this formula, and here it is mass, so,
Mass = Density x Volume
So, by using the above information, 100 cm^3 bar weighs 1930gm.
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The students in a school are all invited to participate in a survey. 48% of the students at the school are males, of whom 16% will participate in the survey. 35% of the females will also participate in the survey. A student is randomly chosen from the school. Find the probability that the student:
a) will participate in the survey
Answer:
If the student is female then the probability that the student will participate is about 67%
If the student is male the probability that they participate is about 33%
Step-by-step explanation:
It is given that 48% of the students in the school are male. That means that the remaining students in this school are (for the sack of this problem) female out 100% of students. You would subtract 48% from 100% which is 52% which is the percentage of students in the school who are female.
From this point you need to find the percentage of students who would participated in the survey. To do that you would divide the number of the type of student who did the survey by the type of student in the school. For example for the male you would divide 16% from 48% or 16 ÷ 48 which would equal to the proposed of males who would participate which is about 33% of males. You would do the same math for finding the probability of females so it would be 35 ÷ 52 which is about 67% of females.
Even though the random student is more likely to be female the chances of the gender of the student is almost 50%/50% because if you round it to the nearest tenth it would be 50.
Aaliyah owns a small textile company that produces shirts. On a particular day,
Aaliyah has one worker come into the shop to make shirts. She must pay the worker
$28 per hour and also pay $2 per shirt for material costs. The worker created an
average of 4 shiris per hour and Aaliyah's total expenses for labor and materials were
$144. Write a system of equations that could be used to determine the number of
hours the worker worked and the number of shirts the worker made. Define the
variables that you use to write the system.
Let _ =
Let _=
System of equations:
1.
2
A system of equations that could be used to determine the number of hours the worker worked and the number of shirts the worker made is 28x + 2(4x) = 144
Let x be the number of working hours
She must pay the worker $28 per hour
So, Cost of labor for x hour = 28x
The worker created an average of 4 shirts per hour.
So, number of shirts produced in x hours = 4x
Cost of 1 shirt = 2
Cost of 4x shirts = 2 (4x)
Total expenses for labor and materials = 28x + 2(4x)
We are given that Aaliyah total expenses for labor and materials were $144
So, 28x + 2(4x) = 144
28x + 8x = 144
x = 4
Hence a system of equations that could be used to determine the number of hours the worker worked and the number of shirts the worker made is 28x + 2(4x) = 144
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How many hundreds are in the hundreds place in the number 243?
Answer:
2 hundreds
Step-by-step explanation:
there is the number 2 in place of the hundreds
the floor of an elevator in a building is 30.5 Ft above ground level. it travels down to the lower level of the building, where the floor is 10.75 feet below ground level . what distance has the elevators floor traveled ?
The distance travelled by the elevators floor is 41.25 feet.
The floor of the elevator was = 30.5 feet above the ground level.
Initial position = + 30.5 feet
Now, the elevator is 10.75 feet below the ground level.
Final position = - 10.75 feet.
So, the distance travelled by the floor of the elevator is:
Distance = + 30.5 feet - ( - 10.75 feet)
Distance = 30.5 feet + 10.75 feet
Distance = 41.25 feet.
Therefore, we get that, the distance travelled by the elevators floor is 41.25 feet.
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What is the value of p?
p-43
p
p+45°
Exterior angle theorem
Answer: p=178/3 degrees
Step-by-step explanation:
Based on the problem, I THINK these three angles add up to 180 degrees
(p-43)+(p)+(p+45)=180
p-43+p+p+45=180
p+p+p-43+45=180
3p+2=180
3p=178
p=178/3 degrees
Which of the following is a counterexample for this conditional statement?
If a number is positive, then it is spelled without the letter 'e'.
6
1
2
4
Explanation:
The number 1 is spelled as "one", which clearly has an "e" in it. This contradicts the original statement that we don't need this letter.
The other numbers of 6 (six), 2 (two), and 4 (four) don't involve "e"s at all. So they can be ruled out.
Khloe is a salesperson who sells computers at an electronics store. She is paid a $5
commission for every computer sale she makes and she also makes a guaranteed base
pay of $90 each day. Make a table of values and then write an equation for P, in
terms of a, representing Khloe's total pay on a day on which she sells a computers.
Number of Computers Sold Khloe's Daily Pay in Dollars
90 ✓
95 ✔
100✓
105 ✓
Answer: P =
By finding and evaluating a linear equation, we will complete the table:
Number of computers sold| Khloe's Daily pay in dollars:
90 $540
95 $565
100 $590
105 $615
How to complete the table?Here we know that Khloe is a salesperson who ells computers, and she gets $5 for each computer sold, plus a base pay of $90 each day.
Then if in a day she sells x computers, the amount that she wins that day is given by the linear function:
f(x) = $90 + $5*x
Now we want to complete the table:
Number of computers sold| Khloe's Daily pay in dollars:
90
95
100
105
To complete the table we just need to evaluate the linear function in these values of x, we will get:
f(90) = $90 + $5*90 = $540
f(95) = $90 + $5*95 = $565
f(100) = $90 + $5*100 = $590
f(105) = $90 + $*105 = $615
Now we just need to input these values in their correspondent place on the given table, we will get:
Number of computers sold| Khloe's Daily pay in dollars:
90 $540
95 $565
100 $590
105 $615
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1) A 14.24 pound bag of cheese is split among
5 pizzas. How much cheese is on each pizza?
Answer:
2.848 pound
Step-by-step explanation:
On 5 pizzas = 14.24 pound cheese
On 1 pizza = 14.24/5 pound
=2.848 pound
Word problem involving average rate of change
Answer:
(a): 190
(b): 750
Please see below for the steps.
Step-by-step explanation:
(a):
Use points (0,1000) and (3.1, 1589)
Use slope formula. The slope formula is also used to find average rate of change (just so you know).
y2-y1/x2-x1
1589-1000/3.1-0=589/3.1=190
Answer for (a) is 190
(b):
Use points (12.4, 4100) and (15.5, 6425)
Use slope formula.
y2-y1/x2-x1
6425-4100/15.5-12.4=2325/3.1=750
The answer for (b) is 750
Hope this helps!
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Have a great day!
Victor is saving his money to buy a new satellite radio for his car. He wants to save enough money for the radio and one year of satellite radio service before he makes the purchase. He started saving for the radio with 50 that he got for his birthday. Since then, he has been adding 15 every week after he cashes his paycheck.
c. How long will it take Victor to save 150 ?
Victor takes approximately 7 weeks to save 150.
Given,
Initial savings of victor = 50
Savings added by victor weekly = 15
We have to find the time taken by victor to save 150.
We know that victor saved 50 which he got for his birthday.
Then, 150 -50 = 100
That is by saving 15 weekly victor has to make a total of 100.
Therefore, to find the time taken by victor to save 100 is:
100 / 15 = 6.66, approx 7
That is victor takes approximately 7 weeks to save 150.
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4. Two brands of cooking fat, Omega 1 and Omega 2 are melt and mixed to produce a new brand, Omega super. The density of Omega 1 is 2.5g/cm³ and that of Omega 2 is 2.0g/cm³, calculate the density of the mixture given that the two brands are mixed in the ratio of 5:3 respectively by volume. (4 mks)
Step-by-step explanation:
2.0
2.5cm,
8888888888888888822
What additional statement is needed in a proc import step when dbms = dlm is specified?
Now let's process the ASCII text file using the IMPORT and EXPORT procedures.
Must specify ASCII text file delimiter in DBMS options.
PROC IMPORT DATAFILE ="c:\sas\ego.csv" OUT=jeeshim.egov DBMS=CSV REPLACE;
GETNAMES=YES;
DATAROW = 2;
RUN
DATAFILE lets you import an external file.
Designates a SAS data file.
The DBMS specifies the type of external file. For example, "DBMS=DLM", "DBMS=CSV", and "DBMS=TAB".
REPLACE overwrites the existing file, if any.
GETNAMES reads the variable names from the first line of the data file.
The DATAROW option tells the row from which SAS reads the observations.
GETNAMES and DATAROW require a semicolon at the end.
This example exports the data set to an ASCII file by the specified range. DATA and OUTFILE respectively define the set of data to be output and the external file to which the data is output.
PROC export
DATA = jeeshim.egov
OUTFILE="c:\sas\ego.txt"
DBMS = DLM REPLACE;
RUN;
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What is the LCM of the expressions?
b. x² + 3x - 4, x² + 2x - 8 , and x² - 4x + 4
LCM of the given expressions x² +3x - 4, x² +2x - 8 , and x² - 4x +4 is
(x-2)²(x+ 4)(x-1).
As given,
Given expressions x² +3x - 4, x² +2x - 8 , and x² - 4x +4
Simplify by factorizing them,
x² +3x - 4 =x² +4x-x-4
=(x +4)(x -1)
x² +2x - 8 =x² + 4x -2x -8
=(x+4)(x-2)
x² - 4x +4 = x² -2(2x) +(2)²
= (x-2)²
LCM = (x-2)²(x+ 4)(x-1)
Therefore, LCM of the given expressions x² +3x - 4, x² +2x - 8 , and
x² - 4x +4 is (x-2)²(x+ 4)(x-1).
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Make a table of values for f(x) after the given translation. 1 unit down.
Using equations of the form y=f(x), you may be able to modify the graph in various ways.
For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications to change it to the desired function.
X F(X) F(X)-1
-1 1 0
1 3 2
3 5 4
5 7 6
7 9 8
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hello giving Brainly
find surface area of composite shape show ur work
what is the outside area of a 3D object
An amusement park ride consists of four circular cars. The ride rotates at a rate of 0.25 revolution per second. In addition, each car rotates 0.5 revolution per second. If Jane is positioned at point P when the ride begins, what coordinates describe her position after 31 seconds?
Let ride rotate in clockwise direction ( cw ) then position will be co - ordinate ( 0, 3)
What does coordinate mean in this case?
To coordinate is to make plans for things to come together or to collaborate with another person to achieve a goal. Coordination occurs when all the details of a journey are planned. When you and a friend divide up a large science project and decide who will do what, that is an example of coordination.As per given problem ride rotates at a rate of .25 revolution /sec
so in every 4 sec it completes 1 full revolution .
In every 1 sec it revolves by 90° only .
In 28 sec car 1 complete 7 full revolution so , in next 3 sec
So , in next 3 sec it completes only 270.
Here car itself also rotates at the rate of .5 revolution .
So in 31 sec it it completes is full revolution .
& in next 1 second it completes 180° revolution .
Case - 1 Let ride rotate in counter clockwise ( ccw) then find position will be at co - ordinate ( 0, - 1 ) .
Case - 2 Let ride rotate in clockwise direction ( cw ) then position will be co - ordinate ( 0, 3)
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Find the domain and range of each relation and determine whether it is a function.
(-3,4),(-1,2),(0,-2),(1,0),(2,2)
The domain and range of the give relation can be determined by listing the x values for the domain and listing the y values from the range. If each x corresponds to only one y, it is a function.
Domain of a relation refers to all the input values of the relation. Hence, domain is the set of all x coordinates. In the given data, the domain is:
{-3, -1, 0, 1, 2}
Range of a relation refers to all the output values of the relation. Hence, range is the set of all y coordinates. In the given data, the range is:
{4, 2, 0, -2}
In order for a relation to be a function, each x must correspond to only one value of y i.e., an x has one y value. For example, for a relation x = 4 and y = 1,2, hence it is not a function.
In our relation, each x value has only one y value, it is a function.
Mapping the relation can also give us the answer in a simpler way.
As there is one arrow leaving each x value, it is a function. (If two arrows are leaving an x value it is not a function.
Hence, for the relation given, Domain: {-3, -1, 0, 1, 2}, Range: {4, 2, 0, -2} and it is function.
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What is the ph at the equivalence point of a weak base-strong acid titration?
a) ph < 7
b) ph = 7
c) ph > 7
d) ph = 14
(B) Between 0 and 7, best describes the pH at the equivalence point of a titration of a weak base with a strong acid.
What is Equivalence Point?A standardized acid/base titrant reactant and an unknown base/acid analyte reactant combine in a specific stoichiometry (molar ratio) to produce the respective conjugate products in an acid-base titration experiment. The analyte reactant is in excess early in the titration, and the titrant is limiting. When enough titrant is added, the analyte reactant is completely consumed and only products remain. This is the titration's equivalence point. At this point, the pH of the solution is determined by the relative strength of the starting reactants.So, consider the following example of ammonia (a weak base) titrated with HCl (a strong acid):
[tex]\mathrm{NH}_3+\mathrm{HCl} \rightarrow \mathrm{NH}_4^{+}+\mathrm{Cl}[/tex]Only the products remain at the equivalence point.
We can disregard the chloride anion. The ammonium cation, on the other hand, is a weak conjugate acid with sufficient acidic strength that we must consider it.It dissociates according to the following equilibrium, resulting in a mildly acidic pH of less than 7:
[tex]\begin{aligned}&\mathrm{NH}_4^{+} \leftrightharpoons H^{+}+\mathrm{NH}_3 \\&K_a=5.6 \times 10^{-10}\end{aligned}[/tex]
Therefore, (B) between 0 and 7, best describes the pH at the equivalence point of a titration of a weak base with a strong acid.
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The correct question is given below:
Which best describes the pH at the equivalence point of a titration of a weak base with a strong acid?
A. less than zero
B. between 0 and 7
C. close to 7.0
D. between 7 and 14
E. greater than 14
help me ...........................................,.........................,.............
The values to the nearest tenth are:
a. 1. 43
b. 26. 41
c. 11. 69
d. 4. 57
e. 15. 77
How to determine the values
Given the equations;
a. 4. 186 - 2. 758
Find the difference
1. 428
1. 43
b. 72. 05 - 45. 64
Find the difference
26. 41
c. 82. 156 - 41. 31 - 29. 16
Find the difference
11. 686
11. 69
d. 17. 054 - 11. 65 - 0. 83
Find the difference
4. 574
4. 57
e. 29. 16 - 12. 48 - 0. 91
Find the difference
15. 77
Thus, the values to the nearest tenth are 1. 43, 26. 41 , 11. 69, 4. 57, 15. 77
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The dual-energy x-ray absorptiometry (dexa) is the gold standard measurement for body composition. (gold standard = most accurate form of measurement) true false
The DEXA is the most accurate form of body composition measurement.
What is an x-ray?
An X-ray is a rapid and painless technique which is commonly used to generate images of the internal parts of a human body. It is a very effective and convenient way of looking for bone damages and other problems.
Explanation
The statement 'the dual-energy x-ray absorptiometry (DEXA) is the gold standard measurement for body composition is true. Here, the gold standard means the most accurate form of measurement.
Hence, the given statement is true.
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How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 1.33%?
Answer:
$19,192,529,147.31
Step-by-step explanation:
Daily compounded = 10,000 * (1.0133)^(365*3) = $19,193,611,648.31
Semi-annually compounded = 10,000 * (1.0133)^(2*3) = $10,825.01
The total difference in cost is 19,193,611,648.31 - 10,825,01 which is $19,192,529,147.31
For questions 1-4, use the word "PROBABILITY."
. What are the possible outcomes of choosing a letter randomly?
2. which outcomes have more than one possibility?
3.How many outcomes are included in the event that a consonant is chosen?
The possible outcomes of choosing a letter randomly-
PROBABILITY is the given letter.
As a result, the total number of letters is 11 vowels 4 consonants = 7.
So I the chance of opting a vowel is4/11
ii) the chance of opting a consonant is7/11
PROBABILITY is the given letter.
As a result, the total number of letters is 11 vowels 4 consonants = 7.
So I the chance of opting a vowel is4/11
ii) the chance of opting a consonant is7/11
The probability expressions listed below might help you better comprehend probability generalities.
trial An trial is a trial or operation that's carried out to induce a result.
A sample space is made up of all of the possible results of an trial.
Favorable outcome is an circumstance that has delivered the intended result or event. For illustration, if we roll two bones and admit the aggregate of the figures on the bones as 4, the possible/ favorable possibilities.
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Jalissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $4.25. Each refill is $2.25. She also decided to get a bagel for $3.15. If Jalissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
The expression 4·125‾‾‾‾√3gives the perimeter of the base of a cube with a volume of 125 cubic inches. What is the length, in inches, of the perimeter of its base?
The length, in inches, of the perimeter of its base is 5in
Volume of a cubeA cube is a three dimensional object with 6 faces and 12 edges.
The formula for calculating the volume of a cube is expressed according to the equation;
V = l³
l = ∛V
where
l is the side length of the cube
Given the following parameters
V = 125in³
Substitute
125 = l³
l = ∛125
l = 5in
Hence the length, in inches, of the perimeter of its base is 5in
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Find the following given the function f(x)=
Plsssss helpppppppp
Answer:
1 /(√5-4)
Step-by-step explanation:
√5 is less than 3.
Therefore
f(√5) = 1 /(√5-4)
Find the surface area of the composite figure.
Answer:
268Cm2
Step-by-step explanation:
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