The linear equation that respects the given conditions is:
[tex]y = \frac{3}{2}x + [/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.
[tex]2x + 3y = 4[/tex]
[tex]3y = -2x + 4[/tex]
[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]
Then:
[tex]-\frac{2}{3}m = -1[/tex]
[tex]m = \frac{3}{2}[/tex]
Hence:
[tex]y = \frac{3}{2}x + b[/tex]
It passes through (−2, 15), that is, when x = -2, y = 15, hence:
[tex]y = \frac{3}{2}x + b[/tex]
[tex]15 = \frac{3}{2}(-2) + b[/tex]
15 = -3 + b
b = 18.
So the equation is:
[tex]y = \frac{3}{2}x + [/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
•Mr. Jones and Mr. Thomas
entered into partnership
I with capital of $12600
and $19200 respectively.
after 3 months they!
were joined by Mr.Forson with a capital of $ 16200.It is agreed that the profit should be shared in proportion to their capitals.During the first 3 month of the year,………..
The profit should be shared in proportion to Mr Jones, Mr Thomas and Mr forson capitals in the ratio 21 : 32 : 27 respectively.
ProportionMr Jones capital = $12600Mr Thomas capital =$19200Mr forson capital = $16200Total capital = $12600 + $19200 + $16200
= $48,000
Mr Jones proportion = $12600 / $48,000
= 21/80
Mr Thomas proportion = $19200 / $48,000
= 32/80
Mr forson proportion = $16200 / $48000
= 27/80
Learn more about proportion:
https://brainly.com/question/1781657
#SPJ1
The population of Kenya is 50 000 000. The population of Pakistan is 4 times greater than the population of Kenya. What is the population of Pakistan?
Answer:
Step-by-step explanation:
Comment
I would think Pakistan should be more than just 4 times as large as Kenya. However if you are given that Kenya is 50 000 000 then Pakistan will be 4 times the size of Kenya.
Pakistan = 4 * Kenya
Pakistan = 4 * 50 000 000
Pakistan = 200 000 000
Answer: Pakistan = 200 000 000
Using an Algebraic Expression to Represent a Problem
CAR
WASH
Fundraiser !!!
Raising money
The science club sponsors a car
wash every year to raise money for
the state robotics competition.
This year, the club raised $20 more
than twice what it raised last year.
Answer these questions to write an algebraic expression for the car wash problem.
Check Your Understanding- Question 1 of 3
Attempt 1 of 2
What missing piece of information would help you write an algebraic expression to
represent the amount of money raised this year?
A. The number of cars that were washed
B. The number of club members going to the robotics competition
C. The price of each car wash
D. How much the science club raised during last year's car wash
Answer:
x= what they raised last year
2x+20= what they raise this year or y
d
Hope This Helps!!!
the arc corresponding to the central angle of 35 degrees in a circle of radius 10 feet measures __feet. Round your answer to two decimal places.
Answer:
[tex]\huge\boxed{\sf Arc \ length = 6.11 \ ft.}[/tex]
Step-by-step explanation:
Given data:Theta = θ = 35°
Radius = r = 10 ft.
Required:Arc length = ?
Formula:[tex]\displaystyle Arc \ length = 2 \pi r(\frac{\theta}{360} )[/tex]
Solution:Put the givens in the above formula
[tex]\displaystyle Arc \ length = 2 (3.14)(10)(\frac{35}{360} )\\\\Arc \ length = 2(3.14)(10)(0.097)\\\\Arc \ length = 6.11 \ ft.\\\\\rule[225]{225}{2}[/tex]
The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.
Part B: Is the rate of change constant? Explain.
Part C: What was the hot air balloon's height at the time the descent began?
Part D: Write , as a linear function of
.
Using a linear function, we have that:
A. The rate of change is of -12 feet per second.
B. The rate of change is constant.
C. The initial height is of 1210 feet.
D. The linear function is: h(t) = -12t + 1210.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, when x changes by 5 seconds, the height decreases by 60 feet, hence the slope is given by:
m = -60/5 = -12 feet per second.
Hence the function is:
h(t) = -12t + b.
When t = 5, h(t) = 1150, hence we use this to find the initial height.
h(t) = -12t + b.
1150 = -12(5) + b.
b = 1210.
Hence the linear function is:
h(t) = -12t + 1210.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $7$.
What is the sum of these three numbers?
Step-by-step explanation:
Smallest two digit number which is multiple of 7 = 14 (7*2)
Smallest three digit number which is multiple of 7 = 105 (7*15)
Smallest four digit number which is multiple of 7 = 1001 (7*143)
Sum = 14+105+1001 = 1120.
Otto has some whipping cream that is 30%, butterfat, and some milk that is 2%, butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.
What does point K represent in this context?
Answer:
CORRECT (SELECTED)
The mixture has the intended volume and has the intended percent of butterfat.
Explanation: Point K is on line b, so it represents a scenario where the mixture has a volume of 500 \,\text{mL}500mL500, start text, m, L, end text. Point KKK is on line aaa, so it represents a scenario where the mixture has 12\%12%12, percent butterfat.
The inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
How to illustrate the information?It should be noted that an inference simply means the conclusion that can be deduced based on the information given.
In this case, the inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
Learn more about inference on:
brainly.com/question/25280941
#SPJ1
Answer: It The mixture has less than the intended volume and has more than the intended percent of butterfat.
Step-by-step explanation:
How many significant figures are in the measurement 1.050 l? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d
There are 4 significant figures in the measurement 1.050 (Option d)
What are significant figures?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. We can determine how many significant figures in a given numbers by counting the number of digits that are significant to indicate the quantity or value of something.
How the measurement 1.050 has 4 significant figures?
Since the quantity 1.050 starts with 1, that is a non-zero digit, we start counting the significant figures starting from this digit. Thus, 1 is the first significant digit here. 0, 5, and 0 are the second, third, and fourth significant digit respectively.
Learn more about significant figures here:
https://brainly.com/question/14359464
#SPJ4
Answer:
option D
Step-by-step explanation:
just took the test
Based only on the information given in the diagram which congruence theorems or postulate could be given as reasons why LMN and OPQ
The congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
What is congruence theorems?Congruence theorems is one that explain that in a case whereby three sides of two triangles are equal to another, we can say they are congruent to each other.
From the given figure, there are two angles as well as one non-included side which is seen to be a congruent.
According to LA theorem , a triangle is congruent in a case whereby, leg as well as an acute angle of one right triangle of two right triangles are congruent to each other.
AAS theorem also explains that incase two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.
Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
CHECK THE FIQURE FOR THE COMNPLETE QUESTION
Learn more about congruence theorems from
https://brainly.com/question/17239468
#SPJ1
Type the correct answer in each box. Use numerals instead of words. A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number. Teacher Doctor Athlete Boys 24 28 56 Girls 45 31 26 The marginal relative frequency of boys and girls who want to be a teacher is %. The joint relative frequency of girls who want to be an athlete is %. The conditional relative frequency of students that selected doctor, given that those students are boys is %.
The marginal relative frequency of boys and girls who want to be a teacher is 32 %. The joint relative frequency of girls who want to be an athlete is 25.4%. The conditional relative frequency of students that selected doctor, given that those students are boys is 51.85 %.
according to the question, the table given is
Teacher - Doctor - Athete
boys 24 28 56 Total boys = 108
girls 45 31 26 Total girls = 102
What is average?Average of the values is the ratio of total sum of values to the number of values.
Conditions
1) for boys and girls whom opt for teacher,
[tex]=\frac{69}{210} \\[/tex]
= 32%
2) for the girls who opt for athlete relative to girls,
[tex]=\frac{26}{102}[/tex]
= 25.4%
3) for the boys whom opt for doctors in boys
= [tex]\frac{28}{108}[/tex]
= 25.9%
Thus, The required values of conditions 1,2,3 is 32%, 25.4%, 25.9% respectively
Learn more about average here:
https://brainly.com/question/24057012
#SPJ1
Answer:
the answer is 33. 12. and 26
Step-by-step explanation:
the length of the flagpole is ?
The length of the flagpole is x - 5 yards
Area of a squareThe formula for calculating the area of the flagpole is expressed as:
A = L²
Given that;
A = x² - 10 + 25
Factorize
A = x² - 5x - 5x + 25
A =(x - 5) - 5(x - 5)
A = (x-5)²
Compare
L = x - 5 yards
Hence the length of the flagpole is x - 5 yards
Learn more on area of a square here: https://brainly.com/question/13389992
#SPJ1
A social security number is a sequence of nine digits. Determine the number of social security numbers that satisfy the following conditions:
a. There are no restrictions.
b. The digit 8 is never used.
c. The sequence does not begin or end with 8.
d. No digit is used more than once.
Answer:
765314290
Step-by-step explanation:
doesn’t use 8
Not start with 8
Digits used only 1’cd
What is the best approximation for the perimeter of polygon ABCDE? A. 11.0 units B. 17.0 units C. 24.3 units D. 22.1 units
TheThe best approximation for the perimeter of polygon ABCDE is: C. 24.3 units.
Perimeter of polygonCoordinate:
A=(-2,3)
B=(0,6)
C=(5,4)
D=(4,-1)
E=(-1,-2)
Distance AB=√(0+2)²+(6-3)²
Distance AB=√4+9
Distance AB=√13
Distance BC=√(5-0)²+(4-6)²
Distance BC=√25+4
Distance BC=√29
Distance CD=√(4-5)²+(-1-4)²
Distance CD=√1+25
Distance CD=√26
Distance DE=√(-1-4)²+(-2+1)²
Distance DE=√25+1
Distance DE=√26
Distance EA=√(-2+1)²+(3+2)²
Distance EA=√1+25
Distance EA=√26
Perimeter of pathogen ABCDE
=AB+BC+CD+DE+EA
=√13+√29+√26+√26+√26
=√13+√29+3√26
=24.2877 units
= 24.3 units (Approximately)
Therefore the correct option is C.
Learn more about Perimeter of polygon here:https://brainly.com/question/3310006
#SPJ1
Step-by-step explanation:
Bobby is at a county fair and is participating in "The Height Game". To play, the booth owner attempts to guess a participant's height. If the owner's guess is no more than 1 inch from the actual height, the owner wins the participant’s money. Otherwise, the participant wins a prize. If Bobby's height is 75 inches, what inequality would give the range of values that the owner could guess (g) in order to for Bobby to win a prize?
The required range for the owner to win the participant's money is given by
g ≤ 76 inches.
In the game of the Height, there is a participant named bobby and the guess maker a booth owner, if the booth owner makes the right guess than he will get the money of the participant who are participating in the game.
What is range?Range, it is the set of the values that come out to an outcome for certain mathematical operation.
As per the condition, the booth owner can guess the height of the participants more than 1 inches of the actual height.
so the range (g) ≤ 76, so the booth owener wins the money
Thus, the required inquility for the condition is given by (g) ≤ 76.
learn more about range here:
https://brainly.com/question/12239390
#SPJ1
What are the medians for the height and weight distribution, respectively?
The median for height is: 167
The median for Weight is: 183
What is the Median of a Data Set?The middle value or the average of the two middle value of an ordered data set is the median of the data.
Given the following data:
Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Arranged in an ordered form, we would have:
54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191
The middle value is 167. The median for height is: 167.
Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
Arranged in an ordered form, we would have:
157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193
The middle value is 183. The median for weight is: 183.
Learn more about the median of a data on:
https://brainly.com/question/16233946
#SPJ1
use the interactive expression equivalent to 4x-4-2x+3.
Answer: x = 1/2
Step-by-step explanation:
4x - 2x - 4 + 3
2x - 1
x = 1/2
What is the final transformation in this sequence of transformations mapping pre-image VWXYZ to final image V''W''X''Y''Z''?
a translation up and to the right
a reflection across point Z'
a rotation 90° about V'
a rotation 180° about Z'
Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
Answer:
It's D
Step-by-step explanation:
Got it right
Find the largest rational number r for which 5r ≤ 33.
Answer:
33/5 or 6.6
Step-by-step explanation:
Well the most 5r can be is 33, since it has the underline under it, so it's less than or equal to.
So set 5r equal to 33
5r = 33
Divide both sides by 33
r = 33/5
You can leave it in this form or convert it to a decimal which is 6.6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Divide \boxed{5} to both sides:}[/tex]
[tex]\mathsf{\dfrac{5r}{5}\leq \dfrac{33}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{r \leq \dfrac{33}{5}}[/tex]
[tex]\mathsf{r \leq 6 \dfrac{3}{5}}[/tex]
[tex]\mathsf{r \leq 6.60}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{r \leq \dfrac{33}{5}}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\large\textsf{The graph will be labeled down below for you :)}\downarrow[/tex]
Use the table to work out the values of a, b,
C, and d.
X
-3
-2
-1
0
1
2
3
y = 5x
—
a
3x² + 3
- 19
-5
3
b
C
d
What is the ratio of 12 blue marbles and 20 red marbles
Answer:
12:20
Step-by-step explanation:
i hope the answer will help you
The principal P is borrowed at a simple interest rate r for a period of time t.
Answer:
simple interest of the given question is 495
Step-by-step explanation:
SIMPLE INTEREST=P*T*R/100
match each equation to one of the graphs
Answer:
I can only see one graph in that screenshot, so I graphed all of them. The one on your screenshot was B.
The difference......
Answer:
[tex] log_{7}(3) [/tex]
Step-by-step explanation:
According to the
Law of logarithms,[tex] log_{7}(18) \: - log_{7}(6) \\ \\ = \frac{ log_{7}(18) }{ log_{7}(6) } = log_{7}(3) [/tex]
-. A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 4% of the population who take this test have the disease .If the test administered to an individual is positive, what is the probability that the person actually has the disease? Suppose 20% of the people who were referred to a clinic for the test did in fact have the disease. If the test administered to an individual from this group is positive, what is the probability that the person actually has the disease?
Answer:
TV focusing urgency hangs amateur ushers sex tendency yachting
Giselle works as a carpenter and as a
blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answer:
12 hours as a carpenter and 18 as a blacksmith.
Step-by-step explanation:
So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)
So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)
So we have the two equations:
c + b = 30
20c + 25b = 690
Now we can solve for c in terms of b and substitute that into the second equation:
Original equation:
c + b = 30
Subtract b from both sides
c = -b + 30
Original equation:
20c + 25b = 690
Substitute -b + 30 as c
20(-b + 30) + 25b = 690
Distribute the 20
-20b + 600 + 25b = 690
Simplify the equation
600 + 5b = 690
Subtract 600 from both sides
5b = 90
Divide both sides by 5
b = 18
Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation
Original equation
b + c = 30
Substitute 18 as b
18 + c = 30
Subtract 18 from both sides
12 = c
Please help me with this asap
Answer:
18
Step-by-step explanation:
So since the two lines are parallel, 3x is congruent to the angle to the left of 6x+18 and since the two angles together are a straight line it's equal to 180 degrees. So
6x + 18 + 3x = 180
9x + 18 = 180
9x = 162
x = 18
Please solve this for me thank you!
Answer:
620.14
Step-by-step explanation:
Original Equation:
[tex]\frac{4y}{1.025^4}+y-2y(1.05)^2=1500[/tex]
Calculate exponents
[tex]\frac{4y}{1.103812890625}+y-2y(1.1025)=1500\\[/tex]
Simplify:
[tex]3.6238025791990193084270042653997y + y - 2.205y = 1500[/tex]
Add like terms
[tex]2.4188025791990193084270042653997y \approx 1500[/tex]
Divide both sides by 7.012
[tex]y\approx 213.91[/tex][tex]y\approx620.14[/tex]
Answer:
y = $620.14 (nearest cent)
Step-by-step explanation:
Given equation:
[tex]\dfrac{4y}{1.025^4}+y-2y(1.05)^2=\$1,500[/tex]
Factor out y from the left side:
[tex]\implies y\left(\dfrac{4}{1.025^4}+1-2(1.05)^2\right)=\$1,500[/tex]
Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:
Calculate the exponents:
[tex]\implies y\left(\dfrac{4}{1.103812891...}+1-2(1.1025)\right)=\$1,500[/tex]
Carry out the multiplication and division from left to right:
[tex]\implies y\left(3.623802579...+1-2.205\right)=\$1,500[/tex]
Carry out the addition and subtraction from left to right:
[tex]\implies y\left(4.623802579...-2.205\right)=\$1,500[/tex]
[tex]\implies y\left(2.418802579...\right)=\$1,500[/tex]
Finally, divide both sides by the coefficient of y to isolate y:
[tex]\implies \dfrac{y\left(2.418802579...\right)}{2.418802579...}=\dfrac{\$1,500}{2.418802579...}[/tex]
[tex]\implies y=\$620.141558...[/tex]
Therefore, y = $620.14 (nearest cent)
PLEASEEE HELP !!!
Review the graph of a piecewise function.
On a coordinate plane, a curve goes through closed circle (negative 3, negative 1) and curves up and approaches x = negative 1 in quadrant 1. A line starts at closed circle (negative 1, negative 3) and goes to open circle (1, negative 1). It then goes to open circle (3, negative 1). A horizontal line starts at open circle (3, negative 3) and goes to (5, negative 3). A closed circle is at (3, negative 4).
For which value of x is the function continuous?
Using the continuity concept, it is found that the function is continuous at x = -3.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, the function is continuous at x = -3, as:
f(3) = -1.[tex]\lim_{x \rightarrow -3^-} f(x) = -1[/tex].[tex]\lim_{x \rightarrow -3^+} f(x) = -1[/tex].At x = -1, we have that [tex]\lim_{x \rightarrow -1^-} f(x) = \infty[/tex], hence it is not continuous.
The function is not defined for x = 1, and at x = 3, the lateral limits are different.
More can be learned about continuity at https://brainly.com/question/24637240
#SPJ1
Andrew has a new job at the local pizza store as a delivery boy
The distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 blocks away.
Distancea. The entire trip based on the given graph is 15 minutes.
b. Distance:
Distance=10-1
Distance=9 block away
c. Andrew stopped for 3 minutes for 1 minutes between third minutes and fourth minutes.
d. Distance:
Distance=10-2
Distance=8
Distance=15-8
Distance=7 minutes
Distance=5-1
Distance=4 minutes
Therefore the distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 minutes.
Learn more about distance here:https://brainly.com/question/1597347
#SPJ1
A freight train was supposed to travel 1300 miles in 50 hours. When the train had traveled 0.4 of this distance, it was delayed by 4 hours. What should the new speed of the train be to arrive on time?HELLPASAP
Answer:
The answer is 30 miles per hour
Step-by-step explanation:
1) From the question we can calculate the initial speed of the train
Initial speed = 1300 miles / 50 hours
= 26 miles / hour
2) Next, we can calculate the amount of distance already traveled:
Distance traveled = 1300 * 0.4
= 520 miles
3) Now let's calculate the amount of time it took to travel the 520 miles:
From point no. 1 we saw that it was traveling at the speed of 26 miles/ hour, so let's calculate the time elapsed.
Time elapsed = 520 miles / 26 hours
= 20 hours
But then again the text states the train was delayed by 4 hours, therefore the total time elapsed was 24 hours
4) Now to find the new speed required to arrive on time, we need to calculate how many hours and distance are left:
From point no. 2 we calculate the distance left
Distance left = 1300 - 520
= 780 miles
From point no. 3 we can calculate the amount of time left:
Time left = 50 - 24
= 26 hours
Finally, we can find the new speed required to arrive on time:
New speed = 780 miles / 26 hours
= 30 miles / hour