Answers
Answer:
Option A
Step-by-step explanation:
→ Multiply both sides by 2
2s = a + b + c
→ Minus b and c from both sides
2s - b - c = a
Related Questions
Can anyone write the equation of the graph?
Answers
The equation of the absolute value function graph is: y = |x - 3| + 5.
What is the Equation of the Absolute Value Function?The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:
The vertex of the graph = (h, k)The value of a is determined by whether the graph opens up or opens down.The horizontal translation factor, which determines how far left or right the parent function is translated = hThe vertical translation factor, which determines how far up or down the parent function is translated = k.From the given graph, we have the following:
(h, k) = (3, 5) [the vertex]
Substitute the values into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:
6 = a|2 - 3| + 5
6 = a|-1| + 5
6 = a + 5
6 - 5 = a
1 = a
a = 1
To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:
y = 1|x - 3| + 5
y = |x - 3| + 5
Learn more about equation of absolute value function on:
https://brainly.com/question/25290500
#SPJ1
HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answers
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
For this problem, write the numbers in scientific notation. 2,156 A. 21.56 × 102 B. 2.156 × 103 C. 2.156 × 102
Answers
Answer:
2,156 A. 21.56
Step-by-step explanation:
: the small town of west fremont has a population of 50,000. if the growth rate of west fremont is 2%, then how long will it take for the population of west fremont to double?
Answers
It takes 35 years for the population of West Fremont to double. We have the following condition;
West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.
Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.
According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.
Doubling time = 70 / Growth rate
= 70 / 2
= 35 years
So, it takes 35 years for the population of West Fremont to double.
To learn more about population Growth click here:
https://brainly.com/question/27424886
#SPJ4
F(x)=x^2+1 what is f(f(x))?
Answers
Answer:
f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2
Step-by-step explanation:
to evaluate f(f(x)), substitute x = f(x) into f(x)
f(f(x))
= f(x² + 1)
= (x² + 1)² + 1 ← expand factor using FOIL
= [tex]x^{4}[/tex] + 2x² + 1 + 1
= [tex]x^{4}[/tex] + 2x² + 2
Answer:
[tex]f[f(x)]=x^4+2x^2+2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+1[/tex]
To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]
Angles ABC and CBD are a linear pair. If m∠CBD=90°, what is m∠ABC in degrees?
NO LINKS OR FILES.
Answers
Measurement of ∠ ABC is 90°
What is Linear pair?A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given that ∠ CBD and ∠ ABC are linear pairs,
Therefore, m∠ CBD + m∠ ABC = 180°
m∠ ABC = 180° - 90° = 90°
Hence, Measurement of ∠ ABC is 90°
For references on Linear pair, click;
https://brainly.com/question/17525542
#SPJ1
Sheri has $15,200 to invest in mutual funds and in bonds. sheri has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. if she wants to earn $548 at the end of the first year, how much does she need to invest into each type of account?
Answers
Sheri should invest $2000 in mutual fund and $13,200 in bond.
Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -
1%×x + 4%×(15,200 - x) = 548
x/100 + 60,800/100 - 4x/100 = 548
60,800 - 3x = 54800
3x = 60800 - 54800
3x = 6000
x = 6000 ÷ 3
x = 2000
Amount to be invested in mutual fund = $2000
Amount to be invested in bond = 15,200 - 2000
Amount to be invested in bond = $13,200
Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.
Learn more about equation -
https://brainly.com/question/21405634
#SPJ4
How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
Answers
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ1
Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answers
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Answers
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
To know more about the permutation, here
https://brainly.com/question/1216161
#SPJ4
The ordered pairs show the number of hours a student studied in a week, x, and that student’s exam score, y.
(1,70) (3,75) (5,80) (9,95) (12,98)
The equation y=2.7x+67 can be used to model the relationship between the number of hours a student studied in a week and their exam scores. Choose a number from each box to make the statement true.
The y-intercept shows that a student who studies____________
A: 0
B: 2.7
C: 67
D: 69.7
hours can expect to get a score of _______on the exam.
A: 0
B: 2.7
C: 67
D: 69.7
Answers
Answers:
1st box: 0
2nd box: 67
===============================================
Explanation:
The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours
Plug x = 0 into the equation
y = 2.7x + 67
y = 2.7*0 + 67
y = 67
Or you can note that the equation is of the form y = mx+b
m = slope = 2.7b = 67 = y interceptThe y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67
The probability that a male’s foot is between 10 and 12. 5 inches is ___%
P(10
Answers
The probability of a foot of male being between 10 and 12. 5 inches is 59%.
Define the term normal distribution?The normal distribution approximates any real-valued random distribution which clusters around one single mean value. A cumulative frequency is a procedure that determines if the total amount of information in such a data set is less than and equal to a specific value.The z score of the distribution is found as-
z = (x - μ)/σ
In which,
μ = mean = (11)
σ = standard distribution (1.5)
The likelihood that a male's foot measures between 10 and 12. 5 inches.
P(10 < x < 12.5)
For x = 10
z = (10 - 11) / 1.5
z = -0.67
check the p-value fro z score table.
p (z = -0.67) = 0.2514
For x = 12.5
z = (1.5 - 11)/1.5
z = 1
p (z = 1) = 0.8413
P(10 < x < 12.5) = 0.8413 - 0.2514
P(10 < x < 12.5) = 0.5899
P(10 < x < 12.5) = 58.99%
P(10 < x < 12.5) = 59%.
Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.
To know more about the normal distribution, here
https://brainly.com/question/4079902
#SPJ4
The complete question is attached in figure.
bob can do a job in 5 hours while bill can do the same job in 8 hours. how many hours would it take them, working together, to do this job?
Answers
Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
To know more about the work and its efficiency refer to the link given below:
https://brainly.com/question/27870797
At a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three. If there are 100 in the party, is the data consistent?
Answers
Answer:
no because 60+48+36 is 144
Step-by-step explanation:
please mark brainliest
The total number of people is 144. The data is not consistent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.
The total number of the people in the party,
60+48+36 is 144
But it is given in the question that there are 100 in the party.
Therefore, the total number of people is 144. The data is not consistent.
To know more about an expression follow
https://brainly.com/question/23941117
#SPJ2
two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
Answers
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
To learn more about function, visit:
https://brainly.com/question/21145944
#SPJ4
Order from least to greatest 3.706, 3.76, 2.5991, 3.7
Answers
Answer:
2.5991 < 3.7 < 3.706 < 3.76
Step-by-step explanation:
in a recent study, it was found that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected. the data follows a binomial distribution. a) what is the mean of the distribution? (round your answer to 3 decimals.)
Answers
The mean of the distribution is 24.444.
Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.
Now, we have to find the mean of the distribution
As, we know
E(x) = np
where, n is the sample and p is the probability of success
So, n = 28 and p = 87.3% = 0.873
Now, on using the formula we get,
E(x) = (28)(0.873)
E(x) = 24.444
So, the mean of the distribution is E(x) = 24.444
Hence, the mean of the distribution is 24.444.
Learn more about Binomial Distribution here https://brainly.com/question/29230506
#SPJ4
The fastest cheetah on record is Sarah who lives at the Cincinnati Zoo in Ohio. The fastest human on record is Usain Bolt. Sarah can
run 161 meters in the same time that Usain can run 100 meters. If Sarah's speed is 6.4 meters per second faster than Usain's, how
fast do Sarah and Usain run? Round values to one decimal place.
sarah’s speed:
usains speed:
Answers
Sarah can run = 100 metres.
Speed of usain bolt.It takes several steps to convert between the two rates of meters per second and miles per hour in this task.Since the units in this case are measured in meters per second, we do not know what this translates to in miles per hour. Since the speedometers in our cars utilize these numbers, the majority of us are accustomed to thinking of speeds in terms of miles per hour; therefore, it is advantageous for students to be able to convert between miles per hour and other units of speed that naturally arise.The first approach displays all units used in the calculations but waits until the very end to perform any calculations. The second option takes a step-by-step approach and offers anacc to our question=
Usain Bolt traveled 100 meters in 9.63 seconds. 1 meter is 3.28 feet, so 100 meters is.Usain Bolt traveled 1 foot in 0.02936 seconds. 1 mile is 5280 feet, so at this speed, he would travel 1 mile in 5280×0.02936=155 seconds.learn more about speed,distance,time click here:
https://brainly.com/question/26046491
#SPJ13
1. in an experiment in which a six-sided dice is rolled twice, what is the probability that 4-dots side appears in at least one roll?
Answers
Answer:
11/36 = 0,305556 = 30,5556%
Step-by-step explanation:
5/6 * 5/6 = 25/36
36/36 - 25/36 = 11/36
Estimate the answer to 4.8 x 47.1
Answers
Answer:
235
Step-by-step explanation:
When estimating the product of two decimals, first round the decimals to their nearest whole numbers.
If the number in the tenth place is less than 5, round down to the nearest whole number.If the number in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
4.8 ≈ 547.1 ≈ 47So an estimate of the product of the two decimals is:
[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]
Partition 47 into tens and units:
[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]
Therefore:
[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]
cheyenne needs to cut a piece of paper so that she has exactly 1/3 of it. if the length of the paper is 11 inches, how long will be the piece that she cuts?
Answers
The lengths of the piece she should cut is = 3 2/3
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
1/3 of 11=1/3*11=11/3=3 2/3hence,The lengths of the piece she should cut is = 3 2/3
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
Can somone help me with this will mark u brainliest
Answers
The simplest radical form of √(11/(x + 4)) when x is 16 is; ¹/₁₀√55
How to simplify surds in radical form?Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.
We are given the expression of the surd as;
√(11/(x + 4))
We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;
√(11/(16 + 4))
= √(11/20)
Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;
√(55/100)
Square root of 100 is 10 and as such we now have;
√(55/100) = ¹/₁₀√55
Read more about radical surd form at; https://brainly.com/question/19569383
#SPJ1
Please help with this
Answers
Step-by-step explanation:
remember, the circumference of a circle is
2×pi×r
and that is for the full 360° of a circle.
how long will the arc length of 1° be ?
well,
2×pi×r / 360
and how long will the arc length of 78° be ?
well,
78 × 1° = 2×pi×r × 78/360
you see ? that is the whole trick ...
now we only need to enter the value for r (radius).
and that is GH = 9 units.
so, the length of the arc GJ is
2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =
= 12.25221135... ≈ 12.25 units
Find the value of x. Then find the measure of each angle and write the answers in ascending order.
Answers
The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle has interior angles are:
(2x)°, (3x)° and (4x)°
As we know that the sum of interior angles is 180 degrees in the triangle.
According to the given figure,
(2x)° + (3x)° + (4x)° = 180°
Apply the addition operation in the above equation,
9x = 180
x = 180/9
x = 20°
Thus, The triangle has interior angles are:
(2x)° = 2 × 20° = 40°
(3x)° = 3 × 20° = 60°
(4x)° = 4 × 20° = 80°
Learn more about the triangles here:
https://brainly.com/question/17997149
#SPJ1
Write an equation in slope-intercept form of the line that passes through $\left(-5,\ 19\right)$ and $\left(5,\ 13\right)$ .
Answers
Answer:
hmmm say 5)13
Step-by-step explanation:
i can't explain it
The equation of the line is y = (-3/5)x + 16
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line is given by:
y = mx + c
The line passes through:
(-5, 19) and (5, 13)
So,
m = (13 - 19) / (5 + 5)
m = -6/10
m = -3/5
Now,
(5, 13) = (x, y)
13 = (-3/5) x 5 + c
13= -3 + c
13 + 3 = c
c = 16
Now,
y = mx + c
y = (-3/5)x + 16
Thus,
The equation of the line is y = (-3/5)x + 16
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
c) Which of these
numbers is a square number?
A: 4x10^5
B:9x10^4
C:4x10^3
D:9x10^3
Answers
B= 90,000 - square (300 x 300)
C= 4,000 - not square
D= 9,000 - not square
So B
A pediatrician prescribes 5 milliliters (ml) of a pain reliever for every 25 pounds of a child's weight. How many milliliters of
medicine will the doctor prescribe for a child who weighs 60 pounds?
Answers
If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .
In the question, '
it is given that
the for every 25 pounds of weight 5 milliliter of pain reliever is required .
we need to find the amount of medicine for the child weighing 60 pounds
So , for 25 pounds = 5 milliliter is needed
for 1 pound = 5/25 ml is needed
hence for 60 pound = 60*(5/25) ml will be prescribed .
on simplifying further ,
we get
= 60*(5/25)
= 60*(1/5)
= 12 ml
Therefore , the doctor will prescribe 12 ml of medicines .
Learn more about Unitary Method here
https://brainly.com/question/13608878
#SPJ1
Supposed the original quality is 1,500 and the new quality is 1,650 what should be the first step in solving for the percent increase what is the percent increase
Answers
The first step is to find the increase in quantity.
The percentage increase is 10%.
How to calculate the percentage?From the information, the original quality is 1,500 and the new quality is 1,650.
The first step is to find the increase in quality will be:
= New quantity - Old quantity
= 1650 - 1500
= 150
The percentage increase will be:
= Increase / Old Quantity × 100
= 150 / 1500 × 100
= 10%
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Having trouble solving this
Answers
Answer:
[tex]r = 2279.41[/tex]
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Answers
There was 110% percent increase in the number of visitors.
Percent:
Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.
Given,
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Here we need to find the increase in the percentage.
While we looking into the given question we have identified that,
The Old population = 3700
And the new population = 4070
So, the value of P is calculated as,
=> p = 4070/3700
=> p = 1.1
When we convert this into percent then we get 110% as increase.
To know more about Percentage here.
https://brainly.com/question/13729841
#SPJ1