For the following word problems, create a system of equations and solve by using the substitution method.
Answers
We will solve as follows:
*We have the equations:
[tex]9.50A+27.00B=4000[/tex]&
[tex]A+B=200[/tex]We solve then for the second equation [Either for A or B], that is:
[tex]A=200-B[/tex]Now, we replace in the first equation and solve for B:
[tex]9.50(200-B)+27.00B=400\Rightarrow1900-9.50B+27.00B=4000[/tex][tex]=17.5B+1900=4000\Rightarrow17.5B=2100[/tex][tex]\Rightarrow B=120[/tex]Now, we replace the value of B in the second equation:
[tex]A=200-(120)\Rightarrow A=80[/tex]So, the investor has 80 shares on stock A and 120 shares on stock B.
Related Questions
A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.What are the odds against exactly 5 cars passing over the bridge in that time?
Answers
A probability is the number of outcomes divided by the number of total outcomes.
An odd is given by a:b, in which a is the number of successes and b is the number of failures.
From the question, the probability of 5 cars will pass over a small bridge is 0.16
That means the total outcomes is 100 and the outcomes of successes are 16
Then to find the failures subtract 16 from 100
The failures = 100 - 16 = 84
Successes = 16
a = 16
Failures = 84
b = 84
Odds = a: b
Odds = 16: 84
Divide each term by 4 to simplify
Odds = (16/4): (84/4)
Odds = 4: 21
The answer is 4: 21
Rewrite the following percents as decimals. i. 4% ii. 76% ii. 120% iv. 100% V. 32.5%
Answers
Answer
i) 4% = 0.04
ii) 76% = 0.76
iii) 120% = 1.20
iv) 100% = 1.00
v) 32.5% = 0.325
Explanation
The key to writing percents as decimals is to divide the percents by 100 to get the decimal equivalent.
i) 4% = (4/100) = 0.04
ii) 76% = (76/100) = 0.76
iii) 120% = (120/100) = 1.20
iv) 100% = (100/100) = 1.00
v) 32.5% = (32.5/100) = 0.325
Hope this Helps!!!
Help me! i need this answer now i am so dead. if i get it worng please help
Answers
Answer:
[tex]260 \: {cm}^{2} [/tex]
Step-by-step explanation:
hope it helped, have a nice day!: )
For the following, find f(2.1) and f(4).
Answers
Answer:
A
Step-by-step explanation:
Comment
The tricky part is f(4)
Log part
That is defined by log_2 which means that the base used for the log is 2.
We don't have log_2 on our calculators so you have to create it.
Substitute 4 for x
log_2 (4) = log_10(4)/ log_10 (2) Which your calculator can handle
log_2 (4) = Log(4)/ log(2) = 2
f(x) = 1/2 x^2
x = 2.1
Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2
1/2 2.1^2 = 1/2 4.41 = 2.205
Answer
A
Answer:
(a) f(2.1) = 2.205 and f(4) = 2
Step-by-step explanation:
You want to evaluate a piecewise-defined function to find f(2.1) and f(4).
DomainThe first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.
for f(2.1), you want to use the definition for the domain 2 < x < 4for f(4), you want to use the definition for the domain 4 ≤ x < 8Function evaluationOnce you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.
f(2.1) = 1/2(2.1)² = 1/2(4.41) = 2.205f(4) = log₂(4) = log₂(2²) = 2The desired function values are f(2.1) = 2.205 and f(4) = 2.
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Vince is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $5 per kilogram for the lobster he picks. At the second restaurant, Vince would pay $8 per kilogram for the lobster, in addition to $33 for the meal. Vince realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Vince pay for his dinner? What is the weight?Dinner would cost $ at either restaurant if Vince's lobster weighed kilograms.
Answers
Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:
51 + 5x cost in the first restaurant
33 + 8x cost in the second restaurant
In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:
51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides
51 - 33 = 8x - 5x simplify
18 = 3x divide by 3 both sides
18/3 = x
6 = x
x = 6
Hence, the weight of the lobster is 6 kg.
The cost of the dinner is:
51 + 5(6) = 51 + 30 = 81
Hence, the cost of the dinner is $81
Find the distance between the two points in simplest radical form.
(-6, 5) and (-3, 7)
Answers
Answer: [tex]\sqrt{13}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]\sqrt{(-6-(-3))^2 +(5-7)^2}=\sqrt{13}[/tex]
Which of the following could be a cross-section of a triangular prism? circle o hexagon O octagon O rectangle
Answers
A triangular prism have two possible cross sections: A triangle and a rectangle
What is the value of x + y² when x = 1 and y = 9?
Answers
Answer:
=82
Step-by-step explanation:
the value of
x + y²
putting x=1,y=9
we get,
1+(9)^²
=1+81
=82
A stack of one dozen cookies of diameter 2.5 in. exactly fits in a cylindrical container of volume 29.452 in3. Which is the thickness of each cooke?
Answers
The volume of a cylinder is given by:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=29.452in^3_{} \\ r=\frac{d}{2}=\frac{2.5}{2}=1.25 \end{gathered}[/tex]solve for h:
[tex]\begin{gathered} 29.452=\pi\cdot(1.25)^2\cdot h \\ h=\frac{29.452}{\pi(1.25)^2} \\ h=5.999912171 \end{gathered}[/tex]divide the height by 12:
[tex]\frac{h}{12}=0.499992681in[/tex]The thickness of each cookie is 0.499992681in or approximately 0.5in
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y=0.75x+2
Step-by-step explanation: Slope as k and constant as b two points that showed by the graph: (0,2) (4,5)
so we can get 2=0*k+b b=2
5=4k+b
4k=5-2
4k=3
k=3/4
k=.75
Question
Solve 6x+3y=−1 for y
Answers
The required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The equation is given in the question below as:
6x + 3y = −1
We have to determine the solution of the equation 6x + 3y = −1 for y.
⇒ 6x + 3y = −1
Rearrange the terms of the variable in the above equation,
3y = - 6x - 1
Divided by 3 both sides of the equation to get
y = -2x - 1/3
Hence, the required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.
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which graph represents the systems of inequalities? there are 4 graphs for this question total please help
Answers
Looking at the inequalities, it involves the 'less than or equal to' symbol. This means that the lines of both inequalities must be solid. In options B, C and D, one or two of the lines is broken. This is an indication that they don't represent the given inequality. We would check option A
Optiona
Ann and Tom want to establish a fund for their grandson's education. what lump sum must they deposit at a 7% annual interest rate compounded monthly in order to have $60,000 in the fund at the end of 10 years?
Answers
Formula to calculate Principal with clompound interest:
[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{n\cdot t}} \\ \\ A=\text{Amount} \\ r=\text{Interest rate (decimals)} \\ n=\text{ number of times per unit t} \\ t=time \end{gathered}[/tex]For the given situation:
A= 60,000
r= 7% =7/100= 0.07
n= 12 (as it is compounded monthly and a year has 12 months)
t= 10 years
[tex]\begin{gathered} P=\frac{60,000}{(1+\frac{0.07}{12})^{12\cdot10}} \\ \\ =\frac{60,000}{(1+\frac{0.07}{12})^{120}} \\ \\ \approx29,855.78 \end{gathered}[/tex]Then, they must deposit approximately $29,855.75
You are 37 years old have accumulated 150000 in your savings account. You intend to add a fixed amount each month for twenty years. For first 5 years you add 100 at the end of each month.
Answers
h(x)=−2x+2
Find h(−2).
Answers
Answer:
6
Step-by-step explanation:
when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2
What is the equation of the line that passes through the point (4,-8) and has a slope of −2
Answers
Answer:
See below
Step-by-step explanation:
Point (4,-8) slope form would be
( y - -8) = -2 ( x -4)
y+8 = -2x + 8 re-arrange to y = mx + b form
y = - 2x
Pls help (give right answer)!!
Answers
seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf
9ab^2*(6a^5+1)
Veronika has 3 daughters. Today the eldest is 7 years older the the second who is 2 years older than the youngest. The sum of their ages 12 years from now will be 56. How old are they today?
Answers
We define the following variables:
• x = age (in years) of the eldest,
,• y = age (in years) of the second,
,• z = age (in years) of the youngest.
From the statement, we know that:
0. the eldest is 7 years older than the second → , x = 7 + y,,
,1. the second is 2 older than the youngest → ,y = 2 + z,,
,2. the sum of the ages 12 years from now will be 56 → x + y + z + 12 = 56 → ,x + y + z = 56 - 12 = 44,.
We have the following system of equations:
[tex]\begin{gathered} x=7+y, \\ y=2+z, \\ x+y+z=44. \end{gathered}[/tex]i) Replacing the second equation in the first one, we have:
[tex]x=7+y=7+(2+z)=9+z\text{.}[/tex]ii) Summing the ages of the three daughters, we have:
[tex]x+y+z=(9+z)+(2+z)+z=11+3z\text{.}[/tex]iii) Equalling the last equation with the third one, we have:
[tex]\begin{gathered} 11+3z=44, \\ 3z=44-11=33, \\ z=\frac{33}{3}=11. \end{gathered}[/tex]Replacing the value of z in the equation of x and y, we get:
[tex]\begin{gathered} x=9+11=20, \\ y=2+11=13. \end{gathered}[/tex]Answer
The ages of the daughters are 20, 13 and 11.
The table shown represents a linear relationship.
x 0 1 3 4
y −8 −6 −2 0
Based on the table, what is the equation of the linear relationship in slope-intercept form?
y = 2x − 8
y = 2x + 8
y = −2x + 4
y = −2x − 4
Answers
Answer: y = 2x - 8
Step-by-step explanation:
When x = 0, y = -8. This is the y-intercept.
As x increases by 1, y increases by 2. This makes 2 the slope.
The equation for the linear relationship given, in slope-intercept form is y = 2x-8
What is slope-intercept form?The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers.
Given that, coordinates representing a linear relationship.
x → 0, 1, 3, 4
y → -8, -6, -2, 0
We need to find an equation for the given linear relationship in slope-intercept form,
Considering points, (0, -8) and (4, 0)
We know that, the equation of a line passing through, two points is given by,
y-y₁ = (y₂-y₁) / (x₂-x₁) (x-x₁)
Here, y₁ = -8, y₂ = 0, x₁ = 0, x₂ = 4
Therefore, the equation is =
y+8 = 8/4(x-0)
y+8 = 2x
y = 2x-8
Hence, the equation for the linear relationship given, in slope-intercept form is y = 2x-8
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On Monday, 365 students purchased a hot lunch in the cafeteria. On Friday, 429 students
purchased a hot lunch. What was the percent increase in students buying hot lunches?
OA 1.75%
O B 2.5%
OC 8.5%
O D 17.5%
Answers
The percent increase of the students in the cafeteria that bought hot lunches is 17.5%
How to calculate the percent increase ?On Monday 365 students purchased hot lunch
On Friday 429 students purchased hot lunch
The first step is to calculate the percent change
429-365
= 64
The percent increase can be calculated by dividing the percent change by the original value and then multiply by 100
64/365 × 100
= 0.175 × 100
= 17.5
Hence the percentage increase in the students purchasing lunch is 17.5%
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I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
a) 0.0187
b) 0.0943
c) 0.2959
Step-by-step explanation:
a) 9/31 * 8/30 * 7/29 = 0.0187
b) 10/31 * 9/30 * 8/29 + 12/31 * 11/30 * 10/29 + 9/31 * 8/30 * 7/29 = 0.0943
c) 21/31 * 20/30 * 19/29 = 0.2959
A triangle has angle measurements of 72, 34 and 74 . what kind of triangle is it?
Answers
We can give two classifications to that triangle
It's a scalene triangle, because all the sides are different (because all the angles are different). Also, it's a acute triangle because all the angles are less than 90°
What can I do to decrease my bill by $25.00 per month?"
Employee: "Your bill is currently __________ per month, so we'll make a change to a less expensive option that will result in a 30% decrease in your monthly payment."
Answers
If he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
The percentage decrease in the monthly payment = 30%
The amount of decrease in the bill per month = $25
Consider the current bill amount as x
Then the equation will be
x × (30/100) = $25
Solve the equation
0.3x = $25
x = 25/0.3
x = $83.33
Hence, if he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
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ASAP i need help rn before i finish this test
The triangles shown are congruent.
What is a correct congruence statement for the triangles shown?
Answers
Answer:
SAS= Side, Angle, Side
Step-by-step explanation:
According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.
msMario bought 3 yeard of ribbon for 1.50 how much would 5 yards of the same ribbon cost? explain how u got your answer
Answers
For 3 yards, it costs, 1.50.
So for one yard,
[tex]\frac{1.50}{3}=0.5[/tex]Therefore for 5 yards,
[tex]5\times0.5=2.5[/tex]Write the equation of the line that is parallel to - 8x-6y = 5 that passes through thepoint (-9, 1)
Answers
First,we will find the slope of the line
Using 8x - 6y = 5
we will have to re-arrange the equation above to be in the slope-intercept form.
That is; it should be in the form y = mx + b
8x - 6y = 5
6y = 8x -5
y = 8/6 x - 5/6
slope = 8/6 = 4/3
In a parellel equation the slope are the same, hence the slope of our new equation is 4/3
Next, we find the intercept of the new equation;
Using the point (-9, 1) and slope(m) = 4/3
we will substitute into the equation below and then solve for b, where b is the slope of our new equation
y = mx + b
1 = 4/3 (-9) + b
1 = 4(-3) + b
1 = - 12 + b
add 12 to both-side of the equation
1+ 12 = b
13 = b
b= 13
Substituting m = 4/3 and b = 13 into the formula; y = mx+ b
y = 4/3 x + 13
[tex]undefined[/tex]Can I get help? Please show your work and steps.
1) -14 = -4(9x-1)
Number 2
⬇️⬇️⬇️
Answers
Question 1
[tex]-14=-4(9x-1)\\\\-14=-36x+4\\\\-18=-36x\\\\x=\frac{1}{2}[/tex]
Question 2
Multiplying both sides by 12,
[tex]4x-7x=8\\\\-3x=8\\\\x=-\frac{8}{3}[/tex]
Last year, Carlos opened an investment account $5,200 with. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of last year?
Answers
ANSWER
[tex]\begin{gathered} 338 \\ 5538 \end{gathered}[/tex]EXPLANATION
The Principal is $5200;
Increase rate is; 6.5%
The increase in dollar is;
[tex]\begin{gathered} \frac{6.5}{100}\times5200 \\ =338 \end{gathered}[/tex]Hence, the amount in the account at the end of the year;
[tex]\begin{gathered} A=P+I \\ =5200+388 \\ =5538 \end{gathered}[/tex]Therefore, the increase in dollar is $338 while the amount in the account at the end of the year is $5538
17. MTR Model Problems Place points on the number line to show 4 equal lengths from 0 to 1.8. How long is each length?
Answers
Answer:
4.5
Step-by-step explanation:
4.5 + 4.5 + 4.5 + 4.5 = 18
You write it like this in the number line:
4.5, 9, 13.5, 18
a. On what interval(s) of x is f(x) positive?
b. On what interval(s) of x is f(x) negative?
c. On what interval(s) of x is f(x) increasing?
d. On what interval(s) of x is f(x) decreasing?
e. On what interval(s) of x does f have positive concavity?
f. On what interval(s) of x does f have negative concavity?
Answers
On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.
What X intervals are beneficial for fx?Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).
The portions of a function that are below the x-axis are known as its negative regions.
How can I determine the time intervals where f is positive?You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.
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