BRAINLIEST!!!!!!!!!!!!!!!!!!!!!
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)
Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)
Answers
A. We have two lines: y = 2-x and y = 4x+3
Given two simultaneous equations that are both required to be true.. the solution is the points where the lines cross... Which is where the two equations are equal.. Thus the solution that works for both equations is when
2-x = 4x+3
because where that is true is where the two lines will cross and that is the common point that satisfies both equations.
B. 2-x = 4x+3
x 2-x 4x+3
-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15
The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3
To find the solution we need to rearrange the equation to the form x=n
2-x = 4x+3
2 -x + x = 4x + x +3
2 = 5x + 3
2-3 = 5x +3-3
5x = -1
x = -1/5
The only point that satisfies both equations is where x = -1/5
Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5
Verify we get the same in the other equation
y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5
Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)
C. To solve graphically 2-x=4x+3
we would graph both lines... y = 2-x and y = 4x+3
The point on the graph where the lines cross is the solution to the system of equations ...
[It should be, as shown above, the point (-1/5, 11/5)]
To graph y = 2-x make a table....
We have already done this in part B
x 2-x x 4x+3
_ __
-1 3 -1 -1
0 2 0 3
1 1 1 7
Just graph the points on a Cartesian coordinate system and draw the two lines. The solution is, as stated, the point where the two lines cross on the graph.
I hope I helped!
I will still trying to see if I can solve them another way that might be clearer.
Write the equation in exponential form.
2^x = (2²)^x - 2
Using (a^m)^n = (a^n)^m, rewrite the equation.
2^x = (2^x)² - 2
Basically this equation states that 2 to the x = 2 to the x squared minus 2. You can use substitution.
Rewrite the equation saying that x = x² - 2.
Solve for x by using the quadratic formula.
Move x to the other side.
0 = x² - x - 2.
After a series of long steps, you would get :
x = 2 and x = -1.
Knowing this information, substitute the numbers into the previous formula : x = 2^x
2 = 2^x and -1 = 2^x
Solve for x.
1) 2^x = 2
2^x = 2¹
Since the bases are the same, the exponents are equal.
x = 1
2) -1 = 2^x
The bases are different signs so there is no solution.
Ultimately, x = 1.
If you look at the graph above, this answer is supported because the graphs intersect at where x = 1.
The point of intersection between the two graphs is (1,2).
B) If you having graphing calculator, you can input the equations 2^x and 4^x - 2 and go to check the tables for each function.
C) Use a graphing calculator to graph both functions individually and see where both functions intersect. The point on intersection is where 2^x = 4^x - 2.
Related Questions
Two plans for reaching a goal are given below.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
Which of the following is a true statement?
a.
Only plan A will work for achieving the goal.
b.
Only plan B will work for achieving the goal.
c.
Both plans will work for achieving the goal.
d.
Neither plan will work for achieving the goal.
Answers
Answer:
The correct option is C) Both plans will work for achieving the goal.
Step-by-step explanation:
Consider the provided information.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
For next 8 weeks by working 9 hours per week at $7.20 per hour, you will earn:
[tex]8 \times 9 \times 7.20 = 518.40[/tex]
We need to save $450 which is less than $518.40. Thus, plan A will work.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
For next 6 weeks by working 15 hours per week at $6.50 per hour, you will earn:
[tex]6 \times 15 \times 6.50 = $585.00[/tex]
We need to save $450 which is less than $585.00. Thus, plan B will work.
Hence, the correct option is C) Both plans will work for achieving the goal.
(1 pt) which point represents the origin? number line from minus5 to 5 with point s at minus2, t at 0, u at 1, and v at 3.
Answers
Which of the following statements does not describe the structure of an atom?
An atom has a small, dense center called the nucleus.
Inside the nucleus of an atom are protons and electrons.
Protons are positively charged sub-atomic particles.
Electrons are negatively charged sub-atomic particles.
Answers
Final answer:
The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.
Explanation:
The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.
Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.
Andrew took a math test with 40 questions. If he scored an 85%, how many questions did he get correct?
Answers
I got the answer by divided the 85% by 100% (100% because it's the total percentage.) I received 0.85 when dividing that. Then, I took the 0.85 and divided it by the total of 40 questions, and that gave me the answer of 34.
Answer:
34 is my answer
Chris runs 7 miles in 80 minutes. at the same rate, how many miles would he run in 64 minutes?
Answers
80 minutes= 7 miles
1 minute= 7 / 80
= 0.875
64 minutes= 0.875 x 64
= 5.6 miles
Hope this helps :))
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you have a gift card worth 90$ you want to buy several movies that costs 12$ each. Write and solve an inequality that represents the number of movies you can buy and still have at least 30$ on the gift card
Answers
find the inverse function for f(x)=square root 2x-6
Answers
-9 and 2x² = 18 - 7xThe roots are-4,and 2y = x² + 2x -8The roots are-8 and 10x² - 2x - 6 = 74The roots are
-15 and-1x² + 15 = - 16xThe roots are-5 and 9y=x² - 4x - 45The roots are
4 and 14x² - x + 56 = 17xThe roots are
2 and 27x² - 29x = - 54
Write an equation of a line that goes through point (4, -5) and is parallel to line y = 2x + 8. Show all work.
I really need help with this.
Answers
Therefore, slope of new line is 2
y=mx+c
Put in values of the point to find c value.
-5= 2(4)+c
-5 = 8 +c
-5-8 = c
-13 =c
Therefore, equation is y = 2x -13 of the new line.
Hope I helped :)
Approximately how many times greater is 8.5×108 than 3.4×105 ? A 2.5 B 250 C 2,500 D 25,000
Answers
Solution:
we have been asked to find that , how many times one number is to the other given numbers.
To do this we will divide the larger number by the smaller number and the resulting number will be the answer of the question.
Here the larger number is [tex]8.5\times10^8[/tex]
The smaller number is [tex]3.4\times 10^5[/tex]
Now lets divide as follows
[tex]\frac{8.5\times10^8}{3.4\times 10^5} =\frac{8.5}{3.4}\times 10^{8-5}\\ \\\frac{8.5\times10^8}{3.4\times 10^5} =2.5\times10^3=2500[/tex]
Hence the correct option is C.
What is a security deposit?
Answers
The cost of a classified ad is based on a daily rate plus a flat service fee. One day cost $3.50 and four days cost $800 write and solve a linear equation to find the cost of a 7-day ad.
Answers
x= 11
hope this helped :)
The linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
The cost of a 7-day ad is $12.50.
Let, the daily rate is "d" dollars and the flat service fee is "f" dollars.
We are given two pieces of information:
One day costs $3.50.
Four days cost $8.00.
Using this information, we can set up two equations:
For one day: d + f = $3.50
For four days: 4d + f = $8.00
Now, we need to solve this system of linear equations to find the values of "d" and "f."
Subtract Equation 1 from Equation 2 to eliminate "f":
(4d + f) - (d + f) = $8.00 - $3.50
3d = $4.50
Now, divide both sides by 3 to solve for "d":
d = $4.50 / 3
d = $1.50
Now that we have the value of "d," we can find the value of "f" by substituting "d" into Equation 1:
d + f = $3.50
$1.50 + f = $3.50
Now, subtract $1.50 from both sides to solve for "f":
f = $3.50 - $1.50
f = $2.00
So, the daily rate (d) is $1.50, and the flat service fee (f) is $2.00.
We get, a linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
Now, to find the cost of a 7-day ad, we can use the daily rate and multiply it by the number of days (7):
Cost of a 7-day ad = 7 * $1.50 + $2.00
Cost of a 7-day ad = $10.50+ $2.00 = $12.50
The cost of a 7-day ad is $12.50.
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The ratio of boys to girls in ms. zombo's class is 33 to 22. in mr. stolarski's class it is 55 to 33. if there are 15 students in ms. zombo's class and 32 students in mr. stolarski's class, what is the ratio of boys to girls in the combined classes?
Answers
Stolarski's class is 55:33 or 5:3
15 students in Zombos
9 boys 6 girls
32 students in Stolarski
20 boys 12 girls
Together is 29 boys and 18 girls
29:18 boys to girls
For combined classes of Ms. Zombo's and Mr. Stolarski's, the number of boys and girls are determined based on their respective ratios and total number of students. The combined ratio of boys to girls is 29:18.
Explanation:The question asks for the combined ratio of boys to girls in both Ms. Zombo's and Mr. Stolarski's classes. Firstly, identify the number of boys and girls in each class based on the given ratio and total students. In Ms.Zombo's class, the ratio of boys to girls is 33:22, and there are total 15 students. So, the number of boys is (33/(33+22))*15= 9 boys and 6 girls. Similarly, in Mr.Stolarski's class the ratio is 55:33, there are 32 students, so there are (55/(55+33))*32 =20 boys and 12 girls.
Next step is to combine the classes. The total number of boys from both classes is 9 (from Ms. Zombo's class) + 20 (from Mr.Stolarski's class) = 29 boys. The total number of girls is 6 (from Ms. Zombo's class) + 12 (from Mr.Stolarski's class) =18 girls.
Therefore, the combined ratio of boys to girls from both classes is 29:18.
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Which of the following expressions represents the area of a trapezoid with bases of 3x and 5x and a height of 6x?
10x
24x
24x2
45x2
Answers
so A = (3x + 5x )(6x/2)= 24x^2
Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60 how much does she need to pay off
Answers
Janet has to pay off $65 to reduce her balance to no more than $60.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.
The amount to be paid will be calculated as,
Amount = 125 - 60
Amount = $65
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The line x+2y=9 intersects the curve xy+18=0 at the points A and B. Find the coordinates of A and B
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Find measure of angle EFG
Answers
You also know from the supplementary angles that 17x+13x should be equal to 180.
So,
17x+13x=180
30x=180
x=180/30
x=6
Therefore 17(6)= 102 degrees
Hope I helped :)
please show me how to solve ... -5x-10=10
Answers
First lets add by the number 10 on each of your sides of the problem
Like: -5x - 10 + 10
= 10 + 10
Second lets divide by a -5 because both numbers equals to that number
Like: -5x / -5 (cancel )
20/-5
x = -4
Good luck on your assessment and enjoy your day
~MeIsKaitlyn:)
What is the width of a rectangle with an area of 5/8in and the length of 10in?
Answers
so W= A divided by L
W= 5/8 DIVIDED BY 10 = 5/80 or 1/16 if we simplify
Sheila purchased ski equipment for $513 using a six-month deferred payment plan. The interest rate after the introductory period is 18.39%. A down payment of $125 is required as well as a minimum monthly payment of $65. What is the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period?
Answers
$65 * 6 = $390 total monthly payments made
The downpayment made is $125, so the total balance at the end is:
balance = $513 – ($125 + $390)
balance = - $2
There is an excess of 2 dollars at the end.
Sheila's balance at the beginning of the seventh month will be approximately $393.95 after considering the deferred payment and applying the interest rate.
To determine the balance at the beginning of the seventh month, follow these steps:
Calculate the initial loan amount: Sheila purchased equipment worth $513 minus a down payment of $125, leaving a balance of $388.Introductory period payments: Over six months, Sheila makes the minimum payment of $65 each month. Therefore, total payments during the introductory period are $65 x 6 = $390.Balance at end of introductory period: Since the deferred payment plan means these monthly payments were applied directly to the purchasing price rather than reducing the balance with interest-free monthly payments, the balance remains $388.Interest application: After the introductory period, interest accrues on the balance of $388 at an annual rate of 18.39%. This translates to a monthly interest rate of 18.39% / 12 ≈ 1.5325%.Calculating the new balance: Applying one month of interest on the balance, $388 increases by 1.5325% or $388 x 0.015325 ≈ $5.95. Therefore, the balance at the beginning of the seventh month is $388 + $5.95 ≈ $393.95.So, Sheila’s balance at the beginning of the seventh month is approximately $393.95.
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Answers
A savings account definitely can help you with A and B. While D may sound a bit dramatic, a responsible savings routine and a savings account with a healthy balance can make great things happen. However, a savings account does not give you the ability to borrow money from members in the community. This is not a feature of a savings account.
Answer:
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Step-by-step explanation:
C) Having a savings account gives individuals the ability to borrow money from members in the community
A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
Answers
To determine the extent of how many times greater is the number of bacteria in petri dish A than petri dish B, we simply have to take the ratio of the two.
1.75 x 10^18 / 6.25 x 10^15 = 280
So the bacteria in petri dish A is 280 times larger.
In scientific notation:
2.8 x 10^2
Answer:
280 is the answer, I did the test.
The length of a photograph is 1 cm less than twice the width. The area is 91cm^2. Find the width and length.
Answers
=>length = 2x-1
91= x(2x-1)=2x^2-x
2x^2-x-91=0
=(2x+13)(x-7)
=> x=-13/2=> no
=>x= 7 cm
The length of the photograph is 13 cm and the width is 7 cm.
What is a rectangle?
A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Given that:-
The length of a photograph is 1 cm less than twice the widthThe area is 91 cm²The length and the width will be calculated as:-
let the width = x
length = 2x - 1
91 = x ( 2x - 1 ) = 2x² - x
2x² - x - 91 = 0
= ( 2x + 13 ) ( x - 7 )
x = - 13 / 2
x = 7 cm
Length will be = 2x - 1 = 2 x 7 - 1 = 13 cm
Therefore the length of the photograph is 13 cm and the width is 7 cm.
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How do you find the area of this triangle?
Answers
This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
Answers
Hope this helps!
Your fortune is "You will find something that you have lost before."
The graph intersects the y-axis the y-coordinate is known as the y-intercept and this can be determined by using the definition of the y-intercept.
Given :
This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
The following steps can be used in order to determine a point at which a graph intersects the y-axis:
Step 1 - According to the example (0, 5) for the equation y = x + 5.
Step 2 - When the graph intersects the y-axis the value of the x-coordinate is zero.
Step 3 - When the graph intersects the y-axis the y-coordinate is known as the y-intercept.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.
Answers
-6x+15<10-5x
5<x
x>5
a incorrect
b -6x-5<10-x
-5x<15
x>-3
incorrect
c -6x+15<10-5x
-x<-5
x>5
correct
d correct
e incorrect
c and d are correct.
Find the value of x that makes m ∥ n
Answers
Answer:
The value of x that makes m || n is x = 20
Step-by-step explanation:
Given a line that is intersected by another two lines (for example line ''m'' and line ''n'' like in the exercise) one of the conditions that makes m || n is that the alternate interior angles must be congruent. Understanding that congruent means the same.
In the exercise, one pair of alternate interior angles are (2x+20)° and 3x°.
We need this two angles to be congruent ⇒ [tex]3x=2x+20[/tex]
Solving this for ''x'' :
[tex]3x=2x+20\\3x-2x=20\\x=20[/tex]
The value of x that makes 3x° congruent to 2x+20° (that makes the alternate interior angles congruents) is x = 20
Answer:
20
Step-by-step explanation:
Theorem:
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
Lines m and n are cut by a transversal.
Angles 3x and 2x + 20 are alternate interior angles.
For lines m and n to be parallel, angles 3x and 2x + 20 must be congruent, so their measures must be equal.
3x = 2x + 20
x = 20
Answer: 20
Find the slope of the line that passes through the pair of points (1/10,6) and (3/16,11/5)
Answers
When Rosina babysits for 5 hours she charges $40 and when she babysits for 6 hours she charges $48. How much does Rosina charge in one hour?
Answers
Claire and rachel plays volleyball for different teams .claire team practices seven hours every two days and rachels team practices eight hours every three days match player to the team that represents the average number of hours that they practice each day over a seven day period
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Joanna bought 1 1/2 pounds of apples, 3/4 pound of strawberries, 1/2 pound of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears. How many pounds of fruit did Joanna buy in all?
Answers
First we need to add all whole numbers
next we need to find the LCD of all fractions which is 4
next we change the denominators into the LCD (4)
next we join them all together so now it will be 3 + 2 + 3 + 1 + 3 + 2 over 4
since 2 + 3 + 1 + 3 + 2 equals 11 we simplify it to 3 + 11/4
now we make 11/4 to a mixed fraction which is 2 3/4
now we add 3 + 2 to make 5 and keep the fraction
Answer: Joanna bought 5 3/4 pounds of fruit in all.
Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.
= 1 1/2 + 3/4 + 1/2 + 1 3 /4 + 1 1/4
= 3/2 + 3/4 + 1/2 + 7/4 + 5/4
= (6 + 3 + 2 + 7 + 5)/4
= 23/4
= 5 3/4
Thus, Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.
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