Answers
Answer:
Answer is in explanation.
Step-by-step explanation:
Part A:
The [tex]x[/tex]-coordinate of the intersection of the curves for the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] is the same as the solution to [tex]4^{-x}=2^{x+3}[/tex] because the equation [tex]4^{-x}=2^{x+3}[/tex] is the result of finding when (for what [tex]x[/tex]'s) the [tex]y[/tex]'s are the same for the the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].
Part B:
Table for [tex]y=4^{-x}[/tex]:
[tex]x[/tex] | [tex]y=4^{-x}[/tex] | [tex](x,y=4^{-x})[/tex] |
-3 | [tex]y=4^{-(-3)}=4^{3}=64[/tex] | [tex](-3,64)[/tex] |
-2 | [tex]y=4^{-(-2)}=4^{2}=16[/tex] | [tex](-2,16)[/tex] |
-1 | [tex]y=4^{-(-1)}=4^{1}=4[/tex] | [tex](-1,4)[/tex]
0 | [tex]y=4^{-(0)}=4^{0}=1[/tex] | [tex](0,1)[/tex]
1 | [tex]y=4^{-(1)}=4^{-1}=\frac{1}{4}[/tex] | [tex](1,\frac{1}{4})[/tex]
2 | [tex]y=4^{-(2)}=4^{-2}=\frac{1}{16}[/tex] | [tex](2,\frac{1}{16})[/tex]
3 | [tex]y=4^{-(3)}=4^{-3}=\frac{1}{64}[/tex] | [tex](3,\frac{1}{64})[/tex]
Table for [tex]y=2^{x+3}[/tex]:
[tex]x[/tex] | [tex]y=2^{x+3}[/tex] | [tex](x,y=2^{x+3})[/tex] |
-3 | [tex]y=2^{-3+3}=2^{0}=1[/tex] | [tex](-3,1)[/tex]
-2 | [tex]y=2^{-2+3}=2^{1}=2[/tex] | [tex](-2,2)[/tex]
-1 | [tex]y=2^{-1+3}=2^{2}=4[/tex] | [tex](-1,4)[/tex]
0 | [tex]y=2^{0+3}=2^{3}=8[/tex] | [tex](0,8)[/tex]
1 | [tex]y=2^{1+3}=2^{4}=16[/tex] | [tex](1,16)[/tex]
2 | [tex]y=2^{2+3}=2^{5}=32[/tex] | [tex](2,32)[/tex]
3 | [tex]y=2^{3+3}=2^{6}=64[/tex] | [tex](3,64)[/tex]
You can see in the two tables the y-coordinates are the same value of [tex]4[/tex] when [tex]x=-1[/tex]. So basically the common point in both tables is [tex](-1,4)[/tex] so [tex](-1,4)[/tex] is a solution.
Part C:
I'm going to graph both [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] on the same coordinate plane. I will then find where they will intersect.
I'm going to graph my points from the table to [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].
This can be seen in my drawing.
I graphed [tex]y=4^{-x}[/tex] in blue.
I graphed [tex]y=2^{x+3}[/tex] in red.
Another way:
An algebraic approach:
[tex]4^{-x}=2^{x+3}[/tex]
[tex](2^2)^{-x}=2^{x+3}[/tex] (since [tex]4=2^2[/tex] and now the bases on both side are the same)
[tex]2^{-2x}=2^{x+3}[/tex]
[tex]-2x=x+3[/tex] (since [tex]2^{a}=2^{b}[/tex] then [tex]a=b[/tex])
[tex]-3x=3[/tex] (subtracted [tex]x[/tex] on both sides)
[tex]x=-1[/tex] (divided both sides by [tex]-3[/tex])
The solution is [tex]x=-1[/tex].
Related Questions
-5(4m - 2) = -2/3 + 6m).
Answers
Answer:
m=16/39
Step-by-step explanation:
-5(4m-2)=-2/3+6m
-20m+10=-2/3+6m
-20m-6m=-2/3-10
-26m=-2/3-30/3
-26m=-32/3
26m=32/3
m=(32/3)/26
m=(32/3)(1/26)
m=32/78
m=16/39
can anyone help to find the answer to this:
17x - 2x/3
Answers
Answer:
49x
Step-by-step explanation:
An amusement park charges an admission fee of 40 dollars per person. The cost, C (In dollars), of admission for a group of p people is give by the following
C=40p
What is the cost of admission for a group of 3 people
Answers
Cost of admission for a group of 3 people is $ 120
Solution:
Given that amusement park charges an admission fee of 40 dollars per person
The cost, C (In dollars), of admission for a group of p people is give by the following expression:
C = 40p
Here "p" denotes the number of people
To find: cost of admission for a group of 3 people
For a group of 3 people, p = 3
Substituting p = 3 in given cost formula, we get the cost of admission for a group of 3 people
[tex]c = 40p\\\\c = 40(3) = 120[/tex]
Thus cost of admission for a group of 3 people is $ 120
If the sum of a number and five is doubled, the results is one less than the number.find the number
Answers
The number is -11.
Step-by-step explanation:
Let,
the number be x.
According to given statement;
Sum of a number and five is doubled;
2(x+5)
is equals to one less than the number
= x-1
Combining both the sides and forming an equation
2(x+5)=x-1
[tex]2x+10=x-1\\2x-x=-1-10\\x=-11\\[/tex]
The number is -11.
Keywords: addition, subtraction
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CAN SOMEONE HELP ME FIND THE DISTANCE..
Answers
The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]
Solution:
Given that we have to find the angle of elevation from point C to Point A
Given in figure that, angle A = [tex]58^{\circ}[/tex]
Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]
We have to find angle C
The angle sum property of a triangle states that the angles of a triangle always add up to 180°
Therefore, in given triangle ABC
angle A + angle B + angle C = 180
[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]
[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]
Therefore angle C = [tex]32^{\circ}[/tex]
15. At a school fair, 70% of the people are under 16 years old. One of the people
teachers. If there are 21 teachers at the fait, how many people are there at the air
Answers
Answer:
210 people.
Step-by-step explanation:
Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?
Now, solving to find total number people in the fair.
Lets assume total number of people in the fair is "x".
As given, there is 70% of total number of people are under 16 year old.
∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]
Next, finding the number of remaining people.
∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]
Number of remaining people is 0.3x
As given, One third of the people remaining are teachers.
∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]
As given there are 21 teachers at the fair.
⇒ [tex]0.1x= 21\ teachers[/tex]
∴ x= [tex]\frac{21}{0.1} = 210[/tex]
Hence, total number of people in the fair are 210.
Match the real-world problem to its constant of proportionality.
$4.16 for 4 pounds of bananas
$16.48 for 8 pounds of potatoes
$18.36 for 2 pizzas
2 cups of flour to make 36 cookies
9.18,1.04,18,2.06
Answers
Real word problem ⇒ constant of proportionality
$4.16 for 4 pounds of bananas ⇒ 1.04
$16.48 for 8 pounds of potatoes ⇒ 2.06
$18.36 for 2 pizzas ⇒ 9.18
2 cups of flour to make 36 cookies ⇒ 18
Solution:
A proportional relationship is one in which two quantities vary directly with each other.
We say the variable y varies directly as x,
if for x ∝ y
then, x = y k
Where "k" is called constant of proportionality
[tex]k = \frac{x}{y}[/tex]
$4.16 for 4 pounds of bananas
x = 4.16 and y = 4
[tex]k = \frac{4.16}{4} = 1.04[/tex]
Thus constant of proportionality is 1.04
$16.48 for 8 pounds of potatoes
x = 16.48 and y = 8
[tex]k = \frac{16.48}{8} = 2.06[/tex]
Thus constant of proportionality is 2.06
$18.36 for 2 pizzas
x = 18.36 and y = 2
[tex]k = \frac{18.36}{2} = 9.18[/tex]
Thus constant of proportionality is 9.18
2 cups of flour to make 36 cookies
x = 36 and y = 2
[tex]k = \frac{36}{2} = 18[/tex]
Thus constant of proportionality is 18
you want to save $5,000 for future family vacation. if the bank pays 4.3% compounded monthly for 3 years, then how much will you need to invest to reach your vacation goal?
Answers
Answer:
The principal amount invested is $4395.93 .
Step-by-step explanation:
Given as :
The Amount that saved for future = A = $5,000
The bank applied rate of interest = r = 4.3% compounded monthly
The time period of loan = t = 3 years
Let the principal amount invested = $p
Now, From monthly Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]
Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]
Or, $5000 = p × [tex](1.003583)^{36}[/tex]
Or, $5000 = p × 1.137414
∴ p = [tex]\dfrac{5000}{1.137414}[/tex]
i.e p = $4395.93
So, The principal amount invested = p = $4395.93
Hence, The principal amount invested is $4395.93 . Answer
dose y= -3 have a negative slope
Answers
Answer:
no because it is just a straight line. a dot is plotted at (0,-3) and a straight line is horizontal.
Factor completely 6x^2 − 11x − 10.
(6x + 2)(x − 5)
(6x − 2)(x + 5)
(3x + 2)(2x − 5)
(3x − 2)(2x + 5)
Answers
Answer:
(3x+2)(2x-5)
Step-by-step explanation:
you can use process of elimination on this one just distribute the equations:
3x(2x-5)+2(2x-5)
6x^2-15x+4x-10 <------ Combine like terms
6x^2-11x-10
Final answer:
Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).
Explanation:
When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.
Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.
Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)
The completely factored form of the quadratic equation is (3x + 2)(2x − 5).
Given that AD and BC are parallel, find the value of x.
Answers
Answer:
Therefore the value of x is 15.
Step-by-step explanation:
Given:
AD || BC
m∠ B = (9x + 15)°
m∠ A = (3x - 15)°
To Find:
x = ?
Solution:
AD || BC ...............Given
If two lines are parallel and sum of the interior angles are supplementary.
i.e m∠ B and m∠ A are interior between Parallel lines.
∴ [tex]\angle B + \angle C =180\\[/tex]
Substituting the given values we get
∴ [tex](9x + 15)+( 3x - 15)=180\\12x=180\\\\x=\frac{180}{12} \\\\\therefore x =15[/tex]
Therefore the value of x is 15.
??????((((((((??????????
Answers
Answer:
G. 17.3
solution:
Find the value of x when a = 7/2, h = 10, k = 15, If
Answers
Answer:
9
Step-by-step explanation:
x= hk/ (k+h)(a-2)
10*15 (15+10) (7/2-2)= 9
How to solve -7-8(6x+5)
Answers
Answer: -47 - 48x
Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.
You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.
So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.
So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.
Now we have -7 + -48x + -40.
Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.
So your answer is just -47 - 48x.
An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off. He wants to know the sale price of the service
Answers
30.00 x .15 = 4.50
30.00 - 4.50 = 25.50
The sale price of the service is $25.50.
Given that,
The city auto is regularly at $30.There is a 15% coupon off.We need to find out the sale price
So, the sale price is
= $30 - (15% of $30)
= $30 - $4.50
= $25.50
Therefore we can conclude that the sale price of the service is $25.50.
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BRAINIAC IN LAW OF SINES?? Ill give brainlest and extra points
Answers
Answer:
[tex]x \approx 31.8[/tex]
Step-by-step explanation:
[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]
Cross multiply:
[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]
Divide both sides by 22:
[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]
Take [tex]\sin^{-1}( )[/tex] of both sides:
[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]
Put left hand side into a calculator now:
[tex]31.7941 \approx x[/tex]
To the nearest tenth that is: [tex]x \approx 31.8[/tex]
What equals the expression if a=2.4 b=0.237 c=9.49. c-2ab
Answers
8.3524 equals the expression c - 2ab if a = 2.4 b = 0.237 c = 9.49
Step-by-step explanation:
The given is:
a = 2.4b = 0.237c = 9.49We need to find the value of the expression c - 2ab
∵ The expression is c - 2ab
∵ a = 2.4
∵ b = 0.237
∵ c = 9.49
- Substitute the values of a , b and c in the expression to find its value
∴ 9.49 - 2(2.4)(0.237) = 9.49 - 2(0.5688)
∴ 9.49 - 2(2.4)(0.237) = 9.49 - 1.1376
- Subtract the two numbers
∴ 9.49 - 2(2.4)(0.237) = 8.3524
8.3524 equals the expression c - 2ab if a=2.4 b=0.237 c=9.49
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What is the slope? Help me please I really am stuck on this
Answers
Step 1: Determine if it is positive/negative
An important factor in slope is the sign that goes before it. If it is positive no sign if needed but if negative it requires a - sign.
If a graph is negative the highest point is on the left side, and the values decrease.
If a graph is positive the highest point is on the right side, and the values increase.
In this case, the highest point is on the left side, so the slope is negative
Step 2: Finding slope
To find slope remember the equation when working with a graph— m= rise/ run
This means that from one point to another, you have to find how many units is up and down between it/ how many units is left or right between it
Using points (0,2) and (1,0) I can see that the slope is -2/1 but we can leave this as -2
Hope this helps comment below for more questions :)
The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a
different spot to place the light. The proposed placements and the lit area that each produces are shown below.
Nikki's Proposed Placement
Light
27.5 ft
Dylan's Proposed Placement
Light
16.5 ft
38
38 ft
Lit area
Lit Area
60
60 ft
How do Nikki's and Dylan's proposals compare? Check all that apply.
Nikki's proposed placement will light a greater area than Dylan's placement
Dylan's proposed placement will light a greater area than Nikki's placement.
Both proposed placements will light the same sized area.
Answers
Answer
THE REAL ANSWER IS c and f
Step-by-step explanation:
I just finished and they are the only 2 and I got it right
Nikki's and Dylan's Both proposed placements will light the same sized area.
Area of triangleThe area of a triangle is defined as the total space that is enclosed by the three sides of the triangle.The area of a triangle can be determined using the formula below,A = 1/2 × b × h.
How to solve this problem?The steps are as follow:
From the question, of the base and height of Nikki's and Dylan's proposed placements are the same which is 60 and 38ft respectively.The area that would be covered by both of them would be,A= 1/2×60×38
A= 30×38
A = 1,140ft.
So, Nikki's and Dylan's Both proposed placements will light the same sized area.
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please help 56 POINTS
Answers
Sarah and George wanted to buy some sweets so they decided to buy brownies and banana bread Sarah bought four boxes of brownies and six loaves of banana bread George bought five boxes of brownies and three loaves of banana bread is Sarah spent $44 and George spent $37 determine how much the cost is for a box of brownies and a loaf of banana bread
Answers
Answer:
Cost of a box of brownies = $5
Cost of a loaf of banana bread = $4
Step-by-step explanation:
Let, x= box of brownies.
y=loaf of banana bread.
Now,
Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-
[tex]4x+6y=44[/tex] --------------------------(equation 1)
And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-
[tex]5x+3y=37[/tex] --------------------------(equation 2)
Now,
[tex]4x+6y=44[/tex]
[tex]4x=44-6y[/tex]
[tex]x=\frac{44-6y}{4}[/tex]
[tex]x=11-\frac{6}{4}y[/tex]
[tex]x=11-\frac{3}{2}y[/tex]------------------(equation 3)
Now substituting equation 3 in equation 2 we get,
[tex]5x+3y=37[/tex]
[tex]5(11-\frac{3}{2}y)+3y=37[/tex]
[tex]55-(\frac{15}{2}\times y) +3y=37[/tex]
[tex]55-37=(\frac{15}{2}\times y)-3y[/tex]
[tex]18=7.5y-3y[/tex]
[tex]18=4.5y[/tex]
[tex]y=4[/tex] ----------------------------------(Equation 4)
Now putting value of y from equation 4 in equation 3
i.e. [tex]x=11-\frac{3}{2}y[/tex]
[tex]x=11-\frac{3\times 4}{2}[/tex]
[tex]x=11-6[/tex]
[tex]x=5[/tex]
Therefore the cost of a box of brownies = $5
the cost of a loaf of banana bread = $4
what is the solution set of -9x greater than 27
Answers
Answer:
x<-3
Step-by-step explanation:
-9x>27
x>27/-9
x>-3
Can someone help me solve this question I can't seem to manage it
Answers
Answer:
LA=6 WA=4 LB=6 WB=2
Step-by-step explanation:
Its a square so the sides are 6cm. 2:1 ratio means A is 6*4=24 cm while B is 6*2=12cm.
A student measures the temperature of boiling water a number of times. If the
boiling point of water is 212 degrees, which of his measurements is the most
accurate?
A: 205.46 degrees F
B: 212.1 degrees F
C: 210 degrees F
D: 213.15 degrees F
Answers
The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
Explanation:The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
When measuring the temperature of boiling water, it is important to consider the accuracy and precision of the measuring instrument. The given options range between 205.46 and 213.15 degrees F, but the boiling point of water is widely accepted to be 212 degrees F at standard atmospheric pressure.
Therefore, the measurement closest to this accepted value is the most accurate, which is option B: 212.1 degrees F.
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25. Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
the trip to Scenic Lake Park?
DATA
Trip to Scenic
Lake Park
10:15 A.M. to 2:30 P.M.
Slide show
4:15 P.m. to 5:10 P.M.campfire 7;55p.m.to 9;30p.m
26. How much longer is dinner than the
Answers
Paulo's family has 1 hour and 45 minutes before the trip to Scenic Lake Park after their arrival at the reunion.
Explanation:The question asks how long Paulo's family has before the trip to Scenic Lake Park if they arrived at a family reunion at 8:30 A.M. and the trip is scheduled to start at 10:15 A.M. To solve this, we need to calculate the time difference between 8:30 A.M. and 10:15 A.M.
Here's how you calculate the time difference:
Start by noting the start time which is 8:30 A.M.The end time is 10:15 A.M.To find the difference, consider how many whole hours are between the times: There is 1 full hour from 8:30 A.M. to 9:30 A.M.Then, we need to account for the remaining time from 9:30 A.M. to 10:15 A.M., which is 45 minutes.Adding the full hour and the remaining 45 minutes, we find that there is a 1 hour and 45 minutes gap between the arrival time and the departure for the trip.
Find the value of x and y.
Answers
Answer:
Step-by-step explanation:
CD and AB are parallel; DB transverse
∠D + ∠B = 180 {co interior angles}
112 + 27 + y = 180
139 + y = 180
y = 180 - 139
y = 41
In ΔABC,
49 + x + y = 180 ( sum of all angles of triangle}
49 + x + 41 = 180
90 + x = 180
x = 180 - 90
x = 90
Avery’s water bottle holds 300 milliliters. Dashawn’s container holds 3/4 as much water how much do both containers hold?
Answers
Answer: Avery's bottle holds 300 milliliters. If Dashawn's container holds 3/4 as much, then his container can hold 225 milliliters. Added together, both containers can hold 525.
Step-by-step explanation: 3/4 of 300 is 225. 300 + 225 = 525.
what interval contains a positive solution to the equation 0.2x^2-0.8x=1.6
Answers
Step-by-step explanation:
0.2x² − 0.8x = 1.6
Multiply both sides by 5.
x² − 4x = 8
Complete the square by adding 4 to both sides.
x² − 4x + 4 = 12
(x − 2)² = 12
x − 2 = ±√12
x = 2 ± √12
The positive solution is x = 2 + √12 ≈ 5.46.
Write the definition of midpoint, provide a supporting figure
Answers
Step-by-step explanation: Using the diagram shown which I have provided in the image attached, the definition of a midpoint states that M is the midpoint of segment LN, then segment LN ≅ to MN.
The definition of a midpoint can also be stated the other way around. using the diagram shown, if segment LN ≅ to segment MN, then M is the midpoint of segment LN.
We can use hash marks in the figure to show that are 2 segments are congruent.
if 10,000 bacteria are present initially and the number of bacteria doubles in 5 hours, how many bacteria will there be in 24 hours?
Answers
Answer:
20,000
Step-by-step explanation: