Answer:
Option B.
Step-by-step explanation:
The given exponential equation is
[tex]y=ab^x[/tex] ...(1)
It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).
The graph passes through the point (-3,24), so substitute x=-3 and y=24 in equation (1).
[tex]24=ab^{-3}[/tex] ...(2)
The graph passes through the point (-2,12), so substitute x=-2 and y=12 in equation (1).
[tex]12=ab^{-2}[/tex] ...(3)
Divide equation (3) by equation (2).
[tex]\dfrac{12}{24}=\dfrac{ab^{-2}}{ab^{-3}}[/tex]
[tex]0.5=b[/tex]
Substitute b=0.5 in equation (2).
[tex]24=a(0.5)^{-3}[/tex]
[tex]24=\dfrac{a}{(0.5)^{3}}[/tex]
[tex]24=\dfrac{a}{0.125}[/tex]
[tex]24\times 0.125=a[/tex]
[tex]3=a[/tex]
Substitute a=3 and b=0.5 in equation (1).
[tex]y=3(0.5)^x[/tex]
Therefore, the correct option is B.
Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan (θ +x) and sin (θ +x))
Answer:
tan (θ+x)= -33/56
sin (θ+x)=33/65
Step-by-step explanation:
cosθ= -4/5 , sin x = -12/13
cosθ= -4/5; θ is in the third quadrant=> sinθ=-√(1-cos² θ)
sinθ=- √(1-16/25)=- √(9/25)=-3/5
sinx= -12/13; x is in the fourth quadrant=> cosx=+√(1-sin²x)
cosx=√(1-144/169)= √(25/169)=5/13
tgθ= sinθ/cosθ=(-3/5)/(-4/5)=3/4
tgx= sinx/cosx=(-12/13)/(5/13)= -12/5
tan (θ+x)=(tgθ+tgx)/(1-tgθ*tgx)
tan (θ+x)=(3/4-12/5)/(1+3/4*12/5)=(-33/20)/56/20)= -33/56
sin (θ+x)=sinθcosx+coxθsinx=-3/5 *5/13 +-4/5 * (-12/13)=-15/65+48/65=33/65
Alvin has 2\3 cup of salad dressing. He uses 1/9 cup of salad dressing for each serving. How many servings of salad dressing can alvin make 100 points pls help
Answer:
Alvin can make six servings of salad.
Step-by-step explanation:
2/3 is equal to 6/9.
Hi there!
Convert all denominators into the same denominator:
[tex]\frac{2}{3}=\frac{6}{9}[/tex]
[tex]\frac{1}{9}=\frac{1}{9}[/tex]
Divide each terms:
[tex]\frac{6}{9}*\frac{1}{9}=6[/tex]
Final Result: 6
PLEASE HELP Three subtracted from x is less than 20
Answer:
x < 23 (x is less than 23)
Step-by-step explanation:
x - 3 < 20
x < 20 + 3
x < 23 (x is less than 23)
PLZ HELPP
Which expressions will help you find the surface area of this right triangular prism? Select all that apply.
11 × 3
1/2 × 3 × 5
4 × 11
5 × 11
Answer:
Select:
11 x 3
4 x 11
5 x 11
Step-by-step explanation:
Notice that the surface area of the prism consists of three rectangles (whose area formula is the product of "length times the width" of each lateral surface), plus the area of two equal right-angle triangles of base 4 and height 3)
Therefore, the formulas we will need to use are:
1) for one of the rectangular faces = 11 x 3
2) for another rectangular face = 5 x 11
3) for the third rectangular face = 4 x 11
4) for each of the triangular bases = [tex]\frac{1}{2}\, base\,*\,height=\frac{1}{2}\,*4\,*\,3[/tex]
Therefore only three formula expressions need to be selected from the given list.
11. An airline charges $20 to check a piece of luggage up to 23 kilograms. For excess weight, it charges $5 more per kilogram. The airline rounds up to the next whole kilogram (a piece of luggage weighing 24.1 kg would be charged as 25 kg). The airline doesn't accept luggage over 32 kg. Which of the graphs below represents this information as a function?
Answer:
i believe it is b
Step-by-step explanation:
Solve |x+2|=10
A {-8,8}
B {-12,8}
C {-12,12}
If the radius of a cone is 3 cm and a height of the Cone is 8 cm what is the surface area
Answer:
24
Step-by-step explanation:
if the radius is 3 cm and the height is 8 cm we would multiply3 x 8 = 24so the answer is 24NEED HELP AGAIN . ASAP PLS AND THX
Answer:
I am pretty sure its (a) and (c)
Step-by-step explanation:
What is the surface area of a cube in which each face of the cube has an area of 7 cm 2 ? surface area = cm 2 PLZZZZZZZZZZZZZZZZ HELP ASAP
Answer:
[tex]42cm^2[/tex]
Step-by-step explanation:
Well there are 6 faces on a cube and if each face is 7, the total should be 42.
The surface area of the cube is A = 42 cm²
What is the surface area of cube?The formula for surface area of a cube is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area.
Surface area S = 6a² ,
where a is the side of the cube
Given data ,
Let the surface area of cube be A
Now , the value of A is
Let the area of one face S = 7 cm²
So , Surface area A = 6a²
On simplifying , we get
A = 6 x 7 cm²
A = 42 cm²
Hence , the surface area is 42 cm²
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Factor 16 x2 + 24 x + 9.
(16 x + 3)( x + 3)
(4 x + 3)(4 x - 3)
(4 x + 3) 2
Answer:
Step-by-step explanation:
(4x + 3)(4x+3) is the factor
the third one is the solution
Duane recorded the temperature outside his window one morning. On the second day,
the temperature went up 7 degrees. On the third day, the temperature went down 10 degrees.
On the fourth day, the temperature went down 6 degrees, and it was 1°F.
What was the temperature on the first day?
A. 0°F
B. 17°F
C. 10°F
D. 7°F
Answer:
C
Step-by-step explanation:
[tex]day 2 = +7\\\\day3 = -10\\\\day 4 = -6\\\\FinalDay = 1[/tex]
so [tex]start +7 -10-6 = 1\\ \\start = 10[/tex]
Graph the linear equation.
Answer:
Look at the image
Step-by-step explanation:
Half of a number plus three
times the number.
Write it in expression or equation solve the equation
Answer:
Step-by-step explanation:
A 39 foot ladder is resting against a wall that is 36 feet high. What is
the distance between the base of the ladder and the bottom of the wall?
5 feet
10 feet
15 feet
Answer:
11
Step-by-step explanation:
Jordan invested $8,500 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,070?
Answer:
52 days
Step-by-step explanation:
if compounding daily we can see what 1 year accumulates using the function
360 / interest rate = 360/4.1 = 87.8048780488 = 87.80 per day
We can use inverse of the balance profit to use the exact amount difference to then divide into the date of withdrawal
$13070- 8500 = 4570
4570/ 87.8048780488 = 52.04 = 52 days.
Scott found the area of the shape to
be 30 square units. If he used a unit
square with longer sides, would his
area measurement be greater than
30 square units or less than 30 square
units? Explain.
Answer:
So if we do this to the area of Scott's shape, the result will be less than 30 squares units.
Step-by-step explanation:
If a shape has "x" square units, it means that we can fit that number of squares with side length of one unit in that given shape. For the case where we change the unit, we are changing the length of the square's sides, if the new one has greater sides, then it means that the square is bigger, therefore for the same shape we will be able to fit less squares. So if we do this to the area of Scott's shape, the result will be less than 30 squares units.
Which of the following is the graph of y= -x-3?
Answer:
Step-by-step explanation:
Which of the following functions is graphed below? Please help ASAP
Answer:
its not very clear can you take a picture again?
Step-by-step explanation:
In a school there are 300 students 90 of them are male students. Find out the percentage of female students.
Answer:
70%
Step-by-step explanation:
Total students = 300
Male students = 90
Female students = 300 - 90 = 210
Percentage of female students
[tex] = \frac{210}{300} \times 100 \\ \\ = \frac{210}{3} \\ \\ = 70\%[/tex]
Answer:
70%
Key Points:
Total Students: 300Male Students: 90Unknowns:
Male Student PercentageFemale Student CountFemale Student PercentageWe are given the overall amount of students as well as the male students. Using these, we can determine how many females are in the school.
300 overall students - 90 male students = ____ female students
Simplify.
Given our above equation, we now know that there are 210 female students at the school.
In order to find the percentage of females at the school, we must divide the female students by the overall size of the school.
[tex]\frac{210}{300} = ?[/tex]
Our next step is to grab a calculator and input 210 ÷ 300. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.7
Now, you need to multiply it by 100 so that you can create a percentage.
0.7 × 100 = 70%
Therefore, 70% of the students are female.
Checking our work:
A great way to ensure that your answer is correct is by checking your work. We can do this by finding the percentage of male students and adding it to the percentage of female students.
If 70% is the correct percentage for female students, the male and female percentages should add up to 100%
Finding the male percentage:
Similar to how we found the percentage of females at the school, we must divide the male students by the overall size of the school. Reminder: there are 300 students and 90 of them are male.
[tex]\frac{90}{300} = ?[/tex]
Again, you should pull out your calculator and input 90 ÷ 300. This should give you 0.3
Next, multiply your answer by 100 to get our percentage.
0.3 × 100 = 30%
Knowns:
Female Percentage: 70%Male Percentage: 30%Add the female percentage with the male percentage: 70% + 30% = 100%
As predicted, our answer was 100%. Therefore, 70% of the students are female.
Learn more about solving for percentages by reviewing these answers!
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A car manufacturer announced that next year the price of a certain model car would increase by 5.5 %. This year the price is $17,635. Find the increase and the new price. The increase in the price of the car is $? (Round to the nearest cent as needed.) The new price of the car is $? (Round to the nearest cent as needed.)
Answer:
Increase: $969.93 New Price: $18,604
Step-by-step explanation:
I got this answer by finding out how much of the initial price 5.5% was, it ended being 969.925 so I rounded that to 969.23 so that I may found how much the price increased, then I added the increase price to the initial price so that I may find out how much the car would cost next year which is, $18,604.
Help me, please!!
If you had a nickel (.05 or five cents) that earned 100 percent interest each day or doubled in value each day. How much would you have after 10 days?
Answer:
Step-by-step explanation:
If the initial amount of nickel is doubling in value each day, it means that the amount of nickel is increasing in geometric progression. The formula for determining the nth term of a geometric sequence is expressed as
Tn = ar^(n - 1)
Where
n represents the common ratio
a represents the first term of the sequence (initial amount)
n represents number of terms in the sequence (days)
r represents common ratio between consecutive terms(days)
From the information given,
r = 2
n = 10
a = 0.05
Therefore, for 10days, T10
T10 = 0.05 × 2^(10 - 1)
T10 = 0.05 × 2^9
T10 = 25.6
Answer:
Having a nickel doubled for 10 days gives 512 nickels, or 2560 cents.
Step-by-step explanation:
Having a nickel doubled in value each day for 10 days, we first write the amount of nickels we have in the first few days, inspect what pattern these numbers take, write a general formula for the sequence formed, and use the formula to find the 10th number easily.
For the first five days we have:
Day1: 1
Day2: 1 + 1 = 2
Day 3: 2 + 2 = 4
Day 4: 4 + 4 = 8
Day 5: = 8 + 8 = 16
...
This is a geometric progression, where the first term is 1, and the common ratio is 2.
The nth term is given as
Tn = ar^(n - 1)
Tn = 1 × 2^(n - 1)
= 2^(n - 1)
That is
Day n = 2^(n - 1)
Day 10 = 2^(10 - 1) = 2^9 = 512 nickels.
But because 1 nickels = 5 cents
512 nickels = 5 × 512 = 2560 cents.
The side lengths of a triangle are 6, 8 and 12. Is this a right triangle?
A. Yes, because 6 to the 2nd power + 8 to the 2nd power < 12 to the 2nd power.
B. No, because 6 + 8 ≠ 12.
C. Yes, because 6 to the 2nd power + 8 to the 2nd power = 12 to the 2nd power.
D. No, because 6 to the 2nd power + 8 to the 2nd power ≠ 12 to the 2nd power.
Answer:
No it's not. 6 to the 2nd power + 8 to the 2nd power ≠ 12 to the 2nd power
Step-by-step explanation:
If you square the shorter lengths and add them together, they add up to one hundred
6^2 + 8^2 --> 38 + 64 = 100
Once you square 12 it equals 144
144 does not equal 100. There for it can't be a right triangle. To be a right triangle, it has to have a ratio pf 3: 4: 5.
Ex: 6: 8: 10, 12: 16: 20, etc.
Hope this helps!
Please help me with the question below
Answer: B) y=4n+8
Step-by-step explanation:
in these type of questions, I use the strategy of trial and error, lets look at the first choice, y=4n+12, if we look at the first term, and substitute the numbers on the equation, we would get y=4(1)+12, which is y=16 which tells us that there are 16 shaded squares in the first term which is not true, then we move on to the next answer. Using this strategy, there is only one answer that makes sense which is B) y=4n+8, Just to make sure if we look at the first term, and use the formula, we get y=4(1)+8, which gives us y=12 which is true.
Hope it helped
7. The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F. Write and solve an equation to
find the decrease in temperature.
Answer:
78-56=22 degrees
Step-by-step explanation:
You wanna take away 56 degrees from 78 degrees and you will get ....
Minnie wants to know if the number of words on a page in her planetary science book is generally more than the number of words on a page in her math book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book. Mean Median Mean Absolute Deviation Planetary science 48.9 41 9.2 Math 34.5 44 1.9 She claims that because the mean number of words on each page in the planetary science book is greater than the mean number of words on each page in the math book, the planetary science book has more words per page. Based on the data, is this a valid inference? No, because there is a lot of variability in the planetary science book data. Yes, because there is a lot of variability in the planetary science book data. Yes, because the mean is larger in the planetary science book. No, because the mean is larger in the planetary science book.
Answer:
I think it is
No, because there is a lot of variability in the geography book data
hope this helps
-lvr
No, Minnie is incorrect, because there is a lot of variability in the Planetary science book data.
Is this a valid inference?We know that, for 25 samples of each book, we have:
Book mean median MAD
Planetary science 48.9 41 9.2
Math 34.5 44 1.9
The claim, is that "the Planetary science book as more words per page"
Notice that even if we subtract the mean standard deviation from the mean in the Planetary science case:
48.9 - 9.2 = 39.7
And we add these in the math case:
34.5 + 1.9 = 36.4
So, even considering the variability, the Planetary science book has more words per page.
The value in the Planetary science case is still larger, so, only with this, we conclude that her claim is not valid.
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Kayla has $45 and wants to buy three shirts that are originally priced at $18 each. They are on sale for 20% off. After applying 5% tax, does Kayla have enough money to purchase the three shirts
Answer: No, as the total cost of the 3 shirts w/ sales tax is $45.36 and she only has $45.
Step-by-step explanation:
Start by finding the price of one shirt on sale.
[tex]18*0.2[/tex]
This equals 3.6 which is how much will be deducted from the original price.
One shirt costs [tex]18-3.6\\[/tex] when its 20% off.
This is equal to $14.40.
Since she wants to buy 3 of them we just multiply the $14.40 by 3.
[tex]14.4*3=\\[/tex]
This equals $43.2 but this is without a 5% sales tax which is normally added to the total end price.
To add a sales tax you take the sales tax percent plus 1 and multiply it to the $43.2.
[tex]43.2*1.05=\\[/tex]
This means the total price of Kayla's purchase will be $45.36.
This is over her $45 she has so she can not buy it.
Answer: she does not and is over $45.36 (.36) cents over
Step-by-step explanation:
is it possible to make a quadrilateral with any four dots as corners?
Answer:
Yes it is possible, given with 4 dots, lets say were set anywhere within a page or anywhere upon a circumference of a circle even. We can draw 4 straight lines to meet each corner and call this a quadrilateral.
Step-by-step explanation:
Squares, Rectangles and Rhombuses are all Parallelograms and squares and rectangles are regular quadrilaterals!
So any other 4 sided shape that is quadrilateral could be made.
The picture below shows all branches of quadrilaterals.
Answer:
No
Step-by-step explanation:
No.
For example, if all 4 dots are on a line, then the 4 dots do not make a quadrilateral.
Answer: No
solve for x in 4x-4/x+4=10
Answer:
-22/3 =x
Step-by-step explanation:
(4x-4) /(x+4) = 10
Multiply each side by (x+4)
(4x-4) /(x+4) * (x+4) = 10 * (x+4)
(4x-4) = 10 * (x+4)
Distribute
4x-4 = 10x+40
Subtract 4x from each side
4x-4-4x = 10-4x+40
-4 = 6x+40
subtract 40 from each side
-4 -40 = 6x+40-40
-44 = 6x
Divide each side by 6
-44/6 = -6x/6
-22/3 =x
Answer:
x = -22/3
Step-by-step explanation:
4x - 4 / x + 4 = 10
=> 4x - 4 = 10(x + 4)
=> 4x - 4 = 10x + 40
=> 4x - 10x = 40 + 4
=> -6x = 44
=> x = -44/6
=> x = -22/3
does anyone know this?
Answer:
Step-by-step explanation:
5•-4= -20
5•-3x= -15x
-6x•-4= 24x
-6x•-3x= 18x^2
Answer:
20 : 15x
:
: : : : :
24x : 18x
:
Step-by-step explanation:
5×-4=20
5×-3x=-15x
-6x×-4=24x
-6x×-3x=18x
// have a great day //
Which expression best estimates 6 and three-fourths divided by 1 and two-thirds? 7 divided by 2 6 divided by 1 8 divided by 3 3 divided by 2
Answer:
[tex]4\frac{1}{20}[/tex]
Step-by-step explanation:
[tex]6\frac{3}{4} \div 1\frac{2}{3}[/tex]
[tex]\frac{27}{4} \div \frac{5}{3}[/tex]
[tex]\frac{27}{4} \times \frac{3}{5}[/tex]
[tex]\frac{27 \times 3}{4 \times 5}[/tex]
[tex]=\frac{81}{20}[/tex]
[tex]=4\frac{1}{20}[/tex]
Answer:
7 divided by 2
Step-by-step explanation:
