Answer:
10.58 feet
Step-by-step explanation:
Hello!
If you think about how it would look in life you will notice that it looks like a right triangle which means we can use the Pythagorean theorem to find the far the ladder needs to be from the house.
The Pythagorean theorem is [tex]a^{2}+ b^{2}= c^{2}[/tex]
a is a leg
b is the other leg
c is the hypotenuse
Since the ladder has to go from the ground to the window ledge it is the hypotenuse and the window ledge is a leg
Put in what we know
[tex]a^{2} +12^{2} =16^{2}[/tex]
Now we solve for a
Simplify
a^2 + 144 = 256
Subtract 144 from both sides
a^2 = 112
Take the square root of both sides
a = 10.583
The answer is 10.58 feet
Hope this helps!
Answer:
11 ft
Step-by-step explanation:
Try to imagine it or draw it out to help you. The ladder is 16 feet long and the window ledge is 12 feet high, so this is a right triangle.
The ladder is the hypotenuse, so use the given values in the pythagorean theorem.
a^2 + b^2 = c^2
12 + b^2 = 16
b = 11
12^2 + 11^2 = 16^2
1 44 + 121 = 265
√265 = 16
The football team need to buy Gatorade for Saturdays big game . They have two option. The first option us they can buy it pre-made in a 48 ounce for $3.84 for each bottle. Or they can buy packet and mix it with water. Each packet make 64 ounces and it will cost $4.80. Find the ounce per cost
The question is incomplete. Here is the complete question.
The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.
a) Find the cost per ounce of each.
b) Which size costs less?
c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?
Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce
b) Packets
c) Save $0.96.
Step-by-step explanation:
a) Cost per ounce:
Pre-made:
[tex]\frac{3.84}{48}[/tex] = 0.08
Packet:
[tex]\frac{4.8}{64}[/tex] = 0.075
b) Comparing costs per ounce, packets costs less than pre-made.
c) Buying packets, the cost will be:
0.075*192 = $14.4
Buying pre-made:
0.08*192 = $15.36
Comparing costs, pre-made is 0.96 more than packets, so they will save 96 cents.
If Log 4 (x) = 12, then log 2 (x / 4) is equal to A. 11 B. 48 C. -12 D. 22
Answer:
[tex]\huge \boxed{\mathrm{D. \ 22}}[/tex]
Step-by-step explanation:
[tex]\mathrm{log_4 (x)=12}[/tex]
Make the base 4 from both sides.
[tex]\mathrm{4^{log_4 (x)}=4^{12}}[/tex]
Simplify the equation.
[tex]\mathrm{x=16777216}[/tex]
[tex]\mathrm{log_2 (\frac{x}{4} )}[/tex]
Let x = 16777216
[tex]\mathrm{log_2 (\frac{16777216}{4} )}[/tex]
[tex]\mathrm{log_2 (4194304)}[/tex]
Evaluate.
[tex]22[/tex]
Answer:
[tex]log_2(\frac{x}{4} )=22[/tex]
which is your answer "D"
Step-by-step explanation:
If [tex]log_4(x)=12[/tex] this means that : [tex]x=4^{12}[/tex] based in the definition of logarithm.
And this exponential expression can also be written using that [tex]4=2^2[/tex]:
[tex]x=4^{12}=(2^2)^{12}=2^{24}[/tex]
so now we know what x is with base 2 (which is needed for the second expression:
[tex]log_2(\frac{x}{4} )=?[/tex]
And this also can be written in exponent form (using the unknown "?" we need to find) as:
[tex]2^?=\frac{x}{4} \\x=4\,*\,2^?\\x=2^2\,*\,2^?\\x=2^{2+?}[/tex]
Since we know the value of x in base 2 (from our first analysis), then:
[tex]x=2^{2+?}=2^{24}\\then\\2+?=24\\?=22[/tex]
Therefore,
[tex]log_2(\frac{x}{4} )=22[/tex]
Ms. Gantt has a $15 gift card to Starbucks. She buys 2 muffins for $2.65 each, 2 hot chocolates for $1.79 each, and a juice for $3.05. How much remains on her gift card? Help please I will mark you brainiest.
Answer:
Remains on her gift card:
$3.07
Step-by-step explanation:
15 - ((2*2.65) + (2*1.79) + (1*3.05))
= 15 - (5.3 + 3.58 + 3.05)
= 15 - 11.93
= 3.07
Remains on her gift card:
$3.07
Question 1
Translate the following information into the
language of algebra. You answer should include an
algebraic expression, and clear definitions of any
variables.
Sophia is in a room filled with people. She is
counting all the shoes in the room.
She thought that the number of shoes would just be
double the number of people in the room. However,
there is also a cupboard in the room containing 4
extra shoes,
Answer:
let people=x
and shoes=y
now,as per the question
2x-4=y
Complete the description of The transformation f(x)=|x| g(x)=|x+9|-5
Answer:
f(x) down 5 units
and shifted to the left 9 units
Step-by-step explanation:
Transforming f(x) = |x| into g(x) = |x+9| - 5
involves:
1) shifting the graph horizontally 9 units to the left (with the subtraction of -9 from the variable "x", getting x+9 inside the absolute value symbols, and
2) shifting its graph 5 units down by subtracting 5 from the full expression
Andrea makes Mother's Day bouquets each year for extra income. This year her goal is to make $300. If she sells each bouquet for $12.50, how many bouquets must she sell to reach her goal?
Answer:
24 bouquet
Step-by-step explanation:
300 divide by 12.50
Find the distance between the two points rounding to the nearest tenth (if necessary).
(4,2) and (8,8)
Answer:
≈ 7.2
Step-by-step explanation:
Use distance formula:
d = √(8-4)² + (8-2)²
During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $50 plus $20 per hour (including taxes). The total charge comes to $150 . Which equation can be used to calculate the number of hours, x, that Dalyn rents the boat?
Answer:
Step-by-step explanation:
10 (x + 50) = 90
how to put these in a simply form?
(-2)* (-2)* 10 *10 *10 *10.
21*21*21+(-1)(-1)(-1)(-1).
Answer:
370,4440,001
Step-by-step explanation:
(-2) • (-2) • (10) • (10) • (10) • (10) = 40,000
21 • 21 • 21 = 9261
(-1) • (-1) • (-1) • (-1) = 1
(40,000) (9261) + 1
(370,440,000) + 1 = 370,4440,001
--
exponents
(-2)² + 10⁴ + 21³ + (-1)⁴
help please so I can pass
Answer:#2 is D and #3 is false
Step-by-step explanation:
what is the length of CC’
Answer:
5.385 Units
Step-by-step explanation:
5²+2²=c²
25+4=c²
29=c²
c=√29
c=5.385
Answer:8
Step-by-step explanation:
A certain game is played on a board that shows a portion of the xy-coordinate plane. During one move in the game, a marker at a point (a,b) is first moved to the point (b,a) and then moved 3 units to the left. During such a move, a marker that is at (4,3) will be moved to
Answer: (0,4)
Step-by-step explanation:
Given: During one move in the game, a marker at a point (a,b) is first moved to the point (b,a) . (i)
And then moved 3 units to the left. (ii)
Translation rule to move a point (x,y) c units left : (x,y)→(x-c,y)
Now, (4,3) first will become (3,4) [using (i)]
Then, (3,4)→(3-3,4)=(0,4) [using (ii) and translation rule]
Hence, During such a move, a marker that is at (4,3) will be moved to (0,4).
Explain how you would find the product of 20 to the power of 12 and 20 to the power of 8. Include either the exponent rule or the expanded method in your explanation. Give your answer in exponential form.
Answer:
See explanation below
Step-by-step explanation:
Using the exponent rule for products:
[tex]x^a\,*\,x^b = x^{(a+b)}[/tex]
we can write:
[tex]20^{12}\,*\,20^8=20^{(12+8)}=20^{20}[/tex]
Juan went to the store to buy some apples. The price per pound of the apples is $4 per pound and he has a coupon for $1.25 off the final amount. With the coupon, how much would Juan have to pay to buy 4 pounds of apples? Also, write an expression for the cost to buy p pounds of apples, assuming at least one pound is purchased.
Answer:
I don’t know this one sorry
Step-by-step explanation:
A cylinder has a height of 7 in. and a diameter of 6 in. What is the volume of the cylinder to the nearest cubic inch? V = 66 in^3 V = 132 in^3 V = 198 in^3 V = 792 in^3
Answer:
The answer is
V = 198 in³Step-by-step explanation:
Volume of a cylinder = πr²h
where
h is the height
r is the radius
From the question
h = 7 in
To calculate the radius from the diameter we use the formula
radius = diameter/2
From the question
diameter = 6
radius = 6/2 = 3 in
Volume of the cylinder is
(3)²(7)π
= 9(7)π
= 63π
= 197.9203
We have the final answer as
V = 198 in³ to the nearest cubic inchHope this helps you
London is driving to a concert and needs to pay for parking. There is an automatic fee of $10 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would London have to pay for parking if she left her car in the lot for 5 hours? How much would London have to pay if she left her car in the lot for tt t hours?
Answer:
1.) 20 dollars
2.) (2t + 10) dollars
Step-by-step explanation:
Given that There is an automatic fee of $10 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot.
1.) How much total money would London have to pay for parking if she left her car in the lot for 5 hours?
5 × 2 = 10 dollars
Then add the automatic price which is $10
Therefore, London will pay a total of
10 + 10 = 20 dollars
2.) How much would London have to pay if she left her car in the lot for tt t hours?
(2 × t) + 10
2t + 10
Suppose you are a scientist who wants to grow cells. Sample 1 is a cell that divides every twenty minutes. Sample 2 is a cell that divides every thirty minutes. Will there be more cells of Sample 1 or 2 after three hours? How many more?
Answer:
a. Assuming we are starting out with the same mass or number of both cells, definitely there would be more cells of sample 2 after three hours
b. If there are equal number of both cells initially, there would be 8 times more of cell 2 than cell 1
Step-by-step explanation:
a.The first part of the question asks if there would be more cells of sample 1 or 2 after three hours.
Now, the first assumption we shall be making is that we have equal numbers or let’s say mass of both cells initially.
Okay, let’s say we have x g of both cells initially.
Now sample 1 cell divides every 20 minutes.
How many times will have divided in 3 hours? The correct way to tackle this is by knowing the number of two minutes in 3 hours.
In an hour, we have 3 20 minutes. So in 3 hours, we will have 9 20 minutes
Let’s take a look at the sample 2 cell.
it divides every 30 minutes.
Now, in an hour, we have 2 30 minutes. In 3 hours, we will be having 6 30 minutes
Since cell 2 underwent 6 divisions while cell 1 underwent 9 divisions within the same 3 hours and they both have the same mass initially, then we will have more of cell 2 after three hours.
b. We want to know by how many more.
Now, for cell 1 since the division is 9 times, and it is definitely an exponential division, the mass or amount of the original left after 9 half divisions would be;
(1/2)^9 = 1/512
So 1/512 of x would be left and that would be x/512 left
For cell 2, we have the same approach. There are six divisions.
The amount left after the 6th division would be;
(1/2)^6 = 1/64
So the amount left after the sixth division would be x * 1/64 = x/64
Now, we want to know by which amount is the division of cell 2 greater.
That would be x/64 divided by x/512 = x/64 * 512/x = 8
Please help, 20 points! :)
Step-by-step explanation:
We are given 4x+y=6x-1 to graph. The easiest way to graph is to turn this equation into slope-intercept form, which is y=mx+b.
First, we are going to subtract 4x from both sides to isolate the y variable which gets us y=2x-1, and now we have slope-intercept form. Now we're going to use what we know about the form to graph.
In such form, m is the slope and b is the y-intercept. Our b in our equation is -1, so you're going to put a dot at (0,-1) on the y-axis. Then for our slope, it is 2, but it's easier to envision as rise over run where 2 is how much we rise and 1 is how much we run (or move to the right). So from our starting point from the y-axis, we're going to move up 2 units and then to the right one unit. And with two dots on the graph, we can run a line through it which will give us our graphed line.
For safe measures, you can continue the pattern of rising 2 and running 1, or you can go down 2 and left 1, which is the opposite and yet still confines to the line.
If you don't understand this explanation, I also recommend checking out desmos! It's a graphing calculator online in which you can plug this equation in and it graphs it for you! The file I have attached to this is from desmos to help you see the graph, I hope you do well!
To solve this problem we will have to convert 4x + y = 6x - 1 to point - slope form, for simplicity --- ( 1 )
4x + y = 6x - 1,
- 2x + y = - 1,
Point - Slope Form : y = 2x - 1
Now let's graph this equation. Consider the x - intercept and y - intercept of this graph --- ( 2 )
0 = 2x - 1
2x = 1
x = 1 / 2 = 0.5 ( x - intercept ),
y = 2(0) - 1 = 0 - 1 = - 1 ( y - intercept )
We know that the x - intercept is 0.5, so we can plot the point (0, 0.5). Similarly we can plot the point ( - 1,0 ) given the y - intercept is - 1. After plotting these points we can run a line through them, creating our graph.
george is loading freight into an elevator. He notices that the weight limit for the elevator is 1000 lbs. He knows that he weighs 210 lbs. He has loaded 15 boxes into the elevator. Each box weighs 50 lbs. identify the rate of change for this situation. Plz help
Answer:
Step-by-step explanation:
The rate of change in this case is 50 pounds per box. The fixed amount that the elevator must carry is 210 pounds, which is how much he weighs. The amount that varies with additional boxes is 50 pounds per box, making it the rate of change. If this situation was graphed, George's weight would be the y-intercept and the rate of change would be the slope.
3-3+x^3+6x^3-3y-3-4x^3
Answer:
3x³ - 3y - 3 or 3(x³ - y - 1)
Step-by-step explanation:
3 - 3 + x³ + 6x³ - 3y - 3 - 4x³
group like terms
= x³ + 6x³ - 4x³ - 3y + 3 - 3 - 3
add similar terms
= 3x³ - 3y - 3 or 3(x³ - y - 1)
Let's start by solving this equation:
4(x + 4) = 7x - 5
Please answer quick
Answer: x=7
Step-by-step explanation: 4(7+4)=44. 7(7)-5=44.
Answer:
x=7
Step-by-step explanation:
4(x + 4) = 7x - 5
Distribute
4x+16 = 7x-5
Subtract 4x from each side
4x+16 -4x = 7x-5-4x
16 = 3x -5
Add 5 to each side
16+5 = 3x-5+5
21 = 3x
Divide by 3
21/3 = 3x/3
7 =x
Jake wants to find out which can of pineapple is the best buy. He has a choice of four different-size cans. Which can has the lowest unit price per ounce
Answer:
Step-by-step explanation:
why isn’t the square root of 10 an integer, answer asap please
Answer:
because the square root of 10 is an irrational number, and only rational numbers are integers. integers are whole numbers and have no fractions or decimels... hope it helps
Five less than tvice a number is equal to one half the difference of three times the number and 13. Find the number.
I think it's -3
[tex]2x - 5 = \frac{1}{2} (3x - 13)[/tex]
[tex]4x - 10 = 3x - 13[/tex]
[tex]x = - 3[/tex]
Solve for a: a - 17 = -10
Answer:
a = 7
Step-by-step explanation:
a - 17 = -10
Add 17 to each side
a - 17+17 = -10+17
a = 7
Answer:
a = 7
Step-by-step explanation:
Add 17 to each side, so it cancels out the -17. It should now looks like this: a = 7I hope this helps!
help please i don’t think constant is the right answer
Answer:
i think it is the control group sorry if i am wrong
Step-by-step explanation:
John has gross biweekly earnings of $743.61. By claiming 1 more withholding allowance, John would have $19 more in his take home pay. How many withholding allowances does John currently claim?
Answer:
Total withholding allowances are 39.
Step-by-step explanation:
Given the gross earning of John = $743.61
It is given that 1 withholding allowance = $19
Now we have to find the total number of withholding allowances. Here, the number of withholding allowances can be determined by dividing the total earnings with $19.
Number of withholding allowances = 743.61 / 19 = 39.14 or 39 (round off).
NEED HELP ASAP ALGEBRA 2
Answer:
[tex]2\sqrt{71}[/tex]
Step-by-step explanation:
[tex]a^{2} + b^{2}=c^{2}[/tex]
[tex]59+225=284[/tex]
[tex]\sqrt{284}= 2\sqrt{71}[/tex]
Answer:
c=[tex]2\sqrt{71}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\15^{2} +(\sqrt{59} )^{2}=c^{2}\\225+59=c^{2}\\284=c^{2} \\2\sqrt{71} =c[/tex]
Rewrite in simplest terms: - 10(5t + 5) – 10(10t + 6)
Answer:
Hey there!
10(5t+5)-10(10t+6)
50t+50-100t-60
-50t-10
Let me know if this helps :)
which is a subset of {1, 2, 4, 5, 6}?
{0, 1, 2}
{3, 4}
{5, 6, 7}
{2, 6}
(believe its the last one but just want to make sure)
Answer:
{2, 6}
Step-by-step explanation:
Subset: A subset is a set of which all the element are contained or can be find in the universal set.
From the question above,
μ = {1,2,4,5,6}
* The first option {0,1,2} is wrong because 0 is not contained in the universal set.
* The second option {3,4} is wrong because, 3 is not contained in the universal set.
* The third option {5,6,7} is wrong because 7 is not contained in the universal set.
* The last option {2,6} is correct because all of the element of the set are contained in the universal set, and as such makes it a subset.
Hence the subset of {1,2,4,5,6} is {2, 6}