Answer:
Remainder=35.25
Quotient = 2x²+8x+10.7
Joshua has a ladder that is 18 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78°. Will the ladder be safe at this height?
For safety reasons \theta should not be greater than 70 and with the current scenario\theta= 79.52
the ladder will not be safe at this height
\theta= 79.52
ArithmeticQuestion Parameters:
Joshua has a ladder that is 18 ft long.
He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft
Generally the equation for the angle ABC is mathematically given as
Let ∠ABC = \theta
In the right angle triangle ACB,
Hence
sin ∠ABC = AC / AB
sin \theta = 17.7 / 18
[tex]\theta = sin-1 (17.7 / 18)\\\\\theta = 79.52[/tex]
For more information on Arithmetic
https://brainly.com/question/22568180
Solve:
Analee, Natalie, Connor, and Patrick placed 1st, 2nd, 3rd, and 4th in a pie-eating contest. their last names are Adams, Baker, Coaster, and Davis, find out each person's full name and place in the contest.
1. Baker said that she would have placed higher if she didn't have to eat blueberry pie.
2. Patrick ranked higher than Davis but lower than Natalie.
3. Coaster's father was proud of her for eating so much pie.
4. Analee ranked lower than Adams.
5. Connor did not come in 3rd.
The correct order and names are 1. Natalia Coaster, 2. Patrick Adams, 3. Analee Baker, 4. Connor Davis.
How to find the correct order?The best strategy is to read one by one the clues and determine possible order and names.
1. Statements 1 and 3 show Baker and Coaster are girls; therefore, Adams and Davis are boys.2. Statement 2 shows the order is: Natalie - Patrick - DavisSince Davis is a boy we can conclude he is Connor Davis and Patrick's last name is Adams.3. Statements 4 and 5 show Analee was the third one because otherwise Connor would be the third one and this is not true. The order is:Natalie - Patrick - Analee - Davis4. Natalie's last name is Coaster because Coaster was the girl who ate a lot of pie, while Analee did not. This means the answer is:Natalia Coaster.Patrick Adams.Analee Baker.Connor Davis.Learn more about clues in: https://brainly.com/question/18250989
Reflect about the line x=5
Hope it helps you mate
have a good night
If it is reflected about the line x = 5, the new point is (3, 2), (3, 6), (1, 1) and (1, 8)
Transformation
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Given the figure with vertices at (7, 2), (7, 6), (9, 1) and (9, 8). If it is reflected about the line x = 5, the new point is (3, 2), (3, 6), (1, 1) and (1, 8)
find out more on Transformation at: https://brainly.com/question/1462871
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12x-20y= 60
Answer:
[tex]y=\frac{3}{5} x-3[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx+ b
m = slope
b = y-intercept
Rearrange the equation:
[tex]-20y=-12x+60[/tex]
Divide each side by -20:
[tex]\frac{-20y}{-20} =\frac{-12x}{-20} +\frac{60}{-20}[/tex]
[tex]y=\frac{3}{5} x-3[/tex]
[tex]y=\frac{3}{5} x-3[/tex] is your simplified, slope-intercept form equation.
A teacher writes the expression 3 (6m + 3) and asks for students to write equivalent expressions. The table shows the students' responses.
Student
1
2
3
4
Response
9m + 6
18m + 3
18m + 9
21m
Select the best answer from the choices below:
Student 1 is correct because distributing the 3 in the teacher's expression yields Om + 6
Student 2 is correct because distributing the 3 in the teacher's expression yields 18m + 3
Student 3 is correct because distributing the 3 in the teacher's expression yields 18m + 9
Student 4 is correct because distributing the 3 in the teacher's expression, and then adding the two terms together yields 21m
What is the volume of the sphere in terms of 17
1 =
Itin.
6 in.
Answer:
V = 288π in³
Step-by-step explanation:
[tex]V = \frac{4}{3}\pi r^3[/tex]
The radius is 6 in
[tex]V = \frac{4}{3} \pi (6)^3[/tex]
[tex]V= \frac{4}{3} \pi (216)[/tex]
[tex]V = \frac{4}{3} (216)\pi[/tex]
[tex]V=\frac{864}{3} \pi[/tex]
[tex]V = 288\pi in^3[/tex]
Factor each expression. 1. 63a − 42b
Answer:
[tex]63a - 42b \\ \\ = 21(3a - 2b)[/tex]
# be care#
a jewerly shop shop sells 240 necklaces in a month. 180 of the necklaces were sold via the shops, website, the rest were sold in a high street shop. work out the ratio of online sales. give your answer in its simplest form
Answer:
The workout ratio of the online sales to shop sales is 1:3.Anna and Sal purchased two tickets at Urban Air Adventure Park for $30.00 each. Both bought a
Gatorade afterwards. Sal used a gift card for $25.00 that he received from his aunt for his birthday.
After using the gift card, their total cost was $40.90.
What is the cost of one Gatorade? ( I mainly need the equation that would be used )
The cost of one Gatorade is $32.95.
What is the cost of one Gatorade?The total cost of both gatorade is the sum of the value of the gift card and the total cost.
Total cost of both gatorade = value of the gift card + total cost
$25 + 40.90 = $65.90
In order to determine the cost of one gatorade, divide $65.90 by 2
The cost of one gatorade = Total cost of both gatorade / 2
$65.90 / 2 = $32.95
To learn more about division, please check: https://brainly.com/question/13281206
When adding like fractions, why is the numerator the only part of the fraction that changes
What is the area of the model
Using derivatives+optimization, find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side 12.
Check the picture below atop.
we know is an equilateral triangle, meaning that all its interior angles are 60°, and thus if we run a line from the top vertex as you see there, we end up with a 30-60-90 triangle, either way there's an equation to get its height, and anyhow the altitude of it is 6√3.
As the rectangle moves up and down the triangle, with the rectangle having a width of "w" and a length of "L", the triangle that it forms above itself is a triangle, always with a base of "L" and a height of 6√3 - w.
BTW we laid the rectangle as you see on the bottom side, but laying it anywhere else it'd have ended up in the same arrangement.
well, with the bottom of the rectangle beign parallel to that of the side of the circumscribing triangle, the small upper triangle is similar to the containing triangle by AAA, and since we have similar triangles, we can say that.
[tex]\cfrac{6\sqrt{3}}{12}=\cfrac{6\sqrt{3}-w}{L}\implies \cfrac{\sqrt{3}}{2}=\cfrac{6\sqrt{3}-w}{L}\implies L\sqrt{3}=12\sqrt{3}-2w \\\\\\ L=\cfrac{12\sqrt{3}-2w}{\sqrt{3}}\implies L=12-\cfrac{2w}{\sqrt{3}}\implies L=2\left(6-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Area of the rectangle}}{A=wL\implies A(w)=w\cdot 2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies A(w)=2\left(6w-\cfrac{w^2}{\sqrt{3}} \right)[/tex]
[tex]\cfrac{dA}{dw}=2\left(6-\cfrac{2w}{\sqrt{3}} \right)\implies \cfrac{dA}{dw}=4\left(3-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ 0=4\left(3-\cfrac{w}{\sqrt{3}} \right)\implies \boxed{w=3\sqrt{3}}[/tex]
hmmm the way I usually run a 1st derivative test is, by using the critical point and slicing from it just a tiny bit, like say 3√3 - 0.000000001 to check the region on the left and then 3√3 + 0.000000001 to check the region on the right.
Check the picture at the bottom, the 1st derivative test more or less gives us those values, positive on the left-side and negative on the right-side, meaning as you can see in the arrows, is a maximum at that point.
[tex]\stackrel{\textit{we know that}}{L=2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies L=2\left(6-\cfrac{3\sqrt{3}}{\sqrt{3}} \right)\implies \boxed{L=6}[/tex]
Graph 0.04x+0.02y=0.08.
Answer: Graph attached
Answer:
view attached graph.
Step-by-step explanation:
0.04x + 0.02y = 0.08.
0.02y = -0.04x + 0.08
/0.02 /0.02
y = -2x + 4
Hope this helps!
(1 point)
1. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the
ratio of the length of the car to the length of the model?
O 18:1
01:18
09:6
06:9
Answer:
9:6
Step-by-step explanation:
Given:
Length of car = 9 feet
Length of model of car = 6 inches
Let's find the ratio of the length of the car to the length of the model.
To find the ratio of the length of the car to the length of the model, apply the formula:
Ratio ==> Length of car : Length of model
Ratio ==> 9 : 6
Therefore, the ratio of the length of the car to the length of the model is = 9 : 6
Please help. Thanks!
Answer:
not sure about this question
Please help me with this
Answer:
I think -1 cuz 2+1--1 so yh I guess
8) You and your friends go out for lunch. You decide to tip the waiter 25%. The total bill is . $78.52.
How to figure out the volume for a 3/4 cylinder
With height of 28
According the contract, which of the following is not a responsibility of the HOA? a. Monitor overnight parking at least once a week b. Give a written warning for the first infraction of overnight parking c. Give a written warning for the second infraction of overnight parking d. Tow the car of a homeowner who has parked in the street overnight five nights in a row.
Answer:
The correct answer is letter D: tow the car of a homeowner who has parked in the street overnight five nights in a row.
This rule was not mentioned in the said contract. HOA specifically notified that if a person violates the rule more than three times, fines will be given to this violator.
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
did the test got it wrong but it showed the answer
Suggest why an increasing number of megacities are located in lower income countries or newly emerging economies.
Answer:
miami
Step-by-step explanation:
Kiara invested $3,500 into two accounts. One account paid 5% interest and the other paid 7. 5% interest. She earned 6% interest on the total investment. How much money did she put in each account?.
The amount invested in the account that pays a 5% interest is $2100 and the amount invested in the account that pays a 7.5% interest is $1400.
What are the simultaneous equations that can be used to represent the question?0.05a + 0.075b = (0.06 x $3500)
0.05a + 0.075b = $210 equation 1
a + b = $3,500 equation 2
Where:
a = amount invested in the account that paid a 5% interest
b = amount invested in the account that paid a 7.5% interest
How much was invested in the account that pays a 7.5% interest?
In order to determine this value, multiply equation 2 by 0,05
0.05a + 0.05b = 175 equation 3
0.025b = 35
b = $1400
How much was invested in the account that pays a 5% interest?
a + $1400 = $3500
a = $3500 - 1400
a = $2100
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Graph 0.04x+0.02y=0.08.
Answer:
see below
Step-by-step explanation:
let's convert it into slope intercept form first as it will get rid of the decimals. so we must get it to follow the form of y = mx + b.
so we must isolate the y variable:
- subtract 0.04x from both sides
- now we have 0.02y = 0.08 - 0.04x, and to follow the form this can also be 0.02y = -0.04x + 0.08
- divide both sides by 0.02
- now we have y = -2x + 4, so we know the slope is -2
now lets find the intercepts:
y intercept => set x=0
y = -2(0) + 4
y = 4
so we have (0,4)
x intercept => set y=0
0 = -2x + 4
-4 = -2x
x= 2
now we have (2,0)
graph it:
with two points (the intercepts) and the slope we can find a graph that looks like this
whats the answer for this oneeeeeeb
Answer:
x ≈ 229.8
Step-by-step explanation:
using the cosine ratio in the right triangle
cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{LM}{KM}[/tex] = [tex]\frac{71}{x}[/tex] ( multiply both sides by x )
x × cos72° = 71 ( divide both sides by cos72° )
x = [tex]\frac{71}{cos72}[/tex] ≈ 229.8 ( to the nearest tenth )
please help! with explanation please
Answer:
x = 13.773
Step-by-step explanation:
cos(∠ABC) = [tex]\frac{BC}{AB}[/tex]
cos(37°) = [tex]\frac{11}{x}[/tex]
x = 13.773
(–3f – 4g + 9) – (2 – 6f + 5g)
Write an exponential function to represent a person consuming a bag of candy in which the initial value in an is 175 pieces and the rate of decay is 20%.
We will see that the exponential decay function is:
f(x) = 175*(0.8)^x
How to find the exponential decay?
The general exponential decay is:
f(x) = A*(1- r)^x
Where:
A is the initial value.r is the rate of decay in decimal form.x is the variable, in this case is the time.Here we know that the initial value is 175, and the rate of decay is 20%. To get this in decimal form, we just divide it by 100%.
20%/100% = 0.2
Replacing that in the exponential function, we get:
f(x) = 175*(1 - 0.2)^x
f(x) = 175*(0.8)^x
If you want to learn more about exponential functions, you can read:
https://brainly.com/question/11464095
Maribel is offered a job as a paralegal at an annual base salary of $47,000. In addition, the company will pay the following benefits: a retirement contribution that is 10.5% of Maribel’s base salary, disability insurance totaling $338, medical insurance totaling $6,500, and a year-end bonus of 17% of her base salary. What is the annual value of this job to Maribel?
Answer:
66763
Step-by-step explanation:
47000*(1+0.105+0.17)+338+6500
(Please answer ASAP) A bag contains three red marbles, five green marbles, and two blue marbles.
a. What is the probability of getting a red marble?
b. What is the probability of NOT getting a red marble?
Answer:
a. 3/10
b. 7/10
Step-by-step explanation:
a. Total number of marbles = 10
Number of red marbles = 3
Probability = Number of outcomes/ Total number of outcomes
= 3/10
b. Total number of marbles = 10
Number of red marbles = 3
Number of marbles excluding the red marbles
= 10 - 3 = 7
Probability = Number of outcomes/ Total number of outcomes
= 7/10
Which statements are true? Check all that apply.
0 6>4
10 9
0 2>7
O 7 < 5
10 12
O 2 < 5
11
음
> 11
20
Answer:
06>4
Step-by-step explanation:
yes that. is the answer because 06 is greater than 4
Please educated people solve my question.. i asked it an hour ago nobody knows it
AB = AX+XB = 6+18 = 24
The ratio of AB to AX is AB/AX = 24/6 = 4
AC = AY+YC = 10+25 = 35
The ratio of AC to AY is AC/AY = 25/10 = 3.5
The results of each division are 4 and 3.5
We do not get the same result, which means that the proportion [tex]\frac{AB}{AX} = \frac{AC}{AY}[/tex] is not true. This is sufficient to prove that the triangles aren't similar. We need them to be in proportion so that we can use the SAS similarity rule.
Answer: The triangles aren't similar