Answer:
Initial speed is 32 m/s
At uniform speed, acceleration is 0, (a = 0).
When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.
From first equation of motion:
[tex]{ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}[/tex]
substitute:
[tex]{ \tt{2.78 = (a \times 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^{ - 2} }}[/tex]
from second equation of motion:
[tex]{ \boxed{ \bf{s = ut + \frac{1}{2} a {t}^{2} }}}[/tex]
substitute:
[tex]{ \tt{60000 = 1800u + ( \frac{1}{2} \times 0.0015 \times {1800}^{2}) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^{ - 1} }}[/tex]
ABCDEFGHIJ is a regular decagon and the measure of <D is 144º. What is the measure of <A?
A) 90°
B) 100°
C) 144°
D 220°
ABC is an equilateral triangle and the measure of <A is 60°. What is the measure of <C?
A) 45°
B) 60°
C) 90°
D) 180°
Answer:
1. 144⁰
2. 60⁰
Step-by-step explanation:
The formula to find the measure of the interior angles of a regular polygon is:
m< = (n - 2) • 180/n where n = the number of sides
For a decagon, there are 10 sides.
m< = (10-2) • 180/10 = 144°
A regular polygon/equilateral triangle is defined as having equal sides and angles.
Answer:
given ABCDEFGHIJ is a decagon
As we know the sum of all ten interior angles of a decagon = 1440°
so measure of each angle of decagon = (1440/10)° = 144°
so the measure of ∠A would be 144° (C)
given Δ ABC is a equilateral triangle
As we know the sum of all three interior angles of a equialter traingle = 180°
so if one angle of an equilateral triangle is 60°
then the remaining of the angles would have the measure of 60° each
So answer = 60°(B)
Hope it helps
Describe the process of creating a linear equation using two points and the point-slope form
Answer:
First find the slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1 and (x2, t2).
Then substitute the values of the slope (m) and one of the points into the point-slope formula
y - y1 = m(x - x1)
Step-by-step explanation:
Find the slope using the slope formula
Use the slope and one of the points to solve for the y-intercept (b).
One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
HELPPP HELP PLS PRONTO ASAP
Ahmed is working at a restaurant. His boss pays him $16.00 per hour and
promises a raise of $1.25 per hour every 6 months. Which sequence
describes Ahmed's expected hourly wages, in dollars, starting with his current
wage?
Answer:
B
Step-by-step explanation:
each of the numbers is just adding 1.25 on to it
Answer: Choice B
16.00, 17.25, 18.50, 19.75, ...
==========================================================
Explanation:
We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.
Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.
We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25
The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.
Daniel incorrectly solved the equations shown. Explain what he did wrong in each situation and then solve both equations correctly. 16x2 - 9 = 16
V16x2 - 19 - + 16
4x - 3 - +4
4x = +7
* = 14
(a)
IN
y3 - 1 = 7
= 8
(b)
y = 2
Step-by-step explanation:
the scanned description is very hard to understand.
so I think what happened :
16x² - 9 = 16
then the first error :
sqrt(16x²) - sqrt(9) = sqrt(16)
that is wrong, as you cannot split a + or - operation inside a sqrt function into + or - separate sqrt results of the parts.
so, correctly, the only possible transformation involving sqrt for both sides :
sqrt(16x² - 9) = sqrt(16)
but it would be even easier to clean up the various constant numbers with each other.
so,
16x² - 9 = 16
16x² = 25
and now we trashes the square root
sqrt(16x²) = sqrt(25)
4x = 5
x = 5/4 or x = -5/4
and I cannot see or understand for my life what the second equation was, as Daniel did something wrong, so I cannot deduct the original equation out of a supposedly wrong
y³ - 1 = 7
1. Find(x) + g(x)
4 options to pick from
What is the distance between (-5, 3) and (7, 3)? Explain using absolute values.
Use pythagoras theorem
d = √((x₁ - x₂)² + (y₁ - y₂)²)
d = √((-5 - 7)² + (3 - 3)²)
d = √((-12)² + 0)
d = √144
d = 12
Answer:
Step-by-step explanation:
distance is √((x2-x1)^2+(y2-y1)^2)
so it will be √((12)^2+(0)^2)
or simply 12. since we are calculating distance, it is always going to be positive so technecally the formula is |√((x2-x1)^2+(y2-y1)^2)|
Sally and Mia run a furniture making company. They work together to build and paint custom dressers.
Sally charges a $100 flat fee for each dresser she builds, plus $420 for each hour she spends building.
Mia charges a $150 flat fee for each dresser she paints, plus $390 for each hour she spends painting.
a) Represent what Sally charges for one dresser as a polynomial. Remember to define any variables!
b) Represent what Mia charges for one dresser as a polynomial. Remember to define any variables!
c) Write a new SIMPLIFIED polynomial that represents their total charges, together, for one dresser.
Answer:
y = 250 + 810x
Step-by-step explanation:
Let
y = total charges
x = cost per hour
Sally: building
y = 100 + 420x
Mia: painting
y = 150 + 390x
Find their total charges of building and painting
Add the total charges of both of them
y = 100 + 420x + 150 + 390x
y = 250 + 810x
Find an explicit rule for the nth term of the arithmetic sequence.
-9, -4, 1, 6, ...
Answer:
hope it's helpful
Step-by-step explanation:
glad to help
Question 4 of 40
If cose= -
5
in quadrant II, what is sine?
Step-by-step explanation:
cosx=adjacent/hypotenuse
adj=3, hyp=5
by pythagoras theorem,
opp^2+3^2=5^2
opposite=4
sine=opp/hyp
sinex=4/5 (second quadrant so sin is positive)
The solution is, The value of sin ∅ in quadrant 2 is 4/5.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
here, we have,
given that,
cos∅ = - 3/5, in quadrant II,
We have;
adjacent = -3
hypotenuse = 5
Let's find the opposite side, using Pythagorean theorem
5^2 = x^2 + (-3)^2
25 = x^2 + 9
collect like terms
x^2 = 25 - 9
x^2 = 16
x = √ 16
x = 4
We have that
sin ∅ = opposite/hypotenuse
sin ∅ = 4/5
It is important to note that the trigonometric identity 'sine' is positive in quadrant 2
sin ∅ = 4/5
Hence, the value of sin ∅ in quadrant 2 is 4/5
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please please jhelp me....
Answer:
2·v - (u + w) = (5, 0, -10)
Step-by-step explanation:
The given values of the vectors are;
u = (2, -1, 3), v = (4, 0, -2), and w = (1, 1, 3)
The required vector is 2·v - (u + w)
2 × v = 2 × (4, 0, -2) = (8, 0, -4)
(u + w) = (2, -1, 3) + (1, 1, 3) = (3, 0, 6)
Therefore;
2·v - (u + w) = (8, 0, -4) - (3, 0, 6) = (5, 0, -10)
2·v - (u + w) = (5, 0, -10)
The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
Answer:
The sample size needed is of 10,484.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars.
This means that [tex]\sigma = 88[/tex]
Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 2.327\frac{88}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 2.327*88[/tex]
[tex]\sqrt{n} = \frac{2.327*88}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*88}{2})^2[/tex]
[tex]n = 10483.3[/tex]
Rounding up:
The sample size needed is of 10,484.
If a sequence of 8 consecutive odd integers with increasing values has 9 as its seventh term. What is the sum of the terms of the sequence?
Answer:
[tex]Sum = 32[/tex]
Step-by-step explanation:
Given
Sequence = Consecutive Odds
[tex]T_7 = 9[/tex]
Required
The sum of the terms
A sequence of odd number has a difference of 2. So, the sequence is represented as:
[tex]S = \{-3,-1,1,3,5,7,9,11\}[/tex]
Add up all terms in the sequence
[tex]Sum = -3-1+1+3+5+7+9+11[/tex]
[tex]Sum = 32[/tex]
Giving brainliest! Graph and solve the inequality y≤2|x+2|-7
Show the vertex, whether it’s a dotted or solid line, and axis of symmetry, also where the graph should be filled in!
Answer:
hope this helps u......
Answer:
Step-by-step explanation:
I don't know why the graphs I have been putting in look like that. simpler way of putting it is the line is where the red and black meet. if that makes sense. I'm sorry if is doesn't. I hope this helps tho.
Find the volume of this cylinder.
As soon as possible please
Answer:
36
Step-by-step explanation:
pi (3) x 1^2 x 12 = 3 x 12 = 36
On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?
Answer:
Step-by-step explanation:
The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:
by finding the slope. Remember, that slope is the same thing as rate of change.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:
[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]
Seena’s mother is 7 times as old as Seena. After 4 years
her mother will be 4 times as old as she will be then .Find
their present ages.
Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.
Solution :✧ Let us assume :
Seena's age be x
Her mother's age be 4x
✧ After 5 years :
Seena's age = x + 5
Her mother's age = 4x + 5
✧ Ratio of age after 5 years :
Seena's mother = 3
Seena's ratio = 1
Hence, the equation is :
[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]
By cross multiplying we get
[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]
[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]
[tex] \looparrowright \frak{x = 10}[/tex]
Hence, the ages are
Seena's age = x = 10 yrs
Her mother's age = 4x = 4 × 10 = 40 years
∴ Seena's age is 10 and her mother's is 40 respectively
QUICK QUESTION! PLEASE HELP ME
Answer:
y=3/x
Step-by-step explanation:
QUESTION 1: Diagram NOT accurately drawn.
OAP is a triangle.
O to A=a
O to B=b
P is the point on AB such that AP: PB = 3:1
(b) Find OP in terms of a and b.
Give your answer in its simplest form.
Answer:
1/4a+3/4b
Step-by-step explanation:
OP=OA+AP
OA=a
AP=3/4AB
AB=-a+b
thus AP=3/4(-a+b) which is-3/4a+3/4b
OP=a-3/4a+3/4b thus 1/4a+3/4b
The sum of two rational numbers is 9 and one of them is − 3, then the other is_.( ) 10
Answer:
12
Step-by-step explanation:
let the rational number be x
x+(-3) = 9
x = 9+3 = 12
Answer:
12
Step-by-step explanation:
x + y = 9
x = -3
=>
-3 + y = 9
y = 12
The length of the pencil is 8x + 2 and length of pen is 4x + 1. Find the difference between their lengths.
Answer:
4x + 1
Step-by-step explanation:
(8x + 2) - (4x + 1)
subtract the terms that are common,,
8x-4x=4x
2-1=1
therefore, it would be 4x + 1
if you need more help with these, feel free to sub to gauthmath on subreddit
Urgent ! Help me please
Answer:
B
Step-by-step explanation:
x -> x and y -> y+5
-1 -> - 1 and - 3 -> 2, so b is the correct answer.
which of the following one is true
what is the solution?
Answer: x = 36
Step-by-step explanation:
[tex]\frac{2}{3} x-4=20\\\\\frac{2}{3} x=20+4\\\\\frac{2x}{3} =24\\\\2x=24*3\\\\x=\frac{72}{2} =36[/tex]
Which is the inverses I still don’t get this
Answer:
C.
[tex]{ \tt{f(x) = \frac{12}{x} - 18}} \: and \: { \tt{g(x) = \frac{12}{x + 18} }}[/tex]
Step-by-step explanation:
[tex]{ \tt{f(x) = \frac{12}{x} - 18}}[/tex]
Let inverse be m:
[tex]{ \tt{m = \frac{12}{x} - 18 }} \\ { \tt{x(m + 18) = 12}} \\ { \tt{x = \frac{12}{m + 18} }} \\ \\ { \boxed{ \sf{f {}^{ - 1} (x) = g(x) = \frac{12}{x + 18} }}}[/tex]
In trying to determine whether air pollution causes reduction in children's lung health a researcher proposes to see if the lung volume of 10-year-old boys who live in high ozone pollution is significantly less than the lung volume of all 10-year-old boys. The mean volume for all 10-year-old boys is 2.05 liters. A random sample of 26 10-year-old boys who live in a community with high levels of ozone pollution is found to have a mean volume of 1.98 liters, with a sample standard deviation of 0.3 liters. Test the researcher's claim that the mean lung volume of 10 -year-old boys who live in a community with high levels of ozone pollution is less than 2.05 at the 5% significance level.
Answer:
The test statistic will be "-2.33". A further explanation is provided below.
Step-by-step explanation:
According to the question,
[tex]H_0: \mu = 2.05[/tex]
[tex]H_0: \mu < 2.05[/tex]
Given:
[tex]\bar x = 1.98[/tex]
[tex]s = 0.3[/tex]
[tex]n = 100[/tex]
The test statistics will be:
⇒ [tex]t_0 = \frac{\bar x - \mu_0}{\frac{s}{\sqrt{n} } }[/tex]
[tex]=\frac{1.98-2.05}{\frac{0.3}{\sqrt{100} } }[/tex]
[tex]=-2.33[/tex]
and the P-value will be:
= [tex]0.011< \alpha[/tex]
* if my savings of $x grows 10% each year how much money would i have in 1 year
I WILL MARK BRAINLIEST
Answer:
10/100*$x
Step-by-step explanation:
You will multiply the $x by 10%
pls halp ////////////////
Answer:
9x^2 + 2x - 5
Step-by-step explanation:
7x^2 - 5x + 3
2x^2 + 7x - 8
__________
9x^2 + 2x - 5
Option B is the correct answer.
An image of a right triangle is shown with an angle labeled x.
If tan x° = e divided by 8 and sin x° = e divided by f, what is the value of cos x°?
A) cos x° = 8 divided by f
B) cos x° = f divided by 8
C) cos x° = 8f
D) cos x° = 8e
Step-by-step explanation:
here's the answer to your question
By using given trigonometric functions, Value of [tex]cosx^{0}[/tex] is [tex]\frac{8}{f}[/tex].
What are trigonometric functions?"Trigonometric functions are the basic six functions that have a domain input value as an angle of a right triangle, and a numeric answer as the range. There are six basic trigonometric functions used in Trigonometry. These functions are trigonometric ratios. The six basic trigonometric functions are sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function."
Given
[tex]sinx^{0}[/tex] = [tex]\frac{e}{f}[/tex] = [tex]\frac{Opposite Side}{Hypotenuse}[/tex]
[tex]tanx^{0}[/tex] = [tex]\frac{e}{8}[/tex] = [tex]\frac{Opposite side }{Adjacent}[/tex]
[tex]cosx^{0}[/tex] = ?
Formula to find the [tex]cosx^{0}[/tex]
[tex]cosx^{0}[/tex] = [tex]\frac{Adjacent }{Hypotenuse}[/tex]
⇒ [tex]cosx^{0}[/tex] = [tex]\frac{8}{f}[/tex]
By using given trigonometric functions, Value of [tex]cosx^{0}[/tex] is [tex]\frac{8}{f}[/tex].
Learn more about trigonometric functions here
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the unknown side of a trapezium.
Answer:
11 mm
Step-by-step explanation:
121=area of a rectangle and area of triangle
121=x*8+(0.5)*x*(14-8), 11x=121, x=11
Answer:
[tex]11mm[/tex]
Step-by-step explanation:
Let the unknown side be x
[tex]Area \: \: \: of \: \: the \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: \: the \: \: parallel \: sides) \times height \\ 121= \frac{1}{2} \times (8 + 14) \times x \\ 121 \times 2 = 22x \\ 242 = 22x \\ \frac{242}{22} = \frac{22x}{22} \\ 11 = x[/tex]
need help with this refer to picture
Answer:
Step-by-step explanation:
