What is the length of the ladder? It is 6 ft. from the house at the bottom and touches the wall 14 ft. up at the top. Simplify your answer
Answer:
15.2
[tex] {c }^{2} = {a}^{2} + {b}^{2} \: \\ {c}^{2} ={6}^{2} + {14}^{2} \\ {c}^{2} = 36 + 196 \\ {c}^{2} = 232 \\ \sqrt{c } = \sqrt{232} \\ c = 15.23154621[/tex]
2. Which group of numbers is in size order?
A. 3.10 - 3.20 - 3.09 - 3.55
B. 3.09 - 3.10 - 3.2 - 3.5
C. 3.10 - 3.20 - 3.09 - 3.55
D. 3.1 - 3.55 - 3.2 - 3.09
Answer:
B. 3.09-3.10-3.2-3.5 is the answer
On the first day of December, 34,789 people went to the mall. On the second day 63,587 people went to the mall. How many people went to the mall over the two days
Answer:
98376
Step-by-step explanation:
Show that 5x^2 + 2x - 3 < 0 can be written in the form | x + 1/5 | < 4/5
if possible with the explanation as well
Step-by-step explanation:
First let solve the inequality
[tex]5 {x}^{2} + 2x - 3 < 0[/tex]
Factor by grouping
[tex]5 {x}^{2} + 5x - 3x - 3 < 0[/tex]
[tex]5x(x + 1) - 3(x + 1)[/tex]
So the factor are
[tex](5x - 3)(x + 1)[/tex]
So the factor are
[tex]x = \frac{3}{5} [/tex]
and
[tex]x = - 1[/tex]
Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics
creates 2 roots and/or double roots.
The inequality
[tex] |x - b| < c[/tex]
works as
b is the midpoint between 2 roots. And c is the
[tex] |x + b| = c[/tex]
We know that the midpoint between both roots is-1/5.
so
[tex] |x - ( - \frac{1}{5} )| < c[/tex]
[tex] |x + \frac{1}{5} | < c[/tex]
Let use roots 3/5
[tex] | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} [/tex]
-1 works as well.
[tex] | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} [/tex]
So the absolute value equation is
[tex] |x + \frac{1}{5} | < \frac{4}{5} [/tex]
Kristen is creating a rectangular garden in her back yard. The length of the garden is 13 feet. The perimeter of the garden must be at least 54 feet and no more than 82 feet.
3 kom 2.7 Eve carves a shape out of wood. What is the volume of the shap 3 cm 1 cm 2 cm 3 cm 4 cm
Answer:
50cm
Step-by-step explanation:
oh apdiya I just wanted to let you
how to calculate bearing
Answer:
Step-by-step explanation:
You will have to interpret the question with the aid of a diagram and make out the relevant angles and either make use of cosine rule,sine rule etc....Your knowledge on angles should be sound
A wall is 1200 sq ft.
A gallon of paint covers 200 sq ft.
Complete the conversion factor: 1 gallon / ? sq ft
Write the number in expanded form 99,763
Answer:
90,000+9,000+700+60+3
Answer:
90,000 + 9,000 + 700 + 60 + 3 I hope this helped
6. The unit circle with center at the origin is a relation but not a function.
Find the two functions which are semicircles of the unit circle, and determin
e
their domains and ranges?
b. Are these functions onto functions? Justify.
c. Find the two functions which are lie in one of the semicircle in part a, and
determine their domains and ranges?
d. Are these functions one to one correspondence functions? Justify.
Whi
Answer:
Step-by-step explanation:
What is the range of exponential function g?
The range of the exponential function is: B. [tex]g(x)>-6[/tex]
Recall:
Range of any function includes all possible values of y (output)
Domain of any function includes all possible values of x (input).
Thus:
The values of y in the exponential function greater than -6 on the y-axis as shown in the graph given.
Therefore:
Range of the exponential function given in the graph is: B. [tex]g(x)>-6[/tex].
Learn more about exponential function here:
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4 2/3 - (1 4/5). PLEASE HELP MEEEEE
Answer: 2 13/ 15
Step-by-step explanation:
1) A spinner is divided into equal red, blue, green,
red, black, and yellow sections. What's the
probability of spinning green and then red.
Answer:
1/18
Step-by-step explanation:
Probability of spinning red=2/6=1/3
Probability of spinning green=1/6
probability of spinning green and then red=(1/6)*(1/3)=1/18
Use the order of operations to evaluate the expression below.
3 + 5 x 5 - 50 ÷ 2 + 3 - 4
Answer here
Answer:
2
Step-by-step explanation:
=3+5×5-25+3-4
=3+25-25+3-4
=28-22-4
=28-26
=2
Answer:
2
Step-by-step explanation:
3 + 5 * 5 - 50 / 2 + 3 - 4
3 + (5 * 5) - 50 / 2 + 3 - 4 => Multiplication what ever comes first
3 + 25 (-50 / 2) + 3 - 4 => Division left to right
(3 + 25) - 25 +( 3 - 4) => Addition what ever comes first
28 - 25 - 1 => Substraction left to right
2
Leave comment if you're curious.
If AB is parallel to DE, then CD is:
Answer:
4
Step-by-step explanation:
because BC=CD as it is parallel that means all the sides are equal
The value of CD is 20/3.
The correct option is (A).
What is Similarity in Triangles?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
In ACB and ECD,
angle CAB= angle DEC
angle CBA= angle EDC
angle DCE = angle ACB
By, AA similarity criteria,
ΔACB~ΔECD
Now,
AC/CE= BC/CD
3/5=4/CD
CD= 20/3
Learn more about similarity property here:
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Let A={1,2,3,4,5,6,7,8}A={1,2,3,4,5,6,7,8}. Define a relation ∼∼ on AA by a∼ba∼b if and only if 33 divides a−ba−b for all a,b∈Aa,b∈A. 1. Find all the pairs (a,b)∈A×A(a,b)∈A×A such that a∼ba∼b. 2. Show that ∼∼ is an equivalence relation on AA. 3. Find the equivalence classes [2][2] and [3][3].
Define relation.
Let A and B are only two non-empty set,then A*B is cartesian product of A*B.Then any subset of A*B is known as the relation fromA to B.
Choose the best description of the commutative property of addition,
O A. When zero is added to a number, the sum is that number.
OB. If two numbers are added in opposite orders, their sum is 0.
O C. The order in which numbers are added does not affect the sum.
D. Numbers should be added in order from smallest to largest.
9514 1404 393
Answer:
C. The order in which numbers are added does not affect the sum.
Step-by-step explanation:
In symbols, the commutative property of addition is ...
a +b = b +a
The order in which numbers are added does not affect the sum.
Answer this question.
Answer:
B) Both functions have a y-intercept of -2.
Step-by-step explanation:
Hi there!
A) Both functions are always increasing.
⇒ False
Let's first take a look at the given equation, [tex]y=3x-2[/tex]. This is a linear equation, and it is organized in slope-intercept form: [tex]y=mx+b[/tex]. m is the slope and b is the y-intercept. When m is positive, it is always increasing.
In [tex]y=3x-2[/tex], 3 is m, and because it's positive, this line is always increasing on a graph.
However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).
B) Both functions have a y-intercept of -2.
⇒ True
In the given equation [tex]y=3x-2[/tex], this is true. -2 is the y-intercept.
On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.
C) Both functions are symmetric about the y-axis.
⇒ False
The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form [tex]y=b[/tex], which isn't the case here with [tex]y=3x-2[/tex]. [tex]y=3x-2[/tex] has a slope.
D) Both functions are linear relationships.
⇒ False
Sure, [tex]y=3x-2[/tex] is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.
I hope this helps!
what is the distance between the points (7, 8) and (9, 10).
Solve M = 5rt^2- 2rv for v.
Can someone please help with this I’ll put it to 100 points
Answer:
(M-5rt^2)/(-2r) =v
Step-by-step explanation:
M = 5rt^2- 2rv
Subtract 5rt^2 from each side
M-5rt^2 = 5rt^2- 2rv -5rt^2
M-5rt^2 = - 2rv
Divide each side by -2r
(M-5rt^2)/(-2r) =- 2rv / (-2r)
(M-5rt^2)/(-2r) =v
Answer:
[tex]v = -\frac{M-5rt^2}{2r}[/tex]
Step-by-step explanation:
[tex]M = 5rt^2 - 2rv[/tex]
Switch sides
[tex]5rt^2-2rv=M[/tex]
Subtract [tex]5rt^2[/tex] from both sides
[tex]5rt^2 - 2rv-5rt^2= M -5rt^2[/tex]
Simplify
[tex]-2rv = M - 5rt^2[/tex]
Divide both sides by [tex]-2r[/tex]
[tex]\frac{-2rv}{-2r} =\frac{M}{-2r} -\frac{5rt^2}{-2r}[/tex]
Simplify
[tex]-\frac{M-5rt^2}{2r}[/tex]
Rewrite as a product of the GCF and another sum 36 + 48
Answer:
72+12
Step-by-step explanation:
HELP!! TRUTH TABLE
I would really appreciate it, if someone could walk me through how they did it! Thanks.
p ∧ q (i.e. "p and q") is true only if both p and q are true. This is the case for the first two rows, but not the third.
Similarly, (p ∧ q) ∧ r is true only if both p ∧ q and r are true. We know when p ∧ q is true, so (p ∧ q) ∧ r is true only when all three of p, q, and r are true. This happens only in the first row.
All other cases are false.
The table should look like this:
[tex]\begin{array}{c|c|c|c|c}p&q&r&p\land q&(p\land q)\land r) \\---&---&---&---&--- \\T&T&T&\boxed T&\boxed T\\&&&&\\T&T&F&\boxed T&\boxed F\\&&&&\\T&F&T&\boxed F&\boxed F\end{array}[/tex]
The perimeter of the square with side length y
Answer:
4y
Step-by-step explanation:
Answer:
perimeter=4y
Step-by-step explanation:
y+y+y+y=4y
..........
8 thousands + 4 thousands
What is the answer in standard form?
Answer:
12000
Step-by-step explanation:
8000+4000=12000
100 yojan=how much km?
Answer:
100 yojan=how much km
1287.48
please brainlist
graph the sequence 2, 4, 6, 8, 10
Answer:
going up in even numbers
Step-by-step explanation:
its like the two times table, and it goes up in even numbers
Answer:
any number you can take
Step-by-step explanation:
like 4'6'8''12
2. STEM A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm more than or less than 100 ohms. Resistors A and B are rejected. Resistor A's resistance differs from 100 ohms by 0.15 ohm. Resistor B's resistance differs from 100 ohms by -0.78 ohm. How do the resistances of these two resistors compare? Explain.
The comparison of both resistors is defined by an inequality. Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
Given that:
[tex]R = 100 \Omega[/tex] ---- the reference resistor
First, we calculate the resistance of both resistors
Resistor A differs by [tex]0.15\Omega[/tex] means that:
[tex]R_A = 100\Omega + 0.15\Omega[/tex]
[tex]R_A = 100.15\Omega[/tex]
Resistor A has a resistance of [tex]100.15\Omega[/tex]
Resistor B differs by [tex]-0.78\Omega[/tex] means that:
[tex]R_B = 100\Omega -0.78\Omega[/tex]
[tex]R_B = 99.22\Omega[/tex]
Resistor B has a resistance of [tex]99.22\Omega[/tex]
By comparing the calculated values, we can conclude that:
Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
Read more about inequality comparison at:
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I need help, NO LINKS
A mountain is 15,062 feet above sea level, and a valley is 350 feet below sea level, what is the difference in elevation between the mountain and the valley?
Answer:
14,712 ft difference
Step-by-step explanation:
15,062 - 350 = 14,712
Answer:
Step-by-step explanation:
Difference in elevation is 15,062-(-350)=15,062+350=15,412
A product is introduced into the market. Suppose a products sales quantity per month q(t) is a function of time t in months is given by q(t) = 5000t-120t^2. And suppose the price in dollars of that product. p(t). is also a function of time t in months and is given by p(t) = 120-t^2.
Required:
a. Find, R'(t). the rate of change of revenue as a function of time t
b. What is the the rate of change of revenue with respect to time 3 months after the introduction?
Answer:
Part A)
[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]
Part B)
After three months, the revenue is increasing at a rate of $391,560 per month.
Step-by-step explanation:
A product is introduced into the market. The quantity per month q sold is given by the function:
[tex]q(t) = 5000t - 120t^2[/tex]
And the price p (in dollars) of the product is given by the function:
[tex]p(t) = 120-t^2[/tex]
Part A)
R(t), or the revenue, will be the product of the quantity sold and its respective price during the month. Hence:
[tex]\displaystyle R(t) = q(t)\cdot p(t)[/tex]
Substitute:
[tex]\displaystyle R(t) = \left(5000t-120t^2\right)\left(120-t^2\right)[/tex]
To find R'(t), take the derivative of both sides with respect to t:
[tex]\displaystyle R'(t) = \frac{d}{dt}\left[ \left(5000t-120t^2\right)\left(120-t^2\right)\right][/tex]
Since the function is a product of two expressions, we can consider using the Product Rule:
[tex]\displaystyle \frac{d}{dx} \left[uv\right] = u'v+uv'[/tex]
Hence:
[tex]\displaystyle R'(t) = \frac{d}{dt}\left[5000t-120t^2\right]\left(120-t^2\right) + \left(5000t-120t^2\right)\frac{d}{dt}\left[120-t^2\right][/tex]
Differentiate. Therefore:
[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]
(We may simplify if we desire, but this is not required by the problem.)
Part B)
To find the rate of change of revenue with respect to time three months after the introduction, we can evaluate R'(t) at t = 3. Hence:
[tex]\displaystyle R'(3) = (5000-240(3))(120-(3)^2)+(5000(3)-120(3)^2)(-2(3))[/tex]
Evaluate:
[tex]R'(3) = 391560\text{ dollars/month}[/tex]
In conclusion, after three months, the revenue is increasing at a rate of $391,560 per month.
(Note: it is increasing because the final value is positive.)