There is an infinite number of length-width pairs that will result in a diagonal value of c.
Let a = the length. This is unknown.
Let b = the width. This is unknown.
Let c = the diagonal. This is a known value.
We have a right triangle with side a, side b, and hypotenuse c.
Since this is a right triangle, we will use the Pythagorean Theorem.
What is the Pythagoras theorem?
The Pythagorean Theorem is
[tex]c^2 = a^2 + b^2.[/tex]
Rearranging this formula gives
[tex]a^2 = c^2 - b^2[/tex]
And,[tex]a = \sqrt{(c^2 - b^2)}[/tex]
Now, if you chose a value for the width, b, then you can compute the corresponding for the length, b, since c is a known value. If you chose another value for the width, you can compute the length value corresponding to your width value.
There is an infinite number of length-width pairs that will result in a diagonal value of c.
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If you vertically stretch the exponential function f(x)=2^x by a factor of 3 what is the equation of the new function
The new equation will become f(x) = 3([tex]2^{x}[/tex]).
The given information is the stretch factor which is 3 and the equation f(x)=[tex]2^{x}[/tex].
When there is a vertical strecth factor, you need to multiply the equation by the stretch factor.
By stretching the function, the value of y has to be multiplied by 3, will now be equal to 3f(x)
The new equation will become f(x) = 3([tex]2^{x}[/tex]).
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how many solutions exists for the given equation?
3x+13=3(x+6)+1
Answer:
No Solutions.
Step-by-step explanation:
original equation
3x+13 = 3(x+6)+1
distribute 3
3x+13 = 3x+18+1
simplify
3x+13 = 3x+19
since the slope is the same for both equations and the y-intercept is different the two equations are parallel meaning they will never intersect so there are no solutions.
Answer:
No solutions
Step-by-step explanation:
3x + 13 = 3 (x + 6) + 1
3x + 13 = 3x + 18 + 1
3x + 13 = 3x + 19
3x + 13 = 3x + 19 meaning no solution since they aren't equivalent to each other
can disjunction introduction (either ∨il or ∨ir ) be used to derive any type of formula other than a disjunction?
It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
What is Disjunction Introduction?A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.
It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
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Express cos L as a fraction in simplest terms
Answer:
cos L = [tex]\frac{23}{25}[/tex]
Step-by-step explanation:
cos L = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{JL}[/tex] = [tex]\frac{23}{25}[/tex]
Write the ratio using fraction notation and reduce.
HINT: Be sure to compare like units.
$5 to $35
A. 7
B. 15
C. 5
D. 17
The ratio using fraction notation of $5 to $35 would be 7.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
To convert a ratio into a fraction,
We will simply use the first number as the numerator and the second number as the denominator.
So the fraction = 35/5.
= 7
Since there are no more common factors, the fraction is in its lowest form which is 7.
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What is the standard form of 0.00849
Answer:
8.49 × 10⁻³
Explanation:
Standard form of a number: A. × 10ᵇ
(where 'A' is the number, b is the exponent over 10)
For the number "0.00849", move the decimal point 3 places right so the exponent of 10 is -3.
Standard form: 8.49 × 10⁻³
Other examples of standard/scientific forms are: standard forms
i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²
ii) 4030, move the decimal point 3 places left = 4.03 × 10³
Answer:
when a number is given in that manner you have to take that decimal between two whole numbers.
and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answer:
the first one listed (y = -[tex]2^{x}[/tex] + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= -[tex]2^x\\[/tex] + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= [tex]-2^x[/tex] + 4
(I chose which graph to test by looking to see which option seemed right)
Can someone help me ASAP.
Answer:
A. JK and LM lie in the same plane
B. JK and LM do not intersect
E. JK and LM are parallel
Step-by-step explanation:
hope this helped
What is the value of y? 17.5ft 12.5ft 11.6ft 16.5ft
Answer:
y = 16.5 ft
Step-by-step explanation:
• in the right triangle BCD :
cos(∠BCD) = 8/14
________
• In the right triangle ABC :
cos(∠BCA) = 14/(8+y)
________
Since ∠BCD and ∠BCA are the same one
then
cos(∠BCD) = cos(∠BCA)
Therefore
[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]
[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]
[tex]\Longleftrightarrow 8y+64=196[/tex]
[tex]\Longleftrightarrow 8y=196-64[/tex]
[tex]\Longleftrightarrow 8y=132[/tex]
[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]
[tex]\Longleftrightarrow y=16.5[/tex]
Find the value of x. Round the length to the nearest tenth.
Answer:
5.1 yd
Step-by-step explanation:
tan(25°) = x/11
x = 11tan(25°)=5.1 yd
4, 2.5, 1, -0.5, -2, , ,
which number is after -2
Answer:
The number after - 2 is - 3.5.
Step-by-step explanation:
Follow the pattern
Let the number be after -2
as in the question after 4 we have 2.5 then 1 and so on.
if we subtract 4 from 2.5 we get
2.5 - 4 = -1.5
similarly: 1 - 2.5 = -1.5
-0.5 - 1 = -1.5
and now
x -(-2) = - 1.5
x = - 1.5 -2
x = - 3.5
so the number after - 2 is - 3.5.
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Identify the height of a triangle in which b=12 m and A=(18x−6) m^2. SHOW YOUR WORK!!!
Answer:
[tex]3x-1[/tex]
Step-by-step explanation:
The formula to find the area of a triangle:
[tex]A = \frac{bh}{2}[/tex]
Here, [tex]A[/tex] is the area, [tex]b[/tex] is the base and [tex]h[/tex] is the height.
However, we are looking for height, so let's rearrange the equation for [tex]h[/tex]:
[tex]A = \frac{bh}{2}\\2A = bh\\h = \frac{2A}{b}[/tex]
Now we know the formula to find the height, let's do so:
[tex]h = \frac{2(18x-6)}{12}\\\\h = \frac{36x-12}{12}\\\\h = 3x - 1[/tex]
Therefore, our final answer is [tex]3x-1[/tex].
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
What is the value of f^-1 (-3)
According to the plot of [tex]f(x)[/tex], whose curve passes through the point (-5, -3), we have
[tex]f(-5) = -3 \implies f^{-1}(-3) = \boxed{-5}[/tex]
5/8 divided by 15/32
Answer: [tex]\frac{4}{3}[/tex] or about 1.333
Step-by-step explanation:
We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.
[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]
Answer: 4/3
Step-by-step explanation:
find the reciprocal of the divisor
15/32
32/15
Now multiply it with the dividend
5/8
15/32
=5/8
32/15
=5/32
8/15
=160/120
after reducing the fraction the answer is 4/3
in mix form 1 1/3
I want to verify my work answer for the below SSAT question.
Thank you
Cindy throws a rock in the air. The rock's height, y, in feet, with respect to time, x, in seconds can be modeled by the function y=-2x^2+10x+28. When does the rock hit the ground in seconds
My work:
y=-2x^2+10x+28
0= -2(x^2-5x-14) (While knowing that the zero is supposed to be there, I don't understand why 0= -2(x^2-5x-14) )
(x-7)(x+2)
(-7,+2)
I put 2 as the answer, but when checking it was 7?
What part did I do wrong?
Answer:
7
Step-by-step explanation:
You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may assume that the ground is y=0, unless the problem says otherwise.
Ok so where you went wrong is that when you factored out and got
(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have
x-7 = 0
and
x+2 = 0
and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.
This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.
Good luck with your exam !
Answer:
7 seconds
Step-by-step explanation:
Given function:
[tex]y=-2x^2+10x+28[/tex]
where:
y = height above the ground (in feet)x = time (in seconds)To find the time when the rock hits the ground, set the equation to zero and solve for x.
First, simplify by factoring out the common term -2:
[tex]\implies -2(x^2-5x-14)=0[/tex]
Divide both sides by -2:
[tex]\implies x^2-5x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -14=-14[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-7x+2x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-7)+2(x-7)=0[/tex]
Factor out the common term (x - 7):
[tex]\implies (x+2)(x-7)=0[/tex]
Therefore:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-7=0 \implies x=7[/tex]
As time cannot be negative, the rock hits the ground in 7 seconds.
Here is a list of ages (years) of children in a room:
8
,
8
,
9
,
5
,
10
,
4
,
9
State the median.
Answer:
5
Step-by-step explanation:
median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9
the median is 5 because left and right middle is 5 that's why it is median
What is the volume of the sphere shown below?
O A. π units3
676
3
8788
3
C. 52 units 3
OD. 104 units3
B.
π units³
-13-
Answer:
B
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ( r is the radius )
here r = 13 , then
V = [tex]\frac{4}{3}[/tex] π × 13³ = [tex]\frac{4}{3}[/tex] π × 2197 = [tex]\frac{4(2197)}{3}[/tex] π = [tex]\frac{8788}{3}[/tex] π units³
The solution is, B. 8788/3 * π units³ is the volume of the sphere shown below.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
the volume (V) of a sphere is calculated as
V = 4/3 πr³ ( r is the radius )
now, we have,
from the given figure, we get,
here r = 13 , then
V = 4/3* π × 13³
= 4/3* π × 2197
= 8788/3 * π units³
Hence, The solution is, B. 8788/3 * π units³ is the volume of the sphere shown below.
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Here are the results of a survey that students conducted at a mall. the students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos. at least one tattoo no tattoo row totals age 18-19 170 320 490 age 30-50 60 445 505 column totals 230 765 995 we randomly select a person who responded to this survey. which calculation gives the probability that the person has a tattoo
Using it's concept, it is found that there is a 0.2312 = 23.12% probability that the person has a tattoo.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 995 people were surveyed, out of which 230 have tattoos, hence the probability is given by:
p = 230/995 = 0.2312.
0.2312 = 23.12% probability that the person has a tattoo.
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PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3 , 6
Step-by-step explanation:
Answer: (2,-3), (2, -3)
Step-by-step explanation: Substitute 2 into each equation. See Attachment and don’t forget to check the work just in case ;)
Kelsey has $100 in an account the interest-rate is 11% compounded annually to the nearest cent how much will she have in two years
Answer:
$123.21 (nearest cent)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
P = $100r = 11% = 0.11t = 2 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=100\left(1+0.11\right)^{2}[/tex]
[tex]\implies \sf A=100\left(1.11\right)^{2}[/tex]
[tex]\implies \sf A=123.21[/tex]
Therefore, the value of the account in 2 years will be $123.21 (nearest cent).
A car drives at a speed of 90 km/h for 2 hours and 20 minutes
How far does the car drive?
Answer:
210km
Step-by-step explanation:
2hours = 180km
2hours = 120minutes
40mins =180/3
=60km
20mins=60/2
=30km
2h and 20mins =30+180
=210km
Answer:
210kms
Step-by-step explanation:
Speed of the car per hour = 90km/h
or, speed of the car per minute = 90/60kms=1.5km/minute
Now,
car drives for 2hours and 20 minutes
or, (2*60 +20) minutes= 140minutes
Distance of the car drive= minutes travelled* speed per minute
= 140*1.5kms
=210kms
whats 27 x 300 / 34 x 6
Answer:
Use Calculator:
Approximately. 1429.411
Step-by-step explanation:
Hope it Helps!!!
The coefficient of 8 · 2N is
Answer:
The coefficient is 2
1. What are you going to make? (6 points) (Note: The maximum
build size is 25 cm by 16 cm by 15 cm - about the size of a small
shoe box.)
Answer: You have already given the answer in the question! You can make a small shoe box.
Identify the constant of proportionality from the table.
xy
3 6
4 8
7 14
9 18
describe the effect of the transformation (x,y) to (x,y+4)
A. vertical stretch without reflection
B. horizontal translation of 4 units
C. vertical stretch with reflection
D. Vertical translation of 4 units
help please!!!!!!!!!
Does this graph represent a function? Why or why not?
Answer:
the answer is D
Step-by-step explanation:
I'm not good at explaining but, it is because the line is not touching more than 1 point on the graph. Basically making it pass the vertical line test, therefore making the answer D.
Good luck, hope this helps !!!
Five sisters bought a present for their mother. They received a 10% discount on the original price of the gift. After the discount was taken, each sister paid $5.40. What was the original price of the gift?
I need an answer soon! Pleasle
Answer:
$30 is the original price.
Step-by-step explanation:
Let x be the original price of the gift. The sisters got a 10% discount, so the price paid by them is 0.90x.
The five sisters each paid $5.40, so the total they paid was:
5*($5.40) = $27.
This is equal to the 0.90x:
0.90x = $27
x = $27/0.90
x = $30
Chocolates
