a. The exact value of cosθ = -5/√74
b. The exact value of secθ = -√74/5
c. The exact value of cotθ = 5/7
How to find the trigonometric ratios
Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.
So, r = √(x² + y²) where
x = -5 and y = -7So, r = √(x² + y²)
r = √((-5)² + (-7)²)
r = √(25 + 49)
r = √74
The value of the trigonometric ratio cosθ
Since the trigonometric ratio cosθ = x/r
Substituting the values of x and r into the equation, we have
cosθ = x/r
cosθ = -5/√74
So, the exact value of cosθ = -5/√74
The value of the trigonometric ratio secθSince the trigonometric ratio, secθ = r/x
Substituting the values of x and r into the equation, we have
secθ = r/x
secθ = √74/-5
secθ = -√74/5
So, the exact value of secθ = -√74/5
The value of the trigonometric ratio cotθ
Since the trigonometric ratio cotθ = x/y
Substituting the values of x and y into the equation, we have
cotθ = x/y
cotθ = -5/-7
cotθ = 5/7
So, the exact value of cotθ = 5/7
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For what value of y does 125 =
(1/25)^y-1
Answer:
[tex] y = -\dfrac{1}{2} [/tex]
Step-by-step explanation:
I assume that y - 1 is an exponent, and the equation is
[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]
[tex] 5^3 = (5^{-2})^{y - 1} [/tex]
[tex] 5^3 = 5^{-2y + 2} [/tex]
[tex] -2y + 2 = 3 [/tex]
[tex] -2y = 1 [/tex]
[tex] y = -\dfrac{1}{2} [/tex]
en un proyecto de innovacion, se deben determinar montos para varios gastos, Se gasta un 25% en equipamiento, un quinto en salarios, un 35% en publicidad, qudando un remanente de $1.500.000 para gastos varios
The amount that's was attributed to the project from the start based on the percentage is $7,500,000.
How to calculate the percentage?From the information given, the remaining percentage will be:
= 100% - (25% + 20% + 35%)
= 100% - 80%
= 20%
Let the total amount be x.
Therefore, 20% of x = 1,500,000
0.2x = 1,500,000
x = 1500000/0.2
x = 7500000
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What is the end behavior of the function f of x equals negative 2 times the cube root of x? as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0. as x → [infinity], f(x) → [infinity], and as x → –[infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity].
The end behavior of the function is as:
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The end behavior of a function will describe the behavior of the graph of the function at the "ends" of the x-axis.
How do determine the end behavior of a function?By determining the highest degree of the polynomial function. As the highest degree term will grow faster than the other terms as x gets very large or very small, its behavior will dominate the graph.
The graph of the function is f(x)=2∛x
the function leads to infinity so the end behavior of the function is
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
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if 3²× = 27 what is x
Answer:
3
Step-by-step explanation:
whenever solving for x, you have to work backwards…like so:
3 squared is 9
27 divided by nine is 3
x=3
To double check the answer, substitute the value that we just found into x
(3x3)x3=27
Answer:
[tex]x=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]3^{2x}=27[/tex]
Rewrite 27 in exponential form with base 3:
[tex]\implies 3^{2x}=3^3[/tex]
As both exponents have the same base,
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies 2x=3[/tex]
Divide both sides by 2:
[tex]\implies x=\dfrac{3}{2}[/tex]
need help with this question.
We have this equation:
[tex]\log(x) + \log(x + 99) = 2[/tex]
First, combine both logarithms using the multiplication property and simplify the expression.
[tex]\log[x(x + 99)] = 2[/tex]
[tex]\log[ {x}^{2} + 99x ] = 2[/tex]
Now, use the definition of logarithm to transform the equation.
[tex] {10}^{2} = {x}^{2} + 99x[/tex]
[tex] {x}^{2} + 99x - 100 = 0[/tex]
Finally, use the quadratic formula to solve the equation.
[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]
With this, we can say that the solution set is:
x = 1x = -100We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
What is the least possible value of (x+1)(x+2)(x+3)(x+4)+2019 where x is a real number?
By completing the square, we have
[tex](x+1)(x+4) = x^2 + 5x + 4 = \left(x+\dfrac52\right)^2 - \dfrac94[/tex]
[tex](x+2)(x+3) = x^2 + 5x + 6 = \left(x + \dfrac52\right)^2 - \dfrac14[/tex]
Then
[tex](x+1)(x+2)(x+3)(x+4) = \left(x+\dfrac52\right)^4 - \dfrac52 \underbrace{\left(x + \dfrac52\right)^2}_{=y} + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = y^2 - \dfrac52 y + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(y - \dfrac54\right)^2 - 1 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(\left(x + \dfrac52\right)^2 - \dfrac54\right)^2 - 1[/tex]
This product has a minimum of -1 when
[tex]\left(x + \dfrac52\right)^2 - \dfrac54 = 0[/tex]
which has two real solutions; then the minimum of the overall expression is -1 + 2019 = 2018.
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!"
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items?
d. If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive?
e. Is it better to apply the 60% discount first or the 20% discount first?
Answer:
a the assumption is that after the 60% discount, the 20% will contribute to the old price, not the adjusted price
b this is incorrect because the 20% discount will be added on after the 60% discount has been used
c the 500 dollars would turn to 100 dollars
d 40
e it would be best to first apply the 60% coupon first over the 20% coupon
Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
what is the lcd of 1/4 and 1/6
Answer:
12
Step-by-step explanation:
LCD of 1/4 and 1/6 is the least common denominator that is divisible by 4 and 6 at the same time and is the least.
So it the same to find least common multiple of 4 and 6 that is 12.
The answer is 12.
What is the simple interest that is missing from the table?
I
?
p
$375
r
2.2%
t
3 years
Answer:
SI =PXRXT/100
Step-by-step explanation:
THIS WOULD HELP YOU
134 A financial analyst believes that if interest rates decrease in a given period then the
probability that the stock market will go up is 0.08. The analyst further believes that
interest rate have a 0.40 chance of decreasing during the period in question. Given the
above information, what is the probability that the market will go up and interes: rate
will go down during the period in question?
The probability that the market will go up and interest rate will go down during the period in question is 0.03.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the market will go up and interest rate will go down = 0.08 X 0.40 = 0.03
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How did I do? for one of the questions I assumed you didnt take in count for the base so I just did lateral area
The area of the exposed surface is 442 square feet
What is a right square pyramid?A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.
Analysis:
The exposed surface is the area of the four triangles.
The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft
Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.
In conclusion, area of exposed surface is 442 square feet.
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The lsrl after an exponential transformation is log yhat=.4785 + 1.468x. What is the exponential form of the regression?
Answer:
[tex]10^{0.4785+1.468x}=y[/tex]
Step-by-step explanation:
So I'm assuming when you typed "log yhat=.4785 + 1.468x", you meant to write: [tex]log(y)=0.4785+1.468x[/tex]. And generally a logarithm can be written in the form [tex]log_ba=c[/tex] which can then be rewritten as [tex]b^c=a[/tex], but since the log has no base, it's assumed to be 10. So in this case you have the equation:
[tex]log_{10}y=0.4785+1.468x[/tex], which can then be written in exponential form as:
[tex]10^{0.4785+1.468x}=y[/tex]
Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10
Hello,
Step-by-step explanation:
[tex]f(x) = ln(x) {}^{4} [/tex]
[tex](ln(u)') = \frac{u'}{u} [/tex]
[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]
[tex]f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} [/tex]
[tex]f(10) = ln(10) {}^{4} [/tex]
[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]
[tex]y = f'(a)(x - a) + f(a)[/tex]
PLS HELP ME Solve the following equation: two fifths plus one fifth equals
one fifth,
three tenths,
two fifths,
or three fifths.
it is three fifths,
and it is the answer.
la longitud del jardín
de Carme es 15 m 24 cm. la longitud del jardín de su amigo es 2 m 98 cm más que el de Carmen . ¿cuál es la longitud del jardín de su amigo?
la longitud del jardín del amigo de Carmen es 18 m 22 cm.
¿Qué es una ecuación?Una ecuación se forma cuando dos expresiones algebraicas se igualan usando un signo igual.
Se da que la longitud de Carme
Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.
y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.
Sea La longitud del jardín de Carmen es x m
Entonces la ecuación se convierte en
La longitud del jardín de su amigo = x + 2m 98 cm
ahora ,
x = 15m 24cm
Sustituyendo los valores en la ecuación
La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm
1m = 100cm
La longitud del jardín de su amigo = 17 m 122 cm
as 100 cm = 1m
122 cm = 1 m 22 cm
so ,
La longitud del jardín de su amigo = 18 m 22 cm.
Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.
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Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run ?
Answer:
6 1/12 miles total
Step-by-step explanation:
3 1/4 = 13/4
2 5/6 = 17/6 to ADD fractions, you must have a common denominator
I will use 12 for these
13/4 = 39/12
17/6 = 34 /12
now you can add and simplify 39/12 + 34/12 = 73/12 = 6 1/12 miles
Dilate ∆ABC about the origin using the scale factor n. Measure and compare the lengths of the sides of the dilated triangle, ∆A'B'C', with those of ∆DEF. Take a screenshot of your dilation, save it, and insert the image below the table.
The attached graph represents the image of the triangles
How to dilate the triangle?To do this, we make use of the following coordinates
A = (1, 0)
B = (5, 0)
C = (1, 6)
The lengths of the triangle are calculated using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]
[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]
[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]
Using the scale factor of 2, we have the image of the dilation to be:
D = (2, 0)
E = (10, 0)
F = (2, 12)
The lengths of these sides are
DE = 8
EF = 14.4
DF = 10
See attachment for the image of the triangles ABC and DEF
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if f(x)=4x-x^2 find f(x+h)-f(x+h)/2h
Answer:
0
Step-by-step explanation:
numerator are the same the difference between same number or variable will be zero
What is the volume of the pyramid shown
in the diagram?
12 cm³
15 cm³
21 cm³
45 cm³
Please help urgent
Answer:
volume = 15 cm^3
Step-by-step explanation:
Volume of pyramid = 1/3 base area * height
= 1/3 ( 3 x 3 ) * 5 = 15 cm^3
A block is a rectangle that measures 100yards by 76yards. How many times around the block do you have to drive in order to drive one mile?
If block has length 100 yards and breadth 76 yards then we have to drive 5 times to drive one mile.
Given The length of block is 100 yards, the breadth of block is 76 yards.
We have to find number of times we need to drive one mile.
The perimeter of a rectangle= 2(length +breadth)
length is 100 yards
Breadth is 76 yards
perimeter=2(100+76)
=2*176
=352 yards.
We know that 1 mile is equal to 1760 yards.
We have to find number of times to drive 1 mile=1760/352
=5 times.
Hence we have to drive 5 times around the block which have length 100 yards and breadth 76 yards.
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Suppose U = The set of one digit numbers and A = {x: x is an even natural number less than or equal to 9} Describe each of the sets by complete listing method: A'
The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
How to list the set elements?The sets are given as:
U = The set of one-digit numbers
A = {x: x is an even natural number less than or equal to 9}
One-digit numbers are numbers 0 - 9.
So, we have
U = {0, 1, 2, 3.....,9}
Natural numbers are numbers from 1.
Even natural numbers can be divided by 2 without remainder'
So, we have
A = {2, 4, 6, 8}
Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
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Answer:
Step-by-step explanation:
Simplify, using the distributive
property.
5f + 16f = (5 +?)f=?f
Applying the distributive property, we would simplify the expression as: 5f + 16f = (5 + 16)f = 21f.
How to Apply the Distributive Property?The distributive property states that, ab + ac = (b + c)a.
Using the distributive property, we have:
5f + 16f
= (5 + 16)f
= 21f
Therefore, 5f + 16f is simplified as 21f.
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22POINTS PLEAS ANsewer
Answer:
2y>-y+5
Step-by-step explanation:
because it has a eligible number at the right hand side
What is the domain and range of this graph?
!!!!!!!A dress pattern uses the scale 2 inches : 1 foot.if the model is 12 inches long how long is the dress!!!!!!pls Hurry
Using the scale ratio, the length of the dress is: 6 ft.
How to Apply Scale to Measurement?Given a scale for the dress pattern as, 2 inches : 1 foot, it means 2 inches of the model equals 1 foot of the actual dress.
Therefore, using the scale ratio, let x represent the length of the dress. We would have:
2/1 = 12/x
x = (12 × 1)/2
x = 6 ft.
The length of the dress is: 6 ft.
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The value of x. if (3x +3) : (9x + 7) is duplicate ratio of 3:5 is
Answer:
(3x + 3) (9x + 7) is the duplicate ratio of 3:5 . the value of x is 2.
which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answer:
d
Step-by-step explanation:
it's kinda hard to explain
77 is the product of 7 and diego's height use the variable d to represent diego';s height
Diego's height is 7 units
How to determine Diego's height?The statement is given as:
77 is the product of 7 and Diego's height
This means that:
77 = 7 * d
Divide both sides by 7
d = 11
Hence, Diego's height is 7 units
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You enter an elevator on the ground floor, which is labeled 0. You get off on the floor labeled +4. What is your location?
A four floors above the ground floor
B. four floors below the ground floor
C. four floors near the ground floor
D. four floors around the ground floor
Answer:
A. four floors above the ground floor
Step-by-step explanation:
if you start at 0 which is the ground floor and go up 4, that would be +4, since, in theory, going up would be considered positive. So the answer is A.