Answer:
-31/17
Step-by-step explanation:
csc²α-cot²α=1
cot²α=csc²α-1=(25/7)²-1=(625-49)/49=576/49
α is in 2nd quadrant so cotα is negative.
cot α=-√(576/49)=-24/7
tan α=-7/24
cos β=√2/2
sec β=2/√2=√2
sec²β-tan ²β=1
tan ²β=sec²β-1
tan²β=(√2)²-1=2-1=1
β is in 1st quadrant ,so tan β is positive.
tan β=1
[tex]tan (\alpha -\beta )=\frac{tan \alpha -tan \beta }{1+tan \alpha tan \beta } \\=\frac{\frac{-7}{24} -1}{1+(\frac{-7}{24}) (1)} \\=\frac{-7-24}{24-7} \\=\frac{-31}{17}[/tex]
Solve for b.
-7b – 12 = -61
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-7b - 12 = -61}[/tex]
[tex]\large\textsf{ADD 12 to BOTH SIDES}[/tex]
[tex]\mathsf{-7b - 12 + 12 = -61 + 12}[/tex]
[tex]\large\textsf{CANCEL out: -12 + 12 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: -61 + 12 because it helps solve for your b-value}[/tex]
[tex]\mathsf{-61+12=\bf -49}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{-7b = -49}}[/tex]
[tex]\large\textsf{DIVIDE -7 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{-7b}{-7}=\dfrac{-49}{-7}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{-7}{7}}\large\textsf{ because that gives you 1}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{\dfrac{-49}{-7}}\large\textsf{ because that gives you your b-value}[/tex]
[tex]\mathsf{\dfrac{-49}{-7}= \bf b}[/tex]
[tex]\uparrow\large\text{SIMPLIFY ABOVE \& YOU HAVE YOUR ANSWER}\uparrow[/tex]
[tex]\mathsf{-49\div -7= \bf 7}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf b = 7}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the distance between the two numbers on a number line.
–7 – 3 2/ 3
The distance between the two numbers is
15
Answer:
ft
Step-by-step explanation:
Answer:
Actually the distance is 3 1/3
A pizza has a diameter of 14 inches
Which measurement is closest to the area
of the pizza in square inches?
A) 13644 in?
B) 153 86 in?
C) 182 14 in
D) 608 62 in
E) 616 55 in
F) None of the above
Please help me with this homework
Answer:
C.
Step-by-step explanation:
The pythagorean theorem shows a^2+b^2=c^2.
a=8, b=15, c= the unknown distance
8^2+15^2=c^2
A car lot has both used and new cars. If 86% of the cars on the lot are new and 45% of the cars are new and have a sunroof, find the probability of randomly choosing a car with a sunroof, given that it is a new car
Answer:
0.523
Step-by-step explanation:
Let :
New car = N
Sunroof = S
P(N) = 0.86
P(N n S) = 0.45
Recall :
P(A|B) = p(AnB) / p(B)
Therefore ;
P(S|N) = P(SnN) / p(N)
P(S|N) = 0.45 / 0.86
P(S|N) = 0.523
Find the y-intercept of the parabola y = x2 + 6x.
Can somebody help?
Given:
The equation of the parabola is:
[tex]y=x^2+6x[/tex]
To find:
The y-intercept of the parabola.
Solution:
We have,
[tex]y=x^2+6x[/tex]
Putting [tex]x=0[/tex] in the given equation, we get
[tex]y=(0)^2+6(0)[/tex]
[tex]y=0+0[/tex]
[tex]y=0[/tex]
Therefore, the y-intercept of the parabola is 0. It means the y-intercept of the given parabola is at point (0,0).
anybody know the answer? please help
Answer:
the first one. slope is 1/2 and y intercebt (b value) is positive 2.
Step-by-step explanation:
Answer:
y=1/2x+2
Step-by-step explanation:
This equation is linear because the graph is a straight line. Therefore, use the slope-intercept form y=mx+b to create the equation.
To find m (the slope), pick two points like (0,2) and (2,3). Find the change in y over the change in x: (y2-y1)/(x2-x1).
y2=3, y1=2, x2=2, x1=0
(3-2)/(2-0)= 1/2
This is the slope which means the equation is one of the first 2 options.
Next find b (the y-intercept) by finding the y value on the graph when x=0. When x=0, y=2. Therefore, b=2 and the final equation is y=1/2x+2
Jonathan's mom is buying him a new PS5 for his birthday. The expression 0.07p represents the sales tax on the system price, p. Write an expression in terms of p to represent the total amount that Jonathan's mom spends on the system, including tax.
Answer:
p + 0.07p
Step-by-step explanation:
tax is a compulsory sum levied by the government on goods and services. taxes increases the price paid for products
If sales tax = 0.07p, total price paid increases by 0.07p
total price paid = price of the good + tax
total amount spent by Jonathan's mom = p + 0.07p
Find the mode, median, mean and range for this set of data.
Number of Hours Slept: 8.5, 7,6.75,5.75, 8.75,6.25,7,7.5, 4.25
Central Tendency is the statistical measure that can be used to represent all the distribution or a dataset using a single value. The most common measures of central tendency are the mode, median, and mean.
How to determine this
Mode is the value that has the highest frequency in a given data set.
So,
8.75 the highest frequency in the data set
Mode = 8.75
Median is the middle of a sorted list of numbers when arranged in ascending order.
So,
4.25, 5.75, 6.25, 6.75, 7, 7, 7.5, 8.5, 8.75 in ascending order
Median = 7
Mean is the average or the most common value in a given set of values.
Mean = 8.5 + 7 + 6.75 + 5.75 + 8.75 + 6.25 + 7 + 7.5 + 4.25/9
Mean = 61.75/9
Mean = 6.8611
Mean = 6.86 to 2 decimal place
Range is the difference between the highest value and lowest values.
Range = Maximum value - Minimum value
Range = 8.75 - 4.25
Range = 4.5
Read more about Central Tendency
https://brainly.com/question/542771
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What is the distance between the points (5, -1) and (5,
3)
By using distance formula (which is attached below), you can solve this problem:
√(x2-x1)^2+(y2-y1)^2
(5, -1) and (5, 3)
√(5-5)^2+(3-(-1))^2
√0^2+4^2
√0+16
√16
4
The distance between the two points is 4.
Which of these tables represents a linear function?
Answer:
Second.
Step-by-step explanation:
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Owen and Jesse go to a restaurant for breakfast. A 7% sales tax is applied to their $21.60 bill. If Owen and Jesse add a 15% tip after the tax is applied, what is the total cost, including tip?
Answer:
The total cost is 26.6 dollars
Step-by-step explanation:
Given
The total bill of the breakfast = $ 21.60
Sales tax = 7% of the total bill value
Total bill after adding the 7% sales tax
$ 21.60 + 7% of $ 21.60
[tex]21.60 + \frac{7}{100} * 21.60\\21.60 + 1.512\\23.112[/tex]dollars
After adding 15% of the tip values to the payable amount of $ 23.112, the total bill becomes
$ 23.112 + 15% of $ 23.112
[tex]23.112 + 3.4668 = 26.5788[/tex]
The total cost is 26.6 dollars
NEED HELPPPPP LOL XDDDDD OH MY GODDD
Answer:
yo w t f is thisssssss
Step-by-step explanation:
b c idek im so cluless rn im in 7th grade XD
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
A= 44.415°
Step-by-step explanation:
i really need help pleasee help
Answer:
I believe your answer is 50.27! :)
The dollar value of a car is a function, f, of the number of years, t, since the car was purchased. The function is defined by the equation f(t)=12,000(3/4)^t.
A. How much was the car worth when it was purchased? Explain how you know.
B. What is f(2)? What does this tell you about the car?
C. About when was the car worth $6,000? Explain how you know.
Answer:
1.) 12000
2.) 6750
3.) 2.41
Step-by-step explanation:
Given the Equation :
f(t)=12,000(3/4)^t. ; where, t = time ; f(t) = worth of car at time, t
When, car was purchased, t = 0
t = 0
f(0) = 12000(3/4)^0
= 12000 * 1
= 12000
2.)
f(2) ; this mean the worth of the car after 2 years :
f(2)=12,000(3/4)^t.
12000(3/4)^2
12000 * 0.5625
= 6750
When car will be worth 6000
f(t) = 6000
f(t)=12,000(3/4)^t.
6000 = 12,000(3/4)^t
6000 / 12000 = (3/4)^t
1/2 = (3/4)^t
Take the log of both sides :
Log(0.5) = log(0.75)^t
log(0.5) = tlog(0.75)
- 0.301029 = - 0.124938t
t = - 0.301029 / - 0.124938
t = 2.4094
t = 2.41 years
i will mark brainliest if correct
Answer:
a = 17.5 ft²
Step-by-step explanation:
break figure into a rectangle and a triangle
Rectangle:
a = 2 * 5 = 10
Triangle
a = (1/2)5 * 3
a = 7.5
Total area
a = 10 + 7.5
a = 17.5 ft²
Si se lanzan 2 dados ¿ cuantas posibilidades hay de que las caras hacia arriba sumen un numero menor que 7?
Answer:
P = 15/36 = 0.4166...
Step-by-step explanation:
Cada dado tiene 6 caras, con los números entre 1 y 6.
Entonces tenemos dos eventos, con 6 posibles resultados cada uno.
El número total de resultados para el evento de lanzar los dos dados, es el producto de los números de resultados para cada dado, entonces tenemos:
C = 6*6 = 36 posibles resultados.
Ahora tenemos que contar el número de resultados en donde la suma es menor a 7.
Usando la notación:
(resultado del dado 1) y (resultado del dado 2) = suma
Esos son:
1 y 1 = 2
1 y 2 = 3
1 y 3 = 4
1 y 4 = 5
1 y 5 = 6
2 y 1 = 3
2 y 2 = 4
2 y 3 = 5
2 y 4 = 6
3 y 1 = 4
3 y 2 = 5
3 y 3 = 6
4 y 1 = 5
4 y 2 = 6
5 y 1 = 6
Hay 15 resultados donde la suma de los resultados individuales es menor a 7.
Entonces de un total de 36 posibles resultados, 15 cumplen lo que queremos, asi que la probabilidad de que las caras hacía arriba sumen un número menor que 7 son de 15 entre 36, o:
P = 15/36 = 0.4166...
help pls .. write an equation to show the function in the table .
Answer:
y = 2x - 2
Step-by-step explanation:
hope this helps
From the list below, select the two properties that are NOT necessarily true for a rhombus.
A
Each pair of opposite sides are congruent.
B
Each pair of opposite angles are congruent
С
All sides are congruent.
D
All angles are congruent.
E
Diagonals are congruent.
F
Diagonals are perpendicular.
Answer:
D, E
Step-by-step explanation:
D. all angles do not have to be congruent
E. diagonals do not have to be congruent
Option D is incorrect 100%
Option E should be incorrect aswell.
bjjjjejrfbhbjjskkcb bhjdhj ja w wj ef hfdsvfgsdfsdhjkskcbdbhjvbhhjxdk f fbvgoxbbx jfvbvfjvdf
Answer:
Step-by-step explanation:d
Answer:
me when i did your mom
Step-by-step explanation:
Find the m BD, given: mZCPA= 42, ZFPC = 90°
and CD & AB are diameters.
HELP PLZZZZ!!! PLZZZ SHOW WORK!!
Please help me with full calculations
Answer:
use formula,
P(x,y)=P'(-y,x)
so.
R(-2,-2)=R'=(2,-2)
S(1,1)=S'(-1,1)
T(-1,-3)=T'(3,-1)
Step-by-step explanation:
plot R,S,T and R',S',T' in the graph
NO LINKS The circumference of a circle is 36 feet. What is the length of the radius of this circler
O 9 ft
18 ft
36 ft
O 72 ft
Thank you so much for your help! :)
Answer:
18ft
Step-by-step explanation:
Formula of circumference * r x r x 3.14* or d x 3.14*
:DDD And ye glad I could help!
Does anyone know what the answer to this would be?
Answer:
D
Step-by-step explanation:
On the first day it was posted online, a music video got 250 views. The number of views that the video got each day increased by 16% per day. How many total views did the video get over the course of the first 12 days, to the nearest whole number?
Using an exponential function, it is found that the video got 8,314 total views over the course of the first 12 days.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growtn rate, as a decimal.On the first day it was posted online, a music video got 250 views, and the number increased by 16% a day, hence the A(0) = 250, r = 0.16, and the equation is given by:
[tex]A(t) = 250(1.16)^t[/tex]
The total amount over the first 12 days is given by:
[tex]T = \int_{0}^{12} A(t) dt[/tex]
[tex]T = \int_{0}^{12} 250(1.16)^t dt[/tex]
[tex]T = 250\frac{(1.16)^t}{\ln{1.16}}|_{t = 0}^{t = 12}[/tex]
Applying the Fundamental Theorem of Calculus:
[tex]T = 250\frac{(1.16)^{12}}{\ln{1.16}} - 250\frac{(1.16)^0}{\ln{1.16}}[/tex]
T = 8314.
The video got 8,314 total views over the course of the first 12 days.
More can be learned about exponential functions at https://brainly.com/question/25537936
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The owner of a flower shop on H street sells 28 roses for $140. What is the cost in dollars per rose?
Answer:
$5 ( sorry if it is incorrect)
Step-by-step explanation:
PLEASE HELP!!! which expression is equivalent to (3√x^2)^6
Answer:
x⁴
Step-by-step explanation:
TRUST ME IT IS CORRECT
Answer:
x⁴
Step-by-step explanation:
(∛x²)⁶ {The cube root of x² is x^(2/3)}
(x^(2/3))⁶ {Now, simply multiply 2/3 by 6 to get 4.}
x⁴
(∛x²)⁶ is equivalent to x⁴.
The mean score on a physics test was 75 points. Amy’s score was 67 points, which was 2 standard deviations below the mean.
What is the variance of the data set?
2
4
8
16
. im only asking because someone asked it and the answers said 2. like no hunny it was 16 and i gatta help out the future ppl who are chea- i mean in need of help . follow mw on insta lol ms.roslynn
Answer:
16
Step-by-step explanation:
Im being asked to put this in simplest form can anyone help me?
What is 0.57 (7 repeating) expressed as a fraction in simplest form?
Answer:
57/100
Step-by-step explanation:
look it up