Answer:
60
Step-by-step explanation:
Cot is the same as 1/tan so:
[tex]1/tan(theta) = tan(30)[/tex]
By rearranging the equation, we get:
[tex]1/tan(30) = tan(theta)[/tex]
By taking the inverse tan, we get:
[tex]theta = tan^-1 (1/tan(30)) =60[/tex]
Sara and jo both ran an 8km race Sarah took 55 mins to run the whole race jo started the race 3 mins later than Sara but caught up when they had both travelled 6 km of Sara and jo both ran at constant speed what is jos speed in 2dp
Answer:
9.41 km/h
Step-by-step explanation:
The total distance of the race, d = 8 km
The time Sarah took to run the race, t = 55 mins
The time Jo started the race = 3 mins later than Sara
The point Jo caught up with Sarah = 6 km into the race
The rate at which Jo and Sarah ran = Constant speed
The required information = Jo's speed
From the information given, Sarah's speed, v = 8 km/(55 mins) = (8/55) km/min × 60min/h = 96/11 km/h
The time it would take Sarah to run 6 km = 6 km/(8 km/(55 mins)) = 41.25 mins
Given that Jo started 3 minutes late, and they both arrive at 6 km into the race at the same point in time, the time it took Jo to arrive at 6 km into the race = The time it took Sarah - 3 minutes
∴ The time it took Jo to run the 6 km = 41.25 minutes - 3 minutes = 38.25 minutes
Given that Jo ran at a constant speed, and speed = distance/time, we have;
Jo's speed = 6 km/(38.25 min) = 8/51 km/min × 60 min/h = (160/17) km/h ≈ 9.41 km/h.
If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x).
O A. 2x-3
O B. 4x+1
ОС. 3х – 3
O D. 2x-1
Answer:
.➌×-➌
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
By definition, (f+g)(x) = f(x) + g(x)
So, (f+g)(x) = 3x - 1 + x + 2
= 4x + 1
m∠DEF = __because they are_________
Answer:
m∠GDE
alternate interior angles
Express each ratio as a fraction in simplest form.
5 miles to 35 miles
Answer:
1 : 7
Step-by-step explanation:
Given
5 miles : 35 miles ( divide both parts by 5 )
= 1 : 7 ← in simplest form
Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.
The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.
m + f = 15
3m + 5f = 51
How many multiple-choice questions are on the test?
3
5
12
14
Answer:
12
Step-by-step explanation:
Answer:
m = 12, f = 3
So, there are 12 multiple-choice questions on the test.
What is the answer and explain why
Answer:
20
Step-by-step explanation:
Take note of the important information/key words:
60 total ornaments
3 grandchildren
Divide them evenly
Set up an equation:
60 ornaments ÷ 3 grandchildren = ornaments per grandchild
60 ÷ 3 = 20 ornaments per grandchild.
In other words, each grandchild will receive 20 ornaments.
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
Answer:
I=70*.03*2.5
I=70*.075
I=$5.25 is the interest.
Step-by-step explanation:
The measurement of a rectangular room on a scale drawing are 8cm x 6cm. If the scale use is 1 : 400, calculate the actual area of the room in m².
Answer:
768 m²
Step-by-step explanation:
8 x 400 = 3200 cm = 32 m
6 x 400 = 2400 cm = 24m
32 x 24 = 768 m²
In the diagram below of triangle MNO, P is the midpoint of MO and Q is the
midpoint of NO.If PQ = 4.c – 18, and MN = 99 72, what is the measure of
PQ?
Answer:
MN = 50
Step-by-step explanation:
GiVEN = PQ = 49 – 8x and c= 41 + 3x
Needed = measurement = MN
Find MN:
MN = 41 + 3x
Plug in the value of x
MN = 41 + 3(3) = 41 + 9
MN = 50
Someone plss help me on this one too!
Thanks :)
Answer: 30%
Step-by-step explanation:
Please help I’ll give brainliest
answer:
ans:
0.03 km³ = 0.03 × 10⁹ m³ = 3×10⁷ m³6052 mL³ =6052×10^(-9) L³ = 6.052×10^(-6) L³5.43 cg³ = 5.43 × 10^(-6) g³ 2100m³ = 2100 × 10^(-9) km³ = 2.1 × 10^(-6) km³Step-by-step explanation:
1000 m = 1 km
1000 mL = 1 L
100 cg = 1 g
3a+5b+2c=?
a+b=15
b+c=14
5b=3b,2b
Step-by-step explanation:
please check you typing 5b = 3b, 2b
?????
Answer:
73
Step-by-step explanation:
3a + 5b + 2c = ?
Given:
a + b = 15
b + c = 14
now express in terms of b
a = 15 - b equation (i)
c = 14 - b equation (ii)
3a + 5b + 2c
substitute the values
3(15 - b) + 5b + 2(14 - b)
45 - 3b + 5b + 28 - 2b
add or subtract like terms
73 + 5b - 5b
plus 5b and minus 5b gets cancel
73
Mr Yadav buys a radio for Rs 640 and sells it for Rs 672 Find it's profit percent In process
Answer:
(672-640)/640 x 100 = 5%
5. In the triangle ABC, M is the midpoint of [AB] and N is the midpoint of [CM].
Find the coordinates of N. Given that A(-1,3), B(7.-3) and C(1,6).
Answer:
The coordinate or the point N is (2,3)
Step-by-step explanation:
The formula for the midpoint of two points is;
(x,y) = (x1 + x2)/2 , (y1 + y2)/2
for AB
A(-1,3) and B (7,-3)
We have;
(x,y) = (-1 + 7)/2 , (3-3)/2 = (6/2, 0/2) = (3,0)
For CM;
C(1,6) and M(3,0)
(x,y) = ( 1 + 3)/2, (6+0)/2 = (4/2, 6/2) = (2,3)
Need help with this
14. A polygon ABCD is inscribed in a circle. Find angle ABC
15. A polygon GHIJ is inscribed in a circle if GHI=76 and HIJ=66 what is IJG
Answer:
m<ABC = 100degrees
m<IJG = 104degrees
Step-by-step explanation:
14. The sum of the opposite angle of the quadrilateral is 180degrees. Hence;
m<ADC + m<ABC = 180
3y+8+4y+4 = 180
7y + 12 = 180
7y = 180 - 12
7y = 168
y = 168/7
y = 24
Get <ABC
m<ABC = 4y+4
m<ABC = 4(24) + 4
m<ABC = 96 + 4
m<ABC = 100degrees
15. Similarly for this;
GHI + IJG = 180
76 + m<IJG = 180
m<IJG = 180 - 76
m<IJG = 104degrees
If Jamie's paddling pool has a diameter of 10m, what is its area in square meters?
pls help
Answer:
use app Gauthmath its will give you the answer
Answer:
100msquare (or) sq.m (diameter in a circle inscripted square is one of its side)
Step-by-step explanation:
area of squr=side*side
=10*10
=100msquare (or) sq.m
(2x-y)2-(y+2)2:::::::::::::::
Answer:
(2x - y )2 - (y + 2)2 = 4 (x - y - 1)
Step-by-step explanation:
[tex](2x -y) 2 - ( y + 2 ) 2 = (4x -2y) -(2y + 4) \\\\[/tex]
[tex]= 4x - 2y -2y - 4\\\\=4x - 4y - 4\\\\=4(x-y-1)[/tex]
Solve for x. Enter your answer below as a fraction in lowest terms, using the
slash (/) as the fraction bar.
x + 9/20 = 9/16
Answer:
x = [tex]\frac{9}{80}[/tex]
Step-by-step explanation:
Given
x + [tex]\frac{9}{20}[/tex] = [tex]\frac{9}{16}[/tex]
Multiply through by 80 ( the LCM of 20 and 16 ) to clear the fractions
80x + 36 = 45 ( subtract 36 from both sides )
80x = 9 ( divide both sides by 80 )
x = [tex]\frac{9}{80}[/tex]
Find the distance between the two points in simplest radical form.
(-8, -2) and (-6,2)
Answer: [tex]2\sqrt{5}\\\\[/tex]
To get that answer, we apply the distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-6))^2 + (-2-2)^2}\\\\d = \sqrt{(-8+6)^2 + (-2-2)^2}\\\\d = \sqrt{(-2)^2 + (-4)^2}\\\\d = \sqrt{4 + 16}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.472136\\\\[/tex]
As an alternative, you could plot the two points on the same xy grid, and then form a right triangle. Afterward, apply the pythagorean theorem and you should get the same result as shown above.
Plz hep me I don’t understand
Answer:
Purple
Step-by-step explanation:
Because the graph has the circle filled in at the point 11, we know that it is a valid solution and that we are looking for a sign with the line under it. However, because we know that the number line extends to the right of 11, these would include answers such as 12, 13, 14, 15, etc. Because all these values are "greater than or equal to" 11, our answer is 11 <or= a, which is the purple one or the one on the right.
Someone help please❤️ & Thankyou!!
Answers:
300 = 12i+36si = 10Yes it's reasonablei = -11Refer to the diagram below.
The explanation for each part is below as well.
========================================================
Part 1
i = number of individual nail polish bottles
s = number of sets of 4
12i = money earned from just selling the individual bottles only
36s = money earned from just selling the sets of 4 only
12i+36s = total money earned = 300
12i+36s = 300 is the equation to set up
This is the same as 300 = 12i+36s because A = B is the same as B = A.
========================================================
Part 2
Plug in s = 5 to represent she sold 5 sets. Let's solve for i
12i+36s = 300
12i+36(5) = 300
12i+180 = 300
12i = 300-180
12i = 120
i = 120/12
i = 10
If she wants to sell $300 worth of product overall, and she already sold 5 sets so far, then she needs to sell 10 individual bottles to reach this monthly goal.
========================================================
Part 3
Yes it's reasonable to reach this goal. This is because the value of i (from part 2) was some positive whole number.
========================================================
Part 4
We'll repeat part 2 but with s = 12
12i+36s = 300
12i+36(12) = 300
12i+432 = 300
12i = 300-432
12i = -132
i = -132/12
i = -11
As the instructions state, we get a negative value. This is not reasonable because we can't sell a negative number of items. A negative number of items in general doesn't make sense.
The instructions further state that $432 was already made and that she exceeded her goal. Meaning that she doesn't have to worry about selling the individual bottles if selling the sets has her reach something over $300.
Using the Pythagorean Theorem, find the distance between the points.
Answer:
(5,7,8.6)
Step-by-step explanation:
Create a line on each the x axis and the y axis which intersects at a right triangle. The x axis line is 7 squares and the y axis is 5 squares. Now you can use the Pythagorean theorem.
a^2+b^2=c^2
7^2+5^2=c^2
49+25=c^2
74=c^2
8.6=c
Find f(4) if f(x) = 3x + 13
We are given the linear function below:
[tex] \large{f(x) = 3x + 13}[/tex]
To find f(4), simply substitute x = 4 in the equation.
[tex] \large{f(4) = 3(4) + 13} \\ \large{f(4) = 12 + 13} \\ \large \boxed{f(4) = 25}[/tex]
Answer
f(4) = 25he tables represent two linear functions in a system.
A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 22, negative 10, 2, 14. A 2 column table with 5 rows. The first column, x, has the entries, negative 6, negative 3, 0, 3. The second column, y, has the entries, negative 30, negative 21, negative 12, negative 3.
What is the solution to this system?
(negative StartFraction 13 over 3 EndFraction, negative 25)
(negative StartFraction 14 over 3 EndFraction, negative 54)
(–13, –50)
(–14, –54)
Answer:
8-22 is the answer ok thanks
Micheal is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 2 new pieces each day. Determine how may days it will Micheal to have 80 pieces of sea glass in his collection.
Answer:
It would take Micheal 22 days.
Step-by-step explanation:
The end goal is to have 80 and we begin with 14
So, 80 - 14 = 66 pieces left to collect
If he collects 3 per day we'll divide 66 by 3, which equals 22
Therefore it takes him 22 days
Question 3 (Multiple Choice Worth 1 points)
(06.05 LC)
The two-way table shows the number of students in a school who like reading and/or gardening.
Like Reading
Do Not Like Reading
Total
Like Gardening
32
?
58
Do Not Like Gardening
19
23
42
Total
51
49
100
What is the missing number in the table?
16
19
26
0
90
Answer:
26
Step-by-step explanation:
Horizontally:
Like reading = 32
Do not like reading = ?
Total = 58
Total = Like reading + Do not like reading
Do not like reading = Total - Like reading
= 58 - 32
= 26
Do not like reading = 26
Vertically:
Like gardening =
Do not like gardening = 23
Total = 49
Total = Like gardening + Do not like gardening
Like gardening = Total - Do not like gardening
= 49 - 23
= 26
Like gardening = 26
Therefore,
The missing number in the table is 26
Which graph shows the solution to the system of linear inequalities below?
y2 2x+1
y<-2x-3
Since there isn't a picture of the graphs, I attached one, of my graph, to this answer.
I'm also assuming (y2 2x+1) is actually (y< 2x+1).
Possible solutions are within the purple section of the attached image.
I hope this is helpful to you.
Graph that represents both the inequality is attached below.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
First, we make the graph,
The border of the inequality y = 2x + 1 has a slope of 2 and a y-intercept of 1. Plotting the y-intercept at (0, 1) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units up (in the positive y-direction) and one unit to the right (in the positive x-direction), we get the point (1, 3).
The answer to y < 2x + 1 may be represented by connecting these points with a dashed line and darkening the area below the line.
A boundary line for the inequality y -2x - 3 has a slope of -2 and a y-intercept of -3. Plotting the y-intercept at (0, -3) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units down (in the negative y-direction) and one unit to the right (in the positive x-direction), we get the point (1, -5).
The answer to y < -2x - 3 may be represented by connecting these points with a dashed line and coloring the area below the line.
Learn more about inequalities here:
https://brainly.com/question/30231190
#SPJ7
The length of a rectangle is 6 yards more than 8 times the width. The perimeter is 102 yards. Find the length and width.
•show work/steps!!
•any links/wrong answers will be reported
If x = 2.7, 5x = ____. (Input decimals only, such as 12.7.)
Answer:
5x=13.5
Step-by-step explanation:
Well, we know that 1x=2.7. So, if we want 5x we need to multiply 2.7*5 becuase 1x=2.7, so 5x=2.7*5.
Multiply. 2.7*5=13.5
So, 5x=13.5.
Hope this helps!
Answer:
13.5
Step-by-step explanation:
5x = ?
Replace 'x' with 2.7.
5(2.7) = ?
5(2.7) = 13.5
Hope this helps.
