Complete question:
A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.
Calculate the angle subtended at the centre by the minor arc after 1 second.
Answer:
the angle subtended at the centre by the minor arc is 30⁰
Step-by-step explanation:
Given;
radius of the wheel, r = 10 cm = 0.1 m
angular speed of the when, ω = 5 rev/min
duration of the motion, t = 1 second
Determine the angular speed in radian per second,
[tex]\omega = 5\ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \ \times \frac{1 \min}{60 \ s} = \frac{10\pi \ rad}{60 \ s} = \frac{\pi }{6} rad/s[/tex]
After 1 second, the angular distance turned by the wheel is calculated as;
[tex]\theta = \omega t\\\\\theta = \frac{\pi \ rad} {6 \ s} \times 1 \ s\\\\\theta = \frac{\pi } {6 } \ rad\\\\in \ degrees; \theta = \frac{\pi \ rad}{6} \times \frac{180^0}{\pi \ rad} = \frac{180^0}{6} = 30^0[/tex]
Therefore, the angle subtended at the centre by the minor arc is 30⁰
This scatter plot shows the relationship between the number of sweatshirts sold and the temperature outside.
1) The y-intercept of the estimated line of best fit is at (0,b). Enter the approximate value of the b in the first response box.
2) Enter the approximate slope of the estimated line of best fit in the second response box.
Answer:
Below.
Step-by-step explanation:
1) 245.
2) Approximate slope = -(245-200)/15 = -3.
The y intercept is 250 and the slope is -10/3.
What is equation of a line?The equation of a line is linear in two variables, usually x and y, that is satisfied by points of the line.
We have the following ordered pairs in the line given:
(0, 250) and (30, 150)
Calculating the slope:
m = 150 - 250/ 30 - 0
m = -100/30
m = -10/3
Therefore, the slope is -10/3
Finding the y-intercept:
The equation of a line has the form:
y = mx + b, where m is the slope
Replacing by the values we know:
150 = -10/3 * 30 + b
b = 150 + 100
b = 250
Therefore, the y intercept is 250.
Hence the y intercept is 250 and the slope is -10/3.
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To make 12 cookies, you need 1.25cups of all-purpose flour, 110grams of butter, half cup of brown sugar and 1 teaspoon (tsp) of baking soda, what is the ratio of brown sugar is to baking soda is to butter to make 24 cookies is ?
Answer:
1 cup of brown sugar to 2 teaspoon of baking soda
Step-by-step explanation:
Given that 1.25cups of all-purpose flour, 110grams of butter, half cup of brown sugar and 1 teaspoon (tsp) of baking soda is needed to make 12 cookies. Therefore to make 24 cookies, double of this value would be needed.
Hence, 2.5 cups of flour, 220 grams of butter, 1 cup of brown sugar and 2 teaspoon of baking soda would be needed to make 24 cookies.
The ratio of brown sugar is to baking soda is to butter to make 24 cookies = 1 cup / 2 teaspoon = 1 cup of brown sugar to 2 teaspoon of baking soda
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A boy has four slices of pizza. Each slice has an equal number of green pepper pieces. He adds on three green pepper pieces to his slices of pizza and ends up with 27 total pieces of green pepper on it. How many pieces of green pepper were on each slice of pizza in the beginning?
Translate this problem into an equation, using x to represent the number of green peppers on a given slice.
Answer: 6 peppers per slice
Step-by-step explanation:
First we subtract, 27-3= 24
now every single slice has an equal amount of peppers.
24/4=6
2.
Which of the quadratic functions has the narrowest graph?
A. [tex]y=\frac{1}{8}x^2[/tex]
B. [tex]y=\frac{1}{3}x^2[/tex]
C. y = –2x2
D. y = –3x2
Answer:
D. y = –3x2
Step-by-step explanation:
Answer:
y = -3x^2
Step-by-step explanation:
A quadratic function has a leading coefficient which determines its width. When |a| < 1 the graph is wider. When |a| > 1 the graph is narrower. This means y = -3x^2 is the narrowest graph since 3 is the greatest.
Answer:
[tex]C)~y=-3x^2[/tex]---------------------
hope it helps...
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60% of the books on a bookshelf are english books. If there are 35 english books on the bookshelf, find the number of the books in the book shelf
Answer: 58 books
Step-by-step explanation:
There are 35 English books on the shelf and this constitutes 60% of the total number of books on the shelf.
Denoting the total number as x, the total number is:
35 = 60% * x
x = 35 / 60%
= 58 books
Janice has a pasta recipe that calls for 2oz. Of cheese for every 3 oz. of cooked pasta find the graph that shows their relationship between cheese and pasta
where is the graph ?
25/24 as a decimal and round it to the nearest hundredth
Answer:
1.04
Step-by-step explanation:
25/24=1.04166667
round: 1.04
Find the value of each variable.
a
59
72
A. a = 59°; b = 49°; c = 72°; d = 98°
B. a = 59°; b = 52°; c = 72°; d = 96°
C. a = 118°; b = 49°; c = 144°; d = 98°
O
D. a = 118°; b = 49°; c = 72°; d = 98°
Answer:
[tex]C. a = 118^o; b = 49^o; c = 144^o; d = 98^o[/tex]
Step-by-step explanation:
[tex]a=2(59)\\\\a=118^o[/tex]
---------------
[tex]b=180-(59+72)\\\\b=180-131=\\\\b=49^o[/tex]
---------------
[tex]C=2(72)\\\\C=144^o[/tex]
----------------
[tex]d=2b\\\\d=2(49)\\\\d=98^o[/tex]
--------------------
hope it helps...
have a great day!!
IM SO CONFUSED! HELP AND EXPLAINNNNNN
Answer:
326.56 sq in
Step-by-step explanation:
SA=2*3.14*4^2+2*3.14*4*9
SA= 100.48+ 226.08
SA= 326.56
Plug numbers in equation and then solve equation. R=4 and h=9.
The second doughnut glazing machine can glare 78 dozen doughnuts in
2 hours
Based on this rate, what is the total number of hours it will take the second
machine tolar 135 doren doughnuts Show or explain how you got you
answer
Answer:
t = 3.46 hours, or 3 hours 28 minutes
Step-by-step explanation:
78 dozen donuts in 2 hours immediately reduces to 39 dozen/hour.
Donuts produced as a function of time: D(t), where t is the number of hours the macine runs.
Set D(t) = 135 dozen = (39 dozen/hr)t.
Solving this equation for t, we get:
t = 135/39 hours, or t = 3.46 hours, or 3 hours 28 minutes
Carter needs to wrap seven presents. He lays the ribbon out flat and says that I'll have just enough pieces if I make six equally spaced cuts, I can use one piece for each package. And I won't have any pieces left over. Does he have enough pieces to wrap all the presents?
Answer:
Yes, he has enough pieces to wrap the present
Step-by-step explanation:
Given
[tex]Presents = 7[/tex]
[tex]Cuts = 6[/tex]
Required
Is there enough pieces to wrap all presents
As a general rule;
When a piece is cut in 1 place, you get 2 pieces
When a piece is cut in 2 places, you get 3 pieces
When a piece is cut in 3 place, you get 4 pieces
This implies that:
n cuts gives n + 1 pieces
i.e.
[tex]n \to n + 1[/tex]
So, we have:
[tex]6\ cuts \to (6 + 1) pieces[/tex]
[tex]6\ cuts \to 7\ pieces[/tex]
Hence, there are enough pieces.
Find the polar equation of the conic with the focus at the pole, directrix x = -5, and eccentricity 2.
Step-by-step explanation:
Given that,
Directrix, d= -5, and eccentricity, e = 2.
The polar equation of the conic is given by :
[tex]r=\dfrac{ed}{1-e\cos\theta}[/tex]
Put all the values,
[tex]r=\dfrac{-5\times 2}{1-2\cos\theta}\\\\=\dfrac{-10}{1-2\cos\theta}[/tex]
As e>1, it is a hyperbola. Hence, this is the required solution.
Find mMLK. IF YOU GIVE A LINK YOU WILL BE REPORTED.
Answer:where is the question
Step-by-step explanation:
Pattern A starts at 0 and uses the rule "add 4." Pattern B starts at 30 and uses the rule "subtract 3."
What are the next four terms in each pattern?
Enter your answers in the boxes.
Answer: 0 4 8 12 16
30 27 24 21 18
Step-by-step explanation:
0 + 4 = 4 4 + 4 = 8 8 + 4 = 12 12 + 4 = 16
30 - 3 = 27 27 - 3 = 24 24 - 3 = 21 21 - 3 = 18
Answer:
Step-by-step explanation:
First column add 4 second column subtract 3
0,30
4,27
8,24
12,21
16,18
use a formula to find the area of the figure
Answer: C. 13.5
Step-by-step explanation:
9x3= 27
27 divided by 2= 13.5
The formula for the area of a triangle is: A = 1/2 * b * h
In this problem, we are given the base (9 ft) and the height (3 ft). Therefore, we can use the formula.
A = 1/2 * 9 * 3
A = 1/2 * 27
A = 13.5 ft^2
Hope this helps!! :)
A. a car travels for 4 hours and it covers a distance of 50km each hour. How many km does it cover for the four hours?
Step-by-step explanation:
distance covered by car each hour=50km
distance covered by car in four hours =4×50
200kmstay safe healthy and happy...200km for four hours
Just multiply 50km times 4
Question about forms of quadratics
pls add explanation for brainliest
Answer:
See below...
Step-by-step explanation:
Zeros of the function: [tex]f(x)=(x-8)(x+2)[/tex]
The zeros are 8 and -2
The coordinates of the vertex: [tex]f(x)=(x-3)^2-25[/tex]
The vertex is the point (3, -25)
The y-intercept: [tex]f(x)=x^2-6x-16[/tex]
The y-intercept is -16
The axis of symmetry: [tex]f(x)=(x-3)^2-25[/tex]
The axis of symmetry is x = 3 (it goes through the vertex)
3. Find the length of the missing side given the information below.
A. 5
B. 25
C. 12.5
D. 157
=================================================
We apply the pythagorean theorem to find this answer.
a = 11 and b = 6 are the given legs
c = unknown hypotenuse
So,
a^2+b^2 = c^2
c = sqrt( a^2+b^2 )
c = sqrt( 11^2 + 6^2 )
c = sqrt( 121 + 36 )
c = sqrt( 157 )
c = 12.52996 approximately
c = 12.5
Side note: once you replace 'a' and b with 11 and 6, you can compute everything with a calculator in one single step more or less. The steps above are shown if you wanted to find the exact value sqrt(157).
There are 345 rows of flowers in a garden. Each row contains 48 flowers. Find the estimated number of flowers in the garden.
Please give the statements and explanation
Answer:
total no. of rows in garden= 345 each row contains= 48 flowers
total no. of flowers in the garden= 345*48=16560
Answer:
16,560
Step-by-step explanation:
No of rows = 345
No. of flowers in each row = 48
Estimated no of flowers in the garden
= No of rows * No of flowers in each row
= 345*48
= 16,560
PLEASE ANSWER THIS: look at the pic for question. Thanks!!!
Answer:
[tex]\text{D. }b^2-4ac>0[/tex]
Step-by-step explanation:
The equation [tex]b^2-4ac[/tex] represents the discriminant of a quadratic. It is the part taken from under the radical in the quadratic formula.
For any quadratic:
If the discriminant is positive, or greater than 0, the quadratic has two solutionsIf the discriminant is equal to 0, the quadratic has one distinct real solution (the solution is repeated).If the discriminant is negative, or less than 0, the quadratic has zero solutionsIn the graph, we see that the equation intersects the x-axis at two distinct points. Therefore, the quadratic has two solutions and the discriminant must be positive. Thus, we have [tex]b^2-4ac>0[/tex].
please help me out !! i rlly need it!
I have no clue helppp me plz
Answer:
13 degrees
Step-by-step explanation:
Triangles have to equal to 180 degrees
Answer:
[tex]180 = 154 + 13 + x[/tex]
Step-by-step explanation:
180= 154° + 13° + X
X = 180° - 154°- 13°
X = 13°
The its an ISOCELES triangle
If I can paint a wall in 20 min and my friend can paint a wall in 30 min. How many minutes would it take for us to paint a wall working together.
Answer: [tex]12\ \text{min}[/tex]
Step-by-step explanation:
Given
It takes 20 min and 30 min for a person and his friend to paint a wall individually i.e.
In 1 min they cover [tex]\frac{1}{20}[/tex] part and [tex]\frac{1}{30}[/tex] part of wall respectively.
If the work together, 1 minute work is
[tex]\Rightarrow \dfrac{1}{20}+\dfrac{1}{30}\\\\\Rightarrow \dfrac{3+2}{60}\\\\\Rightarrow \dfrac{5}{60}[/tex]
Time required will be reciprocal of it
[tex]\Rightarrow \dfrac{60}{5}=12\ \text{min}[/tex]
classifying quadrilaterals
Answer:
D, E, F
Step-by-step explanation:
Answer:
D and F
Step-by-step explanation:
a parallelogram is a quadrilateral with two sets of parallel sides
a quadrilateral is a shape with 4 edges
The Space Club is having some
posters printed. The printer charges
$250 plus $2 per poster. How many
posters can be printed for $1000?
Answer:
375
Step-by-step explanation:
250+2/poster=1000
2/poster=750
poster =375
check answer
250+2(375)=1000
250+750=1000
1000=1000
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-6,3). What is the vertex of the function defined as
g(x) = f(x - 2) – 5?
Answer:
The vertex of g(x) is (-4, -2)
Step-by-step explanation:
Let's define general translations:
Vertical translation:
For a function f(x), a vertical translation of N units (So the whole graph of f(x) is translated N units in a given direction) is defined as:
g(x) = f(x) + N
such that:
If N is positive, the translation is upwards
if N is negative, the translation is downwards.
Horizontal translation:
Similar than before, for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
Where, if N is positive, the translation is to the left
If N is negative, the translation is to the right.
Here, we have the transformation:
g(x) = f(x - 2) - 5
This is a transformation that moves the whole graph of f(x):
2 units to the right
5 units downwards.
So, if a point like (x, y) was in the graph of f(x)
After the translation, that point will be (x + 2, y - 5)
Then, if the original vertex was (-6, 3), the new vertex will be:
(-6 + 2, 3 - 5)
(-4, -2)
The vertex of g(x) is (-4, -2)
fnd the value of x................
The formula of the area of a square is
Answer:
Step-by-step explanation:
A=lw
Answer:
A = bh
Step-by-step explanation:
you multiply the base length by the height length.
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Given the system of linear equations:
2 – 2y = 4
4x + 3y = 5
What would be a possible FIRST STEP in the process of SOLVING by ELIMINATION?