Answer:
centre = (6, - 2 )
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 6)² + (y + 2)² = 9 ← is in standard form
with (h, k ) = (6, - 2 ) ← centre
On a map, two locations are 0.75 cen timeter apart. Their actual distance is 15 kilometers apart. What scale could be shown on the map? Select three options.
Options:
A.0.25 centimeter = 3 kilometers
B.0.4 centimeter = 8 kilometers
C.0.75 centimeter = 15 kilometers
D.3 centimeters = 60 kilometers
E.6 centimeters = 144 kilometers
Answer:
B, C, D
Step-by-step explanation:
Distance between the two locations :
On map = 0.75 centimeter
Actual = 15 km
Using the scale drawing notation :
On map : actual
0.75 cm : 15 km
Therefore,
Actual / on map
15 / 0.75 = 20
This means :
1 cm on map represents 20 km on land
0.25 cm on map = (20 * 0.25) = 5 kilometers
0.4 cm on map = (20 * 0.4) = 8 kilometers
0.75 cm on map = (20 * 0.75) = 15 kilometers
3 cm on map = (20 * 3) = 60 kilometers
6 cm on map = (20 * 6) = 120 kilometers
Hence, only options B, C and D are correct
Answer:
b,c,d are correct.
Step-by-step explanation:
just shortened the answer above me°∪°
please someone help me...
2cos pi/13 cos 9pi/13+ cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 8 pi/13 +cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 3pi/13 +cos 8pi/13 +cos 5pi/13
=2 cos pi/2 .cos 7 pi/26 +2 cos pi/2 .cos 3 pi /26
=2 (0)cos 7 pi /26 + 2(0) cos 3pi/26
=0 =R.H.S.
Answer: see proof below
Step-by-step explanation:
Use the following identities:
2cos x · cos y = cos(x + y) + cos(x - y)
cos x + cos y = 2 cos (x + y)/2 · cos(x - y)/2
Use the Unit Circle to evaluate: cos(π/2) = 0
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad 2\cos \dfrac{9\pi}{13}\cos \dfrac{\pi}{13}\quad +\quad \cos \dfrac{3\pi}{13}+\cos \dfrac{5\pi}{13}\\\\\text{Identity:}\qquad \quad \cos\bigg(\dfrac{9\pi}{13}+\dfrac{\pi}{13}\bigg)+ \cos\bigg(\dfrac{9\pi}{13}-\dfrac{\pi}{13}\bigg)+\quad \cos\bigg(\dfrac{3\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Simplify:}\qquad \qquad \cos\bigg( \dfrac{10\pi}{13}\bigg)+\cos \bigg(\dfrac{8\pi}{13}\bigg)+\qquad \cos\bigg(\dfrac{3\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Regroup:}\qquad \qquad \cos\bigg( \dfrac{10\pi}{13}\bigg)+\cos \bigg(\dfrac{3\pi}{13}\bigg)\quad +\quad \cos\bigg(\dfrac{8\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Identity:}\qquad 2\cos \bigg(\dfrac{10\pi+3\pi}{13\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{10\pi-3\pi}{13\cdot 2}\bigg)+\quad 2\cos\bigg(\dfrac{8\pi+5\pi}{13\cdot 2}\bigg)\cdot \cos\bigg(\dfrac{8\pi-5\pi}{13\cdot 2}\bigg)[/tex]
[tex]\text{Simplify:}\qquad 2\cos \bigg(\dfrac{13\pi}{26}\bigg)\cdot \cos \bigg(\dfrac{7\pi}{26}\bigg)+\quad 2\cos\bigg(\dfrac{13\pi}{26}\bigg)\cdot \cos\bigg(\dfrac{3\pi}{26}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2}\bigg)\cdot \cos \bigg(\dfrac{7\pi}{26}\bigg)+\quad 2\cos\bigg(\dfrac{\pi}{2}\bigg)\cdot \cos\bigg(\dfrac{3\pi}{26}\bigg)\\\\\\\text{Factor:}\qquad =2\cos\bigg(\dfrac{\pi}{2}\bigg)\bigg[ \cos \bigg(\dfrac{7\pi}{26}\bigg)+ \cos \bigg(\dfrac{3\pi}{26}\bigg)\bigg][/tex]
[tex]\text{Unit Circle:}\quad 2(0)\bigg[ \cos \bigg(\dfrac{7\pi}{26}\bigg)+ \cos \bigg(\dfrac{3\pi}{26}\bigg)\bigg][/tex]
Product of Zero 0
LHS = RHS: 0 = 0 [tex]\checkmark[/tex]
is y = -5x a function
Answer:
Yes, it is.
Step-by-step explanation:
For each x we get y, and no two xes give the same y
The temperature of a freezer started at 18 degrees Celsius.After cooling for a few hours, the freezer had a temperature of -12 degrees Celsius. What is the difference between the new,colder temperature and the original temperature?
Answer:
Step-by-step explanation:
Difference = New temperature - original temperature
= -12 - (18)
= - 30
New temperature is 30° less than the original temperature
The entire graph of the function f is shown in the figure below. Write the domain and range of f using interval notation?
========================================================
Explanation:
The domain is the set of allowed x values. In terms of a graph, we look at the left most point to see that x = -5 is the smallest x value possible. However, there's an open hole at this endpoint, so -5 itself is actually not part of the domain. So x must be larger than -5. At the same time, x can be as large as x = 3. Look at the very right tip of the graph to find this x value.
So x spans from -5 to 3, excluding -5 but including 3. We would write [tex]-5 < x \le 3[/tex] which converts to the interval notation (-5, 3]. Note the mix of curved parenthesis and square bracket. The curved parenthesis means to exclude the endpoint, while the square bracket means include the endpoint.
-----------
The range is the set of possible y outputs. Find out the lowest point of the graph. That is when y = -4 and this value is included due to the filled in circle at the endpoint. But we do not include the largest y value y = 5 as there's an open hole at this endpoint.
So the range is the set of y values such that [tex]-4 \le y < 5[/tex] which in interval notation would be written as [-4, 5)
-----------
So in short, you're looking for the min and max of x and y to get the domain and range respectively. Be sure to exclude any values where there are open holes as those do not count as part of the graph.
For a given function f(x), we define the domain as the set of the possible inputs for that function.
Here we will see that the domain is (-5, 3]
So, to find the domain by looking at a graph, we need to see the smallest x-value and the largest x-value.
In the graph, at the left, we can see that we have a white dot at x = -5
This means that the point itself does not belong to the domain, so here we need to use an open interval symbol, which is (
Then at the moment, we have:
domain = (-5
Now if we look at the right side, we can see that we have a black dot at x = 3.
This means that the value x = 3 belongs to the domain, so here we need to use the close symbol ].
Then the domain will be:
(-5, 3]
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2% Of A=3% OF B = 4% of c then A:B:C: is?
Answer:
6:4:3.....................
The ratio between A, B, and C is 6:4:3.
To determine the ratio between A, B, and C based on the given information, we can set up the following equations:
2% of A = 3% of B
4% of C = 3% of B
Let's solve for the variables and find the ratio:
First equation: 2% of A = 3% of B
0.02A = 0.03B
A/B = 0.03/0.02
A/B = 1.5
Second equation: 4% of C = 3% of B
0.04C = 0.03B
C/B = 0.03/0.04
C/B = 0.75
Now, let's express the ratio A:B:C based on the ratios we found:
A:B = 1.5:1
B:C = 1:0.75
To obtain a common ratio, we can multiply both ratios by 4:
A:B = 6:4
B:C = 4:3
Combining these ratios, we have:
A:B:C = 6:4:3
Therefore, the ratio between A, B, and C is 6:4:3.
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Give an example of an exponential function that includes the following transformations: o Vertical Compression o Reflection in the y-axis o Horizontal Stretch o Horizontal Translation to the left o Vertical Translation down
Step-by-step explanation:
A transformation may be defined as taking a basic function and then changing it slightly with the predetermined methods. This changes will cause the required graph of that function to shift, move or stretch, which depends on the type of the transformation.
For example:
Let a function be : [tex]$f(x)= B^x$[/tex]
For any constants m and n, the function [tex]$f(x)= B^{x+m}+n$[/tex] shifts the parent function.
- vertically n units and in same direction of the sign of n.
- horizontally m units and towards the opposite direction of the sign of m.
- The y-intercept becomes ([tex]$0, b^m+n$[/tex])
- The horizontal asymptote becomes y = n.
- the reflection about x -axis becomes [tex]$f(x)=- B^x$[/tex]
A bricklayer is building a wall. Each layer of the wall has the same number of bricks. The points on the following coordinate plane show how many bricks he used to make 2, 3, and 4 layers of the wall.
Answer:
50
Step-by-step explanation:
Follow the graph and the bricks go up by 50 per 1 layer
For 1 layer 50 bricks, for 2 layers 100 bricks, for 3 layers 150 bricks, and for 4 layers he uses 200 bricks.
What is a linear graph?The graph for a straight line is called the linear graph in the linear graph the increment of the data for both the axes is constant so it gave a linear relationship.
As we can see in the graph there is a relationship between the number of bricks and the layers of the bricks.
Therefore, for 1 layer 50 bricks, for 2 layers 100 bricks, for 3 layers 150 bricks, and for 4 layers he uses 200 bricks.
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the square of an integer creates a
Answer:
It creates a positive integer.
Step-by-step explanation:
Integers are whole number which could be negative or positive. Examples are; 2, 3, -1, -7 -5 etc.
Whenever an integer is squared, a positive integer is created. For example, let us consider integers; 3, 4, -3 and -4.
[tex](3)^{2}[/tex] = 3 × 3 = 9
[tex](-3)^{2}[/tex] = -3 × -3 = 9
Also,
[tex](4)^{2}[/tex] = 4 × 4 = 16
[tex](-4)^{2}[/tex] = -4 × -4 = 16
Therefore, the square of an integer creates a positive integer.
What is the first derivative of r with respect to t (i.e., differentiate r with respect to t)? r = 5/(t2)Note: Use ^ to show exponents in your answer, so for example x2 = x^2. Also, type your equation answer without additional spaces.
Answer:
The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).
Step-by-step explanation:
Let be [tex]r(t) = \frac{5}{t^{2}}[/tex], which can be rewritten as [tex]r(t) = 5\cdot t^{-2}[/tex]. The rule of differentiation for a potential function multiplied by a constant is:
[tex]\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}[/tex], [tex]\forall \,n\neq 0[/tex]
Then,
[tex]r'(t) = (-2)\cdot 5\cdot t^{-3}[/tex]
[tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3})
The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).
Simplify the expression -1/2(-5/6 + 1/3)
Answer: 1/4
Step-by-step explanation:
-
Answer:
5/12 - 1/6
Step-by-step explanation:
Took the diagnostic
Find the value of x. A. 13 B. 9 C. 12 D. 10
Answer:
D. 10
Step-by-step explanation:
9+4=13
x+3=13
x=10
The value of x is 10 which is correct option (D).
What is the Angles of Intersecting Secants Theorem?Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Given that,
Length of CW = 9 units,
Length of WV = 4 units,
Length of WU = 3 units,
Length of TW = x units,
⇒ Length of CW + Length of WV = Length of CV
⇒ 9 + 4
⇒ 13
⇒ Length of TW + Length of WU = Length of CV
⇒ x + 3 = 13
⇒ x = 10 - 3
⇒ x = 10
Hence, the value of x is 10 which is correct option (D).
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Solve the following
equation
85= -5(1 - 2n)
n=12
n = 15
n = -15
n=-8
Answer:
n = 9
Step-by-step explanation:
Step 1: Solve the equation
85 = -5 + 10n
90 = 10n
n = 9
Therefore n is equal to 9
If the line L has a slop of 0, which of the following could be the graph for L?
Answer:
Graph A
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Since we are dealing with a slope of zero, we replace m with 0:
y = 0x + b
y = b
Here, we see that we would have a horizontal line. Therefore, graph A would be our answer.
Answer:
A
Step-by-step explanation:
A slope of zero is a horizontal line, because it does not change vertically
A would be the graph of a line with a slope of zero
If there is a discount of 40% on an article costing #7000, then the price after discount is
Answer:
The answer is # 4200Step-by-step explanation:
A discount of 40% was allowed on the price
To find the price after the discount first calculate the discount and subtract it from the original price
That's
[tex] \frac{40}{100} \times 7000[/tex]
= 2800
So the price after the discount is
#7000 - #2800
Which is
# 4200Hope this helps you
can i get the answer for number 16
Answer:
25
Step-by-step explanation:
For each problem, the two numbers on the left are perfect squares. The number in the upper right is the square of the difference between the two numbers on the left. The number on the bottom right is equal to the number on the upper right plus the number on the upper left.
For problem 16, we know that the square of the difference between 36 and the missing number is 121. The square root of 121 is 11, so the missing number is 36 - 11 = 25 which fits the pattern because it is also a perfect square.
(Also if you look at problem 15, it basically gives you the answer to problem 16.)
Answer:
See below
Step-by-step explanation:
The upper left box and the bottom left box are being subtracted. When the result is obtained we square it and the squared answer is written in the top right box. After that , the squared answer and the top left answer are added to get the bottom left answer.
See the attached file.
The perimeter of a rectangle is 24 m. The length is 30 m less than five times the width. Find the dimensions of the rectangle. List answer as follows: width, length.
Answer:
width = 7 mlength = 5 mStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
Perimeter = 24m
The statement
The length is 30 m less than five times the width is written as
l = 5w - 30
Substitute the expression into the above formula and solve for the width
That's
24 = 2( 5w - 30) + 2w
24 = 10w - 60 + 2w
84 = 12w
Divide both sides by 12
w = 7
Substitute this value into l = 5w - 30
That's
l = 5(7) - 30
l = 35 - 30
l = 5
Therefore the dimensions are
width = 7 m
length = 5 m
Hope this helps you
Graph (-4, 5), (2, 3), (-3.0), (-4. -5). (-5. 2), and (-5,3) and connect the points to form a polygon. How many sides does the polygon have?
Answer:
I think the sides of polygon are 6
Step-by-step explanation:
Because to form a polygon we need to the first to form a horizontal and vertical line,to find the number in that line,and join the line based on the numbers given, then you will get a polygon with 6 side
The table represents the total miles traveled, y, after a number of hours, x.
Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420
Which linear equation represents the situation?
y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x
Answer: Y=60x
Step-by-step explanation:
find the slope (Y2-Y1)/(X2-X1)
(240-150)/4-2.5)
90/1.5 =60
It's multiple choice so it can only be a or b. If you do 60 x 2.5 you get 150 so there's no way you will add 480 so you are done it's A. If it's not a multiple choice question then you would do the who y=mx+b and plug in x, y and m and then find the b which in this case would be 0.
Answer:
(2.5,150)(4,240)
slope = (240 - 150) / (4 - 2.5) = 90 / 1.5 = 60
y = mx + b
slope(m) = 60
(4,240)...x = 4 and y = 240
now we sub and find b, the y int
240 = 60(4) + b
240 = 240 + b
240 - 240 = b
0 = b
so ur equation is : y = 60x + 0 which is written as : y = 60x <==
Solve the following equation.
Round to the nearest TENTH
-3.7 - 9.7x = 7x – 5.2
Answer:
x=0.1
Step-by-step explanation:
-3.7-9.7x=7x-5.2
-3.7+5.2=7x+9.7x
1.5=16.7x
x=0.08982
x=0.1
Which expression is equivalent to y.y.y.z.z.z.z
Answer:
y^3z^4
Step-by-step explanation:
y*y*y*z*z*z*z
y*y*y=y^3
z*z*z*z=z^4
Together,
y^3z^4
Hope this helps ;) ❤❤❤
Answer:
your answer is A, y³ z⁴
Step-by-step explanation:
it was correct for me.
what is 8.5 divided by 390
0.2017 this is the answer i got
Answer:
0.02179
Step-by-step explanation:
8.5÷390 = 0.02179
A body at rest and of mass
5kg is acted upon by a force
for 0.2s. Find the increase in
momentum.
-6 + x = -5
Solving one and two step equations
Answer:
1
how did i get it:
-6 - (-5) = 1
Solve for x
-2x+2-7x= -70
Answer:
x=8
Step-by-step explanation:
-2x+2-7x=-70
Minus two from each side.
-2x-7x=-72
Combine like terms.
-9x=-72
Divide -9 from each side.
x=8
f(x) = x; translation
6 units down followed by a
vertical stretch by a factor
of 5
g(x) = 5x = 6
Answer:
the transformed function becomes: g(x) = 5 x - 30
Step-by-step explanation:
When the function f(x) = x is shifted down by a factor of 6 we have the following transformation:
f(x) --> x - 6
After this, a vertical stretch by a factor of 5 should affect the full functional expression in the following way:
5 ( x - 6) = 5 x - 30
Therefore the transformed function becomes: g(x) = 5 x - 30
An elevator in an office building made the following moves: Up 7 floors, down 14 floors, up 6 floors, down 2 floors, up 9 floors, down 5 floors. If the elevator stopped on the 54th floor, what floor did it start on?
Answer:
It started on the 55th floor.
Step-by-step explanation:
We can work backwards from the 54th floor. Since we are working backwards, if the elevator goes up, we will subtract and if it goes down, we will add. Starting with 54, we get 54 + 5 = 59, then 59 - 9 = 50, then 50 + 2 = 52, then 52 - 6 = 48, then 48 + 14 = 62, then 62 - 7 = 55.
Write a problem based on the given information.
P = Cost of dinner
0.15p = cost of a 15% tip
P + 0.15p = 23
Answer:
Total cost of dinner = P + 0.15p = 23
Step-by-step explanation:
Consider the information provided.
The cost of dinner at a restaurant is $P.
The tip offered for the service was, $0.15p.
The total of the cost of dinner and the tip offered for the service is:
T = P + 0.15p = 23
what value of x that will make x/3 - 2 = - 11/4
Answer:
x = -9/4
Step-by-step explanation:
x/3 - 2 = - 11/4
Add 2 to each side
x/3 - 2+2 = - 11/4+2
Get a common denominator on the right
x/3 = -11/4 + 8/4
x/3 = -3/4
Multiply each side by 3
x/3*3 = -3/4 *3
x = -9/4
Answer:
[tex]$ x= -\frac{9}{4} $[/tex]
Step-by-step explanation:
[tex]$\frac{x}{3} - 2 = -\frac{11}{4} $[/tex]
[tex]$\frac{x}{3} -\frac{6}{3} = -\frac{11}{4} $[/tex]
[tex]$ \frac{x-6}{3} = -\frac{11}{4} $[/tex]
Multiply both sides by 3
[tex]$ x-6 = -\frac{33}{4} $[/tex]
[tex]$ x= -\frac{33}{4} + 6$[/tex]
[tex]$ x= -\frac{33}{4} + \frac{24}{4} $[/tex]
[tex]$ x= -\frac{9}{4} $[/tex]
Juan ran the lemonade stand for 3 more days after his first day profit of $12. Each day, he used the money from sales to purchase more lemons, cups, and sugar to make more lemonade. The table shows how much he spent and earned each day. What is the expression needed to find his total earnings?
Answer:
16-7+22-12+18-9
The correct answer is $28
Step-by-step explanation:
Thanks
The expression that uses adding the additive inverse to rewrite the expression is 16 + (–7) + 22 + (–12). Therefore, option C is the correct answer.
The given expression 16 – 7 + 22 – 12.
We need to rewrite the expression needed to find his total earnings.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The additive inverse of a particular number refers to the number that when the added will to the number will be equal to 0.
Now, based on the information given in the question, the additive inverse will be 16 + (–7) + 22 + (–12).
Therefore, option C is the correct answer.
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Your question is incomplete, probably the complete question/missing part is:
Juan ran the lemonade stand for 3 more days. Each day, he used the money from sales to purchasing more lemons, cups, and sugar to make more lemonade. On day 2, he earned $16 and spent $7 on supplies. On day 3, he earned $22 and spent $12. The expression 16 – 7 + 22 – 12 can be used to model the situation for these 2 days.
Identify the expression that uses adding the additive inverse to rewrite the expression.
–16 + (–7) + (–22) + (–12)
–16 + 7 + (–22) + 12
16 + (–7) + 22 + (–12)
16 + (–7) + 22 + 12