Answer:
(x – 8)² + (y – 9)² = 3 (x – 8)² + (y – 9)² = 14Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Circles concentric with one having its center at (8, 9) will have equations of the form ...
(x -8)² +(y -9)² = r²
The offered answer choices that have this form are ...
(x – 8)² + (y – 9)² = 3 (x – 8)² + (y – 9)² = 14Answer:
B C
Step-by-step explanation:
edg2021
∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA by:
the vertical angle theorem.
the alternate interior angles theorem.
the reflexive property.
None of these choices are correct.
Answer:
the alternate interior angles theorem.
Hope this helps.. Good Luck!
What is the equation of the parabola with vertex (-2,5) and an x-intercept of x = 3
Step-by-step explanation:
if parabola has a vertex not in x-axis, it should have 2 x intercept
x-vertex = -2
first x intercept = 3
second x intercept should -7
so the equation will like this
y = a(x-x1)(x-x2)
y = a (x-3)(x+7)
y = a(x² + 4x - 21)
5 = a((-2)² + 4(-2) - 21)
5 = a(4 - 8 - 21)
5 = a(-25)
a = 5/(-25)
a = -1/5
then the equation is
y = (-1/5)(x² - 4x - 21)
or you can write as
y = -x²/5 + 4x/5 + 21/5
or as this one
5y = -x² + 4x + 21
This given equation represents a parabola that is downward facing, has a vertex at (-2, 5), and has an x-intercept of x = 3.
The equation of a parabola with vertex (h, k) is given by:
y = [tex](ax - h)^{2}[/tex] + k
We know that the vertex of the parabola is (-2, 5), so h = -2 and k = 5. We also know that the parabola has an x-intercept of x = 3, so when x = 3, y = 0. Substituting these values into the equation of the parabola, we get:
0 = [tex](a(3 - (-2))^{2}[/tex] + 5
0 = a × 25 + 5
-5 = 25a
a = -1/5
Therefore, the equation of the parabola is:
y = -(1/5)(x + 2) + 5
or
y = -(x + 22/5 + 5
We can also write the equation in vertex form as:
y = -(x - (-2))2 + 5
This equation represents a parabola that is downward facing, has a vertex at (-2, 5), and has an x-intercept of x = 3.
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HELP YOU WILL GET 30 POINTS Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After reading for 4 hours, he had 330 pages left to read. How long is the book? _____=pages How long did it take Naoya to read the entire book?______=hours
total number of pages = 550 pages
total amount of time to read the full book = 10 hours
======================================================
Work Shown:
1 hour = 55 pages
4 hours = 220 pages ... multiply both sides by 4
After 4 hours, he had read 220 pages. Since he has 330 still left to read, this brings the total to 220+330 = 550 pages overall
550/55 = 10 hours is the total amount of time needed to read the entire book at a rate of 55 pages per hour. This is assuming the rate is kept constant.
While 10 hours is a lot, it's somewhat plausible to get the full book read in one continuous session. Though he is better off taking (short) breaks every now and then.
Answer:
550 pages
10 hrs
Step-by-step explanation:
he reads 55 pages per hour
4 hrs* 55 pages/hrs=220 pages
the book is 550 pages long
220 pages+330=550 pages
to find the time to read the whole book:
330/55=6 hrs +4 hrs=10
or
550/55=10 hrs
In the diagram, what is the measure of angle 1 to the nearest degree? a) 82° b) 92° c) 94° d) 98°
Answer:
98
Step-by-step explanation:
7x+4 = 88 because they are vertical angles and vertical angles are equal
7x = 88-4
7x = 84
Divide by 7
7x/7 = 84/7
x = 12
<1 and 7x-2 are supplementary angles since they form a line
<1 + 7x-2 = 180
<1 + 7(12) -2 = 180
<1 +84-2 =180
<1 +82 = 180
<1 = 180-82
<1 = 98
Answer-
98
step by step explanation -
7x+4=88
7x=84
x=12
7x-12=7*(12)-2=82
angle 1=180-82 =
98Three triangles are shown on the centimetre grid.
A
B
C
(a I already did)
b)
Work out the area of this triangle.
Give your answer as a decimal.
Answer:
C has the largest area. It is 4.5 square units.
Step-by-step explanation:
A:
area = bh/2 = 2 * 3/2 = 3
B:
area = bh/2 = 2 * 3/2 = 3
C:
area = bh/2 = 3 * 3/2 = 4.5
C has the largest area. It is 4.5 square units.
What is the surface area of a sphere with a diameter of 16 cm?
Answer:
804.25 cm² (corrected to 2 decimal places)
Step-by-step explanation:
Radius = diameter / 2
= 16/ 2
=8 cm
Surface area of sphere = 4πr²
= 4π8²
=804.25 cm² (corrected to 2 decimal places)
please help me solve!!
Answer:
(2×1+2)+(2×2+2)+(2×3+2)+(2×4+2)
=28
Find the approximate side lengths and perimeter of quadrilateral WXYZ. If necessary, round your answers to the nearest hundredth.
The approximate length of segment WX is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment XY is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment YZ is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate perimeter of quadrilateral WXYZ is [tex]\left[\begin{array}{ccc}14\\14.47\\15\\15.59\end{array}\right][/tex]
Answer:
The answer is given below
Step-by-step explanation:
Given that the location of the points are W = (3, 1) , X = (7, -1), Y = (7, -3) and Z = (3,-3)
The distance between two points A(x1, y1) and B(x2, y2) is given by the formula:
[tex]|AB|=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the side length of the quadrilaterals are:
[tex]|WX|=\sqrt{(-1-1)^2+(7-3)^2}=\sqrt{20} =4.47[/tex]
[tex]|XY|=\sqrt{(-3-(-1))^2+(7-7)^2}=\sqrt{20} =2\\\\|YZ|=\sqrt{(-3-(-3))^2+(3-7)^2}=\sqrt{20} =4\\\\|ZW|=\sqrt{(-3-1)^2+(3-3)^2}=\sqrt{20} =4[/tex]
The Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units
Answer:
4.47,
2
4
14.47
Step-by-step explanation:
Find all of the missing angle measures. Remember you cannot assume right angles or diameters. Also think about how many degrees are in a triangle. Angle 1: Angle 2: Angle 3: Angle 4: Angle 5: Angle 6: Angle 7: Angle 8: Angle 9: Angle 10: Angle 11: Angle 12: Angle 13: Angle 14: Angle 15:
Answer:
See text below or attached figure
Step-by-step explanation:
Given arcs
AC=70
CR=18
therefore AR = 88
RB=80
BE=130
therefor EA = 360-(70+18+80+130) = 360-298 = 62
angles will be denoted (1) for angle 1, etc.
We ASSUME
ARD is a straight line
PFRB is a straight line
FCE is a straight line
Using inscribed angle theorem, angles subtended by chords/arcs equal to half the arc central angle.
Therefore
(4)=80/2=40
(13)=130/2=65
(12)=62/2=31
(11)=70/2=35
(5) = (70+18)/2 = 44
Consider triangle AEG,
(7)=(13)+(11)=65+35=100 [exterior angle]
Consider triangle EGB,
(10)=180-100-31 = 49 [sum of angles of a triangle]
Consider triangle AEH,
(3) = 180-(4)-(13)-(11) = 180-40-65-35 = 40 [sum of angles of a triangle]
From cyclic quadrilateral ARBE,
ARB+AEB=180 =>
ARB=180-AEB=180-(35+49) = 96
By the intersecting secants theorem,
(2) = (130-18)/2 = 56 [secants FE, FB]
(1) = (130+62 - (18+70))/2 = 104/2 = 52 [secants PA,PB]
(8) = (130+62 -80)/2 = 112/2 = 56
ARD is straight line (see assumptions above)
(9) = 180-96 = 84 [sum of angles on a line]
ARP = (9) = 84 [vertically opposite angles]
Consider triangle ARP
(14) = 180-52-84 = 44
Consider tangent PA
(15) = 180-(44+40+65) = 31 [sum of angles of a triangle]
Consider triangle ABD
(6) = 180 - (40+44+56) = 40 [sum of angles of a triangle]
This completes the search for all sixteen angles, as shown in the diagram, or in the text above.
Which two operations are needed to write the expression that represents “eight more than the product of a number and two”? multiplication and subtraction division and subtraction multiplication and addition division and addition
For this case we must represent the following expression algebraically:
"eight more than the product of a number and two"
Let "x" be the variable that represents the unknown number
We have to:
the product of a number and two is represented as: 2x
Then, the full expression will be:
2x + 8
Thus, we use multiplication and addition.
hope this answer correct
Can someone help me with this question please.
Answer:
x=88° a=+3 b=4a-3
Step-by-step explanation:
as triangles ADE and BCE are congruent by sss axiom
so correponding angles are equal
i.e<AED = <BEC
and <DAE =90-60
=30°
so
62°+x+30°=180°
therefore x=88°
Xavier is a sales person who is paid a fixed amount of $455 per week he also earns a commission of 3% on sales he makes Xavier wants to earn more than $575 in one week how many dollars in sales must he make
Answer:
557.75
Step-by-step explanation:
575 - 3% = 557.75 is the minimum amount in sales that has to be made
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
The answer is
the last graphStep-by-step explanation:
To find the graph which shows (f + g)(x) we must first find (f + g)(x)
That's
f(x) = - x² + 3x + 5
g(x) = x² + 2x
To find (f + g)(x) add g(x) to f(x)
That's
(f + g)(x) = -x² + 3x + 5 + x² + 2x
Group like terms
(f + g)(x) = - x² + x² + 3x + 2x + 5
We have (f + g)(x) as
(f + g)(x) = 5x + 5
Since (f + g)(x) is linear the graph which shows (f + g)(x) is the last graph
Hope this helps you
Answer:
last graph or D
Step-by-step explanation:
Plz help(by solving for x)
Answer:
x = 5.85641
Step-by-step explanation:
Step 1: Find missing leg of left triangle
sin30° = x/16
16sin30° = x
x = 8
Step 2: Find missing leg of right triangle
8² + b² = 16²
b² = 192
b = 8√3
Step 3: Find x by taking the difference
8√3 - 8 = 5.85641
Can someone please help with the answer!!! Thank you :)
Answer:
This sequence is a geometric sequence.
The common ratio of the sequence is
3/9 = 1/3
Hope this helps
Leslie went out for a jog. When she returned she went to the tap and filled up her 500 mL reusable water bottle. She drank 250 mL at a constant rate in one minute. Her phone rang, she set down the bottle of water and talked to her friend for four minutes. After her phone call she sipped the rest of her bottle at a constant rate in two minutes. Create a voulme vs. time graph for this story.
Answer:
Please find attached the required graph and
Step-by-step explanation:
The values for the information given can be written down as follows;
Time, seconds Volume mL
0, 500
12, 450
24, 400
36, 350
48, 300
60, 250
72 250
84 250
96 250
108 250
120 250
132 250
144 250
156 250
168 250
180 250
192 250
204 250
216 250
228 250
240 250
252 250
264 250
276 250
288 250
300 250
312 225
324, 200
336, 175
348, 150
360, 125
372, 100
384, 75
396, 50
408, 25
420, 0
I take variable $b$, double it, and add four. I subtract $4b$ from this new expression, and divide the resulting difference by two. What is my final expression in simplest form?
Answer:
-b+2 or 2-b
Step-by-step explanation:
We first obtain 2 * b + 4. Next, we get 2b + 4 - 4b = -2b +4. Dividing this by two, we have -2/2b + 4/2 = 2/2 b + 4/2.
The final expression obtained after given operations is 2 - $b$.
What are linear expressions?Linear expressions are expressions involving constants and variables.
How do we solve the given question?We are given that the person takes a variable $b$, doubles it, and adds four to it. He subtracts $4b$ from this and then divides the whole by 2.
So, we perform these operations on our variable $b$, to obtain the linear expression.
Variable: $b$
Doubles it, that is we multiply it by 2: 2*$b$
Adds 4: 2$b$ + 4.
Subtracts $4b$: 2$b$ + 4 - $4b$ = 4 - $2b$
Divides by 2: (4 - 2$b$)/2 = 2 - $b$
The expression now: 2 - $b$.
∴ The final expression obtained after given operations is 2 - $b$.
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Last year there were 500 children in a school. This year there are 565. What is the percentage increase in the number of pupils?
Answer:
13%
Step-by-step explanation:
[tex]percentage \: increase = \frac{565 - 500}{500} \times 100 \\ \\ = \frac{65}{500} \times 100 \\ \\ = \frac{65}{5} \\ = 13 \% [/tex]
How many different "words" can be made from the given word by re-arranging the letters? 1. KINDNESS 2. MATHEMATICIAN
Answer:
Step-by-step explanation:
Permutation has to do with arrangement.
To form different word by rearranging the word KINDNESS, this can be done in the following way;
The total letters present in kindness = 8 letters
Repeated letters are 2N's and 2S's
The arrangement is done in [tex]\frac{8!}{2!2!}[/tex] ways
[tex]= \frac{8!}{2!2!} \\= \frac{8*7*6*5*4*3*2!}{2!*2}\\ = 8*7*3*5*4*3\\= 10,080 \ different\ words[/tex]
For MATHEMATICIAN;
The total letters present in kindness = 13 letters
Repeated letters are 2M's, 2T'S 2I'sand 3A's
The number of words formed =
[tex]\frac{13!}{2!2!2!3!} \\= \frac{13*12*11*10*9*8*7*6*5*4*3!}{6*3!}\\= 13*2*11*10*9*8*7*6*5*4\\= 172,972,800\ different\ words[/tex]
Henrik grew 3 times as many potatoes as Derek grew. Derek managed to grow 49 potatoes. Henrik already had 173 potatoes harvested from his other field. How many potatoes does Henrik have in all?
Answer:
Step-by-step explanation:
Analysis
Answer:
49 x 3 = 147
147 + 173 = 320
Step-by-step explanation:
Step 1 Henrik grew 3 times as many potatoes as Derek grew. Derek managed to grow 49 potatoes.
49 x 3 = 147
Step 2 Henrik already had 173 potatoes harvested from his other field.
173 + 147
Please answer this fast in two minutes
Answer:
H(0, -7)
Step-by-step explanation:
x:
(16 + x)/2 = 8
16 + x = 16
x = 0
y:
(-2 + y)/2 = -4.5
-2 + y = -9
y = -7
H(0, -7)
Simplify fully
e x e x e x e x f ÷ e x e x e x f x f
Answer:
e/f
Step-by-step explanation:
Common factors in the numerator and denominator cancel.
[tex]\dfrac{e\times e\times e\times e\times f}{e\times e\times e\times f\times f}=\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{f}\times\dfrac{f}{f}=1\times1\times1\times\dfrac{e}{f}\times1=\boxed{\dfrac{e}{f}}[/tex]
The required simplification of the expression is [tex]\dfrac{e}{f}[/tex].
We have to the given expression, e x e x e x e x f ÷ e x e x e x f x f.
The given expression is simplify in the following steps given below.
Expression; [tex]\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}[/tex]
Then,
The simplification of the given expression,
[tex]=\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}\\\\[/tex]
Cancel out the same term from denominator and numerator,
[tex]= \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{f}{f} \\\\= 1 \times 1 \times 1 \times \dfrac{e}{f} \times 1 \\\\= \dfrac{e}{f}[/tex]
Hence, The required simplification of the expression is [tex]\dfrac{e}{f}[/tex]
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Choose the inequality that represents the following graph.
+
H+
-5 -4 -3
+
4
-2 -1
0
1
2.
3
5
Choose 1 answer:
2<-4
23 -4
2 - 4
2-4
Answer:
x ≤ -4
Step-by-step explanation:
There is a closed circle at -4, which requires and equals sign
The line goes to the left, which is less than
x ≤ -4
The diagram shows an incomplete polygon. How do I determine whether it is a regular polygon or not? How should I write my reasoning?
Answer:
see explanations below.
Step-by-step explanation:
The shown sides are all equal.
If it is a regular polygon, it must have all interior angles equal, and all sides equal.
IF
all sides are equal and all angles are equal,
THEN
it is a regular polygon, with 12 sides, because in regular polygons, all exterior angles are equal, and add up to 360 degrees.
No. of sides = 360/(180-150) = 360/30 = 12 sides.
(Please Help) Which equation represents the number of years (t) that it takes $200 to grow to $500 if it is growing at an exponential rate of 15% per year?
Answer:
A
Step-by-step explanation:
in 1 years it grows 15% of $200= $30+200=$230
in x yrs it grows to $500
.... number of yrs= 500/230= 2.17 yrs
Prove that (〖sin〗^2 θ)/(1+cosθ)=1-cosθ
Answer:
proved
Step-by-step explanation:
prove that : (sin^2 θ)/(1+cosθ)=1-cosθ
(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =
sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:
(sin^2Ф)(1-cosФ)/sin^2Ф =
1-cosФ (sin^2Ф/sin^Ф=1)
proved
Answer:
Step-by-step explanation:
take it befor delete
a) A graph is drawn below.
Explain how you know that y is not directly proportional to x.
Step-by-step explanation:
y isn't directly proportional with x because the graph doesn't cross O the origin, it starts from a y-intercept wich is not a property for proportional portions
PLEASE ANSWER ASAP THANKS
Answer:
Scale factor of dilation = 2
Step-by-step explanation:
The bigger triangle divided by 2 to get to the smaller triangle. If you count the tiles next to the bigger triangle and the smaller one you can see that it's dilated by 2.
Hope this helps!
Answer:
2 is the answer.Step-by-step explanation:
The lengths of all the sides have decreased by half.
So
A-B = 3 A'-B' = 6
A-B = 3 Because 6/2 = 3
This proves the scale factor is 2.
Hope this helped!
Kavitha
HELPPP ME PLEASEEEEEEEEE
Answer:
7. a = 50 degrees
b = 50 degrees
c= 50 degrees
d = 75 degrees
8.
Step-by-step explanation:
7.
a. Vertically opposite angles are equal
b. Vertically opposite angles are equal
c Alternate angles
d. Angles on a straight line.
8. 45 + 45 + 65 + 35 + 40 + 30 = 200m
Hope this helps
What is the solution to the system of equations? y = –5x + 3 y = 1
a(0.4, 1) b(0.8, 1) c(1, 0.4) d(1, 0.8)
Answer:
A
Step-by-step explanation:
We know that the y-coordinate has to be 1 so we can eliminate options C and D. If we plug y = 1 into y = -5x + 3 to solve for x we get:
1 = -5x + 3
-2 = -5x
x = 0.4 so the answer is A.