Answer:
21 quarters and 11 dimes = 32 coins
Step-by-step explanation:
x + y = 32
0.25x + 0.10y = 6.35 [take the first equation and make it equal to x]
x = 32 - y [now take this equation and plug it in the above]
0.25 (32-y) + 0.10y = 6.35
8 - 0.25y + 0.10y = 6.35
8 - 0.15y = 6.35 [subtract 8 from both sides]
-0.15y = -1.65 [divide by -0.15 to isolate y]
y = 11 so there are 11 dimes
plug it into the first equation: x + 11 = 32; x = 21 so there are 21 quarters
The Picture above please do 4a and 4b I’m so lost. Thank you.
Answer:
First, we know that the function IxI works as follows:
IxI = x if x ≥ 0
IxI = -x if x < 0
So IxI is always positive.
then:
a) f(x) = Ix - 2I
this is:
f(x) = (x - 2) if (x - 2) ≥ 0
-(x - 2) if (x - 2) < 0
Then the graph of this function will be two lines (where the separation of the lines depends on the vale of x)
For the case of b we have
g(x) = -IxI + 1
then we have:
g(x) = -x + 1 if x ≥ 0
g(x) = -(-x) + 1 if x < 0
To graph the functions, you need to graph these lines for the given values of x. You also can see the graphs below. Where the red graph is the one for the point 4a, and the blue graph is the one for point 4b.
Now, let's find the domain and range:
4a) f(x) = Ix - 2I
The domain is the set of the possible values of x that we can input in that function. For this case, we do not have any value of x that generates a problem (like a zero in a denominator, for example) then the domain is the set of all real numbers: x ∈ R
The range is the set of the possible values of y.
f(x) = Ix - 2I is always equal or greater than zero (as you can also see in the graph) then the range will be:
R: y ∈ R, such that y ≥ 0.
4b) g(x) = -IxI + 1
Similar as the prior case, here the domain is the set of all real numbers:
D: x ∈ R
For the range, now we have:
y = -IxI + 1
if IxI is always equal or larger than zero, then -IxI is always equal or smaller than zero. If we add a + 1 to that, then the function will be always equal or smaller than 1.
Then the range is:
R: y ∈ R, such that y ≤ 1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
What is the solution set of this inequality?
Answer:
(-3,1) U (3,8) is the right answer.Roberto has run the first 18 miles of a race, which means he is 72% finished. How long is the race
Answer:
25 miles
Step-by-step explanation:
18 ÷ 72% =
18 ÷ (72 ÷ 100) =
(100 × 18) ÷ 72 =
1,800 ÷ 72 =
25
The image of F(-5,-9) after translating along <4, 6 > and then translating along < 3, 5> is? F’(?,?)
==============================================
Explanation:
The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"
In general, "translated along <m,n>" is the same as writing [tex](x,y) \to (x+m, y+n)[/tex]. If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.
-------------
With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.
We can say
[tex](x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\[/tex]
Showing that (-5,-9) moves to (-1,-3)
This is after the first translation, but there's a second translation.
We'll apply the same idea, but different numbers this time
[tex](x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\[/tex]
So (-1,-3) moves to (2,2)
Overall we have
(-5,-9) move to (-1,-3) after the first translation(-1,-3) move to (2,2) after the second translationTherefore, the original point ends up at (2,2) which is the final answer
--------------
Extra info:
A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.
A professor gives a test to a large class. The time limit for the test is 50 minutes, and the first student to finish is done in 35 minutes. The professor assumes that the random variable T for the time it takes a student to finish the test is uniformly distributed over [35, 50]. At what time T will 60% of the students be finished with the test?
Answer: at 44 minutes, 60% of the students will be finished with the test
Step-by-step explanation:
Given the data in the question;
we have a uniform distribution between 35 and 50
so
50 - 35 = 15
now, we simply multiply 15 by 60%; 15 × 0.6 = 9
so after 9 minutes, 60% percent of the students are done
Hence, 9min + 35 min = 44 minutes
Therefore at 44 minutes, 60% of the students will be finished with the test
The time T when 60% of the students will be finished with the test is 44 minutes.
What is the percentage?The percentage is the value per hundred.
The time limit for the test = 50minute
The first student finishes in 35 minutes
The last student finishes in 50 minutes
So the difference between time = 15 minutes
It is given that the time it takes a student to finish the test is uniformly distributed over [35, 50].
So, the time T when 60% of the students will be finished with the test
T=35 + 60% of 15 minutes
T= 35 + 60*15/100
T= 44 minutes
Therefore, the time T when 60% of the students will be finished with the test is 44 minutes.
To get more about the percentage visit:
What is the quotient of 63 and 0
Answer:
0
Step-by-step explanation:
Something divided OR multiplied by 0 always ends with 0
Answer:
63/7 = 9.
I think
Hope this helps
What is the solution for the system of equations shown in this graph?
Answer:
[tex]\huge\boxed{\sf x = 2 , y = -2}[/tex]
Step-by-step explanation:
The common point where the lines of the two equations meet is exactly the solution of the system of equations.
So,
The common point is (x,y) = (2,-2)
This means that x = 2 and y = -2.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807evaluate the expression when y=-4 y^2+5y+1
Step-by-step explanation:
❀ [tex] \underline{ \underline{ \text{Given}}} : [/tex]
y = -4❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Value of y² + 5y + 1❀ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]
~Plug the value of y at first :
➾ [tex] \sf{ {-4}^{2} + 5 \times (-4 )+ 1}[/tex]
~ Evaluate the power : 4²
➾ [tex] \sf{16 + 5 \times (-4 )+ 1}[/tex]
Follow the BODMAS { Bracket , Of , Division , Multiplication , Addition and Subtraction } rule :
~Multiply -5 and 4
➾ [tex] \sf{16 + (-20)+ 1}[/tex]
~ Multiply the signs : ( + ) and ( - ) :
➾ [tex] \sf{16 - 20 + 1}[/tex]
~Add the numbers : 16 and 1
➾ [tex] \sf{17-20}[/tex]
~ Subtract 20 from 17
➾ [tex] \sf{-3}[/tex]
[tex] \pink{ \boxed{ \boxed{ \tt{⟿ \: Our \: final \: answer : -3}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ツ
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Use algebraic rules to show that n(n+1)+2n +2 is equivalent to (n+1)(n+2)
Answer:
This question is asking us to solve both of these equations, so let's do exactly that!
First equation:
[tex]n(n+1)+2n+2\\n^2+1n+2n+2\\n^2+3n+2[/tex]
Second Equation:
[tex](n+1)(n+2)\\n^2+2n+1n+2\\n^2+3n+2[/tex]
Both of the equations result with the same answer, therefore n(n+1)+2n+2 is equivalent to (n+1)(n+2).
Hope that helped! :)
Need help :) with this question
Answer:
D
Step-by-step explanation:
Leave everything the same except you add -5 and 2 =-3
If all of be the simple the side lengths of a triangle had a length of 1 what would be the simplified laws of sines be?
Answer:
sin A = sin B = sin C
Step-by-step explanation:
The sine rule is a law which relates all the three sides of a triangle with the sine of their opposite angles in the triangle. Given a triangle with a side of a and an opposite angle of A, side b with opposite angle B and side c with opposite angle C. The sine rule is given as:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Given that all the side of the triangle have a length of 1, that is a = b = c = 1, hence the equation becomes:
[tex]\frac{sin(A)}{1}=\frac{sin(B)}{1}=\frac{sin(C)}{1}\\\\sin(A)=sin(B)=sin(C)[/tex]
Answer:
sin A = sin B = sin C
Step-by-step explanation:
edg
what is the point slope form of a linear equation?
Answer:
y= m(x-x1) +y1
Step-by-step explanation:
that is point slope form
Answer:
answer 4 is correct
y-y1=m(x-x1)
putting value of m that is slope formula .
Circle A has a circumference of B centimeters.
Circle C’s diameter is 3 times as long as circle A’s diameter.
What is the circumference of circle B?
Circle B has a diameter that is 1 1/2 times as long as Circle A's diameter. What is the circumference of Circle B? Solution. 4 m. If the diameter ...
11/5-1/2= Fraction fraction
Answer:
11/5-1/2 = 22/10-5/10= 17/10 = 1 7/10
Step-by-step explanation:
The answer is 1 7/10
Answer:
17/10 or in mixed numbers 1 and 7/10
Step-by-step explanation:
So first they both have to share a common denominator which will be 10 so for 11/5 you multiply 2 to the denominator. Whatever you do to the bottom you do to the top so 2 times 11 is 22. For 1/2 you multiply the bottom by 5, whatever you do to the bottom you do to the top so 5 times 1 is 5, everything converted should be 22/10-5/10 and that equals 17/10
If x < 0 and y > 0, determine the sign of the real number. (a) x y positive negative (b) xy2 positive negative (c) x − y xy positive negative (d) y(y − x) positive negative
Answer:
From the question it is given that x<0 and y>0 or in other words x is negative and y is positive.
(a)x y : x is negative and y is positive
⇒negative x positive = negative
Therefore, xy is negative
(b)x[tex]y^{2}[/tex] : x is negative and [tex]y^{2}[/tex] is positive
⇒negative x positive = negative
Therefore, x[tex]y^{2}[/tex] is negative
(c) (x − y)xy : x is negative and [tex]y^{2}[/tex] is positive
⇒(x − y) is negative and xy is negative {from (a)}
⇒negative x negative = positive
Therefore, (x-y)xy is negative
(d) y(y − x): x is negative and y is positive
here y - x is positive
⇒positive x positive = positive
Therefore, (y-x)y is negative
Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq.cm,find the total surface area of the cylinder.
Answer:
925.04cm²
Step-by-step explanation:
Curved surface area of a cylinder = 2πrh
r is the radius
h is the height
If the sum of the radius of the base and height of the cylinder is 21 cm, then;
r + h = 21
r = 21-h..... 1
Recall:
CSA = 2πrh
616 = 2πrh ....2
Substitute equation 1 into 2;
616 = 2π(21-h)h
616 = 2π(21h-h²)
616 = 42(3.14)h - 2(3.14)h²
616 = 131.88h - 6.28h²
98.09 = 21h - h²
h²-21h+98.09 = 0
h = 21±√21²-4(98.09)/2
h = 21±√441-392.36/2
h = 21±√48.64/2
h = 21±6/97/2
h = 21+6.97/2 and 21-6.97/2
h = 27.97/2 and 14.03/2
h = 13.985 and 7.015
Since r = 21-h
r = 21 - 13.985
Using r = 7.015
The total surface area = 2πrh + 2πr²
The total surface area = 616 + 2(3.14)7.015²
The total surface area = 616 + 309.04
The total surface area = 925.04
Hence the total surface area of the cylinder is 925.04cm²
Write two different congruent statements that indicate the triangles in each pair are congruent ( ODD NUMBER QUESTIONS ONLY)
Answer:
Step-by-step explanation:
13) QR ≅ BP ; RP ≅ PA ; PQ ≅ AB
ΔQRP ≅ΔBPA by Side Side Side Congruent
QR ≅ BP ; ∠R ≅ ∠BPA ; RP ≅ PA
ΔQRP ≅ ΔBPA by Side Angle Side congruent
15) ML ≅ WV ; MX ≅ WX ; LX ≅ VX;
ΔMLX ≅ ΔWVX Side side side congruent
∠L ≅ ∠V ; ML ≅ WV ; ∠M ≅ ∠W
ΔMLX ≅ ΔWVX Angle side Angle congruent
Identify the equation of the parabola in vertex form if a = 1 and the vertex is (4, 6).
a) y = (x - 6)2 + 4
b) y = (x + 6)2 +
+4
c)y=(x + 4)² +6
d) y = (x - 4)2 + 6
Answer:
B
Step-by-step explanation:
find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon round of the nearest tenth if necessary
16
24
30
14
22
40
Answer:
Int 2520, Ext 360
Int 3960, Ext 360
Int 5040, Ext 360
Int 2160, Ext 360
Int 3600, Ext 360
Int 6840, Ext 360
Step-by-step explanation:
Interior angles of a polygon = (sides - 2) × 180
Exterior angles are always 360
Please Mark as Brainliest if you found it helpful!
The measures of an exterior angle are 2520°, and an interior angle is 360° in the given regular polygon with 16 sides.
What is the interior Angle?An interior angle is defined as an angle produced on the inside of a polygon by extending the sides of the polygon.
Interior angles of a polygon = (sides - 2) × 180°
To determine the measures of an exterior angle and an interior angle given a regular polygon with 16 sides.
Interior angles of a polygon = (sides - 2) × 180°
In this case, the number of sides is 16
Interior angles of a polygon = (16 - 2) × 180
Interior angles of a polygon = (14) × 180
Interior angles of a polygon = 2520
And, Exterior angles are always 360° in the regular polygon.
Similarly, the other regular polygons :
A regular polygon with 24 sides: Int 3960, Ext 360
A regular polygon with 30 sides: Int 5040, Ext 360
A regular polygon with 14 sides: Int 2160, Ext 360
A regular polygon with 22 sides: Int 3600, Ext 360
A regular polygon with 40 sides: Int 6840, Ext 360
Learn more about the exterior angles here :
https://brainly.com/question/28835566
#SPJ2
Can someone help please!
Answer:
650
Step-by-step explanation:
because it says that she earns 50 for each hour so if u multiple 50×13 u get =650
10x + 3 when x=5
Is it 18 553 53 or 23
Answer:
The answer is 53, C.
Step-by-step explanation:
10 * 5 + 3
50 + 3
53
I will give brainiest to whoever answers correctly !!
9514 1404 393
Answer:
a) interest: $215.33
b) proceeds: $3584.67
c) effective rate: 9.01%
Step-by-step explanation:
a) The problem statement tells you the loan was discounted 8.5%. The amount of interest paid is ...
I = Prt
I = $3800·0.085·8/12 ≈ $215.33
__
b) The proceeds of the loan are ...
$3800 -215.33 = $3584.67
__
c) The actual rate is found using the same formula as above, solving for r:
r = I/(Pt) = $215.33/($3584.67·2/3) ≈ 0.0901 = 9.01%
Given \qquad m \angle QPS = 107^\circm∠QPS=107 ∘ m, angle, Q, P, S, equals, 107, degrees \qquad m \angle RPS = 4x + 27^\circm∠RPS=4x+27 ∘ m, angle, R, P, S, equals, 4, x, plus, 27, degrees \qquad m \angle QPR = 9x - 115^\circm∠QPR=9x−115 ∘ m, angle, Q, P, R, equals, 9, x, minus, 115, degrees Find m\angle QPRm∠QPRm, angle, Q, P, R:
Answer:
20°
Step-by-step explanation:
4x+27°+9x-115°=107°
4x+9x + 27°-115°=107°
13x-88°=107°
add 88 on both sides
13x=195°
divide 13 on both sides
x=15
9(15°)-115°
135°-115° = 20
The answer is 20
Answer:
20
Step-by-step explanation:
Find the volume of the prism
Answer:
D
Step-by-step explanation:
volume=1/2 ×6×8×7=168 units³
Each figure shows a triangle with one of its angle bisectors.
Answer:
x = 7
Step-by-step explanation:
XP bisects <X into two equal parts, <1 and <2. Therefore,
<1 = <2
<1 = 5x - 2
<2 = 4x + 5
Thus:
5x - 2 = 4x + 5
5x - 2 - 4x = 5 (subtraction property of equality)
x - 2 = 5
x = 5 + 2 (addition property of equality)
x = 7
PLEASE HELP OMG I WILL DO ANYTHING
Answer:
86.6
Step-by-step explanation:
Given the graph below, write the equation for the line in slope - intercept form.
1
2
A y = 22 + 2
B y = x + 1
C y= -2x - 2
D y= -2x +2
Answer:
A
Step-by-step explanation:
slope is -,y-intercept is 2
y=+mx+2
A
What percent of 30 is 16.5
Answer:
Its 55
Step-by-step explanation:
hope this helps
Answer:
55%
Step-by-step explanation:
Hope this helps you :)
Have a great day!
How long should $1,000 be invested compounded
bimonthly to produce a final balance of $2,000 at
4.15%?
A. 16.70 years
B. 16.72 years
C. 16.76 years
D. 16.73 years
Answer: B. 16.72 years
Step-by-step explanation:
If interest is compounded bi-monthly, the formula to calculate the accumulated amount (A) is given by:-
[tex]A=P(1+\dfrac{r}{24})^{24x}[/tex] , where P = principal , r= rate of interest, x= time period(years).
[1 year =12 months, total periods in 12 months if period per month is 2 = 2 x 12 =24]
Given: P= 1000, A= 2000, r= 4.15% = 0.0415
Substitute all values in formula , we get
[tex]1000\times (1+\dfrac{0.0415}{24})^{24x}=2000\\\\\Rightarrow\ (1.00172916667)^{24x}=2\\\\\text{Taking log on both sides, we get}\\\\\Rightarrow \ln(1.00172916667)^{24x}=\ln2\\\\\Rightarrow 24x\ln(1.00172916667)=\ln2\\\\\Rightarrow\ x=\dfrac{\ln 2}{24\ln(1.00172916667)}\approx16.72\ years[/tex]
Hence, option B. is correct.
Given that XH bisects
Answer choices
A.) 50
B.) 48
C.) 62
D.) none of the above