Answer:
(1/2, 5)
Step-by-step explanation:
8x + 7y = 39
-2(4x - 14y = -68)
-8x + 28y = 136
8x + 7y = 39
add the two equations together
35y = 175
y = 5
8x + 7(5) = 39
8x = 4
x = 1/2
Answer:
Using the linear combination method, you can multiply the first equation by 2 and add the equations to get 20x = 10. Dividing both sides by 20, x = 1/2. To solve for y, substitute 1/2 for x in the equation 8x + 7y = 39 to get 4 + 7y = 39. Solving this equation, y = 5. Checking this in the other equation, 4(1/2) – 14(5) = –68 results in 2 – 70 = –68 or –68 = –68. The solution of the system shown is (1/2, 5). The system 8x + 7y = 39 and 20x = 10 is formed by replacing 4x –14y = –68 by a sum of it and a multiple of 8x + 7y = 39. Since 20(1/2) = 10, the system 8x + 7y = 39 and 20x = 10 also has a solution of (1/2, 5).
Step-by-step explanation:
exactly from EDGE 2020
(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
Expand the following bracket -5(3c+6)
Answer:
-15c - 30
Step-by-step explanation:
-5(3c+6)
Expand or distribute the term outside the bracket to the terms inside.
-5(3c) - 5(6)
-15c - 30
Answer:
The answer is -15c - 30
Step-by-step explanation:
You have to apply Distributive Law :
[tex]a(m + n) = am + an[/tex]
So for this question :
[tex] - 5(3c + 6)[/tex]
[tex] = - 5(3c) - 5(6)[/tex]
[tex] = - 15c - 30[/tex]
A bank is advertising that new customers can open a savings account with a 2% interest rate compounded annually. Kristy invests $3000 in an account at this rate. If she makes no additional deposits or withdrawals on her account, find the amount of money she will have after 5 years. A.)1020.21 B.)2274.57 C.)3312.24 D.)4158.18
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
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
Which table of values represents the exponential function f(x)=(15)x?
Answer:
Step-by-step explanation:
Unfortunately, f(x)=(15)x is not an exponential function. I will assume that you meant
f(x) = 5^x
The second table fits this function. Note that if x = -2, f(-2) = 5^(-2) = 1/25.
PLEASE HELP!!:(((
A sphere has a circumference of its great curled equal to 20 Pi what is the volume of that sphere
If you could please answer this I would highly appreciate it!!!
Answer:
Third one
Step-by-step explanation:
The circumference of a circle is given by the formula:
P = d*π d is the diameterP= 20π ⇒ d*π = 20π ⇒ d= 20
The volume of a sphere is given by the formula:
V = [tex]\frac{4}{3}[/tex]*π*r³ r is the radius wich is d/2r = 20/2 = 10V= [tex]\frac{4}{3}[/tex]*π*10³
V= 1333.33*π
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
The admission fee at an amusement park is $1.75 for children and $4.80 for adults. On a certain day, 303 people entered the park, and the admission fees collected totaled $881. How many children and how many adults were admitted? Number of children equals= ? Number of adults equals=?
Answer:
Children 188
Adults. 115
Step-by-step explanation:
Let the no. of children be x and adults be y
x + y = 303
x = 303 - y. .... .....(1)
1.75x + 4.80y = 881. ...........(2)
Substituting,
1.75(303-y) +4.80y = 881
530.25 -1.75y + 4.80y = 881
530.25 + 3.05y = 881
3.05y = 881 - 530.25
y = 350.75 / 3.05 = 115 = adults
Children = 303-115 = 188
Solve (x - 4)2 = 5.
O A. x-5+
O B. * = 41.5
O C. X = 9 and x = -1
O D. X=-4115
Answer:
x=4_+√5option B is the correct option.
Solution,
[tex] {(x - 4)}^{2} = 5 \\ [/tex]
x-4=_+√5
X=4_+√5
Hope this helps...
Good luck on your assignment...
Answer:
(x-4)^2 =5
x^2-16=5
x^2=5+16
x^2=21
√x^2=√21
x=√21
Step-by-step explanation :
First of all open the bracket which has square
Secondly change the position of 16
Note: when a number changes its place , the symbol also changes
then when you get the value take the square root on both sides
and you'll get the answer
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
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]
To know more about Multiplication click the link given below.
https://brainly.com/question/16871801
out of 8000 students of Chitwan district 10% take tuition in various subject before the SLC examination. Among them 40% take tuition in English only,20% in math only and 80 students in other subject. Compare the number of students who take tuition on both subject and the total number of students.
Answer:
Out of 8000 students, 10% take tuition in various subjects before the exam.
10% of 8000 is:
10/100 * 8000 = 800
Among the 800, 40% take tuition in English only and 20% take tuition in Math only.
80 students take tuition in other subjects, therefore, in percentage:
80/800 * 100 = 10%
Therefore, the percentage of students that take tuition in both Math and English is:
100% - (40% + 20% + 10%) = 100% - 70% = 30%
30% of the 800 students take tuition in both subjects. That is:
30/100 * 800 = 240 students
Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.
In percentage:
240/8000 * 100 = 3%
3% of students take tuition in both English and Math.
In Ratio:
3 : 100
3 out of 100 students take tuition in English and Math.
Given that r = (7,3,9) and v=(3,7,-9), evaluate r + v. A. (-21,-21,81) B. (10,10,0) C. (21,21,-81) D. (-10,-10,0)
Answer:
B. (10, 10, 0)
Step-by-step explanation:
Each component of the sum is the sum of corresponding components:
r + v = (7, 3, 9) +(3, 7, -9) = (7+3, 3+7, 9-9) = (10, 10, 0)
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
can you help me to find the values of abc and cde ?
Answer:
88° and 132°
Step-by-step explanation:
The sum of angles in a pentagon ( a 5-sided shape) is given as
= (5 - 2) 180°
= 540°
The angles ∠EAB and ∠AED are supplementary hence the sum is 180° Therefore,
∠AED + 110 = 180
∠AED = 180 - 110
= 70°
Given that the sum of the angles in a pentagon is 540° then
110 + 70 + 2k + 140 + 3k = 540
5k + 320 = 540
5k = 540 - 320
5k = 220
k = 220/5
= 44°
Hence the angle ∠ABC
= 2 × 44
= 88°
∠CDE
= 3 × 44
= 132°
Erin travels north and south from Main Station. The distance, in km, of the train from Main Station is
modeled by the function d(t) = t3 - 9t2 + 6t, where North is positive and South is negative. Time
elapsed after the start of a shift, in hours, is represented by t, where t € (0,12]. 'If the shift starts at
noon, determine at which time(s) the train is more than 16 km south of Main Station.
Answer:
The times are t = 9, t = 10, t = 11 and t = 12
Step-by-step explanation:
For the train to be more than 16 km South and since south is taken as negative,
d(t) > -16
t³ - 9t² + 6t > -16
t³ - 9t² + 6t + 16 > 0
Since -1 is a factor of 16, inserting t = -1 into the d(t), we have
d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)
So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16
Factorizing t² - 10t + 16, we have
t² - 2t - 8t + 16
= t(t - 2) - 8(t - 2)
= (t -2)(t - 8)
So t - 2 and t - 8 are factors of d(t)
So (t + 1)(t -2)(t - 8) > 0
when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0
when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0
when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0
when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0
Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8
Since t ∈ (0, 12]
In the interval 0 < t < 2 the only value possible for t is t = 1
d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2
Since d(1) < -16 this is invalid
In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.
So,
d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km
d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km
d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km
d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km
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 =
98If 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:
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.
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
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
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
∠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!
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
Three 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.
Which linear inequality is represented by the graph? y ≤ 2x + 4 y ≤ one-halfx + 3 y ≥ One-halfx + 3 y ≥ 2x + 3
Answer:
Option B.
Step-by-step explanation:
From the given graph it is clear that the related line passes through the points (0,3) and (2,4).
So, the equation of related line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]
[tex]y-3=\dfrac{1}{2}x[/tex]
Add 3 on both sides, we get
[tex]y=\dfrac{1}{2}x+3[/tex]
The related line is a solid line and shaded portion lies below the line. So, the sign of inequality must be ≤.
[tex]y\leq \dfrac{1}{2}x+3[/tex]
Therefore, the correct option is B.
Answer:
y ≤ one-halfx + 3
Step-by-step explanation:
The population, P (t), of an Ontario city is modeled by the function p(t) = 14t^2 + 650t + 32,000. If t = 0 corresponds to the year 2,000. When was the population 25,000?
Answer:
The population of the city was 25,000 in 1970 and 1983.
Step-by-step explanation:
In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.
[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]
Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.
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 - $b$.
Learn more about linear expressions at
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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]