Answers
Given equations:
x + y = 15 . . . . . . . . (1)y = 4x . . . . . . . . . . . (2)To find :
value of xvalue of yPut value of y of second equation (i.e y = 4x) in equation one (i.e x + y = 15)
➞ x + y = 15
➞ x + 4x = 15
➞ 5x = 15
Divide both LHS and RHS by 5
➞ (5x)/5 = 15/5
➞ x/1 = 3/1
➞ x = 3
Now put value of x in equation 2
{Note : value of x can be inserted both in equation 1 and 2}
➞ y = 4x
➞ y = 4 × 3
➞y = 12
Verification :
put value of x and y in equation 1 :
x + y = 1512 + 3 = 1515 = 15LHS = RHS
hence verified !
put value of x and y in equation 2 :
y = 4x12 = 4 × 312 = 12LHS = RHS
hence verified !
∴ Value of x and y is 3 and 12 respectedly .
REQUIRED ANSWER :
(x , y) = (3 , 12)
Answer:
(3, 12)
Step-by-step explanation:
Given equations:
Equation 1: x + y = 15Equation 2: y = 4xSubstitute Equation 2 into Equation 1 and solve for x:
⇒ x + 4x = 15
⇒ 5x = 15
⇒ x = 15 ÷ 5
⇒ x = 3
Substitute the found value of x into Equation 2 and solve for y:
⇒ y = 4(3)
⇒ y = 12
Therefore, the solution of the system is (3, 12)
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Answers
Answer:
42 degrees
Step-by-step explanation:
48 + x = right angle = 90 degrees
48+ x = 90
x = 42 degrees
Situation:
You invest $100 in an account that pays
an interest rate of 6.5%, compounded
continuously.
Calculate the balance of your account after 6
years. Round your answer to the nearest
hundredth.
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 6.5\%\to \frac{6.5}{100}\dotfill &0.065\\ t=years\dotfill &6 \end{cases} \\\\\\ A=100e^{0.065\cdot 6}\implies A=100e^{0.39}\implies A\approx 147.70[/tex]
The balance of your account after 6 years with continuous compounding would be approximately $147.56.
To calculate the balance of your account after 6 years with continuous compounding, you can use the formula:
[tex]\[ A = P \times e^{rt} \][/tex]
where:
[tex]\( A \) =[/tex] the balance after [tex]\( t \)[/tex] years
[tex]\( P \) =[/tex]the principal amount (initial investment) = $100
[tex]\( r \) =[/tex] the annual interest rate (in decimal form) = 6.5% = 0.065
[tex]\( t \) =[/tex] the number of years = 6
[tex]\( e \) =[/tex] Euler's number (approximately 2.71828)
Let's plug in the values and calculate the balance:
[tex]\[ A = 100 \times e^{0.065 \times 6} \]\[ A = 100 \times e^{0.39} \]\[ A = 100 \times 1.47560080488 \]\[ A = 147.560080488 \][/tex]
Rounding the answer to the nearest hundredth:
[tex]\[ A \approx $147.56 \][/tex]
So, the balance of your account after 6 years with continuous compounding would be approximately $147.56.
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a bookstore sells 7 books for $99.75 which table represents the relationship between number of books and total price?
Answers
Answer:
You did not provide the tables to choose from, but the relationship between number of books and total price is that each book is 14.25. Hope that helps at least.
please help due in 13 mins.
Answers
Answer:
Graph A
Step-by-step explanation:
Becuase if we rewrite it in slope-intercept form then we get y=3/4x-13/2
Which of the following are square roots of the number below? Check all that
apply.
400
A. -20
B. -4001/2
C. 40
D. 4001/2
E. 10
F. 20
Answers
What is the value of the x-coordinate of point A?
Choose 1 answer
A) sin(50)
B) cos(50)
C) sin(140)
D) cos(140)
E) sin(230)
F)cos(230)
Answers
Explanation:
Cosine corresponds to the x coordinate of points on a circle when the radius is drawn in like this, so the answer would be the cos of that angle, but you have to account for the fact that the 50 degree angle marked is just the reference angle not the entire angle so you have to add 180 degrees to that to get 230.
The function g is given by g(x) = ax^2 − b, where a and b are real numbers. If g(2) = −5 and g(−1) = 2, find the values of a and b.
Answers
Answer:
a = 1
b = -1
Step-by-step explanation:
[tex]g(x)=ax^2-b \quad \quad \textsf{(where }\:a\:\textsf{ and }\:b\:\textsf{ are real numbers)}[/tex]
Create 2 equations with b as the subject using the given information.
Equation 1
[tex]\begin{aligned}g(2) &=-5\\\implies a(2)^2-b &=-5\\4a-b &=5\\ b&=4a-5\end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}g(-1) &=2\\\implies a(-1)^2-b &=2\\a-b &=2\\ b &=a-2\end{aligned}[/tex]
Equate the equations and solve for a:
[tex]\begin{aligned}b & =b\\\implies 4a-5 & = a-2\\3a & = 3\\a & = 1\\\end{aligned}[/tex]
Substitute the value of a into Equation 2 and solve for b:
[tex]\begin{aligned}b & =a-2\\a=1 \implies b & =1-2\\b & = -1\end{aligned}[/tex]
Answer:
a = -7/3
b = -13/3
Step-by-step explanation:
Making equations in terms of 'a' and 'b' :
g(2) = -5 = a(2)² - b ⇒ 4a - b = -5 [Equation 1]g(-1) = 2 = a(-1)² - b ⇒ a - b = 2 [Equation 2]Subtract : Equation 1 - Equation 2
4a - b - a + b = -5 - 23a = -7a = -7/3Finding b :
-7/3 - b = 2b = -7/3 - 6/3b = -13/3Kayden walked 18 miles in 6 hours. What was his walking rate in miles per hour?
Answers
Answer:
3
Step-by-step explanation:
If he went 18 miles in 6 hours we can simpliy divide 18 by 6 which is 3 miles per hour
need help ASAp pleaseeeeeeeeeeeeeeeee
Answers
Henry made a shirt using 1/3 yards of yellow fabric and 1/2 yards of red fabric. How many yards of fabric did he use in all?
Write your answer as a fraction in simplest form.
Answers
I think that the answer is 123
Evaluate x + y when x = -19/12 and y = -7/5
Answers
Hey there!
x + y
= -19/12 + (-7/5)
= -19/12 - 7/5
= -95/60 + -84/60
= -95/60 - 84/60
= -95 + (-84) / 60 - 0
= -95 - 84 / 60
= -179 / 60
Therefore, the answer should be:
-179 / 60
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
x+y= -2 59/60
Step-by-step explanation:
=-19/12-7/5 = -95-84
60
=-179
60
= -2/59/60
What is the y-value of the vertex of 4x^+ 8x - 8?
Answers
Answer: The y-value of the vertex is
Step-by-step explanation: we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
In this problem we have
-----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
The vertex is the point
The y-value of the vertex is
When paying off debts, you should _____.
Answers
Answer:
Continue to make the minimum monthly payment on all of your debts while putting as much extra money as possible toward your smallest debt
Step-by-step explanation:
Once that debt is paid off, put your extra money toward your next-smallest debt, and so on. The bigger you build your debt snowball, the closer you'll get to debt freedom
Find the sum of the first 20 term of the Series 5+8+11+14+....
Answers
Step-by-step explanation:
Sn=n/2(2a+(n-1)d). n=20
S20= 20/2 (2x5+(20-1)3 a=5
S20=10(10+57). d=8-5=3
S20=10x67
S20= 670
Hope this helps you
have a great day
ryan’s mom randomly chooses two days each week for Ryan to do his chores. what is the probability that she picks Saturday and Sunday?
Answers
Answer:
2/7= 28.6%
Step-by-step explanation:
Since those are 2 specific days out of seven, we divide it so that there are 2/7 days. Then we change it to a percentage, which would be the equation of 2/7*100, which is equal to 28.57%, which rounds to 28.6%.
I need help plss, whoever answers me, I’ll give brainliest.
Answers
Answer:
12.
Step-by-step explanation:
36 = 3 * 12
48 = 4 * 12,
write the equation of the line that passes through (-7,-4) and (-6,-2) in slope intercept form
Answers
Answer:
y = 2x + 10
Step-by-step explanation:
Hi there!
We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, we need to find the slope (m) of the line
The slope can be calculated from 2 points using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes
[tex]x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2[/tex]
Substitute these values into the formula (note: remember that the formula has subtraction in it!)
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-2--4}{-6--7}[/tex]
Simplify
m=[tex]\frac{-2+4}{-6+7}[/tex]
Add the numbers
m=[tex]\frac{2}{1}[/tex]
Divide
m=2
The slope of the line is 2
We can substitute that in:
y = 2x + b
Now we need to find b
As the equation passes through both (-7,-4) and (-6,-2), we can use either point to help solve for b
Taking (-6, -2) for example:
Substitute -6 as x and -2 as y into the equation.
-2 = 2(-6) + b
Multiply
-2 = -12 + b
Add 12 to both sides
-2 = -12 + b
+12 +12
___________
10 = b
Substitute 10 as b.
y = 2x + 10
Hope this helps!
Topic: Finding the equation of a line
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Which graph best represents this relationship?
distance = 20 x time
OA. graph A
OB. graph B
O C. graph C
OD. graph D
Answers
Answer:
graph C represents this relationship best.
please help and ty if u do <33
Answers
Answer:
[tex]3^{-5} =\frac{1}{3^{5} } = (\frac{1}{3} )^{5}[/tex]
[tex]5^{-3} = \frac{1}{5} *\frac{1}{5} *\frac{1}{5} = \frac{1}{5*5*5}[/tex]
Step-by-step explanation:
15 and 1/15 do not equal anything.
Hope this helped!
The area of the pool when viewed from above is approximately 78.5 m2. What is the radius of the pool? (Use 3.14 for pi.)
5 m
11 m
6 m
12 m
Answers
Step-by-step explanation:
I guess it is a circular pool.
the area of a circle is
pi×r²
in our case we know
pi×r² = 78.5
3.14×r² = 78.5
r² = 78.5/3.14 = 25
r = 5 m
Q6.
Jake and Sarah each played a computer game six times.
Their scores for each game are shown below.
Jake
10 9
8
11 12
8
10
Sarah
2
10 7
14 4
(a) Who had the most consistent scores, Jake or Sarah?
You must give a reason for your answer.
Answers
Calculate the accumulated amount after 3 years, if R5 000 is invested at an interest rate of 10% compounded quarterly?
Answers
Answer:
R6,724.44 or so I think that's right
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=5000\left(1+\frac{0.10}{4}\right)^{4\cdot 3}\implies A=5000(1.025)^{12}\implies A\approx 6724.44[/tex]
Kathy sells encyclopedias and earns $40 for each set she sells. How many sets did she sell if she earned $600 last week?
Answers
Answer:
15
Step-by-step explanation:
Given:
Kathy sells encyclopedias and earns $40 for each set she sells.
To Find:
How many sets did she sell if she earned $600 last week?
Solve:
Since kathy sells encyclopedias and earns $40 for each set she sells.
And if kathy total is $600
then we do
$600 divide by $40
600/40 = 15
Hence, she sold 15 sets last week.
Kavinsky
Answer:
15
Step-by-step explanation:
This is basically 600/40
600/40 = 15
When a plane intersects a sphere, what two-dimensional shape describes the cross-section?
Answers
Answer:
A Circle
Step-by-step explanation:
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 43 people is taken. Step 1 of 2 : What is the probability of a random person on the street having an IQ score of less than 98? Round your answer to 4 decimal places, if necessary.
Answers
Using the normal distribution, it is found that there is a 0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Normal Probability Distribution
In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean.After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, given by and.
The probability of a random person on the street having an IQ score of less than 98 is the p-value of Z when X = 98, hence:
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]Z=\dfrac{98-100}{15}[/tex]
[tex]Z=-0.13[/tex]
Has a p-value of 0.4483.
0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.
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Find the area of the circle. Use 3.14 for pie. Do not round your answer.
and inside the circle it says 14 inches
Answers
radius= 14 inches
to find:the area of the circle.
solution:[tex]area = \pi {r}^{2} [/tex]
[tex]a = \pi \times {14}^{2} [/tex]
[tex]a = 615.75216[/tex]
[tex]a = 615.75 \: {in}^{2} [/tex]
therefore, the area of the circle is 615.75 square inches.
The area is:
615.44 in²
Work/explanation:
The formula for the area of a circle is:
[tex]\sf{A=\pi r^2}}[/tex]
Where
A = area
π = 3.14
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 14\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times14^2}\\\\\sf{A=3.14\times196}\\\\\sf{A=615.44\:in^2}[/tex]
Hence, the area is 615.44 in².Find the median of the data set: 5, 19, 11, 3, 21, 9. (Round your answers to one decimal place, if necessary.)
Answers
Answer:
3.33
Step-by-step explanation:
In this case, the number we have is an even number so you can not choose the one in the middle so you would take those two and add the then divide them by how many numbers you have there which would be 6 in the case and then round it to the nearest decimal.
Complete Syd’s work to find the scale factor Scale factor = StartFraction scale drawing dimension over Original dimension EndFraction = StartFraction 7.5 over 3 EndFraction What is the scale factor? 2.5 3 4.5 7.5
Answers
Answer:
2.5
Step-by-step explanation:
i really need help bad!!
Answers
Answer:
5. x = 17
7. x = 2
Step-by-step explanation:
The applicable relation is, "the product of the near distance to the circle and the far distance to the circle is the same for each secant." Distance is measured from the point where the secants intersect.
__
5.Using the rule, we have ...
7(7+x) = 8(8+13)
7+x = 24 . . . . . . . . . divide by 7
x = 17 . . . . . . . . . . subtract 7
__
7.The same rule applies.
7(7 +6x -1) = 9(9 +x +3)
42x +42 = 9x +108 . . . . . . simplify
33x = 66 . . . . . . . . . . . . . subtract 9x+42
x = 2 . . . . . . . . . . . . . . divide by 33
Solve the division problem:
10)430
O A. 40
B. 43
C. 400
D. 403
Answers
Answer is option B.43
430÷ 10 = 43
By : Modern Einstein
