Answer:
The initial amount of investment was $7,822
Step-by-step explanation:
The formula for compound interest, including principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
A is the future value of the investment/loan, including interestP is the principal investment amount r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forLet us use this rule to solve the question
∵ Sam invests a sum of money in a retirement account with a fixed
annual interest rate of 7% compounded quarterly
∴ r = 7% = [tex]\frac{7}{100}[/tex] = 0.07
∴ n = 4 ⇒ compounded quarterly
∵ After 13 years, the balance reaches $19,280.02
∴ A = 19,280.02
∴ t = 13
Substitute these values in the rule above to find P
∵ [tex]19,280.02=P(1+\frac{0.07}{4})^{4(13)}[/tex]
∴ [tex]19,280.02=P(1.0175)^{52}[/tex]
→ Divide both sides by [tex](1.0175)^{52}[/tex]
∴ 7,821.99888 = P
→ Round it to the nearest dollar
∴ 7,822 = P
∴ P = $7,822
∴ The initial amount of investment was $7,822.
20 mi/h=___________ ft/hr
Answer:
105600
Step-by-step explanation:
Answer:
105,600 feet per hour
Step-by-step explanation:
1 mile = 5,280 feet
5,280 feet x 20 miles = 105,600 feet
Hope I helped!
What’s -4•9-3=
And the dot is multiplication!
Answer:
-39
Step-by-step explanation:
Answer:
-39
Step-by-step explanation:
1. -4 × 9 -3
2. -36-3
3. -39
Please Help me with question
i rly need plz help so plz help :/
Answer:
Step-by-step explanation:
Follow PEMDAS
P = parenthasees
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
There are no P or E or M
so divide
-3 = h + 4
then we just subtract four on both sides
h = -7
Solve the equation below. SHOW UR WORK
10x − 6 = 24
Answer:
3
Step-by-step explanation:
10x-6=24
10x = 24+6 (You switch sides because you can add 24 and 6. You cannot add 10x to 24 or 6)
10x= 30
x= 30/10
x= 3
The answer is 3.
Answer:
x=3
Step-by-step explanation:
10x-6=24
Subtract 6 from 6 and then add 6 to 24
10x=30
30÷10=3
Divide 30 by 10
x=3
Write two inequalities that would have the solution set as graphed below.
Answer:
The answer is x > -1
Step-by-step explanation:
This is because if it were a closed circle, it would have to the include the inequality -1 but since it is an opened circle, that inequality is not included. So in conclusion, Any number could be used to represent x as long as it is a greater number than -1. I hope this makes sense.
x>-1 and x<-2 are two inequalities that would have the solution set as graphed.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
x>-1 and x<-2 are the solutions of the given graph
This is because if it were a closed circle, it would have to the include the inequality -1 but since it is an opened circle, that inequality is not included.
Any number could be used to represent x as long as it is a greater number than -1.
Hence, x>-1 and x<-2 are two inequalities that would have the solution set as graphed.
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Show work please I’ll mark brainliest
Answer:
2 and 4
Step-by-step explanation:
if the area of a right isosceles triangle is 128 sq . m, what will be length of the identical side of the triangle
Let's see. What is a right isosceles triangle?
A right isosceles triangle is a triangle with one right angle with at least two equal sides. In this case, it would have to be ONLY two because it has a right triangle.
What is the formula for the area of an isosceles triangle?
When y = the identical side lengths of the triangle,
and A = area,
(y × y) ÷ 2 = A
Note: Remember to compute from left to right! :)
We divide by two because when you multiple the two identical sides, you would get a square. However, we're trying to find the right isosceles triangle, and we divide by two.
Now, we can plug-in our values!
(y × y) ÷ 2 = 128
(y × y) = 64
Now, we square root both sides!
y = √64
y = 8
The length of the identical sides of the triangle is 8 meters.
[tex]\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}[/tex]
Given that area of an isosceles triangle is 128m² .
And the triangle is right Angled ∆ .
So , the measure of sides along 90° that is perpendicular and the base will be equal .
Let us say that each of the equal sides is x .
Then , we can find the area of the triangle as ,
[tex]\boxed{\bf{\red{ Area_{triangle}=\dfrac{1}{2}\times(base)\times(height)}}}[/tex]
Now , here substitute the respective values ,
[tex]\implies \sf \dfrac{1}{2}\times(base)\times(height)=128m^2[/tex]
[tex]\sf\implies \dfrac{1}{2}\times x \times x = 128m^2[/tex]
[tex]\sf \implies \dfrac{x^2}{2}=128m^2[/tex]
[tex]\sf\implies x^2=128\times2 m^2[/tex]
[tex]\sf\implies x^2=256 m^2[/tex]
[tex]\sf\implies x=\sqrt{256m^2}[/tex]
[tex]\underline{\boxed{\red{\sf\longmapsto x=16m}}}[/tex]
Hence the value of value of identical side of the triangle is 16m .
A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
O y--3x+1
O y-5x+7
O y = -2x - 8
O y = 2x + 16
Answer:
[tex]\displaystyle y=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The equation of any line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
Assume we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Two points are given: (-6,4) and (-2,2). Calculating the slope:
[tex]\displaystyle m=\frac{2-4}{-2+6}=\frac{-2}{4}=-\frac{1}{2}[/tex]
The equation of the line is, so far:
[tex]\displaystyle y=-\frac{1}{2}x+b[/tex]
To calculate the value of b, we use any of the given points, for example (-6,4):
[tex]\displaystyle 4=-\frac{1}{2}(-6)+b[/tex]
[tex]\displaystyle 4=3+b[/tex]
Solving:
b = 1
The equation of the line is:
[tex]\boxed{\displaystyle y=-\frac{1}{2}x+1}[/tex]
We can see none of the choices is correct.
The Smiths spend 11% of their budget on entertainment. Their total budget this year is $1,000 more than
last year, and this year they plan to spend 4,730 on entertainment What was their total budget last year?
Their total budget last year was
fred has $28 to buy sketch paper for his art class. Each sketch pad costs $9. how many sketch pads can he buy?do not include units in your answer
Answer:
3
Step-by-step explanation:
9/3=3.11111111 round it and you get 3
79x10 to the power of 7 +6.5x10 to the power of 6
Express your answer in scientific notation
Answer: 10⁶⁵⁰⁰⁰⁰⁷ × 79
y=t+a/t-b
express t in terms of a, b and y.
t-b
Answer:
t=(a+by)/(y-1)
Step-by-step explanation:
(t-b)y =t+a
ty-by = t+a
ty-by=t+a
ty-by=a+by
t(y-1)=a+by
thus,
t=(a+by)/(y-1)
solve by substitution
y=6x-23, 4x-5y=37
Answer:x=3 , y=-5 OR (3,-5)
Step-by-step explanation:
I can add fractions with unlike denominators 3/7 + 1/6 =
PLEASE WITH THIS QUESTION
Answer:
25/42
Step-by-step explanation:
first find same denominators
18/42 + 7/42
then add the new fractions
18/42 + 7/42 = 25/42
Hope this helps :)
Have a nice day :)
Can you give me brainliest plz :)
Answer:
25/42
Step-by-step explanation:
You can get to 25/42 by finding the least common denominator, or in layman's terms, by seeing what the lowest number the two denominators can both EQUALLY go in to. in this case it's 42, as both 6 and 7 can go into 42 equally, and 42 is the lowest number that they both can go into. So after you find the least common denominator, you make that the denominator of both fractions, and multiply the two numerators by however many times you had to multiply the denominators by. for example, to get 7 to 42, you need to multiply it by 6, so you would then multiply the numerator, in this case it's 3, 6 times, netting you 18. you do the same thing with the other fraction, since the numerators 1, you multiply it by 7, since you had to multiply 6 by 7 to get 42. this leaves you with 18/42 + 7/42, which you can now normally add together to get 25/42, and since it can't be reduced, it stays this way. Hope this helps :)
help me plz its urgent
Answer:
2 and 3
Step-by-step explanation:
Which of the following is a true statement?
The opposite of −45 is equal to the absolute value of −45.
The opposite of 45 is equal to the absolute value of −45.
The opposite of −45 is not equal to the absolute value of 45.
The opposite of 45 is equal to the absolute value of 45.
Answer:
The opposite of 45 is equal to the absolute value of -45.
Absolute value means switching to to a negative if it's a positive and if it's a negative to a positive. For 0, it remains 0 and doesn't switch to a -/+.
Answer:
The opposite of 45 is equal to the absolute value of -45
Step-by-step explanation:
Hope this helps!
what expression is equivalent to 6(3+0.5)
A.6(3)+0.05
B.(6+3)+(6+0.5)
C.6(3)+6(0.05)
D.6(3)x6(0.05)
A hot air balloon is flying 260 feet in the air. It descends at a rate of 10 feet per second. Identify the rate of change
Answer:
26 secs until reaching ground level
Step-by-step explanation:
260/10=26
Which ratio shown below is NOT equivalent to − 15 23
Answer:
what is the answer below
Step-by-step explanation:
A plumber charges $25 for a service call and $50 per hour of service.
Write an equation for the cost, c, after h hours of service. If a plumber
spent 3 and a half hours at my house, how much is my bill?
Equation:
Answer:
Answer:
25+50h=c
$200 is the your bill
Step-by-step explanation:
50×3.5=175
175+25=200
A store buys a jacket for 20:00$ and then sells it to a customer for 80% more than that. What is the selling price of the jacket
Answer:
$36
Step-by-step explanation:
20(1.80) = 36
Graph the exponential function
f(x)=2/5)x
Answer:
Step-by-step explanation:
What’s is
the slope of the line
that contains these Points -2,8) (1,2)(2,0)(4,-4)
Solve with algebra
Answer:
-2x
Step-by-step explanation:
1.) you pick two points I am going to use (2,0) and (4,-4)
2.) use the slope formula y2-y1/x2-x1
3.) substitute the points into the equation -4-0/4-2
4.) solve the equation (-4-0= -4) / (4-2= 2)
5.) the slope is -4/2 or -2
What is the equation of the line that passes through the points (-6,-7) and (6,3)
Answer:
[tex]y=\frac{5}{6} x-2[/tex]
Step-by-step explanation:
Point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]where [tex](x_1, \ y_1)[/tex] are coordinates of a point that the line passes through, and [tex]m[/tex] is the slope of the line.
We are given two points that the line passes through, but we are not given the slope.
We can find the slope by using the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]where [tex](x_1, \ x_2)[/tex] and [tex](y_1, \ y_2)[/tex] are two points that the line passes through.
Substitute (-6, -7) and (6, 3) into the slope formula:
[tex]\frac{3-(-7)}{6-(-6)} = \frac{10}{12} = \frac{5}{6}[/tex]The slope of this line is 5/6. Now we are able to use the point-slope equation to find the slope-intercept equation [tex](y=mx+b)[/tex] of this line.
Substitute a point that the line passes through and the slope of the line into the point-slope equation. I'm using the point (6, 3).
[tex]y-y_1=m(x-x_1)[/tex][tex]y-(3)=\frac{5}{6} (x-(6)[/tex][tex]y-3=\frac{5}{6} (x-6)[/tex]Distribute 5/6 inside the parentheses.
[tex]y-3=\frac{5}{6} x-\frac{30}{6}[/tex][tex]y-3=\frac{5}{6} x-5[/tex]Add 3 to both sides of the equation.
[tex]y=\frac{5}{6} x-2[/tex]This is the equation of the line that passes through (-6, -7) and (6, 3) in slope-intercept form.
Imani is making costumes for a play. She spent $146.58 on 21 yards of fabric. Write and solve an equation to find how much Imani paid for each yard of fabric.
Multiple choice question.
A)
21p=146.58; $6.98 per yard
B)
146.58p=21; $0.14 per yard
C)
146.58(21)=p; $3078.18 per yard
D)
21p=146.58; $3078.18 per yard
Answer:
A
Step-by-step explanation:
21 yards and Total cost of $146.58
p = 1 yard
Equation: 21p = 146.58
p = 146.58/21
p = 6.98
21p=146.58 will describe the equation and the amount paid for each yard is $6.98 so option (A) will be correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Amount of fabric = 21 yards
Since cost per yard of fabric is given by p
So,
The total cost of fabric = Amount of fabric × cost per yard
146.58 = 21p
21p=146.58
Now,
p = 146.58/21 = 6.98.
Hence "21p=146.58 will describe the equation and the amount paid for each yard is $6.98".
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Help!!!!!!!!!!!!!!!!!!!!!!
Answer:
w - 7 < -22
Step-by-step explanation:
Answer:
w - 7 < -22
Step-by-step explanation:
This should be correct. Let me know!
Please help with this legit answers only please!!!
Calculate and Find the slope of the line
Answer:
3
Step-by-step explanation:
the slope id going up at a rate of 3
A video game console uses 154 watt-hours of energy each hour. The console was used 276 hours last year. How many watt-hours of energy did the console use?
Answer:
The console was used 42,504 watt-hours of energy last year
Step-by-step explanation:
video game console uses 154 watt-hours of energy each hour
The console was used 276 hours last year.
How many watt-hours of energy did the console use?
Watt hours of energy used = 154 × 276
= 42,504 watt-hours of energy
The console was used 42,504 watt-hours of energy last year
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,112) and (6,168) to find the number of soda bottles the machine can make each minute.
Using y to represent number of bottles filled in x minutes, y = 250x.
This is rather basic, and I urge you to think about it so that it's very clear to you, and you will be able to do similar problems on your own in the future.
The graph will be a straight line passing through the origin (0,0).
Answer:This is rather basic, and I urge you to think about it so that it's very clear to you, and you will be able to do similar problems on your own in the future.
Step-by-step explanation: