If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.
If we knew that two angles were complementary and were given the measure of one of those angles, then we can find the measure of the other angle by subtracting the given measure of one angle from 90
Solution:
Given that,
If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle
Yes we can find the measure of another angle
Complementary angles:
Complementary angles are two angles whose sum is 90 degrees
Therefore, if measure of one angle is given, then we can find the measure of another angle
Measure of another angle = 90 - measure of one angle
Example:
If x and y are complementary angles
Given that measure of angle x is 45 degrees
Then we can say,
According to complementary angles definition
x + y = 90
45 + y = 90
y = 90 - 45
y = 45
Thus measure of other angle y is found to be 45 degrees
Knowing the measure of one angle in a pair of complementary angles allows you to find the measure of the other angle because the sum of their measures is equal to 90 degrees.
Explanation:Yes, you would be able to find the measure of the other angle. This is because in geometry, two angles are said to be complementary if the sum of their measures is equal to 90 degrees. Thus, knowing the measure of one angle allows you to find the measure of the other angle by subtracting the known angle from 90.
For instance, if you were told one angle measures 35 degrees and you know the two angles are complementary, you could calculate the measure of the other angle as follows: 90 - 35 = 55 degrees. So, the other angle measures 55 degrees.
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suppose that phil had decided to take out a private loan for $9,000 where loan payments start as soon as the loan amount is deposited in his student account and continue for 10 years.the interest rate is 8.1% what is the total amount he will pay back?
The total amount he will pay back=$16290
Step-by-step explanation:
Given, Phil had decided to take out a private loan for $9,000 where loan payment start as soon as the loan amount is deposited in his student account for 10 year. The interest rate is 8.1% .
P =$ 9,000 r = 8.1% and t = 10 years
Simple interest
Interest(I) [tex]= \frac{P\times r \times t}{100}[/tex]
[tex]=\$\frac{9000\times 8.1 \times 10}{100}[/tex]
[tex]=\$ 7290[/tex]
The total amount he will pay back =$(7290 + 9,000)=$16290
Final answer:
To calculate the total amount Phil will pay back on a $9,000 private loan with 8.1% interest over 10 years, multiply the principal by (1 + interest rate) raised to the number of years. The total amount paid back is $17,925.56.
Explanation:
To calculate the total amount Phil will pay back, we need to calculate the loan payments for 10 years. First, we can calculate the annual payment using the formula:
Annual Payment = Principal x (1 + Interest Rate)^Number of Years
Substituting in the values Principal = $9,000, Interest Rate = 8.1% (or 0.081), and Number of Years = 10, we have:
Annual Payment = $9,000 x (1 + 0.081)^10 = $9,000 x 1.991729 = $17,925.56
Therefore, the total amount Phil will pay back over 10 years is $17,925.56.
Nancy opened a savings account 7 years ago. The account earns 5% interest, compounded quarterly. If the current balance is $1,000.00, how much did she deposit initially?
The amount deposited initially is $ 706.22
Solution:
The formula for amount using compound interest is given as:
[tex]A = p(1+\frac{r}{n})^{nt}[/tex]
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
From given,
t = 7 years
A = 1000
P = ?
[tex]r = 5 \% = \frac{5}{100} = 0.05[/tex]
n = 4 (since compounded quarterly)
Substituting the values we get,
[tex]1000 = p(1+\frac{0.05}{4})^{4 \times 7}\\\\1000 = p(1+\frac{0.05}{4})^{28}\\\\1000 = p(1+0.0125)^{28}\\\\1000 = p(1.0125)^{28}\\\\1000 = p \times 1.4159923\\\\p = \frac{1000}{1.4159923}\\\\p = 706.2185 \approx 706.22[/tex]
Thus amount deposited initially is $ 706.22
Is -8-2(3+2n)+7n equivalent to -30-13n. Explain why or why not.
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
Step-by-step explanation:
Let us revise the operation of the negative and positive numbers
(-) + (-) = (-)(-) × (-) = (+)(-) + (+) = the sign of greatest [(-) if the greatest is (-) or (+) if the greatest is (+)](-) × (+) = (-)(-) - (+) = (-)(+) - (-) = (+)∵ The expression is -8 - 2(3 + 2n) + 7n
- Simplify it
∵ 2(3 + 2n) = 2(3) + 2(2n) = 6 + 4n
∴ -8 - 2(3 + 2n) + 7n = -8 - (6 + 4n) + 7n
- Multiply the bracket by (-)
∴ -8 - (6 + 4n) + 7n = -8 - 6 - 4n + 7n
- Add the like terms
∴ -8 - (6 + 4n) + 7n = (-8 - 6) - 4n + 7n
∴ -8 - (6 + 4n) + 7n = -14 + 3n
∴ -8 - 2(3 + 2n) + 7n is equivalent to -14 + 3n
∵ -14 + 3n ≠ -30 - 13n
∴ -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
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You can learn more about the directed numbers in brainly.com/question/10364988
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What is the slope of the line represented by the equation f(x) = -3x + 7?
Answer:
Step-by-step explanation:
Analyze the following pattern
1, 2, 5, 10, 17,....
what's the 8th term of the pattern
Answer:
50
Step-by-step explanation:
Add the next odd number to get the next term
1
1+1=2
2+3 =5
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50
A company rents bicycles for a few of $10 plus $4 per hour of use. Write an algebraic expression for the total cost in dollars for renting a bicycle for h hours.
Answer: Cost(c) t（time)
c=10+4t
Step-by-step explanation:
Suppose y varies directly with x , if y =-14 when x = -7 , what is the value of x when y =22
3b+14 b=0
random stuff cuz need to reach limit
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{If\ b = 0\ then\ replace\ b\ in\ the\ equation\ with\ 0\ to\ make\ it\ easier\ to\ solve}[/tex]
[tex]\mathsf{New\ equation: 3(0)+ 14}[/tex]
[tex]\mathsf{3(0) + 14=\ ?}\\\mathsf{3(0) = 0}\\\mathsf{0+14=?}\\\mathsf{0+14=14}\\\boxed{\boxed{\bf{Answer:\mathsf{14}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
B = 0
You solved it thx for the points :v
Select the appropriate terms from the drop down boxes below to correctly complete the statement.
The quadrilaterals are similar because quadrilateral FGHJ is the image of quadrilateral ABCD under a dilation with a center of
Answer: The quadrilaterals are similar because quadrilateral FGHJ is the image of quadrilateral ABCD under a dilation with a center of.....
all of it! it school! very inappropriate!
Step-by-step explanation: it looks like it's inappropriate
Answer:
all
Step-by-step explanation:
A food stand sold hamburgers, ice cream cones, and hot dogs at a football game. Hamburgers were sold for $3.25, ice cream cones were sold for $2.50, and hot dogs were sold for $1.75. The total number of hamburgers, ice cream cones, and hot dogs sold was 104, and the total amount of money from these items was $248.75. If $80.50 was made just from selling hot dogs, how many ice cream cones were sold?
Answer y=27
27 ice cream cones were sold
Round 227 to the nearest 100
Find the exact values below. If applicable, click on "Undefined".
cot 7pi/6
Answer:
√3
Step-by-step explanation:
We cannot solve this operation directly. Because cot7pi/6 is undefined.
We know that 1/tan= cot.
so we will first take the reciprocal of cot that is 1/tan.
So,
cot7pi/6= 1/tan 7π/6
∵7π/6 = 210 where pi=180
so cot7π/6 =1/tan210
cot7π/6 =1/1÷√3
cot7π/6 = √3
which point is a solution to the equation Y = 4x - 5
A. (-3,-17) B. (4,7) C. -2,-18) D. (3,17)
Answer:
A
Step-by-step explanation:
To determine which point is a solution, substitute the x- coordinate into the equation and if the value obtained agrees with the y- coordinate of the point then it is a solution.
A (- 3, - 17)
y = 4(- 3) - 5 = - 12 - 5 = - 17 ← (- 3, - 17) is a solution
B (4, 7)
y = 4(4) - 5 = 16 - 5 = 11 ≠ 7 ← not a solution
C (- 2, - 18)
y = 4(- 2) - 5 = - 8 - 5 = - 13 ≠ - 18 ← not a solution
D (3, 17)
y = 4(3) - 5 = 12 - 5 = 7 ≠ 17 ← not a solution
Write an exponential function to model the following situation.
A population of 140,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?
Write an exponential function in terms of x.
y=
0
Write an exponential function in terms of x
Answer:
Part 1) The exponential function is [tex]y=140,000(1.05)^x[/tex]
Part 2) [tex]305,602\ people[/tex]
Step-by-step explanation:
Part 1) Write an exponential function
we know that
The exponential growth function is given by the formula
[tex]y=a(1+r)^x[/tex]
where
y is the population
x is the number of years
a is the initial population
r is the rate of change
we have
[tex]a=140,000\ people\\r=5\%=5/100=0.05[/tex]
substitute
[tex]y=140,000(1+0.05)^x[/tex]
[tex]y=140,000(1.05)^x[/tex]
Part 2) How much will the population be after 16 years?
For x=16 years
substitute the value of x in the exponential function
[tex]y=140,000(1.05)^{16}=305,602\ people[/tex]
An exponential function to model the population growth of 5% per year from an initial population of 140,000 after 16 years is y = 140,000(1 + 0.05)^x. After substituting x with 16, you calculate the growth and multiply by the initial population to find the population size after 16 years.
Explanation:To model the population growth in this scenario, we use an exponential growth function. The formula for exponential growth is y = P(1 + r)^t, where y is the final amount, P is the initial principal balance, r is the rate of interest, and t is the number of time periods the interest is applied. In this case, the population P is 140,000, the growth rate 'r' is 5% (or 0.05 when expressed as a decimal), and the number of years 't' is 16.
The exponential function in terms of 'x' (where 'x' represents the number of years) will be: y = 140,000(1 + 0.05)^x.
After plugging in 't' as 16 years, we calculate the population after 16 years as follows: y = 140,000(1 + 0.05)^16. Now we calculate the growth factor (1 + 0.05)^16 and multiply this by the initial population of 140,000 to determine the population after 16 years.
Which graph represents the solution set of the compound inequality Negative 4 less-than-or-equal-to 3x minus 1 and 2 x + 4 less-than-or-equal-to 18?
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7.
A number line goes from negative 10 to positive 10. A closed circle appears at negative 7 and positive 1. The number line is shaded from negative 7 to positive 1.
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1. The number line is shaded from negative 1 toward negative 10.
A number line goes from negative 10 to positive 10. A closed circle appears on positive 7. The number line is shaded from positive 7 toward positive 10.
Answer:
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7.
Step-by-step explanation:
The set of compound inequality are - 4 ≤ 3x - 1 and 2x + 4 ≤ 18.
Now, - 4 ≤ 3x - 1
⇒ 3x ≥ - 3
⇒ x ≥ - 1
And, 2x + 4 ≤ 18
⇒ 2x ≤ 14
⇒ x ≤ 7
Therefore, the solution will be 7 ≥ x ≥ - 1
Hence, the graph that shows the solution is 'a number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7'. (Answer)
Answer:
Graph A is your answer.
Step-by-step explanation:
Select the correct graph of −4x + 3y = 6. (1 point)
Answer:
[tex]Line\ passing\ through\ (-1.5,0)\ and\ (0,2).\\\\Correct\ graph\ is\ attached.[/tex]
Step-by-step explanation:
[tex]The\ given\ equation\ represents\ a\ line\\\\[/tex]
y-intercept:
[tex]Substitute\ x=0\\\\-4\times 0+3y=6\\\\3y=6\\\\y=\frac{6}{3}\\\\y=2\\\\The\ line\ passes\ through\ the\ point\ (0,2).[/tex]
x-intercept:
[tex]Substitute\ y=0\\\\-4x+3\times 0=6\\\\-4x=6\\\\x=-\frac{6}{4}\\\\x=-1.5\\\\The\ line\ passes\ through\ the\ point\ (-1.5,0).[/tex]
The correct graph is attached.
The area of a square garden is 98m squared. How long is the diagonal?
Answer:
diagonal is 14 m
Step-by-step explanation:
We are given;
The area of a square garden as 98 m²We are required to determine the diagonal of the square.
We know that;
Area of a square = s² , where s is the side of the square
Therefore;
s² = 98
Thus;
s = √98
To get the diagonal
s² + s² = diagonal squared
Hence;
Diagonal squared = (√98)² + (√98)²
= 98 + 98
= 196
Thus;
Diagonal = √196
= 14 m
Thus, the diagonal is 14 m
12. Write an equation to solve for the following strip diagram:
421
158
628
Equation:
on:
Answer:
[tex]c + 421 + 158 = 628[/tex]
[tex]c + 579 = 628[/tex]
[tex]c = 49[/tex]
write an equation of the line with a slope of 3 and a y-intercept of -3.
Answer:
solution is
y + 3 = 3(x - 0)
y + 3 = 3x - 0
y = 3x - 3
Find the variance for the given data. Round your answer to one more decimal place than the original data. The billing rates for six dental procedures are listed below: $663 $273 $410 $622 $174 $374
Answer:
The variance is 30698.6
Step-by-step explanation:
The billing rates for six dental procedures are listed below:
$663
$273
$410
$622
$174
$374
The mean is given by:
[tex]\bar X=\frac{663+273+410+622+174+374}{6}=\frac{2516}{6}=419.333[/tex]
The variance is given by:
[tex]\sigma^2=\frac{\sum(x-\bar x)^2}{n}[/tex]
[tex]\sigma^2=\frac{(663-419.333)^2+(273-419.333)^2+(410-419.333)^2+(622-419.333)^2+(174-419.333)^2+(374-419.333)^2}{6}[/tex]
[tex]\sigma^2=30698.56[/tex]
Therefore the variance is 30698.6
The variance for the given set of data points, which are billing rates for dental procedures, is $35439.73. The variance is calculated as the average of the squared differences from the mean.
Explanation:The subject of this question is the variance, which is a statistical characteristic used in mathematics to measure how much individual numbers in a set diverge from the average. So, to find the variance for this given data follow these steps:
Find the mean of the data. This is done by adding all the numbers together and then dividing by the number of numbers. The mean in this case is $427.67 ($(663 + 273 + 410 + 622 + 174 + 374) / 6$). Subtract each number in the set by the mean, and then square the result. The squared differences are $55427.23$, $23856.23$, $312.23$, $37804.23$, $64368.23$, and $2870.23$, respectively. The variance is the mean of these squared differences. Adding them all up and dividing by 6 (the total number of numbers in the set) gets us a variance of $35439.73$ rounded to two decimal places. Learn more about Variance here:https://brainly.com/question/33654267
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Two arcs of concentric circles are intercepted by the same central angle. The resulting arc length of the arc of the smaller circle is 36 ft and radius is 30 ft. The radius of thr larger circle is 45 ft. Find tye length of the corresponding arc of the larger circle.
The length of the corresponding arc of the larger circle = 54 ft.
Step-by-step explanation:
step 1 :
"Concentric circles" have same center but different radius.So, the angle formed by the arcs of the two circles with same center will also be same.step 2 :
Small circle :
Length of the arc = 36 ftRadius of the circle = 30 ftArc length = (∅/360)2πr
where,
∅ = arc angle
π = 3.14
r = radius of circle
step 3 :
Arc length = (∅/360)2[tex]\times[/tex]3.14[tex]\times[/tex]30
⇒ 36 = (∅/360)[tex]\times[/tex]188.4
⇒ ∅ = 36[tex]\times[/tex]360 / 188.4
∅ = 68.79
step 4 :
Large circle :
Radius of large circle = 45 ftThe arc angle, ∅ = 68.79Arc length = (∅/360)2πr
= (68.79/360) 2[tex]\times[/tex]3.14[tex]\times[/tex]45
Arc length = 54 ft
Hadley has 3/6 of a box of white envelopes and 1/3 of a box of gray envelopes. When full, each box of envelopes has the same number of envelopes. Hadley said she has 4/9 of a box when she puts the white envelopes and gray envelopes together. Which statements describe this situation? Select the two statements that apply.
A. Hadley’s answer is incorrect, because 3/6 is equal to 1/2 , and 4/9 is less then 1/2 .
B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6.
C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6 .
D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9.
PLS HELP I WILL MARK BRAINLIST IF CORRECT !! :) SELECT 2 ANSWERS !!
Answer:
The two statements that apply are A and B.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
White envelopes Hadley has = 3/6 of a box
Gray envelopes Hadley has = 1/3 of a box
When full, each box of envelopes has the same number of envelopes
Hadley said she has 4/9 of a box when she puts the white envelopes and gray envelopes together.
2. Which statements describe this situation? Select the two statements that apply.
Let's add 3/6 and 1/3
3/6 + 1/3 = 3/6 + 2/6 = 5/6
A. Hadley’s answer is incorrect, because 3/6 is equal to 1/2 , and 4/9 is less then 1/2 . This is correct.
B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6. This is correct.
C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6. This is wrong
D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9. This is wrong.
The two statements that apply are A and B.
Answer: Answer:
The two statements that apply are A and B.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
White envelopes Hadley has = 3/6 of a box
Gray envelopes Hadley has = 1/3 of a box
When full, each box of envelopes has the same number of envelopes
Hadley said she has 4/9 of a box when she puts the white envelopes and gray envelopes together.
2. Which statements describe this situation? Select the two statements that apply.
Let's add 3/6 and 1/3
3/6 + 1/3 = 3/6 + 2/6 = 5/6
A. Hadley’s answer is incorrect, because 3/6 is equal to 1/2 , and 4/9 is less then 1/2 . This is correct.
B. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 5/6. This is correct.
C. Hadley's answer is incorrect, because 3/6 plus 1/3 equals 2/6. This is wrong
D. Hadley's answer is correct, because 3 and 1 is 4, and 6 and 3 is 9. This is wrong.
Step-by-step explanation: A B
How to find the solution to an f(x)=g(x) equation
1.) Set the equation equal to each other
2.) Solve for y by itself and simplify the equation
3.) Solve for when x=0 to find the x-value
4.) Plug that x-value back into one of the equation to find the y-value.
jamal ate 1/4 bag of peanuts. his 3 friends ate equal shares of the remaining peanuts. which expression represents the peanuts that each friend ate?
Answer:
4/4-1/4 is 3/4 so 3/4 divided by 3 is 1/4 bag of peanuts per friend.
Step-by-step explanation:
To find the expression that represents the peanuts that each friend ate, start with the fraction representing the remaining peanuts after Jamal ate 1/4 bag, which is 3/4. Divide the remaining peanuts equally among the 3 friends by dividing the fraction 3/4 by 3, which gives us 1/4. Therefore, each friend ate 1/4 of the peanuts.
Explanation:To find the expression that represents the peanuts that each friend ate, we need to follow the steps:
Start with the fraction representing the remaining peanuts after Jamal ate 1/4 bag, which is 1 - 1/4 = 3/4.Divide the remaining peanuts equally among the 3 friends. This can be done by dividing the fraction 3/4 by 3, which gives us (3/4) / 3 = 1/4.Therefore, the expression that represents the peanuts that each friend ate is 1/4.
Greatest Common Factor (GCF)
1. 12a - 27
Answer:
3
Step-by-step explanation:
The factors of 12a are ...
2×2×3×a
The factors of 27 are ...
3×3×3
The only common factor is 3.
_____
12a -27 = 3(4a -9)
Final answer:
The Greatest Common Factor (GCF) of the expression 12a - 27 is 3, since 3 is the highest number that divides evenly into both 12 and 27 with no common variables present.
Explanation:
To find the Greatest Common Factor (GCF) of the expression 12a - 27, you look for the highest number and any variables that divide evenly into both terms. Note that 12 and 27 can both be divided by 3. Therefore, 3 is a common factor. Since there are no more common variables or higher factors, the GCF of 12a and 27 is simply 3.
To calculate the GCF, divide each term by 3:
12a ÷ 3 = 4a
27 ÷ 3 = 9
While the expression is factored as 3(4a - 9), the GCF is just the number 3.
.........................................................................................
Answer:
...................................../................................................................
Step-by-step explanation:
......................................................................................
What is 8/12 as a whole number & unit fraction
Answer:
1/4
Step-by-step explanation:
The fraction 8/12 simplifies to 2/3. The whole number is 0, and the unit fraction is 2/3, which can be expressed as the sum of two unit fractions, 1/2 and 1/6.
Explanation:The fraction 8/12 can be simplified to a whole number and a unit fraction. First, divide both the numerator and denominator by their greatest common divisor, which is 4. This yields the simplified fraction 2/3. Thus, the whole number is '0' and the unit fraction is '2/3' as 2/3 is less than 1 and cannot be represented as a whole number. A unit fraction is a fraction where the numerator is '1'. Although 2/3 is not a unit fraction itself, it can be expressed as the sum of two unit fractions, '1/2 + 1/6'.
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Fractions to percentage
Answer:
If u want to change fraction into percentage then multiply it with 100.for eg.83/90*100%
Sales Tax
nbsp Selling Price nbsp
nbsp Rate of Sales Tax nbsp
nbsp Sales Tax nbsp
$70.00
3%
?
The sales tax for an item priced at $70.00 with a tax rate of 3% is $2.10. This can be found by multiplying the selling price by the tax rate.
Explanation:To find the amount of sales tax, you can multiply the selling price by the rate of sales tax. In your case, the selling price is $70.00 and the rate of sales tax is 3%. So, your calculation will look like this: $70.00 * 0.03 (because 3% is the same as 0.03 when used in a calculation). The result of this multiplication will be the amount of sales tax. So, the sales tax for an item which costs $70.00 at a tax rate of 3% is $2.10.
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