The height of the house, given the angle of elevation and the distance of the point is 25. 98 meters.
How to find the height ?
You can use the tangent function because it relates the angle of elevation to the opposite side and the adjacent side (the horizontal distance).
The tangent of the angle of elevation is equal to the ratio of the height to the horizontal distance:
tan(30 degrees) = h / 45 meters
Solve for "h" by multiplying both sides by 45 meters:
h = 45 meters x tan(30 degrees)
You can calculate the value of tan(30 degrees):
tan(30 degrees) = 0.5774
Multiply:
h = 45 meters x 0.5774
= 25.98 meters
2(x−3)=(x−1)+7
x = ___
Answer:
x=12
Step-by-step explanation:
Answer:
x = 12
Add 6 to both sides, simplify then subtract x from both sides
When graphing two systems the break even point:
A. is the point of intersection of the two lines
B. includes the points greater than the line
C. includes points less than the line
Is 3a a term for expressions
Answer:
yes
Step-by-step explanation
because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.
When Elmer empties his bank, he found 17 pennies, 4 nickels, 5 dimes, and 2 quarters. What was the value of the coins in his bank?
Elmer's bank contained coins totaling $1.37, calculated by summing the value of each type of coin separately.
Explanation:To find the total value of the coins in Elmer's bank, we need to calculate the value of each type of coin separately and then sum them up. The value of coins is counted based on their denomination, with pennies being worth 1 cent, nickels 5 cents, dimes 10 cents, and quarters 25 cents.
Pennies: 17 pennies × 1 cent = 17 centsNickels: 4 nickels × 5 cents = 20 centsDimes: 5 dimes × 10 cents = 50 centsQuarters: 2 quarters × 25 cents = 50 centsAdding these amounts gives us a total value of 17 + 20 + 50 + 50 = 137 cents. Therefore, the value of the coins in Elmer's bank is $1.37.
The value of the coins in Elmer's bank is $2.17.
17 pennies = $0.17
4 nickels = $0.20
5 dimes = $0.50
2 quarters = $0.50
Adding these amounts together: $0.17 + $0.20 + $0.50 + $0.50 = $2.17.
(-4+6i) + (-6-2i)
How do I solve
Answer:
(-4+(-6))+(6i-2i)
(-10+4i)
Answer:
-10+4i = -2(5-2i)
Step-by-step explanation:
(-4+6i) + (-6-2i)
Collecting like terms
(-4-6) + (6i-2i)
-10+4i
-2(5-2i)
Simplify 15 × 1316 in decimal form
Answer:
i multiplied them together and the result is 19740 but in decimal it would be 19740.0
Final answer:
To simplify 15 × 1316, you multiply to get 19740, which is rounded to 19700 when limited to three significant figures.
Explanation:
To simplify the expression 15 × 1316 in decimal form, you need to perform basic multiplication. Multiplying 15 times 1316 gives you a result of 19740.
However, to express this answer in terms of significant figures, specifically limiting to three significant figures, you would round this number to 19700, as the number 740 does not contribute to the first three significant digits.
Complete the statements about the cone.
-The height is___
units.
-The radius is___
units.
-The volume is___
Pi cubic units.
Answer:
The height is 6 units.
The radius is 8 units.
The volume is 128 Pi cubic units
Step-by-step explanation:
The height is 6 units.
Use Pythagorean Theorem to find the radius.
6² + x² = 10²
36 + x² = 100
-36 -36
x² = 64
x = 8
V = πr²h/3
V = π(8)²6/3
V = π(64)2
V = 128π
Answer:
6,8,128
Step-by-step explanation:
6(5x-3) distributive property gcf
Answer:
Step-by-step explanation:30x-18
1. Suppose that AB and EF are corresponding sides of similar triangles. AB = 6 and the scale factor is 3, what is EF?
A. 3
B. 6
C. 9
D. 18
Answer:
d
Step-by-step explanation:
since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18
The length of the Side EF is 18.
What is the scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
Given that corresponding sides are AB and EF, and EF is a side of the larger (second) triangle.
scale factor 3 means each length of the second is 3 times as long as the first.
Therefore, the length of the side EF when the length of side AB is 6 units is,
EF = 3 x AB
= 3 x 6 units
= 18 units.
Therefore, Side EF is 18.
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Graph the line that has a slope of 1/9 and includes the point (0,8)
Answer:
Step-by-step explanation:
y = mx + b
slope(m) = 1/9
y int (b) = 8.....or (0,8)
y = 1/9x + 8.....this is ur equation
ur x intercept is : (can be found by subbing in 0 for y
0 = 1/9x + 8
-1/9x = 8
x = 8 * -9
x = - 72....or (-72,0)
The equation of line is y = ( 1/9 )x + 8
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is given by
The slope of the line m = 1/9
So , Slope m = 1/9
The point on the line is given by P = P ( 0 , 8 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = ( 1/9 ) ( x - 0 )
y - 8 = ( 1/9 ) x
On simplifying the equation , we get
Adding 8 on both sides of the equation , we get
y = ( 1/9 )x + 8
Therefore , the value of A is y = ( 1/9 )x + 8
Hence , The equation of line is y = ( 1/9 )x + 8
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Suppose that a code consists of 5 digits, none of which is repeated. ( A digit is one of the 10 numbers 0,1,2,3,4,5,6,7,8,9.) How many codes are possible?
Answer:
30240
Step-by-step explanation:
There are two primary ways to approach this problem - the logical and the mathematical.
The logical way is very simple:
Since you know that there are 5 digits and each must be different, start with the first digit and work your way up.
The first digit can be any of 10 digits (0–9).
However, the second digit can be any of only 9 digits as 1 digit has already been used and cannot be repeated.
Similarly, applying the same logic, there are only 8 options for the third digit, 7 for the fourth digit, and 6 for the fifth and final digit.
Now, multiply all these numbers together to get the total number of configurations like so:
10⋅9⋅8⋅7⋅6=30240
The more mathematically inclined way requires the use of a special formula. Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:
P(n,r)=n!(n−r)!
where n is the number of numbers in the set and r
is the subset.
Since there are 10 digits to choose from, we can assume that n=10
.
Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r=5
.
Now, plug these values into the formula and solve:
=10!(10−5)!
=10!5!
=10⋅9⋅8⋅7⋅6
=30240
Which of the following equations represents a line that is parallel to y = 3x +2
and passes through the point, (1, 6)?
O A. y = 3x +6
O B. y = 3x +9
O c. y=-3x+2
O D. y = 3x+3
The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.
Explanation:To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.
Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).
Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.
A ball is dropped off the side of a bridge. after falling 1.55 s, what is its velocity?
Use the basic kinematic equation of
Final velocity = initial velocity + acceleration * time (shown in image)
simply plug the numbers in to get
Velocity(final) = 0 + -9.80 m/s^2 * 1.55 s
to give us
-15.19 m/s for our final velocity
Riding an exercise bike burns 6 calories per min how many calories will a person burn if he/she bikes for 23 1/2 minuets
Answer: 141
Step-by-step explanation:
23 1/2 *6=141
Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61,600, how much does Tina pay in state income tax?
$ 2772 is paid in state income tax
Solution:
Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income
Federal taxable income = $61,600
To find: Amount paid by Tina in state income tax
Tax rate = 4.5 %
Which means, 4.5 % of $61,600 is paid as tax
[tex]Tax\ Rate = 4.5 \% \text{ of } 61600[/tex]
Here, "of" means multiplication or product
[tex]Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772[/tex]
Thus $ 2772 is paid in state income tax
4.5% of 61,600
0.045(61,600) = 2772
Estimate what’s 32.27/7
Answer:
The answer we can solving the above division is 4.61
Step-by-step explanation:
Given:
The given divider is 7 and the given dividend is 32.27.
To find:
Quotient and remainder
Formula:
The basic division formula that we all know is,
Quotient + Remainder/Divisor = Dividend/Divisor
where we know both dividend and divisor.
By using normal division method we get,
= 32.37/7
= 4.61
Thus we got the quotient as four and remainder as six.
a total of 345 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Answer:
115
Step-by-step explanation:
a + s = 345
s = 2a
a + 2a = 345
3a = 345
a = 345/3
a = 115 <===== adult tickets
s = 2a
s = 2(115)
s = 230......student tickets
What is the inverse of the function f(x) = 2x – 10?
Answer:
f^-1 (x)=1/2x+5
Step-by-step explanation:
y=2x-10
x=2y-10
2y=x+10
y=1/2x+10/2
y=1/2x+5
In a video game,you score p game points and b triple bonus points. An expression for your score is p+3b. What is your score when you earn 245 games points and 20 triple bonus points
Your score in the game is 305 points.
Step-by-step explanation:
Given,
Expression used for score = p + 3b
p = game points
b = triple bonus points
Game points earned by you = p = 245 games point
Triple bonus points = b = 20
Putting these values in given expression
Total points = [tex]245+3*20[/tex]
Total points = [tex]245+60[/tex]
Total points = 305 points
Your score in the game is 305 points.
Keywords: addition, expression
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Ashley had a summer lemonade stand where she sold small cups of lemonade for 41.25 AND LARGE CUPS FOR $2.50. If Ashley solf a total of 155 cups of lemonade for $265, how many cups of each tpe did she sell?
Question:
Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each did she sell
Answer:
The number of small cups of lemonades is 98
The number of Large cups of lemonades is 57
Step-by-step explanation:
Given:
Cost of small lemonade cups = $1.25
Cost of large Lemonade cups = $2.50
Total number of lemonade cups = 155 cups
The total cost for which the lemonade is sold = $265
To Find:
Number of each types of lemonade sold = ?
Solution:
Let the number of small cups of lemonade sold be x
the number of large cups of lemonade sold be y
Then according to the question,
x+y = 155-----------------------------(1)
Then the amount earned by selling small and large lemonade cups is $265
Then
1.25x+2.50y = 265------------------(2)
From (1)
y = 155-x----------------------------------(3)
Substituting (3) in (2), we get
1.25x+ (155-x)2.50 = 265
1.25 + (387.5 -2.50x) =265
-1.25x + 387.5 = 265
-1.25x= 265 -387.5
-1.25x = -122.5
[tex]x = \frac{-122.5}{-1.25}[/tex]
x= 98--------------------------------(4)
Substituting (4) in (3)
y = 155-98
y =57
A local grocery store kept track of the types of items sold in 2 hours. Express the ratio that compares the amount of produce sold to the total number of grocery items sold.
Answer:
Step-by-step explanation:
Tracking sales in a small convenience store does not require sophisticated sales monitoring software or expensive computer equipment, although basic point of sale software can save time and prevent mathematical errors. Daily monitoring of inventory, saving sales receipts and using a simple spreadsheet may be all you need to track sales. Depending on the size of your store and foot traffic the store receives each day, tracking sales may take only an hour or so each day.
Round 37,748 to the tens
Answer:
37750
Step-by-step explanation:
What is the value of x?
5 cm
3 cm
Enter your answer in the box
40 cm
2x + 10
Answer: 7cm
Step-by-step explanation:
Answer: the answer is 7
Step-by-step explanation:
Liam has $7.50 How much does liam earn in a 35 hour work week (gross pay without benefits)
Answer:
7.50*35=262.50
Step-by-step explanation:
Cynthia has the choice of taking out a 25-year loan for $155,000 at 4.4%
interest, compounded monthly, or the same loan at 20 years for a higher
monthly payment. If she would pay a total of $100,831 in interest on the 25-
year loan, how much in total would she pay in interest on the 20-year loan?
Answer:
D. Less than $100,831
Step-by-step explanation:
There is an equation for calculating monthly payment:
x = p • r • (1+r)^n / (1+r)^n - 1
It may seem a bit complicated, but let's explain it step by step:
- p is the amount of loan, in this case $155,000
- r is monthly interest rate, in this case (4.4/12) / 100, which is 0.00367
- n is the number of months for paying back, or in this case 20 • 12 = 240
Now that we know all the values, all that's left is to plug them in and solve it on the calculator:
x = 155,000 • 0.00367 • (1.00367^240) / (1.00367^240) - 1
x = $972.27
So, the monthly payment is around $972.3. We now multiply it by the number of months to get total payment:
$973.3 • 240 = $233,352
So, the total amount, loan plus interest, is 233,352 dollars.
To only find amount of interest, we simply subtract loan from total amount:
$233,352 - $155,000 = $78,352
Susan uses a credit card with an APR of 22.2%. What is the monthly percentage rate on the card?
Answer:
1.85 %
Explanation:
APR refers to the "Annual Percentage Rate." This refers to the rate that is being charged to the borrower on a yearly basis.
It is very easy to get the monthly percentage rate once you know the APR. All you have to do is to divide the APR by the total number of months.
In the situation above, we just have to divide the APR of 22.2% by 12 (number of months on one year).
22.2% ÷ 12 months = 1.85 % per month (this is the monthly percentage rate on the card. Thus, this is the answer.If y is an nonnegative , would it be describing a inequality or interval notation?
I owe my friend Miguel $4.00. I also owe my friend Gloria $7.50. Which equation correctly shows this relationship?
A. -4 - 7.50 = 11.50
B. 7.50 - 4 = 3.50
C. 4 + (-7.50) = -3.50
D. -4 + (-7.50) = -11.50
The variable x represents the number of long sleeve shirts Nancy bought and the variable y represents the number of short sleeve shirts she bought.
Nancy bought 531 shirts for her business. She bought 2 times as many short sleeve shirts as long sleeve shirts.
How many of each type of shirt did she buy?
Final answer:
Nancy bought 177 long sleeve shirts and 354 short sleeve shirts for her business by solving a system of linear equations based on the provided constraints that she bought a total of 531 shirts and twice as many short sleeve shirts as long sleeve shirts.
Explanation:
The student's question involves solving a system of linear equations to find out how many of each type of shirt Nancy bought for her business. Following the given relationships between long sleeve shirts (x) and short sleeve shirts (y), we understand that Nancy bought a total of 531 shirts and that she bought twice as many short sleeve shirts as long sleeve shirts. The two equations that can represent this scenario are:
Equation 1: x + y = 531
Equation 2: y = 2x
To solve this system, we substitute Equation 2 into Equation 1 to get:
x + 2x = 531
Which simplifies to:
3x = 531
Dividing both sides by 3, we find that:
x = 531 / 3 = 177
Using the value of x to find y from Equation 2, we get:
y = 2 * 177 = 35
Therefore, Nancy bought 177 long sleeve shirts and 354 short sleeve shirts.
Expression equivalent to 5(3m + n)
Answer:
Step-by-step explanation:
5(3m + n) = 15m + 5n
Final answer:
The expression equivalent to 5(3m + n) is found by applying the distributive property, resulting in 15m + 5n, where the 5 is multiplied by each term inside the parentheses.
Explanation:
The expression 5(3m + n) is an example of the distributive property in algebra. To find an expression equivalent to this, we need to distribute the 5 across the terms inside the parentheses. This means we multiply 5 by each term inside the parentheses.
Multiply 5 by 3m, which gives us 15m.Multiply 5 by n, which gives us 5n.Putting these two results together, the equivalent expression is 15m + 5n. This is a straightforward application of the distributive property, which is a fundamental concept in algebra.