A deposit of $35.45 was made to a checking account. Before the deposit, the account had a balance of −$12.39 . What was the account balance after the deposit?
Answer:
23.06
Step-by-step explanation:
Find the coordinates of point P
P
along the directed line segment AB
AB
, from A(1, 6)
A(1, 6)
to B(−2,−3)
B(−2,−3)
, so that the ratio of AP
AP
to PB
PB
is 5
5
to 1
1
.
The calculated coordinates of the point P is P (-3/2, -3/2)
How to determine the coordinates of the point PFrom the question, we have the following parameters that can be used in our computation:
A = (1, 6)
Also, we have
B = (-2, -3)
And we have the partition to be
m : n = 5 : 1
The coordinate of the partition is calculated as
P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Substitute the known values in the above equation, so, we have the following representation
P = 1/(5 + 1) * (5 * -2 + 1 * 1, 5 * -3 + 1 * 6)
This gives
P = 1/6 * (-9, -9)
So, we have
P = (-3/2, -3/2)
Hence, the coordinate is P = (-3/2, -3/2)
Read more about line segment ratio at
brainly.com/question/17374569
#SPJ3
To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula and plug in the given values to find the coordinates (-3/2, -3/2).
Explanation:To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula. The section formula states that if a point P divides a line segment AB in the ratio m:n, then the coordinates of P can be found using the formula:
P(x,y) = [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)]
Using this formula, we can plug in the values: m=5, n=1, x1=1, y1=6, x2=-2, y2=-3 to find the coordinates of point P.
P(x,y) = [(5*(-2) + 1*1)/(5+1), (5*(-3) + 1*6)/(5+1)] = [(-10+1)/6, (-15+6)/6] = [-9/6, -9/6] = (-3/2, -3/2)
Learn more about Section Formula here:https://brainly.com/question/30242641
#SPJ3
Quinn spends $16.49 for 3 magazines and 4 sheets of stickers. The magazines cost $3.99 each and the sales tax was $1.02. Quinn also used a coupon for $1.50 off her purchase. If each sheet of stickers had the same cost, how much did each sheet of stickers cost?
Every 2/3 hour, Harris can sew 1/6 pair of jeans. what is the unit rate?
Write the expressions without using log. Can someone please help with this?
(i) log m^2 n =?
(ii) log (m/n^3)=?
Fo two disk i problem 3 what is the ratio of linear accerlation of a point on the rim of disk a
The ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \), where \( r_A \) and \( r_B \)[/tex] are the radii of disks A and B, respectively.
Linear acceleration ( a ) of a point on the rim of a rotating disk is given by [tex]\( a = r \alpha \)[/tex], where ( r ) is the radius of the disk and [tex]\( \alpha \)[/tex] is the angular acceleration.
Since both disks are rotating with constant angular acceleration, the linear acceleration of a point on the rim of each disk is directly proportional to the radius of the disk.
Therefore, to find the ratio of the linear accelerations, we only need to compare the radii of the two disks.
Let [tex]\( r_A \) and \( r_B \)[/tex] be the radii of disks A and B, respectively.
The ratio of linear accelerations is given by [tex]\( \frac{a_A}{a_B} = \frac{r_A \alpha}{r_B \alpha} \)[/tex].
Notice that the angular accelerations cancel out since both disks have the same angular acceleration.
Thus, the ratio simplifies to [tex]\( \frac{r_A}{r_B} \)[/tex].
This ratio represents how many times larger the radius of disk A is compared to the radius of disk B.
For example, if [tex]\( r_A = 2r_B \)[/tex], then the linear acceleration of a point on the rim of disk A is twice that of disk B.
Therefore, the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \)[/tex].
Complete Question:
For the two disks in problem 3, what is the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B? Please show detailed calculation.
Which of the following rules describes the function graphed below? a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
Answer:
Option C
output=0.5(input)+1.5
Step-by-step explanation:
Let
y------> the output
x------> the input
we have
[tex]A(-1,1), B(5,4)[/tex]
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{4-1}{5+1}[/tex]
[tex]m=\frac{3}{6}=0.5[/tex]
Find the equation of the line
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=0.5[/tex]
[tex]A(-1,1)[/tex]
substitute
[tex]y-1=0.5(x+1)[/tex]
[tex]y=0.5x+0.5+1[/tex]
[tex]y=0.5x+1.5[/tex]
remember that
y=output
x=input
substitute
output=0.5(imput)+1.5
HELP!!!!
Which addition expression has the sum 8 – 3i ?
(9 + 2i) + (1 – i)
(9 + 4i) + (–1 – 7i)
(7 + 2i) + (1 – i)
(7 + 4i) + (–1 – 7i)
The expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i) which correct option(B).
What is complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
For example 4/2 = 2
(B) (9 + 4i) + (–1 – 7i)
⇒ (9 + 4i) + (–1 – 7i)
⇒ 9 + 4i –1 – 7i
Rearrange the terms like wise and apply arithmetic operations
⇒ 9 - 1 + 4i - 7i
⇒ 8 – 3i
Hence, the expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i).
Learn more about complex number here:
brainly.com/question/19007885
#SPJ6
Answer: the first part is option B
the second part is option C
Step-by-step explanation:
A pizza parlor offers a choice of 16 different toppings. how may three-topping pizzas are possible
Explain how two amounts of change can be the same but the percent of change can be different
How do I write y-3=2/3(x-2) in standard form
The Statue of Liberty and its pedestal are 92.99 meters tall. The pedestal is 0.89 meters taller than the Statue of Liberty. How tall is the Statue of Liberty? Equation and answer.
Final answer:
To find the height of the Statue of Liberty, we set up an equation considering the total height of the pedestal and the height difference between the statue and the pedestal. Solving the system of linear equations, we determine that the height of the Statue of Liberty itself is 46.05 meters.
Explanation:
To find how tall the Statue of Liberty is, excluding its pedestal, we can set up an equation based on the information given. Let's denote the height of the Statue of Liberty as S, and the height of the pedestal as P.
We know that the total height of the Statue of Liberty and its pedestal is 92.99 meters, and we can express that as:
S + P = 92.99
Additionally, it is given that the pedestal is 0.89 meters taller than the Statue of Liberty, so we have:
P = S + 0.89
Using substitution, we can replace P in the first equation with S + 0.89:
S + (S + 0.89) = 92.99
This simplifies to:
2S + 0.89 = 92.99
To find the height of the Statue of Liberty (S), we subtract 0.89 from both sides of the equation:
2S = 92.99 - 0.89
2S = 92.10
And then we divide both sides by 2 to solve for S:
S = 92.10 / 2
S = 46.05
So, the height of the Statue of Liberty itself is 46.05 meters.
Solve the polynomial equation. State the multiplicity of each root. x3 + 15x2 + 75x + 125 = 0
Find the median: 95, 103, 98, 62, 31, 15, 82
11 relaxing after work. the 2010 general social survey asked the question: "after an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 americans.41 a 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). (a) interpret this interval in context of the d
The 95% confidence interval for the mean number of hours Americans spend relaxing or engaging in enjoyable activities post-work is between 1.38 and 1.92 hours per day, which signifies the statistical range where the true mean likely falls. This statistic is crucial for understanding leisure's role in health and well-being.
The 95% confidence interval given in the General Social Survey of (1.38, 1.92) hours for the mean number of hours spent relaxing or pursuing activities after an average workday suggests that we can be 95% confident that the actual mean number of hours all Americans have for such activities falls within this range. This is an important statistic considering that leisure and recovery are essential for well-being, mental health, and stress prevention, as pointed out by researchers like Sonnentag & Zijlstra and Juliet Schor. Juliet Schor also highlighted that Americans have significantly declined in leisure time. The comparison of leisure time across different countries, such as Americans working more hours compared to Europeans, adds context to the importance of this interval in reflecting Americans' potential lack of leisure that could impact health.
Jose and a group of friends bought concert tickets for $257. The booking agency also charged a fee, bringing the total cost to $274.99. The amount of change is $17.99. What is the percent increase in the cost due to the fee? 6% 7% 8% 9%
Answer:
7%(plzzzz brainlist thiss!!!)
Step-by-step explanation:
The soap recipe is increased so that 75 grams of shea butter are needed. Complete the ratio table to find the amount of sodium hydroxide.
Solve 8x − 2(x + 1) = 7x + 8. (5 points)
6
−6
10
−10
Which of the following represents the correct expansion of (x + 2)^5?
A. x5 + 10x4 + 40x3 + 40x2 + 10x +32
B. x5 + 8x4 + 12x3 + 8x2 + x +32
C. x5 + 10x4 + 20x3 + 20x2 + 10x +32
D. x5 + 10x4 + 40x3 + 80x2 + 80x +32
What is the relationship between 0.04 and 0.004?
Each beehive on Larson's Honey Farm usually produces 85 pounds of honey per year. About how many pounds of honey will 1000 hives produce a year
The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
As per the given question,
Larson's Honey Farm usually produces 85 pounds of honey per year.
If one family is producing 85 pounds of honey per year then,
1000 hives will produce ⇒ 85 × 1000 = 85000 pounds.
Hence "The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced".
For more information about multiplication,
brainly.com/question/14059007
#SPJ5
What construction does the image below demonstrate?
Answer:
The construction depicts the inscribing of a hexagon in a circle.
Step-by-step explanation:
These are the following steps to inscribe a hexagon in a circle.
1. We mark a point anywhere on the circle. This mark is the first vertex of the hexagon.
2. Now we will set the compass on this vertex and set the width to the center of the circle. This is the radius of the circle.
3. Now we will make an arc across the circle which is the next vertex of the hexagon.
4. Now moving the compass on to the next vertex and drawing another arc, which becomes the third vertex of the hexagon.
5. Repeat step 4 until all vertices are marked.
6. Lastly, we will draw a line between each successive pairs of vertices, for a total of six lines.
Now we can see a hexagon inscribed in a circle.
a metalworker has a metal alloy that is 15% copper and another alloy that is 55% copper. how many kilograms of each alloy should the metalworker combine to create 90kg of a 47% copper alloy
x = amount at 15%
90-x = amount of 55%
0.15x + 0.55(90-x) = 0.47(90)
0.15x +49.5 - 0.55x = 42.3
49.5 - 0.40x = 42.3
-0.40x = -7.2
x = -7.2 / -0.4 = 18 kg of 15% copper
90-18 = 72 kg of 55% copper
what is 8/20 of an hour
Suppose an airline policy states that all baggage must be box shaped with a sum of length, width, and height not exceeding 162 in. what are the dimensions and volume of a square-based box with the greatest volume under these conditions
Final answer:
To find the dimensions and volume of a square-based box with the greatest volume under the given conditions, we need to maximize the volume. The dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume is 157,464 cubic inches.
Explanation:
The airline policy states that the sum of the length, width, and height of the baggage must not exceed 162 inches. To find the dimensions and volume of a square-based box with the greatest volume under these conditions, we need to maximize the volume of the box.
Let's assume the length, width, and height of the box are all equal to a. Therefore, the sum of the three dimensions is 3a.
According to the policy, 3a must not exceed 162 inches, so we have:
3a ≤ 162
a ≤ 54
Since the length, width, and height of a square-based box are all equal, a is the side length of the square base. Therefore, the dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume can be calculated as:
Volume = a³ = 54³ = 157,464 cubic inches.
solve the system
x+3y=7 2x-4y=24
A. (2,-6)
B. (10,-1)
C. (-2,8)
D. Infinitely many solutions
The solution of given system of equations is [tex]\boxed{(10,-1)}[/tex].
Further explanation
The system of equations is given as follows:
[tex]\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}[/tex]
The equations are the form of linear equation in two variables.
The general form of linear equation in two variables is [tex]ax+by+c=0[/tex] where [tex]a,b,c[/tex]are real numbers.
Here, the system of equations is as follows:
[tex]x+3y=7[/tex] .....(1)
[tex]2x-4y=24[/tex] ......(2)
Now, we can rewrite the equation (1) as follows:
[tex]x=7-3y[/tex]
Substitute the value of [tex]x=7-3y[/tex] in equation (2) as follows:
[tex]2(7-3y)-4y=24[/tex]
Solve the above expression to find the value of [tex]y[/tex].
[tex]\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]-1[/tex].
Now, Substitute the value of [tex]y=-1[/tex] in equation (1) to get the value of [tex]x[/tex].
[tex]\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]10[/tex].
The solution of given system of equations is [tex](10,-1)[/tex].
Option (a)
In option (a) it is given that the solution is [tex](2,-6)[/tex].
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (a) is incorrect.
Option (b)
In option (b) it is given that the solution is [tex](10,-1)[/tex].
As per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (b) is correct.
Option (c)
In option (c) it is given that the solution is [tex](-2,8)[/tex].
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (c) is incorrect.
Option (d)
In option (d) it is given that there are infinte solution.
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex] which is a unique solution.
Therefore, option (d) is incorrect.
Learn more
1. Problem on the equation of the circle https://brainly.com/question/1952668
2. Problem on the center and radius of an equation https://brainly.com/question/9510228
3. Problem on the general form of the equation of the circle https://brainly.com/question/1506955
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equations in two variables
Keywords: Linear equations in one variable, linear equations in two variables, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open interval.
Derek decided to take a trip to France this summer. He had $30 in U.S. dollars to exchange for Euros. For every U.S. dollar, Derek received .76 Euros. How many Euros did Derek receive for his 30 U.S. dollars?
What is the value of the fraction given below? 24/(-2/3)
Kaia needs braces, which will cost $2,400. Her insurance deductible is $1500, after which her insurance pays 80% of all costs. How much will Kaia need to pay for her braces?
A.$2,200
B.$1,680
C.$180
D.$480
Kaia will pay a $1,500 deductible and the remaining 20% not covered by insurance after the deductible, totaling to $1,680 for her braces.
To calculate how much Kaia will need to pay for her braces, we need to take into account her insurance deductible and the percentage her insurance will cover after that deductible is paid. Kaia's braces cost $2,400, so let's break it down step-by-step:
Kaia pays her insurance deductible, which is $1,500. So, $2,400 - $1,500 = $900 remains.
Her insurance then covers 80% of the remaining $900. To calculate this, we use 80% of $900: ($900 x 0.80) = $720.
Since the insurance pays $720 of the remaining cost, Kaia is left with 20% of $900 to pay out of her pocket. To calculate this, we take 20% of $900: ($900 x 0.20) = $180.
Therefore, Kaia will need to pay $1,500 (deductible) plus $180, for a total of $1,680.
Express 32 = x as a logarithmic equation
the answer is log3x=2!
hope this helps :D. just took a test online and this was one of the questions. got it right btw.