Answer:
To find the slope of line AB, we use the slope formula:
slope of AB = (yB - yA) / (xB - xA)
where A = (-10, 8) and B = (2, 3).
slope of AB = (3 - 8) / (2 - (-10)) = -5/12
The slope of a line perpendicular to AB will have a negative reciprocal slope, so its slope will be 12/5.
Using the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept, we can find the equation of the line that passes through point X (-5, 10) and has a slope of 12/5.
10 = (12/5)(-5) + b
10 = -24/5 + b
b = 74/5
Therefore, the equation of the line that is perpendicular to AB and passes through point X is:
y = (12/5)x + 74/5
Will mark as brainliest
The expressions, when written as products , would be:
81a² + 6bc - 9b² - c² ⇒ (9a - c)(9a + c) + 6bcb²c² - 4bc - b² - c² + 1 ⇒ (b² - 1)(c² - 4c + 1)1 - 25x² + 10xy - y² ⇒ (1 - 5x + y)(1 + 5x + y)How to write as products?To factor this expression, let's first rearrange the terms:
(81a² - c²) + (6bc - 9b²)
Now, we can see that the first part is a difference of squares, which can be factored as:
(9a - c)(9a + c)
However, the second part (6bc - 9b²) cannot be factored further as a product of binomials. So the expression can be written as:
(9a - c)(9a + c) + 6bc
1 - 25x² + 10xy - y²
This expression remains:
(1 - 5x + y)(1 + 5x + y)
Using the same rule as above.
Find out more on expressions at https://brainly.com/question/1852123
#SPJ1
The difference between the tens digit and ones digit of a two-digit number is 2. The number is 27 greater than the number created when the digits are reversed. What is the two-digit number?
Thus, the two digits are 9 and 11.
What is the Two-Variable Equations?
Two-variable equations are algebraic equations that involve two variables, typically x and y, and describe a relationship between them.
Let's call the tens digit "T" and the ones digit "O". Based on the problem, we know that:
T - O = 2 (the difference between the tens and ones digit is 2)10T + O = 10O + T + 27 (the number is 27 greater than the number created when the digits are reversed)T = 2 + O
Then substitute this equation in 10T + O = 10O + T + 27 i.e.
10T + O = 10O + T + 27
10T - T = 10O - O + 27
9T = 9O + 27
9(2 + O) = 8O + 27
9(2 + O) = 8O + 27
18 + 9O = 8O + 27
9O - 8O = 27 - 18
O = 9
Then,
T = 2 + 9
T = 2 + 9
T = 11
Thus, the two digits are 9 and 11.
To learn more about Two-Variable Equations, Visit
https://brainly.com/question/24085666
#SPJ1
Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5
Tina and Carl will use 6 and 12 ounces of clay, respectively. Tina uses 3/10 of the 20-ounce bucket and Carl uses 3/5 of the 20-ounce bucket.
To determine how much clay Tina and Carl will use, we need to first find the total amount of clay they will use together.
If 3/10 of the clay is used by Tina and 3/5 of the clay is used by Carl, we can find the total amount of clay used by adding these fractions:
3/10 + 3/5 = (3/10 * 1/2) + (3/5 * 1/2) (we multiply by 1/2 to find the common denominator of 10)
= 3/20 + 6/20
= 9/20
Therefore, Tina and Carl will use a total of 9/20 of the 20-ounce bucket of clay.
To find how much each of them will use, we can multiply the total amount of clay by each person's fraction:
Tina: (3/10) x 20 ounces = 6 ounces
Carl: (3/5) x 20 ounces = 12 ounces
Therefore, Tina will use 6 ounces of clay, while Carl will use 12 ounces of clay.
To learn more about ounces please click on below link
https://brainly.com/question/29047570
#SPJ4
Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5, how much of the clay each of them will use?
calculate (5)^-2+3 giving your answers to two decimal places
Answer: 3.04
Step-by-step explanation:
3.04
Paul gets $5 every week for doing his chores. He is saving his money to buy a skateboard that costs $85. He has already saved $25.
Which equation describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard?
Let x be the number of weeks it will take Paul to save enough money to buy the skateboard.
In one week, Paul earns $5, so in x weeks he will earn 5x dollars.
Since he already has $25 saved, the total amount of money he will have after x weeks is:
5x + 25
To be able to buy the skateboard that costs $85, Paul needs to save up an additional:
85 - 25 = 60
Therefore, we can set up the following equation to find the number of weeks it will take Paul to save up enough money:
5x + 25 = 60
Simplifying and solving for x:
5x = 35
x = 7
Therefore, it will take Paul 7 weeks to save up enough money to buy the skateboard.
The equation that describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard is:
5w + 25 = 85
what is most likely true about melting these two types of chocolate?
Dark chocolate usually takes longer to melt than milk chocolate, as shown by the fact that the median melting time for dark chocolate is higher than the median melting time for milk chocolate.
What is the role of median?Based on the given box plots, it is most likely true that after 64 seconds, about half of the brands of milk chocolate are likely to melt, and none of the brands of dark chocolate are likely to melt.
After 259 seconds, none of the brands of milk chocolate are likely to melt, and about a quarter of the brands of dark chocolate are likely to melt.
This conclusion is based on the fact that the box plot for milk chocolate shows a wider spread of melting times, indicating more variation in melting times among the different brands.
while, the box plot for dark chocolate shows a narrower spread of melting times, indicating less variation in melting times among the different brands.
Therefore, Additionally, the median melting time for dark chocolate is higher than the median melting time for milk chocolate, indicating that dark chocolate generally takes longer to melt.
Learn more about median here:
https://brainly.com/question/28060453
#SPJ9
How do you find the surface area for this? Anything helps! (will give brainliest)
Answer:
95.2 square yards
Step-by-step explanation:
8(3) + 2(1/2)(3)(7.2) + 2(1/2)(8)(6.2)
= 24 + 21.6 + 49.6 = 95.2 square yards
The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
2x3 + 6x2 + 4x + 12
2x3 + 6x2 + 6x + 18
2x2 + 6x + 5
2x2 + 5
The width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
Given that:
Area, A(x) = 2x³ + 6x² + 5x + 15
Length, L = x + 3
The formula for the area of a rectangle is:
A = length x width
A(x) = (x + 3) · W
A(x) / (x + 3) = W
W = (2x³ + 6x² + 5x + 15) / (x + 3)
W = [2x²(x + 3) + 5x(x + 3)] / (x + 3)
W = [(2x² + 5)(x + 3)] / (x + 3)
W = 2x² + 5
Therefore, the width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ1
how can you use the unit circle to define the trigonometric functions of any angle
By following these steps, you can use the unit circle to define the trigonometric functions of any angle.
Steps: Draw a unit circle, place the angle, Identify the point of intersection, Define the trigonometric functions.
To use the unit circle to define the trigonometric functions of any angle, follow these steps:
1. Draw a unit circle: This is a circle with a radius of 1, centered at the origin (0, 0) of the coordinate plane.
2. Place the angle: Position the angle in standard position, which means that the initial side (starting side) of the angle is along the positive x-axis and the terminal side (ending side) is formed by rotating the initial side counterclockwise to a certain position.
3. Identify the point of intersection:
Determine the point where the terminal side of the angle intersects the unit circle.
This point will have coordinates (x, y).
4. Define the trigonometric functions:
Using the coordinates (x, y), define the six trigonometric functions as follows:
- Sine (sin): sin(angle) = y
- Cosine (cos): cos(angle) = x
- Tangent (tan): tan(angle) = y/x
- Cosecant (csc): csc(angle) = 1/y
- Secant (sec): sec(angle) = 1/x
- Cotangent (cot): cot(angle) = x/y.
For similar question on trigonometric.
https://brainly.com/question/29615325
#SPJ11
Alex's porch has a length and width of 12 feet each. He wants to paint the porch with a
water sealant that costs $35 per square foot. However, his wife wants him to change
the length of the porch to 14 feet. What would the difference in cost of applying sealant
be if Alex does extend his porch length?
Answer: $1820
Step-by-step explanation:
Area = Length*Width
Forst we have to solve for the area.
A = 12 * 12
A = 144 ft^2
Next we have to multiply be the cost per square foot.
144 * 35
= $5040
Solve for the area.
A = 14 * 14
A = 196 ft^2
Multiply by the cost per square foot.
196 * 35
= $6860
Lastly subtract both costs:
6860 - 5040 = 1820
Therefore the difference in cost would be $1820.
Hope this helps :)
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
The ratio of false positives to false negatives in this scenario is 3.5.
3.5 is the correct answer. False positives are lightning detector activations when there is no lightning in the area. False negatives are lightning detector not activations when there is lightning in the area. To calculate the ratio of false positives to false negatives, divide the false positives (7%) by the false negatives (2%). 7/2 = 3.5. Therefore, the ratio of false positives to false negatives in this scenario is 3.5.
The ratio of false positives to false negatives in this scenario is 3.5.
Learn more about ratio here
https://brainly.com/question/13419413
#SPJ1
Answer:
i took the test :)
Step-by-step explanation:
3.5
Obtain the volume of rectangular boxes with a, 2b and 3c as length, breadth and height respectively
Step-by-step explanation:
The volume of a rectangular box is given by the formula:
Volume = length x breadth x height
In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:
Volume = a x 2b x 3c
= 6abc
Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.
the two plates of a capacitor hold 2500 μc and –2500 μc of charge, respectively, when the potential difference is 960 v. what is the capacitance?
2.6 * 10⁻⁶ F is the capacitance.
What is a capacitor short answer?
A capacitor is a component used in electrical circuits to hold charges. The idea behind how a capacitor functions is that when an earthed conductor is moved close to a conductor, its capacitance increases noticeably.
As a result, a capacitor contains two plates with equal and opposing charges that are spaced apart. Two conductors that are near to one another and are isolated from one another make up a capacitor, a device for storing electrical energy. The parallel-plate capacitor is a straightforward illustration of such a storage device.
We have realtion Q=CV
where Q is charge , C is capacitance and V is voltage.
C=Q/V
C=(2500 * 10⁻⁶)/960
C= 2.6 * 10⁻⁶ F
Learn more about capacitor
brainly.com/question/17176550
#SPJ1
Find the square of: 5i√3
Answer: We have:
(5i√3)² = (5i)²(√3)² = -25(3) = -75
Therefore, the square of 5i√3 is -75.
Step-by-step explanation:
The square of the complex number of 5i√3 is 75.
What is a complex number?A complex number is the sum of a real number and an imaginary number.
To find the square of the complex number, 5i√3, we use the following Steps below
Step1: Square the expression
(5i√3)²Step 2: use the law of surd to seperate each of the terms in the expression
[(5i)²(√3)²]Note: In complex number notation,
i×i = 1Therefore,
25(3)75Hence, square of 5i√3 is 75
Learn more about complex number here: https://brainly.com/question/28007375
#SPJ1
please help with this question! thank you :))
Answer:
2x
Step-by-step explanation:
it is x+x or 2x, since if x>=0, the absolute value of x is just x, then we can say that it is x+x without the absolute value symbols. :)
Can someone please help me?
Answer:
2) x = 3√5; y = 6;
3) x = 12√2; y = 12;
4) x = 45∘; y = 45∘;
5) x = 60∘; y = 30∘
Step-by-step explanation:
2) Use trigonometry:
[tex] \cos(60∘) = \frac{3}{y} [/tex]
Use the property of the proportion to find y:
[tex]y = \frac{3}{ \cos(60∘) } = \frac{3}{1} \div \frac{1}{2} = \frac{3}{1} \times \frac{2}{1} = 6[/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {3}^{2} = {6}^{2} + {3}^{2} = 36 + 9 = 45[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{45} = 3 \sqrt{5} [/tex]
3) Use trigonometry:
[tex] \sin(45∘) = \frac{12}{x} [/tex]
Use the property of the proportion to find x:
[tex]x = \frac{12}{ \sin(45∘) } = \frac{12}{1} \div \frac{ \sqrt{2} }{2} = \frac{12}{1} \times \frac{2}{ \sqrt{2} } = 12 \sqrt{2} [/tex]
Use trigonometry:
[tex] \tan(45∘) = \frac{12}{y} [/tex]
Use the property of the proportion to find y:
[tex]y = \frac{12}{ \tan(45∘) } = \frac{12}{1} = 12[/tex]
4) Use trigonometry:
[tex] \tan(x∘) = \frac{3}{3} = 1[/tex]
x = 45∘
[tex] \tan(y∘) = \frac{3}{3} = 1[/tex]
y = 45∘
5) Use trigonometry:
[tex] \cos(x∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]
x = 60∘
[tex]x = \sin(y∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]
y = 30∘
someone help me with this
The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.
What is a direct proportion?In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.
By applying direct proportion to the given information, we have the following mathematical equation:
15 gallons of gasoline = 214.5 miles
X gallons of gasoline = 111.54 miles
By cross-multiplying, we have the following:
214.5x = 15 × 111.54
x = 1,673.1/214.5
x = 7.8 gallons of gasoline.
Read more on direct proportion here: https://brainly.com/question/29672991
#SPJ1
suppose you have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5. which data set is more spread out?
Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.
What do we understand by sparse data set?Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.
[tex]Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25[/tex]
Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.
See more information about the variance in: https://brainly.com/question/9304306
#SPJ11
5 less than a qoutient of a number and 3
Answer:
The solution to the equation is -7
Step-by-step explanation:
I hate these kinds of Questions but it all comes down to how you mathematically interpret it.
Find the difference
Answer:
Step-by-step explanation:
425 - 59 is 366
:)
Answer:
366.
Step-by-step explanation:
someone please help I'll give brain list (I'm failing)
Answer:
1) 3rd one down 1 7/12 ( the one you've selected well doneee)
2)pretty sure its also the 3rd one down ( don't come for me if its wrong)
Step-by-step explanation:
4 1/6 = 25/6
5 3/4= 23/4
25/6 x4= 100/24
23/4 x 6 = 138/24
138/24 - 100/24 = 38/24
divide by 2:
19/12= 1 7/12
Identify the area of a regular pentagon with side length 21
in.
rounded to the nearest tenth.
The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)
What is pentagon?A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.
Here is a regular pentagon with side length 21 in.
Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]
Here a= 21 in
So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.
= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex] "
≈758.73053 square in
= 758.7 square in. ( rounded to the nearest tenth).
Hence the area of regular pentagon is 758.7 square in.
To know more about pentagon
https://brainly.com/question/27231177
#SPJ1
the coc admissions department wants to see how many students would be in favor of using a new program to register for classes. they put a link on their website so that any students that want to try out the program can. the students can then take a survey and say how well they like the new system. this is what method of collecting data was used: group of answer choices convenience census cluster systematic voluntary response simple random sample (srs) stratified
The method of collecting data that was used in the given scenario is voluntary response.
A voluntary response method of data collection is a research technique that allows participants to decide whether or not they want to be included in the sample.
When participants are allowed to choose whether or not to participate, this is known as self-selection.
This method has a disadvantage in that it could lead to bias in the data because those who respond to the survey may not represent the entire population of interest.
In the given scenario, the COC admissions department put a link on their website so that any students that want to try out the program can. The students can then take a survey and say how well they like the new system. This means that the method of collecting data that was used is voluntary response.
Know more about voluntary response here:
https://brainly.com/question/13298621
#SPJ11
Which angle(s) below is/are supplementary?
A. X and Y
B. Z
C. V
D. W and U
Answer:
Only Z
Step-by-step explanation:
Supplementary angles are angles whose sum up to 180 degrees.
If the vertex of the function is at the. 0, 0. 5 what is the recommended amount of mulch for a flower bed with a radius of 20 feet round to the nearest 10th if necessary
the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.
The formula to find the recommended amount of mulch for a circular flower bed is:
Mulch = π * r^2 * d
Where r is the radius of the flower bed and d is the desired depth of the mulch.
Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:
Mulch = π * (20 feet)^2 * 0.5 feet
Mulch = π * 400 square feet * 0.5 feet
Mulch = 200π cubic feet
To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:
Mulch ≈ 200 * 3.14
Mulch ≈ 628 cubic feet
Rounding to the nearest tenth, we get:
Mulch ≈ 628.3 cubic feet
Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
To know more about amount of mulch click here:
brainly.com/question/2049018
#SPJ4
Please help to complete this chart pleaseeeeeee
The completed chart for a one-time investment made in the amount of $9,200 is attached below.
How to calculate interest rate and compounding periods?For Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.06)¹⁵
A = $9,200 (1.06)¹⁵
A = $22,048.34
For Semi-Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.03)³⁰
A = $9,200 (1.03)³⁰
A = $21,214.29
For Quarterly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.015)⁶⁰
A = $9,200 (1.015)⁶⁰
A = $20,947.34
For Monthly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.005)¹⁸⁰
A = $9,200 (1.005)¹⁸⁰
A = $20,812.09
For Weekly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0012)⁷⁸⁰
A = $9,200 (1.0012)⁷⁸⁰
A = $20,756.54
For Daily compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0002)⁵⁴⁷⁵
A = $9,200 (1.0002)⁵⁴⁷⁵
A = $20,726.55
Learn more on compound interest here: https://brainly.com/question/24924853
#SPJ1
Image transcribed:
1. Fill in the chart for the following investment.
A one-time investment is made in the amount of $9,200 for 15 years at an APR of 6%.
Compound Interest: A = P (1 + i)", where A is the final amount, P is the principal invested, i is the interest rate per compounding period, and n is the number of compounding periods.
7. Write the equation of a line passing through the points (4,-3) and (16, 6). Show all of your work.
15 is the distance of the equation of a line passing through the points.
What is distance ?
Distance is the separation between two objects. Moreover, it serves as a gauge for the distance between two objects. It is measurable along any route. So even though his position does not change, a person who circles about has moved a certain amount of distance.
the points (4,-3) and (16, 6)
D = √(x₂ - x₁)² + (y₂ - y₁)²
= √(16 - 4)² + (6 -(-3)²
= √(12)² + (9)²
= √144 + 81
= √225
= 15
Learn more about distance
brainly.com/question/15172156
#SPJ1
Adrienne earns $98 for working 8 hours. If she earned $453.25, How many hours did she work?
Answer:
37 hours
Step-by-step explanation:
First, we will find the amount of money that Adrienne makes per hour: 98/8, which equals $12.25.
Now, we can find the number of hours it takes to earn $453.25 by dividing it by $12.25:
$453.25 / $12.25 = 37 hours
Tamara earns her living as a salary plus commission employee. Her annual salary is $48,000, and she earns 4% commission on all sales she makes. If Tamara wants to make a total of $6,000 this month, how much in sales does she need to have?
a.
$30,000
b.
$50,000
c.
$100,000
d.
$150,000
Please select the best answer from the choices provided
A
B
C
D
Answer:
B. $50,000
Explanation:
4%=.04
50,000 x .04=2000
48000/12=4000
She makes $4000 off of her salary each month. Then because she only gets 4% of her commissions you multiply the 50000 by .04 and you get 2000. So she gets $2000 in commissions and $4000 off of her salary.
What is the hundredth digit of pi? This would include the 3 in the beginning.