Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:
y = -4x + 20
Step-by-step explanation:
The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).
To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.
Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:
y - y1 = m(x - x1)
Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:
y - 4 = -1/2(x + 6)
Which can be written as:
y = -1/2x + 4
So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:
y = -1/2x + 4
Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.
Which table represents the second piece of the function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 3.5 x + 0.5, 2nd column x less-than 1 2nd row 1st column 8 minus 2 x, 2nd column x greater-than-or-equal-to 1 EndLayout?
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 0, 1. The second column is labeled f (x) with entries 4, 0.5, negative 3.
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 0, 1. The second column is labeled f (x) with entries 10, 8, 6.
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column is labeled f (x) with entries 6, 4, 2.
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 2, 3. The second column is labeled f (x) with entries negative 3, negative 6.5, negative 10.
The values in the table that represent the second piece of the function f(x) is the option;
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column ism labeled f(x) with entries 6, 4, 2
What is a mathematical function?A function maps the values in the set of input variables to the values in the set of output variables.
The functions are presented as follows;
First row; f(x) = -3.5·x + 0.5; x < 1
Second row; f(x) = 8 - 2·x; When x ≥ 1
The second piece of the function is therefore;
f(x) = 8 - 2·x; When x ≥ 1
The possible values of x, which are values in the domain are; 1, 2, 3
The values of f(x), which are values in the range are therefore;
f(1) = 8 - 2 × 1 = 6
f(2) = 8 - 2 × 2 = 4
f(3) = 8 - 2 × 3 = 2
The values of x and f(x) are therefore;
x [tex]{}[/tex] f(x)
1 [tex]{}[/tex] 6
2 [tex]{}[/tex] 4
3 [tex]{}[/tex] 2
The correct option that represents table for the second piece of the function, f(x) is therefore;
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column is labeled f(x) with entries 6, 4, 2
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Answer: C. or third chart
Step-by-step explanation:
Got it right!!
I need to be resolved with the number line
The solution of the inequality is less than 1.75 which is shown on the diagram.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
5/8 > (1/2)x - 1/4
Simplify the inequality, then we have
5/8 > (1/2) x - 1/4
5/8 + 1/4 > (1/2) x
(5 + 2)/8 > (1/2) x
7 / 8 > (1/2) x
(1/2) x < 7 / 8
x < 7 / 4
x < 1.75
The solution of the inequality is less than 1.75 which is shown on the diagram.
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There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
According to the given information, there is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/55
Conversion between units: Calculating kilograms of dog foodFrom the question, we are to determine the statement that is true
From the given information,
There is 25 pounds of dog food in a bag.
and
There are approximately 2.2 kilograms in 1 pound.
If there are 2.2 kilograms in 1 pound
Then,
There would be x kilograms in 25 pounds
x = 2.2 × 25
x = 55 kilograms
Hence, there are 55 kilograms
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ben has a piece of plywood that measures 1 yard on each side .he cuts the wood into 6 equal pieces .each piece is 1/3 yard wide and 1/2 yard long. what is the area of each piece that ben cuts. explain how the product 1/2x1/3 relates to the model
Answer:
Step-by-step explanation:
Ben has a piece of plywood that measures 1 yard on each side, and he cuts it into 6 equal pieces.
The width of each piece is 1/3 yard, and the length of each piece is 1/2 yard.
To find the area of each piece that Ben cuts, we can multiply the width and length of each piece:
Area = (1/3 yard) x (1/2 yard)
Area = (1/3) x (1/2)
Area = 1/6 yard^2
So each piece that Ben cuts has an area of 1/6 yard^2.
The product 1/2x1/3 relates to the model in that it represents the area of the piece. In other words, the length and width are multiplied to find the area of the piece.
In this case, we can see that Ben cuts the plywood into 6 pieces of equal area, which is 1/6 of a square yard.
Please help, having trouble getting answer.
Answer:
C. 2 ≤ x
Step-by-step explanation:
EDGE
Borrowed 600$ from the bank. Interest is $14.25 for 90 days. What is interest rate?
Answer:
0.01 %
Step-by-step explanation:
The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.
To find the interest rate, we can use the formula:
Interest Rate = Interest / Principal x Number of days / 365
We know that the principal is 600$, the interest is 14.25$ and the number of days is 90
so we can substitute the values into the formula:
Interest Rate = 14.25 / 600 x 90 / 365
Interest Rate = 0.02375 * 90 / 365
Interest Rate = 0.0104
Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %
The rectangle below has the dimensions 6.9 x 5.2 create another rectangle that is scaled to 4 times the size of the current rectangle I need this answer fast
A rectangle that is scaled to be 4 times the size of the given rectangle would have the dimensions of 27.6 x 20.8.
How to create the rectangle ?When a rectangle is said to be scaled to be a certain number of times more than the size of another rectangle, it means that both rectangles will have the same shape and orientation, but their dimensions will be different.
This difference will come from the change that the scale factor brought about. In this instance, the scale factor is 4 times which means that the second rectangle will be 4 times the size of the first.
The first dimension would be :
= 6 . 9 x 4
= 27.6 units
The second dimension would be:
= 5 . 2 x 4
= 20. 8 units
The dimensions would then be:
27. 6 x 20. 8
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Which set of numbers is correctly ordered from greatest to least?
221
07,207.36, 2.4-√3x
7.36, 221, 2.4-√3x
30
0 7 1,7
O 2.4√√3,7.36, 221 1,7/1/1
30
221
O
○ 2.4-√3x, 230, 7. 36,7
The set of number that is correctly ordered from the question in the attachment is option D.
How to solve for the solution in order to get the ordering1. [tex]7\frac{1}{3}[/tex] = 7 + 0.3333
= 7.3333
2. 221 / 30 = 7.3666
3. 7.36 = 7.36363636
4. [tex]2.4\sqrt{3\pi }[/tex] = 2.4 * [tex]\sqrt{9.43}[/tex]
= 7.36999
We would have to arrange all of the values from their highest to the least values
7.36999, 7.3666, 7.36363636, 7.3333
[tex]2.4\sqrt{3\pi }[/tex], 221 / 30, 7.36 , 7.3333
Hence the last option is the answer. It shows how the solution is ordered from the greatest to the smallest value
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I need help with written steps please
Answer:
a. To find the cost to surround the forest with a fence, we first need to determine the perimeter of the forest. The problem tells us that the perimeter is 45 yd. To convert this to feet, we can use the conversion factor of 3 feet per 1 yard. So, the perimeter in feet is:
45 yd x (3 ft/1 yd) = 135 ft
Next, we need to multiply the perimeter by the cost per foot to install fencing. We're told this cost is $6 per foot, so we can calculate the cost as:
135 ft x $6/ft = $810
b. To determine which region costs more to prepare, we need to calculate the cost per square yard for both the grassland and the forest. We're told that the cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is $25.
To find the total cost for the grassland, we'll multiply the area of grassland with the cost per square yard:
2400 yd x $15/yd = $36,000
To find the total cost for the forest, we'll multiply the area of forest with the cost per square yard:
60 yd x $25/yd = $1,500
We can see that the grassland cost $36,000 to prepare while the forest cost $1,500 which means Grassland costs more to prepare.
( Look at picture) Thx btw
Step-by-step explanation:
930 = -20×|t - 15| + 1010
one solution is for (t - 15) > 0
930 = -20×(t - 15) + 1010
-80 = -20×(t - 15)
4 = t - 15
t = 19
that means 2019.
the second solution is for (t - 15) < 0
930 = 20×(t - 15) + 1010
-80 = 20×(t - 15)
-4 = t - 15
t = 11
that means 2011.
Have 5 minutes left!!!!!
Which system of equations below has exactly one solution?
O y = -8x - 6 and y = -8x + 6
O y = -8x -6 and 7y = -4x - 3
O y = -8x - 6 and y = 8x - 6
Q y = -8x - 6 and -y = 8x + 6
Answer:
Y=-8x-6 and x=-8x+
Step-by-step explanation:
Match each of the equations with their corresponding graph.
a) y= x^3 +2x^2-1
b) 2x^2-x-3
c) 1/x +1
d) 2-3x^2 -x^3
Answer:
I think so the answer is a)y=x³+2x²-1
Write the expression 15½ in radical form.
A finance charge includes which elements?
A) Interest and fees
B) Interest, fees, and principal
D
Fees and principal
192
Interest and principal
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
What Is a Finance Charge?A finance charge is a fee incurred when using a credit or extending credit that already exists. A fixed rate or a percentage of borrowings may be used to calculate finance charges; the latter is more common.
A finance charge is usually made up of the cost of carrying the debt as well as any related transaction fees, account management fees, or late fees imposed by the lender.
Finance charges are a way for a lender to get paid for giving a borrower credit or access to funds. These costs could be one-time payments, like the origination fee for a loan, or they could be interest payments that could be repaid daily or monthly. A finance charge includes Interest, fees, and principal
Therefore,
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
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HELP PLS URGENTT
Image attached
The equation, 6(-2 + 4) = -12 + 24, illustrates E. the Distributive Property of Multiplication over Addition.
What Is Distributive Property?In this mathematical property, the multiplication of two or more addends by a number results in the same value as multiplying each addend individually by the number and then adding the products together.
For instance, 6(-2 + 4) = -12 + 24
= 12
OR:
6(-2 + 4) = 6 x 2
= 12
In this situation, we can either multiply the numbers in parenthesis individually by 6 or sum the parenthesis and then multiply the sum by 6. Either way yields the same result, showing that multiplication is distributive.
Thus, in the equation, the property illustrated is Option E, not the commutative properties of addition and multiplication, the inverse properties of addition and multiplication, the associative properties of addition and multiplication, or the identity properties of addition and addition multiplication.
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Question 8
You decide to begin saving toward the purchase of a new car in five years. If you put
RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent
compounded annually, how much will you accumulate after 5 years?
If you save RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, the future value or the amount you will accumulate after 5 years is RM5,637.09.
What is the future value?The future value is the compounded present value of the periodic deposits.
The future value formula or FV table can determine the accumulated future value of periodic investments.
We can also use an online finance calculator to determine the future value.
N (# of periods) = 5 years
I/Y (Interest per year) = 6%
PV (Present Value) = RM0
PMT (Periodic Payment) = RM1,000
Results:
Future Value (FV) = RM5,637.09
Sum of all periodic payments = RM5,000(RM1,000 x 5)
Total Interest = RM637.09
Thus, in 5 years, you will have an accumulated future value of RM5,637.09 in the savings account.
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a dealer gains 7% by selling a sofa set for rs 3852 .find his gain percent if he sells it for rs 4050
The gain percentage is 12.5%
First, let`s find the Cost price (C.P) of the sofa.
Let C.P of the sofa be x.
Now, according to the question:
x+ 7% of x=Rs.3852
x + (7/100 * x) = 3852
x + 0.07x = 3852
1.07x = 3852
x=3852/1.07,
x = Rs 3600.
Now the dealer sells it for Rs 4050.
so, the Formula for gain% is=(Selling price-Cost price/Cost price)x100
Gain %= (4050-3600/3600)x100
Gain%=(450/3600)x100
Gain%=(450/36)
i.e = 12.5%.
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please help asap
• it would mean sm and make my day
Answer:
I know it
Step-by-step explanation: Btw did somone already answer this?
The diagram shows solid pyramid ABCDE.
The base BCDE of the pyramid is a horizontal square w side lengths 12cm
The vertex A of the pyramid is vertically above the midpoint of BD
The volume of the pyramid is 768cm3
Calculate the size of the angle between AB and the base of the pyramid.
Id the base BCDE of the pyramid is a horizontal square w side lengths 12cm . The size of the angle between AB and the base of the pyramid is 62 degree.
How to find the size of the angle between AB and the base of the pyramid?Side of square of base BCDE =12cm
Area of base =12² =144cm²
Volume of pyramid = 768cm³
1/3 a² × h= 768
1/3 × 144 × h =768cm³
h =768 × 3 /144
h =16 cm
BD² =BC² +CD²
BD² = 12² + 12²
BD² = 288
BD =√288 cm
BD = 16.97cm
BD = 17cm
So,
BF = 1/2 BD
BF = 1/2 × 17
BF =8.5cm
So since ΔABF is angle between AB and base of pyramid
tan <ABF = Tan-1 (16/8.5) = 62°
Therefore the size of the angle between AB and the base of the pyramid is 62 degree.
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Please look at the picture and answer the question thank you
The respective answers are 5 and 4
What is addition in math?Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.
Given: 5 means 5+0+0 which equals to 5
4 means 4+0+0+0 which equals 4
Hence the respective answers are 5 and 4
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Is -2 a solution of 6g-14>21
Answer:
-2 is not a solution of the inequality 6g - 14 > 21.
Step-by-step explanation:
To determine if -2 is a solution of the inequality 6g - 14 > 21, we need to substitute -2 for g in the inequality and see if it is true.
6g - 14 > 21
6(-2) - 14 > 21
-12 - 14 > 21
-26 > 21
This inequality is not true. Because -26 is not greater than 21.
[tex]6g-14 > 21[/tex]
Substitute -2 for g:
[tex]6(-2)-14 > 21[/tex]
[tex]-12-14 > 21[/tex]
[tex]-26 > 21[/tex]
-2 is not a solution because -26 is not greater than 21.
I question below and select the best answer choice. *
What property was used to simplify the expression?
12 × 47 = 12 × (40 + 7)
= 12 X 40 + 12 × 7
= 480 + 84
= 564
The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is distributive property.
What is distributive property?The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.
In other words, distributive property is a rule that states that you can distribute the terms of an expression.
Therefore, let's check the property used on the expression as follows:
12 × 47 = 12 × (40 + 7)
12 × 40 + 12 × 7
480 + 84
564
Hence, the property used on the expression is distributive property.
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If P = 4s represents the square’s perimeter in terms of the square’s side length (in inches), write a formula that represents the perimeter’s side length 's' in terms of the square’s perimeter 'P.'
The side of the square in terms of the perimeter is P/4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
P = 4s
Where s is the side of the square and P is the perimeter of the square.
Now,
The side of the square.
P = 4s
Divide 4 into both sides.
s = P/4
Thus,
The side of the square is P/4.
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There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome | Frequency
Brown | 13
Black | 9
Green | 7
Gold | 11
Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
A. The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
B. The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
C. The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
D. The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.
The correct option is A.
"The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%."
How to find the probabilities?First, let's find the theoretical probability.
We know that there are:
10 brown marbles10 black marbles10 green marbles10 gold marblesFor a total of 40 marbles.
The theoretical probability of randomly pulling a gold marble is equal to the quotient between the total number of gold marbles and the total number of marbles, it is:
P = 10/40
P = 1/4 = 0.25
For the experimental probability, we need to take the quotient between the number of times that the outcome of the experiment was a gold marble and the total number of times that the experiment was performed.
The experiment was performed 40 times and 11 times we got the gold marble, then:
E = 11/40 = 0.275
Then the correct statement is A:
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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Step-by-step explanation:
2. In 2000, Social Security tax was 7.5%, to the maximum income of $53,000. If Mary earned $61,711 in 2000, how
much Social Security did she pay?
Mary paid Social Security tax of $4,378.325 in 2000. This is calculated by multiplying 7.5% by the amount of income over the maximum taxable income of $4,378.325.
How much Social Security did she pay?The theory used in this question is the marginal tax rate, which is the tax rate that applies to the income earned over the maximum taxable income. In this case, the marginal tax rate is 7.5%, which is the Social Security tax rate.
Step 1: Calculate the amount of income over the maximum taxable income.
Maximum taxable income: $53,000
Income earned: $61,711
Amount of income over the maximum taxable income: $8,711 ($61,711 - $53,000 = $8,711)
Step 2: Calculate the Social Security tax.
Social Security tax rate: 7.5%
Amount of income over the maximum taxable income: $8,711
Social Security tax paid: $4,378.325 ($8,711 x 0.075 = $4,378.325)
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Diego brought 16candy bars $25. large candy bars cost $1.25 and regular candy bars cost $0.75. How many candy bars of each size did he buy? (with explanation if u can)
There are 10 and 26 candy bars of each size did he buy.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Diego brought 16 candy bars $25.
And, large candy bars cost $1.25 and regular candy bars cost $0.75.
Now, Let number of large candy bars = x
And, Number of regular candy bars = y
Here, Diego brought 16 candy bars.
Hence, We get;
⇒ x + y = 16 .. (i)
And, large candy bars cost $1.25 and regular candy bars cost $0.75.
Hence, We get;
⇒ 1.25x + 0.75y = 25 .. (ii)
Multiply by 1.25 in (i) and subtract from (ii), we get;
⇒ 1.25y - 0.75y = 20 - 25
⇒ 0.5y = - 5
⇒ y = - 10
And, from (i);
⇒ x + y = 16
⇒ x - 10 = 16
⇒ x = 26
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simplify 7m-2(3m^2 +mn)
Answer: 7m-6m²-2mn
Step-by-step explanation:
Multiply each term in parenthesis by -2
Calculate product (2x3=6)
7m-6m²-2mn
Write and solve an inequality.
Please show work
Chris earns $8 per hour working on the weekends. He needs at least $320.00 for his class trip. How many hours, h, does Chris need to work on the weekends to be able to go on the class trip
We can start solving the problem by using the formula:
Hours worked = Total cost / Hourly wage
In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:
Hours worked = $320.00 / $8.00
To solve this equation, we divide 320 by 8:
Hours worked = 40
So Chris needs to work 40 hours on the weekends to be able to go on the class trip.
I hope this helps :)
Answer:
Chris needs to work at least 40 hours.----------------------------------------
Chris earns $8 per hour and he needs at least $320.00 for his class trip.
If he works h hours, he will get 8h dollars.
Set up inequality:
8h ≥ 320Solving we get:
h ≥ 320/8h ≥ 40Chris needs to work at least 40 hours.
NO LINKS!!
Find the area of this shape.
Answer:
54 units²---------------------------------
It is a combination of 3 rectangles.
All dimensions are given apart from the middle one. The missing dimension is:
6 - 2 = 4 unitsThe total area is:
8*2 + 5*4 + 6*3 = 16 + 20 + 18 = 54 units²A Man bought 5 Crates of 60 of drinks. On his way home, he drank 5 bottles and broke 25 bottles what percentage of the bottles are left?
Answer:50%
Step-by-step explanation:
