The slope of the line that passes through (-8,-1) and (12,4) is 1/4.
The equation of the line in slope intercept form is y = x/4 - 31/4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (4 + 1)/(12 + 8)
Slope, m = 5/20
Slope, m = 1/4.
At point (-8, -1), a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 1/4(x - (-1))
y + 8 = x/4 + 1/4
y = x/4 - 31/4.
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What is the amplitude of the function given? f(x) = -7cos(1x) + -3
On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7
What exactly is trigonometry?Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.
Trigonometry is used here.
f(x) = -7cos(1x) plus -3
f(1) = -7
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Help with algebra questions
The values of the operations between the two functions are, respectively:
(f + h)(5) = 7(h - f)(2) = 0(f · h)(3) = 0(h / f)(0) = 3 / 5How to determine the result of operation between two functionsIn this problem we find the representations of two functions, each on one Cartesian plane: f(r), h(r). Based on that information we can determine the result of operations between functions, which are defined below:
Addition
(f + h)(x) = f(x) + h(x)
Subtraction
(f - h)(x) = f(x) - h(x)
Multiplication
(f · h)(x) = f(x) · h(x)
Division
(f / h)(x) = f(x) / h(x)
Now we proceed to determine each operation:
(f + h)(5) = f(5) + h(5) = 3 + 4 = 7
(h - f)(2) = h(2) - f(2) = 1 - 1 = 0
(f · h)(3) = f(3) · h(3) = 4 · 0 = 0
(h / f)(0) = h(0) / f(0) = 3 / 5
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A worker earned a 3% increase in her annual salary for each of 5 years. They plan to continue working in
their position for an additional n years. If they continue to earn a 3% increase in their annual salary, which
statement describes the expression that can be used to calculate the total percent increase in their annual
salary from the first year to the last year?
A. The expression 1.035 can be used because (1.035)" = 1.035.
OB. The expression 1.035 ca
can be used because 1.035 x 1.03 = 1.035.
O C. The expression 1.035+ can be used because 1.035 x 1.03 = 1.035+
O D. The expression 1.035+ can be used because 1.035 +1.03n = 1.035+n.
Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:
P= 100%[([tex]1.03^{t}[/tex]) - 1]
What is an exponential function?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
An increasing exponential function is modeled by:
A(t)= A(0)[tex](1+r)^{t}[/tex]
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
As a percentage, the increase is modeled by:
P= 100%[[tex](1+r)^{t}[/tex] - 1]
In this problem, the growth rate is of r = 0.03, hence:
P= 100%[ [tex](1+0.03)^{t}[/tex]- 1]
P= 100%[[tex](1.03)^{t}[/tex]- 1]
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Question is in the picture
The relations that represent functions are given as follows:
Table.The square of a number x plus one.y = x/2 + 5.Graph at the bottom.When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
Hence the two items that are not functions in this problem are given as follows:
Graph -> second item -> vertically aligned points for x > 0, meaning that the values of x > 0 are mapped to two values of y.The set of ordered pairs, as the input of 4 is mapped to outputs of -2 and 2.More can be learned about relations and functions at brainly.com/question/10283950
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Final question no more lives
who ever gives me correct answer will get brainliest
The time take to fill the pool will be 494 hours.
How to calculate the TimeInlet pipe fills in 38 hours = 1 pool
Inlet pipe fills in 1 hours = 1/38
Drain pipe empty in 39 hours = 1 pool
Drain pipe empty in 1 hour = 1/39
If both pipes are opened together then in pool fills in 1 hour = 1/38 - 1/39
= 1/1482
Therefore, 1/1482 fills in 1 hour.
. Therefore, 1/3 will be:
= 1/3 × 1482
= 494 hours.
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If Lisa works part-time, she will make 35% less than she does now.
How much will her monthly net income be?
What will their new total net income be?
Answer:
Lisa: $3302Family: $11372Step-by-step explanation:
Given a family net income of $13150, Lisa's current annual gross of $76200, deductions of 20% of Lisa's gross salary, you want to know Lisa's monthly net income and the new family net income if Lisa makes 35% less by working part-time.
Lisa's incomeLisa's current annual income is $76200, and her annual net income is 80% of that, or $60960. On a monthly basis, her net income is ...
$60960/12 = $5080 . . . . . . Lisa's current net monthly income
If her income is reduced by 35%, the reduction is ...
0.35 × $5080 = $1778
Then Lisa's part-time monthly net income will be ...
$5080 -1778 = $3302 . . . . . Lisa's part-time monthly net income
Family incomeThe family net income will be reduced by the same amount:
$13150 -1778 = $11372 . . . . . new family monthly net income
__
Additional comment
It appears the total of budgeted items is $10343, so those items can be paid even if Lisa works part-time. The family's current surplus income of $2807 would be reduced to $1029, about a 63% reduction. That gives a lot less cushion to pay for off-budget expenses that may come up.
Skylar has 12 pieces of candy left in her Halloween bag. There are 8 pieces of chocolate and 4 pieces of non-chocolate. She
chooses a piece of candy at random and then chooses another piece of candy, without replacement. Draw a tree diagram to
represent this situation and use it to calculate the probabilities that she picks:
Two pieces of non-chocolate
Chocolate only
At least one piece of chocolate
One piece of each type
The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat: 1 - P(kit-kat)
What is probability?Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. The value is expressed as a number between 0 and 1.To forecast how likely occurrences are to occur, probability has been introduced in mathematics. The words "probable" and "probability," as well as its cognates in various modern languages, come from the medieval Latin word "probabilis," which Cicero borrowed and used to denote "plausible" or "commonly accepted" in expressing opinions.You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.
In this case, the desired confectionery is P(snickers). 12 in number.
In total, the bag contains 20 sweets.
P(snickers) = 12/20 = 3/5
The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:
1 - P(kit-kat)
The complete question is:
Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.
a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)
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Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one
of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is
answer
C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123
explanation
The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).
The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.
I need help on my homework! Answer number 15, please :)
15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.
16) The value of the algebraic expression is 2.
What is the evaluation of an expression?The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.
PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.
-10 -144/(-12)
-10 + (144/12)
-10 + 12
= 2
Thus, we have evaluated the expression to have a value of 2.
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Help solve please !!
Answer:
2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7
8) A certain rubber ball, when dropped from a height of 2 meters onto a
hard floor, bounces back up to 75% of the height from which it was
dropped.
What is the height of the ball after the 5th bounce?
The height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.
What is called height?
Height, altitude, and elevation mean the vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.
Each time the ball bounces, it reaches a height of 75% of its previous height.
Since the ball was dropped from a height of 2 meters, its height after the first bounce will be:
2 meters x 0.75 = 1.5 meters
After the second bounce, the height of the ball will be:
1.5 meters x 0.75 = 1.125 meters
After the third bounce, the height of the ball will be:
1.125 meters x 0.75 = 0.84375 meters
After the fourth bounce, the height of the ball will be:
0.84375 meters x 0.75 = 0.6328125 meters
After the fifth bounce, the height of the ball will be:
0.6328125 meters x 0.75 = 0.474609375 meters
Therefore, the height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.
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Find a positive angle less than 360° that is coterminal with the given angle
-1025°
The positive coterminal angle less than 360° is, 55°
What are coterminal angles ?Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).
To find a positive angle that is coterminal with -1025°,
we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.
Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:
= -1,025° + 1080°
= 55°
Since this angle is less than 360°,
Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.
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You rent an apartment that costs \$900$900 per month during the first year, but the rent is set to go up \$120$120 per year. What would be the monthly rent during the 11th year of living in the apartment?
Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.
The total increase in rent over 10 years is $120 per year * 10 years = $1200.
So, the monthly rent during the 11th year would be $900 + $1200 = $2100.
Therefore, the monthly rent during the 11th year would be $2100.
Step-by-step explanation:
riya wants to buy a mirror which one of these shapes has only one line of symmetry
Answer:
Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.
Step-by-step explanation:
Assume that the variables, x and y, have been assigned integer values. Write a boolean expression which evaluates to True if x is non-negative and y is negative. Note that zero is a
non-negative number.
The boolean expression that evaluates to True if "x is non-negative and y is negative" is: (x >= 0) ∧ (y < 0).
A boolean expression is a logical expression that evaluates to either true or false. Boolean expressions can be composed of one or more boolean operators, such as AND, OR, and NOT, and can involve one or more variables.
We need to find boolean expression for: "x is non-negative and y is negative", then output is true.
The boolean expression is:
(x >= 0) ∧ (y < 0), or (x>=0) AND (y<0)
In this expression, the ∧ symbol represents the logical AND operator. The expression (x >= 0) checks if x is greater than or equal to 0 (i.e. non-negative), and the expression (y < 0) checks if y is less than 0 (i.e. negative).
If both conditions are true, the overall expression evaluates to true, indicating that x is non-negative and y is negative.
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Help with these questions Pls?
Answer:12
Step-by-step explanation:30-6=24
24 divided by 2 =12
Solve it down guys :)
Refer to the attached images.
**Should be arctan(tanx)=x on the last page**
DUE TODAY THANK YOU HELP
Answer:
smaller value = 4yd
larger value = 8yd
Step-by-step explanation:
Let's call the garden's width and length W and L respectively.
The area of the garden is 36yd². We can write this mathematically as W*L=36
If 26yd is enough fencing to perfectly enclose the garden, then this must be the garden's perimeter. Written mathematically, this is 2W+2L=26. We can simplify this by dividing each term by two to get W+L=13
If W and L multiply to get 36, they must be both a factor pair of 36. The factor pairs of 36 (the pairs of numbers which multiply to get 36) are '1 and 36', '2 and 18', '3 and 12', '4 and 9', and '6 and 6'.
W and L must also add to 13, and the only factor pairs of 36 which add to 13 are '4 and 9' so these are our dimensions.
Answer:
smaller value = 4yd
larger value = 8yd
mark brainly
Please help me with this please
Answer:
1,3 or 4,2
Step-by-step explanation:
Triangle XYZ is rotated 90° clockwise about the origin to form triangle x'Y'Z'.
Which statement is true?
The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.
The rotation is a rigid transformation
This means that it does not change the side length and angles of a shape when applies
Using the above as a guide, we have the following:
The image and the preiamage have the same area
Hence, the true statement is (d)
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Complete question
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.
y. z. y. x. x.
Which statement is true?
The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.
The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.
Triangle XYZ is not congruent to triangle X'Y′Z'.
The area of triangle XYZ is equal to the area of triangle X'Y′Z
Find the values of x and y.
The value of x is 5, while the value of y is 24
How to solve for x and yIn order to get the value of x we would first have to find the value of y
The sum of angles on a straight line = 180
hence we would have:
5y + 2y + 12 = 180
7y = 180 - 12
7y = 168
y = 24 degrees
The angle that is made at R is 90 degrees
we would have
2y + 12 + 5x = 90
y = 24
2 * 24 + 12 + 5x = 90
60 + 5x = 90
5x = 90 - 60
5x = 30
x = 30 / 6
x = 5
Hence the value of x is 5
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Write as a product.
(5c-3d)²-9d²
Answer:
the answer is 25c²
Step-by-step explanation:
(5c-3d)²-9d²
5²c²+3²d²-9d²
25c²+9d²-9d²
25c²
Answer:
= 25c² - 30cd
Step-by-step explanation:
(5c-3d)²-9d²
[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total is made up of Green?
9.19% of the total is made up of Green.
What is a percentage?The percentage formula is dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of green cars = 120
Number of green planes = 250
Number of green trains = 500
Total = 870
Now,
The total number of all colors of the car, plane, and train.
= 870 + 1250 + 820 + 800 + 990 + 4730
= 9460
Now,
The percentage of green cars, planes, and trains.
= 870/9460 x 100
= 9.19%
Thus,
9.19% of the total is made up of Green.
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Faith needs 300 milliliters of a 57% acid solution for a chemistry experiment. She has two acid solutions, A and B, that can be mixed together to form the solution. Solution A is 50% acid, and Solution B is 60% acid. How much of each solution should she use to create the mixture?
She should use milliliters of Solution A.
She should use milliliters of Solution B.
The needed amount of each solution is given as follows:
90 milliliters of Solution B.210 milliliters of Solution B.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable x: amount of Solution A.Variable y: amount of Solution B.Faith needs 300 milliliters of the solution, hence:
x + y = 300.
x = 300 - y.
The percentage is of 57%, hence:
0.5x + 0.6y = 0.57 x 300
0.5x + 0.6y = 171.
Replacing the first equation into the second, the value of y is obtained as follows:
0.5(300 - y) + 0.6y = 171
0.1y = 21
y = 21/0.1
y = 210.
The value of x is then given as follows:
x = 300 - 210
x = 90.
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Find the length of the midsegment of each trapezoid.
The length of the midsegment of trapezoid is 24 units.
What is Trapezoid ?An open, flat figure with four successive sides and one pair of parallel sides is termed to as a trapezoid or trapezium.
The parallel and non-parallel sides of a trapezium are called as the bases and the legs, respectively. A trapezium may also have parallel legs. The parallel sides can be slanted, vertical, or horizontal.
The altitude is the evaluation of the angle perpendicular to the parallel sides.
Now in the given question,
a = 15
b = 23
length of mid segment EF,
[tex]l=\frac{a+b}{2} \\\\l=\frac{15+23}{2} \\\\l=\frac{48}{2} \\\\l=24[/tex]
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here is a probability that a randomly selected 30-year-old male lives through the year. A life insurance company charges $154 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $ as a death benefit. Complete parts (a) through (c) below. Question content area bottom Part 1 a. From the perspective of the -year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ negative 195. The value corresponding to not surviving the year is $ 99,805. (Type integers or decimals. Do not round.) Part 2 b. If the -year-old male purchases the policy, what is his expected value? The expected value is $ enter your response here.
Answer: a. From the perspective of the 30-year-old male, the monetary value corresponding to surviving the year is -$154 (the cost of the insurance policy). The monetary value corresponding to not surviving the year is $99,805 (the death benefit payout).
b. If the 30-year-old male purchases the policy, his expected value can be calculated using the formula:
Expected Value = (Probability of Event A) * (Value of Event A) + (Probability of Event B) * (Value of Event B)
In this case, the probability of surviving the year and not surviving the year can be assumed to be the same, as we don't have any specific information on the individual's health or life expectancy. Therefore, the probabilities can be assumed to be 0.5 each.
Plugging in the values, we get:
Expected Value = (0.5) * (-$154) + (0.5) * ($99,805) = ($50,326)
So, the expected value for the 30-year-old male purchasing the policy is $50,326.
Step-by-step explanation:
Solve the system by graphing.
a)
y = x
y = 2x+2
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
Solving the system of equations:To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.
In the next step, we need to Identify the solution to the system.
If the lines are intersected, the point of intersection is the solution.
If the lines are parallel, the system will have no solution.
If the lines are the same or coincident, then the system will have an infinite number of solutions.
Here we have
y = x ----- (1)
y = 2x+2 ---- (2)
From (1) and (2)
=> y = 2y + 2
=> 2y - y = -2
=> y = - 2
Hence, the solution of the given system of the equation is (-2, -2)
We can check it by graphing the lines as shown figure.
Therefore,
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
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Enter the letter of the graphed function(image)
answer c)
cross x at x = -2, x = 3, and x = 1
the square root tells us that it bounces off that location rather than intercepting
Find the length of CD.
E
2
D
A1 B
The length of CD is
5
C
unit(s).
The length of CD can be found to be 7. 21 units .
How to find CD ?The length of CD can be found by using the distance formula which is :
= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]
Given the points, ( 3, - 2 ) and ( 7, - 8 ).
The length of CD is :
= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]
= 7. 21
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A bank developed a model for predicting the average checking and savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth
The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.
Given that;
The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.
Now,
-17,732 is a constant amount credited from the savings acount
367 is the amount saved per year of age
1300 is the amount saved per year of education
0.116 is the amount save per household wealth
Therefore, the following are the interpretations of the equation.
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