[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]
Answer:
[tex]\boxed{\bf Slope(m):-1}[/tex]
Step-by-step explanation:
We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).
The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.
[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]
[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]
[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]
[tex]\bf m=-\cfrac{5}{5}[/tex]
[tex]\bf m=-1[/tex]
Therefore, the slope is -1.
__________________
Hope this helps!
Have a great day!
. Descompuneti in factori:
a) 4x + 4x -35;
c) 4x2+ 20x - 11;
e) 4x2 + 12x - 16;
g) 16x7 + 24x - 40;
i) 25x + 10x - 48;
h ) 25x2 -
j) 16x2 + 40x - 39.
The factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
A) 4x+4x-35
= 8x-35
C) 4x²+20x-11
= 4x²+22x-2x-11
= 2x(2x+11)-1(2x+11)
= (2x+11)(2x-1)
E) 4x²+12x-16
= 4x²+16x-4x-16
= 4x(x+4)-4(x+4)
= (4x-4)(x+4)
= 4(x-1)(x+4)
G) 16x⁷+24x-40
= 8(2x⁷+3x-5)
I) 25x+10x-48
= 35x-48
J) 16x²+40x-39
= 16x²-12x+52x-39
= 4x(4x-3)+13(4x-3)
= (4x-3)(4x+13)
Therefore, the factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
To learn more about the factorisation of polynomial visit:
https://brainly.com/question/16789195.
#SPJ1
In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest. Jennifer plans to repay the loan in January. Assume this loan is a simple interest loan calculated monthly. What will be the total amount she will owe to the bank on January 31st? If necessary, round to the nearest cent.
Answer: The total amount Jennifer will owe to the bank on January 31st is $3,458.75
Step-by-step explanation: In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest for 4 months. As this loan is a simple interest loan calculated monthly, we need to calculate the total amount she will owe to the bank on January 31st.
We use the formula for simple interest which is:
Interest = Principal x Interest rate x Time
Interest = $2,500 x 11.75/100 x 4/12 = $958.75 (rounding to the nearest cent)
Now we can add the interest to the principal amount to get the total amount that Jennifer will owe to the bank on January 31st.
Total amount = Principal + Interest
Total amount = $2,500 + $958.75 = $3,458.75 (rounding to the nearest cent)
So, the total amount Jennifer will owe to the bank on January 31st is $3,458.75
I need help on this question please
Answer:
600 ml
Step-by-step explanation:
One of the rules of ratio includes sorting ratio in order according to the question. In this case, squash is mentioned first, then water. Hence, the ratio is:
squash:water = 1:6
Use cross multiplication:
1 : 6
100 : ?
Multiply 100 by 6 then divide it by 1: which basically means 100 * 6 = 600 ml.
If you are unfamiliar with cross multiplication, then simply find out how many times did you have to multiply the 1 in the squash ratio to result to 100, which is 100, then multiply 6 by that answer = 6 * 100.
Hope you understood :)
If tan x =
3
4
and cot y =
12
5
π
, where x and y lie in the interval of 0 to --
2
, find tan (x-y). [4]
The tangent of the subtraction of angles x and y is defined as follows:
tan(x - y) = (36 - 20π)/(48 + 15π)
How to obtain the tangent of the subtraction?The tangent of the subtraction of two angles is obtained according to the identity presented as follows:
tan(x - y) = [tan(x) - tan(y)]/[1 + tan(x)tan(y)]
The tangent of angle x is given as follows:
3/4.
The tangent and cotangent are defined as follows:
tan(x) = sin(x)/cos(x).cot(x) = cos(x)/sin(x) = 1/tan(x).Hence the tangent of angle y is obtained inverting the numerator and the denominator of the function, as follows:
tan(y) = 5π/12.
The subtraction of the two tangents is given as follows:
tan(x) - tan(y) = 3/4 - 5π/12 = 9/12 - 5π/12 = (9 - 5π)/12.
The quotient of the two tangents is given as follows:
tan(x)tan(y) = 3/4 x 5π/12 = 15π/48.
Then the denominator of the expression is given as follows:
1 + 15π/48 = (48 + 15π)/48.
Considering the division of the two fractions, the tangent of the subtraction is defined as follows:
tan(x - y) = (9 - 5π)/12 x 48/(48 + 15π)
tan(x - y) = (36 - 20π)/(48 + 15π)
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
Elimination
3x-y=-1 and -3x-y=5
The equation 3x - y = - 1; - 3x - y = 5 when solved using the elimination method is x = -1 and y = -2 respectively.
How to solve simultaneous equation using elimination method?3x - y = - 1
- 3x - y = 5
Subtract the equation to eliminate y
3x - (-3x) = - 1 - 5
3x + 3x = - 6
6x = - 6
divide both sides by 6
x = -6 / 6
x = -1
Substitute x = -1 into
3x - y = - 1
3(-1) - y = -1
-3 - y = - 1
- y = - 1 + 3
-y = 2
y = -2
Therefore, the solution to the simultaneous equation is (x, y) = (-1, -2)
Read more on elimination method:
https://brainly.com/question/25427192
#SPJ1
This graph shows the solutions to the inequalities y> x+2 and y< x-3.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
B
C
O There are no solutions.
OB. There are solutions, and they are the points in region C.
OC. There are solutions, and they are the points in region B.
OD. There are solutions, and they are the points in region A.
The system of inequalities y > x + 2 and y < x - 3. when solved will not have solutions
A. There are no solutionsWhen will system of linear equations not have a solution?When the graphs meet at a point, a system of linear equations has just one solution.
No solution, When the graphs are parallel, a system of linear equations cannot have a solution.
examining the system of linear equations y > x + 2 and y < x - 3, the slope of the two linear functions are equal with a value of 1.
Because of this, the equations will not intersect and the lines are said to be parallel and no solution expected
Learn more about linear equation at:
https://brainly.com/question/2030026
#SPJ1
A toy rocket is launched from the ground at an angle of 45° and an initial velocity of 100 feet
per second. How far does the rocket travel in the air before hitting the ground?
A. 170.7 ft
B. 213.4 ft
C. 312.4 ft
D.423.1 ft
[tex]\textit{Horizontal Range}\\\\ R=\cfrac{(v_0)^2\cdot \sin(2\theta )}{g} ~~ \begin{cases} v_o=\textit{initial velocity}\\ \theta =\textit{initial angle}\\ g=gravity\\[-0.5em] \hrulefill\\ v_o=100\\ \theta =45^o\\ g\approx 32~\frac{ft}{s^2} \end{cases}\implies R\approx\cfrac{(100)^2 \sin(2\cdot 45^o)}{32} \\\\\\ R\approx\cfrac{10000\sin(90^o)}{32}\implies R\approx\cfrac{10000(1)}{32}\implies R\approx 312.5~ft[/tex]
There are total 52 flowers name the multiples of 4 in this..
Answer: multiples of 4 are -4,8,12,16,20,24,28,32,36,40,44,48,52
Step-by-step explanation:
4x1=4
4x2=8
4x3=12
4x4=16
4x5=20
4x6=24
4x7=28
4x8=32
4x9=36
4x10=40
4x11=44
4x12=48
4x13=52
Answer:
208
Step-by-step explanation:
52×4=208
Paolo wrote the following equation for the perimeter of a rectangle.
uppercase P = 2 (l + w)
Which equation is equivalent to the equation Paolo wrote?
w = uppercase P minus 2 l
2 = uppercase P minus l
w = StartFraction uppercase P minus 2 l Over 2 EndFraction
w = StartFraction uppercase P + 2 l Over 2 EndFraction
The equivalent equation to Paolo's equation is,
w = Start Fraction uppercase P minus 2l Over 2 End Fraction.
What is algebraic operation?
A basic algebraic operation in mathematics is any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power).
Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.
Given:
uppercase P = 2 (l + w)
Simplifying this,
uppercase P = 2l + 2w
Subtract 2l from both sides,
uppercase P - 2l = 2l + 2w - 2l
uppercase P - 2l = 2w
Divide both sides by 2,
(uppercase P - 2l) / 2 = 2w / 2
(uppercase P - 2l) / 2 = w
Hence, the equivalent equation to Paolo's equation is,
w = Start Fraction uppercase P minus 2l Over 2 End Fraction.
To know more about algebraic operation, click on the link
https://brainly.com/question/29800389
#SPJ1
Elijah currently owes a total of $2,127.50 on his revolving credit accounts. What is Elijah's debt-to-credit ratio if the total of his revolving credit limits is $5,750.00? Round the final answer to the nearest whole percent.
a
27%
b
37%
c
41%
d
50%
Answer: Elijah's debt-to-credit ratio is 37%.
Step-by-step explanation:
Elijah's debt-to-credit ratio is the ratio of the amount of money he owes to the total amount of credit he has available.
To calculate the debt-to-credit ratio, we need to divide the amount of debt by the total amount of credit, and then multiply by 100 to get the answer in percentage.
Debt = $2,127.50
Credit = $5,750.00
Debt-to-credit ratio = (Debt / Credit) * 100
Debt-to-credit ratio = (2127.50 / 5750) * 100 = 37.29 ~ 37%
So the answer is: b) 37%
Percious bought one goldfish for $32 and one star fish for $12. She spends the rest of her money on guppies. She starts with $80 and each guppy costs$6. Write an inequality for the number of guppies she can purchase
Answer:
Let x be the number of guppies Percious can purchase.
We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.
We can use this information to write an inequality:
32 + 12 + 6x <= 80
This inequality represents the total cost of the goldfish, starfish, and guppies.
By solving this inequality we can find the number of guppies Percious can purchase.
To solve this inequality, we can first simplify it by combining like terms:
44 + 6x <= 80
Then we can subtract 44 from both sides:
6x <= 36
And finally, we divide both sides by 6:
x <= 6
So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.
x is less than or equal to 6.
Step-by-step explanation:
Let x be the number of guppies Percious can purchase.
We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.
We can use this information to write an inequality:
32 + 12 + 6x <= 80
This inequality represents the total cost of the goldfish, starfish, and guppies.
By solving this inequality we can find the number of guppies Percious can purchase.
To solve this inequality, we can first simplify it by combining like terms:
44 + 6x <= 80
Then we can subtract 44 from both sides:
6x <= 36
And finally, we divide both sides by 6:
x <= 6
So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.
x is less than or equal to 6.
Samantha received a $100 gift card to an online store. She wants to purchase some bracelets that cost $15 each. There will be a $25 overnight shipping fee. How many bracelets can she buy?
Your business requests a 3-month loan for
$550,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.8%?
inferest paid = $[?]
The total interest paid for the period of three months will be $600 on the loan amount of $550000.
What is interest?The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.
Here in the question given data is
P= $550000
R=2.0%+2.8%=4.8%
T=1/4 years or three months
So from the simple interest formula
SI = PRT / 100
= 550000 x 4.8 x 1/4 / 100
= 6600
Hence, the total interest paid for the period of three months will be $600 on the loan amount of $550000.
To know more about Simple interest follow
brainly.com/question/25793394
#SPJ1
I don't understand this, USE YOUR SKILLS AND HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
The required cost of the construction of a 4.5-inch tower is the amount of $114.75.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
The cost of construction is $25.50 per inch.
We have to determine the amount it costs to fund 4.5 inches of the construction.
As per the question, we have
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction would be:
= 25.50 × 4.5
Apply the multiplication operation, and we get
= $114.75.
Thus, the required cost of the construction is $114.75.
Learn more about Multiplication operations here:
brainly.com/question/25834626
#SPJ1
Set up a ratio. If the ratio cannot be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain three-figure accuracy.
Don, Bob, and Ron Maloney’s partnership interests in Maloney Bros. Contracting are in the ratio of their capital contributions of $78,000, $52,000, and $65,000, respectively.
What is the ratio of Bob's to Ron's to Don's partnership interest?
The ratio of Bob's to Ron's to Don's partnership interest is 26.6% : 33.3% : 40.0%.
What does partnership interest mean?A partnership interest is the percentage of a partnership that a specific member or individual owns. In this context, partnerships refer to a specific method of organizing business ownership in which each owner is a partner, with equal rights, privileges, and obligations to the company as a whole.
Data
Partnership interests in Maloney Bros:
Don - $78,000
Bob - $52,000
Ron Maloney’s - $65,000
The total capital contribution is:
= $78,000 + $52,000 + $65,000
= $195,000
Bob's partnership interest is:
= $52,000/$195,000
= 0.266 or 26.6%.
Ron's partnership interest is:
= $65,000/$195,000
= 0.333 or 33.3%.
Don's partnership interest is:
= $78,000/$195,000
= 0.400 or 40.0%.
Read more about partnership interest
brainly.com/question/14835194
#SPJ1
If a1=8 and an= an-1
Answer:
Step-by-step explanation:
242424
Check all that apply. – is the reference angle for:
3
MA. T
3
B.
] c.
☐ D.
15:
3
2;}
3
19:1
3
Answer:
A, C, D
Step-by-step explanation:
You want the angles in the list that have π/3 as the reference angle.
Reference angleThe reference angle is the smallest angle between the angle's terminal side and the x-axis. The cosine and sine of the reference angle have the same magnitude of the cosine and sine of the angle in question.
The attached table shows that 7π/3, 2π/3, and 19π/3 have the same reference angle: π/3.
If job growth in your state is projected to be 7 percent and you have 16,000,000 workers, how many new jobs would be created?
If job growth in your state is projected to be 7 percent and you have 16,000,000 workers, how many new jobs would be created?
Answer:
Step-by-step explanation:
The number of new jobs that would be created would be 1,120,000. This is calculated by multiplying the number of workers (16,000,000) by the projected job growth rate (7%) which equals 1,120,000.
Given the figure below, find the values of x and z.
92°
(10x + 32)°
Since Z and 92 both have vertical angles, they are equal. Subtract from 180 to determine the measure of the other angle, which is 88 degrees since it forms a straight line with the 92-degree angle. Solve the expression by setting the value at 88.
What is meant by vertical angle?The intersection of two straight lines produces a pair of vertical angles, which are not next to one another. Vertical angles that are across from one another form the corners of the "X" formed by two straight lines.The fact that they are located across from one another gives them the name "vertically opposite angles." Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees. For instance, if two lines cross and form an angle with a given value (X=45°), then the opposing angle also has a value of 45°. The angle measure of vertical angles is constant, making them congruent.∠AOB + ∠BOC = 180°
92°+( 10x + 32 )° = 180°
10x + 32° = 180 - 92
10x + 32° = 88
10x = 88 - 32
10x = 56
x = 56 ÷ 10
x = 5.6°
Hence, the value of X is 5.6 and Z is 92.
To learn more about vertical angle refer to:
https://brainly.com/question/1673457
#SPJ1
Please look at the picture and answer the question thank you
Value of the expression 10z + 5w is 40.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
For example, x + y is an expression, where x and y are terms having an addition operator in between.
Given expression
10z + 5w
z = 3
w = 2
Substituting value of z and w in the expression
10z + 5w = 10(3) + 5(2)
⇒ 10z + 5w = 30 + 10
⇒ 10z + 5w = 40
Hence, 40 is the value of the expression 10z + 5w.
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ1
Sonya bought 2 movie tickets for $17.00 Ralph bought 5 movie tickets for $42.50. based on this information which equation can be used to determine the total cost c, for a certain number of movie tickets, F
The equation that can be used to determine the total cost, given the number of movie tickets, is c = 8. 50 c
How to find the equation ?The equation that shows the total cost when you buy a certain number of tickets, can only be found after you solve for the ticket price.
The ticket price is :
= Cost of tickets / Number of tickets
= 42. 50 / 8
= $ 8. 50
The equation for the total cost would therefore be:
Total cost = Number of tickets x Cost per ticket
c = f x 8. 50
c = 8. 50 f
Find out more on total cost at https://brainly.com/question/29399491
#SPJ1
56,259 divided 57=i ?
Answer:
987
Step-by-step explanation:
57√56259= 987
Answer:
987
Step-by-step explanation:
56259 ÷ 57 = 987
Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 37 and the age of the winner for best actress was 52. For all best actors, the mean age is 45.2 years and the standard deviation is 8.3 years. For all best actresses, the mean age is 32.3 years and the standard deviation is 11.6 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
1.6982 is the actress age is more extreme when winning the award, the actor or the actress .
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Z score for actor = ( 37 - 45.2 )/8.3
= - 0.9879
Z score for actress = ( 52 - 32.3 )/11.6
= 1.6982
since I - 0.9879 l < l 1.6982 l , the actress age is more extreeme .
Learn more about Z-score
brainly.com/question/15016913
#SPJ1
find the average of the numbers 11, 20, 13, and 16
The average of the numbers 11, 20, 13, and 16 is 15
Why is average called mean?The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.
Why do we calculate the average?Finding an average helps us understand a general pattern of behavior or trend. For example, knowing Mrs. Mansell's average shopping expenditure helps us understand whether she typically spends a lot or little money, and knowing Keiran's average spelling score helps us understand how proficient he typically is.
In the above question:-
The average of the numbers 11, 20, 13, and 16 is
15
To learn more about average, click the following link:-
https://brainly.com/question/130657
#SPJ1
Harry drew the number line below to solve a word problem he drew8 numbers and 36
where’s the answer choices??? the picture?? did you finish the question??
Answer:
Step-by-step explanation:
A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 21° and that the angle of depression to the bottom of the
tower is 20°. How tall is the tower?
Round your answer to 2 decimal places as needed.
Answer:
We can use the tangent function to solve for the height of the tower. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
First, we'll find the opposite side (the height of the tower) using the angle of elevation:
tan(21°) = opposite / 300
opposite = 300 * tan(21°)
Then we'll find the opposite side (the depth of the base of the tower below the window) using the angle of depression:
tan(20°) = opposite / 300
opposite = 300 * tan(20°)
Now we can add the two opposite sides we found to get the total height of the tower
height = opposite(elevation) + opposite(depression)
height = 300 * tan(21°) + 300 * tan(20°)
The angle should be converted to radians before using the tangent function, and the final answer should be rounded to 2 decimal places.
Step-by-step explanation:
What proportion of the data points in a data set are expected to be within one standard deviation of the mean.
Answer:
Step-by-step explanation:
Approximately 68% of the data points in a dataset are expected to be within one standard deviation of the mean, assuming that the data follows a normal distribution. This is known as the Empirical Rule or the 68-95-99.7 rule. According to this rule, approximately 95% of the data points are expected to be within two standard deviations of the mean, and approximately 99.7% of the data points are expected to be within three standard deviations of the mean.
Please note that this rule applies only to a normal distribution, if the data is not normally distributed, the proportion may be different.
Answer:
Approximately 68% of the data points in a data set are expected to be within one standard deviation of the mean because of the 68-95-99.7 rule.
Step-by-step explanation:
This rule states that approximately 68% of the data points in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
37 hundredths= ____ tenths + ____ hundredths
Answer:
30 TENTHS + 7 HUNDREDTHS
Step-by-step explanation:
what is
4 divided by 4/5
Answer:
5
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36. Therefore, option A is the correct answer.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The standard form for finding the equation of a circle is expressed as;
(x-a)²+ (y-b)² =r²
Where; (a, b) is the center of the circle and r is the radius of the circle
Given that, diameter = 12 units
So, radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)² + (y-3)² = 6² equivalent to x²+ (y-3)² = 36
Therefore, option A is the correct answer.
To learn more about an equation of a circle visit:
https://brainly.com/question/23799314.
#SPJ1
