The equation of the asymptote of the hyperbola is y = 3x + 10
How to determine the asymptote?From the complete question the asymptote passes through the points:
(x,y) = (-1, 7) and (-3,1)
The slope of the line is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{7 - 1}{-1 + 3}[/tex]
This gives
m = 3
The equation is then calculated using:
y = m(x -x1) + y1
This gives
y = 3(x + 1) + 7
Evaluate
y = 3x + 3 + 7
y = 3x + 10
Hence, the equation of the asymptote is y = 3x + 10
Read more about asymptotes at:
https://brainly.com/question/4138300
#SPJ4
Can someone answer this problem??
Answer: The answer is 9
Answer:
9% of her monthly income is spent on 'Other expenses'
Step-by-step explanation:
[tex]900+120+80+100+320=1820[/tex]
but if you divide 180 by 2000 you'll get 0.09 but times that by 100 you'll get 9%
In ⊙P, QR≅ST. Which statement must be true? Select all that apply.
A circle with center point P and four points Q,R,S,T on the circumference. Line segments join the points to make three chords QR,RS and ST. All the four points are connected to center point P making three triangles QPR,RPS and SPT.
A. △QRP ≅ △STP
B. QR¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
C. ∠QPS ≅ ∠RPT
D. △RPS ≅ △SPT
E. QR¯¯¯¯¯¯¯¯ ≅ ST¯¯¯¯¯¯¯Which is the length of PQ expressed in terms of π?
A circle with center point N and radius 1. It has a minor arc PQ whose angle measures 99 degree
A. 1140π
B. 2940π
C. 1120π
D. 2920π
The true statement about the circle with center P is that triangles QRP and STP are congruent, and the length of the minor arc is 11/20π
The circle with center PGiven that the circle has a center P
It means that lengths PQ, PR, PS and PT
From the question, we understand that QR = ST.
This implies that triangles QRP and STP are congruent.
i.e. △QRP ≅ △STP is true
The length of the minor arcThe given parameters are:
Angle, Ф = 99
Radius, r = 1
The length of the arc is:
L = Ф/360 * 2πr
So, we have:
L = 99/360 * 2π * 1
Evaluate
L = 198/360π
Divide
L = 11/20π
Hence, the length of the minor arc is 11/20π
Read more about circle and arcs at:
https://brainly.com/question/3652658
#SPJ1
What is the valuAt which integer value of x are the functions y = 1 2 x + 12 and y = ( 1 4 ) x closest to being equal? A. –2 B. 12 C. 11 D. –1e of x in this triangle? 18493 A. 30 B. 45 C. 90 D. 60
The closest integer value of x where both functions are equal is 1
How to determine the integer value of x?The equations are given as:
y = 12x + 12
y = (14)^x
Next, we plot the graph of both equations.
From the attached graph, both functions intersect at:
x = 1.249
Approximate this value
x = 1
Hence, the closest integer value of x where both functions are equal is 1
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
12250 depreciates by 6% per year how much is the tractor worth after six years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &12250\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=12250(1 - 0.06)^{6}\implies A=12250(0.94)^6\implies A\approx 8450.90[/tex]
At devon's new job he spent $12.99, $10.50, $9.89, $6.90, and $7.58 on lunch the first week.
in the second week, he spent $2 more in total for the 5 lunches than the first week.
what is the increase in the mean for the second week compared to the first?
round the answer to the nearest penny.
A mean is an arithmetic average of a set of observations. The increase in the mean for the second week compared to the first is 0.4.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
Given the spending in the first week is $12.99, $10.50, $9.89, $6.90, and $7.58, therefore, the mean will be,
[tex]\rm (Mean)_1 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 }{5} = \$9.57[/tex]
Also, the spending in the second week is $2 more than the total of the first week, therefore, the mean will be
[tex]\rm (Mean)_2 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 + \$2}{5} = \$9.97[/tex]
Hence, the increase in the mean for the second week compared to the first is 0.4.
Learn more about Mean:
https://brainly.com/question/16967035
#SPJ1
I really need help with this. This is for AP Calculus. I just need to find the derivative for this function.
Answer: 40x^4 + 56x^3 − 16x − 14
Step-by-step explanation:
1. For any two functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
2. The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0.
3. Simplify
4. Multiply 4x^2 + 7x^1 times 6x^2
5. Multiply 2x^3 - 2 times 8x^1 + 7x^0
6. To multiply powers of the same base, add their exponents.
7. Simplify
8. Combine like terms
9. For any term t, t^1 = t
10. For any term t except 0, t^0 = 1
How Do You Graph This Equation
Answer:
Rearrange both inequalities to make y the subject.
Momentarily swap the inequality sign for an equals sign in order to calculate two points for each line.
Inequality 1
[tex]2y \leq x-10[/tex]
[tex]\implies y < \dfrac{1}{2}x-5[/tex]
[tex]x=0\implies y=\dfrac{1}{2}(0)-5 \implies (0,-5)[/tex]
[tex]x=4 \implies y=\dfrac{1}{2}(4)-5 \implies (4,-3)[/tex]
Inequality 2
[tex]x+y\leq -3[/tex]
[tex]\implies y\leq -x-3[/tex]
[tex]x=0\implies y=-(0)-3\implies (0,-3)[/tex]
[tex]x=4\implies y=-(4)-3\implies (4,-7)[/tex]
When graphing inequalities
< or > : dashed line
≤ or ≥ : solid line
< or ≤ : shade below the line
> or ≥ : shade above the line
Therefore,
Inequality 1: plot points (0, -5) and (4, -3) and draw a solid line through them.
Inequality 2: plot points (0, -3) and (4, -7) and draw a solid line through them.
Shade the area below both lines from where the lines intersect.
Answer:
See below ~
Step-by-step explanation:
Inequality 1 :
Convert into y = mx + b form2y ≤ x - 10y ≤ x/2 - 5Taking 2 points :
0 ≤ x/2 - 5x/2 ≥ 5x ≥ 10⇒ Point 1 = (10, 0)y ≤ 0 - 5y ≤ -5⇒ Point 2 = (0, -5)Inequality 2 :
x + y ≤ -3y ≤ -x - 3Taking 2 points :
0 ≤ -x - 3x ≤ -3Point 1 = (-3, 0)y ≤ 0 - 3y ≤ - 3Point 2 = (0, -3)Plot the two 2 lines using the 2 points and shade as per the sign of the inequality. The result will be this graph :
HELP ASAP PLS
a survey asked two age groups about the car color that they most preferred. the results are down in the table below. which car color eat most preferred by people ages 16-24 and what is the relative frequency within this age group?
A.) Blue, 71.4%
B.)Red, 60.6%
C.)Blue, 26.8%
D.)33.9%
Answer:
blue i think good luck
What is the length of DE?
A. 5
B. 7
C. 6
D. 8
Answer:
the answer is 5. I think because it's a trian
A. 5 I think.....the length of DE is 5.
Mac has 40 ounces of juice. He pours 6 ounces in each glass. How many glasses can he fill?
Answer:
6
Step-by-step explanation:
The vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). what is the maximum value of the objective function p if p = 180x 250y? 2,940 3,020 3,080 3,250
The maximum value of the objective function p if p = 180x + 250y is 3020
How to determine the maximum value?The coordinates of the feasible region are given as;
(14, 2), (0, 9), (6, 8), and (10, 3)
The objective function is given as:
P = 180x + 250y
Substitute the coordinates of the feasible region in the above function
P = 180 * 14 + 250 * 2 =3020
P = 180 * 0 + 250 * 9 = 2250
P = 180 * 6 + 250 * 8 = 3080
P = 180 * 10 + 250 * 3 = 2550
The maximum value in the above computation is:
P = 180 * 14 + 250 * 2 =3020
Hence, the maximum value of the objective function p if p = 180x + 250y is 3020
Read more about objective functions at:
https://brainly.com/question/16826001
#SPJ4
Linear Programming Quiz - Edge
Question 1: D
Question 2: D
Question 3: D
Question 4: B
Question 5: C
Question 6: C
Question 7: D
Question 8: A
Question 9: C
Question 10: C
It says I can't add anymore attachments but the rest are correct trust me
A rectangle sticker had a perimeter of 32 centimeters and a area of 48 square centimeters. what are the dimensions of the sticker
Answer:
4 cm ×12 cm
Step-by-step explanation:
To find the dimensions of the sticker, start by forming 2 equations for its area and perimeter.
Perimeter of rectangle= 2(length +breadth)
Let the length and breadth of the rectangle be L and B cm respectively.
2(L +B)= 32
Divide both sides by 2:
L +B= 16 -----(1)
Area of rectangle= length ×breadth
LB= 48 -----(2)
From (1): L= 16 -B -----(3)
Substitute (3) into (2):
(16 -B)(B)= 48
Expand:
16B -B²= 48
B² -16B +48= 0
(B -4)(B -12)= 0
B -4= 0 or B -12= 0
B= 4 or B= 12
Substitute into (3):
L= 16 -4 or L= 16 -12
L= 12 or L= 4
Thus, the dimensions of the sticker is 4 cm ×12 cm.
How many different trains can you make of length three?
Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
The order in which the parts are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
#SPJ1
Factorize algebraic expressions by pulling out highest commom factor.
10x - 15y
Answer:
5(2x-3y)
Step-by-step explanation:
10x-15y
=(5)(2x)-(5)(3y)
=5(2x-3y)
A linear regression is done on data the line of best fit is y= 1.25x-6.25. What is the residual for the point (1,1)?
Answer:
6
Step-by-step explanation:
Find the predicted y value when x=1:
[tex]\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5[/tex]
Find the residual:
[tex]\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6[/tex]
Because our residual is positive, this is an indicator that our predicted y value is too low.
Practice solving problems involving the area Assignment Which are true about the area of a circle? Check all that apply. The diameter is used in the formula. The units are always squared. The area can be found when given the diameter by first finding the radius. The area is the distance around the circle. Circumference can be used to find area.
whats the probability of Rolling an even number on a dice, then flipping a coin to get a tails
Answer:the probabilities of getting a head and a tail are equal to 12 . The probability of getting an even number on a die is 36=12
Step-by-step explanation:because among 6 results there are 3 even numbers.
Does anybody know this? I don't have much time and Also it is not the forth option. What is the approximate surface area of the cylinder shown?
Answer:
C) [tex]628\:\text{cm}^2[/tex]
Step-by-step explanation:
[tex]SA=2\pi rh+2\pi r^2\\\\SA=2\pi(\frac{10}{2})(15)+2\pi(\frac{10}{2})^2\\ \\SA=150\pi+50\pi\\\\SA=200\pi\:\text{cm}^2\approx628\:\text{cm}^2[/tex]
is 0.4285714285714 a rational number
Answer:
No it is not a rational number
Step-by-step explanation:
A rational number is a number that can be written in the form
p
q
, where
p
and
q
are integers and
q
≠
o
.
All fractions, both positive and negative, are rational numbers. A few examples are
4
5
,
−
7
8
,
13
4
,
and
−
20
3
Which equation gives the line shown on the graph?
y
y = 22 +4
10
9
8
y = 224
7
6
三一z-4
5
u
3
y= 22 + 4
N
1
O
0 1 2 3 4 5 6 7 8 9 10
Done >
Answer:
6
Step-by-step explanation:
line graph start at 5 equations
A graph shows the horizontal axis numbered 4 to 16 and the vertical axis numbered 4 to 12. points and a line show an upward trend. which is most likely the correlation coefficient for the set of data shown? –0.872 –0.191 0.191 0.872
Answer:
Its 0.191
Step-by-step explanation:
Answer:
c) 0.191
Step-by-step explanation:
Find the prime factorization of 1296
METHOD WAY!
Answer:
[tex]1296 = 6 \times 6 \times 6 \times 6 = {6}^{4} = {2}^{4} \times {3}^{4} [/tex]
I need help on this please
Answer:
9.45 ounces
Step-by-step explanation:
The formal definition of the standard deviation of a population is that it is the square root of the mean of the squares of the differences between the data values and their mean.
The calculation can be done more simply as the root of the difference between the mean of the squares and the square of the mean. That is the calculation shown in the attachment.
The population standard deviation is about 9.45 ounces.
_____
Additional comment
The easier way to do the calculation is to use the calculator or spreadsheet function that gives the result directly. For the Desmos calculator shown, that function is stdevp(w) for the definition of w that we used. The function has the same name in many spreadsheet programs.
Can you create a data set which contains median=6 and mode=4?
1, 4, 6, 9, 15, 4, 3, 12, 11
Answer:
hey!
Step-by-step explanation:
Please help don’t understand radical
Simplified
[tex]x\sqrt[3]{x}[/tex]
The relationship between the number of pounds (lb) of almonds and the price in dollars is shown in the graph. What is the unit price of almonds?
Answer:
B
Step-by-step explanation:
Slope is change of y over change of x
Y is going up by 8 and x is going over by 1
Therefore, $8/1 lb
please give answer asap i’ll give brainlist to correct answer
Answer:
I believe the answer is; The median is 4.5 inches.
let me know if this is right for you! :)
Step-by-step explanation:
In a bag, there are oranges and bananas. If we give away 135 bananas, the percentage of fruits in the bag that are bananas will decrease from 60% to 15%. How many oranges are there in the bag
The number of oranges that are in the bag is 120.
How many oranges are in the bag?The equation that represents the initial amount of bananas in the bag is: bananas / total number of fruits = 0.60
bananas = 0.60t equation 1
The equation that represents the number of bananas in the bag after 135 was removed is:
(b - 135) / t = 0.15
b - 135 = 0.15t equation 2
Where :
b - total number of bananas t = total number of fruitsSubstitute for b in equation 2 using equation 1
0.6t - 135 = 0.15t
0.6t - 0.15t = 135
t = 135 / (0.6 - 0.15)
t = 300
The initial number of bananas : 0.6 x 300 = 180
Number of oranges = 300 - 180 = 120
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ1
If segment A is perpendicular to segment B, then they intersect at a 90° angle.
Choose the equivalent statement.
A. If segment B is not perpendicular to segment A, then they
intersect at a 90° angle.
B. If segment A is perpendicular to segment B, then they do not
intersect at a 90° angle.
C. If segments A and B do not intersect at a 90° angle, then they are
not perpendicular to each other.
The average speed of a car on the highway is 65 miles per hour? How many feet per
second is this?
Answer:
95.3333 ft/s
Step-by-step explanation: