[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]
A two-variable inequality is shown in the graph. upward opening parabola which is solid with vertex at 1 comma 2, travels through points negative 1 comma 6 and 3 comma 6, with shading inside the curve Which point is not included in the solution set for the inequality?
The point among the answer choices which is not in the solution set of the inequality is; (-1, 3).
Which point is not included in the solution set of the inequality?It follows from the task content that the vertex of the two-variable inequality in discuss is; (1, 2).
On this note, it follows that; the two variable inequality described by a parabola opening upward can be written by means of its vertex as;
y >= (x - (1))² + 2
y >= (x-1)² + 2.
By testing points among the answer choices, the point which is not part of the solution set is; (-1,3).
This follows from the fact that; at x=-1;
The value of y is;
y >= (-1-1)² +2
y >= 6
Hence, since the value of y= 3 which is less than, 6, it follows that the point (-1,3) is not in the solution set.
Remarks: The answer choices in the complete question are as follows;
(–1, 3)
(0, 4)
(1, 5)
(2, 4)
Read more on solution set of inequalities;
https://brainly.com/question/12681658
#SPJ1
Carlos went to PetSmart to get his hamster an exercise ball. There was a small one with a 5 inch diameter and a 13 inch ball. How much more space (volume) is in the larger than the smaller? Round to the nearest tenth.
Answer:
150.8 in³
Step-by-step explanation:
The volume of the 5 inch ball is
[tex]\frac{4}{3}\pi (5/2)^{3}[/tex]
The volume of the 13 inch ball is
[tex]\frac{4}{3}\pi (13/2)^{3}[/tex]
Subtracting these volumes, we get about 150.8 in³.
The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³
What is the Volume of a Spherical Solid?To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³,
where r is the radius of the sphere, which is half the measure of the diameter.
Diameter of the smaller spherical ball = 5 inches
Radius = 5/2 = 2.5 inches
Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³
Volume ≈ 65.5 in.³
Diameter of the larger spherical ball = 13 inches
Radius = 13/2 = 6.5 inches
Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³
Volume of the larger spherical ball ≈ 1,150.3 in.³
The amount of space (volume) that is in the larger spherical ball than the smaller.
= 1,150.3 - 65.5
The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³
Learn more about the volume of sphere on:
brainly.com/question/22807400
#SPJ2
How to find exponential function?
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\bold{y=Ce^{kt}}[/tex][tex]\bold{(5,5)}[/tex][tex]\bold{(0, \dfrac{6}{7} )}[/tex][tex]\small\leadsto\bold{Substitute:}[/tex]
[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]
[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]
[tex]\longrightarrow\sf{e^0=1}[/tex]
[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]
[tex]\therefore\sf{5=Ce^{k*5}}[/tex]
[tex]\\[/tex]
[tex] \bold{Solve \: to \: find \: k:}[/tex]
[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]
[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]
[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]
[tex]\longrightarrow\sf{1.76=5k}[/tex]
[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]
The numbers 1, 2, 3, 4,5, 6, 7, 8, 9 are arranged in a list so that each number is either greater than all the numbers that come before it or is less than all the numbers that come before it. For example, 4, 5, 6, 3, 2, 7, 1, 8, 9 is one such list: Notice that (for instance) the 6 is greater than all the numbers that come before it, and the 2 is less than all the numbers that come before it. How many such lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are possible?
The lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 that are possible is; 256
How to Solve Probability Combinations?
We are told that the last digit has to be either a one (1) or nine (9), then are two (2) options (>,<) for the remaining eight digits, so there are 2⁸ = 256 arraignments where each digit is either greater than or less than the preceding digits. This can be confirmed as below;
Numbers beginning with 1 = 8C0 = 1
Numbers beginning with 2 = 8C1 = 8
Numbers beginning with 3 = 8C2 = 28
Numbers beginning with 4 = 8C3 = 56
Numbers beginning with 5 = 8C4 = 70
Numbers beginning with 6 = 8C5 = 56
Numbers beginning with 7 = 8C6 = 28
Numbers beginning with 8 = 8C7 = 8
Numbers beginning with 9 = 8C8 = 1
Total lists of numbers possible = 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 256
Read more about Probability Combinations at; https://brainly.com/question/25688842
#SPJ1
What shape best describes the cross-section cut perpendicular to the base of a right rectangular prism? O Parallelogram Trapezoid O Rectangle O Rhombus
The cross-section perpendicular to the base of a right rectangular prism is a rectangle.
What is a three dimensional shape?A shape or a solid that has three dimensions that is length, width and height is called a 3D shape. 3D shapes have faces, edges, and vertices. Examples are cylinder, cone, prism, pyramid.
A shape that has two dimensions is called a 2D shape. 2D shapes have breadth and length.
The cross-section perpendicular to the base of a right rectangular prism is a rectangle.
Find out more on three dimensional shape at: https://brainly.com/question/326906
#SPJ1
How many pairs of two digit natural numbers have a difference equal to 50
The number exists 99, then 99 - 49 = 50
Therefore, the pair of two-digit numbers exist between 99 and 49.
What is the difference?In math, the word difference exists as the outcome of subtracting one number from another.
Let the first pair of two-digit numbers be xy and the second pair of numbers be yx.
we want a two-digit number, a two-digit number begins from 10 and ends with a two-digit number that exists 99.
Let the difference of 50 exists possible when we take the biggest two-digit number
Therefore, the number exists 99
99 - 49 = 50
Therefore, the pair of two-digit number exists 99 and 49.
To learn more about differences refer to:
https://brainly.com/question/14335054
#SPJ9
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
What is the height of the building?
Given the data in the question;
Angle of elevation θ = 35°Distance between the person and the building | Adjacent = 80ftHeight of the person h = 4ft.Height of the building from the eye level | opposite = xSince the scenario depicts a right angle triangle, we use trigonometric ratio.
tanθ = Opposite / Adjacent
We height of the building from the eye level x
Substitute given into the equation,
tan( 35 ) = x / 80ft
x = tan( 35 ) × 80ft
x = 0.7002075 × 80ft
x = 56ft
Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.
Height of building = x + 4ft
Height of building = 56ft + 4ft
Height of building = 60ft
Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
Learn more about trigonometric ratio here: brainly.com/question/28016662
#SPJ1
Tell if each pairs of segments are congruent
Yes/No
A. AB and BC
B. AC and BD
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
Calculating length of a segmentFrom the question, we are to determine if the given pairs of segments are congruent
To do this, we will determine the length of the line segments
Consider the given number line,
AB = -2 - (-5) = -2 + 5 = 3
BC = 0 - (-2) = 0 + 2 = 2
AC = 0 - (-5) = 0 + 5 = 5
BD = 5 - (-2) = 5 + 2 = 7
Now,
A. AB and BC
AB = 3 and BC =2
∴ AB and BC are not congruent.
Thus, No
A. AC and BD
AC = 5 and BD = 7
∴ AC and BD are not congruent.
Thus, No
Hence,
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
Learn more on Calculating length of segments here: https://brainly.com/question/4806140
#SPJ1
Use the order of operations to evaluate (PEMDAS): -9 + 8 + (-2 x 6)
Answer:
-13
Step-by-step explanation:
-2x6 = -12
-9+8= -1
-1+-12=-13
Hope this helps
cual es el valor x-2=1
Write expressions for the length and width of a rectangle that has an area equal to 3x2-5x+2.
Answer:
x - 2, x - 3
Step-by-step explanation:
3x² - 5x + 2
x² - 5x + 6
(x - 3)(x - 2)
length = x - 2
width = x - 3
50% is what percent of 40%?
Answer:
125%Step-by-step explanation:
[tex] \frac{50}{100} \times 40[/tex][tex] = 125\%[/tex]Find the dy/dx using implicit differentiation
x³-3x²y+2xy² = 12
The dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].
We are required to find dy/dx of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.
Differentiation is basically finding the change in variables.
It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.
Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]
Differentiating with respect to x.
3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0
3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0
Taking dy/dx at one side and take the other part to other end.
[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]
dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]
Hence the dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
Learn more about differentiation at https://brainly.com/question/954654
#SPJ1
8 ft
10 ft
20 ft
A trapezoid has a height of 10 feet,
and base measurements of 20 feet and
8 feet. What is the area?
[?] square feet
Hint: The formula for the area of a trapezoid is: (b₁b2). h
Enter
ग
15
The area of the trapezoid is 140 square feet
What are areas?The area of a shape is the amount of space on that shape
How to determine the area of the trapezoid?The dimensions of the trapezoid are given as:
Height = 10 feet
Parallel bases = 8 feet and 20 feet
The area of a trapezoid is calculated using
Area = 0.5 * (Sum of parallel bases) * Height
Substitute the known values in the above equation
Area = 0.5 * (8 + 20) * 10
Evaluate the equation
Area = 140
Hence, the area of the trapezoid is 140 square feet
Read more about areas at:
https://brainly.com/question/24487155
#SPJ1
Which is the best approximation of the solutions to the system of equations graphed below?
According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
What is the solution of a nonlinear system formed by two quadratic equations?
Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.
According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
To learn more on quadratic equations: https://brainly.com/question/17177510
#SPJ1
Evaluate the following expression at x = 3 and y = -4. 7x - 3y + 2.
provide your answer below:
Answer:
35
Step-by-step explanation:
first, you look at 7x, from the previous equation, you know that x=3, so you take 7x3=21 then you evaluate -3y. as you did with x on the last one you will look at the equation for y and see that it's -4. A negative times a negative is a positive, so -4x(-3)= 12. Then you add them all together, since 12 is a positive, the equation would now look like 21+12+2. After adding all three numbers together, you get 12.
an employee at a factory is paid $9.25 per hour plus a $8.00 bonus for every 20 transformers assemble.
Answer:
Step-by-step explanation
Answer:
$13.47 per hour
Step-by-step explanation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
What does ! mean in a math problem?
Divide each number in sequence from that number to 1.
Add each number in sequence from that number to 1.
Multiply each number in sequence from that number to 1.
Subtract each number in sequence from that number to 1.
It is an exciting problem.
! is shorthand for the factorial function. If [tex]n[/tex] is a non-negative integer, then
[tex]n! = n\times(n-1)\times(n-2)\times\cdots3\times2\times1[/tex]
with [tex]0! = 1[/tex].
So how to compute [tex]n![/tex] ?
Multiply each number in sequence from that number to 1.
Which is a factor of 144 - 49x²?
O 12-7x²
O 72-7x²
O 12-7x
O 72 + 7x
Answer: C: 12-7x
Step-by-step explanation:
This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.
Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].
Let's factor our expression.
[tex]144-49x^2=(12+7x)(12-7x)[/tex]
Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.
Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
A large high school has 3,000 students.
During a one-week period, 75 students were
selected at random various times of the day.
Each student was asked if he or she had one
or more social media accounts. The survey
found that 3 out of 75 students did not have
any social media accounts. Estimate the
number of students in the entire school who
do not have social media accounts.
Answer:
120 students don't have social media accounts
Step-by-step explanation:
Whether the sample is representative:
Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]
Hope this helps
what is 11- 2 to the 3rd power
Answer:
See below
Step-by-step explanation:
Question is unclear
could be (11-2)^3 = 9^3 = 729
could be 11 - 2^3 = 11 - 8 = 3 Pick the one you want !
Asap help with this PLEASE
Answer:
124.5°
Step-by-step explanation:
Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.
Using the sum of an arithmetic series formula,
[tex]\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5[/tex]
So, the third angle is 110.5+14=124.5
(3x) (4x) =
A. – x
B. 7x
C. 12x
D. 12x²
E. none of these
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textbf{Equation: }[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textbf{Solving:}[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textsf{= 3x} * \large\textsf{4x}[/tex]
[tex]\large\textbf{Combine the like terms:}[/tex]
[tex]\large\textsf{(3x * 4x)}[/tex]
[tex]\large\textsf{= 3x * 4x}[/tex]
[tex]\large\textsf{= 12x}^2[/tex]
[tex]\large\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
pls help a gurlll out
Answer:
x = 15°
Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:
165 + x = 180
x = 180 - 165
x = 15
Let r(x)=x^2 - x + 14. Find all values of a such that r(a) = 20.
Answer:
a=–2, 3
Step-by-step explanation:
r(a)=20
a²–a+14=20===> a²–a–6=0===> (a–3)(a+2)
Suppose the reserve requirement is changed to 4 percent. Reconstruct the balance sheet of the total banking system after all banks have fully utilized their lending capacity.
c. By how much has the money supply changed as a result of the lower reserve requirement (part b)?
$
billion
The total amount in the transaction account is
= $625.
The amount in the transaction account is
=75
What is a transaction account?
Your salary and any other payments that you get may be deposited into an account known as a transaction account, which is an account that you utilize on a day-to-day basis. When connected to a Visa card, your transaction account may also be used to pay bills, go shopping, and make other types of payments that are commonplace. Balances in transaction accounts do not accrue any interest for the account holder.
b) Now if the reserve requirement changes to 5%, we need to reconstruct the balance sheet of the total banking system.
Calculate the initial total reserve using the new reserve requirement as follows:
= 4% x500
= 0.04×500
=20
Calculate the excess reserve as follows:
=30-20
= $10
Calculate the money multiplier as follows:
=1/4%
=1/0.04
=25
Calculate the increase in transaction account as follows:
=25x $5
= $125
Hence, the total amount in the transaction account is
$500+ $125
= $625.
c)
Therefore, the amount in the transaction account is
=600-525
=75
Read more about the transaction account
https://brainly.com/question/14643061
#SPJ1
Lets find the digit in blank space of thr following numbers so hat the number formed is divisible by 11.
a.27.......3
17, 18, 22, 31, 47, ? Continue the pattern
Answer:
17 +1^2=18
18+2^2=22
22+3^2=31
31+4^2=47
47+5^2=72
72+6^2=108
Step-by-step explanation:
If my goal was to be above 85% I my final number was 80 what was my percentage for the month?
Using it's concept, your percentage for the month was of 94.12%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
P = a/b x 100%
In this problem, your goal was of 85, with a grade of 80, hence the percentage is:
P = 80/85 x 100% = 94.12%.
Hence, your percentage for the month was of 94.12%.
More can be learned about percentages at https://brainly.com/question/10491646
#SPJ1
