Answer:
y = 4x + 3
Step-by-step explanation:
as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:
to calculate for the y intercept, it is best to express the equation in slope intercept form:
y = mx + b
in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).
y = 4x + b
what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.
Using this information, we can replace x and y in the equation:
-5 = 4(-2) + b
with consideration to the order of operations, it is important to solve the brackets first
-5 = -8 + b
now to get b by itself add 8 to both sides of the equation:
-5 + 8 = -8 + 8 + b
3 = b
now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.
y = 4x + b
replace b with the number we solved for (3).
y = 4x + 3
this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)
hope this helps :)
Select the correct answer. what is this series written in sigma notation? 2.5 2.5(1.2) 2.5(1.2)2 ⋯ 2.5(1.2)87 a. ∑ k = 1 87 2.5 ( 1.2 ) k b. ∑ k = 1 87 2.5 ( 1.2 ) k − 1 c. ∑ k = 1 88 2.5 ( 1.2 ) k d.
∑ k = 1 88 2.5 ( 1.2 ) k is this series written in sigma notation.
What is the series written in sigma notation?
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .Given:
2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87
If we look at the power it is always one less the term i.e., for first term the value of k=0.
So, the series in the form of summation can be written as
∑ k = 1 88 2.5 ( 1.2 ) k
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Select the graph of the solution. Click until the correct graph appears.
| x | + 1 > 2
Answer: Third Graph
Step-by-step explanation:
Given inequality
|x| + 1 > 2
Subtract 1 on both sides
|x| + 1 - 1 > 2 - 1
|x| > 1
Simplify the absolute value sign
x > 1 or x < -1
Apply the inequality to the graph
Since it is less than or greater than, the circle should be hollow
Since it is less than -1 or greater than 1, one line should point to the left and another should point to the right
Therefore, it should be the Third Graph
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails?
Answer:
give it a try
Step-by-step explanation:
Okay. I'm gonna flip five coins, but I'm told the first coin is Tell there's no choice there at all. It is certain the first coin shows a tail and then I want to have four heads in a row. Okay, so one for tell which means certain getting ahead is a half chance. Again a half chance again a half and again a half So that you work out and it's 1/16. That's the answer. There's no choice about the foreheads. It just has to be head every time I said.
Can someone please help me with this, i’m a little stuck
Answer: 420 minutes in 7 hours. 2 minutes in 120 seconds.
Step-by-step explanation: Multiply 7x60, as there are 60 minutes per hour. Divide 120/60 to find how many minutes are within those many seconds.
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.57
Step-by-step explanation:
The mean absolute deviation is the mean of the absolute values of the differences from the mean.
ApplicationThe mean of the dataset is the sum of values, divided by their number:
mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18
The absolute values of the differences from 18 will have an average of ...
mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7
mad(data) ≈ 2.57
__
Additional comment
Some calculators have the mad( ) function built-in. See the second attachment, for example.
What is the domain of the function in the graph?
A. 4≤y≤6
B. 20≤y≤70
C. 4≤x≤6
D. 20≤x≤70
Answer:
C. 4≤x≤6
Step-by-step explanation:
First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.
Hope that helps! Have a fantastic day!
A(n) Blank______ is a two-dimensional representation of data in which values are represented by colors. Multiple choice question. disintermediation long tail heat map interactivity
Answer:
heat map is the answer
marcel plugged in his work tablet and phone. the phone had a battery charge of 13% and started increasing by 2 percentage points every 3 minutes. the tablet had charge of 25% and started increasing by 1 percentage point every 3 minutes.
Let t represent the time, in minutes, since Marcel plugged in the phone and tablet.
Complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet
Answer:
t ≥ 36
Step-by-step explanation:
took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.
The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.
We know that t is the time, in minutes, since Marcel plugged in the phone and the tablet.
For phone:-
Initial battery charge = 13%.
Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.
Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.
For tablet:-
Initial battery charge = 25%.
Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.
Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.
We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.
Since the phone is required to have at least as much battery charge as the tablet, we can show this as:
The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,
or, 13% + t(2/3)% ≥ 25% + t(1/3)%,
or, t(2/3)% - t(1/3)% ≥ 25% - 13%,
or, t(1/3)% ≥ 12%,
or, t ≥ 12%/(1/3)%,
or, t ≥ 36.
Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.
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Eduro solved -4x > 120 by adding 4 to each side lf the inequality what mistake did he make?
Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
Inequalityminus four x greater than 120
-4x > 120
divide both sides by -4x < 120/-4
There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4
x < -30
Check:
-4x > 120
-4(-30) > 120
120 > 120
Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
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Find the area of the surface. the part of the plane 3x 5y z = 15 that lies in the first octant
The area is 97.211 sq units.
This part of the plane is a triangle. We can Call it δ. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that y=z=0 means 3x=15 i.e., x=3 , so that (3, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 15) are the other two vertices.
Next, we can parameterize the surface by
s(u,v)=[tex]\int\limits^a_b {3(1-u)(1-v),5u(1-v),15v} \, dx[/tex]
so surface element is
dS= IIsu*svII =15[tex]\sqrt{42}[/tex](1-v)dudv
Then the area of is given by the surface integral
[tex]\int\limits^a_b {} \, \int\limits^a_b {dS} \, dx = 15\sqrt[n]{42} \int\limits^a_b {x} \, dx \int\limits^a_b {1-v} \, dudv[/tex]=97.211
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The midpoint of EF is (-6, 1). One endpoint is E(-9, 7). Find the coordinates of endpoint F.
Answer:
Step-by-step explanation:
here is an solution :
Answer:
Its (-3,-5)
Step-by-step explanation:
Hope This Helps:))
If takes 3/4 hour to paint 12by 12 room how long does it take to paint 15by 16 room
This table gives a few ( x , y ) (x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. x xx y yy − 72 −72minus, 72 25 2525 − 54 −54minus, 54 13 1313 − 36 −36minus, 36 1 11 What is the y yy-intercept of the line?
The y-intercept of the line is (0,7).
Given the pairs of a line in the coordinate plane are (x, y) (-72,25), (-54,13) and (-36,11).
First we will find the slope of the linear equation
The formula for calculating the slope between two points is equal to
m = (y₂-y₁) / (x₂-x₁)
take points (-54,13) and (-36.,11)
by substituting the values in the above formula, we get
m = (11-13) / (- 36 - (- 54))
m = -2 / 18
m = -1 / 9
Now, we will find the equation for the line in point-slope form
y-y₁ = m (x-x₁)
we have m = -1 / 9 and (x₁, y₁) = (- 36.11)
Further, substitute the values in the above equation, we get
y-11 = (- 1/9) (x + 36) ..... (1)
Convert the equation to the form of a slope intercept
y = mx + b
isolate the variable y in equation (1), we get
y-11 = (- x / 9) -4
y = (- x / 9) - 4 + 11
y = (- x / 9) +7
Here, b=7
Hence, the y-intercept of the line for the pairs of lines in the coordinate plane(x,y) is (-72,25), (-54,13) and (-36,11) is the point (0,7).
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1 y = 3x - 4
2 x + y = 8
use the method of substitution
Answer:
x = 2.4; y = 3.2
Step-by-step explanation:
y = 3x - 4
2x + y = 8
2x + 3x - 4 = 8
5x - 4 = 8
5x = 12
x = 12 / 5
x = 2.4
y = 3(2.4) - 4
y = 7.2 - 4
y = 3.2
The population of a certain city can be modeled by the exponential * 1 poi
function below, where x represents the number of years since 2010. The graph for the function is also shown below. Which of the following statements are true? SELECT ALL THAT APPLY. I need help now please
The true statements about the functions are:
b. The population of the city in 2010 is 25000c. The rate at which the population decreases every year is 4% f. The function value would approach 0 as it decreasesHow to determine the true statement?The function is given as:
f(x) = 25000 * 0.96^x
Set x = 0 to determine the initial value of the function
f(0) = 25000 * 0.96^0
Evaluate
f(0) = 25000
This means that the population of the city in 2010 is 25000 i.e. option (B) is correct
Also, we have:
f(x) = 25000 * 0.96^x
The rate at which the population decreases every year is calculated as:
r = 1 - 0.96
Evaluate the difference
r = 0.04
Express as percentage
r = 4%
This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct
The population after 5 and 10 years are:
f(5) = 25000 * 0.96^5
f(5) = 20384
f(10) = 25000 * 0.96^10
f(10) = 16621
Divide these populations by the initial population in 2010
20384/25000 = 82%
16621/25000 = 66%
This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.
So, options (d) and (e) are false
Lastly, because the population function is an exponential decay function;
The function value would approach 0 as it decreases
This means that option (f) is correct
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Draw an area model to represent 4x^2+12x+9 = (2x+3)^2. Label the length and width of the whole square and label each individual small square and rectangle.
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
What are area models?Area models are shapes used to model or illustrate products, multiplications, divisions and quotients
How to draw the area model?The equation is given as:
4x^2+12x+9 = (2x+3)^2
Express (2x+3)^2 as the product of (2x+3) and (2x+3)
4x^2+12x+9 = (2x+3) * (2x+3)
The above means that the area model is a square.
So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
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If these two shapes are similar, what is the measure of the missing length w 20 in 15 in 12 in
Answer:
Step-by-step explanation:
The real solutions to the quadratic -x² - 2x+5=0 are:
2± √√29
2
-1±-√6
No real solutions.
None of the choices are correct.
Answer:
No real solutions.
Step-by-step explanation:
To solve this, we need to use Quadratic Formula.
Quadratic Formula:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]
in the form of:
[tex]a {x}^{2} + bx + c[/tex]
Given information from the question, we can deduce:
a = -1
b = -2
c = 5
Let's substitute these values into the formula.
[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]
if you punch these into the calculator.
Distributions of data can be characterized along three aspects or dimensions. Which aspect represents the spread or distribution of the data?
The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.
About the Distribution of Data:
The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.
The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.
Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.
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Ramiro was on a two day road trip.on the first day he drove at an average speed of 40 mph.on the second day he drove at an average of 60 mph.if he drove 2 hours longer and went 20 miles farther on his first day find the total distance ramiro traveled on his road trip.
Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.
What is the relationship between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first day, we have that:
v = 40, t = t + 2, d = d + 20, hence:
40 = (d + 20)/(t + 2)
For the second day, we have that:
v = 60
60 = d/t
d = 60t
Then, replacing in the first equation:
40 = (60t + 20)(t + 2)
60t + 20 = 40t + 80
20t = 60
t = 3.
Then the distances are given by:
First day: d = 60t + 20 = 60 x 3 + 20 = 200 miles.Second day: d = 60t = 60 x 3 = 180 miles.Total: 200 miles + 180 miles = 380 miles.More can be learned about the relationship between velocity, distance and time at https://brainly.com/question/28143163
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Can anyone solve 12? ASAP FIND EACH LENGTH TO THE NEAREST TENTH
Answer:
no solution
Step-by-step explanation:
The Law of Sines tells you the relationship between sides and angles of a triangle.
Law of SinesThe Law of Sines tells you ...
sin(A)/a = sin(B)/b = sin(C)/c
Using the given information, this would tell us ...
sin(55°)/12 = sin(B)/b = sin(C)/27
Then angle C would be ...
sin(C) = (27/12)sin(55°) ≈ 1.843
There is no angle whose sine is greater than 1. The triangle we seek does not exist. (Side BC is too short relative to side AB.)
What is the answer and explain
Answer:
B) 57 is the answer
Step-by-step explanation:
Let's try to make the given figure a parallelogram by extending DE and BA to F.
So now we have a complete parallelogram.
<AEF = 180 - 112 Since they are linear pairs
so, <AEF = 68
Now,
<EAF = 180 - 125 = 55
So, <AFE = 180-68-55 (interior angles of triangle sum up to 180)
<AFE = 57
Opposite angles of parallelogram are equal so,
<AFE = <BCD = 57°
In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the
alternate vertices. Show that △ BDF is equilateral
Answer:
Step-by-step explanation:
Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.
ProofAB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon
∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon
ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence
FB ≅ BD ≅ DF . . . . CPCTC
ΔBDF is equilateral . . . . definition of equilateral triangle
12. Make a hexagonal pyramid with a base edge of 6 cm, base apothem of 4 cm and pyramid height of 10 cm. You can do it in clay, porcelain or cardboard. (40%) It is supported by the following information • Side area • Total area • Volume • Used material • Elements of the figure outlined or marked.
the volume of the hexagonal prism is 184. 75 cm^3
How to determine the volume of the hexagonal prismIt is important to note that the volume of a hexagonal prism is given as;
V = (2/√3) × ap2 × h
Where
ap is the apothemh is the height of the prismFrom the information given, we have the values of the following parameters;
height = 10cm
apothem = 4cm
base edge = 6cm
Now, let's substitute the value of the parameters
Volume = (2/√3) × ap^2 × h
Volume = 2/√3 × 4^2 × 10
Multiply through
Volume = 1. 1547 × 16 × 10
Volume = 184. 75 cm^3
Thus, the volume of the hexagonal prism is 184. 75 cm^3
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Please help..this is due tomorrow morning.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
speed equals distance over time.
To and fro, distance=speed×time(ts)
distance=900×18=16,200km.
therefore, ts=16,200
since, speed = distance/time
therefore, time taken is inversely proportional to speed making D the best option.
y = x - 4
2x + y = 5
solve for x and y
Answer:
X = 2
Y = 1
Step-by-step explanation:
Solve by substitution
[tex]y = x - 4 \\ 2x + y = 5 \\ \\ y = x - 4 \\ 2x - 5 = - y \\ \\ y = x - 4 \\ - y = 2x - 5 \\ \\ add \: the \: two \: equations \\ \\ 0 = 3x - 9 \\ 9 = 3x \\ \frac{9}{3} = \frac{3x}{x} \\ x =3 \\ \\ substitute \: 3 \: for \: x \: in \: one \: of \: the \: equations \: to \: find \: y \\ \\ y = x - 4 \\ y = 3 - 4 \\ y = - 1 \\ \\ solution \: (3. - 1)[/tex]
Find the sum of the geometric series 9000-900 +...+ 0.009
Based on the calculations, the sum of this geometric series is equal to 9,990.
The standard form of a geometric series.Mathematically, the standard form of a geometric series can be represented by the following expression:
[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]
Where:
a₁ is the first term of a geometric series.r is the common ratio.How to calculate the sum of a geometric series?Also, the sum of a geometric series is given by this mathematical expression:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]
Given the following data:
First term, a = 9000.Common ratio, r = 900/9000 = 0.1Substituting the given parameters into the formula, we have;
[tex]S=\frac{9000(1-0.1^3)}{1-0.1}\\\\S=\frac{9000(1-0.001)}{1-0.1}[/tex]
S = 9000(0.999)/0.9
S = 8,991/0.9
S = 9,990.
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There are 20 points on a line, each spaced two inches apart. How far, in inches, is it from the first point to the last one?
Answer: 40 inches
Step-by-step explanation: If the 20 points on the line were spaced 1 inch apart, the result would be 20 inches. Each point you're going to is 1 inch in spacing and there is only going to be 20 inches of spacing (1 inch per point.)
For 2 inches spaced apart, the result would be simply 40 inches. You just need to add the distance of 20 more to the already distance of 20 points, since if 2 were to be divided, it would be 1, which is 20 inches in distance as stated. Another 20 points would be another inch in distance, and adding them gives you 2 inches in distance or 40 inches all together.
I apologize if I wasn't clear enough, I couldn't find a way to explain it as good as I thought it was in my mind.
Hope it helped though!
A circle is shown. Chords A C and B D intersect at point E.
Chords AC and BD intersect at E, with BD = 7 units, DE = 2 units, and AE = 4 units.
What is the length of segment CE?
units
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Given : Chords A C and B D intersect at point E. Length of Different segments is given in terms of x
To find : Length of chord BD
Solution:
Chords A C and B D intersect at point E.
=> AE * CE = BE * DE
AE = x
CE = x + 12
BE = x + 2
D = x + 5
=> x(x + 12) = (x + 2)(x + 5)
=> x² + 12x = x² + 7x + 10
=> 5x = 10
=> x = 2
BD = BE + DE
= x + 2 + x + 5
= 2x + 7
putting x = 2
=> BD = 2 (2) + 7
Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.
What is the Intersecting Chords Theorem?In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.
According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.
In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:
BE = BD - DE = 7 - 2 = 5 units
DE = 2 units
AE = 4 units
CE = ?
Based on the intersecting chord theorem, we have:
(BE)(DE) = (AE)(CE)
Plug in the values
(5)(2) = (4)(CE)
10 = 4(CE)
Divide both sides by 4
10/4 = 4(CE)/4
2.5 = CE
CE = 2.5 units
Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.
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