A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.
Given that,
The point is (2,3).
We have to find the equation of the horizontal and vertical line that pass through point.
Take the point,
(2,3)
The value of x, in this example 2, will never change for a vertical line. This holds true regardless of y's value.
A vertical line passing through this point has the following equation:
x=2
The value of y, in this case 3, for a horizontal line will also never change. This holds true regardless of the value of x.
A horizontal line passing through this point has the following equation:
y=3.
Therefore, A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.
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a certain insecticide kills 60% of all insects in laboratory experiments. a sample of 9 insects is exposed to the insecticide in a particular experiment. what is the probability that exactly one insect will die? round your answer to four decimal places.
The probability that exactly one insect will die is 142.611.
Define probability.The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.
Given,
P( an insect will die) = 0.60
q = 1 - p
q = 1 - 0.60
q = 0.40
Sample size,
n = 9
Binomial distribution:
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
Probability that exactly one insect will die = P(X = 1)
= ⁹C₁ × 0.6¹ × 0.4⁸
= 362880 × 0.6 × 0.000655
= 142.611
The probability that exactly one insect will die is 142.611.
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if a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (round your answer to the nearest second.)
The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
Who is peregrine falcon dove?It can be found with in Arctic tundra of North America and Greenland, and it migrates to Central and South American countries as during winter.The peregrine falcon is the world's swiftest bird, diving to acquire its prey at speeds of over 321 kph (200 mph). They are also among the most tolerant species and can flourish in populated places.For the given question;
The maximum speed of peregrine falcon dove is 200 mph.
Time of travel = 0.5 miles.
The relation of distance and speed is;
speed = distance/time
200 mph = 0.5 miles / time
Time = 0.5 miles / 200 mph
Time = 0.5 × 60 × 60 miles / 200 m/ sec
Time = 9 sec
Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
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Triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2). Graph AFGH and its image after a rotation of 180° about (-3, -6).
Answer:
Im gonna assume its counter clockwise (excuse the bad drawing)
Step-by-step explanation:
The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
So, (x, y) → (x+3, y+6)
F(-3, 4) → (-3+3, 4+6) → F'(0, 10)
G(2, 0) → (2+3, 0+6) → G'(5, 6)
H(-1, -2) → (-1+3, -2+6) → H'(2, 4)
Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
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A primary school had 1200 students enrolled in 2013 and 1500 students in 2016.if the students population grows as a linear function of time t,where t is the number of years after 2013.how many will be enrolled in the school in 2020?and find the linear function that relates the students population to time t.
Answer:
y=100t+1200, where t is years since 2013 and
Step-by-step explanation:
We only have two points from which to form an equation. Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0). Let's make the x axis the year and y the student population.
Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013. "t is the number of years after 2013." (0,1200) becomes is the data point for 2013. The school's population will be the y-axis.
(0,1200) [primary school had 1200 students enrolled in 2013], and
(3,1500) [1500 students in 2016]
---
First calculate m, the slope. Slope is the Rise/Run between the two points (the change in y over the change in x)
Going from (2013,1200) to (2016,1500) we find that:
Rise (in y) = (1500 - 1200) = 300 students
Run (on x) = (2016 - 2013) = 3 years
The Rise/Run, or slope, m, is 300/3 or 100: m = 100
Lets put that into our equation format:
y = 100x + b
X will be the time, in years. The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:
y = 100t +b, where t is years after 2013.
(The 100 tells us that the student population increases by 100 per year)
We now need b, the y-intercept. One can either graph this and look for the value of y when x=0, of simply input either of the data points. This looks easy enough to input a point and solve for b:
Remember that t is the (year - 2013)
y = 100t +b Solve for (2013,1200)
t = 2013 - 2013 = 0
1200 = 100*(0) + b
b = 1200
Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).
The equation becomes y = 100t + 1200
See the attached graph.
which equations are true when k = - 50? Select two correct answers.
1.5 - k/5 = 11.5
-2k + 78 = -22
-4k + 80 = -120
6k - 150 = -150
K/10 -3 = -8
30 POINTS IF YOU ANSWER!!
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
Given,
The equations;
1.5 - k/5 = 11.5-2k + 78 = -22-4k + 80 = -1206k - 150 = -150K/10 -3 = -8The value of k = -50
We have to solve the given equations using k as -50 and find the true ones;
Lets check;
1.5 - k/5 = 11.51.5 - (-50/5) = 11.5
1.5 - (-10) = 11.5
1.5 + 10 = 11.5
11.5 = 11.5
This equation is true.
-2k + 78 = -22(-2 x -50) + 78 = -22
100 + 78 = -22
178 ≠ -22
This equation is false
-4k + 80 = -120(-4 x -50) + 80 = -120
200 + 80 = -120
280 ≠ -120
This equation is false
6k - 150 = -150(6 x -50) - 150 = -150
-300 - 150 = -150
-450 ≠ -150
This equation is false
k/10 -3 = -8(-50/10) - 3 = -8
-5 - 3 = -8
-8 = -8
This equation is true.
That is,
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
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q1 suppose you take a sample of 16 people and ask them how fast they drive on interstate 94. after collecting your sample, you calculate that the mean is 75mph with a variance of 9mph. calculate a 90% confidence interval for the average speed of all drivers on i94.
A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)
Given that,
Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.
Solution is as given below :
90% Confidence Interval for μ is
μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]
μ = 75 ± (1.75) * 3/[tex]\sqrt{16}[/tex]
μ = (73.69, 76.31)
Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)
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PLS HELP, it’s due tmrw and I need it done
a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0b. option A
c. The river barge can safely ship the agricultural products
How to determine the equation the agricultural products of soybeans and corn the river barge can carryinformation gotten from the question include
Corn weighs about 60 pounds per bushel
soybeans weigh about 90 pounds per bushel
A river barge can safely carry up to 4,500,000 pounds of cargo.
Let x = bushels of corn and y = bushels of soybeans.
a. From the statement, it can be deduced that the equation is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0
b. some interpretation on inequality
shading above a line is greater than and below a line is less thandotted lines mean the inequality do not have equal to while solid lines mean the inequality has equal tofrom the interpretation
The inequality has "equal to" as result the graph must be a solid lineThe inequality used is less than as a result the shading must be below the linethe correct option is A (graph attached)
c. 60 * 24000 + 90 * 24000
= 3,600,000
The value is ≤ 4,500,000 hence the river barge can carry it
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describe a situation that could be represented by f(x) // pls help
Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.
Step-by-step explanation:lol i have no idea
it takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 11 inches wide, and 13 inches tall. how long will it take the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches?
It takes almost 5.7 hours the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches.
First, we must determine how quickly the hose operates.
By dividing the volume of the first aquarium by the length of time it took to fill it, we may determine that.
The following formula can be used to determine the volume of the first aquarium: V =L*B*H
where the aquarium's length is L and its width is B
Its height is H.
Thus, the first aquarium's volume is:
V =L*B*H = 3*8*11 = 264 inches^3
We have the filling rate as:
264/3 inches ^3 per minute,
Let's now determine the second aquarium's volume.
The first formula is what we employ.
The volume is as follows:
V =L*B*H = 26*33*35 = 30030 inches ^3
Now, we divide the capacity of the second aquarium by the pace of the first aquarium to obtain the amount of time.
According to mathematics, that is:
30030 * 3/264 = 341.25 minutes = 5.7 hours approximately
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find the equation of the line in slope-intercept form. e through (−5, 6) with slope = 2
Answer:
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is your slope and b is your y-intercept.
To find your equation with what you are given, you have to plug in your values.
(-5, 6) = (x, y) so plug -5 in where there is x and 6 in where there is y
then your slope, m, is 2 so plug 2 in where there is m.
so it should look like
6=2(-5)+b, now you are solving for b.
6 = -10+b
+10 +10
___________
16 = b Then take the values and plug back into the slope intercept formula, y=mx+b.
Plug 16 in for b and 2 in for m (m represents slope and they told us the slope =2)
*you no longer need the y and x values because you only use those to solve for m or b, in this case b, so leave y and x in your equations*
y=2x+16
A community hall is in the shape of a cuboid.
The hall is 40 m long, 15m wide and
3 m high.
The community hall needs re-decorating
with new paint for the walls and ceiling,
and new tiles on the floor.
A 10 litre tin of paint covers 25 m² and costs £10.
Work out the total cost of paint needed
to re-decorate the community hall.
The total cost of painting is $564.
What is surface area of cuboid ?
A cuboid is a three-dimensional figure enclosed by six rectangular planes, each of which has a different size in terms of length, breadth, and height. Anything in the shape of a rectangle, such as a box, brick, or other object, may be a cuboid if you look about. When viewed from any of the ends, a cuboid (3-dimensional) can be seen to be made up of different-sized rectangles (2-dimensional). A cuboid's area is its surface because it is a solid with three dimensions. Since a cuboid's faces are rectangular, its area may be determined using the formula for the area of a rectangle.
Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units
We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.
The paint will be required for 4 walls and ceiling.
Let us find area of walls and ceiling.
Area of walls and ceiling = 2( 40*15) + 2(3*15) + (40*3)
=> Area of walls and ceiling = 2(600)+2(45)+120
=> Area of walls and ceiling = 1200+90+120
=> Area of walls and ceiling = 1410 [tex]m^2[/tex]
Therefore, the area of walls and ceiling is 1410 square meters.
Here Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter.
Then total cost of paint = 10*[tex]\frac{1410}{25}[/tex] = 10*56.4 = $564.
Hence cost of paint is $564.
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A bowling ball is pushed with a force of 22. 0 N and accelerates at 5. 5 m/s2. What is the mass of the bowling ball?
When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.
Newton's Second Law of Motion states that force is the result of mass times acceleration.
[tex]F=m*a[/tex]
[tex]m = F / a[/tex]
A force of 22.0 Newtons ( [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.
F = 22.0 [tex]kgms^{-2}[/tex] and
a = 5.5 [tex]ms^{-2}[/tex]
Put the values in the formula as replacements.
M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]
Meters per second squared (m/s2) units cancel each other out.
M = 22 kg / 5.5
= 4 kg
The bowling ball weighs 4 kilogram.
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A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, what is y
A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889
The general cosine function is given by
f(x)= A cos (B x -C) +D
where A= 1/3 is the amplitude,
period = 2π /B
π/3 =2π/B
B= 2/3
C= -2π is the horizontal shift and D= -3s a downward vertical shift.
If we substitute all these values into the formula we obtain;
f(x)= 1/3 cos (2/3 x +2π ) -3
if x= π then we have to calculate y
y= 1/3*0.3333 -3
y= -2.8889
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Thank you for those answering!
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Find DE, please help me
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
Parallelogram ABCD has vertices A(1,1) , B(17,1) , C(22,13) , and D(6,13) what is the area in units of parallelogram ABCD
The vertices of a parallelogram are given, according to which the area of the parallelogram will be equal to 58 units.
What is perimeter?The perimeter of a shape is its boundary's length, regarded as a whole. A form's circumference can be calculated by adding the lengths of all of its sides and edges. Utilizing linear length units like centimeters, millimeters, yards, and feet, it is determined.
The total of all a parallelogram's sides is its perimeter.
Firstly, solve for vertices AB:
AB = √(17- 1)² + (1 - 1)² = 16
Then,
BC = √(22 - 17)² + (13 - 1)² = 13
Then,
CD = √(6 - 22)² + (13 - 13)² = 16
Lastly,
AD = √(6 - 1)² + (13 - 1)² = 13
Add all the values,
P = 16 + 13 + 16 + 13
P = 58 units.
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2x + 4y < 20 what is the inequality simplifies
Answer:
x < 10 - 2y
Step-by-step explanation:
In the diagram below, GH is parallel to DE. If FH is 5 more than GF, DF:
and FE = 48, find the length of GF. Figures are not necessarily drawn to scal
State your answer in simplest radical form, if necessary.
Answer: GF =
The length of side GF from the similar triangles shown is GF = √10 units
What is an equation?A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.
If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.
In a similar triangle, DE = GF, Hence:
GF/DF = GH/DE
GF / 5 = 2 / GF
GF² = 10
GF = √10
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Make x the subject of y = 3x-2
You may use the flowchart to help you if you wish.
x 3
- 2
Answer:
x=y/3 + 2/3
Step-by-step explanation:
Is this what you wanted?
what is the difference between -3 and 10
Answer:
13
Step-by-step explanation:
-3-10, or 10+3 is equal to 13
Answer:
13
Step-by-step explanation:
-3+13=10
When is an equation true?
Answer: when the value on each side of the equal sign is the same
Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation
Given that f(x)=-5x+9/2 and g(x)=1.5x^2-8
The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.
According to the question,
We have the following expressions:
f(x) = -5x+9/2
Now, we will find the all the values of f(x) by replacing x with the given digits:
f(4) = -5*4+4.5
f(4) = -20+4.5
f(4) = -15.5
The value of f(1/4):
f(1/4) = -5/4+4.5
f(1/4) = -1.25+4.5
f(1/4) = 1.375
The value of x when f(x) = 2:
-5x+4.5 = 2
-5x = 2-4.5
-5x = -2.5
x = 2.5/5
x = 0.5
g(x) = 1.5[tex]x^{2}[/tex]-8
Now, we will find all the values of g(x) by replacing x with the given digits.
The value of g(-2):
g(-2) = 1.5(-2)(-2)-8
g(-2) = 6-8
g(-2) = -2
The value of g(2.5):
g(2.5) = 1.5*2.5*2.5-8
g(2.5) = 9.375-8
g(2.5) = 1.375
The value of x when g(x) = 16:
1.5[tex]x^{2}[/tex]-8 = 16
1.5[tex]x^{2}[/tex] = 16+8
1.5[tex]x^{2}[/tex] = 24
[tex]x^{2}[/tex] = 24/1.5
[tex]x^{2}[/tex] = 16
x = +4 and -4
Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.
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Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes?
Answer
Step-By-Step-Explanation
2 mangoes=eleven lassis
×6 ×6
12 mangoes=66 lassis
Answer=66 lassis
what is the correct postulate to prove these two triangles congruent?
A. SAS
B. ASA
C. SSS
D. AAS
E. HL
Answer:
SAS
Step-by-step explanation:
By applying the Side Angle Side Postulate (SAS), you can be sure that your two triangles are congruent.
if
x/y=y/z=z/x
show that x=y=z
Step-by-step explanation:
x/y = y/z = z/x
x = y²/z = zy/x and y = z²/x
x = y²/z
putting this into the 3rd part of the original equation :
z/x = z/ y²/z = z²/y²
now using the y identity of the second part there :
y = z²/x
z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)
so,
x²/z² = z/x
x³/z³ = 1
x/z = 1
x = z
then
y/z = y/x = z/x (= 1)
and therefore,
y/x = z/x meaning
y = z (and therefore = x)
so,
x = y = z
the square root of $x$ is greater than 3 and less than 4. how many integer values of $x$ satisfy this condition?
6 integers that satisfy the given condition are 10,11,12,13,14,15.
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
we have the number X
Of which the square root is greater than 3 and less than 4
so,
[tex]3 < \sqrt{X} < 4[/tex]
on squaring both sides
[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]
[tex]9 < X < 16[/tex]
so the integer that satisfies the condition is 10,11,12,13,14,15.
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Answer:
6
Step-by-step explanation:
Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.
Can someone at least explain this to me I’m very confused.
For given line segments RS = TR
In this question, we have been given two line segments QS and TU intersected at point R.
Also, we have been given QS = TU, QR = RU
We need to prove, RS = TR
We can observe that,
QS = QR + RS
and UT = UR + RT
QS = TU ................(Given)
QR + RS = UR + RT
QR + RS = QR + RT .............(Given QR = RU )
QR + RS - QR = QR + RT - QR .............(subtraction property of equality)
RS = TR
Hence proved.
Therefore, for given line segments RS = TR
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The area of a rectangular floor is 8x² + 6x-20. The width of the floor is 2x + 4. What is the length of the floor?
Answer:
Length = 4x - 5
Step-by-step explanation:
A = length x width
Which table of values satisfies the linear equation y=−47x−2?
x y
−7 −6
0 −2
7 2
x y
−14 6
0 0
14 −10
x y
−7 2
0 −2
7 −6
x y
−14 −10
0 0
14 6
The values satisfies the linear equation y = −47x−2 is (0, -2).
Describe the word linear equation?an equation where every term has either a constant else includes only one variable, each variable does have an exponent of one, and the graph is always a straight line.The general form of such a linear equation is y = mx + b, where m and b can be any real number.For the given question.
The linear equation is given as;
y = −47x −2
Check the result by putting the values from option.
For : −7 −6
Put x = -7
y = −47(-7) −2
y = 799 -2
y = 498 (incorrect)
For: 0 −2
Put x = 0
y = −47x −2
y = −47(0) −2
y = -2 (correct)
Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).
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Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
Answer:
$210 in bank
Step-by-step explanation:
Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
70% = 0.7
300 * 0.7 = $210 in bank