The coordinate will make perpendicular AB to CD is D(x, x/3 + 3). We have used the slope concept to solve this problem.
The slope of a line segment between two points (x1,y1) and (x2,y2) is given by the ratio of change in the y coordinate to the change in the x coordinate.
Slope = (y2 - y1)/(x2- x1)
Slope of line AB = (-5-4)/(2-(-1)) = -9/3 = -3
Let the slope of another segment CD be m.
As the product of two perpendicular segments is equal to -1.
So,
-3m = -1
m = 1/3.
Let,s assume point D is (x,y)
Slope of segment CD = (y - 4) / (x-3)
(y - 4) / (x-3) = 1/3
3(y-4) = (x-3)
3y = x+9
y = x/3 + 3
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8. A table holds 4 cheese pizzas, 4 pepperoni
pizzas, and 2 supreme pizzas. How can
you write a ratio that compares part of
the pizzas to the total?
Answer: I don't know
Step-by-step explanation:
You got this pal!
Which statement correctly describes the relationship between the graph of f (x) and the graph of g (x) =f (x) - 4?
A) The graph of g(x) is the graph of f(x) translated 4 units down.
B) The graph of g(x) is the graph of f(x) translated 4 units left.
C)The graph of g(x) is the graph of f(x) translated 4 units right.
D)The graph of g(x) is the graph of f(x) translated 4 units up.
The statement which describes the relationship between the graph of f (x) and the graph of g(x) = f (x) - 4 is the graph of f(x) translated 4 units down.
What is meant by standard form of transformation?The standard form of transformation can be described as,
g(x) = f(x + a) + b .... (1)
If a > 0, then the graph of f(x) shifts left side by a unit and if If a < 0, then the graph of f(x) shifts right side by a units.
If b > 0, then the graph of f(x) shifts upward by b unit and if If a < 0, then the graph of f(x) shifts downward by b units.
Since the relationship between the graph of f(x) and g(x) exists,
g(x) = f(x − 4)
From (1), we get
The value of a exists -4, therefore the graph of f(x) translated 4 units down.
The value of a function exists defined on a graph by the vertical distance from the x-axis. When that vertical distance exists reduced by 4, the corresponding point exists shifted down 4 units.
Therefore, the correct answer is option A) The graph of g(x) is the graph of f(x) translated 4 units down.
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FILL IN THE BLANK. Overall, available research suggests jurors exposed to pretrial publicity are ________________ to favor the ________________.
Answer:
Overall, available research suggests jurors exposed to pretrial publicity are more likely to favor the prosecution.
What is the common ratio between successive terms in the sequence 27 9 3 1?.
Which number line represents the solution set for the inequality 1/2 * x >= 4?.
The number line which represents the solution set for the inequality is second one.
What is number line?
In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.
Main body:
Start by solving for x.
-1/2x ≥ 4
Multiply each side by 2
-1x ≥ 8
then divide by -1....
but remember to flip your sign its a negative number.
x ≤ -8
hence, the second one is correct.
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Pythagorean Theorem of an equilateral triangle?
The Pythagorean Theorem of an equilateral triangle is a²+b²=c²
What is meant by an equilateral triangle?The height of an equilateral triangle is defined as a line drawn from any vertex on the opposite side of the triangle. This is the opposite side's perpendicular bisector. This means it cuts the opposite side in half and produces a 90° angle with it. The altitude that separates an equilateral triangle into two congruent right-angled triangles is also known as the triangle's height.
To calculate the missing side lengths of an equilateral triangle, use the Pythagorean theorem and the height of the right triangles within the equilateral.
The area of an equilateral triangle can therefore be determined using the formula A = 3/4 (a2).
The Pythagorean Theorem of an equilateral triangle is,
a(√3/2a)+b(√3/2b)=c(√3/2c)
√3/2a²+√3/2b²= √3/2c²
√3/2(a²-b²)= √3/2(c²)
a²+b²=c²
This is the Pythagorean Theorem of an equilateral triangle.
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The number of newspapers sold decreases exponentially by x% each year.
Over a period of 21 years the number of newspapers sold decreases from 1763 000 to 58000.
Calculate the value of x.
In the exponential decrease function, the rate of decline is approximately 17.7%
Exponential FunctionAn exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828. An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
In this problem, we can write an exponential function as
58000 = 1763000(1 + x)⁻²¹
Solving for x
x = 0.1765
Converting this into percentage;
x = 0.1765 * 100 = 17.7%
The rate is 17.7%
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TRUE/FALSE return values are type-specific in php functions (a function only returns a value of a specified data type.)
Return values are type-specific in php functions The answer is False.
What is php function?
A PHP function is a piece of code that is very reusable. It can accept an argument list as input and return a value. Inbuilt functions in PHP number in the thousands.
You can develop your own functions in addition to the built-in PHP functions.
A function is a collection of statements that a programme can use repeatedly.
When a page loads, a function won't start running immediately.
A call to a function will cause the function to run.
In this a function only returns a value of a specified data type.
Hence, the given statement return values are type-specific in php functions is FALSE
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An ice cream factory make 320 quart of ice cream in 10 hour. How many quart could be made in 48 hour
Answer:
In 48 hours the ice cream factory can make 1,680 quarts.
Step-by-step explanation:
Multiply UNIT RATE 35 by 48 to answer your first question.
Caroline buys 5 rubbers and 5 crayons for £10.
Elliot buys 1 rubber and 2 crayons for £2.75.
Work out the cost of one rubber and one crayon.
Answer:
5R + 5C = 1000
1R + 2C = 275
(1R + 2C = 275) x 5 = 5R + 10C = 1375
(5R + 10C = 1375) - (5R + 5C = 1000) = 5C =375
CRAYON = 75p
RUBBER = 125p
If 1 2 gallon of paint covers 1 12 of a wall, then how many quarts of paint are needed for the entire wall?.
If 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.
One gallon is equal to 4 quarts.
The amount of gallon that covers 1/12 of a wall = 1/2.
1/2 gallon = 2 quarts
This means that 2 quarts are needed to cover 1/12 of a wall.
Now, the number of quarts needed to cover the entire wall = 1/12 × 2= 1.
Therefore, if 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.
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Mr. Cho received a container of fresh eggs. He sold 1/3 of the eggs in the morning and sold 320 eggs in the afternoon. At the end of the day, he found that 1/4 of the egs were not sold. How many eggs did he receive in the beginning?
Answer:
768
Step-by-step explanation:
Define the variable:
Let x be the number of eggs Mr Cho received in the beginning.Given information:
Mr Cho sold 1/3 of the eggs in the morning.Mr Cho sold 320 eggs in the afternoon. At the end of the day, Mr Cho found that 1/4 of the eggs were not sold.Create an equation with the defined variable and the given information:
[tex]\implies x - \dfrac{1}{3}x-320=\dfrac{1}{4}x[/tex]
Solve for x:
[tex]\implies \dfrac{2}{3}x-320=\dfrac{1}{4}x[/tex]
[tex]\implies \dfrac{2}{3}x-320-\dfrac{1}{4}x=\dfrac{1}{4}x-\dfrac{1}{4}x[/tex]
[tex]\implies \dfrac{5}{12}x-320=0[/tex]
[tex]\implies \dfrac{5}{12}x-320+320=0+320[/tex]
[tex]\implies \dfrac{5}{12}x=320[/tex]
[tex]\implies 12 \cdot \dfrac{5}{12}x= 12 \cdot 320[/tex]
[tex]\implies 5x=3840[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{3840}{5}[/tex]
[tex]\implies x=768[/tex]
Therefore, Mr Cho received 768 eggs in the beginning.
Total eggs be x
Form a equation
x-x/3-320=x/4x-320=x/4+x/3x-320=7x/1212x-3840=7x5x=3840x=768Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,P(5) = 1/6, P(6) = 0.(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,P(spades) = 16/52.Part (a) The distribution is legitimate.Part (b) The distribution is not legitimate.Part (c) The distribution is legitimate.
From the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
How to know legitimate probability distribution?We should know that Probability is the chance of occurrence of an even (E) over a period of time.
A legitimate probability distribution must be that which adds up to 1 and cannot be negative.
Legitimate Distribution= P(a)+P(b)+P(c)+.....+P(n)
Where a,b,c and n are Probabilities of events.
From the given Parameters
(a) Rolling a die to record P(1) =0, P(2)=[tex]\frac{1}{6}[/tex], P(3)=[tex]\frac{1}{3}[/tex], P(4)=[tex]\frac{1}{3}[/tex], P(5)=[tex]\frac{1}{6}[/tex], P(6)=0
Add up the probabilities to get 1
⇒0+[tex]\frac{1}{6} +\frac{1}{3}+\frac{1}{3}+\frac{1}{6}+0[/tex]
⇒[tex]\frac{0+1+2+2+1+0}{6}[/tex]
P(E)=[tex]\frac{6}{6}=1[/tex]
This implies that the distribution is legitimate
(b) Choosing a college student at random,
Add up the probabilities to get 1
P(female full time)+P(male full time)+P(female part time)+P(male part time)
⇒0.56+0.44+0.24+0.17
=1.41
The probability of the distribution is not legitimate because it is greater than one.
(c) Deal a card from a shuffled deck.
Add up the probabilities to get 1
P(club)+P(diamond)+P(hearts)+P(spades)
[tex]\frac{12}{52} +\frac{12}{52}+\frac{12}{52}+\frac{52}{16}[/tex]
[tex]\frac{12+12+12+16}{52}[/tex][tex]\frac{52}{52}=1[/tex]
The distribution is legitimate because the sum of the probabilities is
equal to 1
In conclusion, from the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
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Which function represents a function with direct variation?.
Functions of the form f(x)=kx represents direct variation.
The table of values that appears a constant proportion between two variables speaks to a direct variation function.
A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0); this is because if we use 0 as x, y = k(0) = 0.
In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion. the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. T
Therefore, A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0); this is because if we use 0 as x, y = k(0) = 0.
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The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y= -0.0127 + 0.0180x Suppose that the legal limit to drive is a blood alcohol content of 0.08.
0.0027 is the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression.
Given that,
In 16 male college students, the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression. This research produced the regression equation shown below: y= -0.0127 + 0.0180x Suppose a blood alcohol level of 0.08 is required to legally operate a vehicle.
We know that,
When five bears d, use x=5 to calculate the blood alcohol concentration.
y= -0.0127+0.0180*5=0.0773
So, his alcohol level is 0.0773 . this is clearly below legal level of 0.08
Then difference between his level and legal level= 0.08-0.0773= 0.0027
So, correct answer is
0.0027 below the legal limit
Therefore, 0.0027 is the association between the quantity of beers d (x) and blood alcohol concentration (y) was investigated using least squares regression.
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Which graph is an example of direct variation?.
Graphs having an equation in the form y = kx, is an example of direct variation.
The graph that represents a function with a direct variation is (b)
For a graph to represent a function with direct variation, the following must be true
The function must be a linear function
The slope of the function must not be 0 or undefined
The function must pass through the origin
The only graph that satisfies the three highlights above is graph (b)
Hence, the graph that represents a function with a direct variation is (b)
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Show that the flux of F =e_{r}/r^2 through a sphere centered at the origin does not depend on the radius of the sphere.
Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F
and 014≤ 640 ≤ 2TT outward normal is
(r = 18) = √x² + y²+z2)
= F = ૪ 3
flux = [[Finds
. Rsing dodo = 83
(from put value of n
13 sind do do 23
2 TT, TT sing do do
R 11 R [["e. / sind dado (r= 171 = radius of ephare)
Π 2T ए [e" [" sind do do= ["- Casp" "do 0
[-(-1-1) do 2TT = 2x (2-0) 2 = do flux
flux = [[F·ñ-ds S = 4π
The flux is 411 and it depends on radius 'R'
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If you travel 4 km south, 2 km north, 5 km south, and 5 km north, what is your displacement?.
Answer:
2 km
Step-by-step explanation:
Write a recursive formula for the sequence described.
It follows a plus one pattern: 8, 9, 10, 11, 12, ...
The recursive formula for the given sequence is, [tex]a_n=a_n_-_1+1[/tex].
What is recursive formula?
Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula
[tex]a_n=a_n_-_1+d[/tex]. [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.
Consider the given sequence,
8, 9, 10, 11, 12, ...
Here each next term is defined by it's preceding term by adding 1 in each preceding term.
That is,
9 = 8 +1
10 = 9 + 1
11 = 10 + 1
12 = 11 + 1
Hence, the recursive formula for the sequence is, [tex]a_n=a_n_-_1 + 1[/tex].
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I will give Brainlest!
The answers will either be yes or no
The classification of the equations as direct or indirect variations are;
1) Direct Variation
2) Direct Variation
3) Indirect Variation
4) Indirect Variation
How to find direct and indirect variation?Direct variation occurs when one quantity changes and the other quantity changes as well in direct proportion. Meanwhile, Inverse variation is exactly opposite of that.
Now, let us answer the questions;
1) y = 4x + 1
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
2) y = 7.5x
This shows that y is directly proportional to x because as x is increasing, y is increasing and vice versa. Thus, it is a direct variation.
3) y = (1/15)x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
4) y = 6/x
This shows that y is inversely proportional to x because as x is increasing, y is decreasing and vice versa. Thus, it is an indirect variation.
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How to determine if a graph represents y as a function of x?.
Answer:
Step-by-step explanation:
If it is not possible to draw a vertical line to touch the graph of a function in more than one place, then y is a function of x. For Example: Use the vertical line test to determine if the graph depicts y is a function of x.
I really need help to get this done, please.
The area of sector q is [tex]\frac{\pi n^{2} }{9}[/tex]
What is a sector of a circle?A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The circle is divided into 9 equal parts meaning that 1/9 the area of the circle is the area of circle q
Area of circle = [tex]\pi r^{2}[/tex]
Area of sector q = [tex]\frac{\pi r^{2} }{9}[/tex]
but r = n
Area of sector q = [tex]\frac{\pi n^{2} }{9}[/tex]
In conclusion, the area of sector q is [tex]\frac{\pi n^{2} }{9}[/tex]
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Can you help me find the radius of the circle?
Answer:
r=4
Step-by-step explanation:
The radius is equal to half of the diameter. The diameter in this problem is 8 units; half of 8 is 4.
Answer:
The radius would be 4.
Step-by-step explanation:
The radius is always half of the diameter, which would be all the way around the circle. The radius would be halfway around the circle.
So looking at the graph, we can see that the circle surrounds the origin (0) 4 spots to the left and 4 spots to the right. This represents the diameter which is 8 and this can be found by adding the two directions (4 + 4) which gets you 8 as a sum. Now knowing this, we simply divide 8 by 2 and we get the radius which is 4.
Therefore, the answer is 4.
Write : linear equation to represent the line shown on the graph.
The equation of the line that passes through the points (0,-2) and (3,2) is 4x-3y-6 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
In the given graph,
The points are (0,-2) and (3,2)
To find the equation of the line,
Find slope by using formula m = (y₂-y₁)/(x₂-x₁)
m = (2-(-2))/(3-0)
m = 4/3
The equation of line is,
y-y₁ = m (x-x₁)
y-(-2) = 4/3(x-0)
y+2 = 4/3x
3y+6 = 4x
4x-3y-6 = 0
The required equation of line is 4x-3y-6 = 0.
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a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. (T/F)
(F)alse
The given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes.is false.
What is a stiff equation
While integrating a differential equation numerically, one would expect the requisite step size to be relatively small in a region where the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with slope approaching to be zero. This is not always true in all the cases. In some cases in order for a numerical method to give a reliable solution to the differential system sometimes the step size is required to be at an very small level in a region where the solution curve is too smooth. The phenomenon is known as stiffness.
So, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
Therefore, the given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. is false.
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there are 96 boys and 112 girls in a primary school . write the ratio of the boys to the girls
Answer:
6 : 7
Step-by-step explanation:
the ratio of
boys : girls
= 96 : 112 ( divide both parts by 16 )
= 6 : 7
1. -6 - 8(x - 5)= algebric expression'
2. x + 8 + 6x=
Answer:
I'm not sure if this is what you want to be solved.
[tex]-6-8(x-5)=-6-8x+40=34-8x[/tex][tex]x+8+6x=7x+8[/tex]studies show that gasoline use for compact cars sold int he untied states is normally distirbuted with a mean use of 25.5 miles per gallon and a standard deviation of 4.5 miles per gallon. what eprcentage of compact obtains 30 or more miles per gallon
0.1587 is eprcentage of compact obtains 30 or more miles per gallon by standard deviation.
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.
P(X> 30 )
Normal distribution
μ = 25.5
σ = 4.5
P(X > 30 ) = Area to the right of 30
we convert this to standard normal using z = x - μ/σ
z = 30 - ( 25.5 )/45 = 1.00
P(Z > 1.00 ) = Area to the right of 1.00
P( X > 30) = P( Z > 100) = 1 - P( Z < 1.00 ) = 1 - 0.8413
= 0.1587
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Jessica is photographing birds. She tilts her camera so that it first forms a 34° angle with the ground. She then tilts it up some more so that it forms a 63° angle with the ground.
How many degrees does she tilt the camera from its first position to its second position?
The photographing of Jessica as depicted shows adjacent angles and the angle she tilt the camera from its first position to its second position is 29 degrees
What are adjacent angles?When two angles have a similar vertex and side, they are referred to as adjacent angles.
The vertex of an angle is the point at which the rays that make up its sides come to an end. Adjacent angles have same vertex and side, they can be a complimentary angle or supplemental angle but in this case the sum is 63 degrees. This is to say that
? + 34 = 63
? = 63 - 34
? = 29
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At 98°F, a certain insect chirps at a rate of 88 times per minute, and at 107°F, they chirp 151 times per minute. Write an equation in slope-intercept form that represents the situation.
The equation in slope-intercept form that represents the situation is y = 7x - 598
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
The ordered pair are ( 98, 88) and (107, 151)
Equation of line in slope-intercept form is y = mx + c
at x = 98, y =88
so that by substituting we have,
88 = 98m + c -------------------1
at x = 107, y = 151 and by substituting we have
151 = 107m + c -----------------2
subtract equation 1 from 2
63 = 9m
m = 63/9
m = 7
substitute m = 7 in equation 1
88 = 98(7) + c
c = 88 - 686c
c = -598
substitute m and c for their values equation becomes
y = 7x - 598
In conclusion, the equation in slope-intercept form is y = 7x - 598
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