The symbol of absolute value is two vertical bars (||).
The absolute value of a number is the distance between that number and zero on a number line. The absolute value of a number is always positive, regardless of the sign of the original number. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5.
In mathematical notation, the absolute value of a number is represented by placing the number between the vertical bars, like this: |x|. When the absolute value is applied to a variable or an expression, the result is the positive value of that variable or expression. For example, |-5| = 5, and |5| = 5.
The absolute value is used in many branches of mathematics, including algebra, calculus and geometry, and it is used to represent the magnitude of a number, regardless of its sign, and also it is used to define the distance between two points on a number line.
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13) Complete the proof. Given: A RST, RT > ST Prove: measure of angle RST > measure of angle R
Proof: Since RT > ST, there exists a point Q on RT, where QT is the same length as ST. By the Isosceles Triangle Theorem, angle 2 is congruent to angle 3, and by definition of congruent angles, the measure of angle 2 = the measure of angle 3.
Answer:
To prove that the measure of angle RST is greater than the measure of angle R, we can use the following steps:
By the definition of a triangle, angle RST is supplementary to angles R, S and T.
Since RT > ST, we can conclude that angle R is less than angle S.
Since angle RST is supplementary to angles R and S, the measure of angle RST is greater than the measure of angle R.
This can be written as measure of angle RST = measure of angle R + measure of angle S > measure of angle R
So, we've proven that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.
Proof by contradiction could also be used to prove that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.
Assume that the measure of angle RST <= measure of angle R. By the triangle inequality theorem, we know that RT + ST > R. But we are given that RT > ST, so RT + ST > RT > R which is a contradiction. Therefore, measure of angle RST must be greater than measure of angle R.
Evaluate the line integral, where
C
is the given curve.
∫ xyds,C:x2,y=2t,0≤t≤2
C
According to the given information the line integral is 8(1+125[tex]\sqrt{110}[/tex]) / 15 .
What distinguishes a line integral from a definite integral?
Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.
[tex]\int\limits_c {xy} \, ds[/tex], C : x = t^2 , y = 2t, 0 ≤ t ≤ 3
x' = 2t , y' = 2
ds = [tex]\sqrt{(x')^2 + (y')^2}[/tex]
[tex]\sqrt{4(t)^2 + 4}[/tex]
[tex]\int\limits C {xy} \, ds[/tex] = [tex]\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt[/tex]
t = tanθ
dt = (1+[tex]tan^{2}[/tex]θ)dθ = ([tex]sec^{2}[/tex]θ)dθ
= [tex]\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt[/tex]
= 8(1+125[tex]\sqrt{110}[/tex]) / 15
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Can someone help me with this? I need an equation and the cup of nuts. It’s due tmr
Answer:
Step-by-step explanation:
I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)
2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]
[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2
[tex]1\frac{1}{2}[/tex] + x = [tex]2\frac{1}{4}[/tex]
x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]
There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.
nd the local maximum and minimum values and saddle point(s) of the function. you are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (enter your answers as comma-separated lists. if an answer does not exist, enter dne.) f(x, y)
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
saddle point : a point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs
The function :
f(x , y) = x³ = y³ = - 3x² - 3y² - 9x
The first partial derivative with respect to x is:
f' x = 3x²-6x-9
And the partial derivative with respect to y is:
f' y = 3y²-6y
Now equate the above derivatives to zero, to obtain the system of equation:
3x²-6x-9 = 0
3y²-6y = 0
On solving the two equations:
The critical points are : A(-1,0), B(-1,-2), C(3,0) and D(3,2)
Now calculate the discriminant
D = f xx(x , y)f y(x , y)-f xy(x , y)²
Here,
f xx = 6x-6
f yy = 6y-6
f xy = 0
On putting the above values we get:
D = (6x-6)(6y-6)
At, A(-1,0)
D = -18<0
Hence , A(-1,0) is a local maximum point.
At, B(-1,2)
D = -72<0
Hence B(-1,2) is saddle point.
At, C(3,0)
D = -72
Hence C(3,0) is also a saddle point
At, D(3,2)
D = 12>0
Hence , D(3,2) is the minimum point.
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
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291 is the same as 359 increased by the product of 125 and m
The equation 291 = 359 + 125m represents the given phrase, and the required value of m is 2.33
What is Algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
The equation 291 = 359 + 125m can be solved for m by subtracting 359 from both sides, resulting in:
291 - 359 = 125m - 359
-68 = 125m - 359
Adding 359 to both sides gives:
-68 + 359 = 125m
291 = 125m
Dividing both sides by 125 gives the solution for m:
291 / 125 = 125m / 125
2.33 = m
So, m is equal to 2.33.
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The question seems incomplete, the completed question would be as:
If 291 is the same as 359 increased by the product of 125 and m. what is the value of f?
the altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 9.5 centimeters and the area is 100 square centimeters?
So, the base of the triangle is decreasing at the rate of 1.6 cm/min.
Given that:
The altitude of is increasing at a rate of 1 centimeters/minute, which means;
dh/dt = 1 cm/min
The area of the triangle is increasing at a rate of 4 square centimeters/minute;
dA/dt = 4 cm2/min
When A = 100 cm2, h = 10 cm
We know that, area of a triangle is given by:
A = 1/2 × b × h
b = 20 cm
Let us differentiate both sides with respect to time:
dA/dt = 1/2 [b dh/dt + h db/dt]
Substituting the values
2 = 1/2 [20 × 1 + 10 × db/dt]
By further simplification, we get
4 = 20 + 10 db/dt
db/dt = -1.6 cm/min
Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.
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if r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?
a. 3 (6)-1/2(6) +1
b. (6)/ 2(6)+1
c. 36-1/26+1
d. (6)-1/(6)+1
If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
What are Algebraic Expression ?
The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : [tex]3x+7[/tex] .
Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;
we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;
By the Division Property of Algebraic Expression ;
it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;
So , Substituting [tex]x=6[/tex] , in r(x) ,
we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)
On Substituting [tex]x=6[/tex] , in s(x) ,
we get ; [tex]s(6) = 2(6)+1[/tex] , ....equation(2) ;
Substituting the values of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;
we get ;
⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;
Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
The given question is incomplete , the complete question is
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?
(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]
(b) [tex]\frac{(6)}{2(6)+1}[/tex]
(c) [tex]\frac{36-1}{26+1}[/tex]
(d) [tex]\frac{(6)-1}{(6)+1}[/tex]
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now using the right side of each slice as the height, sketch in 4 rectangles on your graph. find the area of these rectangles and add them up. this is your second approximation of the area under the curve, and hence ln(2). what is your answer (as a decimal with at least four digits of precision)? is this an over-estimate or an under-estimate
The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.
What is Geometry?
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
What is an area in math definition
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares
A slice is made parallel to the base of a right rectangular pyramid, as shown.
Then the area of the resulting two-dimensional cross-section will be
Area = 2 in × 2.5 in
Area = 5 in²
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what is the sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) ?
The sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) is 1440°
A polygon having ten sides (or a ten-sided polygon) is called a decagon or ten-gon, in geometry. Also, it has ten vertices and ten angles.
The summation of the interior angles of a polygon is ( n - 2 ) x 180 where n is the number of sides.
The sum of interior angles = (10 - 2) x 180
The sum of interior angles = 1440º
Therefore the measure of each angle is
10 angles = 1440
1 angle = 1440 ÷ 10 = 144º
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a carnival game offers a 100 cash prize for anyone whjo can break a balloon by throwing a dart at it. find the expected winnings
a carnival game offers a 100 cash prize for anyone whjo can break a balloon by throwing a dart at it. then The expected number of darts you'll throw is 3.44 darts .
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Expected = ∑ value * probability
= $1*0.01 + 2.(0.09) + 3(0.081) + 4(0.0729)
= 3.44
Thus, 3.44 darts .
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What is the difference between X1 and x1? O X1 is a random variable, and X1 is a specific numerical value. a. X1 is a random variable, and X1 is a specific numerical value. b. There is no difference. c. They are both random variables. d. There is no difference. e. They are both specific numerical values.
The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.
In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.
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Masha is three times as old as Pete. Their age difference is
10 years. How old is Pete?
Pete is
years old.
Answer:
Pete is 5
Step-by-step explanation:
Let Pete's age be x
Therefore Masha is 3x
since their age difference is 10,
3x - x = 10
2x = 10
x = 5
check:
3x = 15
x = 5
15 - 5 = 10
3/5 + 5/7 = ____
6/12 + 9/12 ____
1/4 + 4/4 = ____
2/3 + 5/3 = ____
(fractions please explain step by step how u got your answer)
The answers are 46/35 ,5/4, 5/4, 7/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: 3/5 + 5/7 = 46/35
6/12 + 9/12=5/4
1/4 + 4/4 = 5/4
2/3 + 5/3 = 7/3
Hence, The answers are 46/35 ,5/4, 5/4, 7/3
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a college student organization wants to start a nightclub for students under the age of 21. to assess support for this proposal, they will select an srs of students and ask each respondent if he or she would patronize this type of establishment. they expect that about 70% of the student body would respond favorably. what sample size is required to obtain a 90% confidence interval with an approximate margin of error of 0.04? show your work.
On solving the provided question we can say that at confidence Level = 90%, we have sample size = 423
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
Confidence Level = 90%
E = 0.04
Corresponding to 90%
confidence level role=="1654454884514" Z = 1.645
formula
n= p(1 - p)(0Z/E)
n = 0.50(1 - 0.50)(1.645/0.04)
= 422.816 = 423
so, sample size = 423
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A bottle holds 850 cL of water. How many liters does the pitcher hold?
Answer:
8.5
Step-by-step explanation:
850/100
Answer:
[tex]8.5l[/tex]
Step-by-step explanation:
1cl = 10ml
850cl = 8500ml
1000ml= 1l
8500ml= 8.5l
Graph the following:
a) y= 2(x-7)^2 -3 using 5 points
b) y= -(x+5)(x+1) using 3 points
A graph of this system of equations with the data points is shown in the image attached below.
How to graph this system of linear equations?In this scenario, we would use an online graphing calculator to plot the given system of equations by using five (5) points and three (3) points respectively;
y = 2(x - 7)^2 - 3 ........equation 1.
y = -(x + 5)(x + 1) ........equation 2.
Generally speaking, the solution to any system of equations is the point of intersection of the lines on the graph representing each of them.
In this scenario, the points that are located on the line of the graph of this equation y = 2(x - 7)^2 - 3 include the following:
Ordered pair (5, 5).
Ordered pair (10, 15).
Ordered pair (7, -3).
Ordered pair (5.775, 0).
Ordered pair (8.225, 0).
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steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 7 am, and walks steadily at 3 miles per hour. elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 10 am. when will the distance between them be 35 miles? (round your answer to the nearest minute.)
At 2.57 hours distance between them is 35 miles
(2t)2 + (2.5(t - 2))2 = 302
4t2 + (2.5t - 5)2 = 900
4t2 + 6.25t2 - 25t + 25 = 900
2.25t2 - 25t - 875 = 0
Let t (hours) be the amount of time Elsie needs to travel in order to reach a distance of 35 miles. Steve travels t + 2 miles to the north in the time it takes him since he is 2 hours early.
Solve for t, then add to 7:00 for your time.
which will give you 2.57 hours.
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The correct question will be
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 3 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 9 AM.
When will the distance between them be 35 miles?
Isabelle was curious if sample maximum was an unbiased estimator of population maximum. She started with a large normally distributed population of test scores whose maximum was 999999 points. She then took a random sample of 666 tests and calculated the maximum of the sample. She replaced those tests and repeated this process for a total of 404040 trials. Her results are summarized in the dotplot below, where each dot represents the maximum score from a sample of 666 tests.
Isabelle concluded that the sample maximum is an unbiased estimator of the population maximum.
What is value?Value is a term used to describe the worth of something. It can refer to monetary value, but it can also be used to describe the worth of intangible things such as relationships, ideas, and experiences. Value creates an understanding between two parties, as each may have a different opinion on what something is worth. It can be seen as an exchange or trade of something that both parties consider to be of equal or greater value.
This conclusion is supported by the high number of samples that had a maximum value of 999999. The dotplot shows that the sample maximum was 999999 in over 95% of the trials. The other samples had maximum values that were lower, but still close to the true maximum of 999999. This indicates that the sample maximum did not systematically overestimate or underestimate the population maximum.
The sample maximum was also consistent across the different trials, with the majority of the samples having a maximum value near 999999. This consistency indicates that the sample maximum is a reliable estimator of the population maximum. While there is always a chance that the sample maximum may deviate from the population maximum, the results suggest that the sample maximum is unbiased and reliable for estimating the population maximum.
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A cereal box has dimensions of 12 inches, 7~
4
inches, and 2 inches. A pastry box
has dimensions of 3.
} inches, 3.
¿ inches, and 2¾ inches, Whatis the difference
in volume, in cubic inches, between the two boxes?
Answer:
To find the volume of the cereal box, we multiply the length, width, and height:
12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches
To find the volume of the pastry box, we multiply the length, width, and height:
3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches
To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:
1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches
So the difference in volume between the two boxes is 1432.842 cubic inches.
Answer:1432.842 cubic inches
Step-by-step explanation:
Shawndra said that it is not possible to draw a trapezoid that is a rectangle, but it is possible to draw a square that is a rectangle. Marcella said that it is possible. Who is correct
Marcella is correct. A square is a type of rectangle.
A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides. Thus, it is not possible to draw a trapezoid that is also a rectangle. However, a square is a four-sided plane figure with four equal sides and all four right angles, making it a type of rectangle. Therefore, it is possible to draw a square that is a rectangle.
A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides.
Marcella is correct. A square is a type of rectangle.
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A television station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.3 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 5 minutes. Calculate the z-score for this amount of advertising time.
The z-score for this amount of advertising time will be -5.217.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A TV slot guarantees how much promotion each hour of transmission time has a normal of 17 minutes and a standard deviation equivalent to 2.3 minutes.
The amount of advertising time is equal to 5 minutes. Then the z-score is calculated as,
z = (5 - 17) / 2.3
z = -12/ 2.3
z = -5.217
The z-score for this amount of advertising time will be -5.217.
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In the figure below, which term best describes point W?
A. Incenter
B. Centroid
C. Orthocenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?
" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
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Hannah has two bags of sweets.
In the first bag there are 5 red sweets and 7 green sweets.
In the second bag there are 7 red sweets and 4 green sweets.
Harmah takes at random a sweet from the first bag.
She then takes at random a sweet from the second bag.
(a) Complete the probability tree diagram.
first bag
red
green
11
second bag
red
(b) Work out the probability that Hannah takes two green sweets.
green
. red.
green
(2)
28
The size of each interior angle of an
Work out how many sides the poly
Answer:
(a) Refer below for the Probability tree diagram
(b) [tex]\frac{7}{33}[/tex]
Step-by-step explanation:
(a) Probability tree diagram:
First bag: Second bag
Red: [tex]\frac{7}{7 + 4}[/tex] = [tex]\frac{7}{11}[/tex]
Red: [tex]\frac{5}{12}[/tex]
Green:[tex]\frac{4}{7 + 4}[/tex] = [tex]\frac{4}{11}[/tex]
Red: [tex]\frac{7}{11}[/tex]
Green [tex]\frac{7}{12}[/tex]
Green: [tex]\frac{4}{11}[/tex]
(b) Probability that Hannah takes two green sweets:
Green sweet from first bag AND green sweet from second bag
= [tex](\frac{7}{12}).(\frac{4}{11} )[/tex]
= [tex](\frac{28}{132})[/tex]
Divide the numerator and denominator by the highest common factor (i.e 4)
= [tex]\frac{7}{33}[/tex]
act math scores are approximately normally distributed, with a mean of 21 and a standard deviation of 5.4. if eli decides to take the act exam, what would he need to score in order to be in the 85th percentile?
In order to be in the 85th percentile Eli would need to score 26.62.
What is called percentile?In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.
Given that act math scores are approximately normally distributed,
mean (μ) = 21 and a standard deviation (σ) = 5.4
percentile P(X>x) = 85 =0.85
P(z<x) = 0.85
z = 1.04
y the formula
z = (x - μ)/ σ
⇒ 1.04 = (x - 21)/5.4
⇒ 1.04*5.4 = x - 21
⇒ 5.616 = x - 21
⇒ x = 5.616 + 21
⇒ x = 26.62
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given the function defined in the table below,find the average rate of change,in simplest form,of the function over the interval 12
Answer: The average rate of change over the interval 12 < x < 30 is -4/3
Step-by-step explanation:
The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.
Given the table:
f(30) = 16 and f(12) = 40
The average rate of change over the interval 12 < x < 30 is:
(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3
So the average rate of change over the interval 12 < x < 30 is -4/3
It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.
A line passes through the point (5, -3) and has a slope of -3. Write an equation in .point-slope form for this line.
Work Shown:
y - y1 = m(x - x1)
y - (-3) = -3(x - 5)
y + 3 = -3(x - 5)
Explanation:
The variable m refers to the slope. The point (x1,y1) is on the line. We do not distribute the -3 through to the terms in (x-5), nor do we isolate y, since your teacher wants this in point-slope form.
The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The two companies, Shirt Box and Just Tees, are represented by this system of equations where x is the number of T-shirts and y is the total cost of the T-shirts. y
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost
The definition of a linear equation.A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.
Here,
The first company's equation is y = 10.5x.
Additionally, the second company's equation is y = 7.5x + 30.
Where
number of T-shirts equals x.
y = overall cost
For the overall cost to be the same for both businesses, we have to:
=> 10.5x = 7.5x + 30
=> 10.5 x - 7.5 x = 30
=> 3 x = 30
=> x = 30/3
=> x = 10
To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.
Total for each business:
=> 10.5x = 10.5 (10) = $ 105
OR
Totals for each company are calculated as follows:
=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30
=> $105
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost.
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Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).
Select the "Polygon" button from the toolbar to plot your triangle. You may use the "Move" button to move the triangle after it is created.
A graph of the image of the triangle with vertices (4, 7), (3, 4), and (8, 2) after a transformation with the rule (x, y) → (−x, y) is shown in the image attached below.
What is a reflection?In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of this triangle the image coordinates include the following:
(x, y) → (-x, y)
Coordinate A = (4, 7) → Coordinate A' = (-(4), 7) = (-4, 7).
Coordinate B = (3, 4) → Coordinate B' = (-(3), 4) = (-3, 4).
Coordinate C = (8, 2) → Coordinate C' = (-(8), 2) = (-8, 2).
Next, we would use an online graphing calculator to plot the coordinates of the image as shown in the image attached below.
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Find the area of shaded figure, use units squared
Answer:
43.5 square units
Step-by-step explanation:
You want to know the area of shading in a 12 by 7 rectangle with a white right triangle of side length 9 removed.
Triangle areaThe area of the white triangle is ...
A = 1/2bh
A = 1/2(9)(9) = 40.5 . . . . square units
Rectangle areaThe area of the rectangle is ...
A = LW
A = (12)(7) = 84 . . . . square units
Shaded areaThe shaded area is the area of the rectangle that is not included in the triangle.
Shaded area = 84 -40.5 = 43.5 . . . . square units
__
Additional comment
The given figure cannot actually be constructed. The triangle is too large to be inscribed in the rectangle. An inscribed right triangle can have a side length between 7 and √74 ≈ 8.6.
junior secondary Use elimination method to solve the following simultaneous equations: 10m-7n=26
7m+7n=42
Using Elimination method the simultaneous equations is -16/3.
How can a three-step elimination equation be solved?Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.
In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.
The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.
10m-7n=26
- 7m+7n=42
3m = -16
m = -16/3
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