Which of the following is a solution of the linear equation 3x 2y 5?
The general solution of the linear equation 3x + 2y = 5 is y = (-3/2)x + 5/2.
To find the solution of the linear equation 3x + 2y = 5, we can use the method of isolating one variable and then substituting that value back into the equation.
3x + 2y = 5
First we can try to isolate y:
2y = -3x + 5
then we divide by 2
y = -(3/2)x + 5/2
So one solution of the equation is (x,y) = (-(3/2)x + 5/2)
Therefore, the solution of the linear equation 3x + 2y = 5 is y = -(3/2)x + 5/2.
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3. For the polynomial function A(x) = x4 - 2x³ - 21x² +22x + 40 we know (x - 5) is
a factor. Select all the other linear factors of A(x).
A. (x + 1)
B. (x - 1)
C. (x + 2)
D. (x - 2)
E. (x+4)
F. (x-4)
G. (x + 8)
ion with its constant term.
#3
Answer:A,D,E,F
Step-by-step explanation:A(x) = x4 - 2x³ - 21x² +22x + 40= A,D,E,F
Given the right triangle ABC with Altitude BD drawn to hypotenuse AC.If AD=11 and BD=33 What is the length of DC
Answer:
DC = 99
Step-by-step explanation:
BD perpendicular AC
AD/BD = BD/DC
=> DC =DB^2/AD
=33^2/11=99
{calculate}
HELP PLEASE ILL GIVE 50 POINTS PLEASE DUE AT 11:59 WHERE I LIVE I HAVE AN HOUR!!!
i need a conclusion paragraph to the question - Was Abby Sunderland too young to sail solo? - SAYING THAT SHE WAS!
pleaseee the best conclusion will get brainliest!!!!!!!!!!
i am aware the subject is math accident
Answer:
Step-by-step explanation:
In conclusion, it can be argued that Abby Sunderland was too young to sail solo. Despite her ambitious and determined nature, her lack of experience and maturity put her at a significant risk during her solo sailing journey. The fact that she had to be rescued twice during her attempt highlights the dangers of attempting such a feat at such a young age. While it is admirable to have the courage to pursue one's dreams, it is important to consider the potential consequences and weigh them against the potential benefits. In this case, it can be argued that the risks far outweighed the potential rewards.
A coffee shop sells a mug for $8.95. Each refill costs $1.50. Last month Rose spent $26.75 on a mug and refills. How many refills did she get?
Rose gets 12 refills by a coffee shop.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A coffee shop sells a mug for $8.95. Each refill costs $1.50.
And, Last month Rose spent $26.75 on a mug and refills.
Let number of refills she get = x
So, We can formulate;
⇒ $8.95 + $1.50x = $26.75
⇒ 8.95 + 1.50x = 26.75
⇒ 1.50x = 26.75 - 8.95
⇒ 1.50x = 17.80
⇒ x = 17.8 / 1.5
⇒ x = 12
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Let $\angle D$ be an acute angle uch that $\co D=0. 33$. Ue a calculator to approximate the meaure of $\angle D$ to the nearet tenth of a degree
Let angle D be an acute angle such that D=0. 33. The measure of angle D is 70.7 degree.
Acute Angle:
An angle is formed when two rays meet at a vertex. If this angle is less than 90°, it is called an acute angle. In the image below, the angle formed between "Ray 1" and "Ray 2" is acute. Bisecting a right angle also creates two acute angles.
Inverse Cosine :
Inverse cosine is the important inverse trigonometric function. Mathematically, it is written cos-1(x) and is the inverse of the trigonometric cosine cos(x). Note that arc cosine is not the reciprocal of cos x. There are six inverse trigonometric functions like sin-1x, cos-1x, tan-1x, csc-1x, sec-1x, cot-1x. The arc cosine is used to determine angular measurements from the trigonometric ratio cos x values.
According to the question:
To approximate the measure of angle D, we will need to use the inverse cosine function on our calculator. All calculators vary, so I am not sure where you would find the button for it on your calculator. However, I know many calculators have it so you click the second button, then cos
cos(D) = 0.33
⇒ D = cos^-1 (0.33)
⇒ D = 70.7 degrees
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Graph the points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) on the coordinate plane.
The points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)
What is the coordinate plane?The Cartesian coordinate system on a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates.
These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph).
The orientation of these two axes is perpendicular.
The graph's exact center is marked by the origin (O).
So, we have the points:
(4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5)
Now, the graph is as follows:
(Refer to the graph attached below)
Therefore, the points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)
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How many solutions the linear equation 2x y 10 has?
The linear equation [ ( 2x PLUS y ) EQUALS 10 ] has only one solution.
A linear equation is an algebraic equation having the form y=mx+b, involving only a constant and a first-order (linear) term, where b is the y-intercept and m is the slope. Occasionally, the above is called a 'linear equation of two variables,' where x and y are the variables.
Now solve the given linear equation which is:
[ ( 2x + y ) = 10 ]
Now solve this equation in order to determine the number of solutions it has,
( 2x + y ) = 10
( 2x + (10 - 2x)) = 10
( 2x + 10 - 2x) = 10
( 2x + 10 - 2x) = 10
(10) = (10)
Since 10 = 10 is correct, therefore, the equation ( 2x + y ) = 10 has only one solution.
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what is the probability that this dancer raised less than £10
The probability that this dancer raised less than £10 is; 19/30
How to find the probability?Probability is defined as the number of successful outcomes divided by the total number of outcomes. Thus;
Probability = number of successful outcomes/total number of outcomes
From the attached table, we see that;
£4.99 of less: Number of dancers are 15
£5 to £9.99: Number of dancers are 23
£10 to £14.99: Number of dancers are 12
£15 to £19.99: Number of dancers are 7
£20 to £24.99: Number of dancers are 3
Thus, we see that the total number of dancers = 15 + 23 + 12 + 7 + 3 = 60 dancers.
If a dancer is chosen at random, the probability that the dancer raised less than £10 = (23 + 15)/60 = 38/60 = 19/30
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Complete question is;
A group of dancers raised some money for a charity here is some information about the money raised
One of the dancers is chosen at random to give the money raised to the charity
What is the probability that this dancer raised less then £10
Write down the ratio 600 km to 12 km.
Give your answer in its lowest form.
Answer:
50 km : 12 km
Step-by-step explanation:
600 km : 12 km
=50 km : 1 km.
Suppose a supermarket wants to sell eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different sized cartons?
The maximum price per egg that the supermarket may charge is $0.245 per egg, which is the difference between the pricing per egg for the 2 distinct cartons.
What do you meant by the term unitary method?The unitary approach involves calculating the price of a specific unit, from which we can calculate the values of the necessary number of units.The answer to the query is
The following details are available to us:
A carton of 12 eggs costs $3.00.18 eggs in such a different carton cost $4.32.We'll first calculate the cost per egg for each of the two different-sized cartons in order to determine the cost per egg that lies between the two costs.
We are aware that the cost of one product is determined by dividing the total cost by the quantity of products.
12 eggs cost in a carton = $3.001 eggs cost = $ (3.00/12) = $0.2412 eggs cost in a second carton = $4.321 eggs cost = $(4.32/18) = $0.24The price of an egg between 0.24 as well as 0.25 must now be determined.
Note that there is a 0.01 difference between the two fees.
To precisely determine the middle charge, we will split it by two:
0.01/2 = 0.005
This can be added to $0.24 or subtracted from $0.25.
$0.24 + $0.005 = $0.245
So, $0.245 is the maximum price the supermarket can charge per egg.
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The complete question is-
A carton of 12 eggs costs $3.00. A carton of 18 eggs costs $4.32. Suppose a supermarket wants to sell the eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different-sized cartons? Explain
whats the intercepts of 2x+y=1 and x-2y=8
Answer:
Step-by-step explanation:
I will assume you want the y-axis intercepts
arrange each equation into the form y = mx + b <==b is y-axis intercept
2x+y =1
y = -2x+1 <==== y axis intercept = 1
x -2y = 8
2y = x-8
y = 1/2x -4 <==== - 4 is the y axis intercept
Another way to find the y-axis intercept is to realize this occurs when x = 0
put x = 0 into the equations to find the intercept value
2x+y =1
2(0) + y = 1
y =1 <=====intercept
x-2y = 8
0 - 2y = 8
y = -4 <=====intercept
To find the where the two lines intersect, equate them
-2x+1 = 1/2x-4
5 = 2.5x
x = 2 then y = -2x+1 = -3 point of intersection (2,-3)
Please help me with my classwork
Answer: 21d^7
Step-by-step explanation:(7x3) x d^(5+2)
= 21 d^7
Answer:
(7d^5)(3d^2)
7*3 = 21
5+2 = 7
21d^7
6. Construction A total of 18.6 cu yd of concrete is required for pouring a
foundation. The ratio of cement to sand to gravel for this application is
1:2:4, and the total amount of these components must be 1½ times the vol-
ume of concrete needed. Use the method of Example 4 to determine how
many cubic yards of each component are needed.
The number of cubic yards of each component needed are 3.99 cubic yards of cement, 7.97 cubic yards of sand and 15.94 cubic yards of gravel
How to determine how many cubic yards of each component are needed?
Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another
Since a total of 18.6 cu yd of concrete is required and the total amount of these components must be 1½ times the volume of concrete needed. We can say:
total amount of these components = 1½ × 18.6 cu yd = 27.9 cu yd
Also, since the ratio of cement to sand to gravel for this application is 1:2:4. We have:
Total share = 1 + 2 + 4 = 7
cement = 1/7 × 27.9 = 3.99 cubic yards
sand = 2/7 × 27.9 = 7.97 cubic yards
gravel = 4/7 × 27.9 = 15.94 cubic yards
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enlarge shape q by a scale factor of -1/2 around the centre point (0,0
The new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
A scale factor of -1/2 around the center point (0,0) would reflect the shape across the origin and also shrink it by a factor of 1/2.
The transformation can be represented by the matrix:
[-1/2 0]
[ 0 -1/2]
This matrix would be applied to the coordinates of each point in the shape to obtain the new coordinates of the transformed shape.
So, if a point in the shape had coordinates (x, y), the new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).
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The question seems to be incomplete the correct question would be:
Enlarge shape q by a scale factor of -1/2 around the center point (0,0). if a point in the shape had coordinates (x, y), what are the new coordinates?
54+23+98+15+09+908
help pls
Answer:
1,107 is your answer
Step-by-step explanation:
2.Which of the following relations is a function?And why?
a. (1,0), (2,0)(3,4)
b. (1,0), (2,0)(2,4)
c. (1,0), (2,0)(3,0)
Answer:
A and B
Step-by-step explanation:
theres one input for each ouput
line L has equation y=1 find the distance between L and the point T(-1,-7)
round answer to nearest tenth
The distance between the line and the point is 8 units.
What is the cartesian plane?When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.
Given a line L,
and the equation of a line is y = 1
actual equation of line is ax + by +c = 0
equation of line is 0x + y - 1 = 0
here a = 0, b = 1 and c = -1
and point T(-1, -7)
distance between line and the point is d = [tex]\frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2} }[/tex]
x₁ = -1, y₁ = -7
|ax₁ + by₁ + c| = |0(-1) + 1(-7) +(-1)|
|ax₁ + by₁ + c| = 8
√(a² + b²) = √(0² + (1)²) = 1
distance between line and the point is d = 8/1 = 8 units
Hence the distance is 8 units.
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A line that passes through the point (1,-6) and has the slope of -9
Write an equation in point slope form for this line
Which type of polynomial has no zero?A) Touches X-axis at any pointB) Intersects X-axis at two distinct pointsC) Does not intersect X-axis at any pointsD) Is in any half-plane of the X-axis.
In mathematics, an algebraic expression is an assertion built up from integer constants, variables, and algebraic operations. This article is all about to Monomials, Binomials, and Polynomials.
1. Monomial
An algebraic expression that carries only one non-zero term is known as a monomial. A monomial is a just like a type of polynomial, like, binomial and trinomial, which is an algebraic expression having only a one single term, which is a non-zero.
It comprises of only a single term which makes it easy to do the operation of addition, subtraction, and multiplication.
2. Binomial
An algebraic expression that comprises of two non-zero terms is known as a binomial. It is expressed in the form equation ax ^m + bx ^n where a and b number, x is variable, m and n are nonnegative distinct integers.
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Jason bought a total of 7 post-cards for $1.80. If the small postcards cost 20c each and the large ones cost 30c each, how many postcards of each size did he buy
Answer:
3 small postcards; 4 large postcards
I know this. Hope it helps :)
Answer:
4 large post cards and 3 small ones
2 1/5 x 2 2/3 fravction
To multiply two mixed numbers, you can convert them to improper fractions and then multiply the numerators and denominators separately.
2 1/5 can be written as (2 x 5 + 1) / 5 = 11/5
2 2/3 can be written as (2 x 3 + 2) / 3 = 8/3
So the product of 2 1/5 x 2 2/3 is (11/5) * (8/3) = 88/15 which is equivalent to 5 8/15 or 5.533 repeating (if you want to express it as decimal)
You can simplify 88/15 by dividing both numerator and denominator by the greatest common divisor (GCD) which is 1 in this case, so the final result is 88/15.
A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If P, is the proportion of smokers in the population who have had a drink in the past week and Po is the corresponding proportion of non-smokers, then a test of the hypotheses H P, -P = 0 against the two-sided alternative produces a test statistic of := 3.07 and a P-value of 0.002. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and P-value?
a. 7-9.42, P-value = 0.002
b. 7-9.42, P-value - 0.004
c. - 3.07, P-value = 0.004
The Correct answer is option a. 7-9.42, P-value = 0.002 which is derived based on the given data about alcohol consumption.
The chi-square test of homogeneity is a statistical test used to determine whether there is a significant difference between the observed frequencies of two categorical variables.
In this case, the test statistic would be the chi-square value calculated using the observed frequencies of alcohol consumption in the sample of smokers and non-smokers, and the P-value would be the probability of obtaining a chi-square value as extreme or more extreme than the calculated value under the assumption that the null hypothesis is true (i.e. no difference in alcohol consumption between smokers and non-smokers).
In this case, the test statistic would be 7.942 and the P-value would be 0.002 which implies that there is a significant difference in alcohol consumption between smokers and non-smokers.
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What are types of exponents?
Exponents can be classified into four types: integer, rational, irrational, and complex exponents. They represent repeated multiplication, roots, and advanced concepts such as complex numbers.
Integer exponents are the most common type of exponents and include positive integers, negative integers, and zero. They are used to represent repeated multiplication, for example, 2^3 represents 2 multiplied by itself 3 times.Rational exponents are the exponents which can be written in the form of a fraction, for example, (2^(1/3)) represent the cube root of 2.Irrational exponents, as the name implies, are exponents that are irrational numbers, for example, 2^(1.23).Complex exponents are the exponents which are complex numbers, for example, 2^(3+4i). These exponents are less common and typically seen in advanced math and engineering.Learn more about Types of Exponents here:
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How do you find the center of dilation with a compass?
To find the center of dilation,We'll fix our compass to a distance that is closer to the overall distance but still greater than halfway between vertex L and point C. Start with the compass's point on vertex L while maintaining the same distance, and then draw a curve that intersects the line connecting L and C.
What is Centre of dilation?Centre of dilation of an image in mathematics refers to a change that results in an image with the same shape but a different size, either larger or smaller. A dilation can only be built with two bits of information.
An operation that moves, flips, or otherwise alters a figure to produce a new figure is called a transformation. Rigid transformations maintain size, whereas non-rigid transformations do not. A dilatation enlarges or reduces a figure while maintaining its original shape. To put it another way, the dilatation resembles the original. Every dilatation has a scale factor and a centre. The scale factor indicates how much the figure stretches or contracts, and the centre serves as the point of reference for the dilation (much like the vanishing point in a perspective drawing). A scale factor is usually identified by a label and is never zero. Additionally, the dilatation would be if the original figure were labelled, for example.
The point from which the image is dilated is known as the centre of dilatation (or point of dilation).
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Find (13x−3)+(−34x−5)
Answer: -21x-8
Step-by-step explanation:
Combine the like terms
martha and axel went to the store to buy 3 apple, but only had a buget of 5 dollars
Answer:
i need more information to answer your question
Step-by-step explanation:
Combine like terms 3x-7x=
Answer:
-4x
Step-by-step explanation:
3-7=-4 just add a x
Which one of the following is not equivalent to P <-> q?p only if qq is necessary for pq only if pp is sufficient for q
if pp is sufficient for q is not equivalent to P <-> q for p and q conditional statement
The true statements for the conditional statement p → q are;
If p then q
p, therefore q
q, if p
p is enough condition for q
Reason for the above selection
The conditional statement p → q is read as If p then q
The deductive validity of the conditional statement is; p, therefore q
The conditional statemen, p → q also means;
1) q, if p
2) q, provided p
3) p, only of q
4) p implies q
5) q whenever, p
6) p is enough condition for q
7) q is a necessary condition for p
Therefore, the correct statements are;
If p then q
p, therefore q
q, if p
p is enough condition for q
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How do you dilate a shape with a scale factor?
Dilating a shape with a scale factor is a process of enlarging or shrinking a shape.
What is scale factor?Scale factor the research between two corresponding length area of the volumes of two similar figure it is used to compare the size of one figure to another as well as the enlarge of reduced to size of a figure the scale factor is expressed as the ratio searches one it's to one.
It can be done using a compass or a ruler. First, measure the length of the side of the shape and calculate the scale factor. Then, use the compass or ruler to draw a line that is the length of the side multiplied by the scale factor. Finally, join the new line with the other side of the shape to complete the dilation.
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