You have the following equation:
x - 3 = x²
In order to determine if the given equation is linear in x, you consider that a linerar equation is an equation in which the maximum exponet of the variable is 1. In this case you have that the higher exponent of the variable, which is x, is 2. 2 is the higher exponent, Becuase of that, the given equation is not linear, instead of that, the equation is quadratic.
17. John is making flower arrangements. He has 45 roses, 27 irises, and 18daisies. What is the GREATEST number of bouquets he can make using atleast one of each flower and each bouquet having the SAME arrangement?(He has to use ALL the flowers) *Options 452193
To find the greates number of bouques he can make, we need to find the greatest number that divdes the three numbers: 45, 27 and 18.
45 can be divided by the following numbers:
1,3,4,5,9,15,45
27 can be divided by the following numbers:
1,3,9,27
18 can be divided by the following numbers:
1,2,3,6,9,18
From the divisors of the three numbers we can see that the greatest number that divide the three of them is 9.
Thus, 9 is the greatest number of bouquets he can make using at leat 1 of each. Also those 9 bouquets would have all the same arrengement.
Answer: 9
picture to the problem sented
Answer:
Explanation:
For the matrix equation
[tex]2X+A=B[/tex]We first subtract A from both sides to get
[tex]2X=B-A_{}[/tex]Now,
[tex]B-A=\begin{bmatrix}{-7} & {-8} & {} \\ {-2} & {6} & {} \\ {4} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-3} & {0} & {} \\ {0} & {3} & {} \\ {-6} & {6} & {}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-7--3} & {-8-0} & {\square} \\ {-2-0} & {6-3} & {\square} \\ {4--6} & {4-6} & {\square}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Hence, we have
[tex]2X=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Dividing both sides by 2 gives
[tex]\begin{gathered} X=\frac{1}{2}\cdot\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix} \\ \end{gathered}[/tex][tex]X=\begin{bmatrix}{-5} & {-4} & {} \\ {-1} & {-\frac{3}{2}} & {} \\ {5} & {-1} & {}\end{bmatrix}[/tex]which is our answer!
line g has an equation of y=-10x-2. Line h, which is perpendicular to line g, includes the point (4,1). what is the equation of line h?
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Given the equation of the line "g":
[tex]y=-10x-2[/tex]You can identify that:
[tex]\begin{gathered} m_g=-10 \\ b_g=-2 \end{gathered}[/tex]By definition the slopes of perpendicular lines are opposite reciprocals. Then, the slope of the line "h" is:
[tex]m_h=\frac{1}{10}[/tex]Knowing a point on the line "h" and its slope, you can substitute them into the equation
[tex]y=m_hx+b_h[/tex]And solve for the y-intercept:
[tex]\begin{gathered} 1=\frac{1}{10}(4)+b_h \\ \\ 1=\frac{2}{5}+b_h \\ \\ b_h=\frac{3}{5} \end{gathered}[/tex]Then, the equation of the line "h" is:
[tex]y=\frac{1}{10}x+\frac{3}{5}[/tex]What is the word for added and subtracted parts of an expression
The word for added and subtracted parts of an expression is known as the term.
What is an expression?An expression in math is an arithmetic set of numbers and variables with signs and calculations. For example, 4x - 2x = 2x is an expression. The parts that are connected with addition or subtraction or other signs are called terms.
Terms that have the same base exponent can be joined with addition and subtraction. These are called like terms. For example, 3 x 3 and 5 x 3 are like terms.
Therefore, the term is the term for the added and removed components of an equation.
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24.) In the figure below, Z1 is supplementary to z3 under which of the followingconditions?F Line a is parallel to line bG Line a is parallel to line c.H Line a is perpendicular to line c.J Line b is perpendicular to line c.the
For this statement to be true, the only condition that is necessary is that Line a is parallel to Line b. The right answer is the first one.
help me please
thank you
The domain is (2,4,6,8,10,12,14) and range is (8,6,4,2,0,2,4).
What is domain and range?The domain of a function refers to the set of values that we are allowed to enter into our function.
The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values , the y values are these.
The range and domain must be understood to be all the values that the variable y can represent, respectively, and the x values.
Since the ordered pairs have the form (x,y), we can determine the values of x and y.
The x and y values of function are:
F(x,y) = (2,8), (4,6), (6,4), (8,2), (10,0), (12,2), (14,4)
Domain (x) = (2,4,6,8,10,12,14)
Range (y) = (8,6,4,2,0,2,4)
.
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In the circle below, G is the center, LM Is a diameter, HF intersects the circle at M, and JN intersects the circle at K and L. Useblanks.
HF, JN
1) Examining this question, we can state that a tangent line is the one that "touches" the circle in one single point.
So, in this diagram we can state that the tangent line is HF
2) On the other hand, a secant line crosses the circle in two points at least. So the one that fits in this definition is the line defined by points JN
3) In Euclidian Geometry, a chord is a line segment that connects two points in a circle or curve. Examning the diagram again, we can state that KM is a chord.
2 subtracted from the product of 5 and a number
Answer:
5x-2
Step-by-step explanation:
the 'x' is "a number"
If the size of an object is 5.0 cm, and the size of the image formed by a lens is 15.0 cm, what is the magnification of the system?
The magnification of the system with an object distance of 5 cm and an image distance of 15 cm is 0.33.
A lens is a transmissive optical tool that employs refraction to focus or disperse a light beam.
In optics, magnification refers to the image's size in relation to the item that produced it. The ratio of the image length to the object length, as measured in planes perpendicular to the optical axis, is referred to as linear magnification, also known as lateral or transverse magnification.
The size of an object is u = 5 cm
The size of the image formed by the lens is v = 15 cm
Then the magnification M will be:
Magnification = Image distance/ Object distance
M = v/u
M = 5/15
M = 1/3
M = 0.33
Hence, the magnification of the system is 0.33.
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Solve the system using the elimination.
On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .
in the question ,
the two equations are given as
3x+y=6 ...(i)
and
-8x+2y= -2 ...(ii)
In elimination method, the equation is multiplied by some constant and then add/subtract the equations to eliminate any variable x or y.
multiplying equation(i) by 2 we get
6x+2y=12 ....(iii)
subtracting , the equation (ii) from equation (iii) , we get
(6x+2y) - (-8x+2y) = 12-(-2)
6x+2y+8x-2y = 12+2
14x = 14
x = 1
We eliminate 'x' from equation (ii) by replacing the value of 'x' with 1 ,
we get
-8x+2y= -2
-8(1)+2y= -2
-8 + 2y = -2
2y = -2 + 8
2y = 6
y = 3
Therefore , On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .
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x +3 +7 = 2x -10 -x how many solutions does it have
Answer:
no solution
Step-by-step explanation:
x + 3 + 7 = 2x + 10 - x ( simplify both sides )
x + 10 = x - 10 ( subtract 10 from both sides )
x = x - 20 ( subtract x from both sides )
0 = - 20 ← not possible
this indicates the equation has no solution
Pls explain I have a test on this number 2
Hello there. To solve this question, we have to remember some properties about equations of circles.
Given the following equation:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]It is called the equation of a circle with center at
[tex](x_0,\,y_0)[/tex]And radius R.
In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).
We have that
[tex](x+4)^2+(y-2)^2=16[/tex]Is the equation of a circle with center at (-4, 2) and radius equal to
[tex]R=\sqrt{16}=4[/tex]For the other equation
[tex](x-2)^2+(y-5)^2=64[/tex]Is also the equation of a circle, with center at (2, 5) and radius equal to
[tex]R=\sqrt{64}=8[/tex]Help mee pleasee!!
thank you <3
Answer:
never to leave the unknown shackspeare
Step-by-step explanation:
it never leaves
or never stays
and never comes back
George is putting trim around his rectangular deck, including the gate. He will need 50 feet of trim to do the entire deck. If the deck is 15 feet long, how wide is the deck?OA. 8 feetOB. 25 feetOC. 10 feetOD. 20 feet
George is putting trim around the rectangular deck, this means that he is surrounding the deck's perimeter with trim.
You know that he needs 50ft of trim to do the entire deck, this value represents the perimeter of the rectangular deck, and the length of the deck is 15ft.
Knowing the perimeter (P) and the length (l) of the rectangular deck, you can calculate the width (w) of the deck.
The formula for the perimeter of the rectangle is:
[tex]P=2l+2w[/tex]Write the formula for w:
[tex]\begin{gathered} P=2l+2w \\ P-2l=2l-2l+2w \\ P-2l=2w \\ \frac{P-2l}{2}=\frac{2w}{2} \\ w=\frac{P-2l}{2} \end{gathered}[/tex]Use P=50ft and l=15ft to calculate the width:
[tex]\begin{gathered} w=\frac{50-(2*15)}{2} \\ w=\frac{50-30}{2} \\ w=\frac{20}{2} \\ w=10ft \end{gathered}[/tex]The width of the deck is 10ft (option C)
the desnity of the conrete is 2400
what is mass
Answer:
360000
Step-by-step explanation:
Fourteen percent of the town's population is over the age of 65. If there are 322 residents over the age of 65, approximately what is the town's population?
If 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
The percentage of people over the age of 65 = 14%
Number of residents over the age of 65 = 322
Consider the total population of the town as x
Then the equation will be
x × (14/100) = 322
From this equation we have to find the value of x, that is the population of the town.
x × (14/100) = 322
x × 0.14 = 322
x = 322/0.14
x = 2300
Hence, if 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
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Nixon will pay for his new car in 36 monthly payments. if his car loan is for 19,061, THEN HOW MUCH will pay each month
4. Tyrell bought 4 pizzas and 5 subs and his bill was $56.25. Annabel bought 3 pizzas and 7 subs and her bill was $59.25. How much does each item cost?
let p represent pizza
let s represent subs
when he bought 4 pizza and 5 subs bill is $56.25
[tex]4p\text{ + 5s = 56.25 --------1}[/tex]when he bought 3 pizzas and 7 subs his bill is $59.25
[tex]3p\text{ + 7s = 59.25}--------2[/tex]solving the two equations simultaneosly
[tex]\begin{gathered} 4p\text{ + 5s = 56.25 x 3 (multiply equation 1 by coefficient of p in equation 2 i.e 3)} \\ 3p\text{ + 7s = 59.25 x 4 ( multiply equation 2 by coefficient of p in eqaution 1 i.e 4)} \\ \text{these multiplications gives equation 3 and 4 below} \end{gathered}[/tex][tex]\begin{gathered} 12p\text{ + 15s = 168.75 -------3} \\ 12p\text{ + 28s = 237}--------4 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{subtracting equation 3 from 4, p is eliminated and the equation below is obtained} \\ 13s\text{ = 68.25} \\ (i\mathrm{}e\text{ 12p - 12p) + (28s-15s) = 237-168.75)} \end{gathered}[/tex]divide both side by 13
[tex]\begin{gathered} \frac{13s}{13}=\frac{68.25}{13} \\ s\text{ = 5.25} \end{gathered}[/tex]substitute s= 5.25 in equation 1
4p + 5(5.25) = 56.25
4p + 26.25 = 56.25
4p = 56.25 - 26.25
4p = 30
divide both side by 4
[tex]\begin{gathered} \frac{4p}{4}=\text{ }\frac{30}{4} \\ p=7.5 \end{gathered}[/tex]each pizza cost $7.5
each sub cost $5.25
Simplify square root of 540 Radical way
Use the rational zero thereom to help find the zeros
Answer
The zeros of the polynomial function using the rational zero theorem is
[tex]\frac{\pm p}{q}=\pm1,\pm\frac{1}{2},\pm\frac{1}{4},\pm2,\pm4[/tex]Explanation
The given polynomial function is
[tex]f(x)=4x^4+8x^3+21x^2+17x+4[/tex]What to find:
To find the zeros of the polynomial function the rational zero theorem.
Step-by-step solution:
The rational zero theorem: If a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Considering the given polynomial function
[tex]f(x)=4x^4+8x^3+21x^2+17x+4[/tex]The constant term, p = 4
The leading coefficient, q = 4
The factors of the constant p and the leading coefficient q are:
[tex]\begin{gathered} p=\pm1,\pm2,\pm4 \\ \\ q=\operatorname{\pm}1,\operatorname{\pm}2,\operatorname{\pm}4 \end{gathered}[/tex]Hence, the zeros of the polynomial function using the rational zero theorem will be
[tex]\begin{gathered} \frac{\pm p}{q}=\frac{\pm1,\pm2,\pm4}{\pm1,\pm2,\pm4} \\ \\ \frac{\operatorname{\pm}p}{q}=\operatorname{\pm}1,\operatorname{\pm}\frac{1}{2},\operatorname{\pm}\frac{1}{4},\operatorname{\pm}2,\operatorname{\pm}4 \end{gathered}[/tex]
1. Given that U = {1, 2, 3, ..., 10}, S = {3, 5, 7, 9} and T = {4, 5, 6, 7}, find S-T
The set of, S - T = {3, 9}
Define Set Operation.
To obtain a combination of components according to the operation done on them, the set operations are conducted on two or more sets.
In a set theory, there are three major types of operations performed on sets, such as:
1) Union of sets (∪)
2) Intersection of sets (∩)
3) Difference of sets ( – )
We know, S -T = S ∩ T'
Given, universal set is U = {1, 2, 3, ..., 10}
S = {3, 5, 7, 9} and T = {4, 5, 6, 7}
Now, find T' (T's compliment),
The complement of set T is defined as a set that contains the elements present in the universal set but not in set T.
T' = {1, 2, 3, 8, 9, 10}
given, S = {3, 5, 7, 9}
Find, S ∩ T'
S ∩ T' = {3, 5, 7, 9} ∩ {1, 2, 3, 8, 9, 10}
The intersection of two sets S and T is a subset of the universal set U and contains elements that are present in both sets S and T. It is represented by the symbol "∩".
so, S ∩ T' = {3, 9}
Hence, S - T = S ∩ T' = {3, 9}
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In an inverse variation, y = 1 when x = 4. Write an inverse variation equation that showsthe relationship between x and y.
In an inverse variation as one quantity increases the other decreases. For example, if x increases, y decreases
We can write it as:
x=k/y
where k is a constant.
or
x*y = k
replacing the values:
4*1=k
4=k
x*y=4
which expression is equivalent to 3(x-y)
MULTIPLY EVERY TERM IN THE BRACKETS BY 3
[tex] = 3(x) + 3( - y) \\ = 3x - 3y[/tex]
ATTACHED IS THE SOLUTION
Find the area of the triangle I’ll send a picture of the triangle
Ok, so
We want to find the area of the following triangle:
Remember that the area of a trangle is given by the following equation:
[tex]A=\frac{bh}{2}[/tex]Where b is the base of the triangle and h is its height.
If we replace our values:
[tex]A=\frac{(11)(2)}{2}=11[/tex]Therefore, the area is equal to 11 square units.
x(4b-a)² + y(4b - a)²
factor the binomial out of each polynomial.
please explain how you got the answer i am deeply confused.
Answer:
(4b - a)²(x + y)
Step-by-step explanation:
x(4b - a)² + y(4b - a)² ← factor out (4b - a)² from each term
= (4b - a)²(x + y)
Consider the followingA(-2.75,3)B(1, -2)Plot the given points on the graph.AnswerKeypadKeyboard ShortcutsTo plot a point on the graph, click on the appropriate position on the graph. To move a point, drag thepoint from its original position to its new position.Points can be moved by dragging or using the arrow keys.
Explanation
two important rules to plot a point in the cartesian plane are given
1.The first coordinate in the ordered pair (x) represents the left/right movement of a point from the origin.
2.The second coordinate in the ordered pair (y) represents the up/down movement of the point from the origin.
so
Step 1
let
[tex](x,y)\Rightarrow A(-2.75,3)[/tex]so
1) 2.75 to the left
2) 3 up
Step 2
B(1,-2)
I hope this helps you
Find the coordinates of the vertices of each figure after the given transformation REFLECTION ACROSS y=-x
The coordinates of the vertices after the reflection are V'(-3,2), U'(0,-2), W'(-1,3) and T'(1,2) .
A reflection in mathematics is a mapping from a Cartesian coordinates to itself which is an isometry with such a set of fixed points known as the hyperplane, also known as the axis or plane of reflection.
The mirror image of a figure in the axis or plane of reflections is the image produced by a reflection. For instance, the minuscule Latin letter p would appear like the letter q when reflected with regard to a vertical axis. It would appear like b when reflected on a horizontal axis. Every object goes back to its original place and every geometric object is returned to its initial condition when a reflection is applied twice consecutively.We know that when a figure is reflected along the line y = -x then the coordinates change their places and they are negated.
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write an expression
1. Richie makes $40 per hour doing web design and $20 per hour doing logo design.
Answer:
Step-by-step explanation:
40x+20y x is for the amount of hours he spends on web design and y for 20 obviously
Choose the graph of the linear equation 24x + 64y = 384?
On a coordinate plane, a line goes through points (0, 6) and (16, 0).
On a coordinate plane, a line goes through points (0, 8) and (12, 0).
On a coordinate plane, a line goes through points (0, 16) and (6, 0).
The graph that represents the linear equation, 24x + 64y = 384 is shown in the diagram.
How to Determine the Graph of a Linear Equation?A linear equation can be expressed as y = mx + b, which is the slope-intercept form where the slope is represented as m and the y-intercept is represented by b. This y-intercept is the point where the line intercepts the y-axis when x is equal to zero.
Given the linear equation, 24x + 64y = 384, rewrite in slope-intercept form to easily figure out the slope:
24x + 64y = 384
64y = -24x + 384
y = -24x/64 + 384/64
y = -6/16x + 6
This shows that the graph would have a y-coordinate, b = 6, while the slope is -6/16. The graph would be the one shown below in the diagram.
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Answer:
A
Step-by-step explanation:
Consider this system of linear equations: y=4/5x-3 y=4/5×+1 a. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning. Hint: answer should be 0, 1, or no solutions
The solution of a system of linear equations is the point where the two lines meet. Note that for the given equations, both lines have the same slope (4/5). If two lines have the same slope, it means that those lines are parallel. Parallel lines do not meet at any point, they stay parallel to the infinite.
Therefore, since this two lines are parallel, they don't meet and the system has no solution.
