Let there are x pets in the store. So 90% of all pets means that 0.9x.
The equation for the dogs anf total pets in the store is,
[tex]0.9x=54[/tex]Simplify the equation to obtain the value of x.
[tex]\begin{gathered} 0.9x=54 \\ x=\frac{54}{0.9} \\ =60 \end{gathered}[/tex]So there are 60 pets in the pet store.
= 186x – 30y5х – 25y= 15
Answer:
There are infinitely many solutions
Explanation:
Given the system of linear equations:
[tex]\mleft\{\begin{aligned}6x-30y=18 \\ 5x+25y=15\end{aligned}\mright.[/tex]To solve using Matrices, we write the equation in the form:
Ax = b
Where A represent the matrix of the coefficient of the variables x and y
x represent the matrix of the variables x and y
and b represents the matrix of the constants on the right hand side.
In matrix form, we have:
[tex]\begin{bmatrix}{6} & {-30} \\ {5} & {-25}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{18} \\ {15}\end{bmatrix}[/tex]We must have a nonzero determinant for A
The determinant of A is:
[tex]\begin{gathered} (-25\times6)-(-30\times5) \\ =-150+150 \\ =0 \end{gathered}[/tex]The determinant of A is zero, without going far, we conclude that the system has infinite number of solutions.
i need help with this question
In the given expression
[tex]x^5+32y^3=\ln y[/tex]To differentiate it with respect to it, we will writ y' for every term of y
The differentiation of
[tex]x^5=5x^{5-1}=5x^4[/tex]The differentiation of
[tex]32y^3=32(3)y^{3-1}y^{\prime}=96y^2y^{\prime}[/tex]The differentiation of
[tex]\ln y=\frac{1}{y}(y^{\prime})=y^{-1}y^{\prime}[/tex]Now let us write all of them in one line
[tex]5x^4+96y^2y^{\prime}=y^{-1}y^{\prime}[/tex]Put the terms of y' on one side and the other term on the other side
[tex]96y^2y^{\prime}-y^{-1}y^{\prime}=-5x^4[/tex]Take y' as a common factor
[tex]y^{\prime}(96y^2-y^{-1})=-5x^4[/tex]Divide both sides by the bracket
[tex]y^{\prime}=\frac{-5x^4}{(96y^2-y^{-1})}[/tex]Since the given point is (-2, 1), then
x = -2 and y = 1
Substitute them to find y'
[tex]\begin{gathered} y^{\prime}=\frac{-5(-2)^4}{(96\lbrack1\rbrack^2-\lbrack1\rbrack^{-1})}=\frac{-5(16)}{(96-1)}=\frac{-80}{95} \\ y^{\prime}=-\frac{16}{19} \end{gathered}[/tex]The value of y' is -16/19
Far from home: A survey asked first-year college students, “How many miles is this college from your permanent home?” Students had to choose from the following options: 5 or fewer, 6 to 10, 11 to 50, 51 to 100, 101 to 500, or more than 500. The side-by-side bar chart shows the percentage of students at public and private 4-year colleges who chose each option.
The average distance between students in public is smaller than that in private.
While the data for the public appears to closely follow a bimodal distribution, the data for the private appears to be negatively skewed, meaning that the tail is lopsided to the left. However, it might be nearly symmetrical. While the modal class for the public is 11–50, it is 101–500 for private.
While the mean for public data is close to 50, it is close to 100 for private data.
Therefore, it is clear from the graphs that students' average distances from Public are closer than those from Private.
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Reflect (1, -3) over the y-axis.
Then translate the result down 1 unit.
What are the coordinates of the final point?
Answer:
(-1 , -4)
Step-by-step explanation:
Hello!
Refer to the graph for the reflection and translation.
The coordinates of the final point would be (-1,-4), given the x and y-values of the point.
(NEED ANSWER ASAP) Tom and Jessica are going to Disneyworld. Snacks are EXPENSIVE there. They each got a Mickey ice cream, and Jessica also got cotton candy. Tom only had $9, so Jessica paid for the rest, which was $4. The ice cream cost $5 each, what was the cost of the cotton candy? Write an equation to represent the word problem and solve it. (Show all of your steps)
The cost of the cotton candy that Jessica purchased is $3.
What is the cost of candy?The first step is to determine total amount spent on snacks. The total amount spent is the sum of the amount paid by Tom and Jessica.
Total amount spent = $9 + $4 = $13
Two ice creams and one cotton candy is bought. This can be represented with:
$13 = total cost of ice cream + cost of the cotton candy
$13 = (2 x$5) + c
$13 = $10 + c
c = $13 - $10
c = $3
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Which equation is equivalent to −(5−x)=5−x? Responses −5−x=5−x − 5 − x = 5 − x −5+x=5−x − 5 + x = 5 − x 5−x=5−x 5 − x = 5 − x 5+x=5−x
The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x
The given equation −(5−x) = 5−x
The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together.
The distributive property of addition
A(B+C) = AB + AC
The distributive property of subtraction
A(B-C) = AB - AC
The given equation is −(5−x) = 5−x
Apply distributive property in the equation
−(5−x) = 5−x
-5+x = 5-x
Hence, The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x
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Answer this graph based Question I will provide you 50 points + make you brainliest.
Part a: The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn.
Part c: Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function is y = -5 - (x + 2)².
Part e: The approximate value of √3 is 1.732.
What is defined as the term function?A function is an expression, rule, or law in mathematics that defines a relationship between one dependent variable (a independent variable) and also one more variable (the dependent variable). Functions are common in mathematics and are required for the formulation of actual relationships with in sciences.For the given function;
y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.
Part a: value of y when x = 2.
Put x = 2 in the function;
y = x² + 4x -1
y = 2² + 4×2 -1
y = 11
The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.
Part c: Range of value of x for which y ≥ -2.
Locate the point of x from the graph for which the value of y y ≥ -2.
Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.
The vertex from the graph is found as (-2, -5) (h, k)
Putt in the equation;
y = k - (x - h)²
y = -5 - (x - (-2))²
y = -5 - (x + 2)²
Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.
It 2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.
The approximate value of √3 is 1.732 which is found by long division method.
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Find the surface area of a cylinder with a height of 7 in and a base diameter of 8 in.
Use the value 3.14 for pi and do not do any rounding.
Be sure to include the correct unit.
The total surface area of the cylinder whose height is 7 units and diameter is 8 units is 226.08 units.
What is surface area?
The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated. This definition of surface area, based on infinitesimal calculus methods, uses partial derivatives and double integration.
The formula to calculate the total surface area of a cylinder is:
[tex]S = 2\pi rh + \pi r^2[/tex]
Where, S = surface area, r = radius, and h = height
As given in the question,
height (h) = 7 units
diameter (d) = 8 units
Since, r = d/2
So, r = 8/2 = 4 units
putting these values in the formula:
[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 4^2)[/tex]
[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 16)[/tex]
[tex]S = 175.84 + 50.24\\[/tex]
S = 226.08 units
Therefore, Surface area of the cylinder is 226.08 units
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Simplify the following exponent (x¹⁰ ÷ x²) x x³
Answer:
x^6
Step-by-step explanation:
Given X¹⁰ ÷ (x² X x³ ÷ x) : Simplify.
We know the law of exponents which states that
a^m x a^n = a^m + n
a^m / a^n = a^m - n
So the problem is x^10 / (x^2 x x^3 / x)
So we have x^10 / x ^5 / x
x ^10 / x ^5 - 1
x^10 / x^4
x ^10 -
x^6
After simplifying we get x^6
Write an equivalent expression for (x+2)+(x+2)
We will proceed as follows in order to get an equivalent expression:
[tex](x+2)+(x+2)=(x+x)+(2+2)=2x+4[/tex]So, one equivalent expression is 2x + 4.
11. It takes 4 hours to type 8 memos. How long will it take to type 56 memos?
Answer:28
Step-by-step explanation:if the unknown hour is x
then it would be
4hr=8memos
x hr=56 memos
cross multiply that would be
4×56÷8=28
and to check this answer you can find how many hours it would take to write one memo and multiply it by 28(your answer) that would be
x hr=1 memo
4hr =8 memo
cross multiply that would be
8÷4=
and then check it by doing 28 × 2=56
The time taken to type 56 memos will be 28 hours.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that it takes 4 hours to type 8 memos. The time taken to type 56 memos will be calculated as,
8 memos = 4 hours
56 memos = ( 56 x 4 ) /8
56 memos = 28 hors
Therefore, it will take 28 hours to type 56 memos.
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You invest $275 to start a sandwich stand and decide to charge 515 per sandwich set of a linear model that determines your profit or loss based on the number of sandwiches
The linear model that determines your profit or loss based on the number of sandwiches is 15y-275, where y is the number of sandwiches sold.
What is a linear model?A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behaviour of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.
It is given that the investment amount is $275.
The charge per sandwich is $15
So, generated revenue= 15 y
where y is the number of sold sandwiches.
Profit/ Loss= Revenue- total investment= 15y-275
So, the linear model determining the profit or loss is 15y-275, where y is the number of sandwiches.
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S = 1/3 x pi x r^2 + pi x r^2 x h
The solved equation for h is h= S/ pi x r^2-1/3.
The problem we are dealing with here is related to the literal equation, where a literal equation is an equation that comprises basically letters. Formulas are an illustration of strict equations. Each variable within the condition "truly" speaks to an important part of the full relationship expressed by the equation. To illuminate a literal equation implies modifying the equation so a different variable stands alone on one side of the equals sign. We got to be told which variable we need to solve.
For the given equation,S= 1/3 x pi x r^2 + pi x r^2 x h
for th the equation will be
=>S= pi x r^2(1/3 +h)
=>S/ pi x r^2= 1/3+h
=>h= S/ pi x r^2-1/3
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S = 1/3 x pi x r^2 + pi x r^2 x h , solve for h
PLS HELP I HAVE LESS THAN 20 MINUTES!!!!
The statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is the following statement - "Samuel will get 25 or more for mowing the lawn".
The given statement is -
Samuel will get $25 or more for mowing the lawn.
Assume that Samuel gets $x for mowing the lawn.
Then according to the question, we can write the inequality as -
x ≥ 25
" ≥ " sign to represent either 25 or more.
So, the inequality can be written as x ≥ 25 and the graph number [2] represents the correct graph.
Therefore, the statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
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Dean started with 5 metersof yarn. He used 300millimeters of yarn each dayfor 5 days. How manymeters of yarn does Deanhave left?
Given:
Dean started a yarn with 5 meters. He used 300millimeters of yarn each day for 5 days.
Required:
Find how many meters of yarn Dean has left.
Explanation:
We know that 1 meter = 1000milimeters
Dean used meters of yarn in the five days
[tex]\begin{gathered} =\frac{300\times5}{1000} \\ =\frac{3}{2}\text{ meter} \end{gathered}[/tex]The left meters are:
[tex]\begin{gathered} =5-\frac{3}{2} \\ =\frac{10-3}{2} \\ =\frac{7}{2} \\ =3.5 \end{gathered}[/tex]Final Answer:
Thus 3.5 meters of yarn left
Your phone plan charges you an initial fee, and then a certain amount depending on the amount of data you use. They send you periodic updates of your usage andyour current bill cost. After using 3 GB of data you owe $30. After 5 GB of data, you owe $40. What is the initial fee prior to the data usage charge?A.$15B.$5C.$2.50D.$10
If for 3 Gb we get a bill for $30 and for 5 Gb we get a bill of $40. It implies that every Gb costs $5, therefor the equation we have use 3 Gb is
[tex]30=3\cdot5+b[/tex]where b is the initial fee. Solving this for b we get that
[tex]b=30-15=15[/tex]so the initial fee is $15
Factoring binomials math
we have the expression
[tex]x^3-125[/tex]we have that
x=5 is a zero of the given equation
so
Divide x^3-125 by (x-5)
x^3-125 : (x-5)
x^2+5x+25
-x^3+5x^2
---------------
5x^2-125
-5x^2+25x
------------------
25x-125
-25x+125
----------------
0
therefore
x^3-125=(x-5)(x^2+5x+25)
the answer is the fourth optionWhat's 2,412 Divided by 25
Answer:
96.48
Step-by-step explanation:
The answer is 96.48.
Answer:
96.48
Step-by-step explanation:
2,412 divided by 25 equals 96.48
Describe the graph of the quadratic function f (x) = -3x^2+ 6x + 5 by stating whether it opens upward or downward and stating how it is stretched or compressed when compared to the parent quadratic functionA. The parabola opens downward. It is compressed shorter by a factor of 3.B. The parabola opens upward. It is stretched taller by a factor of 3.C. The parabola opens downward. It is stretched taller by a factor of 3.D. The parabola opens upward. It is compressed shorter by a factor of 3.
Answer:
B. The parabola opens upward. It is stretched taller by a factor of 3.
Step-by-step explanation:
You want to know how the quadratic opens, and how it is stretched or compressed, given its equation is f(x) = -3x^2 +6x +5.
Leading coefficientThe "leading coefficient" is the coefficient of the highest-degree term. That term is -3x^2, and its coefficient is -3.
The minus sign tells you the parabola opens downward.
The magnitude of 3 tells you the parabola is stretched vertically (taller) by a factor of 3.
8.1÷0.9+0.4^(3)÷0.8×30
Answer:
11.4
Step-by-step explanation:
Answer:
11.4
p.s you try it may help
i need help asap!!! im bad at graphing
Points are (1, -3)
What is equation?In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given Data
Slope = -[tex]\frac{1}{2}[/tex]
Points (-1, -5)
The line's general equation is y=ax+b.
Since we are aware that the slope is -[tex]\frac{1}{2}[/tex], an is equal to -[tex]\frac{1}{2}[/tex].
We also understand that if x = -1, then y = -5.
Let's connect it:
-5=1*(-1)+b
-5=-1+b
b= -4
So, y=x -4 is the line's equation.
Let x = 1
y = 1 - 4
y = -3
(1, -3)
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Simplify completely (7x²+11x-6)/(7x²-10x+3)
One way of simplifying the given expression is by factoring them, and then simplifying the common terms.
So, we need to write:
[tex]\begin{gathered} 7x^{2}+11x-6=7(x-a)(x-b) \\ \text{and} \\ 7x^{2}-10x+3=7(x-c)(x-d) \end{gathered}[/tex]The constants a and b are the zeros of the first expression, and the constants c and d are the zeros of the second expression.
So, we can find those zeros using the quadratic formula. We obtain, for the first expression:
[tex]\begin{gathered} x=\frac{-11\pm\sqrt[]{11^{2}-4(7)(-6)}}{2(7)} \\ \\ x=\frac{-11\pm\sqrt[]{289}}{14} \\ \\ x=\frac{-11\pm17}{14} \\ \\ a=\frac{-11-17}{14}=-2 \\ \\ b=\frac{-11+17}{14}=\frac{6}{14}=\frac{3}{7} \end{gathered}[/tex]And, for the second expression, we obtain:
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^{2}-4(7)(3)}}{2(7)} \\ \\ x=\frac{10\pm\sqrt[]{16}}{14} \\ \\ x=\frac{10\pm4}{14} \\ \\ c=\frac{10-4}{14}=\frac{6}{14}=\frac{3}{7} \\ \\ d=\frac{10+4}{14}=1 \end{gathered}[/tex]Then, we can write:
[tex]\begin{gathered} 7x^2+11x-6=7(x-(-2))(x-\frac{3}{7})=7(x+2)(x-\frac{3}{7}) \\ \\ 7x^2-10x+3=7(x-\frac{3}{7})(x-1) \end{gathered}[/tex]Thus, the given function can be simplified as follows:
[tex]\frac{7x²+11x-6}{7x²-10x+3}=\frac{7(x+2)(x-\frac{3}{7})}{7(x-\frac{3}{7})(x-1)}=\frac{x+2}{x-1}[/tex]Therefore, the answer is:
[tex]\mathbf{\frac{x+2}{x-1}}[/tex]Write the correct inequality for the following statement and then solve for the given number of
guests.
You are in charge of planning your mother's surprise party. You have
found a hall that rents for $225 and a caterer that will charge you $15 per
guest. Write an inequality to calculate your total cost (T) based on the
number of guests (g).
If you have a total budget of $1000 how many guests can you
invite?
The inequality that can be used to calculate total cost (T) based on the number of guests (g) is 225 + 15g ≤ 1000.
If you have a total budget of $1000, 51.67 guests can be invited.
How to write inequality equation?Cost of hall rent = $225Caterer's charge per guest = $15Total cost = TNumber of guests = gTotal cost = Cost of hall rent + Caterer's charge per guest(Number of guests)
225 + 15g ≤ T
If you have a total budget of $1000
225 + 15g ≤ T
225 + 15g ≤ 1000
substract 225 from both sides15g ≤ 1000 - 225
15g ≤ 775
divide both sides by 15g ≤ 775 / 15
g ≤ 51.66666666666666
Approximately,
g ≤ 51.67
So therefore, the inequality to represent the situation is 15g ≤ 1000 - 225 and about 51.67 guests can be invited if you have a budget of $1000
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64,32,16,8 what is the next three terms of it? (no negatives)
Notice that each new term is half the previous one. For example, 32 is half 64, 16 is half 32, and so on.
Having said that, the constant ratio is 1/2. Using this ratio we can find the next three terms.
[tex]\begin{gathered} 8\cdot\frac{1}{2}=4 \\ 4\cdot\frac{1}{2}=2 \\ 2\cdot\frac{1}{2}=1 \end{gathered}[/tex]Therefore, the next three terms are 4, 2, and 1.PLEASE AWNSER NOW Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
7 and one fourth pounds
8 and one half pounds
10 and one half pounds
14 and one fourth pounds
Answer:
The answer is 10 and one half pounds
Explanation:
3.5/7 = 2
21/2 = 10.5
10 and one half pounds use to make 21 small vases.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Sandy uses clay= 3 1/2 pounds for 7 vase
So, for 1 vase amount of clay used
= 7/2 x 1/7
= 1/2 pounds
Now, for 21 small vases amount of clay used
=21 x 1/2
= 21/2
= 10 1/2 pounds.
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Bobby can work at most 20 hours next week, but she needs to earn at least $150. Herdog-walking job pays her $6 per hour and her iob as a car wash attendant pays her $10 perhour. If d is the number of hours she walks dogs this week and w is the number of hours sheworks at the car wash, write a system of inequalities that represents Bobby's situation.
Solution:
Let d represent the number of hours Bobby walks dogs,
and w be the number of hours she works at the car wash.
Given that she can work at most 20 hours next week, this implies that the total number of hours she works is expressed as
[tex]d+w\leq20[/tex]If her dog-walking job pays her $6 per hour, this implies that for d number of hours, she will earn
[tex]\begin{gathered} \frac{\$6}{1\text{ hour}}\times d\text{ hours} \\ =\$\text{ 6d} \end{gathered}[/tex]and her iob as a car wash attendant pays her $10 per hour, similarly for w number of hours, she will earn
[tex]\begin{gathered} \frac{\$10}{1\text{ hour}}\times w\text{ hours} \\ =\$10w \end{gathered}[/tex]Given that she needs to earn at least $150, this implies that her total earnings will be expressed as
[tex]6d+10w\ge150[/tex]Hence, the system of inequalities that represents Bobby's situation is:
[tex]\begin{gathered} d+w\leq20 \\ 6d+10w\ge150 \end{gathered}[/tex]1. Round to the nearest thousand. Use the number line to model your thinking.
9,340=
After rounding off the number we get ; 9,300
What does rounding off to thousand mean?When a number is rounded to the closest thousand, it is changed to an approximated value that is simpler to recall and utilize. The closest value to the supplied integer is this value, which is a multiple of 1000. For instance, 342984 becomes 343000 if it is rounded to the closest thousand.
So as in this question the number given is 9340
Since we have to round it off to thousands
and the number next to 9 is 3
Thus we can say that after rounding off the number will be
9,300.
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How do you know when an equation has one solution? A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define an equation with one solution
You can tell that an equation has one solution if you solve the equation and get a variable equal to a number. A system of linear equations has one solution when the graphs intersect at a point.
STEP 2: Examine the options
An equation is said to have "no solution" when the coefficients are the same and the constants are different as seen below:
[tex]\begin{gathered} 4x+12=24+4x \\ 4x-4x=24-12 \\ 0=12 \end{gathered}[/tex]When the coefficients are the same and the constants are the same, the equation is said to have "infinitely many solutions as seen below:
[tex]\begin{gathered} 4x-14=-6-8+4x \\ 4x-14=-14+4x \\ 4x-4x=-14+14 \\ 0=0 \end{gathered}[/tex]When the coefficients are different, the equation is said to have one solution as seen below:
[tex]\begin{gathered} 2x+56=3x-12 \\ 2x-3x=-12-56 \\ -x=-68 \\ x=68 \end{gathered}[/tex]Hence, the answer is:
"When the coefficients are different"
Hiro picks up four digits card, he says: I can make a multiple of 10 with these cards. I can also make a number that rounds to 5300 and a number where the digit 8 is worth 800?
Find the distance between each pair of points. Round youranswer to the nearest tenth, if necessary.(7, 6), (0, 2)
Chris, this is the solution to the exercise:
• Point 1 = (7, 6)
,• Point 2, (0, 2)
Now, let's use the formula to calculate the distance between the two points, as follows:
d = √(0 - 7)² + (2 - 6)²
d = √-7² + (-4)
d = √49 + 16
d = √65
d = 8.0622
d = 8.1 (rounding to the nearest tenth)