For each system to the best description of a solution if applicable give the solution
Answers
System A
[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]solve the first equation for x
[tex]x=4+4y[/tex]replace in the second equation
[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solutions, They must satisfy the following equation
[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]System B
[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]solve for x for the first equation
[tex]x=6+2y[/tex]replace in the second equation
[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]The system has no solution.
Related Questions
three fifths of the students in a room are girls. 1/3 of the girls have blond hair. one half of the boys have brown hair. what fraction of all the students are girls with blonde hair ?what fractions are all this book for boys with brown hair ?
Answers
3/5 of the students are girls-
1-3/5 = 2/5
2/5 of the students are boys
1/3 of the girls have blonde hair.
So, multiply, the number of girls that have blonde hair (1/3) by the number of girls (3/5)
1/3 * 3/5 = 3 /15 = 1/5
of all students, 1/5 are girls with blonde hair.
For the boys;
1/2 of the boys have brown hair. of all students 2/5 are boys
2/5 * 1/2 = 2/10 = 1/5
Of all students 1/5 are boys with brown hair
What is the value of 0.5+0.3( the 3 is repeating)? Write the answer as a fraction in the lowest terms 
Answers
we have the following:
[tex]0.5+0.\hat{3}[/tex]therefore:
[tex]\begin{gathered} 0.5+0.\hat{3}=0.8\hat{3} \\ 08\hat{3}=\frac{5}{6} \end{gathered}[/tex]therefore, the answer is 5/6
Find the root of the function f(x) = ³/1.A. x = -5OB. z = 0OC. x = 5OD. noneReset Selection
Answers
Explanation
We have
[tex]f(x)=\frac{5}{x}[/tex]Because upon solving we have
[tex]\begin{gathered} \frac{5}{x}=0 \\ 5=0 \\ no\text{ solution} \end{gathered}[/tex]Therefore, it has no root
The answer is none
Op
help meeeeeeeeeeeeeeeeeeeeeeeeee
Answers
When c=0 It's 75 when x= 0 It's 75 when x= 100 It's 100 when x= 200 its 125 when x= 300 its 150
Step-by-step explanation:
For A, The printer would be 75 dollars and each newspaper printed is .25 cents
Answer:
c
Step-by-step explanation:
help me please !!!
thank youuu
Answers
The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range.
Where can I find a fraction's domain?By factoring the numerator and denominator and setting them both to zero, the domain of a fraction function can be determined. The domain's values are the roots of the ensuing equation. Using the algebraic method of factoring is another method for determining the domain of a fraction function.
The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
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Type the correct answer in the box. Use numerals instead of words.
Consider AABC.
Determine the measure of angle C.
A= 48.36
B= 59.49
C=?
Answers
The measure of angle c is 72.15.
What is angle sum property for a triangle?
Angle sum property of triangle states that The measure of all interior angles of a triangle is [tex]180^{o}[/tex] that is sum of all 3 interior angle is 180
We are given a Δ[tex]ABC[/tex]
Measure of interior angles of ABC is 180.
Hence the equation can be given as,
∠A+∠B+∠C=180
48.36+59.49+∠C=180
107.85+∠C=180
∠C=72.15
Hence the measure of ∠C is 72.15
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Answer:72.15
Step-by-step explanation:
what is the total area, in square inches, of the shaded sections of the trapezoid below?
Answers
Answer: 81.9 in^2
I need help solving this practice problem from my prep guide
Answers
ANSWER
[tex]\lim _{n\to\infty}\text{ }(\frac{3n^5^{}}{6n^6+1})\text{ = 0}[/tex]EXPLANATION
Step 1: Given that:
[tex]\sum ^{\infty}_{n\mathop=1}(\frac{3n^5^{}}{6n^6+1})[/tex]Step 2: Expand the limit
[tex]\begin{gathered} \lim _{n\to\infty}(\frac{3n^5^{}}{6n^6+1})\text{ } \\ \text{ = }\lim _{n\to\infty}\frac{n^5}{n^5}(\frac{3^{}}{6n^{}+\frac{1}{n^5}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6n^{}+\frac{1}{n^5}}) \\ =\text{ }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+\frac{1}{(\infty)^5}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+\frac{1}{\infty}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+0^{}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}^{}})\text{ = 0} \\ \end{gathered}[/tex]Hence,
[tex]\lim _{n\to\infty}(\frac{3n^5}{6n^6+1})\text{ = 0}[/tex]
Jamal's math teacher pointed out that the number of Jamal's free throws and the number of
two-point field goals (FG) were two consecutive odd numbers. He made more two-point
throws and no three-point FGs. If Jamal made a total
FGs
of 19 points, how many field goals did he make?
than free
Answers
Answer:
Step-by-step explanation: free throws are worth 1 point?
We have to find how many field goals he made.
We know that the number of free throws (FT) and the number of two-point field goals (FG) are two consecutive odd numbers. As they are consecutive odd numbers, they differ by two, so we can write:
There are no three-point field goals and the total number of points was 19, so this score has to be the sum of the points from free throws and the points from two-point field goals.
Answer:
He made 7 two-point field goals and 5 free throws.
He made 2 more field goals than free throws.
Answer: We have to find how many field goals he made.We know that the number of free throws (FT) and the number of two-point field goals (FG) are two consecutive odd numbers. As they are consecutive odd numbers, they differ by two, so we can write:There are no three-point field goals and the total number of points was 19, so this score has to be the sum of the points from free throws and the points from two-point field goals.Answer:He made 7 two-point field goals and 5 free throws.He made 2 more field goals than free throws.
Step-by-step explanation: hope this helps0^0
if RS = RU, ST = b + 72 and TU = 5b, what is the value of B?
Answers
The value of b is 18.
Here, we are given a triangle as shown in the figure above.
RS = RU
ST = b + 72
and TU = 5b
In triangle TRU, by Pythagoras theorem, we get-
(TU)² = (TR)² + (RU)²
⇒ (5b)² = (TR)² + (RU)²
(TR)² = (5b)² - (RU)²
Similarly, in triangle STR, we will get-
(TR)² = (b + 72)² - (SR)²
Equating the two equations, we get-
(5b)² - (RU)² = (b + 72)² - (SR)²
Since RS = RU,
(5b)² - (RS)² = (b + 72)² - (SR)²
25b² = b² + 72² + 2(72)b
24b² = 5,184 + 144b
b² = 216 + 6b
b² - 6b -216 = 0
Solving this quadratic equation will give us 2 values for b
b = 18 or b = -12
Since length of the side cannot be negative, the value of b will be 18.
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Using the following coordinates, what is the slope of the line ?
Answers
lets take m as slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]x1=4 y1=13 x2=5 y2=16
[tex]m=\frac{16-13}{5-4}=3[/tex]so we get the slope as 3.
so the answer is 3.
NO LINKS!! Part 3: Please help me with this Similarity Practice
Answers
Answer: (10,5) or (14,3) are two possible answers.
Infinitely many answers are possible. Pick one to write as the final answer to your teacher.
=====================================================
Explanation:
Focus on the points B(1,4) and C(5,2)
More specifically, focus on the x coordinates 1 and 5. To go from B to C, we move to the right 4 units since 1+4 = 5
We also move down 2 units since we go from y = 4 to y = 2
In short, the translation motion is "right 4, down 2". We can further abbreviate this into the vector notation <4, -2>. This translation vector only applies going from B to C.
The vector notation <4,-2> is the same as writing [tex](x,y) \to (x+4,y-2)[/tex] but the first method is much faster to write out since it avoids needing to write x or y.
--------------------
Now if we want to construct a similar triangle A'B'C', we will use that vector to scale it up or down. Let's scale it up and double each coordinate.
<4, -2> doubles to <8,-4>
So instead of "right 4, down 2" we now follow the path "right 8, down 4". Take notice how both motions involve the same slope.
Start at B'(2,9) and move right 8 and down 4 to arrive at C'(10,5)
See figure 1 below.
This is one possible answer out of infinitely many. This is because we can change the scale factor to any nonnegative real number we want.
-------------------
Another example:
Instead of doubling the coordinates of the translation vector, let's triple them.
<4,-2> triples to <12,-6>
Then start at B'(2,9) and move right 12 and down 6 to arrive at C'(14,3) which is another possible answer out of infinitely many.
See figure 2 below.
Pick whichever of (10,5) or (14,3) is your favorite to get the final answer, assuming your teacher wants you to write one (x,y) location only. Or pick some other scale factor (other than 2 or 3) and follow the same idea to get some other possible location of point C'.
Answer:
C' = (10, 5)
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.
Step-by-step explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Therefore, to maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)Given vertex of triangle A'B'C':
B' = (2, 9)If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8). If the triangle is then translated 1 unit up, B' = (2, 9), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation.Translation of 1 unit up.Mapping Rule: (x, y) → (2x, 2y + 1)
Therefore, the coordinates of point C' are:
⇒ C' = (2(5), 2(2) + 1) = (10, 5)
Select the correct choice for now and if necessary fill in the answers box to complete your choice
Answers
We have
[tex]\begin{gathered} (A\cup B)^{\prime}=U-(A\cup B)=\mleft\lbrace1,2,3,4,5,6,7\mright\rbrace-\mleft\lbrace2,3,4,5,6\mright\rbrace \\ (A\cup B)^{\prime}=\mleft\lbrace1,7\mright\rbrace \end{gathered}[/tex]Answer: A.
[tex](A\cup B)^{\prime}=\lbrace1,7\rbrace[/tex]Find the x-intercepts and the vertex of the parabola y = (x − 4)(x + 2)Write as ordered pairsWrite the equation y =(x − 4)(x +2)in standard formuse the quadratic formula to identify the x-value of the vertex.Part IV: Substitute the x-value of the vertex from Part III into the original equation to find the y-value of the vertex. Then, write the coordinates of the vertex.
Answers
Solution
Step-by-step explanation:
we have:
Part 1) Find the x-intercepts of the parabola and write them as ordered pairs
The x-intercepts are the values of x when the value of y is equal to zero
so
For y=0
[tex](x-4)(x+2)[/tex]For x=4 and x=-2 the equation is equal to zero
therefore
The x-intercepts are the points (-2,0) and (4,0)
Part 2) Write the equation y=(x-4)(x+2) in standard form
The quadratic equation in standard form is equal to
[tex]y=ax^2+bx+c[/tex]applying distributive property
[tex]\begin{gathered} y=(x-4)(x+2) \\ y=x^2+2x-4x-8 \\ y=x^2-2x-8 \end{gathered}[/tex]where a = 1, b = -2, c = -8
Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex
we know that
the x-value of the vertex is -b/2a
we have
where a = 1, b = -2, c = -8
substitute
x = -b/2a = -2/2(1) = 1
therefore
The x-coordinate of the vertex is 1
Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.
we have
[tex]y=(x-4)(x+2)[/tex]For x=1
substitute and solve for y
[tex]\begin{gathered} y=(1-4)(1+2) \\ y=-3(3) \\ y=-9 \end{gathered}[/tex]therefore
The y-coordinate of the vertex is -9
The coordinate of the vertex is the point (1,-9)
These marbles are placed in a bag and twoof them are randomly drawn.What is the probability of drawing two yellowmarbles if the first one is NOT placed back intothe bag before the second draw?
Answers
Given the figure of marbles:
As shown, the number of marbles = 10
Two marbles are randomly drawn
We will find the probability of drawing two yellow marbles
The probability the first marble is yellow:
The number of yellow marbles = 2
so, the probability the first marble is yellow = 2/10 = 1/5
The first one is NOT placed back into the bag before the second draw
So, the number of marbles = 10 - 1 = 9
The number of yellow marbles = 2 - 1 = 1
So, the probability the second marble is yellow = 1/9
So, the probability of drawing two yellow =
[tex]\frac{1}{5}\times\frac{1}{9}=\frac{1}{45}[/tex]So, the answer will be 1/45
BRAINLIEST (statistics) (please help fast)
A statistics student gave a survey to students which asked how many first cousins they have. The data from the first nine responses are shown below.
6, 2, 7, 8, 8, 8, 5, 10, 10
What is the standard deviation of the data?
2.38 first cousins
2.52 first cousins
5.65 first cousins
6.36 first cousins
Answers
The student's survey of nine student with regards to the number of first cousins they have gives the standard deviation of the data as the option;
2.52 cousinsWhat is standard deviation in statistics?The standard deviation gives a measure of the variability or dispersion of a set of data.
The survey is with regards to a data obtained from a sample of the population (the first nine response),
The standard deviation of a sample is given by the formula;
[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } }} [/tex]
Where;
n = The data count = 9
[tex] \displaystyle{ \bar x = \frac{6+2+7+8+8+8+5+10+10}{9 } = \frac{64}{9} }[/tex]
Which gives;
[tex]\displaystyle{ \sum (x_{i} - \bar x)} [/tex]
(6-64/9)+(2-64/9)+(7-64/9)+(8-64/9)+(8-64/9)+(8-64/9)+(5-64/9)+(10-64/9)+(10-64/9) = 50.888889
Therefore;
[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } } = \sqrt{\frac{50.888889}{8}} \approx 2.52 } [/tex]
The standard deviation of the data is therefore;
2.52 first cousins
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what digit is in the
Answers
We want to do the following operation:
[tex]\frac{1}{27}+\frac{7}{15}[/tex]To add fractions, we need to put both denominators in the same value. We need to find the LCM between 27 and 15. Factorizing those numbers in prime numbers, we have:
[tex]\begin{gathered} 15=5\times3 \\ 27=3\times3\times3 \end{gathered}[/tex]The LCM is the result of multiplying all those prime factors the most times they occur. Since 3 appears on both factorizations, we'll use only the most occuring 3(in this case, 3 times).
[tex]LCM(15,27)=3\times3\times3\times5=135[/tex]Now, we need to rewrite those fractions with the new denominator. To do that we just need to multiply both the numerator and the denominator by the same factor. To find those factors we just need to find the ratio between the denominator and 135.
[tex]\begin{gathered} \frac{135}{27}=5 \\ \frac{135}{15}=9 \end{gathered}[/tex]Now, converting those fractions to this denominator:
[tex]\begin{gathered} \frac{1}{27}=\frac{1\cdot5}{27\cdot5}=\frac{5}{135} \\ \frac{7}{15}=\frac{7\cdot9}{15\cdot9}=\frac{63}{135} \end{gathered}[/tex]Now, to finally do the addition, we just add the numerators.
[tex]\frac{1}{27}+\frac{7}{15}=\frac{5}{135}+\frac{63}{135}=\frac{5+63}{135}=\frac{68}{135}[/tex]Since 68 and 135 don't share any divisors, this is the simplest form of this fraction. The result is 68/135.
Help me solve this algebra 1 homework (question 10) please
Answers
From the question,
We are given the equation
[tex]3+7m=4m+3(m+1)[/tex]First, we will expand the RHS of the equation
This will give
[tex]3+7m=4m+3m+3[/tex]By simplifying the RHS we will get
[tex]3+7m=7m+3[/tex]From the equation above, the terms on the LHS equal to the terms on the RHS
This implies that the equation has infinite number of solutions
That is, if we insert any value the equation will always be true
simply [tex] \sqrt{3} \times \sqrt{21} [/tex]please help
Answers
We have
[tex]\sqrt[]{3}\times\sqrt[]{21}[/tex]we can reduce the expression
[tex]\begin{gathered} \sqrt[]{3}\times\sqrt[]{21} \\ \sqrt[]{3}\times\sqrt[]{3\times7} \\ \sqrt[]{3}\times\sqrt[]{3}\times\sqrt[]{7} \\ 3\sqrt[]{7} \end{gathered}[/tex]the solution is
[tex]3\sqrt[]{7}[/tex]Question 4(Multiple Choice Worth 2 points)
(01.03 LC)
Simplify 4x√3x-x√√3x-2x√√3x.
x√3x
x√9x
2x√6x
2x√√6x³
Answers
x√3x is value of x in surds.
What is surds in maths?
A square root, cube root, or other root sign is a part of a surd. Irrational numbers cannot be stated accurately in decimal form because their decimals do not finish or recur. Surds are used to write irrational numbers precisely.Surds are employed when precise calculations call for a root that can be a square root, cube root, or another root. As an illustration, the square root of three and the cube root of two are both roots. It is irrational to use the value 5 2.23606 as a square root of 5. 5 is squared, which is a surd.= 4x√3x-x√√3x-2x√√3x
= √3x ( 4x - x - 2x )
= √3x ( 4x - 3x )
= √3x ( x)
= x√3x
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Amaka gets N2 500 as pocket money. She spends N1 500
and saves the rest. What is the ratio of her savings to the
amount she spends?
Answers
Answer:
A the answer is a
Step-by-step explanation:
it's corn a beautiful thing for me it has the juice
Find the savings plan balance after 4 years with an APR of4 % and monthly payments of $100.00.
Answers
The savings plan balance (future value), after 4 years with an APR of 4% and monthly payments of $100, is $5,213.28.
What is the future value?The future value is the compounded amount of monthly payments after four years of monthly savings.
The future value can be computed using an online finance calculator.
N (# of periods) = 48 months (4 x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
PMT (Periodic Payment) = $100
Results:
Future Value (FV) = $5,213.28
Sum of all periodic payments = $4,800 ($100 x 48)
Total Interest = $413.28
Thus, in 4 years, the savings plan will have a future value of $5,213.28.
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7) What is the slope of the line below
Answers
as this is a vertical line, the slope is undefined
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The function notation f(-5) has a value of -6
What are functions?Functions are graphs, ordered pairs, relations, tables and equations that are used to relate independent and dependent variables
How to solve the function?The function notation is given as
f(-5)
Also, we have the graphs to be f(x) and g(x)
This is represented by
Blue curve = f(x)Red curve = g(x)So, we use the blue curve i.e. f(x)
On the blue curve, we have
f(-5) = -6
Hence, the value of the function is -6
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a store Mark's down toys by 15% in january. how much does each toy cost during january? use p for price in December
Answers
A store Mark's down toys by 15% in january. how much does each toy cost during january? use p for price in December
__________________________
P
and Subtract Fractions - Real World
3
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
5
Mark and Lisa each had a water bottle which contained 4 liters of water.
Mark drank 3 liter of water. How much water does Mark have after drinking 3 liter of water?
After Lisa accidentally spilled her water, she had 5 liter of water left. How much water did Lisa spill?
Reset
Submit
liter(s)
liter(s)
Answers
Answer:mark has 1 liter, lisa has an impossible -1 liter
Step-by-step explanation:
3. Han wanted to find the intercepts of the graph of the equation 10x + 4y = 20.He decided to put the equation in slope-intercept form first. Below is his work.He concluded that the x-intercept is (1/2, ) and the y-intercept is (0,5)10x + 4y = 204y = 20 – 10.3y=5 - 10.23a. What error did Han make?3b. What are the x- and y-intercepts of the line? Explain or show yourreasoning.
Answers
Given the equation:
[tex]10x+4y=20[/tex]The slope-intercept form will be as follows:
[tex]\begin{gathered} 4y=20-10x\rightarrow(\div4) \\ y=\frac{20}{4}-\frac{10}{4}x \\ \\ y=5-2.5x \end{gathered}[/tex]3a. What error did Han make?
He didn't divide 10 by 4
3b. What are the x- and y-intercepts of the line?
First, we will find the y-intercept
so, put x = 0
y = 5 - 0 = 5
So, the point of y-intercept is (0, 5)
Second, we will find the x-intercept
So, put y = 0
So,
[tex]\begin{gathered} 0=5-2.5x \\ 2.5x=5 \\ x=\frac{5}{2.5}=2 \end{gathered}[/tex]So, the point of the x-intercept is (2, 0)
You are asked to use the grouping method to factorx² − 14x + 33. How should the term - 14x berewritten?O 3x + 11xO-3x - 11xO -1x - 33xO 1x +33x
Answers
Given the Quadratic Polynomial:
[tex]x^2-14x+33[/tex]You need to factor it using the Grouping Method.
You can identify that it has this form:
[tex]ax^2+bx+c[/tex]Notice that, in this case:
[tex]\begin{gathered} a=1 \\ b=-14 \\ c=33 \end{gathered}[/tex]In order to rewrite it in a form that then you can apply the Grouping Method, you need to find two numbers whose product is the value of "c" and whose sum is the value of "b".
Notice that:
[tex]\begin{gathered} (-3)(-11)=33 \\ -3-11=-14 \end{gathered}[/tex]Therefore, you can set up that:
[tex]-14x=-3x-11x[/tex]Hence, the answer is: Second option.
Wouldn’t the angle of fge be 1/2 the distance of the incercepted arc which would 135?
Answers
Answer:
m∠FGE=52.5 degrees
Explanation:
Angle FGE is formed by the intersection of two secants (BG and GD).
The intercepted arcs are BD and FE.
Therefore:
[tex]m\angle\text{FGE}=\frac{1}{2}(m\widehat{\text{BD}}-m\widehat{FE})[/tex]Substitute the given values:
[tex]\begin{gathered} m\angle\text{FGE}=\frac{1}{2}((100+35)-30) \\ =\frac{1}{2}(105) \\ m\angle\text{FGE=52.5}\degree \end{gathered}[/tex]
Please help me!!!!!!!
Answers
Answer:
With what?
Step-by-step explanation:
